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Q: Save page source from Amazon in Java I am trying to save a page source from Amazon so I can see the price of an item. When I try to save it to a file, it only saves about 60 lines, most of them being white space. I can see the source from my browser and it is thousands of lines long. It goes for any page that I am trying to search. Heres the link I tried: http://www.amazon.com/gp/product/B015WCV70W/ref=s9_simh_gw_g147_i2_r?ie=UTF8&fpl=fresh&pf_rd_m=ATVPDKIKX0DER&pf_rd_s=desktop-2&pf_rd_r=0XHXJAF2NQ35BP5Y435K&pf_rd_t=36701&pf_rd_p=dc68ddd1-99ac-45e5-8c23-e9e0811a2b2c&pf_rd_i=desktop
Is there an easier way to do this?
Here's my code:
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.net.URL;
import java.net.URLConnection;
import java.util.Scanner;
public class DownloadPage {
public static final Scanner in = new Scanner(System.in);
public static void main(String[] args) throws IOException {
System.out.print("Enter URL: ");
savePage(in.nextLine());
}
static void savePage(String entURL) throws IOException{
URL url = new URL(entURL);
URLConnection con = url.openConnection();
InputStream is = con.getInputStream();
BufferedWriter bw = new BufferedWriter(new FileWriter("text.txt"));
BufferedReader br = new BufferedReader(new InputStreamReader(is));
String line = null;
int count = 0;
while (br.ready()) {
bw.write(br.readLine());
bw.newLine();
count++;
}
line = null;
bw.close();
System.out.println("wrote successfully " + count);
}
}
Sorry if I didn't format it right, its my first post.
A: The url is just a load point for a javascript app, which renders the HTML into your browser.
If you want to capture the rendered page, try Selenium/WebDriver which emulates a browser (and will run a javascript app).
A: This is because you use br.ready(), so every network pause cause the end of cycle
This block gives me 20632 lines of html
int count = 0;
while (true) {
String line = br.readLine();
if (line == null) {
break;
}
bw.newLine();
count++;
}
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 274 |
Q: 404 error on java web app with tomcat, struts2, and eclipse I am building my first struts2 app and am getting the error:
*
*HTTP Status 404 - /Struts2Beginner/Input.jsp
*type Status report - message /Struts2Beginner/Input.jsp description The requested resource
is not available.
*Apache Tomcat/7.0.64
There are a lot of posts on this problem and I think I eliminated 2 of the common problems:
*
*I am using StrutsPrepareAndExecuteFilter (instead of
FilterDispatcher)
*I have both commons-lang-2.4.jar and commons-lang3-3.2.jar in my WEB-INF/lib
I am following the tutorial http://www.codejava.net/frameworks/struts/struts2-beginner-tutorial-eclipse-tomcat-xml?showall=&limitstart=
WEB-INF lib
*
*commons-fileupload-1.2.2.jar
*commons-io-2.0.1.jar
*commons-lang-2.4.jar
*commons-lang3-3.1.jar
*commons-logging-1.1.1.jar
*commons-logging-api-1.1.jar
*freemarker-2.3.19.jar
*javassist-3.11.0.GA.jar
*ognl-3.0.6.jar
*struts2-core-2.3.8.jar
*xwork-core-2.3.8.jar
struts.xml
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE struts PUBLIC
"-//Apache Software Foundation//DTD Struts Configuration 2.0//EN"
"http://struts.apache.org/dtds/struts-2.0.dtd">
<struts>
<package name="Struts2Beginner" extends="struts-default">
<action name="calculateSumAction" class="net.codejava.struts.SumAction"
method="calculate">
<result name="success">Result.jsp</result>
<result name="input">Input.jsp</result>
</action>
</package>
</struts>
web.xml
<?xml version="1.0" encoding="UTF-8"?>
<web-app xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
xmlns="http://java.sun.com/xml/ns/javaee"
xmlns:web="http://java.sun.com/xml/ns/javaee/web-app_2_5.xsd"
xsi:schemaLocation="http://java.sun.com/xml/ns/javaee
http://java.sun.com/xml/ns/javaee/web-app_3_0.xsd"
id="WebApp_ID" version="3.0">
<display-name>Struts2Beginner</display-name>
<filter>
<filter-name>struts2</filter-name>
<filter-class>
org.apache.struts2.dispatcher.ng.filter.StrutsPrepareAndExecuteFilter
</filter-class>
</filter>
<filter-mapping>
<filter-name>struts2</filter-name>
<url-pattern>/*</url-pattern>
</filter-mapping>
</web-app>
SumAction.java
package net.codejava.struts;
import com.opensymphony.xwork2.ActionSupport;
public class SumAction extends ActionSupport {
private int x;
private int y;
private int sum;
/**
* The action method
* @return name of view
*/
public String calculate() {
sum = x + y;
return SUCCESS;
}
// setters and getters for x, y, and sum:
public int getX() {
return x;
}
public void setX(int x) {
this.x = x;
}
public int getY() {
return y;
}
public void setY(int y) {
this.y = y;
}
public int getSum() {
return sum;
}
public void setSum(int sum) {
this.sum = sum;
}
}
Input.jsp
<%@ taglib prefix="s" uri="/struts-tags" %>
<%@ page language="java" contentType="text/html; charset=ISO-8859-1"
pageEncoding="ISO-8859-1"%>
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
"http://www.w3.org/TR/html4/loose.dtd">
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Struts2 beginner example application</title>
</head>
<body>
<center>
<h2>Calculate sum of two numbers</h2>
<s:form action="calculateSumAction" method="post">
<s:textfield name="x" size="10" label="Enter X" />
<s:textfield name="y" size="10" label="Enter Y" />
<s:submit value="Calculate" />
</s:form>
</center>
</body>
</html>
Result.jsp
<%@ taglib prefix="s" uri="/struts-tags" %>
<%@ page language="java" contentType="text/html; charset=ISO-8859-1"
pageEncoding="ISO-8859-1"%>
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
"http://www.w3.org/TR/html4/loose.dtd">
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Sum Result</title>
</head>
<body>
Sum of <s:property value="x"/>
and <s:property value="y"/>
is:
<s:property value="sum"/>
</body>
</html>
I have spent several hours trying to debug this with no luck so far.
A: 404 error will be faced when there is no welcome-file-list in the web.xml.
Add below piece of code in web.xml,
<welcome-file-list>
<welcome-file>Input.jsp</welcome-file></welcome-file-list>
And run project by right click -> Run as -> Run on Server. and let us know if you are able to run the application. i have tried this program in my local tomcat server and its working fine.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,515 |
namespace media {
class V4L2DecodeSurfaceHandler
: public DecodeSurfaceHandler<V4L2DecodeSurface> {
public:
V4L2DecodeSurfaceHandler() = default;
V4L2DecodeSurfaceHandler(const V4L2DecodeSurfaceHandler&) = delete;
V4L2DecodeSurfaceHandler& operator=(const V4L2DecodeSurfaceHandler&) = delete;
~V4L2DecodeSurfaceHandler() override = default;
// Append slice data in |data| of size |size| to pending hardware
// input buffer with |index|. This buffer will be submitted for decode
// on the next DecodeSurface(). Return true on success.
virtual bool SubmitSlice(V4L2DecodeSurface* dec_surface,
const uint8_t* data,
size_t size) = 0;
// Decode the surface |dec_surface|.
virtual void DecodeSurface(scoped_refptr<V4L2DecodeSurface> dec_surface) = 0;
};
} // namespace media
#endif // MEDIA_GPU_V4L2_V4L2_DECODE_SURFACE_HANDLER_H_
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,874 |
WashPost PR Blog
The Washington Post to release new book examining Russian interference in the 2016 election and its impact beyond
By WashPostPR
August 5, 2018 at 10:00 PM EDT
The Washington Post today announced plans to release a book detailing Russian interference in the 2016 election and the subsequent political, legal and diplomatic fallout. In "The Apprentice: Trump, Russia and The Subversion of American Democracy," The Post's two-time Pulitzer-Prize winning National Security Correspondent Greg Miller, along with contributions from fellow Post reporters, provides readers with a comprehensive account of the pre- and post-election story stretching from the Kremlin to the West Wing.
"Greg Miller, along with his colleagues on our national security and political teams, has been at the forefront of coverage of Russia's intervention in the 2016 presidential campaign. A highly accomplished investigative reporter and a magnificent writer, Greg digs deep into what produced this stunning turn in American presidential history," said Martin Baron, Executive Editor of The Washington Post. "The events of the past several years called for a revelatory and riveting book, and Greg delivered."
The book draws on reporting over the last two years by the National, Foreign, Business and Local staffs and is illustrated, in part, with photos by Washington Post staff photographers. A number of reporters also did additional reporting for The Apprentice, notably Devlin Barrett, Karen DeYoung, Elizabeth Dwoskin, Tom Hamburger, Rosalind Helderman, Sari Horwitz, Greg Jaffe, Ellen Nakashima, Julie Tate, Craig Timberg, Anton Troivanovksi and Matt Zapotosky.
The Apprentice will be published by Custom House, a division of HarperCollins Publishers, and is scheduled for release on October 2, 2018.
"Greg Miller and the team at The Washington Post have been working on The Apprentice since April 2017, and it shows–no other book has covered the investigation into Russian interference in the 2016 election with greater scope and determination to get to the truth." said Custom House Editorial Director Geoff Shandler in a press release. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,189 |
\section{Branch-and-Bound Algorithm}\label{sec:branch_and_bound}
Our protocol $ \ensuremath{\small{\textsc{Kep-IP}}} $ (cf.~Section~\ref{sub:kep_protocol}) for solving the KEP is based on the Branch-and-Bound algorithm~\cite{Land_BranchAndBound_1960} which is a common algorithm for IP.
The main problem that is solved by the Branch-and-Bound algorithm is that we may obtain fractional solutions if we just solve the LP relaxation of the subset formulation using an LP solver such as the Simplex algorithm~\cite{Dantzig_LinearProgrammingSimplex_1963}. For the KEP, however, it has to hold that all solutions are integral as a cycle can either be part of the solution or not, i.e., a variable can either have value 1 or 0.
The core idea of the Branch-and-Bound algorithm is to repeatedly run an LP solver until an integral solution of optimal value is found.
More specifically, the Branch-and-Bound algorithm generates a tree of subproblems where each node of the tree states an upper bound on a possible optimal solution. Each node also stores the best known integer solution $ \ensuremath{X^*} \in \ensuremath{\mathbb{Z}}^n $ (called the \emph{incumbent}) and its value $ \ensuremath{z^*} \in \ensuremath{\mathbb{R}} $. The solution of a subproblem is then determined using an LP solver. Throughout this paper, we use the Simplex algorithm as it is the most prominent method for solving LPs~\cite{Schrijver_LinearProgramming_1998} and there are already SMPC protocols for it (cf.~Section~\ref{sub:rw_pp_lp}).
\begin{algorithm}[t]
\caption{Branch-and-Bound algorithm, based on~\cite{Land_BranchAndBound_1960}.}
\label{alg:branch_and_bound}
\input{./protocols/plain_branch_and_bound.tex}
\end{algorithm}
Algorithm~\ref{alg:branch_and_bound} contains pseudocode for the Branch-and-Bound algorithm. At the beginning, an initial tableau $ \ensuremath{\tableau} $ of the LP relaxation for the IP is built. Together with the initial upper bound $ \ensuremath{\overline{b}} = \infty $, this tableau forms the first subproblem in the list of subproblems $ L $ (i.e., it forms the root node of the Branch-and-Bound tree). The algorithm then solves the subproblems in the list $ L $ one by one until $ L $ is empty. For each subproblem $ (\ensuremath{T}, \ensuremath{\overline{b}}) $, it is first checked whether the best known solution $ \ensuremath{z^*} $ is larger than the upper bound $ \ensuremath{\overline{b}} $ of the subproblem. If this is the case, this subproblem cannot improve the solution and the whole subtree is pruned. Otherwise, the LP with tableau $ T $ is solved yielding a solution $ \ensuremath{X} $ of value $ \ensuremath{z} $. If the solution is integral, the incumbent $ \ensuremath{X^*} $ is updated if this improves its value (i.e., if $ \ensuremath{z} > \ensuremath{z^*} $). If the solution is fractional, one currently fractional variable $ x_i $ is chosen and two new child nodes $ (\ensuremath{T}_1, \ensuremath{z}) $ and $ (\ensuremath{T}_2, \ensuremath{z}) $ are created such that the new value of $ x_i $ is set to $ \lfloor \ensuremath{X}(i) \rfloor $ for one child node and to $ \lceil \ensuremath{X}(i) \rceil $ for the other. Both new subproblems are added to the list $ L $. The algorithm terminates when $ L $ is empty.
Figure~\ref{fig:bb_tree} shows a Branch-and-Bound tree for the IP
\begin{equation}\label{eq-example-ip-bb}
\begin{alignedat}{2}
\max\: & z = 3 x_1 + 2 x_2 + 2 x_3 \\
\text{s.t. }& x_1 + 2 x_2 + 3 x_3 \le 3 \\
& 3 x_1 + x_2 + 2 x_3 \le 3 \\
& 2 x_1 + 3 x_2 + x_3 \le 3 \\
& x_1, x_2, x_3 \ge 0.
\end{alignedat}
\end{equation}
Note that the subproblem at Node~2 has an integer solution. Since the upper bound $ \ensuremath{\overline{b}} $ of the subproblems at Nodes 4 and~5 is lower than the incumbent value $ \ensuremath{z^*} $, they do not have to be evaluated, i.e., their whole subtrees can be pruned.
\begin{figure}[t]
\input{figures/branch_and_bound_tree.tex}
\vspace*{-2em}
\caption{Example Branch-and-Bound tree for the IP in Equation~\ref{eq-example-ip-bb}. The order~in which subproblems are evaluated and their bounds are given above the nodes.}
\label{fig:bb_tree}
\end{figure}
\customParagraph{Simplifications for the KEP.}
The subset formulation (Equation~\ref{eq:subset_formulation}, Section~\ref{sub:integer_programming}) allows us to make several simplifying assumptions when using Algorithm~\ref{alg:branch_and_bound} for solving the KEP. We can use the feasible initial solution $ x = (0,\ldots,0)^\top $ of value $ 0 $ as the starting point $ (\ensuremath{X^*}, \ensuremath{z^*}) $. This corresponds to selecting no exchange cycle at all. Furthermore, we can use the initial upper bound $ \ensuremath{\iota} $ (instead of $ \infty $) for the initial subproblem as the best solution for the KEP is that all patient-donor pairs are included in the computed exchange cycles. Finally, the LP relaxation of the subset formulation already guarantees that $ 0 \le x_i \le 1$ for all variables $ x_i $. Thus, the new constraints in Step 6 of Algorithm~\ref{alg:branch_and_bound} are always $ x_i = 0 $ and $ x_i = 1 $. Note that adding the constraints $ x_i = 0 $ or $ x_i = 1 $ cannot lead to an infeasible problem as we can always obtain a feasible point where $ x_i = 1 $ by setting all other fractional variables to $ 0 $.
\section{Conclusion and Future Work}
We have developed a novel privacy-preserving protocol for solving the KEP using IP which is the most efficient method for solving the KEP in the non-privacy-preserving setting. We have implemented and evaluated our protocol and shown that it significantly outperforms the existing privacy-preserving protocol for solving the KEP.
While we have evaluated our protocol for a fixed set of patient-donor pairs, existing kidney exchange platforms are dynamic in that the pairs arrive at and depart from the platform over time. In future work, we plan to evaluate the efficiency of our protocol when used in such a dynamic setup. Another interesting direction for future research is the inclusion of \emph{altruistic donors} who are not tied to any particular patient.
\section{Evaluation}\label{sec:evaluation}
In this section, we evaluate the performance of our implementation of our protocol~$ \ensuremath{\small{\textsc{Kep-IP}}} $ (Protocol~\ref{prot:kep_ip}). First, we describe the evaluation setup (Section~\ref{sub:eval_setup}). Then, we evaluate runtime and network traffic of our protocol and compare the results to the existing protocol from~\cite{Breuer_KEprotocol_2020} (Section~\ref{sub:eval_runtime}).
\subsection{Setup}\label{sub:eval_setup}
We implemented our protocol~$ \ensuremath{\small{\textsc{Kep-IP}}} $ using the SMPC benchmarking framework MP-SPDZ~\cite{KellerMPSPDZ2020}. We adopt the setup from~\cite{Breuer_Matching_2022}, where different containers on a single server with an AMD EPYC 7702P 64-core processor are used for computing peers and input peers. Each container runs Ubuntu 20.04 LTS, has a single core, and 4GB RAM. In our evaluations, we then run each of the three computing peers on a separate container. A fourth container is used to manage the sending of input and the receiving of output for all patient-donor pairs. Similar to~\cite{Breuer_Matching_2022}, we evaluate our protocol for three different values for the latency $ L $ (i.e., 1ms, 5ms, and 10ms) and a fixed bandwidth of 1Gbps between the computing peers.
In order to provide realistic values for the medical data of the patient-donor pairs, we use a real-world data set from the United Network for Organ Sharing (UNOS) which is a large kidney exchange platform in the US.~\footnote{The data reported here have been supplied by the United Network for Organ Sharing as the contractor for the Organ Procurement and Transplantation Network. The interpretation and reporting of these data are the responsibility of the author(s) and in no way should be seen as an official policy of or interpretation by the OPTN or the U.S.\ Government.} The data set contains all patient-donor pairs that registered with the platform between October 27th 2010 and December 29th 2020 yielding a total of 2913 unique patient-donor pairs from which we sample uniformly at random for each protocol execution.
\subsection{Runtime Evaluation}\label{sub:eval_runtime}
\begin{table}
\caption{Runtime and network traffic for our protocol~\textsc{Kep-IP} and the implementation~\textsc{Kep-Rnd-SS}~\cite{Breuer_Matching_2022} of the protocol from~\cite{Breuer_KEprotocol_2020}.}
\label{tab:runtimes}
\input{tables/runtimes_compared_latencies.tex}
\end{table}
Table~\ref{tab:runtimes} shows runtime and network traffic of our protocol~$ \ensuremath{\small{\textsc{Kep-IP}}} $ and the protocol~$ \ensuremath{\small{\textsc{Kep-Rnd-SS}}} $ from~\cite{Breuer_Matching_2022}, which is a more efficient implementation of the protocol from~\cite{Breuer_KEprotocol_2020}. For both protocols, we consider a maximum cycle size $ \ensuremath{l} = 3 $ as this is the most common maximum cycle size used in existing kidney exchange platforms~\cite{Biro_EuropeanKE_2019,AshlagiKidneyExchangeOperations2021}. The results for our protocol~$ \ensuremath{\small{\textsc{Kep-IP}}} $ are averaged over 50 repetitions for each value of $ \ensuremath{\iota} $ (number of patient-donor pairs).
When comparing the performance of our protocol $ \ensuremath{\small{\textsc{Kep-IP}}} $ to the protocol~$ \ensuremath{\small{\textsc{Kep-Rnd-SS}}} $, we observe that the runtime of our protocol is larger for up to $ 9 $ patient-donor pairs. However, for larger numbers of patient-donor pairs our protocol significantly outperforms the protocol~$ \ensuremath{\small{\textsc{Kep-Rnd-SS}}} $. For example, for 12 pairs our protocol is already about 34 times faster. This is due to the brute force nature of protocol~$ \ensuremath{\small{\textsc{Kep-Rnd-SS}}} $ which scales in the number of potential exchange constellations between the involved patient-donor pairs (cf.~Section~\ref{sub:rw_pp_ke}). While this number is still very low for small values of $ \ensuremath{\iota} $, it quickly increases for larger numbers of pairs.
Furthermore, we observe that the runtime of our protocol $ \ensuremath{\small{\textsc{Kep-IP}}} $ increases with increasing values for the latency $ L $. The factor between the runtimes for the different latencies is nearly constant which is to be expected as the latency is just a constant delay for each message. In particular, the runtimes for $ L = 5ms $ and $ L = 10ms $ are always about a factor of $ 4.76 $ and $ 9.39 $, respectively, larger than for $ L = 1ms $.
Another important observation is that the runtime of our protocol varies for different inputs. Figure~\ref{fig:runtimes} shows boxplots for latency $ L = 1ms $. We observe that there are outliers where our protocol performs significantly worse than the average. This is due to the nature of the Branch-and-Bound algorithm and the Simplex algorithm which require different numbers of subproblems and iterations depending on the input. However, even for the worst case which we measured in our evaluations, our protocol outperforms the protocol~$ \ensuremath{\small{\textsc{Kep-Rnd-SS}}} $ from~\cite{Breuer_Matching_2022}.
Figure~\ref{fig:runtimes} also shows that the runtime of our protocol increases sub-exponentially on average. Thus, we can assume that the runtimes for more than 30 patient-donor pairs will still be feasible for the use case of kidney exchange where a match is usually computed once every couple of days or even only once every 3 months~\cite{Biro_EuropeanKE_2019}.
\begin{figure}
\input{figures/boxplots_runtimes.tex}
\caption{Boxplots for the runtime of protocol~$ \ensuremath{\small{\textsc{Kep-IP}}} $ for L = 1ms.}
\label{fig:runtimes}
\end{figure}
\section{Introduction}
In living kidney donation, a patient tries to find a friend or relative who is willing to donate one of her kidneys to the patient. Even if a patient finds such a living donor, this donor is often not medically compatible with the patient. Kidney exchange tries to solve this problem by finding constellations in which multiple such incompatible \emph{patient-donor pairs} can exchange their kidney donors among each other. These exchanges are usually carried out in \emph{exchange cycles} where the donor of a patient-donor pair always donates to the patient of the succeeding pair in the cycle and the patient of a pair receives a kidney donation from the donor of the preceding pair. In practice, the maximum size of these exchange cycles is commonly restricted to two or three due to the amount of medical resources that are required to carry out a transplant~\cite{AshlagiKidneyExchangeOperations2021}.
More formally, the \emph{Kidney Exchange Problem} (KEP) is to find an \emph{optimal} set of exchange cycles \emph{up to} a maximum cycle size $ \ensuremath{l} $ for a fixed set of patient-donor pairs such that the number of possible transplants that can be carried out is maximized~\cite{AbrahamClearingAlgorithms2007}.
In many countries, there are already central platforms that facilitate the solving of the KEP for registered incompatible patient-donor pairs~\cite{Biro_EuropeanKE_2019,AshlagiKidneyExchangeOperations2021}. The drawbacks of this centralized approach are that these platforms possess the medical data of all registered patient-donor pairs and that they exhibit complete control over the computation of the possible exchanges. Thus, a compromise of such a central platform would have severe consequences for the registered patient-donor pairs.
In recent research, initial approaches to address these shortcomings of the existing platforms have been proposed~\cite{Breuer_KEprotocol_2020,Breuer_Matching_2022}. These approaches use \emph{Secure Multi-Party Computation} (SMPC) to solve the KEP in a distributed and privacy-preserving fashion. In particular, they implement the ideal functionality that obtains the private medical data of the patient-donor pairs as input and for each patient-donor pair outputs its possible exchange partners such that the overall number of possible transplants is maximized. Still, these initial approaches exhibit some drawbacks. While the protocol from~\cite{Breuer_Matching_2022} only solves the KEP for a maximum cycle size $ \ensuremath{l} = 2 $, the protocol from~\cite{Breuer_KEprotocol_2020} allows for an arbitrary maximum cycle size but only yields practical runtimes for a very small number of incompatible patient-donor pairs.\footnote{The KEP is NP-complete for $ \ensuremath{l} \geq 3 $~\cite{AbrahamClearingAlgorithms2007}.}
In this paper, we aim to address these drawbacks.
To this end, we turn to the most efficient algorithms employed in the non-privacy-preserving setting to solve the KEP, which are based on Integer Programming (IP)~\cite{AbrahamClearingAlgorithms2007}. Even though these algorithms have exponential time complexity in the worst case~\cite{Schrijver_LinearProgramming_1998}, they have been shown to efficiently solve the KEP in practice~\cite{AbrahamClearingAlgorithms2007}. Therefore, we explore whether and if so how they can be used to devise an efficient privacy-preserving protocol for solving the KEP for an arbitrary maximum cycle size $ \ensuremath{l} $.
\textbf{Approach.} As the basis of our novel privacy-preserving protocol, we use the Branch-and-Bound algorithm introduced in~\cite{Land_BranchAndBound_1960}. At its core, this algorithm builds a tree of subproblems whose branches are pruned as soon as the upper bound on solutions in a branch is worse than the best known solution so far. This makes it more efficient than a brute force approach that explores the complete search space. Each subproblem in the tree requires the solving of a Linear Program (LP). In our protocol, we solve these LPs using an existing privacy-preserving implementation of the Simplex algorithm~\cite{Toft_PPLinearProgramming_2009},
which is the most prominent algorithm for solving LPs~\cite{Schrijver_LinearProgramming_1998}.
It is hard to predict the number of iterations that IP- and LP-based approaches require to find an optimal solution. Therefore, the output of the ideal functionality of the respective SMPC protocols typically includes additional information. For instance, the output of the ideal functionality of the SMPC protocols known to date for the Simplex algorithm include the number of iterations that Simplex requires to find an optimal solution~\cite{Catrina_PPLinearProgramming_2010,Toft_PPLinearProgramming_2009}. Since we use the protocol from~\cite{Toft_PPLinearProgramming_2009} as a building block, the output of the ideal functionality for our novel privacy-preserving protocol includes the number of Simplex iterations for each of the subproblems in the Branch-and-Bound tree. Furthermore, the output also includes the structure of the Branch-and-Bound tree corresponding to the pruning decisions of the Branch-and-Bound algorithm.\footnote{Note that these extended outputs do not compromise the privacy of the medical data of the incompatible patient-donor pairs~(cf.~Section~\ref{sub:kep_protocol}).}
\textbf{Contributions.}
Our paper provides the following three main contributions:
First, we devise an efficient SMPC protocol for solving the KEP for an arbitrary maximum cycle size $ \ensuremath{l} $ based on the Branch-and-Bound algorithm and prove its security (Section~\ref{sec:protocol}).
Second, we implement our novel protocol in the SMPC benchmarking framework MP-SPDZ~\cite{KellerMPSPDZ2020} and evaluate its performance based on a real-world data set from a large kidney exchange in the US (Section~\ref{sec:evaluation}).
Third, we compare the implementation of our protocol to the protocol from~\cite{Breuer_KEprotocol_2020} which to date is the only known SMPC protocol for solving the KEP for an arbitrary maximum cycle size~$ \ensuremath{l} $~\cite{Breuer_KEprotocol_2020}. We show that our protocol allows for a significant improvement of the runtime (Section~\ref{sec:evaluation}).
\section{Preliminaries}
In this section, we provide the formal background on which our privacy-preserving protocol for solving the Kidney Exchange Problem (KEP) is based. In Section~\ref{sub:notation}, we introduce the notation used in this paper. In Section~\ref{sub:smpc}, we describe the Secure Multi-Party Computation (SMPC) setting for our protocols. In Section~\ref{sub:integer_programming}, we give an introduction to Integer Programming (IP) in the context of kidney exchange.
\subsection{Notation}\label{sub:notation}
A \emph{directed graph} is a graph $ G = (\ensuremath{V}, E) $ where the edge $ (v, w) \in E $ ($ v, w \in \ensuremath{V} $) is directed from node~$ v $ to node~$ w $. Such a graph is usually represented as an \emph{adjacency matrix}~$ \ensuremath{M} $ of size $ \vert \ensuremath{V} \vert \times \vert \ensuremath{V} \vert $ such that $ M(i, j) = 1 $ if $ (i, j) \in E $ and $ M(i, j) = 0 $, otherwise. Given a matrix $ M $, we write $ M(i, -) $ for its $ i $-th row, $ M(-, j) $ for its $ j $-th column, and $ M([i_1 : i_2], [j_1 : j_2]) $ for the submatrix with entries $ M(i, j) $ where $ i_1 \leq i \leq i_2 $ and $ j_1 \leq j \leq j_2 $.
We adopt the notation for kidney exchange from~\cite{Breuer_KEprotocol_2020}. In particular, we denote the index set of all patient-donor pairs $ \partysymbol{1}, ..., \partysymbol{\ensuremath{\iota}} $ ($ \ensuremath{\iota} \in \ensuremath{\mathbb{N}} $) by $ \ensuremath{\mathcal{P}} := \{1, ..., \ensuremath{\iota}\} $. We call the graph induced by the patient-donor pairs' medical input the \emph{compatibility graph} $ G = (V, E) $ where $ V = \ensuremath{\mathcal{P}} $ and $ (u, v) \in E $ if the donor of pair $ \partysymbol{u} $ can donate to the patient of pair $ \partysymbol{v} $. An \emph{exchange cycle} of size $ m $ is a tuple $ \ensuremath{C} = (\partysymbol{i_1}, ..., \partysymbol{i_m}) $ with $ i_j \neq i_k $ such that for $ j \in \{1, ..., m-1\} $ it holds that $ (v_j, v_{j+1}) \in E $ and $ (v_m, v_1) \in E $.
\subsection{Secure Multi-Party Computation}\label{sub:smpc}
In SMPC a set of $ \ensuremath{\kappa} $ parties computes a functionality in a distributed way such that each party does not learn anything beyond its private input and output and what can be deduced from both. We adopt the setting for privacy-preserving kidney exchange from Breuer et al.~\cite{Breuer_Matching_2022}. In particular, we distinguish between \emph{computing peers} and \emph{input peers}. The computing peers execute the actual SMPC protocol for computing the functionality among each other, whereas the input peers only provide private input to the functionality and receive their private output. In the kidney exchange setting, each patient-donor pair forms one input peer and the computing peers can be run by large transplant centers or governmental organizations.
Our SMPC protocols rely on Shamir's $ (t,\ensuremath{\kappa}) $ threshold secret sharing scheme~\cite{ShamirSecretSharing1979}, i.e., at least $ t+1 $ shares are required to reconstruct the shared value. We denote a shared value $ x $ by $ \enc{x} $, a vector $ V $ of shared values by $ \enc{V} $, and a matrix $ M $ of shared values by $ \enc{M} $. Furthermore, we write $ \enc{V}(i) $ (resp.~$ \enc{M}(i,j) $) to denote a single element of a secret vector $ \enc{V} $ (resp.~matrix $ \enc{M} $).
Computations on shared values are executed in a finite field $ \mathbb{Z}_p $ where $ p > n $ is a prime and a negative value $ -x $ is defined as $ p - x \in \mathbb{Z}_p $.
This setup enables the computing peers to compute linear combinations of shared values locally whereas for the multiplication of two shared values they have to execute a protocol among each other. We denote the multiplication of two shared values $ \enc{x} $ and $ \enc{y} $ by $ \enc{z} \leftarrow \enc{x} \cdot \enc{y} $.
\customParagraph{Complexity metrics.} We follow Catrina and de Hoogh~\cite{Catrina_PrimitivesSMPC_2010} and use the two metrics communication and round complexity. The former is defined as the number of invocations of primitives that require each computing peer to send a share to the other computing peers. The latter is defined as the number of sequential invocations. A multiplication thus corresponds to a single invocation in a single round~\cite{Catrina_PrimitivesSMPC_2010}. Invocations that can be executed in parallel are considered as a single round.
\begin{protocol}[t]
\caption{$ \ensuremath{\small{\textsc{Sel-Min}}\small} $}
\label{prot:min_sel}
\input{./protocols/min_sel.tex}
\end{protocol}
\customParagraph{Building Blocks.}
For our protocol~$ \ensuremath{\small{\textsc{Kep-IP}}} $ (cf.~Section~\ref{sec:protocol}), we require privacy-preserving protocols for several basic primitives. For the secure comparison of two shared values $ \enc{x} $ and $ \enc{y} $ we write $ \enc{x} \ensuremath{\stackrel{?}{>}} \enc{y} $. A protocol for this primitive can be realized with linear communication and constant round complexity~\cite{Catrina_PrimitivesSMPC_2010}. Conditional selection is defined as choosing between two values based on a secret shared bit~$ \enc{b} $, i.e., we choose $ \enc{x} $ if $ b $ is equal to $ 1 $ and $ \enc{y} $, otherwise. This corresponds to computing $ \enc{b} \cdot (\enc{x} - \enc{y}) + \enc{y} $ and we denote this by $ \enc{b} \ ? \ \enc{x} : \enc{y} $. Finally, we require a protocol $ \ensuremath{\small{\textsc{Sel-Min}}\small} $ for selecting the index of the first element in a vector that is larger than zero. The specification of this protocol is given in Protocol~\ref{prot:min_sel}. The communication complexity of $ \ensuremath{\small{\textsc{Sel-Min}}\small} $ is $ \bigo{\vert U \vert \ensuremath{s}} $ and its round complexity is $ \bigo{1} $, where $ \ensuremath{s} $ is the bit length of the input to the comparison protocol.
\customParagraph{Security Model.}
Same as Breuer et al.~\cite{Breuer_Matching_2022} we prove our protocol to be secure in the \textit{semi-honest model}. This means that we assume a set of corrupted computing peers who strictly follow the protocol specification but try to deduce as much information on the honest computing peers' input as possible. As security in the semi-honest model already prevents an adversary from learning the medical data of the patient-donor pairs and thereby from influencing the computed exchanges in any meaningful way, we consider it to be sufficient for our use case. Besides, the input peers can not learn anything beyond their private input and output since they are not part of the protocol execution itself. Finally, we consider an honest majority of computing peers and the existence of encrypted and authenticated channels between all participating parties. For the security proofs of our protocols, we use the standard simulation-based security paradigm. We denote the values simulated by the simulator by angle brackets $ \simval{\cdot} $. For further details on the semi-honest security model and the simulation-based security paradigm, we refer the reader to~\cite{GoldreichFoundationsTwo2004}.
\subsection{Integer Programming for the Kidney Exchange Problem}\label{sub:integer_programming}
A \emph{Linear Program (LP)} is a formulation for an optimization problem of the following form: Let $ c \in \ensuremath{\mathbb{R}}^n, a_i \in \ensuremath{\mathbb{R}}^n $, and $ b_i \in \ensuremath{\mathbb{R}} $ for $ i \in \{1, ..., \ensuremath{m}\} $. The LP is then defined as
\begin{align}\label{eq:lp}
\begin{split}
\text{maximize } & \ensuremath{c}^\top x \\
\text{s.t. } & \ensuremath{A} x = \ensuremath{b} \\
& x \ge 0,
\end{split}
\end{align}
where $ \ensuremath{x \mapsto \objectiveVec^\top x} $ is the \emph{objective function}, $ \ensuremath{A} $ is the \emph{constraint matrix}, and $ \ensuremath{b} $ is the \emph{bound vector}. This form of an LP where only equality constraints occur is called the \emph{standard form}. Inequalities $ \ensuremath{a}_i^\top x \leq \ensuremath{b}_i $ can be represented in standard form as $ \ensuremath{a}_i^\top x + \ensuremath{s}_i = \ensuremath{b}_i $ where $ s_i \geq 0 $ is called a \emph{slack variable}.
In our protocols, we represent an LP in form of a \emph{tableau}
\begin{align}\label{eq:tableau-structure}
T=\left(\begin{array}{ccc|c}
&c^\top & & z \\\hline
& A & & b \TstrutLarge\BstrutLarge
\end{array}\right)
\end{align}
with objective value $ -\ensuremath{z} = \ensuremath{c}^\top \ensuremath{x} $ (the sign is flipped as the tableau method is designed for minimization whereas we aim at maximizing the objective function).
In contrast to an LP, for IP the additional restriction that all solutions have to be integers (i.e., $ x \in \ensuremath{\mathbb{N}}^n $) is imposed. This is a natural requirement for the KEP as an exchange cycle is either part of the solution or not.
\customParagraph{Cycle Formulation.}
For the restricted KEP where only cycles of bounded length $ \ensuremath{l} $ are allowed, the most efficient known IP formulation is the cycle formulation where a constraint is introduced for each possible cycle of length at most~$ \ensuremath{l} $~\cite{AbrahamClearingAlgorithms2007}.
\begin{definition}[Cycle Formulation]
\textit{
Let $ \ensuremath{\mathcal{\singleCycle}} $ be the set of all cycles of length at most $ \ensuremath{l} $ in the compatibility graph $ G = (V, E) $. Then, the \emph{cycle formulation} is defined as
\begin{equation}\label{eq:cycle_formulation}
\begin{alignedat}{3}
\text{maximize }& \sum_{\ensuremath{C} \in \ensuremath{\mathcal{\singleCycle}}} \vert \ensuremath{C} \vert \ \ensuremath{x_\singleCycle} \\
\text{s.t. } & \sum_{\substack{\ensuremath{C} \in \ensuremath{\mathcal{\singleCycle}} \\ v \in V(\ensuremath{C})}} \ensuremath{x_\singleCycle} \leq 1 && \text{ for all }v \in V \\
& \ensuremath{x_\singleCycle} \in \{0,1\} && \text{ for all }\ensuremath{C} \in \ensuremath{\mathcal{\singleCycle}}
\end{alignedat}
\end{equation}
where $ \ensuremath{x_\singleCycle} \in \{0, 1\} $ for $ \ensuremath{C} \in \ensuremath{\mathcal{\singleCycle}} $ such that $ \ensuremath{x_\singleCycle} = 1 $ iff cycle $ \ensuremath{C} $ is chosen and $ \ensuremath{x_\singleCycle} = 0 $, otherwise.
}
\end{definition}
\customParagraph{Subset Formulation.}
In the privacy-preserving setting, we have to keep secret which cycles are present in the compatibility graph. Therefore, we have to consider the set $ \ensuremath{\mathcal{\singleCycle}} $ of all \emph{potential} cycles in the complete directed graph $ K = (V, E') $
with $ V = \ensuremath{\mathcal{P}} $ and $ (u, v) \in E' $ for all $ u, v \in V $. Thus, if two cycles $ \ensuremath{C}_1, \ensuremath{C}_2 \in \ensuremath{\mathcal{\singleCycle}} $ contain the same vertices in a different order, their coefficients for the objective function in the cycle formulation are exactly the same. We eliminate this redundancy by proposing the more efficient \emph{subset formulation}.\footnote{This formulation is only more efficient in the privacy-preserving case as only there the complete graph~$ \ensuremath{K} $ has to be considered.}
\begin{definition}[Subset Formulation]
\textit{
Let $ \ensuremath{\mathcal{\singleSubset}} $ contain all vertex sets of size $ k $ with $ 2 \leq k \leq \ensuremath{l} $ and let $ \ensuremath{\mu}: \ensuremath{\mathcal{\singleSubset}} \rightarrow \ensuremath{\mathcal{\singleCycle}} \cup \{\emptyset\} $ be a mapping that assigns an arbitrary cycle $ \ensuremath{\mu}(\ensuremath{S}) \in \ensuremath{\mathcal{\singleCycle}} $ with $ \ensuremath{V}(\ensuremath{\mu}(\ensuremath{S})) = \ensuremath{S} $ to each $ \ensuremath{S} \in \ensuremath{\mathcal{\singleSubset}} $. If there is no such cycle, let $ \ensuremath{\mu}(\ensuremath{S}) = \emptyset $. Then, the \emph{subset formulation} is defined as
\begin{equation}\label{eq:subset_formulation}
\begin{alignedat}{3}
\text{maximize } & \sum_{\ensuremath{S} \in \ensuremath{\mathcal{\singleSubset}}} \vert \ensuremath{\mu}(\ensuremath{S}) \vert \ \ensuremath{x_\singleSubset} \\
\text{s.t. } & \sum_{\substack{\ensuremath{S} \in \ensuremath{\mathcal{\singleSubset}} \\ v \in \ensuremath{S}}} \ensuremath{x_\singleSubset} \leq 1 && \text{ for all } v \in \ensuremath{V} \\
& \ensuremath{x_\singleSubset} \in \{0, 1\} && \text{ for all } \ensuremath{S} \in \ensuremath{\mathcal{\singleSubset}}
\end{alignedat}
\end{equation}
where the variable $ \ensuremath{x_\singleSubset} \in \{0, 1\} $ indicates for each $ \ensuremath{S} \in \ensuremath{\mathcal{\singleSubset}} $ whether any cycle consisting of the vertices in $ \ensuremath{S} $ is chosen.
}
\end{definition}
For our protocol, we assume that $ \ensuremath{\mathcal{\singleSubset}} = \{\ensuremath{S}_1, ..., \ensuremath{S}_{\vert \ensuremath{\mathcal{\singleSubset}} \vert}\} $ is a fixed enumeration of the subsets and for $ 1 \leq i \leq \vert \ensuremath{\mathcal{\singleSubset}} \vert $ we have an enumeration $ \ensuremath{\mathcal{\singleCycle}}_i = \{\ensuremath{C}_{i, 1}, ..., \ensuremath{C}_{i, \ensuremath{k_i}}\} $ of the cycles in the complete graph~$ \ensuremath{K} $.
\begin{figure}
\input{./figures/subset_formulation_example.tex}
\caption{Example of a compatibility graph and its exchange cycles.}
\label{fig:subset_formulation_example}
\end{figure}
Observe that the number of subsets is smaller by a factor of $ (\ensuremath{l} - 1)! $ as there are $ (\ensuremath{l} - 1)! $ cycles on a set of size $ \ensuremath{l} $. Hence, for the subset formulation we have to consider significantly less variables at the initial cost of determining the mapping~$ \ensuremath{\mu} $ from subsets to cycles.
\customParagraph{Example.}
For an intuition on the relation between the initial tableau of the LP relaxation\footnote{The LP relaxation of an IP is the LP that we obtain if we remove the integrality constraint on the variables of the IP.} for the subset formulation and the compatibility graph, consider the example compatibility graph provided in Figure~\ref{fig:subset_formulation_example}. To build the initial tableau for the subset formulation for this graph, we add one column for all subsets of nodes that could form a cycle between four nodes. For our example, this yields the subset variables $ \explicitSubsetVar{12}, \explicitSubsetVar{13}, \explicitSubsetVar{14}, \explicitSubsetVar{23}, \explicitSubsetVar{24}, \explicitSubsetVar{34}, \explicitSubsetVar{123}, \explicitSubsetVar{124}, \explicitSubsetVar{134}, \explicitSubsetVar{234} $ and the initial tableau $ T := $
\begin{align*}
\left(\begin{array}{rrrrrrrrrrrrrr|r}
0 & 0 & 0 & 2 & 0 & 0 & 0 & 3 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\hline
1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 \Tstrut\\
1 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 \\
0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 \\
0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1
\end{array}\right)
\end{align*}
\section{Privacy-Preserving Kidney Exchange using Integer Programming}\label{sec:protocol}
In this section, we present our novel SMPC protocol~$ \ensuremath{\small{\textsc{Kep-IP}}} $ for solving the KEP using a privacy-preserving implementation of the Branch-and-Bound algorithm (cf.~Section~\ref{sec:branch_and_bound}). First, we formally define the ideal functionality~$ \ensuremath{\ensuremath{\pazocal{F}}_{\small{\textsc{Kep-IP}}}} $ that is implemented by our protocol (Section~\ref{sub:ideal_func}). Then, we describe the setup of the initial tableau for the subset formulation (Section~\ref{sub:tableau_setup}) and provide the specification of our protocol for Branch-and-Bound (Section~\ref{sub:pp_branch_and_bound}). Finally, we provide the complete specification of the protocol~$ \ensuremath{\small{\textsc{Kep-IP}}} $ (Section~\ref{sub:kep_protocol}).
\subsection{Ideal Functionality}\label{sub:ideal_func}
The ideal functionality that is implemented by the existing SMPC protocols for the KEP takes the medical data of the patient-donor pairs as input and outputs their respective exchange partners~\cite{Breuer_KEprotocol_2020,Breuer_Matching_2022}. As we use the Branch-and-Bound algorithm as basis for our novel privacy-preserving protocol for solving the KEP, the ideal functionality in our case additionally has to output the structure of the Branch-and-Bound tree~$ \ensuremath{\mathcal{B}} $ and the number of Simplex iterations $ \ensuremath{\mathcal{I}} $ required to solve each subproblem in the tree. This is necessary as the Branch-and-Bound algorithm repeatedly prunes the search space for the values of the solution $ \ensuremath{X} $. If we want to implement the algorithm in a privacy-preserving fashion, we have to include these pruning decisions and thus the structure of the Branch-and-Bound tree~$ \ensuremath{\mathcal{B}} $ in the output of the ideal functionality.
To solve the LP at each node in the tree in a privacy-preserving fashion, we require a privacy-preserving protocol for the Simplex algorithm. Since the output of the ideal functionality that is implemented by the existing privacy-preserving protocols for Simplex (e.g.,~\cite{Catrina_PPLinearProgramming_2010,Toft_PPLinearProgramming_2009}) includes the number of iterations that Simplex needs to solve the LP, the output of the ideal functionality implemented by our protocol has to include the number of Simplex iterations~$ \ensuremath{\mathcal{I}} $ necessary to solve the subproblems in the Branch-and-Bound tree.
Functionality~\ref{func:kep_ip} contains the definition of the ideal functionality~$ \ensuremath{\ensuremath{\pazocal{F}}_{\small{\textsc{Kep-IP}}}} $ implemented by our novel privacy-preserving protocol for solving the KEP. We adopt the compatibility computation between two patient-donor pairs from~\cite{Breuer_KEprotocol_2020} where the bloodtype of donor and patient, the HLA antigens of the donor, and the patient's antibodies against these are considered.
\begin{functionality}[$ \ensuremath{\ensuremath{\pazocal{F}}_{\small{\textsc{Kep-IP}}}} $ - Solving the KEP based on~IP]\label{func:kep_ip}
\textit{
Let all computing peers hold the secret input quotes $ \enc{\inputQuote{i}} = (\enc{\donorbloodvec{i}} $, $ \enc{\antigenvec{i}} $, $ \enc{\patientbloodvec{i}} $, $ \enc{\antibodyvec{i}}) $ of patient-donor pairs $ \partysymbol{i} $ ($ i \in \ensuremath{\mathcal{P}} $), where $ \donorbloodvec{i} $ and $ \antigenvec{i} $ are the donor bloodtype and antigen vectors and $ \patientbloodvec{i} $ and $ \antibodyvec{i} $ are the patient bloodtype and antibody vectors as defined in~\cite{Breuer_KEprotocol_2020}. Then, functionality~$ \ensuremath{\ensuremath{\pazocal{F}}_{\small{\textsc{Kep-IP}}}} $ is given as
\begin{equation*}
((\enc{d_1}, \enc{r_1}), ..., (\enc{d_1}, \enc{r_1}), \ensuremath{\mathcal{B}}, \ensuremath{\mathcal{I}}) \leftarrow \ensuremath{\ensuremath{\pazocal{F}}_{\small{\textsc{Kep-IP}}}}(\enc{\inputQuote{1}}, ..., \enc{\inputQuote{\ensuremath{\iota}}}),
\end{equation*}
where $ \ensuremath{\mathcal{B}} $ is the structure of the Branch-and-Bound tree, $ \ensuremath{\mathcal{I}} $ is the necessary number of Simplex iterations for solving the subproblems in the tree, and $ (d_i, r_i) $ are the indices of the computed donor and recipient for patient-donor pair~$ \partysymbol{i} $ for a set of exchange cycles that maximizes the number of possible transplants between the patient-donor pairs $ \partysymbol{i} $ ($ i \in \ensuremath{\mathcal{P}} $).
}
\end{functionality}
Note that the tree structure~$ \ensuremath{\mathcal{B}} $ and the number of iterations~$ \ensuremath{\mathcal{I}} $ do not reveal any information on the medical data of the patient-donor pairs.
In our protocol~$ \ensuremath{\small{\textsc{Kep-IP}}} $, this is ensured by randomly shuffling the compatibility graph before applying Branch-and-Bound on it (cf.~Section~\ref{sub:kep_protocol}).
\subsection{Tableau Setup}\label{sub:tableau_setup}
The first step when solving the KEP using the Branch-and-Bound algorithm is the construction of the initial tableau of the LP relaxation for the subset formulation. Recall that $ \ensuremath{\mathcal{\singleSubset}} $ is the set of all subsets $ \ensuremath{S}_i \subseteq \ensuremath{V} $ with $ 2 \le \left| \ensuremath{S}_i \right| \le \ell $, and for $ \ensuremath{S}_i \in \ensuremath{\mathcal{\singleSubset}} $ the set $ \ensuremath{\mathcal{\singleCycle}}_i = \left\{\ensuremath{C}_{i, 1}, \ldots, \ensuremath{C}_{i, k_i}\right\} $ contains all exchange cycles that consist of the nodes in $ \ensuremath{S}_i $.
\begin{protocol}[t]
\caption{$ \ensuremath{\small{\textsc{IP-Setup}}\small} $}
\label{prot:ip_setup}
\input{./protocols/ip_setup.tex}
\end{protocol}
Protocol~$ \ensuremath{\small{\textsc{IP-Setup}}\small} $ (Protocol~\ref{prot:ip_setup}) computes the initial tableau~$ \enc{\ensuremath{T}} $ based on the adjacency matrix~$ \enc{\ensuremath{M}} $ which encodes the compatibility graph. It also creates a mapping~$ \enc{\ensuremath{\mathcal{M}}} $ such that $ \enc{\ensuremath{\mathcal{M}}}(i, j) = 1 $ (with $ i \in \{1, ..., \vert \ensuremath{\mathcal{\singleSubset}} \vert\} $ and $ j \in \{1, ..., \ensuremath{k_i}\} $) iff all edges of the cycle~$ \ensuremath{C}_{i, j} $ are present in the compatibility graph and $ j $ is the smallest index with this~property.
First, the initial tableau $ \enc{T} $ is computed based on the subsets $ \ensuremath{\mathcal{\singleSubset}} $ and the number of patient-donor pairs~$ \ensuremath{\iota} $. Then, the computing peers set the first row of the tableau (i.e., the objective coefficients~$ \vert \ensuremath{S}_i \vert $ for $ \ensuremath{S}_i \in \ensuremath{\mathcal{\singleSubset}} $) based on the adjacency matrix~$ \enc{\ensuremath{M}} $ which encodes the compatibility graph. In particular, they determine for each cycle $ \ensuremath{C}_{i, j} $ ($ i \in \{1, ..., \vert \ensuremath{\mathcal{\singleSubset}} \vert\} $, $ j \in \{1, ..., \ensuremath{k_i}\} $) whether it exists in the compatibility graph. To this end, they verify that all edges $ (v, w) $ of the cycle $ \ensuremath{C}_{i, j} $ are present in the matrix~$ \enc{\ensuremath{M}} $. For each subset, the first cycle which exists in the compatibility graph is chosen. Finally, the entry $ \enc{\ensuremath{T}}(1, i) $ is set to the objective coefficient $ \vert \ensuremath{S}_i \vert $ if a cycle of that subset exists in the compatibility graph and to $ \enc{0} $, otherwise. This ensures that only variables for subsets for which there is a cycle in the compatibility graph are used for the optimization.
\customParagraph{Security.}
The simulator can compute the initial tableau $ T $ as specified in the protocol since this only requires knowledge of information that is publicly available. For the values of $ \simval{\enc{M'}} $, the simulator can just choose random shares from $ \ensuremath{\mathbb{Z}}_p $ and the call to the protocol $ \ensuremath{\small{\textsc{Sel-Min}}\small} $ can be simulated by calling the corresponding sub-simulator on $ \simval{\enc{M'}} $. The output of $ \ensuremath{\small{\textsc{Sel-Min}}\small} $ can again be simulated by choosing a random share. Finally, the simulator can compute $ \simval{\enc{T}}(1, i) $ as specified in the protocol using the simulated values $ \simval{\enc{\ensuremath{\mathcal{M}}}}(i, j) $ and the initial tableau $ T $ which he computed at the beginning.
\customParagraph{Complexity.}
Protocol~$ \ensuremath{\small{\textsc{IP-Setup}}\small} $ requires $ \vert \ensuremath{\mathcal{\singleSubset}} \vert \cdot \ensuremath{k_{\text{max}}} \cdot \ensuremath{l} $ comparisons and $ \vert \ensuremath{\mathcal{\singleSubset}} \vert $ calls to $ \ensuremath{\small{\textsc{Sel-Min}}\small} $, where $ \ensuremath{k_{\text{max}}} = \max_{\ensuremath{S}_i \in \ensuremath{\mathcal{\singleSubset}}}(\ensuremath{k_i}) $. As all involved loops can be executed in parallel, $ \ensuremath{\small{\textsc{IP-Setup}}\small} $ has constant round complexity. The communication complexity is $ \bigo{\ensuremath{k_{\text{max}}} \cdot \ensuremath{l} \cdot \vert \ensuremath{\mathcal{\singleSubset}} \vert \cdot \ensuremath{s}} $, where $ \ensuremath{s} $ is the bit length of the secret values.
\subsection{Privacy-Preserving Branch-and-Bound Protocol}\label{sub:pp_branch_and_bound}
\begin{protocol}[t]
\caption{$ \ensuremath{\small{\textsc{Branch-and-Bound}}} $}
\label{prot:branch_and_bound}
\input{./protocols/branch_and_bound.tex}
\end{protocol}
Protocol~\ref{prot:branch_and_bound} contains the specification of our SMPC protocol $ \ensuremath{\small{\textsc{Branch-and-Bound}}} $ for Algorithm~\ref{alg:branch_and_bound}. It receives the initial tableau~$ \enc{\ensuremath{\tableau}} $ for the subset formulation and the upper bound $ \enc{\ensuremath{\overline{b}}} $ as input and returns an optimal solution $ \enc{\ensuremath{X^*}} $ stating for each subset $ \ensuremath{S}_i \in \ensuremath{\mathcal{\singleSubset}} $ whether it is part of the optimal solution or not.
\customParagraph{Setup Phase.}
At the beginning, the trivial solution to choose no subset at all is established, i.e., all entries of $ \enc{\ensuremath{X^*}} $ are set to $ \enc{0} $ which leads to the value $ \enc{\ensuremath{z^*}} = \enc{0} $ of the initial solution. Then, the initial problem is added to the list of problems $ L $ that have to be solved. A problem is defined by a tableau~$ \enc{\ensuremath{T}} $, an upper bound~$ \enc{\ensuremath{\overline{b}}} $ for all solutions in the subtree, and the vector~$ \enc{\ensuremath{Q}} $ which stores the subsets that have already been added to the solution on the current path in the tree.
The main loop of the protocol is then executed until there is no further subproblem in the list $ L $. At the start of each iteration, the first subproblem $ P $ from the list $ L $ is chosen.
\customParagraph{Solution Phase.}
Before solving the subproblem $ P $, the computing peers check whether the upper bound $ \ensuremath{\overline{b}} $ for solutions of $ P $ is larger than the currently best solution $ \ensuremath{z^*} $. If this is not the case (i.e., $ t = 0 $), the current subtree is pruned and the next subproblem is chosen. Otherwise, a privacy-preserving protocol for the Simplex algorithm is executed to find a solution for $ P $. To this end, we use the SMPC protocol for Simplex by Toft~\cite{Toft_PPLinearProgramming_2009}. The protocol $ \ensuremath{\small{\textsc{Simplex}}\small} $ returns the optimal solution $ \enc{\ensuremath{X'}} $ with value~$ \enc{\ensuremath{z}} $ and the common denominator $ \enc{\ensuremath{d}} $, which is used to avoid fractional solutions (i.e., the actual solution is $ \enc{\frac{\ensuremath{X'}}{\ensuremath{d}}} $ and has value $ \enc{\frac{\ensuremath{z}}{\ensuremath{d}}} $). However, in our protocol the solution returned by Simplex does not consider those subset variables that have already been forced to $ 1 $ in a previous iteration. Therefore, the partial solution $ \enc{\ensuremath{Q}} $ (which was stored with the subproblem $P$) is added to the Simplex solution $ \enc{\ensuremath{X'}} $ resulting in the complete solution $ \enc{\ensuremath{X}} $ for the current subproblem.
\begin{protocol}[t]
\caption{$ \ensuremath{\small{\textsc{IP-Update}}\small} $}
\label{prot:ip_update}
\input{./protocols/ip_update.tex}
\end{protocol}
\customParagraph{Update Phase.}
In the next step, the protocol $ \ensuremath{\small{\textsc{IP-Update}}\small} $ (Protocol~\ref{prot:ip_update}) is used to update the incumbent $ \enc{\ensuremath{X^*}} $ (i.e., the best integer solution found so far) based on the solution $ \enc{\ensuremath{X}} $ for the current subproblem. The protocol also derives an upper bound~$ \enc{u} $ for solutions in the current branch and the index vector $ \enc{\ensuremath{F}} $ of the first fractional variable if~$ \enc{\ensuremath{X}} $ is fractional.
Instead of dividing the solution~$ \enc\ensuremath{X} $ and the optimal value $ \enc{\ensuremath{z}} $ by the common denominator $ \enc{\ensuremath{d}} $, we propose a method based on comparisons using the known bounds on $ \ensuremath{X} $ and $ \ensuremath{z} $. Thereby, we avoid fractional values and integer division, which is computationally expensive~\cite{Toft_PPLinearProgramming_2009}. In particular, we exploit the fact that $\frac{\ensuremath{X}(i)}{\ensuremath{d}} \in [0,1]$, which implies that $\frac{\ensuremath{X}(i)}{\ensuremath{d}}$ is fractional iff both $\ensuremath{X}(i) > 0$ and $ \ensuremath{X}(i) < \ensuremath{d} $. These two comparisons are then evaluated such that $ \enc{G}(i) = \enc{1} $ iff $\frac{\ensuremath{X}(i)}{\ensuremath{d}}$ is fractional. Afterwards, the index vector~$ \enc{\ensuremath{F}} $ of the first fractional entry and the upper bound $ \enc{\ensuremath{u}} =\enc{\left\lfloor\frac{\ensuremath{z}}{\ensuremath{d}}\right\rfloor} $ on the value of integer solutions in this branch are determined.
Finally, the incumbent is updated iff the newly computed solution~$ \enc{\ensuremath{X}} $ is better (i.e., if $ \frac{\ensuremath{z}}{\ensuremath{d}} > \ensuremath{z^*} $) and integral (i.e., $ \ensuremath{F} = (0,\ldots,0) $). Note that $ t < t^* $ iff the solution is fractional since $ \ensuremath{\iota} \cdot \ensuremath{d} $ is an upper bound on $ \ensuremath{z} $. Furthermore, if $ \ensuremath{X}(i) \in \left\{0, \ensuremath{d}\right\} $, then $ \enc{L}(i) = [\ensuremath{X}(i) > 0] = \enc{\frac{\ensuremath{X}(i)}{\ensuremath{d}}}$ already encodes the solution $ L = \frac{1}{\ensuremath{d}} \cdot\ensuremath{X} $ with value $ \ensuremath{u} = \frac{\ensuremath{z}}{\ensuremath{d}} $.
\customParagraph{Branching Phase.}
In this phase, we create two new subproblems based on the new constraint encoded by~$ \enc{\ensuremath{F}} $. Note that we create them even if the solution is not fractional. In that case, the new subproblems are pruned when checking the upper bound~$ \ensuremath{\overline{b}} $ against the value $ \ensuremath{z^*} $ of the incumbent (Line 9, Protocol~\ref{prot:branch_and_bound}) since $ \ensuremath{\overline{b}} $ will be equal to or less than $ \ensuremath{z^*} $.
Protocol~$ \ensuremath{\small{\textsc{IP-Branch}}\small} $ (Protocol~\ref{prot:ip_branch}) creates two tableaux~$ \enc{\ensuremath{T}_1} $ and $ \enc{\ensuremath{T}_2} $ for the new subproblems such that the fractional variable indicated by $ \enc{\ensuremath{F}} $ is once set to $ \enc{0} $ and once to $ \enc{1} $. Instead of adding a new row to the tableau, we just set all entries of the corresponding column to $ \enc{0} $ and update the bounds accordingly. To this end, we first determine the column $ \enc{D} $ corresponding to the branching variable. Afterwards, the entry $ \enc{D_k} $ is multiplied to the new constraint $ \enc{\ensuremath{F}^\top, v} $ for each value $ v \in \{0,1\} $ of the branching variable. The protocol~$ \ensuremath{\small{\textsc{IP-Branch}}\small} $ concludes by subtracting the matrix $ \enc{\Delta} $ from $ \enc{T} $.
\begin{protocol}[t]
\caption{$ \ensuremath{\small{\textsc{IP-Branch}}\small} $}
\label{prot:ip_branch}
\input{./protocols/ip_branch.tex}
\end{protocol}
Note that we never branch on a slack variable as the subset formulation (Equation~\ref{eq:subset_formulation}) ensures that if there is a fractional slack variable, then there is also a subset $ \ensuremath{S}_i \in \ensuremath{\mathcal{\singleSubset}} $ where the variable $ \subsetVariableIndexed{i} $ is fractional. Since Protocol $ \ensuremath{\small{\textsc{IP-Update}}\small} $ takes the fractional variable with the lowest index, it always chooses~$ \subsetVariableIndexed{i} $. Hence, we do not have to handle the special case of branching on a slack variable for our protocol $ \ensuremath{\small{\textsc{IP-Branch}}\small} $.
\customParagraph{Security.}
For the initialization of $ \enc{\ensuremath{Q}} $, $ \enc{\ensuremath{X^*}} $, and $ \enc{\ensuremath{z^*}} $, the simulator chooses random shares from $ \ensuremath{\mathbb{Z}}_p $. The calls to $ \ensuremath{\small{\textsc{Simplex}}\small} $, $ \ensuremath{\small{\textsc{IP-Update}}\small} $, and $ \ensuremath{\small{\textsc{IP-Branch}}\small} $ can be simulated by calling the respective simulators on random inputs. For the security of the protocol~$ \ensuremath{\small{\textsc{Simplex}}\small} $, we refer to~\cite{Toft_PPLinearProgramming_2009}. The security of the protocols~$ \ensuremath{\small{\textsc{IP-Update}}\small} $ and $ \ensuremath{\small{\textsc{IP-Branch}}\small} $ is trivial to prove as they only operate on secret values and use secure primitives.
Note that for the simulator of $ \ensuremath{\small{\textsc{Simplex}}\small} $ it has to be assumed that he knows the number of iterations that Simplex requires.
For the computation of the value $ \enc{t} $, which determines whether the current subproblem is pruned or not, the simulator then requires knowledge of the tree structure $ \ensuremath{\mathcal{B}} $. However, recall that the tree structure is part of the output of the ideal functionality~$ \ensuremath{\ensuremath{\pazocal{F}}_{\small{\textsc{Kep-IP}}}} $. Hence, the simulator can also infer the tree structure and thus knows in which iterations $ t = 0 $ and in which $ t = 1 $. Based on this knowledge, he can simulate the value $ \simval{\enc{t}} $ (Line~9, Protocol~\ref{prot:branch_and_bound}) such that the reconstruction of $ \enc{t} $ yields the correct result. Thereby, he can also determine which subproblems are added to the list $ L $ and which problems are chosen in which iteration. Finally, the simulator only has to set the output $ \simval{\enc{\ensuremath{X^*}}} $ to the known share of the output $ \enc{\ensuremath{X^*}} $.
\customParagraph{Complexity.}
The complexity of protocol~$ \ensuremath{\small{\textsc{Branch-and-Bound}}} $ is dominated by the call to the protocol~$ \ensuremath{\small{\textsc{Simplex}}\small} $ for each subproblem. According to~\cite{Toft_PPLinearProgramming_2009}, one Simplex iteration requires $ \bigo{\ensuremath{m} \cdot (\ensuremath{m} + \ensuremath{n})} $ multiplications and $ \bigo{\ensuremath{m} + \ensuremath{n}} $ comparisons, where $ m $ is the number of constraints and $ n $ the number of variables of the LP. The round complexity of one iteration is $ \bigo{\log\log(\ensuremath{m})} $. Our protocols $ \ensuremath{\small{\textsc{IP-Update}}\small} $ and $ \ensuremath{\small{\textsc{IP-Branch}}\small} $ have constant round complexity, and communication complexity $ \bigo{\ensuremath{n} \cdot \ensuremath{s}} $ and $ \bigo{\ensuremath{m} \cdot \ensuremath{n}} $, respectively. Thus, protocol~$ \ensuremath{\small{\textsc{Branch-and-Bound}}} $ has communication complexity $ \bigo{\ensuremath{\mathcal{I}} \cdot (\ensuremath{m}^2 + \ensuremath{m} \ensuremath{n} + \ensuremath{m} \ensuremath{s} + \ensuremath{n} \ensuremath{s})} $ and round complexity $ \bigo{\ensuremath{\mathcal{I}} \cdot \log\log(\ensuremath{m})} $, where $ \ensuremath{\mathcal{I}} $ is the overall number of Simplex iterations required for an execution of protocol~$ \ensuremath{\small{\textsc{Branch-and-Bound}}} $. Note that the number of Simplex iterations is $ 2^\ensuremath{n} $ in the worst case~\cite{Schrijver_LinearProgramming_1998}. Furthermore, $ m = \ensuremath{\iota} $ and $ n = \vert \ensuremath{\mathcal{\singleSubset}} \vert + \ensuremath{\iota} $ for the subset formulation.
\subsection{Privacy-Preserving Protocol for the KEP}\label{sub:kep_protocol}
\begin{protocol}[t]
\caption{$ \ensuremath{\small{\textsc{Kep-IP}}} $}
\label{prot:kep_ip}
\input{./protocols/kep_ip.tex}
\end{protocol}
Protocol~\ref{prot:kep_ip} contains the specification of our novel privacy-preserving protocol~$ \ensuremath{\small{\textsc{Kep-IP}}} $ that computes the optimal set of exchange cycles for a given set of patient-donor pairs using our protocol~$ \ensuremath{\small{\textsc{Branch-and-Bound}}} $ (Protocol~\ref{prot:branch_and_bound}). Previous to the actual protocol execution each pair $ \partysymbol{i} $ ($ i \in \ensuremath{\mathcal{P}} $) secretly shares the relevant medical data of its patient and its donor (as defined in Functionality $ \ensuremath{\ensuremath{\pazocal{F}}_{\small{\textsc{Kep-IP}}}} $) among the computing peers. After the protocol execution, the computing peers send the shares of the computed exchange partners (indicated by $ \ensuremath{D}(i) $ and $ \ensuremath{R}(i) $) to each patient-donor pair $ \partysymbol{i} $ ($ i \in \ensuremath{\mathcal{P}} $).
\customParagraph{Graph Initialization Phase.} At the start of the protocol, the adjacency matrix $ \enc{\ensuremath{M}} $ is computed such that entry $ \enc{\ensuremath{M}}(i,j) $ encodes the medical compatibility between the donor of patient-donor pair~$ \partysymbol{i} $ and the patient of pair $ \partysymbol{j} $. To this end, we use the protocol~$ \ensuremath{\small{\textsc{Comp-Check}}} $ from~\cite{Breuer_KEprotocol_2020} which considers the donor of pair~$ \partysymbol{i} $ as compatible with the patient of pair~$ \partysymbol{j} $ if $ \donorbloodvec{i}(k) = \patientbloodvec{j}(k) = 1 $ for at least one $ k \in \{1, ..., \vert \ensuremath{B^{d}} \vert \} $ and if for all $ k \in \{1, ..., \vert \ensuremath{A^{p}} \vert \} $ with $ \antigenvec{i}(k) = 1 $ it holds that $ \antibodyvec{j}(k) \neq 1 $.
Note that even if this compatibility check indicates that two pairs are compatible, the final choice of whether a transplant is carried out lies with medical experts.
To guarantee that the structure of the Branch-and-Bound tree~$ \ensuremath{\mathcal{B}} $ and the number of Simplex iterations~$ \ensuremath{\mathcal{I}} $ do not reveal any information on the compatibility between the patient-donor pairs or on their medical data, the adjacency matrix is shuffled at random before computing the exchange cycles. This makes it impossible to link any entry in the tableaux used in the Branch-and-Bound protocol to a particular patient-donor pair. It also ensures unbiasedness in the sense that two pairs with the same input have the same chance of being part of the computed solution (independent of their index). We reuse the protocol $ \ensuremath{\small{\textsc{Shuffle}}} $ from~\cite{Breuer_Matching_2022} for the shuffling of~$ \enc{\ensuremath{M}} $.
\customParagraph{Setup Phase.} In the next step, the computed adjacency matrix is used to set up the initial tableau for the subset formulation of the KEP (cf.\ Equation~\ref{eq:subset_formulation}). To this end, we call the protocol~$ \ensuremath{\small{\textsc{IP-Setup}}\small} $ on the shuffled adjacency matrix~$ \enc{\ensuremath{M}} $. Again note that by using the shuffled adjacency matrix, we hide the relation between the rows in the tableau and the indices of the patient-donor pairs. In addition to the secret initial tableau $ \enc{\ensuremath{T}} $, the protocol~$ \ensuremath{\small{\textsc{IP-Setup}}\small} $ returns the matrix $ \enc{\ensuremath{\mathcal{M}}} $ mapping each subset $ \ensuremath{S}_i \in \ensuremath{\mathcal{\singleSubset}} $ to an exchange cycle (cf. Section~\ref{sub:tableau_setup}).
\customParagraph{Optimization Phase.} Now we can just call our protocol $ \ensuremath{\small{\textsc{Branch-and-Bound}}} $ on the tableau $ \enc{\ensuremath{T}} $ using the number of patient-donor pairs $ \ensuremath{\iota} $ as upper bound $ \ensuremath{\overline{b}} $. This yields the solution $ \enc{\ensuremath{X^*}} $ with $ \enc{\ensuremath{X^*}}(i) = 1 $ iff the optimal set of exchange cycles contains a cycle with vertex set $ \ensuremath{S}_i $ and $ \enc{\ensuremath{X^*}}(i) = 0 $, otherwise.
\customParagraph{Resolution Phase} Based on the chosen subsets indicated by $ \enc{\ensuremath{X^*}} $, we determine the particular cycles that comprise the optimal solution. To this end, we convert $ \enc{\ensuremath{X^*}} $ into the matrix $ \enc{Y} \in \{0, 1\}^{\ensuremath{\iota} \times \ensuremath{\iota}} $ such that $ Y(i, j) = 1 $ iff cycle $ \ensuremath{C}_{i, j} $ is part of the optimal set of exchange cycles (i.e., iff $ \ensuremath{X^*}(i) = 1 $ and $\ensuremath{\mathcal{M}}(i, j)=1$). Then, we construct the solution matrix $ \ensuremath{A} \in \{0, 1\}^{\ensuremath{\iota} \times \ensuremath{\iota}} $ where $ \enc{\ensuremath{A}}(v, w) $ indicates whether the edge~$ (v, w) $ is part of the computed set of exchange cycles. In particular, we compute $ \enc{\ensuremath{A}}(v, w) $ as the sum over those entries $ \enc{Y}(i, j) $ that correspond to cycles $ C_{i, j} $ where $ (v, w) \in E(\ensuremath{C}_{i. j}) $.
\customParagraph{Output Derivation Phase.}
In the last phase, we map the solution matrix to each patient-donor pair's exchange partners. First, the initial shuffling of the pairs is reverted by calling the protocol $ \ensuremath{\small{\textsc{Reverse-Shuffle}}} $ on the solution matrix. As by definition of the KEP each pair can only be involved in at most one exchange cycle, we know that each row and each column of the solution matrix can only contain at most one entry which is equal to $ 1 $. Therefore, we can just add up all entries of row $ i $ multiplied with their column index $ j $ to obtain the index of the pair $ \partysymbol{j} $ whose donor donates to the patient of pair $ \partysymbol{i} $. In a similar fashion we obtain the index of the recipient for the donor of pair $ \partysymbol{i} $ summing up the entries of the $ i $-th column multiplied by their row index~$ j $.
\customParagraph{Security.}
The simulator can compute the adjacency matrix $ \ensuremath{M} $ by calling the simulator of $ \ensuremath{\small{\textsc{Comp-Check}}} $ on the corresponding inputs of the patient-donor pairs, simulating the output using a random share. Similarly, he can simulate the calls to the protocols $ \ensuremath{\small{\textsc{Shuffle}}} $, $ \ensuremath{\small{\textsc{IP-Setup}}\small} $, $ \ensuremath{\small{\textsc{Branch-and-Bound}}} $, and $ \ensuremath{\small{\textsc{Reverse-Shuffle}}} $. Recall that the simulation of the protocol~$ \ensuremath{\small{\textsc{Branch-and-Bound}}} $ requires knowledge of the structure of the Branch-and bound tree~$ \ensuremath{\mathcal{B}} $ and the number of Simplex iterations~$ \ensuremath{\mathcal{I}} $. However, since this information is part of the output of the ideal functionality~$ \ensuremath{\ensuremath{\pazocal{F}}_{\small{\textsc{Kep-IP}}}} $, it is available to the simulator. The initialization of the matrix $ A $ can then again be simulated using random shares. Afterwards, the simulator can compute the values for $ \simval{\enc{Y}} $ and $ \simval{\enc{A}} $ as specified in the protocol based on the previously simulated values $ \simval{\enc{\ensuremath{X^*}}} $, $ \simval{\enc{\ensuremath{\mathcal{M}}}} $, and $ \simval{\enc{A}} $. Finally, the simulator just has to set the values of the output vectors $ \simval{\enc{\ensuremath{D}}} $ and $ \simval{\enc{\ensuremath{R}}} $ to the known shares of the protocol output. Thus, protocol~$ \ensuremath{\small{\textsc{Kep-IP}}} $ securely implements functionality~$ \ensuremath{\ensuremath{\pazocal{F}}_{\small{\textsc{Kep-IP}}}} $.
\customParagraph{Complexity.}
Communication and round complexity of protocol~$ \ensuremath{\small{\textsc{Kep-IP}}} $ are dominated by the call to the protocol~$ \ensuremath{\small{\textsc{Branch-and-Bound}}} $, i.e., protocol~$ \ensuremath{\small{\textsc{Kep-IP}}} $ has the same complexities as protocol~$ \ensuremath{\small{\textsc{Branch-and-Bound}}} $.
\section{Related Work}
In this section, we review relevant related work including SMPC protocols for kidney exchange (Section~\ref{sub:rw_pp_ke}) and LP (Section~\ref{sub:rw_pp_lp}) as well as privacy-preserving approaches for distributed constraint optimization~(Section~\ref{rw:pp_dcop}).
\subsection{Privacy-Preserving Kidney Exchange}\label{sub:rw_pp_ke}
The first SMPC protocol for solving the KEP was developed by Breuer et al.~\cite{Breuer_KEprotocol_2020} based on homomorphic encryption, which was improved upon in~\cite{Breuer_Matching_2022} with a more efficient implementation based on secret sharing. This protocol uses a pre-computed set of all possible constellations of exchange cycles that can exist between a set of patient-donor pairs. For each of these constellations it then determines whether the contained cycles also exist in the compatibility graph induced by the input of the patient-donor pairs. Finally, the protocol chooses one of those sets that maximize the number of patients that can receive a transplant uniformly at random.
The runtime of the protocol increases quickly for an increasing number of patient-donor pairs due to the brute force nature of the approach. In contrast, our protocol $ \ensuremath{\small{\textsc{Kep-IP}}} $ (Section~\ref{sec:protocol}), uses IP as the underlying technique which leads to a significantly better performance.
In a second line of work, Breuer et al.~\cite{Breuer_Matching_2022} present a dedicated protocol for crossover exchange (i.e., exchange cycles of size $ 2 $) that computes a maximum matching on general graphs. In contrast, our protocol~$ \ensuremath{\small{\textsc{Kep-IP}}} $ allows for the specification of an arbitrary upper bound $ \ensuremath{l} $ on the maximum cycle size.
In comparison to~\cite{Breuer_KEprotocol_2020,Breuer_Matching_2022}, the output of the ideal functionality that is implemented by our protocol~$ \ensuremath{\small{\textsc{Kep-IP}}} $ includes not only a set of exchange cycles that maximizes the number of possible transplants but also the structure of the Branch-and-Bound tree and the number of Simplex iterations necessary to solve each subproblem in the tree.
Recently, Birka et al.~\cite{Birka_PPKidneyExchange_2022} present another SMPC protocol in the greater context of kidney exchange. In contrast to the protocols by Breuer et al.~\cite{Breuer_KEprotocol_2020,Breuer_Matching_2022} as well as the newly-developed protocol in this paper, the protocol introduced in~\cite{Birka_PPKidneyExchange_2022} does not solve the KEP.
Instead, their protocol implements an ideal functionality that outputs some set of possible exchanges for a single fixed cycle size~$ \ensuremath{l} $ as well as the number of cycles that exist in the otherwise private compatibility graph.
This set is only an approximation to a solution of the KEP since it neither maximizes the number of exchange cycles for the fixed~$ \ensuremath{l} $ nor does it consider all possible cycle sizes up to~$ \ensuremath{l} $. While~\cite{Birka_PPKidneyExchange_2022} exhibits a superior runtime performance compared to the protocols in \cite{Breuer_Matching_2022} and~\cite{Breuer_KEprotocol_2020}, it fails to analyze the quality of the approximation. This is highly problematic for the use case of kidney exchange where any possible exchange that is not found may have severe ramifications for the respective patient-donor pairs.
\subsection{Privacy-Preserving Linear Programming}\label{sub:rw_pp_lp}
In privacy-preserving LP, there are transformation-based approaches where constraint matrix and objective function are hidden using a monomial matrix (e.g.,~\cite{Dreier_PPLinearProgramming_2011,Vaidya_PPLinearProgramming_2009}) and SMPC-based approaches where the whole LP solver is implemented as an SMPC protocol~\cite{Catrina_PPLinearProgramming_2010,Li_PPLinearProgramming,Toft_PPLinearProgramming_2009}. As the transformation-based approaches cannot guarantee security in the cryptographic sense that we require for our use case, we do not further discuss them and focus on SMPC-based approaches.
To the best of our knowledge, the only LP solver for which there are privacy-preserving implementations is the Simplex algorithm.
Li and Atallah~\cite{Li_PPLinearProgramming} propose a two-party protocol for a version of Simplex without divisions. However, in their protocol a single Simplex iteration can double the bitsize of the values in the tableau making their protocol only feasible for problems where the required number of Simplex iterations is small. Toft~\cite{Toft_PPLinearProgramming_2009} devises an SMPC protocol for Simplex based on secret sharing which uses integer pivoting to make sure that the protocol can be run using secure integer arithmetic. Finally, Catrina and de Hoogh~\cite{Catrina_PPLinearProgramming_2010} propose a more efficient protocol for Simplex relying on secure fixed-point arithmetic.
For our protocol for Branch-and-Bound (Section~\ref{sub:pp_branch_and_bound}), we require a privacy-preserving protocol for Simplex that uses integer arithmetic. Therefore, we use the approach by Toft~\cite{Toft_PPLinearProgramming_2009}. However, any SMPC protocol for Simplex that uses integer arithmetic can be used in our protocol.
\subsection{Privacy-Preserving Distributed Constraint Optimization}\label{rw:pp_dcop}
A related field to IP is Distributed Constraint Optimization (DCOP) where the goal is to find an assignment from a set of variables (each held by a different agent) to a set of values such that a set of constraints is satisfied. There are some privacy-preserving approaches to DCOP which use an adaptation of the Branch-and-Bound algorithm (e.g.,~\cite{Grishpoun_PPDCOP_2016,Tassa_PPDCOP_2021}). However, these approaches cannot be applied to our problem, as DCOP is different from the KEP in that each agent holds a variable and knows its value whereas in the KEP the values of the variables in the IP have to remain secret to all patient-donor pairs as they indicate which exchange cycles are chosen.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,587 |
using System;
using System.Collections.Generic;
using Frapid.Account.DataAccess;
using Frapid.Account.Entities;
namespace Frapid.Account.Api.Fakes
{
public class CanRegisterWithFacebookRepository : ICanRegisterWithFacebookRepository
{
public bool Execute()
{
return new bool();
}
}
} | {
"redpajama_set_name": "RedPajamaGithub"
} | 794 |
\section{Rationale}
Since in 2013 Kittur et al. \cite{kittur2013future} envisioned the future of crowdsourcing, technological advancements made crowdsourcing more efficient, cost-effective and streamlined. Yet, they lag in terms of humanizing the work outside of citizen science projects and efforts driven by volunteers and communities of practice or platforms catering to professional workers. Crowdsourcing platforms offering paid microtask crowd-work place little value in expendable workers, who in turn, may provide poor quality contributions, as the tasks are boring and repetitive \cite{brewerwouldCHI2016}, but the more they do, the better the pay. But even citizen science efforts could up their game to motivate and retain more groups of contributors driven by diverse intrinsic and extrinsic motivations.
Thus, crowdsourcing systems are riddled with shortcomings which inhibit participation for all, but especially for older adults. These barriers, related e.g. to motivation, communication and accessible platform, project and task design are summarized in Fig \ref{barriers} \cite{brewerwouldCHI2016,kobayashimulti2015,crowdolder2020chi,nielek2017,onlinecommunitiesolder2014,volunteerbasedonlinestudies,skorupska2018smarttv,skorupska2020chatbot,sustainablechi2020,kopecspiral2018,mhealtholder2018,accessiblecrowd2015}.
\begin{figure*}
\includegraphics[width=\linewidth]{images/dropoutpoints.PNG}
\caption{A diagram showing the user story on crowdsourcing platforms with indicated possible points of failure based on barriers shown in Fig \ref{barriers}. Potential support elements shown with pink borders.} \label{mapexpe}
\end{figure*}
As the share of older adults, here understood as people aged 65+, especially in western societies, is increasing it more and more important to design remote and scalable ICT-based activities, such as crowdsourcing, that provide them with cognitive challenges, enable positive interaction and active ageing \cite{skorupska2018smarttv,opensourceolder2014,sustainablechi2020,AmorimMotivation2019BrazilOldCrowd,olderadultssocial2020}. Crowdsourcing projects, on the other hand can benefit from the massive, and largely untapped, potential of older adults' collective intelligence, experience and time \cite{skorupska2018smarttv,knowles2020Conflating,olderadultssocial2020}. Especially that they have proven to be dedicated, diligent and successful contributors \cite{kobayashimulti2015,crowdolder2020chi,skorupska2018smarttv,olderadultssocial2020,zooni2021Interact} who are held back not only by inaccessible task-driven project design, which is incompatible with their prevailing motivations \cite{kittur2013future} and possible age-related cognitive decline in the processing speed and working memory \cite{murman_impact_2015} and the idea of worker expendability \cite{brewerwouldCHI2016,opensourceolder2014,nielek2017,volunteerbasedonlinestudies} but also a lack of support mechanisms \cite{opensourceolder2014,skorupska2018smarttv}, which all result in preventable dropouts, as shown in Fig \ref{mapexpe}.
Therefore, based on our experience with using, designing and developing crowdsourcing platforms, and a keyword-driven literature review done in a form of a mind-map, which allowed us to cluster relevant findings, in this article we envision the way forward to create more engaging, accessible and inclusive experience of crowdwork, encouraging contributions from underrepresented populations \cite{toeppe_conducting_2021,skorupska2020chatbot}. Designing crowdsourcing experiences with older adults in mind, due to the curb-cut effect\footnote{The existence of the curb-cut effect has long been documented in the digital space \cite{hessecurbcut1995} and it differs from universal design, as it first focuses on specific populations who could benefit most from a unique approach.}, will not only improve the experience for them, but also for the general population. To further this goal first we analysed the key barriers to crowdsourcing for older adults, as shown in Fig \ref{barriers} and mapped them over the generalized crowd work user story depicted in Fig \ref{mapexpe} to mark dropout points. Finally, we took Kittur et al.'s proposed framework \cite{kittur2013future} as the starting point for the construction of an actionable framework addressing these dropout hot-spots. Challenges are many, as visible in Fig \ref{barriers}, both related to the accessibility and the required ICT-proficiency \cite{skorupska2018smarttv} and to communication of projects, tasks and their importance. \cite{volunteerbasedonlinestudies,brewerwouldCHI2016} Crowdsourcing systems designed to encourage older adults' contributions ought to not only mitigate barriers but also highlight older adults strong suits: their lifelong experience, skills and patience\cite{skorupska2018smarttv}. They should meet their preferences regarding the experience of contributing, including their individual aspirations.\cite{crowdolder2020chi}
The analysis and elements of the proposed framework are based on our experience with the design of crowdsourcing systems encouraging older adults' contributions in exploratory studies \cite{skorupska2018smarttv,skorupska2019smartTV,skorupska2020chatbot,kopec2017living}, related work, as well as research at the intersection of older adults' use of ICT \cite{orzeszek2017design,balcerzak2017F1,kopecspiral2018} and crowdsourcing \cite{nielek2017wikipedia,nielekcrowdclas2016}. Our resulting framework aims to serve as an actionable reference for designing more sustainable and motivating crowdsourcing experiences that better engage older adults to boost the rates of their participation and help them reap the benefits and protective factors that come from online volunteering, lifelong learning, and staying active longer.
\begin{figure*}
\includegraphics[width=\linewidth]{images/lemframeworkbarreirs.PNG}
\caption{Crowdsourcing framework updated with elements important for older adults' engagement - elements in violet are changed, while in pink added in relation to the framework by Kittur et al. \cite{kittur2013future}. Moreover, the barriers addressed by each element are referred to by the first letters of titles of rows and columns in Fig. \ref{barriers}, so e.g. SM stands for System Motivation.} \label{fig1}
\end{figure*}
\section{Proposed Framework}
What follows is the description of the proposed actionable framework addressing the analysed (Fig. \ref{barriers}) and mapped (Fig. \ref{mapexpe}) barriers. The discussion of framework elements is supported by examples from related research and practice. Special consideration is given to the elements important for designing experiences for older adults.
\subsection{Platform}
When starting a crowdsourcing project the choice of the \textbf{platform (1)} is the project-defining moment, as some of the features described in the framework may not be present in the platform and will need to be supplemented outside of the crowdsourcing system. This is a common problem with the \textbf{feedback (6)} and \textbf{training (5)} module, as well as \textbf{impact (7)} measures and follow-up information on the performance and importance of completed tasks, and quite a challenge, when it comes to \textbf{user empowerment (8)} -- a necessary step when working with older adults using technology \cite{kopecspiral2018,orzeszek2017design}. The \textbf{platform (1)} may also be custom-built, and there was some success with crowdsourcing platforms designed with older adults in mind, especially with co-design \cite{kopecspiral2018,knowles2020Conflating}, which accounted for such aspects as familiarity with the interfaces \cite{Pan2016TheRO}, to help bridge the digital divide, and cater to the characteristic motivation and strengths of older adults \cite{skorupska2018smarttv,crowdolder2020chi}. The importance of this point is clearly visible when evaluating platforms and experiences which were created incrementally and their technical and procedure-driven complexity increased overtime, such as Wikipedia \cite{nielek2017wikipedia}. In the end this complexity constitutes another barrier contributing to the inequality of contributions in terms of less ICT-privileged or experienced user groups which then are underrepresented \cite{skorupska2020chatbot}.
Even platform-specific communication makes a big difference. For example, Amazon Mechanical Turk's worker-facing communication focuses on communicating benefits to businesses, calling itself a "crowdsourcing marketplace". On the other hand, the Prolific platform caters to both requesters and participants (contributors) equally and acknowledges the diverse motivations of the crowd with a call to action: "Take part in engaging research, earn cash, and help improve human knowledge" \footnote {Quote and data retrieved on 12.04.2021 from two platforms, commonly used for conducting research: https://www.mturk.com/ and https://www.prolific.co/}. On the other hand, accessibility still plays a role with crowdsourcing platforms active on the market now, small fonts, cryptic pictograms, unfamiliar interfaces and complex procedures make many crowdsourcing platforms inaccessible by default to many groups of users \cite{nielek2017,opensourceolder2014}. This problem, however, is not limited to crowdsourcing platforms or tasks and persists even in applications marketed at older adults \cite{mhealtholder2018}. To alleviate this problem crowdsourcing in a non-computer scenario may bring good results, such as with a remote on a TV screen \cite{skorupska2018smarttv}, making use of familiar modes of interaction, as visible in Fig \ref{fig2} or via a voice interface \cite{skorupska2020chatbot,crowdtasker2020CHI}.
\begin{figure*}
\includegraphics[width=\linewidth]{images/dreamtvstretch.png}
\caption{Screenshots from a crowdsourcing system designed for older adults and based on the idea of familiar interaction. It also allowed for pausing, viewing the context and free navigating through the task. Source: https://github.com/manununhez/dreamtv-app.} \label{fig2}
\end{figure*}
\subsection{Tasks}
The input of the crowdsourcing project should be prepared so that it may be divided into microtasks. However, based on previous research such tasks are often too far removed to understand their purpose \cite{brewerwouldCHI2016} and too short to be meaningful \cite{kittur2013future}. On the other hand, easily relatable tasks, such as tagging historical photos \cite{yu2016productive} or proofreading texts \cite{kobayashiproofreading2013}, are quite encouraging for older adults. Therefore, \textbf{task decomposition (2)} step should strive to produce recognizable work units that the contributors can engage with and become immersed, but can be paused if needed, even for a longer period of time \cite{accessiblecrowd2015} -- perhaps self-specified by the contributor within a pre-set limit, so that users can take a break if they are tired \cite{skorupska2018smarttv} or feel sick \cite{accessiblecrowd2015} and have an overview of the broader context of their work upon return, so that they may again find their footing easily as shown in Fig \ref{fig1} \cite{skorupska2018smarttv}.
These \textbf{mezzo-tasks} should be between microtasks and macrotasks, short enough to complete in a self-defined session length of about 15-30 minutes, but long enough to offer a skill or a piece of knowledge that is valuable to the contributors. Especially older adults are often driven by intrinsic motivation of wanting to learn something interesting \cite{kittur2013future,zooni2021Interact}. For this reason \textbf{task evaluation (3)} is important, so that tasks can be categorized by the skills they utilize, the interest they belong to as well as the level of challenge they pose. Matching the interest, preferred skills and challenge level to the profile of the contributor is necessary for them to stay engaged and to support their development \cite{ordinarychiaging2018}. \textbf{Select task recommendations (4)} ought to be suggested to the contributors to choose from, so that they may exercise their autonomy \cite{skorupska2018smarttv,crowdolder2020chi} and pick work based on their interests, knowledge, skills and energy levels that may change over time \cite{sustainablechi2020}. Very commonly tasks get abandoned \cite{hanabandonment2019} which results in effort and time being wasted, but also in discouragement of the contributors. Crowdsourcing platforms and projects get abandoned along with them. There are many reasons it can happen \cite{opensourceolder2014} including not receiving help, not finding an adequate project at all, or fast enough -- but it can happen at almost any stage of the user journey, as shown in Fig \ref{mapexpe}. This is why \textbf{user profiling (9)} and a shortlist with \textbf{select task recommendations (4)} are so important. Once a user rejects a recommendation an adaptive system could suggest another one, with an increasingly better fit to ensure that they are able to find a task, and successfully complete it -- increasing their well-being \cite{skorupska2020chatbot} and lowering dropout \cite{opensourceolder2014}.
\begin{figure*}
\includegraphics[width=\linewidth]{images/zooniversecall2.png}
\caption{Two example calls to action from Zooniverse.org, a citizen science platform -- both appealing to extrinsic motivation. Rephrasing them based on user-profiling, while still keeping true to the nature of the project, could bring better results.} \label{figzooni}
\end{figure*}
\subsection{Empowerment}
Older adults are often apprehensive towards technology and online services, especially if they had little prior contact with them \cite{kopecspiral2018}. In this context \textbf{user profiling (9)} ought to be preceded by \textbf{user empowerment (8)}, so that any self-stereotypes are caught before they affect the profiling. Held stereotypes may affect performance, beliefs about oneself as well as one's skills \cite{knowles2020Conflating}. To address this danger of self-stereotyping and pave way for increased engagement the users ought to learn about crowdsourcing, its purpose and see representative examples. The empowerment step is recommended in many ICT-contexts where older adults are expected to contribute \cite{kopecspiral2018}. They should also be encouraged to trust their own life-course skills, experience and abilities \cite{knowles2020Conflating} which benefit crowdsourcing projects, such as their high crystallized intelligence -- equal to or higher than this of younger adults. Because crystallized intelligence encompasses aspects such as knowledge, understanding vocabulary and concepts and reasoning older adults may be perfect partners for human-in-the-loop systems, which could do the bulk of the crowdsourcing work, with \textbf{quality assurance} left to older adults in areas of their greatest strengths (e.g. language skills, life-course experience, sense-making, individual professional mastery). So, empowerment ought to:
\begin{enumerate}
\item include ICT-empowerment by explaining the importance of crowdsourcing within the ICT practice,
\item incorporate psycho-education to make older adults aware of their strengths which may benefit such projects,
\item and at later stages involve \textbf{training (5)} to do the tasks better,
\item as well as incorporate \textbf{feedback (6)} into the contribution cycle,
\item allow to choose the type of contribution based on individual preferences, \cite{sustainablechi2020}
\item and finally, inform the users of the \textbf{impact (7)} of their contribution, to showcase its societal importance \cite{brewerwouldCHI2016}.
\end{enumerate}
\subsection{Training}
The aspect of \textbf{training (5)} and receiving \textbf{feedback (6)} is important to increase contributors' confidence and skills. Older adults may feel apprehensive of unfamiliar interfaces and new technologies so a sandbox mode, where they can practice without the fear of breaking anything is a requested feature \cite{skorupska2018smarttv}. Another need is related to staying mentally active through challenging oneself \cite{skorupska2018smarttv}, while doing something of societal importance \cite{brewerwouldCHI2016} and learning new things can be such challenge. So, \textbf{task evaluation (3)} should incorporate such tags as "knowledge gained" and "skills practiced" on ladder of different challenge levels, so that users may gain skills to become even better contributors and gain new roles \cite{sustainablechi2020}. The platform ought to also support efforts such as community tutorial generation, either by providing a place to gather collective task insights \cite{microtaskingskillframework} or fostering in-platform communication between users regarding specific tasks, or specific task parts \cite{opensourceolder2014}, but in a positive learning environment, as not to discourage contributors \cite{Halfakerwikidis2013}. Feedback and task performance should stay visible on the contributors' profile for their later reference \cite{volunteerbasedonlinestudies}. The ability to grow one's skill through participation and self-correction is also important, as advancement path and the ability to choose one's role within the project may facilitate sustainable engagement \cite{sustainablechi2020}. Moreover, to increase engagement going beyond online space may be of value, especially to older adults who are isolated and may prefer face-to-face communication \cite{onlinecommunitiesolder2014,crowdolder2020chi}. Such offline supplementary activities can involve training, tutorial writing or content-creation marathons.
\subsection{Profiling and Motivation}
Older adults are a very heterogeneous group which spans decades of life \cite{knowles2020Conflating} during which even successful aging may take very diverse forms in different people. As individual differences are prominent \textbf{user profiling (9)} has to catch diverse users' motivations, aspirations as well as abilities, skills and interests, to enable the system to adapt to its users. Profiling enables to \textbf{select task recommendations (4)} that would be appropriate for each individual, to still grant them freedom to choose their tasks, without causing overload. As small monetary rewards do not sufficiently motivate older adults \cite{crowdolder2020chi,brewerwouldCHI2016} focusing communication on other extrinsic and intrinsic motivators is important. Especially intrinsic motivation plays a greater role for older adults \cite{kittur2013future} so it is necessary to clearly establish aspirations, which especially in western societies most affected by the changing demographic situation, may include the need for entertainment, engaging with their interests or learning new things, and sometimes even staying mentally active to prevent cognitive decline \cite{skorupska2018smarttv,opensourceolder2014,crowdolder2020chi}. Extrinsic motivation, such as the value and usefulness of the task also plays a role, especially if a specific beneficiary is clearly communicated \cite{crowdolder2020chi}. So, the \textbf{impact (7)} that the project has in the real world, including the users' contribution should be made evident \cite{skorupska2020chatbot}. Also, as the energy levels, knowledge, skills, abilities and interests may change over time due to i.e. learning, or natural aging processes \cite{sustainablechi2020} the system should reassess the profile based on task performance, choices and engagement patterns \cite{skorupska2020chatbot}, or even adapt to users' moods and emotions \cite{Shen2017EfficientSI}.
\subsection{Discovery and Communication}
Finally, older adults in general are not familiar with crowdsoucing \cite{brewerwouldCHI2016}, even if they have good ICT skills \cite{zooni2021Interact}. Here, \textbf{promotion (10)} of the crowdsourcing project is necessary in places that older adults already visit online, on platforms they are familiar with. A technology skill and familiarity barrier also exist, but other research suggests that older adults often teach each other tech skills \cite{kowalski2019CHI} if they find them useful and engaging, so it may be enough to promote the project among a group of early adapters, who then take it further. Possibly, they could also recruit each other, as they know the places they frequent best \cite{volunteerbasedonlinestudies}. In communication, it is good to underline such aspects as fun, entertainment or edutainment \cite{skorupska2018smarttv} and the fact that engaging in such activities may support "the increase of self-esteem and social engagement" \cite{AmorimMotivation2019BrazilOldCrowd} along with other benefits of active ageing and project-specific skill and interest highlights.
In general, communication efforts throughout the crowdsourcing platform ought to focus on the evident benefits for older adults themselves and then the society, or, better, a well-specified group within this society, such as children \cite{crowdolder2020chi} or planetary researchers as visible in the message in Figure \ref{figzooni}. Project communication should also be easy, open and two-way, as contributors quite often ask questions about the goals of a project, even in places not designed for this purpose, i.e. comment boxes \cite{volunteerbasedonlinestudies}. Transparent communication is very important \cite{brewerwouldCHI2016} and it should clearly uncover all study and work goals \cite{volunteerbasedonlinestudies} and cover as much context of the work as possible, as limiting information on the project can negatively impact motivation \cite{kobayashimulti2015}. In addition to communication related to recruitment and ongoing issues, such as current projects and open tasks, post-contribution communication is crucial, as older adults especially need to have a proof that their time was purposeful, meaningful and well-spent \cite{olderadultsstrengths2019fomo}.
\section{Conclusions}
\begin{figure*}
\includegraphics[width=\linewidth]{images/fullframework.PNG}
\caption{A summary of key assumptions of the framework discussed in Section 2.} \label{fullframe}
\end{figure*}
A crowdsourcing project aiming to be successful among older adults ought to be \textbf{well-promoted (10)}, discoverable, available on an accessible \textbf{platform (1)}, consisting of pausable, longer \textbf{self-contained mezzo-tasks (2)}, that are \textbf{evaluated and tagged (3)} based on the interest, skills involved, length and challenge levels. The users should be able to \textbf{select task recommendations (4)} provided based on \textbf{user profiling (9)} done after an \textbf{empowerment (8)} step that levels the playing field for contributors. The users should receive help in the form of tutorials, including \textbf{training (5)} in a sandbox mode. After completing a task, the users should get \textbf{feedback (6)} either from experienced users based on \textbf{quality assurance} or from automated systems, and a chance to \textbf{train (5)} the skills involved as well as information about the \textbf{impact (7)} of their contribution to fulfill both their need to learn, get better and progress in the ranks (intrinsic motivation) and contribute to Social Good (extrinsic motivation) as well as strengthen their motivation to continue contributing. The elements of the framework are summarized in Fig \ref{fullframe} together with key recommended functionalities.
Our hope is that this framework will be used as guidance for other researchers and practitioners delving into the area of creating crowdsourcing systems and experiences for older adults. Moreover, based on the future emerging studies we hope to develop the framework into a more comprehensive guide, towards better inclusion of older adults in ICT-mediated activities.
One limitation of the current crowdsourcing-focused framework is that there are no systems which incorporate all of the elements proposed -- but it is also the motivation behind writing this paper. These proposed elements mitigate the analysed (Fig. \ref{barriers}) and mapped (Fig. \ref{mapexpe}) barriers making crowdsourcing more attractive to some groups of older adults, and due to the curb-cut effect, also to other groups of potential users. Therefore, they should be incorporated into crowdsourcing systems to cater not only to current devoted contributors or task requesters, but also the fringe of the user base -- older adults who soon will be joining the ranks of contributors in greater numbers.
\\
\textit{This research was partially supported by grants 2018/29/B/HS6/02604 and 2019/35/J/HS6/03166 from the National Science Centre of Poland.}
\bibliographystyle{ACM-Reference-Format}
\balance
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"redpajama_set_name": "RedPajamaArXiv"
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\section{Introduction}
\paragraph{Presentation of the models}
This paper is concerned with the large time behaviour and propagation phenomena
for reaction-diffusion equations with a line of fast diffusion. Our model will degenerate, when a small parameter tends to 0,
to a singular limit. The results that we will present will be uniform with respect to this small parameter.
The model under study (\ref{RPeps}) was introduced in 2014 by the author in \cite{Pauthier}.
\begin{equation}
\label{RPeps}
\begin{cases}
\partial_t u-D \partial_{xx} u = -\overline{\mu} u+\int \nu_\varepsilon(y)v(t,x,y)dy & x \in \mathbb{R},\ t>0 \\
\partial_t v-d\Delta v = f(v) +\mu_\varepsilon(y)u(t,x)-\nu_\varepsilon(y)v(t,x,y) & (x,y)\in \mathbb{R}^2,\ t>0.
\end{cases}
\end{equation}
A two-dimensional environment (the plane $\mathbb{R}^2$) includes a line (the line $\{(x,0), x\in\mathbb{R}\}$) in which
fast diffusion takes place while reproduction and usual diffusion only occur outside the line. For the sake of simplicity, we will refer
to the plane as ``the field`` and the line as ``the road``, as a reference to the biological situations.
The density of the population is designated by $v=v(t,x,y)$ in the field,
and $u=u(t,x)$ on the road. Exchanges of population between the road and field are defined by two nonnegative compactly supported functions
$\nu$ and $\mu.$ These functions will be called the \textit{exchange functions}. The density of individuals who jump from a
point of the field to the road is represented by $y\mapsto \nu_\varepsilon(y)$, from the road to a point of the field by
$y \mapsto \mu_\varepsilon(y),$ with the following scaling with $\varepsilon>0:$
$$
\nu_\varepsilon(y)= \frac{1}{\varepsilon}\nu\left(\frac{y}{\varepsilon}\right),\ \mu_\varepsilon(y)= \frac{1}{\varepsilon}\mu\left(\frac{y}{\varepsilon}\right).
$$
We use the notation $\overline{\mu}=\int \mu,$ $\overline{\nu}=\int\nu.$
It is easy to see that
$\nu_\varepsilon\to \overline{\nu}\delta$ and $\mu_\varepsilon\to\overline{\mu}\delta$ as $\varepsilon\to 0$ in the distribution sense, where $\delta=\delta_0$, the Dirac function in 0.
Hence, at least formally, the above system (\ref{RPeps}) tends to the following system (\ref{BRReq2})
where exchanges of population are localised on the road:
\begin{equation}
\label{BRReq2}
\begin{cases}
\partial_t u-D \partial_{xx} u= \overline{\nu} v(t,x,0)-\overline{\mu} u & x\in\mathbb{R},\ t>0\\
\partial_t v-d\Delta v=f(v) & (x,y)\in\mathbb{R}\times\mathbb{R}^*,\ t>0\\
v(t,x,0^+)=v(t,x,0^-), & x\in\mathbb{R},\ t>0 \\
-d\left\{ \partial_y v(t,x,0^+)-\partial_y v(t,x,0^-) \right\}=\overline{\mu} u(t,x)-\overline{\nu} v(t,x,0) & x\in\mathbb{R},\ t>0.
\end{cases}
\end{equation}
This model was introduced in 2013 in \cite{BRR1} by H. Berestycki, J.-M. Roquejffre and L. Rossi to describe
biological invasions in a plane when a strong diffusion takes place on a line.
Considering a nonnegative, compactly supported initial datum
$(u_0,v_0)\neq(0,0)$, the authors proved
the existence of an asymptotic speed of spreading $c^*_0$ in
the direction of the road for the system (\ref{BRReq2}) for a KPP-type nonlinearity.
They also explained the dependence of $c^*_0$ on $D,$ the coefficient of diffusion on the road.
The same kind of results was investigated in \cite{Pauthier} for our system (\ref{RPeps}) with fixed $\varepsilon,$
say $\varepsilon=1$ for instance. The main theorem was the following spreading result:
\begin{theorem}\label{spreadingthm}
We consider the nonlocal system (\ref{RPeps}) with a KPP-type nonlinearity and two nonnegative compactly supported exchange functions
$\nu$ and $\mu,$ with $\overline{\nu},\overline{\mu}>0.$
Let $(u_\varepsilon,v_\varepsilon)$ be a solution of (\ref{RPeps}) with a nonnegative, compactly supported initial datum $(u_0,v_0)$.
Then, for all $\varepsilon>0,$ there exists an asymptotic speed of spreading $c^*_\varepsilon$ and a unique positive bounded stationary solution of (\ref{RPeps})
$(U_\varepsilon,V_\varepsilon)$ such that,
pointwise in $y$, we have:
\begin{itemize}
\item for all $c>c^*_\varepsilon$, $\displaystyle\lim_{t\to\infty}\sup_{|x|\geq ct}(u(x,t),v(x,y,t)) = (0,0)$ ;
\item for all $c<c^*_\varepsilon$, $\displaystyle\lim_{t\to\infty}\inf_{|x|\leq ct}(u(x,t),v(x,y,t)) = (U_\varepsilon,V_\varepsilon)$.
\end{itemize}
\end{theorem}
This result is similar to the one showed in \cite{BRR1}, where
the steady state is given by $(U_0,V_0)=\left( \frac{\overline{\nu}}{\overline{\mu}},1\right).$
So, a natural question is: are the limits in Theorem \ref{spreadingthm} uniform in $\varepsilon$ ?
A first reasonable guess is that the spreading speed $c^*_\varepsilon$ tends to the spreading speed $c^*_0$
associated to the limit model (\ref{BRReq2}). This point will be developed in the second section of this paper.
The problem of the commutation of the two limits $\varepsilon\to0$ and $t\to+\infty$ in Theorem \ref{spreadingthm} is more intricate.
It is the main purpose of this paper. It involves both tools
from functional analysis concerning singular limits and reaction-diffusion methods about spreading phenomena.
\paragraph{Assumptions}
We always assume that the initial datum $u_0,v_0$ is nonnegative, continuous and compactly supported, with
$(u_0,v_0)\not\equiv(0,0).$ The reaction term $f$ satisfies:
\begin{equation}\label{kppassumtions}
f\in C^2([0,1]), \ f(0)=f(1)=0, \ \forall s\in (0,1),\ 0<f(s)\leq f'(0)s.
\end{equation}
Such a reaction term is, as usual, referred to as of KPP type (from the article of Kolmogorov, Petrovsky and Piskounov \cite{KPP}).
We extend it to a uniformly Lipschitz function outside $(0,1),$ satisfying
\begin{equation}\label{lipf}
\lim_{s\to +\infty} \frac{f(s)}{s}<-2\frac{\overline{\nu}^2}{d}.
\end{equation}
In particular, we suppose $2\frac{\overline{\nu}^2}{d}<\left\Vert f\right\Vert_{Lip}<+\infty.$ The assumption (\ref{lipf}) seems to be technical, but such a kind of uniform
coercivity appears to be crucial in order to get a uniform bound for the stationary solutions.
We make the following assumptions on the exchange functions.
\begin{itemize}
\item The exchange functions $\nu$ and $\mu$ are smooth, nonnegative and compactly supported. Without loss of generality we will assume
\begin{equation}\label{supportmunu}
\textrm{supp}(\mu,\nu)\subset(-1,1).
\end{equation}
\item For the sake of simplicity, we will take $\overline{\nu} = 1$, as in ~\cite{BRR1}.
\end{itemize}
The parameters $d,D,\overline{\mu},f'(0)$ and the two functions $\nu$ and $\mu$ are fixed once and for all.
\paragraph{Main results of the paper}
The main result of the paper is that spreading in the $x$-direction is indeed uniform in $\varepsilon.$
Set $c^*_0$ the asymptotic speed of spreading associated to the
initial model (\ref{BRReq2}).
\begin{theorem}\label{uniformspreading}
For $\varepsilon>0,$ let us denote $(u_\varepsilon,v_\varepsilon)$ the solution of system (\ref{RPeps}). There exists $m>0$ such that if $(u_0,v_0)\leq \left(\frac{m}{\overline{\mu}},m\right)$
we have:
\begin{itemize}
\item $\forall c>c^*_0,$ $\forall \eta>0,\ \exists T_0,\varepsilon_0$ such that
$\forall t>T_0,\forall \varepsilon<\varepsilon_0,$ $\displaystyle \sup_{|x|>ct} |u_\varepsilon(t,x)|<\eta.$
\item $\forall c<c^*_0,$ $\forall \eta>0,\ \exists T_0,\varepsilon_0$ such that
$\forall t>T_0,\forall \varepsilon<\varepsilon_0,$ $\displaystyle \sup_{|x|<ct} \left| u_\varepsilon(t,x)-\frac{1}{\overline{\mu}}\right|<\eta.$
\end{itemize}
\end{theorem}
The idea of the proof is to show that every solution $(u_\varepsilon,v_\varepsilon)$ is above some travelling subsolutions
in finite time. Then, we use the convergence of the spreading speed $c^*_\varepsilon$ to $c^*_0$, which yields travelling subsolutions
at some speed close to $c^*_0.$ Hence, our main tool relies on the following convergence theorem.
\begin{theorem}\label{convsol}
Let $(u,v)$ be the solution of the limit system (\ref{BRReq2})
and $(u_\varepsilon,v_\varepsilon)$ be the solution of the $\varepsilon$-system (\ref{RPeps}) for $\varepsilon>0.$ Let $(u_0,v_0)$ be a common initial datum for both systems. Then:
\begin{equation*}
\|(u-u_\varepsilon)(t)\|_{L^\infty(\mathbb{R})}+\|(v-v_\varepsilon)(t)\|_{L^\infty(\mathbb{R}^2)}\underset{\varepsilon\to0
}{\longrightarrow} 0.
\end{equation*}
The above convergence is uniform in every compact set in $t$ included in $(0,+\infty).$
\end{theorem}
Notice that the convergence is global in space, but local in time.
\paragraph{Bibliographical background}
Reaction-diffusion equations of the type
$$
\partial_t u-d\Delta u=f(u)
$$
have been introduced in the celebrated articles of Fisher ~\cite{fisher} and Kolmogorov, Petrovsky and Piskounov ~\cite{KPP} in 1937.
The initial motivation came from population genetics. The reaction term are that of a logistic law, whose
archetype is $f(u)=u(1-u)$ for the simplest example. In their works in one dimension,
Kolmogorov, Petrovsky and Piskounov revealed the existence of propagation waves, together with an asymptotic speed of spreading
of the dominating gene, given by $2\sqrt{df'(0)}$. The existence of an asymptotic speed of spreading was generalised in $\mathbb{R}^n$
by D. G. Aronson and H. F. Weinberger in ~\cite{AW} (1978). Since these pioneering works, front propagation in
reaction-diffusion equations have been widely studied. Let us cite, for instance, the works of Freidlin and G\"artner \cite{FG}
for an extension to periodic media, or \cite{W2002}, \cite{BHN1} and \cite{BHN2} for more general domains.
An overview of the subject can be found in ~\cite{BHbook}.
New results on the model under study (\ref{BRReq2}) have been recently proved. Further effects like a drift or
a killing term on the road have been investigated in \cite{BRR2}. The case of a fractional diffusion on the road was studied
and explained by the three authors and A.-C. Coulon in \cite{BRRC} and \cite{these_AC}. See \cite{BRRC2} for a summary of the results on this model.
Models with an ignition-type nonlinearity
are also studied by L. Dietrich in \cite{Dietrich1} and \cite{Dietrich2}.
\paragraph{Organisation of the paper}
The second section of the paper is devoted to the convergence of the asymptotic
speed of propagation $c^*_\varepsilon$ with $\varepsilon$ goes to 0. For this, we will also
investigate some useful convergence result concerning travelling
supersolutions. The third
section deals with the convergence of the stationary solutions,
which will be helpful for the control of the long time behaviour
for Theorem \ref{uniformspreading}.
Theorem \ref{convsol} is proved in sections \ref{sectionresolvent} and \ref{sectionconvsol}, with an argument from geometric
theory of parabolic equations. Section \ref{sectionresolvent}, which is the most technical, is devoted to resolvent bounds.
They are used in section \ref{sectionconvsol} to prove some convergence properties for the linear systems.
Then, we use them in a Gronwall argument to deal with the nonlinearity.
We prove
Theorem \ref{uniformspreading} in the last section.
\paragraph{Acknowledgements} The research leading to these results has received
funding from the European Research Council under the European Union's
Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n.321186 - ReaDi -Reaction-Diffusion Equations, Propagation and Modelling.
I am grateful to Henri Berestycki and Jean-Michel Roquejoffre for suggesting me the
model and many fruitful conversations. I also would like to thank the anonymous referees for their helpful comments.
\section{Asymptotic spreading speed}\label{sectionvitesse}
Let $c^*_0$ be the asymptotic spreading speed associated with the above system (\ref{BRReq2}), and $c^*_\varepsilon$ the spreading speed given
by Theorem \ref{spreadingthm} associated with the system (\ref{RPeps}). Under our assumptions,
the main result of this section is
\begin{prop}
\label{convergencec}
$c^*_\varepsilon$ converges to $c^*_0$ as $\varepsilon$ goes to 0, locally uniformly in $d,D,\overline{\mu}$.
\end{prop}
For the sake of simplicity,
we will consider that $\nu$ is an even function. The general case is similar but heavier.
\subsection{Prerequisite - linear travelling waves and speed of propagation}
All the results given in this subsection have been investigated in \cite{BRR1} by H. Berestycki, J.-M. Roquejoffre, and L. Rossi
for the local system or in \cite{Pauthier}
by the author for the nonlocal.
Our purpose is to recall the derivation of the asymptotic speed of spreading for both systems.
Because $f$ is of KPP-type (that is, satisfies $f(v)\leqf'(0) v$ for nonnegative $v$),
we are interested in the linearised systems:
\begin{equation}
\label{RPlieps}
\begin{cases}
\partial_t u-D \partial_{xx} u = -\overline{\mu} u+\int \nu_\varepsilon(y)v(t,x,y)dy & x \in \mathbb{R},\ t>0 \\
\partial_t v-d\Delta v = f'(0)v +\mu_\varepsilon(y)u(t,x)-\nu_\varepsilon(y)v(t,x,y) & (x,y)\in \mathbb{R}^2,\ t>0
\end{cases}
\end{equation}
for the nonlocal case, and
\begin{equation}
\label{BRRli}
\begin{cases}
\partial_t u-D \partial_{xx} u= v(t,x,0)-\overline{\mu} u & x\in\mathbb{R},\ t>0\\
\partial_t v-d\Delta v=f'(0)v & (x,y)\in\mathbb{R}\times\mathbb{R}^*,\ t>0\\
v(t,x,0^+)=v(t,x,0^-), & x\in\mathbb{R},\ t>0 \\
-d\left\{ \partial_y v(t,x,0^+)-\partial_y v(t,x,0^-) \right\}=\overline{\mu} u(t,x)-\overline{\nu} v(t,x,0) & x\in\mathbb{R},\ t>0
\end{cases}
\end{equation}
for the local one. This motivates the following definition.
\begin{definition}\label{deftravelling}
For any of the two systems (\ref{RPlieps})-(\ref{BRRli}), we call a \textbf{linear travelling wave} a 3-tuple
$(c,\lambda,\phi)$ with $c>0,$ $\lambda>0,$ and $\phi\in H^1(\mathbb{R})$ a positive function such that
$$
\begin{pmatrix}
u(t,x) \\ v(t,x,y)
\end{pmatrix}
= e^{-\lambda(x-ct)} \begin{pmatrix}
1 \\ \phi(y)
\end{pmatrix}
$$
be a solution of the corresponding linearised system (\ref{RPlieps}) or (\ref{BRRli}). The quantity $c$ is the speed of the exponential travelling wave.
\end{definition}
\begin{remark}\label{remark1}
From the KPP assumption (\ref{kppassumtions}) on $f$, a linear travelling wave for the linearised system (\ref{RPlieps}) (resp. (\ref{BRRli}))
provides a supersolution for the nonlinear system (\ref{RPeps}) (resp. (\ref{BRReq2})). This will be a powerful tool
to get $L^\infty$ and decay estimates in the sequel.
\end{remark}
The previous definition for travelling waves provides us a helpful characterisation for spreading speed.
\begin{prop}\label{defspreadingspeed}\cite{BRR1,Pauthier}
For any of the systems (\ref{RPeps})-(\ref{BRReq2}), for all $\varepsilon>0,$
the \textbf{spreading speed $c^*=c^*_0$} or $c^*_\varepsilon$ given by Theorem \ref{spreadingthm}
can be defined as follows:
$$
c^*=\inf\{c>0 | \text{ a linear travelling wave with speed $c$ exists}\}.
$$
\begin{enumerate}
\item If $D\leq 2d,$ then $c^*_0=c^*_\varepsilon=c_{KPP}=2\sqrt{df'(0)}.$
\item If $D>2d,$ then $c^*_0,c^*_\varepsilon>c_{KPP}$ and the infimum is reached by a linear travelling wave, denoted $(c_0^*,\lambda_0^*,\phi^*)$
or $(c_\varepsilon^*,\lambda_\varepsilon^*,\phi^*_\varepsilon).$
\end{enumerate}
\end{prop}
Proposition \ref{defspreadingspeed} provides the construction of $c^*$ thanks to a nonlinear eigenvalue
problem. We give an outline of a proof in both cases to make the sequel easier to read. We focus only on the case
$D>2d,$ the other being trivial.
\paragraph{Resolution for the local case}
Inserting the definition supplied by Proposition \ref{defspreadingspeed} into (\ref{BRRli}), we obtain the following system
in $(c,\lambda,\phi):$
\begin{equation}\label{clambdaphi0}
\begin{cases}
-D\lambda^2+\lambda c+\overline{\mu}=\phi(0) \\
-d\phi''(y)+\left(\lambda c-d\lambda^2-f'(0)\right)\phi(y)=0 \qquad y\in\mathbb{R}^*\\
\phi(0^+)=\phi(0^-),\ \phi\geq0,\ \phi\in H^1(\mathbb{R}), \\
-d\left(\phi'(0^+)-\phi'(0^-)\right)=\overline{\mu}-\phi(0).
\end{cases}
\end{equation}
From now, we set
$$
P(\lambda)=\lambda c-d\lambda^2-f'(0),\ \lambda_2^\pm(c)=\frac{c\pm\sqrt{c^2-c_{KPP}^2}}{2d}
$$
and
$$
\mathcal{D}=\left\{ (c,\lambda),\ c>c_{KPP} \textrm{ and } \lambda\in(\lambda_2^-(c),\lambda_2^+(c))\right\}.
$$
Hence, the existence of a linear travelling wave is equivalent to the following system in $(c,\lambda,\phi(0))$
provided that $c>c_{KPP}$ and $\lambda\in[\lambda_2^-(c),\lambda_2^+(c)]$:
\begin{equation}\label{systemelaphilocal}
\begin{cases}
-D\lambda^2+\lambda c+\overline{\mu}=\phi(0) \\
\phi(0)=\frac{\overline{\mu}}{1+2\sqrt{dP(\lambda)}}.
\end{cases}
\end{equation}
The first equation of (\ref{systemelaphilocal}) gives the graph of a function
\begin{equation}\label{gamma1}
\lambda\mapsto\Psi_1^0(c,\lambda):=-D\lambda^2+c\lambda+\overline{\mu}
\end{equation}
which is intended to be equal to $\phi(0),$
provided $(c,\lambda,\phi)$ defines a linear travelling wave. Let us denote $\Gamma_1$ its graph, depending on $c,$
in the $(\lambda,\Psi_1^0(\lambda))-$plane.
The second equation of (\ref{systemelaphilocal}) gives the graph of a function
\begin{equation*}
\Psi_2^0 : \left\{ \begin{array}{ccl}
\overline{\mathcal{D}} & \longrightarrow & \mathbb{R} \\
(c,\lambda) & \longmapsto &\frac{\overline{\mu}}{1+2\sqrt{dP(\lambda)}}.
\end{array} \right.
\end{equation*}
Let us denote $\Gamma_2^0$ its graph in the same plane, still depending on $c.$
Hence, (\ref{systemelaphilocal}) amounts to looking for the first $c\geq c_{KPP}$ such that the two graphs
$\Gamma_1$ and $\Gamma_2^0$ intersect.
It was shown that there exists $(c^*_0,\lambda^*_0)\in\mathcal{D}$ and an exponential function
$$\phi^* : y \mapsto \phi^*(0)e^{-\sqrt{P(\lambda_0^*)}|y|}$$
such that $(c^*_0,\lambda^*_0,\phi^*)$ defines a linear travelling wave for (\ref{BRRli}), and $c^*_0$ is
the first $c$ such that (\ref{clambdaphi0}) admits a solution. Hence, $c^*_0$ is the speed defined by Proposition \ref{defspreadingspeed}.
\paragraph{Resolution for the nonlocal case}
In this case, Proposition \ref{defspreadingspeed} yields the following system in $(c,\lambda,\phi).$
\begin{equation}\label{clambdaphieps}
\begin{cases}
-D\lambda^2+c\lambda+\overline{\mu} = \int_\mathbb{R} \nu_\varepsilon(y)\phi(y)dy \\
-d\phi''(y)+\left( c\lambda-d\lambda^2-f'(0)+\nu_\varepsilon(y)\right)\phi(y) = \mu_\varepsilon(y),\ \phi\in H^1(\mathbb{R}).
\end{cases}
\end{equation}
Once again, the first equation of (\ref{clambdaphieps}) gives the function $\Psi_1^0$ defined by (\ref{gamma1}), which is intended to be equal to $\int \nu_\varepsilon\phi$
provided $(c,\lambda,\phi)$ defines a linear travelling wave for (\ref{RPlieps}). The second equation of (\ref{clambdaphieps}) defines implicitly the
function
\begin{equation*}
\Psi_2^\varepsilon : \left\{ \begin{array}{ccl}
\mathcal{D} & \longrightarrow & \mathbb{R} \\
(c,\lambda) & \longmapsto & \int \nu_\varepsilon(y)\phi(y;\varepsilon,c,\lambda)dy
\end{array} \right.
\end{equation*}
where $\phi(.;\varepsilon,c,\lambda)$ is the unique solution in $H^1(R)$ of
\begin{equation}
\label{gamma2e}
-d\phi''(y)+(\lambda c-d\lambda^2-f'(0)+\nu_\varepsilon(y))\phi(y) = \mu_\varepsilon(y),\qquad y\in\mathbb{R}.
\end{equation}
For fixed $c,$ we denote $\Gamma_2^\varepsilon$ the graph of $\Psi_2^\varepsilon$ in the $(\lambda,\Psi_2^\varepsilon(\lambda))-$plane.
$\Psi_2^\varepsilon$ is smooth in $\mathcal{D}$ and can be continuously extended in $\overline{\mathcal{D}}.$ It has also been proved that
$\phi,$ hence $\Psi_2^\varepsilon$ is decreasing in $c.$
It was shown that for all $\varepsilon>0,$ there exists $(c^*_\varepsilon,\lambda^*_\varepsilon)\in\mathcal{D}$ and $\phi^*_\varepsilon=\phi(.;\varepsilon,c^*_\varepsilon,\lambda^*_\varepsilon)$ solution
of (\ref{gamma2e}) such that $(c^*_\varepsilon,\lambda_\varepsilon^*)$ $\Gamma_1^0$ and $\Gamma_2^\varepsilon$ intersect, and $c_\varepsilon^*$ is the first $c$ such that it occurs.
The main ingredients of this proof are:
\begin{itemize}
\item the functions $c\mapsto\Psi_1^0(c,\lambda)$ and
$c\mapsto\lambda_2^-(c)$ are respectively increasing and decreasing;
\item the function $\lambda\mapsto\Psi_2^\varepsilon(c,\lambda)$ is strictly concave.
\end{itemize}
These behaviours summed up in Figure \ref{2graphs}.
\begin{figure}[!ht]
\centering
\input{2graphs}
\caption{\label{2graphs}representation of $\Gamma_1$ and $\Gamma_2^\varepsilon,$ behaviours as $c$ increases}
\end{figure}
The main purpose of the rest of this section will be to show that the curve $\Gamma_2^\varepsilon$ converges locally uniformly in $(c,\lambda)$
to $\Gamma_2^0$ as $\varepsilon$ goes to 0.
\subsection{Convergence of the spreading speed}
\paragraph{Uniform boundedness of $\phi$ in $C^1(\mathbb{R})$}
\begin{lem}\label{borneuniformephi}
Let us consider $\phi:=\phi(y;\varepsilon,c,\lambda)$ the unique solution of (\ref{gamma2e}) for $\varepsilon>0$
and $(c,\lambda)$ in $\mathcal{D},$ that is to say $c>c_{KPP}$ and $\lambda$ in $]\lambda_2^-(c),\lambda_2^+(c)[.$
Then the family $\left(\|\phi\|_{L^\infty(y)}+\|\phi'\|_{L^\infty(y)}\right)_\varepsilon$ is uniformly bounded in $\varepsilon>0$ and every compact set on
$\overline{\mathcal{D}}.$
\end{lem}
\begin{proof}
We consider $\phi=\phi(y;\varepsilon,\lambda,c)$ defined for $\varepsilon>0$, $(c,\lambda)$ in $\mathcal{D},$ and $y\in\mathbb{R}$. We know
that $\phi$ can be continuously extended to $\overline{\mathcal{D}}.$
Moreover, from the elliptic maximum principle, it is easy to see that $\phi>0$ on $\mathbb{R},$ for all admissible parameters.
Considering the hypotheses (\ref{supportmunu}) on $\mu, \nu$, we get that:
\begin{itemize}
\item $\forall \varepsilon>0,\ supp(\nu_\varepsilon,\mu_\varepsilon)\subset(-\varepsilon,\varepsilon)$ ;
\item $y\mapsto \phi(y)$ is even.
\end{itemize}
Hence there exists $K=K(\varepsilon,c,\lambda)$ such that
\begin{equation}\label{referee2}
\forall |y|>\varepsilon,\ \phi(y;\varepsilon,c,\lambda)=K(\varepsilon,c,\lambda)e^{-\sqrt{\frac{P(\lambda)}{d}}|y|}.
\end{equation}
\textit{Step 1}. It is enough to bound $K$ to get the uniform boundedness of $\|\phi(\varepsilon,c,\lambda)\|_{L^{\infty}(\mathbb{R})}$.
Indeed, using the scaling $\xi=\frac{y}{\varepsilon}$, with $\psi(\xi)=\phi(y)$, the function $\psi$ satisfies
\begin{equation}
\label{eqrescal1}
\begin{cases}
-d\psi''(\xi)+(\varepsilon^2 P(\lambda)+\varepsilon\nu(\xi))\psi(\xi) = \varepsilon\mu(\xi) \\
\psi(\pm 1)=Ke^{-\sqrt{\frac{P(\lambda)}{d}}}.
\end{cases}
\end{equation}
Now, let us recall that $\mu,\nu$ are continuous and compactly supported. Then,
by the Harnack inequality (theorem 8.17 and 8.18 in ~\cite{GT} for instance), there
exist $C_1,C_2\geq 0$, independent of $\varepsilon,c,\lambda$, such that
$$
\underset{[-1,1]}{\sup} \psi \leq C_1(\underset{[-1,1]}{\inf}\psi + C_2),
$$
which gives immediately
$$
\underset{\mathbb{R}}{\sup}\ \phi \leq C_1(K(\varepsilon,c,\lambda) + C_2).
$$
\textit{Step 2}. Let us prove a uniform bound for $K$. Set $c_1\in]c_{KPP},+\infty[$, and assume by contradiction that
\begin{equation}\label{absurde}
\lim_{\varepsilon\to0}\sup \left\{ K(\varepsilon,c,\lambda),\ (c,\lambda)\in\overline{\mathcal{D}},c\leq c_1\right\}=+\infty.
\end{equation}
That is, there exist $(\varepsilon_n)_n,(\lambda_n)_n,(c_n)_n$ with $\varepsilon_n\to 0$ and $c\leq c_1,$ $\lambda_2^-(c_1)\leq\lambda\leq\lambda_2^+(c_1)$
such that
$$
K(\varepsilon_n,\lambda_n,c_n):=K_n\underset{n\to \infty}{\longrightarrow} +\infty.
$$
Set $$\tilde{\phi}_n = \frac{\phi(.;\varepsilon_n,\lambda_n,c_n)}{K_n}.$$
The function $\tilde{\phi}_n$ satisfies
\begin{equation}
\label{phitilde}
\begin{cases}
-d\tilde{\phi}_n''+(P(\lambda_n)+\nu_{\varepsilon_n})\tilde{\phi}_n = \frac{\mu_{\varepsilon_n}}{K_n} \ y\in\mathbb{R} \\
\tilde{\phi}_n(y) = e^{-\sqrt{\frac{P(\lambda_n)}{d}}|y|},\ \forall |y|>\varepsilon_n.
\end{cases}
\end{equation}
Again by the Harnack inequality, $(\|\tilde{\phi}_n\|_\infty)_n$ is bounded, and $\tilde{\phi}_n$ is positive by the elliptic maximum principle.
Integrating (\ref{phitilde}) between $-\infty$ and $y$ gives
$$
d\tilde{\phi}_n'(y) = P(\lambda_n)\int_{-\infty}^y\tilde{\phi}_n+\int_{-\infty}^y \nu_{\varepsilon_n} \tilde{\phi}_n-\frac{1}{K_n}\int_{-\infty}^y \mu_{\varepsilon_n},
$$
so
\begin{align*}
d\|\tilde{\phi}_n'\|_\infty & \leq P(\lambda_n)\int_\mathbb{R} e^{-\sqrt{\frac{P(\lambda_n)}{d}}|y|}dy+P(\lambda_n)\int_{-\varepsilon}^{+\varepsilon}\tilde{\phi}_n(y)dy+
\|\tilde{\phi}_n\|_\infty+\frac{\overline{\mu}}{K_n} \\
& \leq 2\sqrt{dP(\lambda_n)}+\|\tilde{\phi}_n\|_\infty\lp1+2\varepsilon P(\lambda_n)\right)+\frac{\overline{\mu}}{K_n}.
\end{align*}
Hence $(\tilde{\phi}_n)_n$ is uniformly Lipschitz.
Specializing to $y=1$, we get:
\begin{equation}\label{inegalite}
-d\tilde{\phi}_n'(1) = \frac{\overline{\mu}}{K_n}-P(\lambda_n)\int_{-\infty}^1\tilde{\phi}_n-\int_{-\infty}^1 \nu_{\varepsilon_n} \tilde{\phi}_n.
\end{equation}
But on the other hand, we have:
\begin{itemize}
\item $-d\tilde{\phi}_n'(1) = \sqrt{dP(\lambda_n)} e^{-\sqrt{\frac{P(\lambda_n)}{d}}}\geq 0$ from (\ref{referee2}) ;
\item $\frac{\overline{\mu}}{K_n}\to 0$ as $n\to\infty$ by assumption (\ref{absurde}) ;
\item $-P(\lambda_n)\int_{-\infty}^1\tilde{\phi}_n\leq 0$ ;
\item $-\int_{-\infty}^1 \nu_{\varepsilon_n} \tilde{\phi}_n\to -1$ as $n\to \infty$. Indeed, the sequence $\nu_{\varepsilon_n}$ tends to the Dirac measure, we have
$\tilde{\phi}_n(\pm\varepsilon_n)=1+O(\varepsilon_n)$ from (\ref{phitilde}), and $(\tilde{\phi}_n)_n$
is uniformly Lipschitz.
\end{itemize}
For $n\to\infty$, this contradicts (\ref{inegalite}) since the left term is nonnegative and the right term tends to a negative limit.
Hence, there is a contradiction. That is, $K(\varepsilon,c,\lambda)$ is bounded for $(c,\lambda)\in\overline{\mathcal{D}}$ satisfying $c\leq c_1.$
Recall that $c\mapsto \phi$ is nonincreasing,
and $\phi$ is uniformly bounded as $\varepsilon\to 0$ in $(c,\lambda)\in\overline{\mathcal{D}}.$
\textit{Step 3}. Boundedness of $\|\phi'\|_\infty$ with $\varepsilon\to 0$. We integrate (\ref{gamma2e}) from $-\infty$ to $y$ which
gives:
$$
d\phi'(y) = P(\lambda)\int_{_\infty}^y \phi + \int_{_\infty}^y \nu_\varepsilon \phi - \int_{_\infty}^y \mu_\varepsilon.
$$
Now, the explicit formula for $\phi$ and its uniform boundedness obtained in step 2 yields:
$$
d\|\phi'\|_{\infty} \leq \|\phi\|_{\infty}\left( 1+2\sqrt{dP(\lambda)}+2\varepsilon\right)+\overline{\mu}
$$
and the family $(\|\phi(\varepsilon,c,\lambda)\|_{\infty})$ is equicontinuous for all $\varepsilon$ close enough to $0$
and for all compact set in $\overline{\mathcal{D}}.$ This implies the uniform boundedness of $\phi$ in $C^1(\mathbb{R})$.
\end{proof}
\paragraph{Convergence of $\phi(.;\varepsilon)$ with $\varepsilon\to 0$, continuity of $\Psi_2^{\varepsilon}$.}
From Lemma \ref{borneuniformephi} the set $\left(\phi(.;\varepsilon) \right)_\varepsilon$ is included in $C_b(\mathbb{R})$ and equicontinuous, locally uniformly in $c,\lambda$.
The Arzel\`a-Ascoli theorem (combined with Cantor's diagonal argument) yields the existence of a sequence $(\varepsilon_n)_n \subset \mathbb{R},\ \varepsilon_n\to 0$ and
a function $\phi_0\in C_b(\mathbb{R})$ such that $\phi(\varepsilon_n)\underset{n\to \infty}{\longrightarrow}\phi_0$ uniformly on compact sets.
Passing to the limit in (\ref{gamma2e}), we obtain that $\phi_0$ satisfies
\begin{equation}\label{eqlimite}
-d\phi_0''+\phi_0(P(\lambda)+\delta_0) = \overline{\mu}\delta_0
\end{equation}
in the distribution sense.
Moreover, $K(\varepsilon_n,c,\lambda)\to K_0(c,\lambda)=\phi_0(0;c,\lambda)$ with $n\to\infty$,
and $$\phi_0(y)=K_0\exp(-\sqrt{\frac{P(\lambda)}{d}}|y|).$$
It remains to show the uniqueness of the limit function. Let $\phi_1$ be another accumulation point for $(\phi(.;\varepsilon))_\varepsilon$. Then $\phi_1$ also satisfies
(\ref{eqlimite}) in the distribution sense, and $\phi_1(y)=\phi_1(0)\exp(-\sqrt{\frac{P(\lambda)}{d}}|y|)$. Then $\psi=\phi_0-\phi_1$ is a solution of
\begin{equation*}
-d\psi''+\psi(P(\lambda)+\delta_0)=0.
\end{equation*}
Now, let us consider $(\psi_n)_n\subset\mathcal{D}(\mathbb{R})$ such that $\psi_n\to\psi$ uniformly on every compact and $\psi_n'\to\psi'$ on every compact
of $\mathbb{R}\backslash\{0\}.$ We get
$$
d\|\psi'\|^2_{L^2}+P(\lambda)\|\psi\|^2_{L^2}+\psi(0)^2=0,
$$
and $\psi\equiv0$. So $\phi_0$ is the unique accumulation point of $(\phi(.;\varepsilon))_\varepsilon$, hence $\phi(.;\varepsilon)\underset{\varepsilon\to0}{\longrightarrow}\phi_0$
uniformly on compact sets. Hence we have proved the following lemma.
\begin{lem}\label{convergencephi}
Let us consider $\phi$ as a function of $\varepsilon,c,\lambda,$ extended to $\phi_0$
for $\varepsilon=0.$ Then $\phi(.;\varepsilon,c,\lambda)$ is continuous from $[0,1]\times \overline{\mathcal{D}}$
to $C^0(\mathbb{R})$ and bounded in $C^1$ as a $y$-function on every compact set on it.
\end{lem}
It is now easy to see that the function $\Psi_2^{\varepsilon}$ converges continuously in $\lambda,c$, to a
limit function
\begin{equation*}
\Psi_2^l: \left\{ \begin{array}{ccl}
]\lambda_2^- , \lambda_2^+[ & \longrightarrow & \mathbb{R} \\
\lambda & \longmapsto & \phi_0(c,\lambda)
\end{array} \right.
\end{equation*}
and the curve $\Gamma_2^\varepsilon$ converges to the graph of $\Psi_2^l$. Let us denote it $\Gamma_2^l$.
\paragraph{The limit curve $\Gamma_2^l$.} Now let us show that $\Gamma_2^l=\Gamma_2^0.$ The limit function
$\phi_0$ is of the form $\phi_0(y)=K_0\exp(-\sqrt{\frac{P(\lambda)}{d}}|y|)$ and satisfies (\ref{eqlimite}) in the distribution sense.
Applying the two sides of (\ref{eqlimite}) to $\phi_0$ (or, to be strictly rigorous, to a sequence $\left(\phi_n\right)$ that tends to $\phi_0$),
we get
$$
d\|\phi_0'\|^2_{L^2}+P(\lambda)\|\phi_0\|^2_{L^2}+\phi_0(0)^2=\overline{\mu} \phi_0(0).
$$
Using the explicit formula for $\phi_0$, we obtain:
$$
2\sqrt{dP(\lambda)}\phi_0(0)^2+\phi_0(0)^2 = \overline{\mu}\phi_0(0).
$$
Hence, because 0 is not a solution,
$$
\phi_0(0)=\frac{\overline{\mu}}{1+2\sqrt{dP(\lambda)}}.
$$
Hence, $\Psi_2^l=\Psi_2^0$ and $\Gamma_2^l=\Gamma_2^0$ which concludes the proof of Proposition \ref{convergencec}.
\qed
\begin{remark}
Actually, the spreading speed in the local case was not devised exactly with the system (\ref{systemelaphilocal}), but with the following system.
\begin{equation*}
\begin{cases}
-D\lambda^2+c\lambda = & \frac{\overline{\mu}}{1+2d\beta}-\overline{\mu} \\
-d\lambda^2+c\lambda = & f'(0)+d\beta^2.
\end{cases}
\end{equation*}
But, setting $\Phi(\beta) = \frac{\overline{\mu}}{1+2d\beta},$ they are equivalent.
\end{remark}
\section{Convergence of the stationary solutions}
We have already showed in \cite{Pauthier} that,
for all $\varepsilon>0,$ there exists a unique positive and bounded stationary solution of
(\ref{RPeps}), which will be denoted $(U_\varepsilon,V_\varepsilon).$ Moreover, this stationary solution is $x-$independent and
satisfies $\displaystyle \lim_{y\to\pm\infty}V_\varepsilon(y)=1.$ The corresponding equation is
\begin{equation}
\label{stationaryeps}
\begin{cases}
\overline{\mu} U_\varepsilon = \int \nu_\varepsilon(y)V_\varepsilon(y)dy \\
-dV_\varepsilon''(y) = f(V_\varepsilon)+\mu_\varepsilon(y)U_\varepsilon-\nu_\varepsilon(y)V_\varepsilon(y).
\end{cases}
\end{equation}
Solutions of (\ref{stationaryeps}) depend only of the $y$-variable, hence $U$ is
constant and $V$ is entirely determined by the following integro-differential equation
\begin{equation}
\label{Veqeps}
-dV''_\varepsilon(y)=f(V_\varepsilon)+\frac{\mu_\varepsilon(y)}{\overline{\mu}}\int \nu_\varepsilon(z)V_\varepsilon(z)dz-\nu_\varepsilon(y)V_\varepsilon(y).
\end{equation}
The main result of this section lies in the next proposition.
\begin{prop}
\label{convVeps}
$(V_\varepsilon)_\varepsilon$ converges uniformly to the constant function 1 when $\varepsilon$ goes to 0.
\end{prop}
Of course, this implies that $U_\varepsilon\to\frac{\overline{\nu}}{\overline{\mu}}$ as $\varepsilon\to0.$ As a
result, the stationary solutions of (\ref{RPeps}) converge to the stationary solutions
of (\ref{BRReq2}) which were identified in \cite{BRR1}.
The difficulties lie in the singularity in $(-\varepsilon,\varepsilon).$ Outside this interval,
$V_\varepsilon$ satisfies
\begin{equation}
\label{portraitphase}
\begin{cases}
-dV_\varepsilon''=f(V_\varepsilon) \\
0<V_\varepsilon<+\infty, \ V_\varepsilon(\pm\infty)=1.
\end{cases}
\end{equation}
As $(V_\varepsilon,V_\varepsilon')=(1,0)$ is a saddle point for the system (\ref{portraitphase}), it is easy to see
that solutions of (\ref{portraitphase}) belong to one of the two integral curves that
tend to $(V_\varepsilon,V_\varepsilon')=(1,0).$ We can also notice that $V_\varepsilon(\varepsilon)>1$ (resp. $<1$) implies that
$V_\varepsilon$ is decreasing (resp. increasing) on $(\varepsilon,+\infty).$ Thus important estimates have to be found inside $(-\varepsilon,\varepsilon).$
From now and without lack of generality, we will assume $d=1.$
\paragraph{A uniform $L^\infty$ boundary for $(V_\varepsilon).$}
Set $z=\frac{y}{\varepsilon}$ and
$
W_\varepsilon(z):=V_\varepsilon(y).
$
Then, we have $\|V_\varepsilon\|_\infty=\|W_\varepsilon\|_\infty,$ $\|V_\varepsilon'\|_\infty=\frac{1}{\varepsilon}\|W_\varepsilon'\|_\infty,$ and $W_\varepsilon$ satisfies in $(-1,1)$
\begin{equation}
\label{Weps}
-W_\varepsilon''=\varepsilon^2f(W_\varepsilon)+\varepsilon\frac{\mu(z)}{\overline{\mu}}\int \nu(s)W_\varepsilon(s)ds-\varepsilon\nu(z)W_\varepsilon(z).
\end{equation}
\textit{Step 1}. Lower bound for $W_\varepsilon(1).$ From (\ref{portraitphase}), there exists at least a point $z_\varepsilon\in(-1,1)$ such that
$W_\varepsilon'(z_\varepsilon)=0.$ Hence,
\begin{equation}\label{Wprime}
\forall z\in (-1,1),\ W_\varepsilon'(z)=\int_{z_\varepsilon}^z W_\varepsilon''(s)ds.
\end{equation}
Integrating (\ref{Weps}) yields the following rough bound, for all $\varepsilon>0:$
\begin{equation}\label{Wprimeeps}
\forall z\in(-1,1),\ |W_\varepsilon'(z)|\leq 2\varepsilon \left(\|\nu\|_\infty+1+\varepsilon\|f\|_{Lip}\right)\|W_\varepsilon\|_{L^\infty(-1,1)}.
\end{equation}
Let us set $K=4\left(\|\nu\|_\infty+\overline{\nu}+\|f\|_{Lip}\right)$ and we get the following estimate for $W_\varepsilon(1)=V_\varepsilon(\varepsilon):$
\begin{equation}
\label{Weps1}
\left| \frac{W_\varepsilon(1)-\|W_\varepsilon\|_{L^\infty(-1,1)}}{\|W_\varepsilon\|_{L^\infty(-1,1)}}\right| \leq K\varepsilon.
\end{equation}
\textit{Step 2.} Lower bound for $W_\varepsilon'(1).$ Using once again (\ref{Wprime}), we have
\begin{equation}
\label{Wprime1}
W_\varepsilon'(1)=\varepsilon\int_{z_\varepsilon}^1 \nu(s)W_\varepsilon(s)ds-\varepsilon^2\int_{z_\varepsilon}^1 f(W_\varepsilon(s))ds-\left(\frac{\varepsilon}{\overline{\mu}}\int_{-1}^1 \nu(s)W_\varepsilon(s)ds\right)\int_{z_\varepsilon}^1 \mu(s)ds.
\end{equation}
The first term in the right handside in (\ref{Wprime1}) is nonnegative, hence
$W_\varepsilon'(1)\geq -\varepsilon(\overline{\nu}+\varepsilon\|f\|_{Lip})\|W_\varepsilon\|_\infty$ and, in the $y$-variable :
\begin{equation}
\label{Vprime1}
V_\varepsilon'(\varepsilon)\geq -\|V_\varepsilon\|_\infty(\overline{\nu}+\varepsilon\|f\|_{Lip}).
\end{equation}
\textit{Step 3}. Proof of the boundedness by contradiction. Let us suppose that
$$\lim_{\varepsilon\to0}\sup \|V_\varepsilon\|_{L^\infty} = +\infty.$$
That is, there exists a sequence $\varepsilon_n\to0$ such that
$\displaystyle
\underset{\mathbb{R}}{\sup }V_{\varepsilon_n}=\underset{(-\varepsilon_n,\varepsilon_n)}{\sup }V_{\varepsilon_n}\underset{n\to\infty}{\longrightarrow}+\infty.
$
From (\ref{Weps1}), we have $V_{\varepsilon_n}(\varepsilon_n)\geq \|V_{\varepsilon_n}\|_\infty(1-K\varepsilon_n).$ Now, recall that on $(\varepsilon_n,+\infty),$
the function $V_{\varepsilon_n}$ satisfies (\ref{portraitphase}). Multiply it by $V_{\varepsilon_n}'$ and integrate, we get
$V_{\varepsilon_n}'^2(\varepsilon_n)=-2F(V_{\varepsilon_n}(\varepsilon_n))$ where $F(t):=\int_1^t f(s)ds$ is an antederivative of $f.$
Considering the hypotheses on $f$ this gives
$$
V_{\varepsilon_n}'(\varepsilon_n)\underset{n\to\infty}{\sim}-\sqrt{\|f\|_{Lip}}V_{\varepsilon_n}(\varepsilon_n).
$$
From hypothesis (\ref{lipf}) on $f,$ $\|f\|_{Lip}>2$ and we get a contradiction with (\ref{Vprime1}) and (\ref{Weps1}). As a result,
$\left(\|V_\varepsilon\|_{L^\infty(\mathbb{R})}\right)_\varepsilon$ and $\left(\|V'_\varepsilon\|_{L^\infty(\mathbb{R})}\right)_\varepsilon$ are uniformly bounded as $\varepsilon$ goes to 0.
\paragraph{Convergence of the stationary solutions} From the previous paragraph and Ascoli's Theorem, $(V_\varepsilon)_\varepsilon$
admits at least one accumulation point, let say $V_0$, and the convergence is uniform on every compact set, thus uniform
on $\mathbb{R}$ (from the monotonicity of $V_\varepsilon$ outside $(-\varepsilon,\varepsilon),$ or even a diagonal argument). So $V_0$ is continuous, bounded,
tends to 1 at infinity.
Passing to the limit in (\ref{Veqeps}), it satisfies in the distribution sense
$$
-V_0''=f(V_0)+\overline{\nu}\delta_0(V_0(0)-V_0).
$$
As the support of the Dirac distribution is reduced to $\{0\}$ , and because of the continuity of $V_0,$ it satisfies
in the classical sense
\begin{equation}\label{groumf}
\begin{cases}
-V_0''(y)=f(V_0(y)), \ y\in \mathbb{R} \\
V_0(\pm\infty)=1.
\end{cases}
\end{equation}
The only solution of (\ref{groumf}) is $V_0\equiv1.$ Hence,
the set $(V_\varepsilon)_\varepsilon$ admits only one accumulation point, so $V_\varepsilon\to 1$ as $\varepsilon$ goes to 0 uniformly on $\mathbb{R},$ and the proof
of Proposition \ref{convVeps} is complete.
\qed
This convergence allows us to assert that there exist $0<m<M<+\infty$ such that
\begin{equation}\label{uniformsupersol}
m < V_\varepsilon(y)< M,\ \forall \varepsilon>0,\ \forall y\in\mathbb{R}.
\end{equation}
Thus, any solution of (\ref{RPeps}) starting from an initial datum $(u_0,v_0)\leq(\frac{\overline{\nu}}{\overline{\mu}}m,m)$
will remain below $M,$ which gives a uniform supersolution in $\varepsilon.$
\section{Uniform bounds on the resolvents}\label{sectionresolvent}
Consider the two linear models
\begin{equation}
\label{RPepsli}
\begin{cases}
\partial_t u-D \partial_{xx} u = -\overline{\mu} u+\int \nu_\varepsilon(y)v(t,x,y)dy & x \in \mathbb{R},\ t>0 \\
\partial_t v-d\Delta v = \mu_\varepsilon(y)u(t,x)-\nu_\varepsilon(y)v(t,x,y) & (x,y)\in \mathbb{R}^2,\ t>0
\end{cases}
\end{equation}
and
\begin{equation}
\label{BRReq2li}
\begin{cases}
\partial_t u-D \partial_{xx} u= v(x,0,t)-\overline{\mu} u & x\in\mathbb{R},\ t>0\\
\partial_t v-d\Delta v=0 & (x,y)\in\mathbb{R}\times\mathbb{R}^*,\ t>0\\
v(t,x,0^+)=v(t,x,0^-), & x\in\mathbb{R},\ t>0 \\
-d\left\{ \partial_y v(t,x,0^+)-\partial_y v(t,x,0^-) \right\}=\overline{\mu} u(t,x)-\overline{\nu} v(t,x,0) & x\in\mathbb{R},\ t>0.
\end{cases}
\end{equation}
The general goal is to give a uniform bound on the
difference between solutions of the two above linear systems. We choose a sectorial
operators approach to get an integral representation of the semigroups generated by (\ref{RPepsli}) and (\ref{BRReq2li}).
They both can be written in the form
\begin{equation}\label{edpedo}
\partial_t \begin{pmatrix}
u \\
v
\end{pmatrix}
=L\begin{pmatrix}
u \\
v
\end{pmatrix}
\end{equation}
where $L=L_\varepsilon$ in (\ref{RPepsli}) and $L=L_0$ in (\ref{BRReq2li}) are linear unbounded operators defined by
$$
L_\varepsilon \ : \ \left\{ \begin{array}{rcl}
\mathcal{D}(L_\varepsilon)\subset X & \longrightarrow & X \\
\begin{pmatrix}u\\v\end{pmatrix} & \longmapsto & \begin{pmatrix}D\partial_{xx}u-\overline{\mu} u+\int \nu_\varepsilon v\\
d\Delta v+\mu_\varepsilon u-\nu_\varepsilon v\end{pmatrix}
\end{array}\right.
$$
$$
L_0 \ : \ \left\{ \begin{array}{rcl}
\mathcal{D}(L_0)\subset X & \longrightarrow & X \\
\begin{pmatrix}u\\v\end{pmatrix} & \longmapsto & \begin{pmatrix}D\partial_{xx}u-\overline{\mu} u+\overline{\nu} v(.,0)\\
d\Delta v\end{pmatrix}
\end{array}\right.
$$
with $X$ the space of continuous functions decaying to 0 at infinity $\mathcal{C}_0(\mathbb{R})\times\mathcal{C}_0(\mathbb{R}^2)$.
The domains are those of the Laplace operator, with
exchange conditions included in $\mathcal{D}(L_0).$
We recall the definition of a sectorial operator:
\begin{definition}\label{sectorialdef}
A linear operator $A : \mathcal{D}(A)\subset X \to X$ is {\bf sectorial}
if there are constants $\varphi\in\mathbb{R},$ $\theta\in (\frac{\pi}{2},\pi),$ and $M>0$ such that
\begin{equation}\label{defsectorial}
\begin{cases}
(i) \qquad \rho(A)\supset S_{\theta,\varphi}:=\{\lambda\in\mathbb{C}:\lambda\neq\varphi,|\arg(\lambda-\varphi)|<\theta\} \\
(ii) \qquad \|R(\lambda,A)\|_{\mathcal{L}(X)}\leq \frac{M}{|\lambda-\varphi|},\ \lambda\in S_{\theta,\varphi}
\end{cases}
\end{equation}
\end{definition}
\begin{prop}
\label{sectorial}
Let $\varphi>\max(2,3\overline{\mu}),$ $\frac{\pi}{2}<\theta<\frac{3\pi}{4}.$ Then $(L_\varepsilon,\mathcal{D}(L_\varepsilon))$ and $(L_0,\mathcal{D}(L_0))$ are sectorial with
sector $S_{\theta,\varphi},$ $\forall \varepsilon>0.$
\end{prop}
Let us denote $M_0,M_\varepsilon$ the corresponding constant for the norm of
the resolvents.
The proof for $L_\varepsilon$ is quite standard and omitted here. There is a general approach of the theory in \cite{henry}. A proof for
$L_0$ can be found in \cite{these_AC}. Assumptions on $\varphi$ and $\theta$ are only technical and can be improved.
From Proposition \ref{sectorial}, we know (see \cite{henry} for instance) that, for all $t>0,$ solutions of (\ref{edpedo}) have the form
$$
\begin{pmatrix} u(t) \\ v(t) \end{pmatrix} =
e^{tL}\begin{pmatrix} u_0 \\ v_0 \end{pmatrix}
$$
where
\begin{equation}\label{semigroup}
e^{tL}=\frac{1}{2\pi i}\int_{\Gamma_{r,\vartheta}}e^{t\lambda}R(\lambda,L)d\lambda
\end{equation}
for any $r>0, \vartheta\in(\frac{\pi}{2},\theta),$ where $\Gamma_{r, \vartheta}:=\{\lambda,|\arg(\lambda-\varphi-r)|=\vartheta\}$ is
a counterclockwise oriented curve which encloses the spectrum of $L,$ and will be denoted $\Gamma$ when there is no possible confusion.
Let us fix from now and for all $r>0$ and the angle $\vartheta$ as above. A parametrisation
of $\Gamma_{r, \vartheta}$ is then given by
$s\in\mathbb{R}\mapsto \varphi+r+s e^{i\vartheta. \sgn(s)}.$
For $\left( U,V\right)\in X,$ we will denote in this section:
\begin{equation*}
\begin{cases}
(u,v)=R(\lambda,L_0)(U,V) \\
(u_\varepsilon,v_\varepsilon)=R(\lambda,L_\varepsilon)(U,V)
\end{cases}
\end{equation*}
that is
\begin{equation}\label{avtfourier0}
\begin{cases}
(\lambda+\overline{\mu}) u- D\partial_{xx}u = v(.,0) + U \qquad x\in\mathbb{R} \\
\lambda v-\Delta v = V \qquad (x,y)\in\mathbb{R}\times\mathbb{R}^* \\
v(x,0^+)=v(x,0^-)\qquad x\in\mathbb{R}\\
-(\partial_y v(x,0^+)-\partial_y v(x,0^-)) = \overline{\mu} u-v(x,0) \qquad x\in\mathbb{R}
\end{cases}
\end{equation}
and
\begin{equation}\label{avtfouriereps}
\begin{cases}
(\lambda+\overline{\mu}) u(x)-D\partial_{xx}u(x) & = \int\nu_\varepsilon(y)v(x,y)dy + U(x) \\
(\lambda+\frac{1}{\varepsilon}\nu(\frac{y}{\varepsilon})) v(x,y) -\Delta v(x,y) & = \frac{1}{\varepsilon}\mu(\frac{y}{\varepsilon})u(x)+V(x,y).
\end{cases}
\end{equation}
The purpose of this section is to give some estimates on the resolvents, that is on the solutions of (\ref{avtfourier0})
and (\ref{avtfouriereps}). They are given in Lemma \ref{grandslambda} and Corollary \ref{corl1}.
Lastly, let us recall (see \cite{henry} or \cite{Lunardi}) that the Laplace operator is also sectorial, with a sector
strictly containing $S_{\theta,\varphi}.$ Thus, there exists a constant $M>0$ such that for $d\in\{1,2\},$
\begin{equation}
\label{boitenoire}
\forall w\in \mathcal{C}_0(\mathbb{R}^d),\ \forall \lambda\in S_{\theta,\varphi},\ \|w\|_\infty \leq \frac{M}{|\lambda|}\|\Delta w-\lambda w\|_\infty.
\end{equation}
\subsection{Large values of $\left|\lambda\right|$}
\begin{lem}
\label{grandslambda}
There exist $\varepsilon_0>0$ and a constant $C_1$ depending only on $D,$ $\overline{\mu}$ and $\vartheta$ such that for all positive $\varepsilon<\varepsilon_0,$ for $\beta>\frac{1}{2},$
$$\textrm{if }\lambda\in \Gamma_{r,\vartheta} \textrm{ and } |\lambda|>\varepsilon^{-\beta} \textrm{, then }\|R(\lambda,L_\varepsilon)\|\leq C_1\max(\varepsilon^\beta,\varepsilon^{2\beta-1}). $$
\end{lem}
\begin{proof}
Let $(U,V)\in X,$ and $(u_\varepsilon,v_\varepsilon)=R(\lambda,L_\varepsilon)(U,V)$ be a solution of (\ref{avtfouriereps})
Assumptions on $\lambda$ imply for $\varepsilon$ small enough that
$|\Im {\lambda}|>\frac{1}{2}\sin(\vartheta)\varepsilon^{-\beta}.$ Thus, $\nu$ being a real nonnegative function,
$\lambda+\frac{1}{\varepsilon}\nu(\frac{y}{\varepsilon})\in S_{\theta,\varphi}, \forall y\in\mathbb{R}$ and
$$
\left|\lambda+\frac{1}{\varepsilon}\nu(\frac{y}{\varepsilon})\right|\geq\Im{\lambda+\frac{1}{\varepsilon}\nu(\frac{y}{\varepsilon})}>\frac{1}{2}\sin(\vartheta)\varepsilon^{-\beta}.
$$
In the same way, we get a similar lower bound for $\left|\lambda+\overline{\mu}\right|.$
Now we use (\ref{boitenoire}) in (\ref{avtfouriereps}) with the above estimates and get
\begin{equation}
\label{gdslambda1}
\begin{cases}
\|u\|_\infty \leq \varepsilon^\beta\frac{2MD^2}{\sin \vartheta}\left( \|U\|_\infty+\|v\|_\infty\right) \\
\|v\|_\infty \leq \varepsilon^\beta\frac{2M}{\sin \vartheta}\left( \|V\|_\infty+\frac{\left\Vert\mu\right\Vert_\infty}{\varepsilon}\left\Vert u\right\Vert_\infty\right).
\end{cases}
\end{equation}
Using the first equation of (\ref{gdslambda1}) in the second one yields
$$
\|v\|_\infty\lp1-\varepsilon^{2\beta-1}\left(\frac{2MD}{\sin \vartheta}\right)^2\left\Vert\mu\right\Vert_\infty\right)\leq
\varepsilon^\beta \frac{2M}{\sin\vartheta}\|V\|_\infty+\varepsilon^{2\beta-1}\left\Vert\mu\right\Vert_\infty \left(\frac{2MD}{\sin \vartheta}\right)^2\|U\|_\infty
$$
i.e., for $\varepsilon$ small enough,
\begin{equation}
\label{gdslambda2}
\|v\|_\infty \leq K_1\max(\varepsilon^\beta,\varepsilon^{2\beta-1})(\|V\|_\infty+\|U\|_\infty)
\end{equation}
with $K_1$ depending only on $D,\overline{\mu},\vartheta.$ In the same vein, using (\ref{gdslambda2}) in the second equation
of (\ref{gdslambda1}) produces the same estimate, and the proof is concluded.
\end{proof}
\subsection{Small values of $\left|\lambda\right|$}
The values are treated with the help of the Fourier transform in $x$-direction.
For $U\in \mathcal{C}_0(\mathbb{R})\cap L^1(\mathbb{R}),$ $V\in \mathcal{C}_0(\mathbb{R}^2)\cap L^1(\mathbb{R},L^\infty(\mathbb{R})),$
we define
$$
\hat{U}(\xi):=\int_{\mathbb{R}}e^{-ix\xi}U(x)dx \qquad \hat{V}(\xi,y):=\int_{\mathbb{R}}e^{-ix\xi}V(x,y)dx.
$$
\begin{prop}
\label{petitslambda}
There exist $\varepsilon_1$ a constant $C_2$ depending only on $D,$ $\overline{\mu}$ and $\vartheta$ such that for all $\varepsilon<\varepsilon_1,$ for $\beta>\frac{1}{2},$ $\gamma>0,$
such that $1-\frac{3}{2}(\beta+\gamma)>0,$ if $\lambda\in \Gamma_{r,\vartheta} \textrm{ and } |\lambda|<\varepsilon^{-\beta}$ then
$$
\left\Vert\left( R(\lambda,L_\varepsilon)-R(\lambda,L_0)\right)(U,V)\right\Vert_\infty\leq C_2\varepsilon^{1-\frac{3}{2}(\beta+\gamma)}
\left( \Vert\hat{U}\|_{L^\infty(\mathbb{R})}+\Vert\hat{V}\|_{L^\infty(\mathbb{R}^2)}\right).
$$
\end{prop}
\begin{cor}\label{corl1}
Under assumptions of Proposition \ref{petitslambda},
$$\left\Vert\left( R(\lambda,L_\varepsilon)-R(\lambda,L_0)\right)(U,V)\right\Vert_\infty\leq C_2\varepsilon^{1-\frac{3}{2}(\beta+\gamma)}
\left( \Vert U\Vert_{L^1(x)}+\left\Vert \left\Vert V\right\Vert_{L^\infty(y)}\right\Vert_{L^1(x)}\right).$$
\end{cor}
The proof requires two lemmas. First, we deal with the high frequencies
in Lemma \ref{gdesfrequences}, i.e. for $|\xi|\gg\varepsilon^{-\beta},$ using Lemma \ref{katoineq} in Appendix. Then,
in Lemma \ref{petitesfrequences}, we make
an almost explicit computation of the solutions for small values of $\lambda.$
\paragraph{Fourier transform of the equations}
Let us consider $U\in \mathcal{C}_0(\mathbb{R})\cap L^1(\mathbb{R})$ and $V\in \mathcal{C}_0(\mathbb{R}^2)\cap L^1(\mathbb{R},L^\infty(\mathbb{R})).$
For $\varepsilon>0$ and $\lambda\in\Gamma_{r,\vartheta},$ $|\lambda|<\varepsilon^{-\beta},$ Recall that
\begin{equation*}
\begin{cases}
(u,v)=R(\lambda,L_0)(U,V) \\
(u_\varepsilon,v_\varepsilon)=R(\lambda,L_\varepsilon)(U,V)
\end{cases}
\end{equation*}
which leads to the spectral problems (\ref{avtfourier0}) and (\ref{avtfouriereps}). The Fourier transforms $(\hat{u},\hat{v})$ and $(\hat{u}_\varepsilon,\hat{v}_\varepsilon)$
solve
\begin{equation}\label{apresfourier0}
\begin{cases}
(D\xi^2+\lambda+\overline{\mu}) \hat{u}(\xi) = \hat{v}(\xi,0) + \hat{U}(\xi) \\
(\xi^2+\lambda)\hat{v} - \partial_{yy}\hat{v}(\xi,y) = \hat{V}(\xi,y) \\
\hat{v}(\xi,0^+)=\hat{v}(\xi,0^-) \\
-(\partial_y v(\xi,0^+)-\partial_y v(\xi,0^-)) = \overline{\mu} \hat{u}(\xi)-\hat{v}(\xi,0)
\end{cases}
\end{equation}
and
\begin{equation}\label{apresfouriereps}
\begin{cases}
(D\xi^2+\lambda+\overline{\mu}) \hat{u}_\varepsilon(\xi) = \int\nu_\varepsilon(y)\hat{v}_\varepsilon(\xi,y)dy + \hat{U}(\xi) \\
(\xi^2+\lambda+\nu_\varepsilon(y)) \hat{v}_\varepsilon(\xi,y) -\partial_{yy} \hat{v}_\varepsilon(\xi,y) = \mu_\varepsilon(y)\hat{u}_\varepsilon(\xi)+\hat{V}(\xi,y).
\end{cases}
\end{equation}
\begin{lem}\label{gdesfrequences}
There exist $\varepsilon_2>0$ and a constant $C_3$ depending only on $\overline{\mu},D$ such that for all $\varepsilon<\varepsilon_2,$ for all $\xi$ with
$\xi^2\geq \varepsilon^{-\beta-\gamma}$ and $\lambda\in\Gamma_{r,\vartheta}$ with $|\lambda|<\varepsilon^{-\beta},$
\begin{align*}
|\hat{u}_\varepsilon(\xi)|+\|\hat{v}_\varepsilon(\xi)\|_\infty\leq \frac{C_3}{\xi^2}\left(|\hat{U}(\xi)|+\|\hat{V}(\xi)\|_\infty\right) \\
|\hat{u}(\xi)|+\|\hat{v}(\xi)\|_\infty\leq \frac{C_3}{\xi^2}\left(|\hat{U}(\xi)|
+\|\hat{V}(\xi)\|_\infty\right)
\end{align*}
where $\|.\|_\infty=\|.\|_{L^\infty(y)}.$
\end{lem}
\begin{proof}
We give the proof only for the nonlocal case, the local one being easier.
Combining the two equations of (\ref{apresfouriereps}), $\hat{v}_\varepsilon$ satisfies
\begin{equation}\label{apresfouriereps2}
-\partial_{yy}\hat{v}_\varepsilon(\xi,y)+\left(\xi^2+\lambda+\nu_\varepsilon(y)\right)\hat{v}_\varepsilon(\xi,y)=\hat{V}(\xi,y)+\frac{\mu_\varepsilon(y)}{D\xi^2+\lambda+\overline{\mu}}\left(\hat{v}(\xi,0)+\hat{U}(\xi)\right).
\end{equation}
As $\gamma>0$ and considering the hypotheses on $\lambda$ and $\xi,$ there exists $k>0$ such that, for $\varepsilon$ small enough, we have:
\begin{equation*}
\min \left\{ \Re{\xi^2+\lambda},\left| D\xi^2+\lambda+\overline{\mu}\right|\right\} >k^2\xi^2.
\end{equation*}
Now, we apply Lemma \ref{katoineq} in Appendix. It gives:
\begin{equation*}
\left|\hat{v}_\varepsilon(\xi,y)\right| \leq \frac{1}{2k|\xi|}\int_\mathbb{R} e^{-k\xi|z|}\left(\hat{V}(\xi,z-y)+\frac{\mu_\varepsilon(z-y)}{k^2\xi^2}\left( \hat{v}(\xi,0)+\hat{U}(\xi)\right) \right) dz .
\end{equation*}
A rough majoration yields
\begin{equation*}
\left\Vert\hat{v}_\varepsilon(\xi)\right\Vert_\infty \leq \frac{1}{k^2\xi^2}\left\Vert\hat{V}(\xi)\right\Vert_\infty+\frac{\overline{\mu}}{k^3|\xi|^3}\left(\left|\hat{v}(\xi,0)\right|+\left|\hat{U}(\xi)\right|\right)
\end{equation*}
which, as $|\xi|>\varepsilon^{-\frac{1}{2}(\beta+\gamma)},$ provides the desired estimate on $\left\Vert\hat{v}_e(\xi)\right\Vert_\infty.$ The estimate on $|\hat{u}_\varepsilon|$ follows from
the first equation of (\ref{apresfouriereps}), and the proof of Lemma \ref{gdesfrequences} is concluded.
\end{proof}
Now that we are done with the high frequencies, to finish the proof of Proposition \ref{petitslambda},
it remains to control the lower frequencies. This is the purpose of the following Lemma.
\begin{lem}
\label{petitesfrequences}
There exist $\varepsilon_3>0$ and a constant $C_5$, for all $\varepsilon<\varepsilon_3,$ for all $\lambda\in\Gamma_{r,\vartheta}$ with $|\lambda|<\varepsilon^{-\beta},$
for all $\xi$ with $\xi^2<\varepsilon^{-(\beta+\gamma)},$
\begin{align*}
\|\hat{v}_\varepsilon(\xi)-\hat{v}(\xi)\|_{L^\infty(y)} & \leq C_5 \varepsilon^{1-(\beta+\gamma)}\left(|\hat{U}(\xi)|+\|\hat{V}(\xi)\|_{L^\infty(y)}\right) \\
\left|\hat{u}_\varepsilon(\xi)-\hat{u}(\xi)\right| & \leq C_5 \varepsilon^{1-(\beta+\gamma)}\left(|\hat{U}(\xi)|+\|\hat{V}(\xi)\|_{L^\infty(y)}\right).
\end{align*}
\end{lem}
\paragraph{Proof of Proposition \ref{petitslambda} thanks to Lemma \ref{petitesfrequences}}
With the same notations,
\begin{equation*}
\left\Vert\left( R(\lambda,L_\varepsilon)-R(\lambda,L_0)\right)(U,V)\right\Vert_\infty=\max \left(\left\Vert u-u_\varepsilon\right\Vert_{L^\infty(\mathbb{R})},\left\Vert v-v_\varepsilon\right\Vert_{L^\infty(\mathbb{R}^2)}\right).
\end{equation*}
Let us prove the domination for $\left\Vert v-v_\varepsilon\right\Vert_{L^\infty(\mathbb{R}^2)},$ the one in $(u-u_\varepsilon)$ being similar. For $(x,y)\in\mathbb{R}^2,$
\begin{align}
(v-v_\varepsilon)(x,y) & = \frac{1}{2\pi}\int_\mathbb{R} e^{ix.\xi}\left( \hat{v}(\xi,y)-\hat{v}_\varepsilon(\xi,y)\right) d\xi. \nonumber \\
\left| (v-v_\varepsilon)(x,y)\right| & \leq \frac{1}{2\pi}\int_\mathbb{R} \left| \hat{v}(\xi,y)-\hat{v}_\varepsilon(\xi,y)\right| d\xi \nonumber \\
& \leq \frac{1}{2\pi} \int_{|\xi|\geq\varepsilon^{-\frac{1}{2}(\beta+\gamma)}} \left\Vert \hat{v}(\xi)\right\Vert_{L^\infty(y)}+\left\Vert \hat{v}_\varepsilon(\xi)\right\Vert_{L^\infty(y)} d\xi \label{controle1} \\
& + \frac{1}{2\pi} \int_{|\xi|<\varepsilon^{-\frac{1}{2}(\beta+\gamma)}} \left\Vert \hat{v}(\xi)-\hat{v}_\varepsilon(\xi)\right\Vert_{L^\infty(y)} d\xi. \label{controle2}
\end{align}
Now, from Lemma \ref{gdesfrequences}, we have:
\begin{align*}
(\ref{controle1}) & \leq \frac{C_3}{\pi}\left( |\hat{U}(\xi)|+\|\hat{V}(\xi)\|_\infty\right) \int_{\varepsilon^{-\frac{1}{2}(\beta+\gamma)}}^{+\infty} \frac{d\xi}{\xi^2} \\
& \leq \frac{C_3}{\pi}\varepsilon^{\frac{1}{2}(\beta+\gamma)}\left( |\hat{U}(\xi)|+\|\hat{V}(\xi)\|_\infty\right).
\end{align*}
From Lemma \ref{petitesfrequences}, we have:
\begin{align*}
(\ref{controle2}) & \leq \frac{C_5}{2\pi}\varepsilon^{1-(\beta+\gamma)}\left(|\hat{U}(\xi)|+\|\hat{V}(\xi)\|_{L^\infty(y)}\right)
\int_{-\varepsilon^{-\frac{1}{2}(\beta+\gamma)}}^{\varepsilon^{-\frac{1}{2}(\beta+\gamma)}} 1 d\xi \\
& \leq \frac{C_5}{\pi}\varepsilon^{1-\frac{3}{2}(\beta+\gamma)}\left(|\hat{U}(\xi)|+\|\hat{V}(\xi)\|_{L^\infty(y)}\right).
\end{align*}
Finally, from the choice of $\beta,\gamma,$ $\frac{\beta+\gamma}{2}>1-\frac{3}{2}(\beta+\gamma)$ and we have the required estimate.
\qed
\subsection*{Proof of Lemma \ref{petitesfrequences}}
The proof requires some explicit computations of the solutions of the spectral problems and is a bit long. First, we compute
$(\hat{u},\hat{v}),$ solution of (\ref{apresfourier0}), introducing four constants $K_1^+,$ $K_2^+,$ $K_1^-,$ $K_2^-$.
Secondly, we do the same for $(\hat{u}_\varepsilon,\hat{v}_\varepsilon)$ outside the strip $\mathbb{R}\times(-\varepsilon,\varepsilon).$
This leads us to introduce four constants $K_1^+(\varepsilon),$ $K_2^+(\varepsilon),$ $K_1^-(\varepsilon),$ and $K_2^-(\varepsilon)$ which determine the behaviour
of $\hat{v}_\varepsilon$ outside the strip. Then, we show that it is enough to focus on $K^\pm_2(\varepsilon)$ to get a global control of $\hat{v}_\varepsilon.$
In a short paragraph, we establish that the derivative $\partial_y \hat{v}_\varepsilon$ is controlled by the norm of $\hat{v}_\varepsilon.$ The last paragraph of the proof
is devoted to the computation of $K^\pm_2(\varepsilon)$ and an estimate of its difference with $K_2^\pm.$
\paragraph{Explicit computation of $(\hat{u},\hat{v})$}
Our choice of $\Gamma_{r,\vartheta}$ allows us to choose a unique determination of the complex logarithm for all systems. From now and until the end of
this proof we set for all $\xi$ and $\lambda$ satisfying the hypotheses of Lemma \ref{petitesfrequences}
\begin{equation}
\label{alpha}
\alpha:=\sqrt{\xi^2+\lambda},\ \Re\alpha>0
\end{equation}
the unique complex root of $(\xi^2+\lambda)$ with positive real part and
\begin{equation}
\label{omega}
\omega:=D\xi^2+\overline{\mu}+\lambda.
\end{equation}
The choice of $\varphi,\theta$ (see the hypotheses of Proposition \ref{sectorial})
yields $\displaystyle \min_{\lambda\in\Gamma_{r, \vartheta}} |\lambda|>\max (\sqrt{2},2\overline{\mu}).$
Moreover, we have $\xi^2>0$ and $D\xi^2+\overline{\mu}>0.$ Then,
\begin{equation}
\forall \overline{\lambda}\in \Gamma_{r, \vartheta},\ \max (\sqrt{2},2\overline{\mu}) < \min_{\lambda\in\Gamma_{r, \vartheta}} |\lambda| \leq \min (D\xi^2+\overline{\mu}+\overline{\lambda},\xi^2+\overline{\lambda}).
\end{equation}
Hence, we can assert:
\begin{equation}\label{controlomega}
\forall\lambda\in\Gamma_{r, \vartheta},\xi\in\mathbb{R}, \ 2< 2+\frac{1}{\alpha}\left( 1-\frac{\overline{\mu}}{\omega}\right)<2+2^{-\frac{1}{4}}+\frac{1}{\sqrt{2\overline{\mu}}}.
\end{equation}
Moreover, considering the hypotheses on $\xi$ and $\lambda,$ there exists a constant $k>0$ such that, for $\varepsilon$ small enough,
\begin{equation}\label{controlalpha}
1<|\alpha|<k\varepsilon^{-\frac{1}{2}(\beta+\gamma)},\qquad 2\overline{\mu}\leq|\omega|<k\varepsilon^{-(\beta+\gamma)},\qquad |e^{\varepsilon\alpha}|<2.
\end{equation}
The first equation of (\ref{apresfourier0}) gives
$$
\hat{u}(\xi)=\frac{1}{\omega}\left(\hat{v}(\xi,0)+\hat{U}(\xi)\right).
$$
Integrating the second equation of (\ref{apresfourier0}) yields the existence of four
constants $K_1^+,$ $K_2^+,$ $K_1^-,$ $K_2^-$, depending on $\xi,$ such that
\begin{equation}\label{vh0}
\left\{
\begin{array}{ll}
\hat{v}(\xi,y) = e^{\alpha y}\left( K_1^+ -\frac{1}{2\alpha}\int_0^y e^{-\alpha z}\hat{V}(\xi,z)dz\right) +
e^{-\alpha y}\left( K_2^+ +\frac{1}{2\alpha}\int_0^y e^{\alpha z}\hat{V}(\xi,z)dz\right) & y>0 \\
\hat{v}(\xi,y) = e^{-\alpha y}\left( K_1^- -\frac{1}{2\alpha}\int_y^0 e^{\alpha z}\hat{V}(\xi,z)dz\right) +
e^{\alpha y}\left( K_2^- +\frac{1}{2\alpha}\int_y^0 e^{-\alpha z}\hat{V}(\xi,z)dz\right) & y<0.
\end{array}
\right.
\end{equation}
The integrability of $\hat{v}$ in $y$ gives
\begin{equation}
\label{k10}
K_1^+=\frac{1}{2\alpha}\int_0^\infty e^{-\alpha z}\hat{V}(\xi,z)dz, \qquad
K_1^-=\frac{1}{2\alpha}\int_{-\infty}^0 e^{\alpha z}\hat{V}(\xi,z)dz.
\end{equation}
The continuity and exchange conditions at $y=0$ impose
\begin{equation}
\begin{cases}
K_1^+ +K_2^+ = K_1^- +K_2^- \\
\alpha \left( K_2^+-K_1^++K_2^--K_1^-\right) = \frac{\overline{\mu}}{\omega}\left( K_1^++K_2^++\hat{U}(\xi)\right)-K_1^+-K_2^+.
\end{cases}
\end{equation}
Combining these two equations yields
\begin{equation}\label{k20}
\begin{cases}
K_2^+\left( 2+\frac{1}{\alpha}\left( 1-\frac{\overline{\mu}}{\omega}\right)\rp = 2K_1^-+K_1^+\frac{1}{\alpha}\left(\frac{\overline{\mu}}{\omega}-1\right)+\frac{\overline{\mu}}{\alpha\omega}\hat{U}(\xi) \\
K_2^-\left( 2+\frac{1}{\alpha}\left( 1-\frac{\overline{\mu}}{\omega}\right)\rp = 2K_1^++K_1^-\frac{1}{\alpha}\left(\frac{\overline{\mu}}{\omega}-1\right)+\frac{\overline{\mu}}{\alpha\omega}\hat{U}(\xi).
\end{cases}
\end{equation}
From (\ref{controlomega}), the above system (\ref{k20}) is well-posed.
From (\ref{vh0}), (\ref{k10}) and (\ref{k20}) we have an explicit formula for $(\hat{u}(\xi),\hat{v}(\xi)).$
\paragraph{Study of $(\hat{u}_\varepsilon,\hat{v}_\varepsilon)$}
\subparagraph{Explicit formula} In the same way as above, the first equation of (\ref{apresfouriereps}) yields
$$
\hat{u}_\varepsilon(\xi)=\frac{1}{\omega}\left(\int_{\mathbb{R}}\nu_\varepsilon(y)\hat{v}_\varepsilon(\xi,y)dy+\hat{U}(\xi)\right).
$$
Integrating the second equation of (\ref{apresfouriereps}) leads us to set four constants
$K_1^+(\varepsilon),$ $K_2^+(\varepsilon),$ $K_1^-(\varepsilon),$ $K_2^-(\varepsilon)$, depending on $\varepsilon$ and $\xi$,
such that
\begin{align}
y>\varepsilon: \ \hat{v}_\varepsilon(\xi,y) = & e^{\alpha y}\left( K_1^+(\varepsilon) -\frac{1}{2\alpha}\int_\varepsilon^y e^{-\alpha z}\hat{V}(\xi,z)dz\right) + \nonumber \\\label{expliciteps1}
& e^{-\alpha y}\left( K_2^+(\varepsilon) +\frac{1}{2\alpha}\int_\varepsilon^y e^{\alpha z}\hat{V}(\xi,z)dz\right) \\
y<-\varepsilon: \ \hat{v}_\varepsilon(\xi,y) = & e^{-\alpha y}\left( K_1^-(\varepsilon) -\frac{1}{2\alpha}\int_y^{-\varepsilon} e^{\alpha z}\hat{V}(\xi,z)dz\right) + \nonumber \\\label{expliciteps2}
& e^{\alpha y}\left( K_2^-(\varepsilon) +\frac{1}{2\alpha}\int_y^{-\varepsilon} e^{-\alpha z}\hat{V}(\xi,z)dz\right) .
\end{align}
For the same integrability reason as in the limit case, we already have an explicit
formula for $K_1^\pm(\varepsilon):$
\begin{equation}\label{k1eps}
K_1^+(\varepsilon)=\frac{1}{2\alpha}\int_\varepsilon^\infty e^{-\alpha z}\hat{V}(\xi,z)dz, \qquad
K_1^-(\varepsilon)=\frac{1}{2\alpha}\int_{-\infty}^{-\varepsilon} e^{\alpha z}\hat{V}(\xi,z)dz,
\end{equation}
which immediately gives us a uniform boundary and, combining with (\ref{k10}), the
first following estimate
\begin{equation}\label{estimeek1}
\left| K_1^\pm-K_1^\pm(\varepsilon)\right|\leq \frac{\varepsilon}{2\alpha}\left\Vert\hat{V}(\xi)\right\Vert_{L^\infty(y)}.
\end{equation}
It remains to determine $K_2^\pm(\varepsilon).$ We set
\begin{equation}\label{newvariable}
z=\frac{y}{\varepsilon} \textrm{ and } \hat{v}_\varepsilon(z):=\hat{v}_\varepsilon(y) \textrm{ for }z\in(-1,1).
\end{equation}
The equation for $\hat{v}_\varepsilon(\xi,z)$, now set for $z\in(-1,1),$ is
\begin{equation}\label{eqeps}
(\varepsilon^2\xi^2+\varepsilon^2\lambda+\varepsilon\nu(z)) \hat{v}_\varepsilon(\xi,z) -\partial_{zz} \hat{v}_\varepsilon(\xi,z) =
\varepsilon\mu(z)\frac{1}{\omega}\left(\int_{\mathbb{R}}\nu(z)\hat{v}_\varepsilon(\xi,z)dz+\hat{U}(\xi)\right)+\varepsilon^2\hat{V}(\xi,\varepsilon z).
\end{equation}
Specifying (\ref{expliciteps1}) and (\ref{expliciteps2}) at $y=\varepsilon$
and $y=-\varepsilon$ gives us the two following boundary conditions for (\ref{eqeps}):
\begin{equation}\label{dirichleteps}
\begin{cases}
\hat{v}_\varepsilon(1,\xi) &=K_1^+(\varepsilon)e^{\alpha\varepsilon}+K_2^+(\varepsilon)e^{-\alpha\varepsilon} \\
\hat{v}_\varepsilon(-1,\xi) &=K_1^-(\varepsilon)e^{\alpha\varepsilon}+K_2^-(\varepsilon)e^{-\alpha\varepsilon}.
\end{cases}
\end{equation}
\begin{equation}\label{neumaneps}
\begin{cases}
\partial_z \hat{v}_\varepsilon(1,\xi)& =\varepsilon\alpha\left( K_1^+(\varepsilon)e^{\alpha\varepsilon}-K_2^+(\varepsilon)e^{-\alpha\varepsilon}\right) \\
\partial_z \hat{v}_\varepsilon(-1,\xi)& =\varepsilon\alpha\left( K_2^-(\varepsilon)e^{-\alpha\varepsilon}-K_1^-(\varepsilon)e^{\alpha\varepsilon}\right).
\end{cases}
\end{equation}
\subparagraph{Blow-up condition for $\hat{v}_\varepsilon$} From now,
we are only considering the rescaled equation (\ref{eqeps}) with the boundary conditions
(\ref{dirichleteps}) and (\ref{neumaneps}). Hence, all functions and derivatives
are to be considered in these rescaled variables (\ref{newvariable}).
We first show that the $L^\infty(z)-$norm of $\hat{v}_\varepsilon$ is controlled by $K_2^\pm(\varepsilon).$
We have:
\begin{align*}
\hat{v}_\varepsilon(z)-\hat{v}_\varepsilon(-1) &= (z+1)\hat{v}_\varepsilon'(-1)+\int_{-1}^{z}\int_{-1}^{s}\hat{v}_\varepsilon''(u)duds \\
&= (z+1)\hat{v}_\varepsilon'(-1)+\int_{-1}^{z}\int_{-1}^{s}\hat{v}_\varepsilon(u)\left( \varepsilon\nu(u)+\varepsilon^2\xi^2+\varepsilon^2\lambda\right) duds \\
& - \int_{-1}^{z}\int_{-1}^{s}\varepsilon\frac{\mu(u)}{\omega}\left( \int\nu\hat{v}_\varepsilon+\hat{U}(\xi)\right)+\varepsilon^2\hat{V}(\xi,\varepsilon u)duds.
\end{align*}
Hence
\begin{align*}
\|\hat{v}_\varepsilon\|_{L^\infty(-1,1)} \leq & \left|\hat{v}_\varepsilon(-1)\right|+2\left|\hat{v}_\varepsilon'(-1)\right|+\varepsilon\|\hat{v}_\varepsilon\|_\infty\left( 2+\frac{2\overline{\mu}}{|\omega|}+4\varepsilon\left|\xi^2+\lambda\right|\right) \\
& +\varepsilon\frac{2\overline{\mu}}{|\omega|}\left|\hat{U}(\xi)\right|+4\varepsilon^2\|\hat{V}(\xi)\|_\infty \\
\leq & \left(|K_1^-(\varepsilon)|+|K_2^-(\varepsilon)|\right)(2+4|\varepsilon\alpha|)+\varepsilon\|\hat{v}_\varepsilon\|_\infty\left( 4+4k^2\varepsilon^{1-(\beta+\gamma)}\right) \\
& +2\varepsilon\left|\hat{U}(\xi)\right|+4\varepsilon^2\|\hat{V}(\xi)\|_\infty.
\end{align*}
Now let us recall that $K_1^-(\varepsilon)$ is uniformly bounded in $\varepsilon$ from (\ref{estimeek1}),
we have $\beta+\gamma<1,$ and $\xi\mapsto(\hat{U}(\xi),\hat{V}(\xi))$ is uniformly bounded.
These facts, combined with the above inequality and the symmetry of the problem, allow us to assert that
\begin{equation}\label{borneK2}
\left(\underset{\varepsilon\to0}{\lim\sup}\|\hat{v}_\varepsilon\|_{L^\infty(y)}=+\infty \right)
\Leftrightarrow
\left(\underset{\varepsilon\to0}{\lim\sup}\left| K_2^-(\varepsilon)\right|=+\infty \right)
\Leftrightarrow
\left(\underset{\varepsilon\to0}{\lim\sup}\left| K_2^+(\varepsilon)\right|=+\infty \right)
\end{equation}
uniformly in $\xi\in\mathbb{R}.$
\subparagraph{Control of the derivative}
In the same way as above we get a control of $\|\hat{v}_\varepsilon'\|_\infty$ by $\|\hat{v}_\varepsilon\|_\infty$ with
a simple integration of (\ref{eqeps}):
\begin{align*}
\hat{v}_\varepsilon'(z)-\hat{v}_\varepsilon'(-1) = & \varepsilon\int_{-1}^{z}\hat{v}_\varepsilon(s)\left( \nu(s)+\varepsilon\xi^2+\varepsilon\lambda\right)-\frac{\mu(s)}{\omega}\left(\int\nu\hat{v}_\varepsilon+\hat{U}(\xi)\right)-\varepsilon\hat{V}(\xi,\varepsilon s)ds \\
\left| \hat{v}_\varepsilon'(s)-\hat{v}_\varepsilon'(-1)\right| \leq & \varepsilon\|\hat{v}_\varepsilon\|_\infty\left( 2+k^2\varepsilon^{1-(\beta+\gamma)})\right)+\varepsilon\left( |\hat{U}(\xi)|+4\varepsilon\|\hat{V}(\xi)\|_\infty\right).
\end{align*}
So for $\varepsilon$ small enough,
\begin{equation}\label{controlderivee}
\|\hat{v}_\varepsilon'\|_{L^\infty(-1,1)}\leq 8\varepsilon\left(\|\hat{v}_\varepsilon\|_\infty+1\right)+4\varepsilon\left( |\hat{U}(\xi)|+\varepsilon\|\hat{V}(\xi)\|_\infty\right).
\end{equation}
\subparagraph{Explicit computation of $K_2^\pm(\varepsilon)$}We are now ready to prove
Lemma \ref{petitesfrequences}. The only argument we will use is, once again, an
integration of (\ref{eqeps}). It yields:
\begin{align*}
\hat{v}_\varepsilon(1)-\hat{v}_\varepsilon(-1) = & 2\hat{v}_\varepsilon'(-1)+\varepsilon\int_{-1}^1\int_{-1}^z\hat{v}_\varepsilon(s)\left(\nu(s)+\varepsilon\xi^2+\varepsilon\lambda\right) dsdz \\
& -\varepsilon\int_{-1}^1\int_{-1}^z\frac{\mu(s)}{\omega}\left(\int\nu\hat{v}_\varepsilon+\hat{U}(\xi)\right)+\varepsilon\hat{V}(\xi,\varepsilon s)dsdz.
\end{align*}
Hence, with (\ref{dirichleteps}) and the estimate (\ref{controlalpha}) on $\alpha$, we have
\begin{multline}\label{calculk2}
\Big\vert e^{-\alpha\varepsilon}\left( K_2^+(\varepsilon)-K_2^-(\varepsilon)\right) - e^{\alpha\varepsilon}\left( K_1^-(\varepsilon)-K_1^+(\varepsilon)\right) \Big\vert \\
\leq 2\left|\hat{v}_\varepsilon'(-1)\right| +\varepsilon\left\Vert\hat{v}_\varepsilon\right\Vert_\infty\left( 6+4k^2\varepsilon^{1-(\beta+\gamma)}\right)
+\varepsilon\left( 4\left|\hat{U}(\xi)\right|+4\varepsilon\left\Vert\hat{V}(\xi)\right\Vert_\infty\right).
\end{multline}
In the same fashion,
\begin{equation*}
\hat{v}_\varepsilon'(1)-\hat{v}_\varepsilon'(-1)=\varepsilon\int_{-1}^1 \hat{v}_\varepsilon(z)\left(\nu(z)+\varepsilon(\xi^2+\lambda)\right)-\frac{\mu(z)}{\omega}\left(\int\nu\hat{v}_\varepsilon+\hat{U}\right)-\hat{V}(\varepsilon z) dz.
\end{equation*}
Hence, using (\ref{neumaneps}),
\begin{multline}\label{calculK21}
\left| \alpha e^{\alpha\varepsilon}\left( K_1^+(\varepsilon)+K_1^-(\varepsilon)\right) -\alpha e^{-\alpha\varepsilon}\left( K_2^+(\varepsilon)+K_2^-(\varepsilon)\right) -
\left( 1-\frac{\overline{\mu}}{\omega}\right)\int\nu\hat{v}_\varepsilon + \frac{\overline{\mu}}{\omega}\hat{U}(\xi)\right| \\
\leq 2k^2\varepsilon^{1-(\beta+\gamma)}\left\Vert\hat{v}_\varepsilon\right\Vert_\infty+2\varepsilon\left\Vert\hat{V}(\xi)\right\Vert_\infty.
\end{multline}
Now we just do a Taylor-Lagrange expansion: for all $\varepsilon,\xi,\lambda,$ there exists a function $c:[-1,1]\mapsto[-1,1]$ such that
\begin{equation}\label{taylornuv}
\int_{-1}^{1}\nu(z)\hat{v}_\varepsilon(z)dz = \left( K_1^+(\varepsilon)e^{\alpha\varepsilon}+K_2^+(\varepsilon)e^{-\alpha\varepsilon}\right)+\int_{-1}^{1}\hat{v}_\varepsilon'(c(z))(z-1)\nu(z)dz.
\end{equation}
Using (\ref{taylornuv}) in (\ref{calculK21}) gives
\begin{multline}\label{calculk22}
\Big\vert e^{-\alpha\varepsilon}K_2^+(\varepsilon)\left(\alpha+\left( 1-\frac{\overline{\mu}}{\omega}\right)\rp + \alpha e^{-\alpha\varepsilon}K_2^-(\varepsilon)
+ e^{\alpha\varepsilon}K_1^+(\varepsilon)\left(\lp 1-\frac{\overline{\mu}}{\omega}\right)-\alpha\right) \\ - \alpha e^{\alpha\varepsilon}K_1^-(\varepsilon)
- \frac{\overline{\mu}}{\omega}\hat{U}(\xi) \Big\vert \leq 2\left\Vert\hat{v}'_\varepsilon\right\Vert_\infty + 2k^2\varepsilon^{1-(\beta+\gamma)}\left\Vert\hat{v}_\varepsilon\right\Vert_\infty+2\varepsilon\left\Vert\hat{V}(\xi)\right\Vert_\infty.
\end{multline}
At this point, we have a system of two inequations (\ref{calculk2}) and (\ref{calculk22}) which will allow us to compute
an approximation of $K_2^+(\varepsilon)$ and $K_2^-(\varepsilon).$ We will give details only for $K_2^+(\varepsilon),$ the other case being similar.
Let us consider $e^{\alpha\varepsilon}\left[(\ref{calculk2})-\frac{1}{\alpha}(\ref{calculk22})\right],$ still using (\ref{controlalpha}).
This reads
\begin{multline*}
\left| K_2^+(\varepsilon)\left( 2+\frac{1}{\alpha}\left( 1-\frac{\overline{\mu}}{\omega}\right)\rp - 2e^{2\alpha\varepsilon}K_1^-(\varepsilon) - e^{2\alpha\varepsilon}K_1^+(\varepsilon)\frac{1}{\alpha}\left(\frac{\overline{\mu}}{\omega}-1\right)
- e^{\alpha\varepsilon}\frac{\overline{\mu}}{\alpha\omega}\hat{U}(\xi) \right| \\ \leq
4\left|\hat{v}_\varepsilon'(-1)\right| +\varepsilon\left\Vert\hat{v}_\varepsilon\right\Vert_\infty\left( 6+4k^2\varepsilon^{1-(\beta+\gamma)}\right)
+2\varepsilon\left( 4\left|\hat{U}(\xi)\right|+4\varepsilon\left\Vert\hat{V}(\xi)\right\Vert_\infty\right) + \\
4\left\Vert\hat{v}'_\varepsilon\right\Vert_\infty + 4k^2\varepsilon^{1-(\beta+\gamma)}\left\Vert\hat{v}_\varepsilon\right\Vert_\infty+4\varepsilon\left\Vert\hat{V}(\xi)\right\Vert_\infty.
\end{multline*}
Let us recall that
(\ref{controlderivee}) gives us a control of $\|\hat{v}_\varepsilon'\|_{L^\infty(z)}$
by $\varepsilon\|\hat{v}\|_{L^\infty(z)}$ in the strip $[-1,1].$
Thus, for some constant $C_6,$ we have:
\begin{multline}\label{calculk2fin}
\left| K_2^+(\varepsilon)\left( 2+\frac{1}{\alpha}\left( 1-\frac{\overline{\mu}}{\omega}\right)\rp - 2K_1^-(\varepsilon) - K_1^+(\varepsilon)\frac{1}{\alpha}\left(\frac{\overline{\mu}}{\omega}-1\right)
- \frac{\overline{\mu}}{\alpha\omega}\hat{U}(\xi) \right| \\ \leq
C_6\left( |\varepsilon\alpha|\left( |K_1^+(\varepsilon)|+|K_1^-(\varepsilon)|\right)+\varepsilon^{1-(\beta+\gamma)}\left\Vert\hat{v}_\varepsilon\right\Vert_\infty+\varepsilon\left|\hat{U}(\xi)\right|+\varepsilon\left\Vert\hat{V}(\xi)\right\Vert_\infty\right).
\end{multline}
The last expression (\ref{calculk2fin})
combined with the control of $\left\Vert\hat{v}_\varepsilon\right\Vert_\infty$ by $K_2^+(\varepsilon)$ given in (\ref{borneK2}) allows us to assert that
$\left(\|z\mapsto \hat{v}_\varepsilon(\xi,z)\|_{L^\infty(-1,1)}\right)_\varepsilon$ is uniformly bounded on $\varepsilon,\xi,\lambda$
under assumptions of Lemma \ref{petitesfrequences}, and so is
$\left(\|y\mapsto \hat{v}_\varepsilon(\xi,y)\|_{L^\infty(\mathbb{R})}\right)_\varepsilon$ with (\ref{expliciteps1}) and
(\ref{expliciteps2}). Comparing (\ref{calculk2fin}) with (\ref{k20}) and using the previous estimate
(\ref{estimeek1}) and the explicit formula for $K_1^\pm(\varepsilon)$ yields, for some constant $C_7:$
\begin{equation}\label{estimeek2}
\left| K_2^+(\varepsilon)-K_2^+\right|\leq C_7\varepsilon^{1-\beta-\gamma}\left(\|\hat{v}(\xi)\|_{L^\infty(y)}+\left|\hat{U}(\xi)\right|
+\|\hat{V}(\xi)\|_{L^\infty(y)}\right).
\end{equation}
Now we are done with the rescaled variables.
To conclude the proof of Lemma \ref{petitesfrequences},
we compute directly the difference from (\ref{vh0}) and (\ref{expliciteps1}), (\ref{expliciteps2}).
We have the explicit formulas (\ref{k10}) and (\ref{k1eps}), the other terms being treated by (\ref{estimeek2}).
As for our previous estimate (\ref{estimeek2}), we will only focus
on the case $y>0,$ the other one $y<0$ being similar. All in all, we have
\begin{align*}
\left|\hat{v}_\varepsilon(\xi,y)-\hat{v}(\xi,y)\right| & \leq e^{-\alpha y}\left| K_2^+(\varepsilon)-K_2^+\right|+
\frac{1}{|2\alpha|}\int_0^{\varepsilon}\left| e^{\alpha(z-y)}\hat{V}(\xi,z)\right| dz \\
& \leq C_7\varepsilon^{1-\beta-\gamma}\left(\|\hat{v}(\xi)\|_\infty+|\hat{U}(\xi)|
+2\|\hat{V}(\xi)\|_\infty\right)
\end{align*}
and the proof of Lemma \ref{petitesfrequences} is finished.
\qed
\section{Finite time convergence}\label{sectionconvsol}
In this section, we finish the proof of Theorem \ref{convsol}. The first ingredient
is Proposition \ref{cordif} which is a corollary of our estimates on the resolvents. It gives a control
of the semigroups generated by the linear operators. The second ingredient is
Lemma \ref{decroissancesolutions} which gives some $L^\infty$ and decay estimates on the solutions.
At last, we will use these two ingredients in a Gronwall argument to deal with the nonlinearity.
\subsection{Difference between the semigroups}
Combined with the explicit formula (\ref{semigroup}), the results
given in Lemma \ref{grandslambda} and Corollary \ref{corl1} allow us to assert
the following estimate on the difference between the analytic semigroups.
\begin{prop}\label{cordif}
Let $t\in (0,T),$ $\beta>\frac{1}{2}$ and $\gamma>0$ such that $1-\frac{3}{2}(\beta+\gamma)>0.$ There exists a constant $C_8$ depending only on
$r, \vartheta,D,\overline{\mu}$ such that, for $\varepsilon$ small enough,
\begin{align*}
\left\Vert\left( e^{tL_0}-e^{tL_\varepsilon}\right)\left( U,V\right)\right\Vert_\infty \leq &
\varepsilon^{1-\frac{3}{2}(\beta+\gamma)}\left(\Vert U\Vert_{L^1(x)}+\left\Vert \left\Vert V\right\Vert_{L^\infty(y)}\right\Vert_{L^1(x)}\right) C_8\left( e^{TC_8}+\frac{1}{t}\right) \\
& + \varepsilon^{2\beta-1}\left\Vert\left( U,V\right)\right\Vert_\infty \frac{C_8}{t}e^{-\frac{t}{C_8\varepsilon^\beta}}.
\end{align*}
\end{prop}
\begin{proof}
\begin{align}
\left\Vert\left( e^{tL_0}-e^{tL_\varepsilon}\right)\left( U,V\right)\right\Vert_\infty \leq & \frac{1}{2\pi}\int_{\Gamma}|e^{t\lambda}|.
\left\Vert\left( R(\lambda,L_0)-R(\lambda,L_\varepsilon)\right)\left( U,V\right)\right\Vert_\infty d\lambda \nonumber \\
\leq & \frac{1}{2\pi}\int_{\lambda\in\Gamma,|\lambda|>\varepsilon^{-\beta}}|e^{t\lambda}|.\left(\left\Vert R(\lambda,L_0)\right\Vert+\left\Vert R(\lambda,L_\varepsilon)\right\Vert\right) \left\Vert(U,V)\right\Vert_\infty d\lambda \label{ligne2} \\
& + \frac{1}{2\pi}\int_{\lambda\in\Gamma,|\lambda|<\varepsilon^{-\beta}}|e^{t\lambda}|.\left\Vert\left( R(\lambda,L_0)-R(\lambda,L_\varepsilon)\right)\left((U,V)\right)\right\Vert_\infty d\lambda. \label{ligne3}
\end{align}
We recall that $\frac{\pi}{2}<\vartheta<\frac{3\pi}{4}.$ Hence, for large $\lambda,$ the curve $\Gamma_{r,\vartheta}$
lies in the half-plane $\left\{ z,\Re z <0\right\}.$
From Lemma \ref{grandslambda} (and Proposition \ref{sectorial} for $L_0$), the
first term of the right handside of the above inequality satisfies, for some constant $C,$
$$
(\ref{ligne2}) \leq 2\int_{s>\varepsilon^{-\beta}} C e^{-ts}\varepsilon^{2\beta-1}\left\Vert\left( U,V\right)\right\Vert_\infty ds.
$$
The second term satisfies from Corollary \ref{corl1}
$$
(\ref{ligne3}) \leq \varepsilon^{1-\frac{3}{2}(\beta+\gamma)}
\left( \Vert U\Vert_{L^1(x)}+\left\Vert \left\Vert V\right\Vert_{L^\infty(y)}\right\Vert_{L^1(x)}\right) \int_{\lambda\in\Gamma,|\lambda|<\varepsilon^{-\beta}}|C e^{t\lambda}|d\lambda.
$$
It remains to notice that $\Gamma\cap \{z,\ \Re z\geq0\}$ is bounded, and the proof of Proposition \ref{cordif} is complete.
\end{proof}
Remark that $e^{tL_\varepsilon},e^{tL_0}\to Id$ as $t\to0.$ So the estimate given in Proposition \ref{cordif} is far from optimal, especially for small $t.$
But it will be enough for our purpose.
\subsection{Uniform decay in $x$}
\begin{lem}\label{decroissancesolutions}
Let $(u,v)(t)$ be the solution of (\ref{BRReq2}), and, for all $\varepsilon\in(0,1),$ $(u_\varepsilon,v_\varepsilon)(t)$ the solution
of (\ref{RPeps}), both with initial datum $(u_0,v_0).$ Then, there exists $K_2,\overline{\lambda},\overline{c}>0$ independent of $\varepsilon$
such that for all
$(x,y)\in\mathbb{R}^2,t>0,$
$$
\max\ \left( u(t,x),u_\varepsilon(t,x),v(t,x,y),v_\varepsilon(t,x,y)\right) \leq K_2 e^{-\overline{\lambda}\left( |x|-\overline{c} t\right)}.
$$
\end{lem}
\begin{proof}
\textit{First case: $D>2d.$} Let $\overline{c}$ be the unique positive solution of
the equation in $c$
$$\lambda_2^-(c):=\frac{c-\sqrt{c^2-c_{KPP}^2}}{2d} = \frac{c}{D}.$$
To this velocity $\overline{c}$ we associate the
decay rate $\overline{\lambda}:=\frac{\overline{c}}{D}.$ Thus, from simple geometric considerations (see Figure \ref{2graphs}),
we have for all $\varepsilon>0$ that $c^*_\varepsilon,c^*_0<\overline{c}$ and $\lambda^*_\varepsilon,\lambda^*_0>\overline{\lambda}.$
Hence, for all $t>0,x\in\mathbb{R},\varepsilon>0,$
$$
e^{-\lambda^*_\varepsilon(|x|-c^*_\varepsilon t)}<e^{-\overline{\lambda}(|x|-\overline{c} t)}.
$$
We recall that the linear travelling waves $(c^*_\varepsilon,\lambda_\varepsilon^*,\phi_\varepsilon^*)$ and $(c^*_0,\lambda^*_0,\phi^*)$ are
supersolutions for (\ref{RPeps}) and (\ref{BRReq2}).
From Lemma \ref{convergencephi},
as $(u_0,v_0)$ is continuous and compactly supported, we know that there exists
a constant $K_1$ such that
$$
\begin{cases}
u_0(x)\leq K_1 e^{-\overline{\lambda} |x|} & \forall x\in\mathbb{R}\\
v_0(x,y) \leq K_1 e^{-\overline{\lambda} |x|} \min\{\phi^*(y), \underset{\varepsilon\in(0,1]}{\inf}\phi_\varepsilon^*(y)\} & \forall (x,y)\in\mathbb{R}^2.
\end{cases}
$$
From Lemma \ref{borneuniformephi}, there exists a constant $K_2$ such that
$$
\underset{\varepsilon\geq0}{\sup}\ \underset{y\in\mathbb{R}}{\sup}\ \phi_\varepsilon(y)\leq K_2.
$$
up to replace $K_2$ by $\max(K_1,K_2),$ the proof is completed.
\textit{Second case: $D\leq2d.$} In this case, for all $\varepsilon>0,$ $c^*_0=c^*_\varepsilon=c_{KPP}.$ Let us choose $\overline{c}>c_{KPP}$ and
$\overline{\lambda}\in\left(\lambda_2^-(\overline{c}),\frac{\overline{c}}{D}\right)$ and we conclude in the same fashion.
\end{proof}
\subsection{Proof of Theorem \ref{convsol}}
For $(u,v)\in X,$ set $F(u,v):=\left( 0,f(v)\right)$ the nonlinear term in the studied systems.
From the regularity of $F$ and Proposition \ref{sectorial}, the solution of (\ref{BRReq2}) $(u,v)$ and of (\ref{RPeps}) $(u_\varepsilon,v_\varepsilon)$
can be written in the form
\begin{align*}
(u,v)(t) & = e^{tL_0}(u_0,v_0) + \int_0^t e^{(t-s)L_0}F\left( u(s),v(s)\right) ds \\
(u_\varepsilon,v_\varepsilon)(t) & = e^{tL_\varepsilon}(u_0,v_0) + \int_0^t e^{(t-s)L_\varepsilon}F\left( u_\varepsilon(s),v_\varepsilon(s)\right) ds.
\end{align*}
Set $0<\tau_1<T.$ For all $t\in(\tau_1,T),$
\begin{align*}
(u,v)(t)-(u_\varepsilon,v_\varepsilon)(t) = & \left( e^{tL_0}-e^{tL_\varepsilon}\right)(u_0,v_0) \\
& + \int_0^t e^{(t-s)L_0}F\left( u(s),v(s)\right)-e^{(t-s)L_\varepsilon}F\left( u_\varepsilon(s),v_\varepsilon(s)\right) ds\\
= & \left( e^{tL_0}-e^{tL_\varepsilon}\right)(u_0,v_0) \\
& + \int_0^t \left( e^{(t-s)L_0}-e^{(t-s)L_\varepsilon}\right) F\left( u_\varepsilon(s),v_\varepsilon(s)\right) ds \\
& + \int_0^t e^{(t-s)L_0}\left( F\left( u(s),v(s)\right)-F\left( u_\varepsilon(s),v_\varepsilon(s)\right)\rp ds.
\end{align*}
It is easy to see (cf \cite{BRR1}) that for all $t>0,$ $\displaystyle \left\Vert e^{tL_0}\right\Vert\leq \max(1,\frac{1}{\overline{\mu}}).$
Set
$$
\delta(t):=\left\Vert(u,v)(t)-(u_\varepsilon,v_\varepsilon)(t)\right\Vert_\infty,\ \alpha=\min(1-\frac{3}{2}(\beta+\gamma),2\beta-1)>0.
$$
and $\delta(t)$ satisfies the following inequation:
\begin{align}
\delta(t) \leq & \left\Vert\left( e^{tL_0}-e^{tL_\varepsilon}\right)\left( u_0,v_0\right)\right\Vert_\infty \label{gron1}\\
& + \int_0^t \left\Vert \left( e^{(t-s)L_0}-e^{(t-s)L_\varepsilon}\right) F\left( u_\varepsilon(s),v_\varepsilon(s)\right) \right\Vert_\infty ds \label{gron2} \\
& + \int_0^{\tau_1} \max\left( 1,\frac{1}{\overline{\mu}}\right)\left\Vert F\right\Vert_{Lip} \left(\left\Vert(u,v)(s)\right\Vert_\infty+\left\Vert(u_\varepsilon,v_\varepsilon)(s)\right\Vert_\infty\right) ds \label{gron2bis} \\
& + \int_{\tau_1}^t \max\left( 1,\frac{1}{\overline{\mu}}\right)\left\Vert F\right\Vert_{Lip} \delta(s) ds \label{gron3}
\end{align}
From Proposition \ref{cordif}, we can assert that for some constant $C_9$ depending
only on $r,$ $\vartheta,$ $D,$ $\overline{\mu},$ $\tau_1,$ and $T,$ the first term (\ref{gron1})
satisfies
\begin{equation}\label{gron4}
\left\Vert\left( e^{tL_0}-e^{tL_\varepsilon}\right)\left( u_0,v_0\right)\right\Vert_\infty \leq
\varepsilon^\alpha C_9 \left(\lp\|u_0\|_\infty+\|v_0\|_\infty\right)\left( 1+|supp(v_0)|+|supp(u_0)|\right)\rp.
\end{equation}
From Lemma \ref{decroissancesolutions}, we get that for all $t>0,\varepsilon>0,$
\begin{equation}\label{dominationl1}
\|u_\varepsilon(t)\|_\infty,\|v_\varepsilon(t)\|_\infty \leq K_2 e^{\overline{\lambda}\overline{c} t},\qquad
\left\Vert \left\Vert v_\varepsilon(t)\right\Vert_{L^\infty(y)}\right\Vert_{L^1(x)} \leq 2\frac{K_2}{\overline{\lambda}}e^{\overline{\lambda}\overline{c} t},
\end{equation}
and the same estimates holds for $(u,v).$ So we get for the third term (\ref{gron2bis})
\begin{equation}\label{gron2terce}
\int_0^{\tau_1} \left(\left\Vert(u,v)(s)\right\Vert_\infty+\left\Vert(u_\varepsilon,v_\varepsilon)(s)\right\Vert_\infty\right) ds \leq
4\tau_1 K_2 e^{\overline{\lambda}\overline{c} \tau_1}.
\end{equation}
Recall that $f'(0)>0.$ Hence, any supersolution of (\ref{RPeps}) is also a supersolution of the linear system (\ref{RPepsli}).
Thus, Lemma \ref{decroissancesolutions} is also available for time-dependent solutions of the linear
system (\ref{RPepsli}), which in particular entails
\begin{equation}\label{normesemigr}
\forall\varepsilon>0,\ \forall t>0,\ \left\Vert e^{tL_\varepsilon}\right\Vert \leq K_2 e^{\overline{\lambda}\overline{c} t}.
\end{equation}
Now we can deal with the second term (\ref{gron2}). Let us choose $\tau_2>0$ small enough,
and set
\begin{align*}
\int_0^t \left\Vert \left( e^{(t-s)L_0}-e^{(t-s)L_\varepsilon}\right) F\left( u_\varepsilon(s),v_\varepsilon(s)\right) \right\Vert_\infty ds & \leq \\
\int_0^{t-\tau_2} \left\Vert \left( e^{(t-s)L_0}-e^{(t-s)L_\varepsilon}\right) F\left( u_\varepsilon(s),v_\varepsilon(s)\right) \right\Vert_\infty ds & + \\
\int_{t-\tau_2}^t \left(\left\Vert e^{(t-s)L_0}\right\Vert+\left\Vert e^{(t-s)L_\varepsilon}\right\Vert\right) \|F\|_{Lip} \left\Vert\left( u_\varepsilon(s),v_\varepsilon(s)\right) \right\Vert_\infty ds.
\end{align*}
From (\ref{dominationl1}) and (\ref{normesemigr}),
\begin{align}
\int_{t-\tau_2}^t \left(\left\Vert e^{(t-s)L_0}\right\Vert+\left\Vert e^{(t-s)L_\varepsilon}\right\Vert\right) \|F\|_{Lip} \left\Vert\left( u_\varepsilon(s),v_\varepsilon(s)\right) \right\Vert_\infty ds & \leq \nonumber\\
\tau_2 \|F\|_{Lip}\left( K_2 e^{\overline{\lambda}\overline{c} T}+1+\frac{1}{\overline{\mu}}\right)\|(u_0,v_0)\|_\infty.
\label{gron5}
\end{align}
From Proposition \ref{cordif} and (\ref{dominationl1}),
\begin{align}
\int_0^{t-\tau_2} \left\Vert \left( e^{(t-s)L_0}-e^{(t-s)L_\varepsilon}\right) F\left( u_\varepsilon(s),v_\varepsilon(s)\right) \right\Vert_\infty ds & \leq \nonumber \\
\varepsilon^\alpha TC_8\left( e^{TC_8}+\frac{1}{\tau_2}\right)\left( 2+\frac{4}{\overline{\lambda}}\right)\left( K_2e^{\overline{\lambda}\overline{c} T}\right). \label{gron6}
\end{align}
We can now conclude the proof of Theorem \ref{convsol} by a classical Gronwall argument in (\ref{gron1})-(\ref{gron3}),
choosing $\tau_1,$ then $\tau_2$ and at last $\varepsilon$. Let $\eta>0$ be any small quantity. Let $\tau_1>0$ small enough
such that $\displaystyle 4\tau_1 K_2 e^{\overline{\lambda}\overline{c} \tau_1}\leq \frac{\eta}{4}.$ Let $\tau_2>0$ such that
$$
\tau_2 \|F\|_{Lip}\left( K_2 e^{\overline{\lambda}\overline{c} T}+1+\frac{1}{\overline{\mu}}\right)\|(u_0,v_0)\|_\infty \leq \frac{\eta}{4}.
$$
Now, let us choose $\varepsilon>0$ such that
\begin{equation*}
\begin{cases}
\varepsilon^\alpha C_9 \left(\lp\|u_0\|_\infty+\|v_0\|_\infty\right)\left( 1+|supp(v_0)|+|supp(u_0)|\right)\rp \leq \frac{\eta}{4} \\
\varepsilon^\alpha TC_8\left( e^{TC_8}+\frac{1}{\tau_2}\right)\left( 2+\frac{4}{\overline{\lambda}}\right)\left( K_2e^{\overline{\lambda}\overline{c} T}\right) \leq \frac{\eta}{4}.
\end{cases}
\end{equation*}
Hence, $(\ref{gron1})+(\ref{gron2})+(\ref{gron2bis})\leq \eta$
and we get from Gronwall's inequality for all $t\in[\tau_1,T]$:
$$
\delta(t)\leq \eta e^{\|F\|_{Lip}\lp1+\frac{1}{\overline{\mu}}\right)(T-\tau_1)}.
$$
\qed
\section{Uniform spreading}
Once again, we consider nonnegative compactly supported initial datum $(u_0,v_0).$
We also made the following assumption on $(u_0,v_0):$
\begin{equation}
(u_0,v_0)\leq(\frac{1}{\overline{\mu}}m,m)
\end{equation}
where $m$ is given by (\ref{uniformsupersol}). The purpose is
now to prove Theorem \ref{uniformspreading}.
Our notations are these of
Section \ref{sectionvitesse}. $c^*_0$ is the asymptotic speed of spreading associated to the limit system (\ref{BRReq2}),
$c^*_\varepsilon$ the one associated to (\ref{RPeps}).
Recall that in the case $D\leq 2d,$ the spreading is driven by the field,
and $c^*_0=c_\varepsilon^*=2\sqrt{df'(0)}.$
In both systems, the spreading in this case is independent
of the line, and the uniform spreading is easy to get.
We will focus on the case $D>2d,$ where the spreading is enhanced by the line.
\paragraph{First part: $c>c^*_0.$}
This is the easiest case. Let $c_1=\frac{c+c^*_0}{2}.$ From Proposition \ref{convergencec}, there exists $\varepsilon_0$ such that $\forall\varepsilon<\varepsilon_0,$
$c_\varepsilon^*\leq c_1.$ From Lemma \ref{decroissancesolutions}, there
exists $K$ such that
$$
\begin{cases}
u_0(x)\leq K_1 e^{-\overline{\lambda} |x|} & \forall x\in\mathbb{R}\\
v_0(x,y) \leq K_1 e^{-\overline{\lambda} |x|} \underset{\varepsilon\in[0,1]}{\inf}\phi_\varepsilon(y;c_1) & \forall (x,y)\in\mathbb{R}^2.
\end{cases}
$$
Then, from Proposition \ref{defspreadingspeed} and Lemma \ref{decroissancesolutions},
$$
\forall \varepsilon<\varepsilon_0,\ u_\varepsilon(t,x)\leq K e^{-\overline{\lambda}(x-c_1t)},
$$
which concludes the proof of the first part of Theorem \ref{uniformspreading}.
\qed
\paragraph{Second part: $c<c^*_0$}
\subparagraph{Background on subsolutions}
Let us recall that in \cite{BRR1} (resp. in \cite{Pauthier}) the argument to prove the spreading was to devise stationary
compactly supported subsolutions of (\ref{BRReq2}) (resp. (\ref{RPeps})) in a moving framework at some speed $c$ less than
and close to $c^*_0$ (resp. $c^*_\varepsilon$). More precisely, for $L$ large enough, set $\Omega^L:=\mathbb{R}\times (-L,L)$
and let us consider the following systems for some $\delta\ll1$
:
\begin{equation}\label{subsolBRR}
\begin{cases}
-DU''+cU' = V(x,0)-\overline{\mu} U & x\in\mathbb{R} \\
-d\Delta V+c\partial_x V = \left( f'(0)-\delta\right) V & (x,y)\in\Omega^L \\
-d\left(\partial_x V(x,0^+)-\partial_x V(x,0^-)\right) = \overline{\mu} U(x)-V(x,0) & x\in\mathbb{R} \\
V(x,\pm L) = 0 & x\in\mathbb{R}.
\end{cases}
\end{equation}
\begin{equation}
\label{subsolRPeps}
\begin{cases}
-DU''+cU'=-\overline{\mu} U+\int_{(-L,L)}\nu_\varepsilon(y)V(x,y)dy & x\in \mathbb{R} \\
-d\Delta V+c\partial_x V=\left( f'(0)-\delta\right) V+\mu_\varepsilon(y)U(x)-\nu_\varepsilon(y)V(x,y) & (x,y)\in \Omega^L \\
V(x,\pm L) = 0 & x\in \mathbb{R}.
\end{cases}
\end{equation}
It was showed by an explicit computation in \cite{BRR1} and an analysis of a spectral problem
in \cite{Pauthier} that there exists a unique $c:=c^*_0(L)$ (resp. $c^*_\varepsilon(L)$) such that (\ref{subsolBRR})
(resp. (\ref{subsolRPeps})) admits a unique solution of the form
\begin{equation}\label{soussolexp}
\begin{pmatrix}
U(x) \\
V(x,y)
\end{pmatrix}
= e^{\lambda x} \begin{pmatrix}
1 \\ \varphi(y)
\end{pmatrix}
\end{equation}
with $c^*_0(L)<c^*_0,$ $c^*_\varepsilon(L)<c^*_\varepsilon,$ and
$$
\begin{cases}
\lim_{\delta\to0}\lim_{L\to\infty}c^*_0(L) = \lim_{L\to\infty}\lim_{\delta\to0}c^*_0(L) = c^*_0 \\
\lim_{\delta\to0}\lim_{L\to\infty}c^*_\varepsilon(L) = \lim_{L\to\infty}\lim_{\delta\to0}c^*_\varepsilon(L) = c^*_\varepsilon.
\end{cases}
$$
Using (\ref{soussolexp}), the system (\ref{subsolRPeps}) reads on
$(c,\lambda,\varphi)$
\begin{equation}
\label{eqsoussol}
\begin{cases}
-D\lambda^2+\lambda c+\overline{\mu} = \int_{(-L,L)} \nu(y)\phi(y)dy \\
-d\varphi''(y)+(c\lambda-d\lambda^2-f'(0)+\delta+\nu_\varepsilon(y))\varphi(y) = \mu_\varepsilon(y) & \varphi(\pm L) = 0
\end{cases}
\end{equation}
and $c^*_\varepsilon(L)$ was given as the first $c$ such that the graphs of the two following
functions intersect
$$
\begin{cases}
\Psi_1 \ : \ \lambda \mapsto -D\lambda^2+\lambda c+\overline{\mu} \\
\Psi_2 \ : \ \lambda \mapsto \int_{(-L,L)}\nu_\varepsilon(y)\varphi(y)dy
\end{cases}
$$
where, for $\Psi_2,$ $\varphi$ is given by the unique solution of second equation
of (\ref{eqsoussol}). Let us call $\Gamma_1,$ resp. $\Gamma_2,$ the graph of $\Psi_1,$ resp. $\Psi_2.$
So we should keep in mind that in (\ref{soussolexp}), both $\lambda$ and $\varphi$ depend on $L,\delta,\varepsilon.$
Using the same kind of arguments as for Lemma \ref{borneuniformephi} and \ref{convergencephi}, we can
assert that this dependence is continuous for the $L^\infty$-topology. In particular, the subsolution
(\ref{soussolexp}) of (\ref{subsolRPeps}) converges uniformly in $\delta,L$ to the subsolution
of (\ref{subsolBRR}) as $\varepsilon$ goes to 0, and of course
$c^*_\varepsilon(L)\to c^*_0(L)$ as $\varepsilon\to0$. Hence, the notations are not confusing, as we can continuously extend
$\varphi(\varepsilon,\delta,L)$ to $\varphi(0,\delta,L)$ as $\varepsilon$ goes to 0.
So we get that both $\varphi$ and $\Psi_2$ are:
\begin{itemize}
\item analytical in $\lambda,c,\delta;$
\item uniformly continuous in $L$ and $\varepsilon,$ up to $\varepsilon=0.$
\end{itemize}
Then, a perturbative argument gives for some $c$ less than but close to $c^*(L)$
a compactly supported subsolution of (\ref{subsolRPeps}), or (\ref{subsolBRR}) in the limit case $\varepsilon=0.$
\subparagraph{Spreading} Let $c<c^*_0.$ Let $c_1=\frac{c+c_0^*}{2},$ $c_2=\frac{c+c_0^*}{4}.$
From Proposition \ref{convergencec}, there exists $\varepsilon_1$ such that for all $\varepsilon<\varepsilon_1,$
$c^*_\varepsilon>c_2.$ Now, for some $\delta$ small enough and some $L$ large enough, \cite{BRR1} and
\cite{Pauthier} give us a family of subsolutions of (\ref{subsolBRR}) and (\ref{subsolRPeps})
denoted $(\underline{u},\underline{v})$ and $(\underline{u}_\varepsilon,\underline{v}_\varepsilon)$ for some $c_\varepsilon>c_1$ for $\varepsilon<\varepsilon_1.$ The uniform continuity
of $\Psi_2$ allows us to take same $\delta$ and $L$ for all $\varepsilon\in[0,\varepsilon_1).$
Hence, the convergence result given in Lemma \ref{convergencephi} adapted to this case
gives that $$(\underline{u}_\varepsilon,\underline{v}_\varepsilon)\underset{\varepsilon\to0}{\longrightarrow}(\underline{u},\underline{v})$$
for the $L^\infty$-norm. Set:
$$
\begin{cases}
u_1(x)=\inf\{\underline{u}_\varepsilon(x),\ \varepsilon\in[0,\varepsilon_1)\},\ v_1(x)=\inf\{\underline{v}_\varepsilon(x,y),\ \varepsilon\in[0,\varepsilon_1)\} \\
u_2(x)=\sup\{\underline{u}_\varepsilon(x),\ \varepsilon\in[0,\varepsilon_1)\},\ v_2(x)=\sup\{\underline{v}_\varepsilon(x,y),\ \varepsilon\in[0,\varepsilon_1)\}.
\end{cases}
$$
Both $u_1,v_1,u_2,v_2$ are nonnegative, continuous and compactly supported. Let us set $\gamma$
such that
$$
\gamma(f'(0)-\delta)\left\Vert v_2\right\Vert_\infty \leq f\left(\left\Vert v_2\right\Vert_\infty\right) \textrm{ and }\gamma \left\Vert u_2\right\Vert_\infty <\frac{1}{\overline{\mu}}.
$$
We know that $(u,v)(t)$ converges locally uniformly to the steady state $(\frac{1}{\overline{\mu}},1).$
So, let $t_1$ such that $(u,v)(t_1)>\gamma(u_2,v_2).$ From Theorem \ref{convsol}, there exists
$\varepsilon_2$ such that for all $\varepsilon<\varepsilon_2,$ $(u_\varepsilon,v_\varepsilon)(t_1)>\gamma(u_2,v_2).$ Up to replace
$\varepsilon_2$ by $\min(\varepsilon_1,\varepsilon_2),$ we get from comparison principle that
$$
\forall t>t_1, \ \forall \varepsilon<\varepsilon_2,\ \left( u_\varepsilon(t,x),v_\varepsilon(t,x,y)\right) > \gamma \left( u_1(x-c_1(t-t_1)),v_1(x-c_1(t-t_1),y)\right).
$$
Let $(\tilde{u},\tilde{v})$ and $(\tilde{u}_\varepsilon,\tilde{v}_\varepsilon)$ the solutions of (\ref{BRReq2}) and (\ref{RPeps}) starting at
$t=t_1$ from $\gamma(u_1,v_1).$ Then, considering the hypotheses on $(u_0,v_0),$ for all
$t>t_1,$ we have:
$$
\begin{cases}
(\tilde{u},\tilde{v})(t)<(u,v)(t)<\left(\frac{1}{\overline{\mu}},1\right) \\
(\tilde{u}_\varepsilon,\tilde{v}_\varepsilon)(t)<(u_\varepsilon,v_\varepsilon)(t)<\left( U_\varepsilon,V_\varepsilon\right).
\end{cases}
$$
Now, from Proposition \ref{convVeps}, there exists $\varepsilon_3$ such that if
$\varepsilon<\varepsilon_3,$ $\displaystyle\left| U_\varepsilon-\frac{1}{\overline{\mu}}\right| <\frac{\eta}{3}.$
Let $t_2$ such that
$$
\forall x\in \textrm{ supp}(u_1), \forall t>t_2,
\ \left|\tilde{u}(t,x)-\frac{1}{\overline{\mu}}\right|<\frac{\eta}{3}.$$
From Theorem \ref{convsol}, there exists $\varepsilon_4$ such that if
$
\varepsilon<\varepsilon_4,$ $\displaystyle\left| (\tilde{u}_\varepsilon-\tilde{u})(t_2)\right|<\frac{\eta}{3}.
$
Now, set $\varepsilon_0=\min(\varepsilon_1,\varepsilon_2,\varepsilon_3,\varepsilon_4),$ $\displaystyle T_0=t_2\frac{c_0^*}{c_0^*-c_2},$ and the
proof of Theorem \ref{uniformspreading} is concluded.
\qed
\newpage
\setcounter{equation}{0}
\begin{appendices}
\renewcommand{\theequation}{A.\arabic{equation}}
\section{}
Here we prove for the convenience of the reader the lemma used in the proof of Lemma \ref{gdesfrequences}.
It relies on a Kato-type inequality.
\begin{lemA}\label{katoineq}
Let $\phi,m,f$ be functions in $BUC(\mathbb{R},\mathbb{C})$ such that
\begin{equation}\label{kato1}
-\phi''(y)+m(y)\phi(y)=f(y), \qquad y\in\mathbb{R}.
\end{equation}
If there exists $\kappa>0$ such that for all $y\in\mathbb{R},$ $\Re{m(y)}\geq \kappa^2$ then
$|\phi|$ satisfies
\begin{equation}\label{conv}
|\phi(y)|\leq \frac{1}{2\kappa}\int_\mathbb{R} e^{-\kappa|z|}\left| f(z)\right| dz.
\end{equation}
\end{lemA}
\begin{proof}
Let us first compute the second derivative of the modulus of a complex valued function. Let $\phi\in BUC(\mathbb{R},\mathbb{C})\cap \mathcal{C}^2.$
An easy computation yields
$$
|\phi|''=\frac{\Re{\overline{\phi}\phi''}}{|\phi|}+\frac{|\phi'|^2}{|\phi|}-\frac{\Re{\overline{\phi}\phi'}^2}{|\phi|^3}.
$$
Hence, for all smooth enough complex-valued function of the real variable, we get
\begin{equation}\label{modulephiseconde}
-\left|\phi\right|''\leq-\frac{\Re{\overline{\phi}\phi''}}{|\phi|}.
\end{equation}
Now, let us multiply (\ref{kato1}) by $\displaystyle \frac{\overline{\phi}}{|\phi|}$ and take the real part. It gives
\begin{equation*}
-\frac{\Re{\overline{\phi}\phi''}}{|\phi|}+\Re{m}|\phi|=\Re{f\frac{\overline{\phi}}{|\phi|}}.
\end{equation*}
Using (\ref{modulephiseconde}) in the above inequality yields the following inequation for $|\phi|:$
\begin{equation*
-|\phi(y)|''+\Re{m(y)}|\phi(y)|\leq|f(y)|.
\end{equation*}
Now we are reduced to an inequation with real functions. If $\varphi$ is the unique solution in $H^1(\mathbb{R})$ of
$$
-\varphi''(y)+\kappa^2\varphi(y)=\left| f(y)\right|,
$$
from the elliptic maximum principle, we get $|\phi|\leq\varphi,$ which is exactly the desired inequality (\ref{conv}).
\end{proof}
\end{appendices}
\newpage
\bibliographystyle{plain}
\footnotesize
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/*!
* n-deep-merge - recursive deep merge for objects and arrays
* (c) 2014 Eric Clifford <ericgclifford@gmail.com>
* MIT Licensed.
*
* http://github.com/eclifford/deep-merge
*/
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if (typeof define === 'function' && define.amd) {
define([], function() {
return (root.deepmerge = factory(root));
});
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} else {
root.deepmerge = factory(root);
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deepmerge = function (dest) {
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var source = arguments[i];
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} | 3,265 |
{"url":"https:\/\/webwork.maa.org\/moodle\/mod\/forum\/discuss.php?d=401&parent=1597","text":"## WeBWorK Problems\n\n### Re: Currency Context\n\nby Davide Cervone -\nNumber of replies: 0\nI agree that that's probably what Perl is trying to do (though it looks more like round-to-odd than round-to-even), but I think the problem really is that the binary representations are not actually equal to the decimal ones, so what you think of as 1.235 is not actually that but something slightly less than that (on the order of 1E-16) and so is not \"really\" 5 followed by 0's but actually more like 1.2349999999999999999999 and so rounds to 1.23.\n\nIn fact, I just did the following: 1.235 - 1.23 and got 0.00499999999999989, not .5, so that confirms it. Similarly, 1.225 - 1.22 yields 0.00500000000000012, so 1.225 rounds up to 1.23. These small errors at the tail of the decimal are due to the fact that the infinite binary expansion has been truncated (or more likely, rounded). For example, the binary expansion for .1 has repeating 1100 digits, giving ...110011001100110011..., so if the cut-off occurs before a zero, as in ..1100110|0110011..., then the resulting binary number is slightly too small, and we have the case like the one in 1.235 (it rounds down because it is slightly below 1.235). On the other hand, if it cuts off before a 1, as in ..11001100|110011..., then the number stored might be rounded up to ..11001101, which is slightly too big. This is like the 1.225, which rounds up, because the internal representation is just a little over 1.225 (by 1.2*10^(-16)).\n\nNumbers stored as IEEE double-precision floating point reals (like the Perl I'm running uses) have 54 binary digits for the mantissa (the constant in front of the 10^(-16)) and 11 for the exponent (yes, that's 65, which I could also explain). So the error should be in the 54th binary \"decimal\" place, so the error should be on the order or 2^(-54). As a rough estimate of how big that is, we can use the fact that 2^10=1024 is about 1000=10^3, so\n\n2^(-54) = 2^6*2^(-60) = 64*2^(10*-6) = 64*(2^10)^(-6) = 64*(10^3)^(-6) = 64*10^(-18) = 6.4*10^(-17)\n\nwhich is just about exactly the sized error we see (and since 1024 is a little bigger than 1000, our estimate is a little smaller than the actual error).\n\nAnyway, the reason the rounding doesn't work as expected is that the numbers actually being rounded are in binary not decimal, and so are not exactly what you think they are. The reason you don't see these error when you print the numbers is that the numbers are printed using one or two fewer (decimal) digits than the binary representation actually allows, and the result is rounded for printing, so 1.234999999999999999 becomes 1.235 even though internally it isn't exactly that.\n\nThe upshot is, you can't trust printed numbers to display the actual number stored, and the actual number stored may not be the one you entered.\n\nDavide\n\nPS, I don't even want to THINK about what banks do.","date":"2021-10-19 11:37:11","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8549730777740479, \"perplexity\": 791.2669520571436}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-43\/segments\/1634323585265.67\/warc\/CC-MAIN-20211019105138-20211019135138-00113.warc.gz\"}"} | null | null |
{"url":"http:\/\/math.stackexchange.com\/questions\/100825\/connected-sum-of-a-torus-and-a-real-projective-plane","text":"# Connected sum of a torus and a real projective plane\n\nMy question is really basic. I was reading on the Massey's Book of algebraic topology on the connected sum of the torus and real projective plane, I felt a little confused his explanation. Someone can explain to me Or at least give a reference where I can find this calculation?\n\n-\n Calculation of what? \u2013\u00a0Chris Eagle Jan 20 '12 at 23:23 Please summarize what Massey did in his book. \u2013\u00a0Erno Nemecsek Jan 22 '12 at 13:52","date":"2013-05-22 21:38:55","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8133652806282043, \"perplexity\": 290.02281247863925}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2013-20\/segments\/1368702448584\/warc\/CC-MAIN-20130516110728-00068-ip-10-60-113-184.ec2.internal.warc.gz\"}"} | null | null |
{"url":"https:\/\/www.doitpoms.ac.uk\/tlplib\/metal-forming-3\/work_formula.php","text":"Dissemination of IT for the Promotion of Materials Science (DoITPoMS)\n\n# Work Formula Method\n\nWhen deforming a body, work has to be done by the applied forces.\u00a0 In the simplest case, the work done can be estimated from the magnitude of the applied stress(es) and the extent of the deformation. This is analogous to simple mechanics in which the work done is equal to force applied multiplied by the distance moved.\u00a0 Clearly, this simple approach assumes, in the first instance, that all the work done by the applied forces results in deformation; this can be called \u201cuseful\u201d work.\u00a0 If it is assumed that all the work done is useful, then the work formula approach leads to an underestimate of the actual forces needed, i.e. a \u201clower bound\u201d.\u00a0 In other words, it would not be possible to deform the body if at least those forces were not applied and hence that work was not done.\u00a0 In practice, frictional forces need to be overcome and heating of the body occurs due to the internal micro-mechanisms of deformation.\u00a0 This non-useful work is called \u201credundant\u201d work and estimates can be made to allow for this, and so better approximations for the necessary forces can be made.\n\nConsider a uniaxial tensile deformation process:\n\nIn this process, \u03c31 = Y, \u03c32 = \u03c33 = 0 and Y = uniaxial yield stress.\n\n-->\n\nSuppose that at some instant, the bar is of length l and of cross-sectional area A\nV = Al\n\nIf the bar extends by an amount \u03b4l, the increment of work done\/unit volume, \u03b4w, is\n\n$${{F\\delta l} \\over V} = {{YA\\delta l} \\over {Al}} = \\delta w$$\n\n$\\delta w = {{Y\\delta l} \\over l}$\n\nSo if the bar extends from length l0 to l1, total work done\/unit volume is\n\n$\\int {\\delta w} = Y\\int_{{l_0}}^{{l_1}} {{{{\\rm{d}}l} \\over l}} = Y\\ln {{{l_1}} \\over {{l_0}}}$\n\nThis can be applied to wire drawing.\n\nIn wire drawing, a tensile force is applied to the product rather than a compressive force applied to the billet (such as in extrusion for example).\n\n-->\n\nTo extend the wire by distance l1, we have to feed in a length l0 to the die where A1l1 = A0l0 by conservation of volume.\n\nWork done by F = Fl1\n\nVolume of metal = A1l1drawn by l1\n\nWork done $$= Y{A_1}{l_1}\\ln$$ $${{{l_1}} \\over {{l_0}}}$$ = $$F{l_1}$$\n\n$\\Rightarrow {F \\over {{A_1}}} = \\sigma = Y\\ln {{{l_1}} \\over {{l_0}}} = Y\\ln {{{A_0}} \\over {{A_1}}}$\n\nwhere \u03c3 = stress required, the drawing stress.\n\nTherefore we can estimate the maximum reduction possible with perfect lubrication.\n\nIf there is no work hardening, $$\\sigma \\le Y$$ then the maximum reduction occurs when\n\u03c3 = Y $$\\Rightarrow \\ln$$ $${{{A_1}} \\over {{A_0}}}$$ = 1\n\n$\\Rightarrow {{{A_0}} \\over {{A_1}}} = 2.72$ \u00a0\u00a0(e to 3 s.f.)\n\n$\\Rightarrow {{{A_1}} \\over {{A_0}}} = 0.37$\n\n63% is therefore the maximum possible reduction of cross-sectional area with a perfect wire-drawing operation for a rigid-plastic material. Work hardening causes this to increase to a slightly higher value. Friction between the wire and the die reduces this value, causing redundant work \u2013 work in excess of the minimum necessary to cause the deformation.\n\nIn practice, the best reduction obtainable with real dies and good lubrication is approximately 50%.\n\nTo allow for redundant work, we can apply empirical corrections, e.g. by using a value of efficiency, \u03b7:\n\n$\\eta = {{{\\rm{Work\\; formula\\; estimate}}} \\over {{\\rm{Actual\\; total\\; work}}}}$\n\nTypical values of \u03b7 are:\n\n\u2022 extrusion\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u03b7 = 45 \u2013 55%\n\u2022 wire drawing\u00a0\u00a0\u00a0\u03b7 = 50 \u2013 65%\n\u2022 rolling\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u03b7 = 60 \u2013 80%\n\nClearly, the work formula method gives a lower band to the true force required for a given deformation processing operation because we are neglecting \u2018redundant work.\u2019\n\nFor metalworking, it is often preferable to have an overestimate of the load required in order to be sure that a given operation or process is possible.","date":"2022-11-30 16:46:08","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 2, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.762470006942749, \"perplexity\": 1066.3421835497181}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-49\/segments\/1669446710765.76\/warc\/CC-MAIN-20221130160457-20221130190457-00140.warc.gz\"}"} | null | null |
Q: Writing to System.in from swing ui and reading the input with Scanner So, I was wondering if Scanner could read from System.in that is set from JFrame. This is what I mean.
This is my WriteToSystemIn (JFrame class), which is the GUI part of the program.
import javax.swing.*;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import java.io.ByteArrayInputStream;
import java.io.UnsupportedEncodingException;
public class WriteToSystemIn extends JFrame {
private static class ChangeNumber implements ActionListener {
@Override
public void actionPerformed(ActionEvent e) {
ByteArrayInputStream s = null;
try {
s = new ByteArrayInputStream("1\n".getBytes("UTF-8"));
} catch (UnsupportedEncodingException ex) {
throw new RuntimeException(ex);
}
System.setIn(s);
}
}
WriteToSystemIn() {
JButton button = new JButton("try click it m8");
button.addActionListener(new ChangeNumber());
this.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
this.add(button);
this.setVisible(true);
this.pack();
}
}
And this is the Main function of the program.
import java.util.Scanner;
public class Main {
private static class MainRunnable implements Runnable {
@Override
public void run() {
new WriteToSystemIn();
}
}
public static void main(String[] args) {
javax.swing.SwingUtilities.invokeLater(new MainRunnable());
Scanner scanner = new Scanner(System.in);
String s = scanner.nextLine();
System.out.println(s);
System.out.println("ended");
}
}
So, when the button is pressed from WriteToSystemIn, it should write "1\n" to System.in for Scanner to read.
But, it isn't doing that. It won't read anything. It has no problem printing to System.out so I thought it would've been a non-issue, but clearly I'm wrong. So, I'm wondering here, is there something that I'm doing wrong here? Or, am I trying to do something that is impossible?
A: When you call new Scanner(System.in); you give the scanner a reference to the stream that is currently set as System.in. When you later call System.setIn(s); you only change the value stored in System.in. The reference that was already given to the scanner is not changed and it still points to the original System.in.
You need to make sure that System.setIn(s); is called before you initialize the scanner. You can add debug printing to both statements to verify the order in which they are executed. This can be helpful when you are learning multithreaded programming.
System.out.println("Resetting System.in");
System.setIn(s);
...
System.out.println("Creating scanner");
Scanner scanner = new Scanner(System.in);
A: Continuing on from @Torben's answer, you need to make class Main wait until the JButton (in class WriteToSystemIn) is clicked. Once the JButton is clicked, you can notify Main that it can stop waiting and continue executing.
Class Main
import java.util.Scanner;
public class Main {
private static class MainRunnable implements Runnable {
private Main main;
public MainRunnable(Main main) {
this.main = main;
}
@Override
public void run() {
new WriteToSystemIn(main);
}
}
public static void main(String[] args) {
Main main = new Main();
javax.swing.SwingUtilities.invokeLater(new MainRunnable(main));
synchronized (main) {
try {
main.wait();
Scanner scanner = new Scanner(System.in);
String s = scanner.nextLine();
System.out.println(s);
}
catch (InterruptedException x) {
x.printStackTrace();
}
}
System.out.println("ended");
}
}
Class WriteToSystemIn
import javax.swing.*;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import java.io.ByteArrayInputStream;
import java.io.UnsupportedEncodingException;
public class WriteToSystemIn extends JFrame {
private static class ChangeNumber implements ActionListener {
private Main main;
public ChangeNumber(Main main) {
this.main = main;
}
@Override
public void actionPerformed(ActionEvent e) {
ByteArrayInputStream s = null;
try {
s = new ByteArrayInputStream("1\n".getBytes("UTF-8"));
System.setIn(s);
synchronized (main) {
main.notifyAll();
}
} catch (UnsupportedEncodingException ex) {
throw new RuntimeException(ex);
}
}
}
WriteToSystemIn(Main main) {
JButton button = new JButton("try click it m8");
button.addActionListener(new ChangeNumber(main));
this.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
this.add(button);
this.setVisible(true);
this.pack();
}
}
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,879 |
Q: C# The request was aborted: Could not create SSL/TLS secure channel with tls1.3 We are unable to connect to an HTTPS server using WebRequest because of this error message:
The request was aborted: Could not create SSL/TLS secure channel.
i use this code on net framwwork 4.8, website use tls 1.3
ServicePointManager.Expect100Continue = true;
ServicePointManager.SecurityProtocol = (SecurityProtocolType)3072;
ServicePointManager.DefaultConnectionLimit = 9999;
ServicePointManager.SecurityProtocol = SecurityProtocolType.Tls11|
SecurityProtocolType.Tls12|
SecurityProtocolType.Tls13;
WebRequest.Create("https://manga1001.com/").GetResponse();
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,902 |
Students Forced to Sign COVID-19 Liability Waivers: Is it Legal?
Home » Blog » Civil Right » Students Forced to Sign COVID-19 Liability Waivers: Is it Legal?
Posted on August 25th, 2020 in Civil Right
Pennsylvania State University faced backlash from students and parents after requiring students to sign a liability agreement and assume all risk of COVID-19 prior to returning to campus for the fall semester.
Now the university has taken a step back and will provide students an alternate legal agreement regarding coronavirus.
The original agreement stated, "I assume any and all risk of exposure to COVID-19 that may result from attending Penn State, or participating in Penn State activities, and I acknowledge that exposure or infection may result in personal injury, illness, permanent disability, or death."
The new agreement will offer modified language to clear the confusion stating,
"Even with the mitigation steps taken by Penn State and my compliance with this compact, I acknowledge that Penn State cannot prevent the risks of exposure to COVID-19 that may result from attending Penn State or participating in Penn State activities."
School officials are reminding students and parents that the intent was never to be a liability waiver, but an acknowledgment of risks.
But parents and students don't agree in all cases. According to InsideHigher Ed, "students enrolled at various colleges across the country are being prompted by their institutions to sign similar agreements acknowledging, and in some cases even assuming, all the risks of returning to campus. Some of the agreements are more explicit than others," implying that students are waiving their rights to pursue litigation if negligence by the university occurs.
While schools are permitting students to take leave if they don't feel safe returning, for those on rigorous academic schedules that must be followed to complete degree requirements, where does that leave them?
Are COVID-19 Liability Waivers Legal?
While no one can be forced to sign a COVID-19 liability waiver, it may impact a student's ability to return to campus for denying the agreement.
Though families will likely have difficulty suing universities if a student contracts COVID-19 and faces serious injury, families who can prove that their college student contracted coronavirus at the university then brought it home, leading to illness or death of another, may be more likely.
Ultimately, these decisions will be made by judges as to enforceability. But protecting your right to pursue action should something happen to you is critical. And Kalinoski Law Offices can help.
COVID-19 Liability Waivers: Protect Your Rights
You may be eager to return to college, but when you are made to waive your rights to pursue legal action should something happen to you in return, it's time to weigh your options. While many universities claim these are only acknowledgments, it is always best to seek legal advice on such contracts.
Life is full of uncertainty. Do not let the world of academia manipulate you into giving your rights away. At Kalinoski Law Offices P.C., we fight for your civil rights in the classroom, in the workplace, and in public accommodations. Contact us today for a free consultation. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,033 |
\section{Introduction} \label{Sec-1}
The interaction of high-power ultra-intense lasers and structured (both nanostructured~\cite{nano_2004,Nishikawa_applied_nano2004,nano_2011_pop,nanosphere_2012_PRL,Blanco_2017_nanostructured,Moreau_2019_nanowire,nanowire_2021_SR} and microstructured~\cite{Attosecond_Naumova,Klimo_2011_micro,Xiao_hollow_channel,microwire_hedp,Feng_micro_effects,Jiang_microengineering,ji2016towards,Stark2016PRL,yu2018generation,Snyder_microchannels,microtube_Beg_PRE}) targets has been a topic of great interest for its capability of enhancing the laser energy conversion efficiency~\cite{nano_2004}, high-order harmonics generation~\cite{HHG_pop_2010,HHG_2018_PRL}, charged particles (relativistic electrons and ions~\cite{nano_2011_pop,nanosphere_2012_PRL,microtube_Beg_PRE}) acceleration and the production of X-ray~\cite{nano_2004,Xray_micro_2016_PRL,xray_2017_pop,Rolles_xray_nano_2018} to $\gamma$-ray~\cite{Stark2016PRL,yu2018generation,gammaray_2018_pnas} radiation. The produced charged particle and photon beams have a wide range of applications from medical ion therapy~\cite{malka2004practicability,robson2007scaling}, nuclear physics~\cite{bychenkov1999nuclear,Bremsstrahlung_NRF} to photon-photon pair production~\cite{yu_2019,wang_pair_comment,PRApplied_power}. The microstructured targets with characteristic size of surface modulation comparable to laser wavelength are able to extensively absorb laser energy through various processes, including surface plasmon resonance excitation~\cite{PRL_nano_plasmon_2003}, multipass stochastic heating~\cite{Breizman_Alex_pop_2005} in dense clusters, prolonged acceleration distance in hollow channels~\cite{Xiao_hollow_channel} and microwires~\cite{microwire_hedp} and relativistic transparency in prefilled channels~\cite{Stark2016PRL}. In this paper, we examine the regime involving hollow micro-channels (see \cref{fig:Schematics}).
When ultra-intense lasers irradiate hollow micro-channels, strong laser fields directly act on electrons, dragging them into the channel and forming periodic electron bunches which then surf along with the laser pulse, gaining energy from the laser. Additionally, the presence of a channel guides the propagation of the electromagnetic fields, confines the electron motion and as a result, leads to a well collimated photon emission. This setup can serve as a promising electron source to further stimulate ion acceleration~\cite{microtube_Beg_PRE} as long as the ion expansion does not significantly impact electron acceleration~\cite{Wang_2019}. However, to successfully apply such an electron source in experiments, careful numerical investigations are needed in order to determine where the electron energy peaks, i.e. the location to cut off the channel and collect an electron source with an optimal spectrum.
To carry out such numerical studies, one can choose between 2D3V and 3D3V Particle-In-Cell (PIC) simulations. Both 2D~\cite{Klimo_2011_micro,Xiao_hollow_channel,Attosecond_Naumova,zou2017microchannel,Gong_hollow_channel} and 3D~\cite{ji2016towards,Jiang_microengineering,Jiang_PRE,Snyder_microchannels,Serebryakov_2019_3Dstructured} numerical simulations have been widely used to characterize laser interactions with structured targets. The appeal of 2D simulations is that they require significantly less computational resources than 3D simulations, so one is able to perform extensive parameter scans using 2D simulations. However, the field topology differs between 2D and 3D setups and it is not immediately clear how the differences impact the particle dynamics. It is then important to evaluate the dimensionality effects on a case-by-case basis. A few publications~\cite{stark_dimensionality_ion,Liu_dimensionality_ion,Xiao_2018_dimensionality_ion,Blanco_2017_nanostructured} have discussed the influences of simulation dimensionality on ion acceleration with various target geometries. But, to our knowledge, nobody has examined and explained the physics of dimensional effects on laser-irradiated hollow micro-channel targets.
In this paper, we show that the chosen dimensionality has a considerable effect on electron acceleration and the associated photon emission. First, we provide theoretical analysis to demonstrate that the dephasing rate between the accelerated electron and laser wave-fonts strongly depends on simulation geometry. Later we show numerical evidence to demonstrate that the dephasing rate differs with simulation dimensionality and such a difference is the key reason for the distinguished observation in terms of electron and photon beam generation. Through collectively evaluating generated particles and detailed particle tracking, we show that the occurrence of high phase velocity in the 3D setup terminates electron acceleration process early in space and time, and leads to a reduction of photon emission.
\begin{figure*}[!htp]
\centering
\includegraphics[width=0.9\textwidth,trim={1cm 0.4cm 0cm 0cm},clip]{Figure1.png}
\caption{\label{fig:Schematics} Laser-irradiated hollow targets in 2D and 3D. (a) 2D setup where a linearly polarized two-dimensional Gaussian pulse interacts with a two-dimensional hollow plasma channel. (b) 3D setup where a linearly polarized and cylindrically symmetric Gaussian pulse interacts with a hollow cylindrical target.}
\end{figure*}
\section{Phase velocity in 2D and 3D waveguides}
Previous studies\cite{Xiao_hollow_channel,Wang_2019,Gong_hollow_channel} have shown that, in a hollow channel without significant ion expansion, the dominant contributor to electron acceleration is the electric field in the direction of the laser propagation, i.e. the longitudinal field $E_x$. The corresponding structure of propagating electromagnetic fields can be characterized as TM (transverse magnetic) modes. The wave equation of TM modes can be written as
\begin{equation}
\bigg(\dfrac{\partial^2}{\partial y^2} + \dfrac{\partial^2}{\partial z^2}\bigg)E_x + \bigg(\dfrac{\omega^2}{c^2}-k^2\bigg)E_x = 0 ,
\label{Eq:wave_equation}
\end{equation}
where $\omega$ is the wave frequency, $k$ is the wavenumber and $c$ is the speed of light. For a two-dimensional waveguide (shown in \cref{fig:Schematics}a), $E_x$ is a function of $y$ and $\partial E_x/ \partial z = 0$. \Cref{Eq:wave_equation} then becomes ${\partial^2}E_x/{\partial y^2} + (\omega^2/c^2-k^2) E_x =0$. We choose $E_x = E_0 sin(\pi y / R)$ as the TM-mode solution that matches the field structure in the incoming pulse (i.e. $E_x=0$ on axis) and the boundary conditions which requires $E_x(y = \pm R) = 0$. Here $R$ represents the radius of the plasma channel. The dispersion equation in the 2D waveguide is then given by
\begin{equation}
\dfrac{\omega^2}{c^2} = k^2 + \dfrac{\pi^2}{R^2} .
\label{Eq:2D_dispersion}
\end{equation}
For the 3D cylindrical waveguide (shown in \cref{fig:Schematics}b), it is convenient to rewrite \cref{Eq:wave_equation} in cylindrical form as
\begin{equation}
\dfrac{1}{r}\dfrac{\partial}{\partial r} \bigg(r \dfrac{\partial E_x}{\partial r}\bigg)
+ \dfrac{1}{r^2}\dfrac{\partial^2 E_x}{\partial \psi^2} + \bigg(\dfrac{\omega^2}{c^2}-k^2\bigg)E_x = 0,
\end{equation}
where $r$ is the axial distance and $\psi$ is the azimuth. Assuming a solution in the form of $E_x = f \sin(\psi)$, the resulting equation for $f$ then reads
\begin{equation}
s^2 \dfrac{\partial^2 f}{\partial s^2} + s \dfrac{\partial f}{\partial s} + (s^2 -1) = f.
\end{equation}
Here $s \equiv \beta r$ and $\beta^2 = \omega^2/c^2 -k^2$. The solution for $f$ is given by $f = E_{\parallel} J_1(s) = E_{\parallel}J_1(\beta r)$ where $J_1(x)$ is a Bessel function of the first kind and $E_{\parallel}$ is the amplitude of the longitudinal field. At the boundary of the cylindrical waveguide, $f(r=R) = 0$ which yields $\beta R \approx 3.8$. The dispersion relation of the 3D cylindrical waveguide
is then written as
\begin{equation}
\dfrac{\omega^2}{c^2} = k^2 + \dfrac{14.7}{R^2}.
\label{Eq:3D_dispersion}
\end{equation}
It is convenient to derive a general expression for $v_{ph}$ of a propagating wave with the dispersion relations given in \cref{Eq:2D_dispersion,Eq:3D_dispersion}.
\begin{equation}
u = \dfrac{v_{ph}}{c} = \dfrac{\omega}{kc} = \sqrt{1+\dfrac{\alpha^2}{R^2k^2}} \approx \sqrt{1+\dfrac{\alpha^2}{R^2k_0^2}},
\label{Eq:combined_dispersion}
\end{equation}
where we set $k \approx k_0=\omega/c$, $\alpha^2 = \pi^2 \approx 9.9$ for the 2D channel and $\alpha^2 = 14.7$ for the 3D cylindrical channel. Subtracting the $v_{ph}$ from $c$, in the limit of $\alpha^2 \ll R^2 k_0^2$ we have
\begin{equation}
\delta u = u - 1 \approx \dfrac{1}{2}\dfrac{\alpha^2}{R^2k_0^2}.
\label{Eq:dephasing}
\end{equation}
$\delta u$ is a dimensionless parameter used to quantify the degree of supuerluminosity~\cite{Robinson_PoP_2015}; it can be understood as a dephasing rate, since it illustrates how quickly the local laser wave-front outpaces the electron in question.
The ratio of the dephasing rate for the case in 2D to that in 3D is
\begin{equation}
\dfrac{\delta u_{3D}}{\delta u_{2D}} \approx 1.5.
\end{equation}
In the following sections we are going to demonstrate via numerical simulations that the lower dephasing rate in 2D leads to an overestimate of electron acceleration and $\gamma$-ray emission.
\section{Impact of dimensionality on electron acceleration}\label{impact_electron}
\begin{figure*}[htp!]
\centering
\includegraphics[width=0.9\textwidth,trim={0cm 0.cm 0cm 0.0cm},clip]{Figure2.png}
\caption{\label{fig:Electron_spectrum_2D3D} Time-resolved electron energy spectrum observed in (a) the 2D simulation (b) the 3D simulation. The colorbar represents the number of electrons collected onto a certain energy bin
d$\varepsilon_e$. (c) The peak energy spectrum in 2D and 3D which occurred at $t=500$ fs (marked with red star) and $t = 255$ fs (marked with gray star) respectively. We define $t = 0$ fs as the time when the laser pulse reaches its peak amplitude in the focal plane at $x = 0$ $\mu$m in the absence of the target. Typical electron trajectories are plotted in (d) $y$-$t$ space for the 2D simulation (e) $r$-$t$ space for the 3D simulation. Here $r=\sqrt{y^2+z^2}$. The color on the trajectories represents electron relativistic energy.}
\end{figure*}
We model the electron acceleration through fully relativistic PIC simulations using the EPOCH code\cite{Epoch} which is available in both 2D and 3D. The target geometries implemented in the simulations are depicted in \cref{fig:Schematics}. In 2D, the target is a straight empty channel enclosed by two uniform plasma slabs. In 3D, the channel is enclosed by a cylindrical wall of plasma, with a channel diameter such that a slice along the target axis would be identical to the 2D setup. The 2D and 3D simulations share the same plasma composition, plasma density, laser intensity, temporal profile, and laser spot size. The laser intensity is set as $1.37 \times 10^{22} \ \rm{W/cm}^2$, corresponding to $a_0 = 100$. Here $a_0 \equiv |e|E_0/(m_e c\omega)$ is the normalized laser amplitude, where $E_0$ is the peak amplitude of the electric field in the incoming laser pulse, and $m_e$ and $e$ are the electron mass and charge. The laser pulse is always focused at the channel entrance. We choose gold as the original target material with a density of 1.5 g/cm$^3$. According to the field ionization model, the considered laser pulse is capable of ionizing gold atoms to the level of $Z = 69$. In the simulations, the target is pre-ionized accordingly to a plasma composed of Au$^{+69}$ (density 4 $n_{cr}$) and $e^-$ (density 276 $n_{cr}$) where $n_{cr} \equiv m_e\omega/(4\pi e^2)$ is the critical density. A detailed comparison of parameters used in the 2D and 3D simulations is listed \cref{table_PIC}. Note that although the target lengths are set differently, this is done such that in different dimensionalities the target is long enough for the electrons to reach their first energy peak.
\begin{table}
\caption{Parameters used in 2D and 3D PIC simulations. $^*$To calculate the laser power, we assume the length of third dimension in 2D simulations as 2 ${\upmu\mathrm{m}}$.}
\label{table_PIC}
\begin{tabular}{ |l|l|}
\hline
\multicolumn{2}{|c|}{Parameters shared by 2D and 3D simulations} \\
\hline
\multicolumn{2}{|l|}{\underline{\bf Laser pulse:} }\\
Peak intensity & $1.37 \times 10^{22}$ W/cm$^2$ \\
$a_0$ & 100\\
Polarization & linearly along $\mathbf{\hat{y}}$\\
Wavelength & $\lambda_L = 1~{\upmu\mathrm{m}}$ \\
Location of the focal plane & $x = 0~{\upmu\mathrm{m}}$, surface of plasma\\
Pulse temporal profile & Gaussian \\
Pulse duration & \\
(FHWM for intensity) & 30 fs\\
Pulse width/focal spot & \\
(FWHM for intensity) & $w_0 = 2.8~{\upmu\mathrm{m}}$\\
\multicolumn{2}{|l|}{\underline{\bf Plasma:} }\\
Composition & gold ions and electrons \\
Channel radius & $R = 4.0~{\upmu\mathrm{m}}$ \\
Target thickness & $d = 0.4~{\upmu\mathrm{m}}$\\
Electron density & $n_e = 276 n_{cr}$ \\
Ion mass to charge ratio & $197 m_p$ : 69 \\
Ion mobility & mobile \\
\hline
\multicolumn{2}{|c|}{Parameters varying in 2D and 3D simulations} \\
\hline
Spatial resolution & {{2D:}} $100/{\upmu\mathrm{m}} \times 100/{\upmu\mathrm{m}}$ \\
& {{3D:}} $50/{\upmu\mathrm{m}} \times 50/{\upmu\mathrm{m}} \times 50/{\upmu\mathrm{m}}$\\
$\#$ of macro-particles/cell & {{2D:}} 100 for $e^-$, 5 for $\rm{Au}^{+69}$\\
& {{3D:}} 10 for $e^{-}$, 5 for $\rm{Au}^{+69}$\\
laser geometry & 2D: symmetric about $y$-axis \\
& 3D: cylindrical symmetry \\
laser power & 2D: 0.82 PW$^*$\\
& 3D: 1.24 PW\\
Target length & {{2D:}} $L = 350~{\upmu\mathrm{m}}$ \\
& {{3D:}} $L = 150 {\upmu\mathrm{m}}$ \\
\hline
\end{tabular}
\end{table}
\Cref{fig:Electron_spectrum_2D3D}(a) and (b) illustrate the time history of the electron energy spectrum observed in both 2D and 3D simulations. There exists more than one energy peak in both \cref{fig:Electron_spectrum_2D3D}(a) and \cref{fig:Electron_spectrum_2D3D}(b) and our focus is on the first energy peak which happens before any deceleration takes effect. It is clear that the maximum electron energy gain achieved in 2D significantly exceeds the gain observed in the 3D case. In fact, the first energy peak in 2D occurs at $t=500$ fs with $\varepsilon_e = 1920$ MeV while in 3D the peak occurs at $t=255$ fs with $\varepsilon_e =1240$ MeV. \Cref{fig:Electron_spectrum_2D3D}(c) gives a direct comparison of the peak spectra observed in the 2D and 3D simulations. In order to facilitate a comparison between the two simulations, we added a gray star to \cref{fig:Electron_spectrum_2D3D}(a) that represents the energy and time of the first peak from \cref{fig:Electron_spectrum_2D3D}(b). Evidently, the acceleration in 2D lasts longer, which results in a more energetic electron spectrum. Note that to make a quantitative comparison with the 3D simulations, we assume a uniform third dimension with a length of $2~{\upmu\mathrm{m}}$ for the 2D simulation.
To further understand the electron acceleration process, we tracked energetic electrons in both simulations. \Cref{fig:Electron_spectrum_2D3D}(d) and \Cref{fig:Electron_spectrum_2D3D}(e) illustrate the trajectories of representative electrons selected from both the 2D and 3D simulations. Plotted in the space of the transverse location ($y$ or $r$) and time, the trajectories are in agreement with the time history of electron spectrum given in \cref{fig:Electron_spectrum_2D3D}(a-b); the electron energies peak at the corresponding moments. Regardless of the dimensionality, the electrons surf along the channel wall while getting accelerated by longitudinal electric fields until reaching their first energy peak. However, the horizontal surfing of electrons in the 3D simulation terminates earlier due to its higher dephasing rate, which will be elaborated in the next section. It is worth noting that the second energy peak observed in \cref{fig:Electron_spectrum_2D3D}(a-b) is correlated with the electron motion of crossing the central axis, indicating an involvement of the transverse electric field in electron acceleration.
Through evaluating the electron energy spectrum and tracking individual electron motion, we have shown that the dimensionality of simulations significantly impacts electron acceleration. The 2D simulations tend to extend the electron acceleration process, leading to an overestimate of the maximum electron energy when compared to more realistic 3D simulations.
\section{Electric field profiles and phase velocity}
An electron travelling in the laser fields gains energy only while staying in the accelerating phase of the electric field. The electron can gain energy from both longitudinal ($E_{\parallel} = E_x$) and transverse ($E_{\perp} = E_y,\ E_z$) electric fields. The total work done by the electric fields on a given electron can be expressed as
\begin{equation}
W_{tot} = W_{\parallel} + W_{\perp} = -|e| \int_{-\infty}^{t} (E_{\parallel}v_{\parallel} + E_{\perp}v_{\perp}) \,dt{'} .
\end{equation}
Figure 3 shows the contributions of $W_{\parallel}$ and $W_{tot}$ to electron relativistic energy at the first peak by binning all electrons according to their energies. In the 2D simulation 95\% of the energy of energetic electrons ($\varepsilon_e > 500$ MeV) comes from the work done by the longitudinal electric fields and in the 3D case the quantity is 86\%. It is then reasonable to approximate
\begin{equation}
W_{tot} \approx W_{\parallel} = -|e| \int_{-\infty}^{t} E_{\parallel}v_{\parallel} \,dt{'} .
\end{equation}
This simply allows us to narrow down the investigation of electron acceleration to a single component of the electric fields.
\begin{figure} [htp!]
\includegraphics[width=0.98\columnwidth,trim={0.2cm 0.1cm 0cm 0cm},clip]{Figure3.png}
\caption{\label{fig:work_para_perp} Contributions to the electron relativistic energy by $E_{\parallel}$ ($W_{\parallel}$, red bars) and the electric fields (including both $E_{\parallel}$ and $E_{\perp}$, $W_{tot}$, green bars) in (a) the 2D simulation and (b) the 3D simulation. The snapshots are taken at $t=500$ fs and $t = 255$ fs respectively, corresponding to the first peak of electron energy spectra in \cref{fig:Electron_spectrum_2D3D}. The bar width in (a) and (b) is set as 75 MeV.}
\end{figure}
At ultra-high laser intensities, the dephasing rate $\delta u$ is approximately $(v_{ph}-c)/c$, since for a relativistic electron co-propagating with laser, $c-v_x \ll v_{ph}-c$. \Cref{fig:phase_v_traj}(a-b) describes the temporal profiles of the transverse electric fields $E_y$ recorded in a moving window. Note that $E_y$ and $E_x$ share the same wave mode and phase velocity. By tracking a fixed field segment, we find that $v_{ph} \approx 1.0031 \ c$ in the 2D simulation, and $v_{ph} \approx 1.0063 \ c$ in the 3D simulation. The dephasing rate in 2D is nearly two times lower than that in 3D, explaining the distinction between the electron energy gain seen in the two simulations. The duration for electrons staying in an accelerating phase of electric fields can be estimated by
\begin{equation}
\delta t \approx 0.5 \lambda_{L} / (\delta u \cdot c),
\end{equation}
where $0.5\lambda_L$ is the width of the accelerating phase. We find that $\delta t \approx$ 540 fs and 260 fs in 2D and 3D, matching well with the times found from the simulations, demonstrating the accuracy of the approximation used to calculate the phase velocity. The previously derived \cref{Eq:dephasing} however gives the analytical values of the phase velocity as $v_{ph} = 1.0078 \ c$ in 2D, and $v_{ph} \approx 1.0116 \ c$ in 3D. Despite the difference in numerical value, the same trend of an increase in phase velocity is consistent in both the analytical treatment and the numerical simulations. There are a number of factors that can lead to this discrepancy between the analytical calculations and the numerical simulations, for example: the analytical calculation assumes a perfectly conducting boundary and so requires the transverse fields to be zero at the channel edges\cite{Gong_hollow_channel}; sinusoidal waves are not a perfect match (though close) for the fields observed in the hollow channels. Our additional simulations with different target size $R$ show that as phase velocity varies with $R$, the ratio of $\delta u$ in 2D to $\delta u$ in 3D is preserved.
To further check how the phase velocity influences electron acceleration, we track representative electrons with respect to $E_{x}$ fields sampled by them, as illustrated in \cref{fig:phase_v_traj}(c-d). It is clear that the electrons remain accelerated when they stay in the favourable phase of $E_x$ fields (the negative fields colored in blue). After exiting the accelerating phase, the electron energy declines. As can be seen from the time scale in \cref{fig:phase_v_traj}(c-d) electrons in the 2D simulation are subject to far longer periods of acceleration than those in 3D, due to the lower phase velocity in 2D. The evolution of energy and longitudinal work of the chosen electrons is shown in \cref{fig:phase_v_traj}(e). At early moments (up to $\sim$260 fs), the curves of $W_{\parallel_{\ {\rm{2D}}}}$ and $W_{\parallel_{\ {\rm{3D}}}}$ almost overlap with each other implying that the amplitudes of accelerating fields in 2D and 3D are similar. It is then clear that the major cause for the smaller electron energy observed in the 3D simulation is the early termination of the acceleration process due to the higher dephasing rate.
\begin{figure*}[!htb]
\includegraphics[width=0.99\textwidth,trim={0cm 0cm 0cm 0cm},clip]{Figure4.png}
\caption{\label{fig:phase_v_traj} (a) Temporal profiles of $E_y$ fields on the central axis in (a) the 2D simulation (recorded at $y=0$) (b) the 3D simulation (recorded at $y=z=0$). The $E_y$ fields are plotted in a moving window which moves with the speed of light. Here $E_0$ with a value of $3.2\times10^{14} \ \rm{V/m}$ is the peak amplitude of the electric field in the incoming laser pulse. The black dashed lines show the segments used to determine $v_{ph}$ in each run. The trajectory of a typical high-energy electron is plotted together with the exact $E_x$ fields sampled by that electron in (c) the 2D simulation (d) the 3D simulation. (e) The comparison of relativistic electron energy and the longitudinal work between the electrons tracked in (c) and (d).}
\end{figure*}
\section{Influence of dimesionality on photon emission}
The focus of the discussion in the previous sections was the impact of simulation dimensionality on the laser-driven electron acceleration and generation of energetic electrons with energies of hundreds of MeV to a few GeV. These high-energy electrons are subject to emitting energetic photons (in x-ray and even up to the $\gamma$-ray range) while accelerating in laser and channel fields. In this section, we investigate how the photon emission changes with the dimensionality of simulations. The emitted power $P_{\gamma}$ of synchrotron emission is determined by the electron acceleration in an instantaneous rest frame. This acceleration is proportional to a dimensionless parameter\cite{LLclassicfields.1975} $\eta$,
\begin{equation} \label{Eq:eta}
\eta \equiv \frac{\gamma_e}{E_S} \sqrt{\bigg(\bf{E} + {\rm{\frac{1}{c}}}[v \times B]\bigg){\rm{^2}} - {\rm{\frac{1}{c^2}}}(E\cdot v){\rm{^2}}},
\end{equation}
where $\bf{E}$ and $\bf{B}$ are the electric and magnetic fields acting on the electron, $\gamma_e$ and $\bf{v}$ are the relativistic factor and the velocity of the electron, and $E_S \approx 1.3 \times 10^{18} \ \rm{V/m}$ is the Schwinger field. The emitted power from an electron scales as $P_{\gamma} \propto \eta^2$. We are interested in photons with energy above 100 keV, a threshold shown to be critical for photon-photon pair production~\cite{PRApplied_power}.
Collecting all the forward-emitted photons over the duration of the simulations, \cref{fig:emission_position} compares the spatial distributions of photons produced in the 2D and 3D simulations. Noting that in the simulations performed here, once a photon is generated, the emission location is marked as the photon location for the duration of the simulation. Corresponding to the electron acceleration, the first peak of emission in 3D takes place at $x \sim 60\ \mu$m, well ahead of that in 2D which is located at $x \sim 140\ \mu$m [see \cref{fig:emission_position}(a)]. Up to the first peaks, 38\% of laser energy in 2D is transferred to particles (photons, electrons and ions) compared to 41\% in 3D. Of the transferred energies 0.47\% is converted into photons ($\varepsilon_{\gamma} > 100 \ \rm{keV}$) in the 2D simulation in contrast to 0.11\% in the 3D simulation. As shown in \cref{Eq:eta}, $\eta$ is directly proportional to electron's relativistic factor, i.e. $\eta \propto \gamma_e$.
In the previous section it is noted that the field amplitudes acting on the electrons are similar in both 2D and 3D. Thus the primary cause of the lower conversion rate in 3D is due to the lack of electrons at very high energies. \Cref{fig:emission_position}(b-c) illustrates the distribution of photons in ($x$,$y$) space. The common feature of both distributions is that most photons are generated close to the channel boundary, corresponding to the surfing motion of energetic electrons depicted in \cref{fig:Electron_spectrum_2D3D}(d-e). The second peak of emission in both simulations becomes weaker in amplitude and accumulates less photon yield following the first peak. The distribution of the emission in the 3D simulation on the transverse plane ($y$,$z$) is given in \cref{fig:emission_position}(d). It is clear that the emission is concentrated around $z=0 \ \mu\rm{m}$ plane with two populated lobes formed near the channel boundaries, meaning that the emission pattern on the transverse plane is correlated with the direction of laser polarization.
\Cref{fig:emission_angular} compares the angular distribution and energy spectrum of 2D and 3D simulations. The photon emission in 3D is projected onto a sphere, as illustrated \cref{fig:emission_angular}(a). Though the target is cylindrical, the emission pattern does not preserve the same symmetry. From \cref{fig:emission_angular}(b), the energy distribution along the azimuthal angle ${\rm{d}}E_{\gamma}/{\rm{d}}\theta_{\gamma}$
demonstrates a divergence of $10^{\circ}$ (i.e. the FWHM of the energy distribution curve), which is more than two times wider than that in the polar angle direction. The photon beam in the 2D case is found to be more collimated with a divergence of $6^{\circ}$ in ${\rm{d}}E_{\gamma}/{\rm{d}}\theta_{\gamma}$. Distributing emission over $\theta_{\gamma}$ and photon energy, \cref{fig:emission_angular}(c-d) manifest the photon beam in 2D is better collimated throughout the whole energy spectrum. To further evaluate the quality of the two photon beams, we compare the beam brilliance. The source size of the 3D target is easily decided by its radius while in 2D the source size is set as 4$\times$2 $\mu$m$^2$. It is found that the brilliance of $\gamma$-ray beams is 2.9$\times$$10^{21}$ and 5.8$\times$$10^{20}$ photons/s mm$^2$ mrad$^2$ 0.1\%BW (at 1 MeV) for 2D and 3D respectively. In \cref{fig:emission_angular}(e) starting from 1.5 MeV, the number of $\gamma$-ray photons in 2D surpasses that in 3D, projecting a larger brilliance in 2D for energy level above 1 MeV.
In this section, we compared the photon yield with regard to the simulation dimensionality. Since photon emission is a direct result of electron acceleration, the emission demonstrates correlated features as observed for electrons in \cref{impact_electron}. The first peak of photon emission in 3D arrives early in space due to the high phase velocity. The lack of high-energy electrons makes the conversion of laser energy to $\gamma$-ray photons less efficient in 3D. Besides the impact on photon number yield, the dimensionality also affects the collimation of the photon beam. With a large divergence angle and a small number of high-energy photons, the 3D $\gamma$-ray beam is less bright than the 2D beam.
\begin{figure*}
\includegraphics[width=0.88\textwidth,trim={0.0cm 0.1cm 0cm 1cm},clip]{Figure5.png}
\caption{\label{fig:emission_position} Photon distribution over space. (a) Photon energy distribution along $x$ axis. Photon number distribution in ($x$,$y$) space for (b) 2D and (c) 3D. (d) Transverse distribution of photon number for the 3D simulation plotted in ($y$,$z$) space. The considered photons are forward-emitted, accumulated up to 1100 fs and 500 fs for 2D and 3D respectively. The photon energy threshold is 100 keV.}
\end{figure*}
\begin{figure*}
\includegraphics[width=1.0\textwidth,trim={0.0cm 0.1cm 0cm 1.02cm},clip]{Figure6.png}
\caption{\label{fig:emission_angular} (a) Photon count per solid angle for the 3D simulation. The solid circles mark polar angles of $5^{\circ}$ and $15^{\circ}$. (b) Photon energy distribution over the azimuthal $\theta_{\gamma}$ and polar angles $\varphi_{\gamma}$ for both 2D and 3D, where $\theta_{\gamma} = {\rm{arctan}}(p_y/p_x)$ and $\varphi_{\gamma} = {\rm{arctan}}(pz/\sqrt{p_x^2+p_y^2})$. To make the curve for ${\rm{d}}E_{\gamma}/{\rm{d}}\theta_{\gamma}$ of the 3D simulation visible, its y axis is multiplied by a factor of 6. The spectral-angular distribution of the generated $\gamma$-ray pulse in the (c) 2D and (d) 3D simulations. Here $s_{\gamma} \equiv \rm{log_{10}}(\varepsilon_{\gamma}/MeV)$. (e) Photon energy spectra. The considered photons are forward-emitted, accumulated upto 1100 fs and 500 fs for 2D and 3D respectively. The photon energy threshold is 100 keV.}
\end{figure*}
\section{Summary and Conclusions}
We have demonstrated the effects of simulation dimensionality on electron acceleration and $\gamma$-ray
production. There are significant distinctions between the results obtained in 2D and 3D setups from both analytical consideration and numerical calculation. Though in numerical values $v_{ph}$ is close to the speed of light, the dephasing rate ($v_{ph}/c-1$) which determines the energy gain varies considerably with simulation geometry. The higher dephasing rate observable in the 3D setup terminates electron acceleration process early in space and time and leads to a reduction of photon emission when compared to 2D.
A 2D channel target presents a planar geometry while a 3D target has a cylindrical symmetry. Analytically we have shown that the phase velocity of laser fields propagating inside the targets closely depends on the target geometry; the phase velocity in 2D is smaller than that in 3D. To be more specific, the dephasing rate in a 2D setup is derived to be 1.5 times slower when controlling for the channel radius and laser wavelength. Through numerical simulations, it is found that the absolute majority of work done on energetic electrons comes from the longitudinal electric field, enabling the investigation of laser-driven particle acceleration based only on one single component of the electric fields. By tracking a fixed segment of laser fields the phase velocity in 2D is again shown to be smaller than in 3D, matching the correct trend shown in the analytical derivation. It is clear that in 2D simulations electrons surf for a longer period in an accelerating phase compared to 3D simulations. As a result, electrons in 2D have an elongated acceleration distance and present a more energetic spectrum, leading to an overestimate of maximum electron energy and the number of high-energy electrons when compared to more realistic 3D simulations.
Similar to electron acceleration, photon emission is strongly impacted by simulation dimensionality. Due to a lack of high-energy electrons, in 3D the photon ($\varepsilon_{\gamma} > 100$ keV) conversion rate is more than 4 times smaller and the emission falls behind on the generation of energetic photons ($\varepsilon_{\gamma} > 1.5$ MeV). In 3D, the emission is accumulated close to the $z=0$ plane with a narrow divergence along the polar angle. However the emission along the azimuthal angle is far more diverged in 3D compared to that in a 2D simulation. As a result, the photon beam produced in a 3D setup is found to be less bright. It is also worth noting that the subsequent peaks of photon emission drop sharply in amplitude and duration.
Though 2D numerical simulations are widely applied in the research of laser and micro-channel interactions, one should not ignore the overestimate and inaccuracy of results caused by the low phase velocity in 2D simulations. In particular, when carrying out numerical simulations to predict and optimize the output for laser micro-channel experiments, it matters to accurately know the exact location of peaked electron spectrum and therefore 3D simulations are indispensable. We conclude that the 2D simulations are capable of qualitatively reproducing the features of 3D simulations, but for quantitative evaluations and reliable predictions, 3D modelling is strongly recommended.
\section*{Acknowledgements}
T.W. and A.A. were supported by AFOSR (Grant No. FA9550-17-1-0382). D.B. was supported by NSF (Grant No. PHY 1903098). K.C. was supported by NSF (Grant No. 1821944). Simulations were performed with EPOCH (developed under UK EPSRC Grants No. EP$\/$G054940$\/$1, No. EP$\/$G055165$\/$1, and No. EP$\/$G056803$\/$1) using HPC resources provided by TACC at the University of Texas. This work used XSEDE, supported by NSF grant number ACI-1548562.
\section*{References}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,587 |
Q: Some questions related to circuits and flow of electrons I have some doubts related to electric fields and flow of current. So, let us assume an electric circuit, which contains a battery and a wire connecting positive and negative terminal of the battery. I read that at its negative terminal, there is a lot of negative charge/electrons, and because of repulsive force, electrons try to move away from each other, and so they try to move to the positive terminal. So, my first question:
When electrons start moving through the wire to the positive terminal,
do they all move at once? Because otherwise, while they are moving,
they will still exert repulsive forces on each other? Does this
repulsive force affect their movement?
So, let us assume they do not move one by one. So, some of them flow through the wire, and because they are moving apart from each other, repulsive force also reduces. So my second question:
Shouldn't some of the electrons stay in the wire itself? If, at some
point of the wire, there is not enough repulsive force present, will
they stop at all, or will they reach the positive terminal?
Now, suppose there are many circuits, in which the shape of wire is different in each case(some straight, some circular). So, my third question:
Will the shape effect the movement of current? Does it have any effect
on the electric field?
And, my final question. Suppose we have a very long wire. Now, I read that as we have concentration of negative charges on the negative terminal, we have concentration of positive charges on the positive terminal. So, if the wire is very long. So, the force between negative charge and positive charge becomes less:
Will the length of the wire effect the speed of the flow of charges?
If we have an infinite length of wire, will charges flow at all?
A: You've asked some really good questions here. Before starting, I want to first mention that the traditional picture of particles moving through a wire in electostatics is missing some physics; for instance, it ignores the quantum mechanical nature of electrons. The reason we still teach this model is because it captures the main effects (the phenomenon of current) without dealing with microscopic details, but I wanted to warn you that some of the answers will involve physics that is probably not contained in your readings in electrostatics.
To put things in perspective, we now know Newtonian physics is "wrong" (or perhaps more accurately, incomplete), and doesn't give the right answers if, for instance, an object is very small or moving very fast. But we still teach Newtonian physics because it's "good enough" for describing macroscopic objects like cars and baseballs.
Now, to answer your questions,
When electrons start moving through the wire to the positive terminal, do they
all move at once? Because otherwise, while they are moving, they will still
exert repulsive forces on each other? Does this repulsive force affect their
movement?
The microscopic picture of a metal is (crudely) a collection of negative charges, aka electrons, moving through a lattice of positive ions. Indeed, there will be an attraction between these ions and the electrons, and repulsion between any two electrons. Surprisingly, there is also an attractive force between the electrons. The origin of this attractive force is that the electrons attract positive charges around them, and can in some cases lead to the formation of a bound state called a Cooper pair, which are relevant for explaining the phenomenon of super-conductivity, a phase of metals where the resistance is exactly zero. Note, this requires quantum mechanics to do properly, and is extremely subtle.
Shouldn't some of the electrons stay in the wire itself? If, at some point of the
wire, there is not enough repulsive force present, will they stop at all, or
will they reach the positive terminal?
Again, we need a more refined model, in this case statistical mechanics. Before connecting the terminals, the electrons all have a random distribution of energy which manifests itself as temperature. The presence of an electrostatic field causes a net flow of charge, but at the micro level, electrons are colliding and moving in a variety of directions. Often times you will see electrostatics books speak of drift velocity of the electrons, which is a statistical representation of the net flow. A single electron is probably moving much faster than the drift velocity, even perhaps in the opposite direction of the current flow, due to the random thermal energy and the collisions between particles.
Will the shape effect the movement of current? Does it have any effect on the electric field?
In electrostatics, no, but in reality, yes. In mechanics, one has statics and dynamics. In electromagnetism, one has electrostatics and electrodynamics. If you keep learning about electromagnetism, you will soon encounter another field, the magnetic field, and you will learn that the electric fields and magnetic fields are intertwined in such a way that lead you to reconsider the two fields as components of a single entity (hence, "electromagnetism"). In particular, you will learn that current carrying wires produce magnetic fields (Ampère's Law) and that changing magnetic fields can produce EMFs (Faraday's Law). This is a legitimate concern for building real world circuits, and the quantity associated with this effect is called impedance. Impedance is measured in Ohms, like resistance, and depends on the geometry of the circuit.
Will the length of the wire effect the speed of the flow of charges? If we have an infinite length of wire, will charges flow at all?
You're definitely on to something here. The resistance of the wire is proportional to the length of the wire. By Ohm's Law, the current is inversely proportional. The current is proportional to the drift velocity, so the current is inversely proportional to the length of the wire. See http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmmic.html#c1 for a derivation.
A: 1.) When you first close a circuit, there is a very brief period of time in which the electrons push each other forward "one by one", so to speak. This very brief period of time is probably on the order of nanoseconds, so we usually ignore it. After that, a steady state condition is established, and the electrons move all at once ... more or less. Don't forget that the electrons are constantly colliding with impurities and lattice vibrations.
2.) So your second question is moot.
3.) Shape can have an effect. Resistance is greater where there are bends in the wire, and all circuits have stray capacitances and inductances which can affect operation. Often, (usually?) these effects are small and negligible. Sometimes they are introduced intentionally.
4.) Length will affect the speed. For a given applied voltage, a longer wire will have a lower voltage per meter (electric field), and the resistance of the wire increases. Eventually, a length will be reached where the current generated is unmeasurably small, lower than the current produced by thermal fluctuations. At that point one the current has effectively stopped.
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Uchanie ist eine Landgemeinde im Powiat Hrubieszowski der Woiwodschaft Lublin in Polen. Ihr Sitz ist das gleichnamige Dorf.
Gliederung
Zur Landgemeinde Uchanie gehören folgende Ortschaften mit einem Schulzenamt:
Aurelin
Białowody
Bokinia
Chyżowice
Drohiczany
Dębina
Feliksów
Gliniska
Jarosławiec
Lemieszów
Łuszczów
Łuszczów-Kolonia
Marysin
Miedniki
Mojsławice
Mojsławice-Kolonia
Odletajka
Pielaki
Putnowice Górne
Rozkoszówka
Staszic
Teratyn
Teratyn-Kolonia
Uchanie-Kolonia
Wola Uchańska
Wysokie
Persönlichkeiten
Jakub Uchański (1502–1581), polnischer Bischof.
Einzelnachweise
Powiat Hrubieszowski | {
"redpajama_set_name": "RedPajamaWikipedia"
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{"url":"http:\/\/sbdp.org.br\/yj6cd2i\/viewtopic.php?77696d=abbreviation-for-standard-deviation","text":"We've got 6 shorthands for standard deviation \u00bb What is the abbreviation for standard deviation? 1 people chose this as the best definition of sd: Sight draft.... See the dictionary meaning, pronunciation, and sentence examples. All content on this website, including dictionary, thesaurus, literature, geography, and other reference data is for informational purposes only. n. Abbr. Is it written with an upper-case \"D\" (Std. Please explain!OK. How is Standard Deviation abbreviated? Glossary of Symbols and Abbreviations ... standard deviation (of a sample, ) - a measure of variability around the mean - Greek lower case sigma (\u03c3) is used for population standard deviation. In financial terms, standard deviation is used -to measure risks involved in an investment instrument. We've got 1 shorthand for Estimated Standard Deviation \u00bb What is the abbreviation for Estimated Standard Deviation? Standard Deviation Example. 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SD stands for Standard Deviation. Data Preparation: Gather the reports that list the data you want to use in your Excel spreadsheet. We can find the standard deviation of a set of data by using the following formula: Where: 1. Deviation can be positive or negative. STD is defined as Standard Deviation very frequently. The standard deviation of X is the square root of this sum: $\\displaystyle \\sigma = \\sqrt{{1.05}} \\simeq {1.0247}$ try it. STAN - STANAG - STANAVFORLANT - STAND - STANDAARD - STANDS4 - STANFINS - STANFINS-R - STANO - STANZA. n. Abbr. That number, 8.40, is 1 unit of standard deviation. Note the lack of periods in acronyms and the lack of apostrophes in their plurals: ACSM, APA, IQ, IQs. Looking for abbreviations of MD? It is equal to the square root of the variance. Looking for the shorthand of Estimated Standard Deviation?This page is about the various possible meanings of the acronym, abbreviation, shorthand or slang term: Estimated Standard Deviation. By Deborah J. Rumsey . standard deviation: standard deviation of random variable X: std(X) = 2: \u03c3 X: standard \u2026 Get instant explanation for any acronym or abbreviation that hits you anywhere on the web! Use abbreviations without explanation for the following terms in the Summary, but define them in the Methods: standard deviation (SD), 95% confidence interval (95%CI), 95% confidence limits (95%CL). \u2026 Look at the graph below and imagine how it would change if the distance between standard deviations were narrower. Need to know how Standard Deviation is abbreviated in Environmental Health? Dev.) STD stands for Standard Deviation. The lower the standard deviation, the closer the data points tend to be to the mean (or expected value), \u03bc. STDEV.P uses the following formula: \u221a[\u2211(x - x\u0303) 2 \/n] where x\u0303 is the average value of x for the entire population and n is the population size. standard deviation (SD) the dispersion of a random variable; a measure of the amount by which each value deviates from the mean. r] is the standard deviation calculated according to ASTM E 74-04 from the differences between the individual measured responses and the corresponding responses computed from Eq. The Standard Deviation is a measure of how spread out numbers are.Its symbol is \u03c3 (the greek letter sigma)The formula is easy: it is the square root of the Variance. Sample Standard Deviation. We are proud to list acronym of SD in the largest database of abbreviations and acronyms. If the data points are further from the mean, there is \u2026 In many cases, it is not possible to sample every member within a population, requiring that the above equation be modified so that the standard deviation can be measured through a random sample of the population being studied. A low standard deviation means that most of the numbers are close to the average, while a high standard deviation means that the numbers are more spread out. On one hand, the average wetted depth of inline is 27.32 cm with standard deviation of 0.98 cm and the coefficient of variation was 3.58 % and the average witted depth of online is 27.27 cm with standard deviation of 1.1 cm and the coefficient of variation was 4.02 %. The Standard deviation formula in excel has below-mentioned arguments: number1: (Compulsory or mandatory argument) It is the first element of the sample of a population. can be used as abbreviation for standard. 95% of all scores fall within 2 SD of the mean. Standard deviation in statistics, typically denoted by \u03c3, is a measure of variation or dispersion (refers to a distribution's extent of stretching or squeezing) between values in a set of data. If you are visiting our non-English version and want to see the English version of Standard Deviation, please scroll down to the bottom and you will see the meaning of Standard Deviation in English language. Ravg\u00a0\u2013 the arithmetic meanBasic Statistics Concepts for FinanceA solid understanding of statistics is crucially important in helping us better understand finance. 99.7% of all scores fall within 3 SD of the mean. By Deborah J. Rumsey . Standard Deviation. Standard Deviation is also known as root-mean square deviation as it is the square root of means of the squared deviations from the arithmetic mean. Deviation: the distance of each value from the mean. STANDS4 LLC, 2020. This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional. When assaying control materials, it is obvious that technologists will not achieve the mean value each and every time a control is analyzed. Basically, a small standard deviation means that the values in a statistical data set are close to the mean of the data set, on average, and a large standard deviation means that the values in the data set are farther away from the mean, on average. . We're doing our best to make sure our content is useful, accurate and safe.If by any chance you spot an inappropriate comment while navigating through our website please use this form to let us know, and we'll take care of it shortly. 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\section{INTRODUCTION}
\label{sec:intro}
The importance of small obstacle discovery for on-road autonomous driving cannot be overstated. Small obstacles such as bricks, stones and rocks pose a veritable hazard to driving, especially to the state estimation modules that are a core constituent of such systems. Some times these obstacles can take the shape of stray dogs and cats that are entailed protection. Many a time these objects are too low on the road and go unnoticed on depth and point cloud maps obtained from state of the art range sensors such as 3D LIDAR. The problem slowly seems to be generating interest in the robotic and vision community \cite{Carsten-IROS16, Carsten-NIPS17}, not without a reason. For one, even the best of range sensors such as 3D LIDAR can find segmenting obstacles of height 15-25cms from a distance of 10m or more rather challenging. The problem is more pronounced with low cost low baseline stereo rigs, wherein the disparity profile can hardly be used to discern such obstacles from the background when they are at a depth of 5m or more.
Introspection reveals that the problem is difficult to solve purely based on appearance cues even with the best of the state of the art deep convolutional networks since gradients in the image can be caused equally due to changes in appearance such as markings and zebra crossings on the road as much as it could be due to obstacle edges. This problem aggravates in case the obstacles are small. Hence, an apt combination of both appearance and depth or disparity evidences is more likely to perform the task better. Recent efforts~\cite{valada2017adapnet} on multi modal fusion also suggests likewise.
Most of the previous works~\cite{Oniga-ITSC11, Carsten-IROS16, Suryansh-ICRA14} in small obstacle detection are based on low level image and depth profile analysis, which are prone to errors due to noise in depth computation (especially while using a stereo rig). The challenge in naive application of recently successful deep learning architectures is the limited availability of annotated data. In this paper, we propose a novel deep learning architecture called MergeNet which can be trained using as low as 135 images to obtain state of the art results.
We pose the problem of obstacle detection as that of segmenting the road scene into multiple classes. The proposed model consists of three key networks, namely the stripe-net, the context-net and the refiner-net. Stripe-net is a fully convolutional encoder-decoder model which is trained with column-wise strips of RGBD input (each training image is divided into a set of non overlapping vertical strips and fed to the network individually). The key idea behind Stripe-net is twofold: (a) learning discriminative features at a low-level by only attending to the vertical pathway of a road scene and (b) sharing parameters across the stripes to ensure lower model complexity and in turn reducing susceptibility to overfit even on small datasets. Context-net is also a fully convolutional encoder-decoder, but is trained on the full image. The role of this network is to incorporate global features which typically span a width higher than the stripe-width used in the previous network. Global coherence and important contextual cues are more suitably learnt using this network. Finally, the refiner-net is used for aggregating both the low and high level features and making the final prediction. Figure~\ref{motivation} illustrates a motivating example, showing the results at different stages of the proposed architecture.
\begin{figure*}[thpb]
\centering
\includegraphics[width=\textwidth,height=0.6\textwidth]{fig1_motivation.png}
\caption{An overview of our network components and their outputs (the obstacle category is marked in red, the off road category is marked in green and the road category is marked in blue). The STRIPE-NET, which takes individual vertical stripes of RGBD data as input, is effective at detecting small objects (but with false positives and noisy road boundaries) whereas the CONTEXT-NET, which takes full RGB images as input, better preserves the overall structure of the scene (but misses out on small objects on the road). The REFINER-NET learns to combine the best of both worlds and outputs accurate and smooth segmentation maps.}
\label{motivation}\vspace{-1em}
\end{figure*}
Formally, we make the following contributions:
\begin{itemize}
\item We propose a novel three-staged architecture for segmenting out the small on-road obstacles. The model design, the multi-modal data input and the fusion of features obtained at multiple spatial scales enable us to exploit the structure in a road scene while preserving the details necessary for small obstacle detection.
\item The proposed network can be efficiently trained for the task of semantic segmentation from as few as 135 images. Thus it makes a much needed effort in the direction of applying deep learning architectures in such data deficient applications.
\item We test our model on the Lost and Found dataset \cite{Carsten-IROS16} and show an improvement of $19\%$ in the instance-level detection rate even when using a tenth of the training dataset and an improvement of around $30\%$ if we use the full dataset. We also achieve comparable results with \cite{Carsten-NIPS17}, while employing only one sixth of the training data.
\end{itemize}
The rest of the paper is organized as follows: Section~\ref{sec:related_work} lists the
related work. The proposed architecture is detailed in Section~\ref{sec:method}. The experiments and results are presented in Section~\ref{sec:experiments} and Section~\ref{sec:results}. The final section comprises of conclusions and future work.
\section{Related Work}
\label{sec:related_work}
Early efforts on small obstacle detection were limited to indoor scenes. Zhou and Baoxin~\cite{zhou2006robust} presented a solution for obstacle detection using homography based ground plane estimation algorithm. The work was extended in~\cite{kumar2014markov} for smaller obstacles by combining multiple cues like homography estimation, superpixel segmentation and a line segment detector into in a MRF framework. Early outdoor efforts on the other hand were focused on problems like curb detection~\cite{Homm-IV10, Oniga-ITS10}. One line of work~\cite{Homm-IV10} was based on probability occupancy maps~\cite{elfes1989using}, which is created by orthogonal projection of the 3D world onto a plane parallel to the road (assuming a structured environment where the floor surface is approximately planar). The plane is then discretized into cells to form a grid and the algorithm then predicts the occupancy likelihood of each cell. Another line of work~\cite{oniga2010processing, Oniga-ITS10} utilized digital elevation map (DEM's), which builds a height based cartesian occupancy grid and uses it for road surface estimation and obstacle detection.
Recent efforts~\cite{Carsten-IROS16,Carsten-NIPS17} have been made to extend the specific problem of small obstacle detection to outdoor settings for applications concerning autonomous driving and driver assistance. In~\cite{Carsten-IROS16} the Lost and Found dataset for small obstacle detection is presented along with three statistical hypothesis tests for detecting small obstacles. The extension of this work~\cite{Carsten-NIPS17} combines deep learning with hypothesis testing. A deep network termed UON which uses a Fully Convolutions Network~\cite{FCN} with GoogleNet architecture is used for obtaining a semantic segmentation map of the scene. The network is trained on 6000 RGB images, combining images from both Lost and Found dataset and the Cityscape dataset~\cite{cordts2016cityscapes}. The UON segmentation of the scene is then converted to a stixel realization~\cite{Frank-BMVC11} and fused with the hypothesis models of~\cite{Carsten-IROS16} to come up with the eventual segmentation. Our method on the contrary is void of any low/mid level post processing.
\begin{figure*}[thpb]
\centering
\includegraphics[width=\textwidth]{fig2_model.png}
\caption{Model architecture is shown. The three components of the pipeline are magnified and illustrated in detail (best viewed in color)}
\label{fig:model}\vspace{-1em}
\end{figure*}
Since the small obstacle detection task can be expressed as that of semantic segmentation of the obstacles, it also makes sense to examine possible architectures pertaining to the segmentation literature. The typical semantic segmentation networks like ~\cite{farabet2013learning}, the Fully Convolutional Network ~\cite{FCN} and SegNet~\cite{badrinarayanan2015segnet} apply hierarchical and bottom-up convolutions and pooling to downsample an image, and then use layers like bilinear upsampling, unpooling, atrous convolution or deconvolution (strided convolution) to obtain a dense segmentation map. More advanced approaches like ~\cite{dai2015convolutional, sharma2015deep} utilize multi-scale or contextual features for learning this dense mapping. Although many competitive architectures for general application of semantic segmentation exist, replication of these models for specific tasks like obstacle detection yields inferior performance. Moreover, the labeled data required for these complex models also limits the direct applicability of standard semantic segmentation models, a problem which we try to resolve in our work.
\section{Learning to detect obstacles}
\label{sec:method}
Before formulating the problem and the model, it is useful to analyze the nature of the problem and the properties a good solution should possess. Firstly, the detection model should be capable of detecting small obstacles which are often far away on the road or don't appear like an obstacle (brick slabs of low height often resemble a cement road). Similarly, detection should preclude artifacts like zebra crossing and chalk markings on the road. Secondly, the effort required for the physical setup of constructing and annotating a small obstacle dataset for autonomous vehicles is considerable, so it makes sense to have a parsimonious learning model which isn't data intensive. Also, less training data makes a sufficiently parametrized model prone to overfitting, which is to be kept in check. Thirdly, the model should be deployable on an autonomous vehicle with respect to the memory and inference speed.
\subsection{Problem formulation}
The obstacle detection problem is posed as that of semantic segmentation of the video frames. The aim is then to learn a mapping $ f(w, x): X \rightarrow L$ for each of the $N$ pixels, where $x_i=(v_i, d_i) \in X$ are ordered pairs of visual RGB and depth input respectively and $l_i \in L$ are the set of labels for each pixel and $w$ are the parameters for the model being used. Three labels, namely \textit{'road'}, \textit{'off road'} and \textit{'small obstacle'} are considered. Due to the various challenges mentioned in the previous section, a staggered approach is used to learn the mapping $f$ as compositions of multiple functions. Each of these mappings is learnt with a loss function defined as the per-pixel cross-entropy loss, given as follows:
\begin{equation}
L(w) = -\sum_{i=1}^{N} \sum_{l=1}^{|L|} \mathds{1}{\{l=y_i\}}log(y_i)
\end{equation}
where, $\mathds{1}$ is the indicator function and $y_i \in Y$ is the softmax probability for pixel $i$. The final output is taken as
\begin{equation}
l_{predicted} = \argmax_{l \in L} (Y)
\end{equation}
\subsection{The MergeNet model}
The core intuition behind the MergeNet model is that learning the low-level features of a road scene, combined with high-level features learnt from the context of the scene can jointly produce better segmentation maps.
The MergeNet consists of three individual CNNs, each implemented as a fully convolutional network. The encoder and decoder blocks used for upsampling and downsampling of the image are similar to Segnet (basic version)~\cite{badrinarayanan2015segnet}, differing only in the number of layers and channels. Each encoder downsamples the input resolution through a series of convolution, batch normalization and pooling layers and then upsamples the encoded features though a series of deconvolution, batch normalization and unpooling layers, back to the original resolution. The first two networks learn at different levels of spatial abstraction while the third is a refiner network which exploits complementary information from the first two networks to produce a refined semantic map. These three models are denoted by functions $g_{stripe}(w_s, x_s)$, $g_{context}(w_c, x_c)$ and $g_{refine}(w_r, x_r)$ in the following sub-sections. Figure~\ref{fig:model} shows the detailed structure of the whole pipeline and its various modules.
\textbf{Stripe Network}
The stripe network is the model responsible for learning low-level features present within a narrow vertical band of the image. The whole image is split vertically into $k$ strips of equal width and the function $g_{stripe}(w_s, x_s)$ is learnt using a shuffled set of strips from the whole training dataset using ground truth labels of corresponding strips as supervision.
The network consists of two parallel encoding and decoding branches, one for the RGB channel and another for the depth channel. Each branch contains four layers of convolutional downsampling in the encoder followed by 4 layers of upsampling in the decoder. These branches are subsequently fused across the channel dimension to obtain a combined map which is used for pixel-wise predictions of the three classes using a softmax layer.
The use of vertical strips $x_s$ offers multiple benefits. It allows the model to concentrate on the discriminative features present only within the narrow vertical band. This, when combined with the context network, can be seen as a form of curriculum learning of features where the easier features are learnt first, followed by learning from more global and information-dense parts of the image. Secondly, the vertical strips allow the disparity map to contribute critical depth information. Within a narrow strip of a typical road scene, the disparity map follows an increasing trend of depth until an obstacle is encountered, the depth at which point, flattens out for some time before regaining its original trend. This can act as a very strong signal for the presence of obstacles. Thirdly, the use of strips allow the network to learn useful features with only a small set of parameters which are shared across all vertically split inputs. This is crucial for preventing overfitting on the small training dataset.
\textbf{Context Network}
The context network is responsible for learning complementary features with respect to the stripe network. The function $g_{context}(w_c, x_c)$ is learnt through full RGB images as input $x_c$, trained with the full image ground truth as supervision. The idea is to learn global context which can complement the stripe network. The context network contains the same number of layers and channels as that of any individual stream of the stripe network and is also similar in architecture to the fully convolutional networks generally used for semantic segmentation task. But the advantage of using it in conjunction with the stripe network is evident from the experimental results which highlight the limitation of the context network in detecting very small obstacles. Apart from providing the global features for obstacle detection, the context network also generates output segmentation maps which are smoother and more coherent with respect to neighboring pixels. Note that as opposed to stripe net, including the depth channel leads to reduced performance, which might be attributed to the use of complex RGBD data coupled with training with very few samples.
\textbf{Refiner Network}
The refiner network $g_{refine}(w_r, x_r)$ is learnt using $x_r$ = $(y_s, y_c)$ where $y_s$ and $y_c$ refer to the class normalized output features from $g_{stripe}(w_s, x_s)$ and $g_{context}(w_c, x_c)$ respectively. The input to this network is therefore the output maps of the previous networks concatenated across the channel axis. This model contains only two convolutional layers each for encoding and decoding as the task of segmentation of raw images is simplified to identifying relevant features from the previously trained outputs. The visualization of features from the stripe and context network underlines the need of a refiner network to learn from the complementarity of features.
The complete MergeNet model is a composition of the three networks:
\begin{equation}
f(w, x) = g_{r}(w_r, (g_{s}(w_s, x_s), g_{c}(w_c, x_c)))
\end{equation}
where $g_{s}$, $g_{c}$ and $g_{r}$ are the stripe, context and refiner models
\subsection{Implementation details}
The context model and refiner model are trained with images of resolution $256*896$ whereas the stripe network is trained with images of size $256*32$ by dividing each image into $k$ vertical strips where $k=28$. Thus each input is of size $256*32$. The strip-width of $32$ is chosen through cross-validation. Adam optimizer~\cite{kingma2014adam} is used while training with an initial learning rate of $0.01$. The batch size is taken as 4 for the context and refiner network and 32 for the stripe network. Training is continued until the model starts to overfit on the validation set. The context and refiner networks are trained with a weighted cross entropy loss to account for the difference in the number of pixels of each class in the dataset. The weights for each class are set as inversely proportional to the ratio of number of class pixels and the number of total pixels. The stripe network is not explicitly weighted at the loss level, but the shuffled stripes are sampled and fed to the network such that the expected value of occurrence of each class pixel is balanced out while training.
During inference, the individual networks are merged and a single segmentation map is produced by the refiner network. The individual strips of the input image $x$ can be passed through the stripe network in parallel as the weights are shared.
\section{Experiments}
\label{sec:experiments}
The following section details the evaluation of our model.
\subsection{Dataset}
The Lost and Found dataset~\cite{Carsten-IROS16} is used for both training and testing of our network. The dataset consists of around 2200 frames of road scene obtained from 112 stereo videos, along with the pixel-level annotation of each frame pertaining to the road category, the off road category and the small obstacle category. The dataset has a challenging test set of 1200 images which contains varying road illumination, different small objects present at long distances, non-uniform road texture, appearance and pathways and many non-obstacle class objects acting as distractors off the road. We train our model using two sets of training data, one with the complete training set of 1036 images and another with a reduced subset of only 135 images sampled equally across all the training image sequences. We evaluate our model on the released test set.
\subsection{Evaluation metrics}
We evaluate our model on both pixel-level and instance-level metrics. While choosing the metrics, there are two primary goals. The first is to ensure fair comparability of our results with the previous state-of-art methods, many of which employ some approach-dependent metric. The second is to assess the performance of our network through generic and approach independent metrics which can be used without any method-coupled adaptation in the future work.
\textbf{Pixel-wise detection rate}
Pixel-level detection rate (PDR) is defined as the fraction of pixels of the obstacle class, taken across the test set, which are correctly detected by the network. Formally, this metric is calculated as:
\begin{equation}
PDR = \dfrac{CDP_{obstacle}}{TP_{obstacle}}
\end{equation}
where $CDP_{obstacle}$ refers to the correctly detected pixels of the obstacle class and $TP_{obstacle}$ refers to the total pixels of the obstacle class.
\textbf{Instance-wise detection rate}
Instance-level detection rate (IDR) is defined as the fraction of obstacle instances, taken across the dataset, which are detected by the network. For this metric, an instance is marked correctly detected if more than $50\%$ of the pixels of the predicted obstacle overlaps with the ground truth of that instance. For extracting instances from pixel-level predictions, we convert the segmented map into a binary image with obstacles/ non-obstacle classes. Then, a 4-connectivity based connected component algorithm is used to obtain instance-level maps of just the obstacle class. The metric is formally calculated as:
\begin{equation}
IDR = \dfrac{CDI_{obstacle}}{TI_{obstacle}}
\end{equation}
where $CDI_{obstacle}$ refers to correctly detected instances of the obstacle class and $TI_{obstacle}$ refers to the total instances of the obstacle class, taken across the entire dataset.
\textbf{Pixel-wise false positives}
Pixel-level false positives (PFP) is defined as the fraction of pixels of the non-obstacle classes, taken across the dataset, which are incorrectly marked as an obstacle. Formally, this metric is calculated as:
\begin{equation}
PFP = \dfrac{IDP_{obstacle}}{TP_{non\_obstacle}}
\end{equation}
where $IDP_{obstacle}$ refers to the incorrectly detected pixels of the obstacle class and $TP_{non\_obstacle}$ refers to the total pixels of the non-obstacle class.
\textbf{Instance-wise false positives}
Lastly, instance-level false positives (IFP) is defined as the fraction of non-obstacle instances, taken across the dataset, which are incorrectly detected by the network. Similar to IDR, connected components algorithm is used to get instance-level predictions. The metric is formally calculated as:
\begin{equation}
IFP = \dfrac{IDI_{obstacle}}{d}
\end{equation}
where $d$ is the number of frames in the testing dataset and $IDI_{obstacle}$ refers to incorrectly detected instances of the obstacle class, taken across the entire dataset.
\section{Results}
\label{sec:results}
\begin{table}[t!]
\begin{center}
\begin{tabular}{l|ll|ll}
\hline \\
\parbox{1cm}{Model}&
\parbox{1.4cm}{\bf IDR (Instance)}&
\parbox{1.4cm}{\bf IFP (Instance)}&
\parbox{0.8cm}{\bf PDR (Pixel)}&
\parbox{0.8cm}{\bf PFP (Pixel)}\\
\\ \hline
\\
Stripe Net@135 & 65.22 & 2.03 &74.65 & 1.98 \\
Context Net@135 & 55.89 & 0.49& 62.76 & 1.73\\
\bf MergeNet@135 & 73.42 &0.69& 85.00 & 2.01\\
Stripe Net@1036 & 77.87 & 2.48 & 86.71 & 4.16\\
Context Net@1036 & 65.00 & 1.40& 74.52 & 3.60\\
\bf MergeNet@1036 & 82.05 &0.76& 92.85 & 3.19\\
\hline
\end{tabular}
\caption{MergeNet and its components' performance on the Lost and Found dataset}
\label{table:final_results}\vspace{-3.5em}
\end{center}
\end{table}
\subsection{Quantitative results}
Table \ref{table:final_results} presents the results of our model and all its components, on the full testing set of 1036 images and on a subset of it containing 135 images. The Stripe-net model performs better than the Context-net, reinforcing two of our basic assumptions. Firstly, that the road scenes afford an inherent vertical structure in the data, for both RGB and depth inputs, which can be exploited effectively by sharing parameters across the strips. Secondly, the local information learnt by the Stripe-net model is more capable of detecting the small obstacles than the standard architectures in semantic segmentation, which operate on full images. On the other hand, the Context-net is much more useful in maintaining the consistency of labels in a globally-aware manner, as evident from the qualitative results in the next section. Furthermore, the Context-net also plays the vital role of learning features which minimize the presence of false positives. This is also verified quantitatively by observing that the false positives are reduced from $2.03$ (Stripe-Net@135) to $0.69$ (Refiner-net@135) and from $2.48$ (Stripe-Net@1036) to $0.76$ (Refiner-net@1036) when going from only Stripe-Net to the Refiner-Net (final model) which uses both Context and Stripe networks.
Table \ref{table:compare_results} shows the comparison of our model against the previous state-of-art methods. FPHT Stixels~\cite{Carsten-IROS16} uses the same 1200 image testing set from Lost and Found dataset that we do. They also have a similar detection metric for pixel-level and instance-level detection which makes a direct comparison feasible. Using only 135 images, we achieve an instance detection rate of $73.4\%$ which is a $19\%$ improvement with $10$ times less the data used for training and much fewer false positives. A similar improvement is also visible in pixel-level detection rates and false positives. Naturally, this performance boost is even higher (around $30\%$) when comparing our approach trained on the full training set with FPHT Stixels.
We also compare our model with a more recent work called UON-Stixels and its extensions~\cite{Carsten-NIPS17} which are prefixed as \textit{FUSION} in table \ref{table:compare_results}. We perform comparable to their state-of-art detection result on instances with only one-sixth of the training data which again affirms the ability of MergeNet to perform better with lesser data (it is to be noted that we use a stricter metric of at least $50\%$ overlap with the ground truth annotation whereas their metric only evaluates on an upper bound). The other metrics like pixel-level detections and false positives can't be compared since they are either not evaluated in the paper or are differently defined. Another important point to be noted here is that UON Stixels and its extensions also learn a fully convolutional network trained for semantic segmentation for generating a semantic class map which is then used by other methods to get the $84.1\%$ detection rate. This means that it is theoretically possible to use our networks in conjunction with their post-processing techniques to further improve our performance.
\begin{figure}[thpb]
\centering
\includegraphics[width=\linewidth]{fig3_chart.png}\vspace{-1em}
\caption{Variation of the cumulative instance detection rate across obstacle distance}
\label{fig:chart}
\end{figure}
Another quantitative experiment which we conduct in Figure~\ref{fig:chart}, similar to that of previous work, is analyzing the variation of cumulative detection performance with respect to the depth of obstacle. The plot shows two of our models, along with the plots from the previous work. The graph presents the typical difficulty in detecting obstacles as the distance from the camera increases.
Finally, we report the inference time of our model. MergeNet generates semantic maps at $5$ FPS on a Nvidia GeForce GTX 1080 Ti GPU which can be run smoothly on top of an autonomous vehicle in real time.
\begin{table}[t!]
\begin{center}
\begin{tabular}{l|ll|ll}
\hline \\
\parbox{1cm}{Model}&
\parbox{1.4cm}{\bf IDR (Instance)}&
\parbox{1.4cm}{\bf IFP (Instance)}&
\parbox{0.8cm}{\bf PDR (Pixel)}&
\parbox{0.8cm}{\bf PFP (Pixel)}\\
\\ \hline
\\
FPHT Stixels@1000 & 55.00 &5.00& 68.00 & 2.00\\
UON-Stixels@6000 & 73.80 &0.103& NA & NA \\
FUSION-OR@6000 & 84.10 &0.669& NA & NA \\
FUSION-Prob@6000 & 82.80 &0.496& NA & NA \\
MergeNet@135 & 73.42 &0.69& 85.00 & 2.01\\
\bf MergeNet@1036 & 82.05 &0.76& 92.85 & 3.19\\
\hline
\end{tabular}
\caption{Comparison of our method with ~\cite{Carsten-IROS16} and ~\cite{Carsten-NIPS17}}
\label{table:compare_results}\vspace{-3.5em}
\end{center}
\end{table}
\begin{figure*}[t!]
\centering
\begin{tabular}[b]{c c c}
\includegraphics[width=0.33\linewidth]{results/rgb_687.jpg}& \hspace{-1.2em}
\includegraphics[width=0.33\linewidth]{results/rgb_725.jpg}& \hspace{-1.2em}
\includegraphics[width=0.33\linewidth]{results/rgb_1132.jpg} \vspace{0.1em}\\
{} & {Images from Lost \& Found dataset} & {} \vspace{0.7em}\\
\includegraphics[width=0.33\linewidth]{results/colored_gt_687.jpg}& \hspace{-1.2em}
\includegraphics[width=0.33\linewidth]{results/colored_gt_725.jpg}& \hspace{-1.2em}
\includegraphics[width=0.33\linewidth]{results/colored_gt_1132.jpg} \vspace{0.1em}\\
{} & {Ground Truth} & {} \vspace{0.7em}\\
\includegraphics[width=0.33\linewidth]{results/snet_687.jpg}& \hspace{-1.2em}
\includegraphics[width=0.33\linewidth]{results/snet_725.jpg}& \hspace{-1.2em}
\includegraphics[width=0.33\linewidth]{results/snet_1132.jpg} \vspace{0.1em}\\
{} & {Outputs of Stripe Net} & {} \vspace{0.7em}\\
\includegraphics[width=0.33\linewidth]{results/cnet_687.jpg}& \hspace{-1.2em}
\includegraphics[width=0.33\linewidth]{results/cnet_725.jpg}& \hspace{-1.2em}
\includegraphics[width=0.33\linewidth]{results/cnet_1132.jpg} \vspace{0.1em}\\
{} & {Outputs of Context Net} & {} \vspace{0.7em}\\
\includegraphics[width=0.33\linewidth]{results/rnet_687.jpg}& \hspace{-1.2em}
\includegraphics[width=0.33\linewidth]{results/rnet_725.jpg}& \hspace{-1.2em}
\includegraphics[width=0.33\linewidth]{results/rnet_1132.jpg} \vspace{0.1em}\\
{} & {Final output of MergeNet} & {} \vspace{0.7em}\\
\end{tabular}\vspace{-1em}
\caption{Obstacle detection results on some of the selected examples using MergeNet@135. The obstacle category is marked in red, the off road category is marked in green and the road category is marked in blue. Please zoom in to clearly see the small obstacles (best viewed in color)}
\label{fig:result2}\vspace{-0.5em}
\end{figure*}
\subsection{Qualitative results}
Results of our method (MergeNet@135) on some of the images from the test set are shown in Figure~\ref{fig:result2}. Additional results can be found in our video. We select the particular road images to highlight the challenges arising due to varying appearance, size, distance, shape and clutter of the obstacles. The qualitative results display all the network outputs of 3 test images in each column. The first column shows three far off obstacles on the road, one of each going undetected by both stripe and context networks. But due to the complementary nature of features, and in turn, detections, the final refiner network output detects all three obstacles successfully. In the second column, three obstacles are present, each with different size, height, texture and illumination. This road also has chalk markings, something which the training set frames do not contain. Even though the context network misses out on all three obstacles, the stripe network detects all of them and this is also passed onto the refiner network, which segments all three objects with higher accuracy than both other networks. Finally, the third column shows a relatively larger obstacle, which is bigger than the strip-width of the stripe network. The stripe network merges it into the off road category, which is reasonable given it looks at each stripe individually. However, the prediction is corrected when merged with the context through the refiner network.
As for the failure cases of our approach, we observe 3 main qualitative scenarios: a) Undetected obstacle - Occurs when the obstacle height is too low (e.g. a thin plank). b) Obstacle detected as off-road - Occurs when obstacle lies too close to the camera.
c) Off-road detected as obstacle - Occurs when irregular artifacts (e.g. patch of grass) are present at the boundary of the road.
\section{Conclusion}
In this paper, we propose a novel deep network architecture for learning to detect small obstacles on the road scene. The model is composed of multiple stages, with each stage learning complementary features which are then fused to predict a segmentation map of the scene. We present thorough quantitative and qualitative experimentation and the results showcase high fidelity segmentation of obstacles on challenging public datasets. The current version of our algorithm runs at 5fps, which makes it suitable for on-road driving applications such as autonomous driving and driver assistant systems. In future work, we plan to investigate the proposed architecture for settings with more number of classes like pedestrian, pot holes, speed breakers and traffic signs.
\bibliographystyle{IEEEtran}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,960 |
/**
* @module node-opcua-address-space.Private
*/
import { assert } from "node-opcua-assert";
import * as _ from "underscore";
import * as util from "util";
import { BinaryStream, OutputBinaryStream } from "node-opcua-binary-stream";
import { BrowseDirection, NodeClass, QualifiedName } from "node-opcua-data-model";
import {checkDebugFlag, make_debugLog} from "node-opcua-debug";
import {
BaseUAObject, FieldCategory,
findBuiltInType,
initialize_field
} from "node-opcua-factory";
import { DataTypeFactory } from "node-opcua-factory";
// import { getEnumeration,getConstructor, hasConstructor } from "node-opcua-factory";
import { NodeId, resolveNodeId } from "node-opcua-nodeid";
import { StatusCodes } from "node-opcua-status-code";
import { lowerFirstLetter } from "node-opcua-utils";
import { Variant } from "node-opcua-variant";
import { DataType } from "node-opcua-variant";
import { VariantArrayType } from "node-opcua-variant";
import { ExtensionObject } from "node-opcua-extension-object";
import {
AddressSpace,
UADynamicVariableArray,
UAObject,
UAReferenceType,
UAVariable as UAVariablePublic} from "../source/address_space_ts";
import { AddressSpacePrivate } from "./address_space_private";
import { UADataType } from "./ua_data_type";
import { UAVariable } from "./ua_variable";
const doDebug = checkDebugFlag(__filename);
const debugLog = make_debugLog(__filename);
function makeStructure(
dataTypeFactory: DataTypeFactory,
dataType: UADataType,
bForce?: boolean
): any {
bForce = !!bForce;
const addressSpace = dataType.addressSpace;
// istanbul ignore next
if (!dataType.binaryEncodingNodeId) {
throw new Error("DataType with name " + dataType.browseName.toString() +
" has no binaryEncoding node\nplease check your nodeset file");
}
// if binaryEncodingNodeId is in the standard factory => no need to overwrite
if (!bForce && (dataTypeFactory.hasConstructor(dataType.binaryEncodingNodeId) || dataType.binaryEncodingNodeId.namespace === 0)) {
return dataTypeFactory.getConstructor(dataType.binaryEncodingNodeId);
}
// istanbul ignore next
if (doDebug) {
debugLog("buildConstructorFromDefinition => ", dataType.browseName.toString());
}
// etc ..... please fix me
const namespaceUri = addressSpace.getNamespaceUri(dataType.nodeId.namespace);
return buildConstructorFromDefinition(addressSpace, dataType);
}
function _extensionobject_construct(this: any, options: any): void {
options = options || {};
const dataType = this.constructor.dataType;
const obj = this;
for (const field of dataType.definition) {
const fieldName = field.$$name$$;
obj[fieldName] = field.$$initialize$$(options[fieldName]);
}
}
(global as any)._extensionobject_construct = _extensionobject_construct;
function initialize_Structure(field: any, options: any): any {
return new field.$$Constructor$$(options);
}
function _extensionobject_encode(this: any, stream: OutputBinaryStream) {
BaseUAObject.prototype.encode.call(this, stream);
const definition = this.constructor.dataType.definition;
for (const field of definition) {
const fieldName = field.$$name$$;
field.$$func_encode$$.call(this[fieldName], stream);
}
}
function struct_encode(this: any, stream: OutputBinaryStream) {
this.encode(stream);
}
function struct_decode(this: any, stream: BinaryStream) {
this.decode(stream);
return this;
}
function _extensionobject_decode(this: any, stream: BinaryStream) {
const definition = this.constructor.definition;
assert(definition, "expected a definition for this class ");
for (const field of definition) {
const fieldName = field.$$name$$;
this[fieldName] = field.$$func_decode$$.call(this[fieldName], stream);
}
}
function initialize_array(func: any, options: any[]) {
options = options || [];
const result = options.map((element: any) => func(element));
return result;
}
function encode_array(
fun_encode_element: (el: any, stream: OutputBinaryStream) => void,
arr: any[],
stream: BinaryStream
) {
stream.writeUInt32(arr.length);
for (const el of arr) {
fun_encode_element(el, stream);
}
}
function decode_array(
fun_decode_element: (stream: BinaryStream) => any,
arr: any[],
stream: BinaryStream
): any[] | null {
const n = stream.readUInt32();
if (n === 0xFFFFFFFF) {
return null;
}
const result = [];
for (let i = 0; i < n; i++) {
result.push(fun_decode_element(stream));
}
return result;
}
function buildConstructorFromDefinition(
addressSpace: AddressSpace,
dataType: UADataType
) {
if (doDebug) {
debugLog("buildConstructorFromDefinition nodeId=", dataType.nodeId.toString(), dataType.browseName.toString());
}
const extraDataTypeManager = (addressSpace as AddressSpacePrivate).getDataTypeManager();
const dataTypeFactory = extraDataTypeManager.getDataTypeFactory(dataType.nodeId.namespace);
assert(dataType.definition && _.isArray(dataType.definition));
const enumeration = addressSpace.findDataType("Enumeration");
const className = dataType.browseName.name!.replace("DataType", "");
assert(enumeration, "Enumeration Type not found: please check your nodeset file");
const structure = addressSpace.findDataType("Structure");
assert(structure, "Structure Type not found: please check your nodeset file");
const Constructor = new Function("options", "_extensionobject_construct.apply(this,arguments);");
assert(_.isFunction(Constructor));
Object.defineProperty(Constructor, "name", { value: className });
(Constructor as any).definition = dataType.definition;
(Constructor as any).dataType = dataType;
util.inherits(Constructor, ExtensionObject);
Constructor.prototype.encode = _extensionobject_encode;
Constructor.prototype.decode = _extensionobject_decode;
for (const field of dataType.definition) {
if (field.valueRank === 1) {
field.$$name$$ = lowerFirstLetter(field.name.replace("ListOf", ""));
} else {
field.$$name$$ = lowerFirstLetter(field.name);
}
const dataTypeId = resolveNodeId(field.dataType);
const fieldDataType = addressSpace.findDataType(dataTypeId) as UADataType;
if (!fieldDataType) {
debugLog(field);
throw new Error(" cannot find description for object " + dataTypeId +
" => " + field.dataType + ". Check that this node exists in the nodeset.xml file");
}
// check if dataType is an enumeration or a structure or a basic type
field.$$dataTypeId$$ = dataTypeId;
field.$$dataType$$ = fieldDataType;
field.$$isEnum$$ = false;
field.$$isStructure$$ = false;
if (fieldDataType.isSupertypeOf(enumeration as any)) {
field.$$isEnum$$ = true;
// todo repair
// makeEnumeration(fieldDataType);
} else if (fieldDataType.isSupertypeOf(structure as any)) {
field.$$isStructure$$ = true;
const FieldConstructor = makeStructure(dataTypeFactory, fieldDataType);
assert(_.isFunction(FieldConstructor));
// xx field
field.$$func_encode$$ = struct_encode;
field.$$func_decode$$ = struct_decode;
field.$$Constructor$$ = FieldConstructor;
field.$$initialize$$ = initialize_Structure.bind(null, field);
} else {
const stuff = findBuiltInType(fieldDataType.browseName.name);
field.$$func_encode$$ = stuff.encode;
field.$$func_decode$$ = stuff.decode;
assert(_.isFunction(field.$$func_encode$$));
assert(_.isFunction(field.$$func_decode$$));
field.schema = stuff;
field.$$initialize$$ = initialize_field.bind(null, field);
}
if (field.valueRank === 1) {
field.$$initialize$$ = initialize_array.bind(null, field.$$initialize$$);
field.$$func_encode$$ = encode_array.bind(null, field.$$func_encode$$);
field.$$func_decode$$ = decode_array.bind(null, field.$$func_decode$$);
}
}
// reconstruct _schema form
const fields = [];
for (const field of dataType.definition) {
const data: any = {
fieldType: field.$$dataType$$.browseName.name,
isArray: (field.valueRank === 1),
name: field.$$name$$
};
if (field.$$isEnum$$) {
data.category = FieldCategory.enumeration;
} else if (field.$$isStructure$$) {
data.category = FieldCategory.complex;
data.fieldTypeConstructor = field.$$Constructor$$;
} else {
data.category = FieldCategory.basic;
}
fields.push(data);
}
Constructor.prototype.schema = {
fields,
id: -1,
name: className
};
return Constructor;
}
/*
* define a complex Variable containing a array of extension objects
* each element of the array is also accessible as a component variable.
*
*/
function getExtObjArrayNodeValue(
this: any
) {
return new Variant({
arrayType: VariantArrayType.Array,
dataType: DataType.ExtensionObject,
value: this.$$extensionObjectArray
});
}
function removeElementByIndex<T extends ExtensionObject>(
uaArrayVariableNode: UADynamicVariableArray<T>,
elementIndex: number
) {
const _array = uaArrayVariableNode.$$extensionObjectArray;
assert(_.isNumber(elementIndex));
const addressSpace = uaArrayVariableNode.addressSpace;
const extObj = _array[elementIndex];
const browseName = uaArrayVariableNode.$$getElementBrowseName(extObj);
// remove element from global array (inefficient)
uaArrayVariableNode.$$extensionObjectArray.splice(elementIndex, 1);
// remove matching component
const node = uaArrayVariableNode.getComponentByName(browseName);
if (!node) {
throw new Error(" cannot find component ");
}
const hasComponent =
uaArrayVariableNode.addressSpace.findReferenceType("HasComponent")! as UAReferenceType;
// remove the hasComponent reference toward node
uaArrayVariableNode.removeReference({
isForward: true,
nodeId: node.nodeId,
referenceType: hasComponent.nodeId
});
// now check if node has still some parent
const parents = node.findReferencesEx("HasChild", BrowseDirection.Inverse);
if (parents.length === 0) {
addressSpace.deleteNode(node.nodeId);
}
}
/**
* @method prepareDataType
* @private
* @param dataType
*/
export function prepareDataType(
addressSpace: AddressSpace,
dataType: UADataType
): void {
if (!dataType._extensionObjectConstructor) {
const extraDataTypeManager = (addressSpace as AddressSpacePrivate).getDataTypeManager();
const dataTypeFactory = extraDataTypeManager.getDataTypeFactory(dataType.nodeId.namespace);
if (doDebug) {
debugLog("prepareDataType ", dataType.nodeId.toString() , dataType.browseName.toString());
}
dataType._extensionObjectConstructor = makeStructure(dataTypeFactory, dataType);
if (!dataType._extensionObjectConstructor) {
// tslint:disable:no-console
console.warn("AddressSpace#constructExtensionObject : cannot make structure for " + dataType.toString());
}
}
}
/**
*
* create a node Variable that contains a array of ExtensionObject of a given type
* @method createExtObjArrayNode
* @param parentFolder
* @param options
* @param options.browseName
* @param options.complexVariableType
* @param options.variableType the type of Extension objects stored in the array.
* @param options.indexPropertyName
* @return {Object|UAVariable}
*/
export function createExtObjArrayNode<T extends ExtensionObject>(
parentFolder: UAObject,
options: any
): UADynamicVariableArray<T> {
assert(typeof options.variableType === "string");
assert(typeof options.indexPropertyName === "string");
const addressSpace = parentFolder.addressSpace;
const namespace = parentFolder.namespace;
const complexVariableType = addressSpace.findVariableType(options.complexVariableType);
if (!complexVariableType) {
throw new Error("cannot find complex variable type");
}
assert(!complexVariableType.nodeId.isEmpty());
const variableType = addressSpace.findVariableType(options.variableType);
if (!variableType) {
throw new Error("cannot find variable Type");
}
assert(!variableType.nodeId.isEmpty());
const structure = addressSpace.findDataType("Structure");
assert(structure, "Structure Type not found: please check your nodeset file");
const dataType = addressSpace.findDataType(variableType.dataType);
if (!dataType) {
throw new Error("cannot find Data Type");
}
assert(dataType.isSupertypeOf(structure as any), "expecting a structure (= ExtensionObject) here ");
const inner_options = {
componentOf: parentFolder,
browseName: options.browseName,
dataType: dataType.nodeId,
typeDefinition: complexVariableType.nodeId,
value: { dataType: DataType.ExtensionObject, value: [], arrayType: VariantArrayType.Array },
valueRank: 1
};
const uaArrayVariableNode = namespace.addVariable(inner_options) as UADynamicVariableArray<T>;
bindExtObjArrayNode(
uaArrayVariableNode,
options.variableType,
options.indexPropertyName);
return uaArrayVariableNode;
}
/**
* @method bindExtObjArrayNode
* @param uaArrayVariableNode
* @param variableTypeNodeId
* @param indexPropertyName
* @return
*/
export function bindExtObjArrayNode<T extends ExtensionObject>(
uaArrayVariableNode: UADynamicVariableArray<T>,
variableTypeNodeId: string | NodeId,
indexPropertyName: string
): UAVariablePublic {
const addressSpace = uaArrayVariableNode.addressSpace;
const variableType = addressSpace.findVariableType(variableTypeNodeId);
if (!variableType) {
throw new Error("Cannot find VariableType " + variableTypeNodeId.toString());
}
assert(!variableType.nodeId.isEmpty());
let structure = addressSpace.findDataType("Structure");
assert(structure, "Structure Type not found: please check your nodeset file");
let dataType = addressSpace.findDataType(variableType.dataType);
if (!dataType) {
throw new Error("Cannot find DataType " + variableType.dataType.toString());
}
assert(dataType.isSupertypeOf(structure as any), "expecting a structure (= ExtensionObject) here ");
assert(!uaArrayVariableNode.$$variableType, "uaArrayVariableNode has already been bound !");
uaArrayVariableNode.$$variableType = variableType;
structure = addressSpace.findDataType("Structure");
assert(structure, "Structure Type not found: please check your nodeset file");
// verify that an object with same doesn't already exist
dataType = addressSpace.findDataType(variableType.dataType)! as UADataType;
assert(dataType.isSupertypeOf(structure as any), "expecting a structure (= ExtensionObject) here ");
uaArrayVariableNode.$$dataType = dataType as UADataType;
uaArrayVariableNode.$$extensionObjectArray = [];
uaArrayVariableNode.$$indexPropertyName = indexPropertyName;
prepareDataType(addressSpace, dataType as UADataType);
uaArrayVariableNode.$$getElementBrowseName = function(this: any, extObj: ExtensionObject) {
const indexPropertyName1 = this.$$indexPropertyName;
if (!extObj.hasOwnProperty(indexPropertyName1)) {
console.log(" extension object do not have ", indexPropertyName1, extObj);
}
// assert(extObj.constructor === addressSpace.constructExtensionObject(dataType));
assert(extObj.hasOwnProperty(indexPropertyName1));
const browseName = (extObj as any)[indexPropertyName1].toString();
return browseName;
};
const options = {
get: getExtObjArrayNodeValue,
set: undefined // readonly
};
// bind the readonly
uaArrayVariableNode.bindVariable(options, true);
return uaArrayVariableNode;
}
/**
* @method addElement
* add a new element in a ExtensionObject Array variable
* @param options {Object} data used to construct the underlying ExtensionObject
* @param uaArrayVariableNode {UAVariable}
* @return {UAVariable}
*
* @method addElement
* add a new element in a ExtensionObject Array variable
* @param nodeVariable a variable already exposing an extension objects
* @param uaArrayVariableNode {UAVariable}
* @return {UAVariable}
*
* @method addElement
* add a new element in a ExtensionObject Array variable
* @param constructor constructor of the extension object to create
* @param uaArrayVariableNode {UAVariable}
* @return {UAVariable}
*/
export function addElement<T extends ExtensionObject>(
options: any /* ExtensionObjectConstructor | ExtensionObject | UAVariable*/,
uaArrayVariableNode: UADynamicVariableArray<T>
): UAVariable {
assert(uaArrayVariableNode, " must provide an UAVariable containing the array");
// verify that arr has been created correctly
assert(!!uaArrayVariableNode.$$variableType && !!uaArrayVariableNode.$$dataType,
"did you create the array Node with createExtObjArrayNode ?");
assert(uaArrayVariableNode.$$dataType.nodeClass === NodeClass.DataType);
assert((uaArrayVariableNode.$$dataType as UADataType)._extensionObjectConstructor instanceof Function);
const addressSpace = uaArrayVariableNode.addressSpace;
let extensionObject: T;
let elVar = null;
let browseName;
if (options instanceof UAVariable) {
elVar = options;
extensionObject = elVar.$extensionObject; // get shared extension object
assert(extensionObject instanceof (uaArrayVariableNode.$$dataType as UADataType)._extensionObjectConstructor,
"the provided variable must expose a Extension Object of the expected type ");
// add a reference
uaArrayVariableNode.addReference({
isForward: true,
nodeId: elVar.nodeId,
referenceType: "HasComponent"
});
// xx elVar.bindExtensionObject();
} else {
if (options instanceof (uaArrayVariableNode.$$dataType as UADataType)._extensionObjectConstructor) {
// extension object has already been created
extensionObject = options as T;
} else {
extensionObject = addressSpace.constructExtensionObject(uaArrayVariableNode.$$dataType, options) as T;
}
browseName = uaArrayVariableNode.$$getElementBrowseName(extensionObject);
elVar = uaArrayVariableNode.$$variableType.instantiate({
browseName,
componentOf: uaArrayVariableNode.nodeId,
value: { dataType: DataType.ExtensionObject, value: extensionObject }
}) as UAVariable;
elVar.bindExtensionObject();
elVar.$extensionObject = extensionObject;
}
// also add the value inside
uaArrayVariableNode.$$extensionObjectArray.push(extensionObject);
return elVar;
}
/**
*
* @method removeElement
* @param uaArrayVariableNode {UAVariable}
* @param element {number} index of element to remove in array
*
*
* @method removeElement
* @param uaArrayVariableNode {UAVariable}
* @param element {UAVariable} node of element to remove in array
*
* @method removeElement
* @param uaArrayVariableNode {UAVariable}
* @param element {ExtensionObject} extension object of the node of element to remove in array
*
*/
export function removeElement<T extends ExtensionObject>(
uaArrayVariableNode: UADynamicVariableArray<T>,
element: any /* number | UAVariable | (a any) => boolean | ExtensionObject */
): void {
assert(element, "element must exist");
const _array = uaArrayVariableNode.$$extensionObjectArray;
if (_array.length === 0) {
throw new Error(" cannot remove an element from an empty array ");
}
let elementIndex = -1;
if (_.isNumber(element)) {
// find element by index
elementIndex = element;
assert(elementIndex >= 0 && elementIndex < _array.length);
} else if (element && element.nodeClass ) {
// find element by name
const browseNameToFind = element.browseName.name!.toString();
elementIndex = _array.findIndex((obj: any, i: number) => {
const browseName = uaArrayVariableNode.$$getElementBrowseName(obj).toString();
return (browseName === browseNameToFind);
});
} else if (_.isFunction(element)) {
// find element by functor
elementIndex = _array.findIndex(element);
} else {
// find element by inner extension object
assert(_array[0].constructor.name === (element as any).constructor.name, "element must match");
elementIndex = _array.findIndex((x: any) => x === element);
}
if (elementIndex < 0) {
throw new Error(" cannot find element matching " + element.toString());
}
return removeElementByIndex(uaArrayVariableNode, elementIndex);
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,221 |
Q: Why the temp pointer points to 0 instead 3? Solving an exercise I got stuck in a problem that I was unable to identify. I have some code that needs to store a given pointer on a tempNode. Instead of it, the pointer structure receives int 0, where x is 3.
for (int i = 0; i <= MAX_NUM; i++) {
if (y->item == x) {
printf("y: %d\n", y->item);
printf("x: %d\n", x);
tempNode->item == y->item;
tempNode->next == y->next;
y = y->next;
printf("tempNode: %d\n", tempNode->item);
}
y = y->next;
}
A: The correct answer, thanks to Sami the identified it.
tempNode->item = y->item;
tempNode->next = y->next;
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 621 |
{"url":"https:\/\/www.physicsforums.com\/threads\/simple-inertia-test-setup.175368\/","text":"# Simple Inertia Test Setup\n\n1. Jun 28, 2007\n\n### remz\n\nAny ideas on a simple experiment I can setup to calculate the moment of inertia for any object (sanity check only).\n\nAnother post on PF proposed using a pendulum however unfortunately did not go into enough detail and my google skills are obviously lacking tonight.\n\nSince...\n\n$$J = \\frac {mgr \\theta} {\\frac {d \\omega} {dt}}$$\n\nwhere...\n\nJ = inertia of object on end of string\nm = mass of object\ng = acceleration due to gravity\nr = distance of object from centre of rotation\n$$\\theta$$ = the angle to which the object is raised ($$sin \\theta \\approx \\theta$$ for small $$\\theta$$)\n$$\\frac {d \\omega} {dt}$$ = angular acceleration of object\n\nSo, in this test setup, the inertia can be deduced through measuring the angular acceleration of the object only as the numerator is already fully known.\n\nIs there a flaw in my proposed test or can anyone suggest any alternative solutions.\n\nRegards,\n\nrem\n\nLast edited: Jun 28, 2007\n2. Jun 28, 2007\n\n### Staff: Mentor\n\nDo the objects have a center of rotation? If so, just make that axis of rotation vertical, and devise a means of applying a known torque and measuring the rotational acceleration. You could use a mass on a string to generate a known force, and translate that down force into a torque on the shaft of your unknown object....\n\n3. Jun 29, 2007\n\n### FredGarvin\n\nTake a look at this:\n\nLast edited: Dec 20, 2007\nKnow someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook","date":"2017-07-27 22:54:16","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.41633501648902893, \"perplexity\": 1495.4268104217724}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-30\/segments\/1500549429548.55\/warc\/CC-MAIN-20170727222533-20170728002533-00075.warc.gz\"}"} | null | null |
\section{Introduction}
\hspace{.5cm}
The concept of a meson cloud is very old in nuclear physics: the
existence of the pion exchange interaction leads
to a pion cloud\cite{de} which could affect the properties of nucleons.
Although a main current goal of hadronic physics is to understand the
properties of hadrons in terms of QCD, in recent years the study of deep
inelastic scattering (DIS) has led to a great deal of interest in the
nucleon's meson cloud. The NMC/CERN experiments\cite{nmc} gave evidence
for the violation of the Gottfried sum rule and the recent
Fermilab/E866\cite{fmlab1,fmlab2}
Drell-Yan measurements show that for small Bjorken x the ratio
$\bar{d}(x)/\bar{u}(x)$, down to up sea quark distributions, is considerably
larger than 1.0, while both perturbative\cite{rs} and nonperturbative
QCD calculations\cite{jk}
show that $\bar{d}(x)/\bar{u}(x)$ for small x differs from unity only by
about 1 $\%$ isospin violations. It is likely that theoretical treatments
with both QCD and Goldstone boson (GB) fields are most efficient in treating
these sea quark problems as well as problems with the spin and strangeness
content of the nucleon. The challenge is to do this consistently.
There have been many theoretical calculations of DIS using the concept of
a meson cloud based on the one-pion interaction of nucleons\cite{s}
(see Ref.\cite{st} for a review). It is obvious that if one only considers
the $\pi^+$-neutron system as an additional component of the proton, that
there are more $\bar{d}$ than $\bar{u}$ sea quarks, but the $\pi^-\Delta$
components tend to cancel this effect. A related model is the chiral quark
model which has been used for flavor and spin properties of
nucleons\cite{cl}. As discussed in Ref.\cite{cl},
although these two models both introduce Goldstone
bosons, in the chiral quark model these are fields internal to the confinement
region, while the meson cloud model describes long-distance effects outside
of the region of confined quarks. In lattice gauge calculations\cite{liu}
of the flavor-singlet axial coupling constant for the nucleon's
quark spin content gluonic effects were included by disconnected
quark loops, which are interpreted as representing Goldstone bosons. In this
method valence quark and GB effects are distinguished.
It was observed that the QCD sum rules for the nucleon mass are
inconsistent with chiral perturbation theory\cite{gc}. First, the quark
condensates terms on the QCD side of the sum rules contain quark condensate
terms which have been shown\cite{nsvz} to introduce $m_\pi^2 ln(-m_\pi^2)$
terms, while the chiral perturpation theory expansion for the nucleon
mass\cite{gz} does not have such terms. Second, the leading non-analytic
correction (LNAC) to the nucleon mass is a m$_\pi^3$/f$_\pi^2$ term, which
is not found in QCD sum rules\cite{gc}. By an analysis of the
phenomenological correlator, given by a term with a pole at the nucleon mass
and the continuum, it was shown\cite{lccg} that the chiral logs cancel;
however, the LNAC term is not present so
the QCD sum rules for the nucleon mass are not consistent with chiral
perturbation theory. Virtual pions have
also been included in QCD sum rule calculations of nucleon masses in nuclear
matter\cite{dl,bi}. A chiral quark model was used to study pion-nucleon
weak and strong coupling within the QCD sum rule method\cite{ph}
The model introduced in the present work uses the method of QCD Sum
Rules\cite{svz} in which hadronic systems are represented by local complex
field operators, usually called currents, so that two-point functions can
be used for defining correlators from which one can determine hadronic
masses. Nonperturbative effects are treated via operator product expansions
(O.P.E.) of the quark and gluon propagators using vacuum condensates, whose
values are determined by fits to experiment as well as lattice gauge
calculations. In this method short-distance effects are treated
perturbatively and the condensates account for the medium-range and long-range
QCD effects within the region of confinement.
The model introduced in the present work treats the nucleon correlator
with a nucleon current that has a quark/gluon component and a component
also involving a Goldstone boson field.
The GB fields are included in the composite-field
nucleon current, with no coupling to either hadrons or quarks and thereby
represent the long-distance meson cloud effects. Thus the model differs from
both the usual meson cloud and the chiral quark models. All internal meson
exchange effects are assumed to be included in the condensates. For
consistency, the coupling between the two currents is also not included, so
the correlator has a standard QCD sum rule part and a QCD/GB part, with a
GB propagator. There is a clear relationship between the present model of
nucleons with a meson cloud and the usual QCD sum rule treatment. In the
usual treatment states with a nucleon and a pion are in the continuum. In the
present model the current explicitly contains pionic fields, so that the
resulting continuum is modified. By doing this we are able to treat
physical effects where explicit pion degrees of freedom are important, as
in sea-quark distributions.
The goals of the present work are to estimate the probability of the meson
cloud component by studying the properties of the nucleon, and to study
the problem of consistency with chiral perturbation theory. This is
similar to the problem of finding the correlator for hybrid hadrons\cite{kl},
where the hybrid components of the nucleon and lowest hybrid baryon were
estimated from the hadronic masses. In Sec. 2 we introduce the correlator
using a standard form\cite{i} for the nucleon with no GB and derive the
sum rules for the nucleon masses including a correlator with a GB.
We find very small effects from the
meson cloud correlator terms. In Sec. 3 we derive the sum rules for the
neutron and proton magnetic dipole moments using
a two-point correlator in an external electromagnetic field\cite{is}.
From the sum rules found with this method
compared to QCD sum rule calculations of Ref.\cite{is} without the cloud,
we conclude that the GB component has roughly the same probability as
the cloudless component. It should be noted that
there is recent work on including instanton effects on the quark propagator
that also modify the sum rules for the nucleon moments\cite{aw}.
In Sec. 4 we show that the model is consistent with chiral perturbation theory.
The chiral logs cancel and the LNAC term appears as in hadronic models.
The known value of the LNAC term from chiral perturbation theory can help
determine the parameters of the model.
\newpage
\section{Correlator with Goldstone Boson Fields: Nucleon Masses }
\hspace{.5cm}
In this subsection we present our model of the pion cloud within the QCD
sum rule method, which means that we introduce a correlator with explicit
Goldstone boson fields. We apply this model correlator, a two-point function,
to the estimate of the masses of nucleons.
The composite field operator for the proton has the form
\begin{eqnarray}
\eta(x) & = & c_1\eta^{p,o} + c_2\eta^{p,\pi} + c_3\eta^{p,K},
\label{eq-eta}
\end{eqnarray}
with constants c$_j$ giving the meson cloud amplitudes. In Eq.(\ref{eq-eta})
$\eta^{p,o}$ is a standard\cite{i} proton field operator used in sum rules:
\begin{eqnarray}
\eta^{p,o}(x) & = &\epsilon^{abc}[u^a(x)^T C\gamma^\mu u^b(x)] \gamma^5
\gamma_\mu d^c(x),
\nonumber\\
<0|\eta^{p,o}(x)|proton> & = & \lambda_p v(x),
\label{eq-etao}
\end{eqnarray}
where C is the charge conjugation operator, the u(x) and d(x) are quark
fields labelled by color, $\lambda_p$ is a structure parameter and $v$(x)
is a Dirac spinor. The neutron operator, $\eta^{n,o}$, is obtained
from $\eta^{p,o}$ by interchange of u and d quarks.
The composite field operator $\eta^{p,\pi}$ used in our present model is
\begin{eqnarray}
\eta^{p,\pi}(x) & = & \frac{1}{\lambda_\pi^2}\partial_\alpha \phi_\pi(x)\cdot
\tau \gamma^\alpha \gamma^5 \eta^{N,o} \nonumber \\
& = & \frac{1}{\sqrt{3}\lambda_\pi^2}
[\sqrt{2} \partial_\alpha
\phi_\pi^+(x) \gamma^\alpha \gamma^5 \eta^{n,o} + \partial_\alpha
\phi_\pi^o(x) \gamma^\alpha \gamma^5 \eta^{p,o}],
\nonumber \\
<0|\eta(x)^{p,\pi}|proton> & = & \lambda'_p v(x),
\label{eq-etapi}
\end{eqnarray}
where $ \phi_\pi(x)$ is the pion field and $\lambda_\pi$ is a D=1 scale
factor. From our experience with hybrid
baryons\cite{kl} and from the p-wave coupling of the pion one expects that
$\lambda^{'2}_p \ll \lambda_p^2$. This simplifies the phenomenological
form for the correlator and enables us to obtain sufficient sum rules
to estimate the pion cloud part of the current.
In the present work we do not consider the kaon cloud term which
would enter through $\eta^{p,K}$, defined similarly to Eq.(\ref{eq-etapi})
but with K fields and strange baryon composite operators.
For estimates of strangeness in nucleons, which is a natural application of
our model, this term must be included.
Our resulting model correlator for the proton with a pion cloud is
\begin{eqnarray}
\Pi^p(p) & =
& i\int d^4 e^{ix\cdot p}<0|T[\eta(x)\bar\eta(0)]|0> \nonumber\\
& = & c_1^2 i\int d^4 e^{ix\cdot p}<0|T[\eta^{p,o}(x)\bar\eta^{p,o}(0)]|0>
+ (1-c_1^2)i\int d^4 e^{ix\cdot p}<0|T[\eta^{p,\pi}(x)
\bar\eta^{p,\pi}(0)]|0>
\nonumber\\
&=& c_1^2 \Pi^{(p,o)}(p) + (1-c_1^2)\Pi^{(p,\pi)}(p).
\label{eq-cor}
\end{eqnarray}
An important aspect of the model is that the coupling of the $\eta^{p,\pi}$
and $\eta^{p,0}$ currents are not included. Only the long-range effects
of the pion are included by the pion cloud contribution, and no pion-quark
interactions are included in order to avoid the double counting of
interactions given by the condensates. In a chiral quark model the
pion-quark coupling would give both the coupling of the two currents and
internal pionic forces. The present model assumes such internal interactions
are given by QCD. Only external fields interact with the pion, giving the
physics of the meson cloud. The neutron correlator can be obtained
from Eq.(\ref{eq-cor}) with obvious isospin changes.
The correlator $\Pi^{(p,0)}(p)$ for the propagation of a proton without
the meson cloud is given in Ref.\cite{is} and many other references.
Next we discuss the correlator with the pion cloud, $\Pi^{(p,\pi)}(p)$.
From Eqs.(\ref{eq-etapi},\ref{eq-cor}) one finds for
$\Pi^{(p,\pi)}(x)$
\begin{eqnarray}
\Pi^{(p,\pi)}(x) & = & \frac{2}{3\lambda_\pi^4}\epsilon^{abc}
\epsilon^{b'a'c'} G_{\alpha\beta}^{\pi}(x)
\gamma_\alpha\gamma_\mu S^{cc'}_d(x) \gamma_\nu \gamma_\beta
\nonumber \\
& & Tr[S^{aa'}_u(x) \gamma^\mu C (S^{bb'}_u(x))^T C\gamma^\nu]
\nonumber \\
& & + 2 [\pi^0 \rightarrow \pi^+\ and\ u \leftrightarrow d] +
\ [4-quark\ terms],
\label{eq-corpi}
\end{eqnarray}
where in the limit of zero pion mass
\begin{eqnarray}
G_{\alpha\beta}^\pi(x) & = & \frac{1}{\pi^2 x^4}(\frac{4x_\alpha x_\beta}
{x^2} - \delta_{\alpha\beta}).
\label{G}
\end{eqnarray}
In momentum space the pion cloud correlator is
\begin{eqnarray}
\Pi^{(p,\pi)}(p) & = & -2\int \frac{d^4k}{(2\pi)^4}\frac{(\hat{p}-\hat{k})
\Pi^{p,o}(k)(\hat{p}-\hat{k})}{(p - k)^2} \nonumber \\
& = & \hat{p} \Pi^{(p,\pi)}(p)_{odd} + \Pi^{(p,\pi)}(p)_{even},
\label{eq-corpip}
\end{eqnarray}
with $\hat{p}$= $\gamma_\alpha p^\alpha$.
We find after the Borel transform from p$^2$ to the Borel mass variable,
M$_B^2$
\begin{eqnarray}
\Pi^{(p,\pi)}(M_B^2)_{even} & = & 0 \nonumber \\
(2 \pi)^4 \Pi^{(p,\pi)}(M_B^2)_{odd} & = & \frac{1}{\lambda_\pi^4
15\cdot 2^8} [12 M_B^{10}E_4 -5 b M_B^6 E_2 - 40 a^2 M_B^4 E_1
\nonumber \\
& & +20 m_o^2 a^2 M_B^2 E_0],
\label{eq-corpim}
\end{eqnarray}
where the parameters for the quark condensate, gluon condensate and mixed
condensate, respectively, are a = -$(2\pi)^2 <\bar{q}q>$, b = $ <\bar{q}
g^2 G^2 q>$ and m$_o^2$ a = $(2\pi)^2 <\bar{q} g \sigma \cdot G q>$.
For these parameters we take a = .55 GeV$^3$, b = .47 GeV$^4$ and m$_o^2$ =
0.8 GeV$^2$. The scale factor $\lambda_\pi^2$ has a value in the range of
M$_B^2/g_{\pi N}$ (see Sec. 4). The functions E$_n$ are
1-exp(-w)$\sum_{k=0}^{n}$w$^k/k!$,
with w = s$_o$/M$_B^2$, s$_o$ being the threshold parameter.
In comparison with Eq.(\ref{eq-corpim}) for the meson cloud
terms in the correlator, the usual(p,0) odd correlator is
\begin{eqnarray}
(2 \pi)^4 \Pi^{(p,0)}(M_B^2)_{odd} & = & \frac{1}{2^5} (-4 M_B^6 E_2
+b M_B^2 E_0 + 16 a^2/3 -4 m_o^2 a^2/(3 M_B^2).
\label{eq-corom}
\end{eqnarray}
The dependence of the correlators on the anamoulous dimensions are not
shown in Eqs.(\ref{eq-corpim},\ref{eq-corom}), since the result is not
essentially changed if this is neglected. In fact it is obvious from
Eqs.(\ref{eq-corpim},\ref{eq-corom}) that if $\lambda^{'2}_p << \lambda_p^2$,
as expected, then the sum rules for the masses are independent of the pion
cloud within the accuracy of the method.
\section{Correlator with Goldstone Boson: Nucleon Magnetic Dipole Moments}
\hspace{.5cm}
For the calculation of the magnetic dipole moments of the proton and
neutron we use the external field formalism, which is one way to avoid the
problem of carrying out an operator product expansion in the momentum transfer
variable. The coupling of a current $J^\Gamma$ to a nucleon is given by
a two-point correlator in the external $J^\Gamma$ current\cite{is}
\begin{eqnarray}
\Pi^\Gamma(p) & =
& i\int d^4 e^{ix\cdot p}<0|T[\eta(x)\bar\eta(0)]|0>_{J^\Gamma}.
\label{eq-gpi}
\end{eqnarray}
For the proton in an electromagnetic field, represented by the field tensor
F$_{\mu\nu}$ the correlator is written as
\begin{eqnarray}
\Pi^{F,p} & = & e (c_1^2 \Pi^{p,o}_{\mu\nu} + (1-c_1^2)\Pi^{p,\pi}_
{\mu\nu}) F^{\mu\nu},
\label{eq-piem}
\end{eqnarray}
with the two terms representing the correlator in the electromagnetic
field without and with the meson cloud. Since at low momentum transfer
the coupling of the photon to the pion does not contribute, the meson
cloud correlator in the presence of the field in our model is given by
\begin{eqnarray}
\Pi^{(p,\pi)}_{\mu\nu}(p) & = & -2\int \frac{d^4k}{(2\pi)^4}
\frac{(\hat{p}-\hat{k}) \Pi^{p,o}_{\mu\nu}(k)(\hat{p}-\hat{k})}{(p-k)^2}
\label{eq-corpipm}
\end{eqnarray}
There are three covariants, and we write the correlator with and without
meson clouds as
\begin{eqnarray}
\Pi_{\mu\nu}(k) & = & [\sigma_{\mu\nu},\hat{k}] \Pi^F_{odd}(k)
+ i(k_\mu \gamma_\nu -k_\nu \gamma_\mu) \Pi^F_{even}(k)
+ \sigma_{\mu\nu} \Pi^F_\sigma (k).
\label{eq-cor2}
\end{eqnarray}
For the two-point effective field treatment at low momentum momentum
transfer $\Pi^\Gamma(x)$ can be evaluated using the operator product
expansion (O.P.E.),
since the variable x is at short distance from the origin for
large p$^\mu$. This is done by an
O.P.E. of the quark propagator in the presence of the the $J^\Gamma$ current
\begin{eqnarray}
S^\Gamma_q(x) & = & <0|T[q(x)\bar{q}(0)]|0>_{J^{\Gamma}}.
\label{eq-gprop}
\end{eqnarray}
There are three susceptibilities for the induced condensates: $\chi,
\kappa$ and $\xi$, which are defined in Ref\cite{is}. For example, the
quark condensate magnetic susceptibility, $\chi$, is defined as
\begin{eqnarray}
(2\pi)^2<\bar{q}\sigma_{\mu\nu}q>_F & = & -e_q \chi a F_{\mu\nu}.
\label{eq-chi}
\end{eqnarray}
The QCD evaluation of the correlator in an electromagnetic field without
a meson cloud gives\cite{is}
\begin{eqnarray}
(2\pi)^4 \Pi^{p,o,F}_{odd}(k) & = & e_u k^2 ln(-k^2) - e_u \chi a^2/(3 k^2)
+C_a/(3 k^4) \nonumber \\
(2\pi)^4 \Pi^{p,o,F}_{even}(k) & = & a[(e_u +e_d/2)/k^2 +
(e_d \chi/3)( ln(-k^2) -b/(24 k^4)],
\label{eq-cor3}
\end{eqnarray}
with C$_a$ = $(a^2/2)[e_d + 2 e_d/3 -e_u(\kappa - 2\xi)] -e_u \chi a^2
m_o^2/8$.
From Eqs.(\ref{eq-corpim},\ref{eq-cor3}) we obtain the correlator for
the nucleon with a pion cloud in an external electromagnetic field, giving
\begin{eqnarray}
(2\pi)^4 \Pi^{p,\pi,F}_{odd}(p) & = & \frac{ln(-p^2)}{3\cdot2^8 \pi^2}
[- e_u p^6 + 40 e_u \chi a^2 p^2/3 +32 C_a] \nonumber \\
(2\pi)^4 \Pi^{p,\pi,F}_{even}(k) & = & - \frac{ln(-p^2)}{2^5\cdot3^3\cdot 5
\pi^2}\chi a[3^2\cdot2^4e_d p^4 - 5 e_d b].
\label{eq-cor4}
\end{eqnarray}
For a rough estimate of the effect of the meson cloud, which is the
goal of the present paper, we follow the prescriptions of Ref.\cite{is}:
For the odd term in the correlator multiply the p term by e$_d$ and subtract
e$_u$ times the n term. Neglecting anamolous dimensions one finds
\begin{eqnarray}
\frac{-\bar{\lambda}^2_N}{4}e^{-M_N^2/M_B^2}(e_d \mu_p - e_u \mu_n)/M_B^2 +
single \ poles & =& (e_d^2-e_u^2)[\frac{a^2}{6M_B^2} + \Delta_{cl}],
\label{eq-del}
\end{eqnarray}
where $\bar{\lambda}^2_N$ = (2$\pi$)$^4 \lambda_N$ and the GB contribution is
\begin{eqnarray}
\Delta_{cl} & = & \frac{1-c_1^2}{c1^2\lambda_\pi^4}\frac{1}{2^7 3^2 \pi^2}
[8 a^2 M_B^2 E_0-6 M_B^8 E_3-\frac{40}{3} \chi a^2 E_1+
\frac{32}{3} a^2 E_0+\frac{1}{8}\chi a^2 m_o^2].
\label{eq-delmu}
\end{eqnarray}
Noting that with a value of $\chi$ a = -4 GeV, which we obtain with our
three-point treatment with nonlocal condensates\cite{k}, a value of c$_1^2$
about 0.5 reduces the neutron and proton magnetic dipole moments by about
ten percent, improving agreement with experiment. From this we conclude that
the component of the correlator with a pion cloud is roughly equal to that
without. As we shall see in the next section, the known LNAC for the nucleon
mass will help determine the scaling parameter, $\lambda_\pi$.
\section{Consistency of Model With Chiral Perturbation Theory}
\hspace{.5cm}
In Ref. \cite{nsvz} it was shown that from the dependence of the quark
condensates on the current quark masses and the Gell-Mann-Oakes-Renner
relation\cite {gor} that the quark condensate has a $m_\pi^2 ln(-m_\pi^2)$
dependence on the pion mass. From this one can see from Eq. (\ref{eq-corom}
that the standard QCD sum rule contains chiral logs that are not consistent
with chiral perturbation
theory\cite{gc}. Moreover, the LNAC term, which is proportional to
m$_\pi^3$/f$_\pi^2$ \cite{gz} does not occur in the QCD sum rule form for
the nucleon mass. in this section we show that both of these problems are
solved in our model.
\subsection{Chiral logarithms}
\hspace{.5cm}
In this subsection we show that by using the
results of
Ref. \cite{lccg} our present model does not contain inconsistent chiral
logarithms. We study the diagrams giving the LNAC in the next subsection.
For simplicity let us take $c_1^2$ = 0.5. Using the observation from
hybrid baryons\cite{kl} that $\lambda^{'2}_p << \lambda_p^2$, as discussed
in Sec. 2, the phenonenological side of the correlator, given by a
dispersion relation has the form of a pole term and a continuum term,
\begin{eqnarray}
\label{cp1}
2 \Pi^{p(Phen)}(p) & = & -\lambda_p^2 \frac{\hat{p} + M_p}{p^2 - M_p^2}
+ \Pi^{p(cont)}(p),
\end{eqnarray}
which is the same as the standard proton correlator except for a factor of
two. As we saw in Sec. 2, the microscopic QCD side of the correlator has
the form
\begin{eqnarray}
\label{cp2}
2 \Pi^{p(qcd)}(p) & = & \hat{p}( \Pi^{(p,0)QCD}(p)_{odd} +
\Pi^{(p,\pi)QCD}(p)_{odd}) + \Pi^{(p,0)}(p)_{even}.
\end{eqnarray}
Using the standard proton current\cite{i} we recall that
\begin{eqnarray}
\label{cp3}
\Pi^{(p,0)QCD}(p)_{even} & = & <\bar{q}q> (p^2 ln(-p^2) - \frac{b}{18 p^2})
+ \cdots \\ \nonumber
\Pi^{(p,0)QCD}(p)_{odd} & = & -ln(-p^2) (\frac{p^4}{4} + \frac{b}{8})
+ \cdots,
\end{eqnarray}
where by the ellipsis we mean four-quark condensates + higher dimensional
terms. Making use of the $m_\pi$ expansion of the quark condensate from
Ref. \cite{nsvz}:
\begin{eqnarray}
\label{cp4}
<\bar{q}q> & = & <\bar{q}q>_o [1-c m_\pi^2ln(-m_\pi^2)]
\end{eqnarray}
where $ c = \frac{3}{32 \pi^2 f_\pi^2}$ and by the symbol $Q_o$
we mean the quantity Q in the limit $m_\pi^2 \rightarrow 0$, one finds
\begin{eqnarray}
\label{cp5}
\Pi^{(p,0)QCD}(p)_{even} & = & [1-c m_\pi^2ln(-m_\pi^2)]
\Pi_o^{(p,0)QCD}(p)_{even} + O(m_\pi^2)
\\ \nonumber
\Pi^{(p,0)QCD}(p)_{odd} & = & [1+O(m_\pi^2)]
\Pi_o^{(p,0)QCD}(p)_{odd},
\end{eqnarray}
as was observed in Ref.\cite{lccg}. For the pion cloud part of the correlator
we observe that
\begin{eqnarray}
\label{cp6}
\Pi^{(p,\pi)}(x) & = & G_{\alpha\beta}^{\pi}(x) \gamma^\alpha \Pi^{(p,0)}
\gamma^\beta + m_\pi^2 \breve{G}_{\alpha\beta}^{\pi}(x) \gamma^\alpha \Pi^{(p,0)}
\gamma^\beta,
\end{eqnarray}
where $\breve{G}_{\alpha\beta}$ is obtained from ${G}_{\alpha\beta}$ of
Eq.(\ref{eq-corpi}) by an expansion of the pion propagator in powers of
$m_\pi^2$, with the first term given by Eq(\ref{G}). From Eq.(\ref{cp6} we
observe that
\begin{eqnarray}
\label{cp7}
\Pi^{(p,\pi)}(x) & = & \Pi^{(p,\pi)}_o(x) + O(m_\pi^2),
\end{eqnarray}
and does not contain any $m_\pi^2 ln(-m_\pi^2)$ chiral log terms.
Therefore we conclude that in our model of the nucleon with a meson cloud
\begin{eqnarray}
\label{cp8}
\Pi^{p(Phen)} & = & [1-c m_\pi^2 ln(-m_\pi^2)] \Pi^{p(Phen)}_o + \cdots
\end{eqnarray}
and
\begin{eqnarray}
\label{cp9}
\Pi^{p(QCD)} & = & [1-c m_\pi^2 ln(-m_\pi^2)] \Pi^{p(QCD)}_o + \cdots;
\end{eqnarray}
and our model the nucleon with pion cloud does not contain spurious
chiral logarithms.
\subsection{Leading Non-Analytic Correction}
\hspace{.5cm}
The leading non-analytic correction (LNAC) from chiral symmetry breaking
can be found in chiral perturbation theory using the method described in
Refs.\cite{lp,gz}, with the Feynman-like diagrams of chiral perturbation
theory given in Ref.\cite{ch}. The main idea is that if one has a broken
symmetry, so that the Hamiltonian has the form
\begin{eqnarray}
\label{cp10}
H & = & H_0\ \ +\ \ m H_I,
\end{eqnarray}
with m being the small parameter of the symmetry breaking, the mass of a
hadron can be found from the relation
\begin{eqnarray}
\label{cp11}
\frac{\partial^2 M^2}{\partial m^2} & = & Lim_{q^0 \rightarrow 0^+,
q^2 \rightarrow 0,{\bf p} \rightarrow 0}i\int d^4x e^{iqx}<p|\theta(x^o)
[\mathcal{H}_I(x),\mathcal{H}_I(0)]|p>,
\end{eqnarray}
including only connected diagrams, with H$_I$ = $\int d^3x \mathcal{H}_I$.
The chiral symmetry breaking in QCD is
\begin{eqnarray}
\label{cp12}
m H_I & = & \int d^3x m_u \bar{u}u + m_d \bar{d}d \nonumber \\
& = & m \int d^3x \mathcal{H}_m.
\end{eqnarray}
In Ref \cite{gz} it is shown that the LNAC for the nucleon mass is
given by the process illustrated in Fig. 1.
\begin{figure}[htpb]
\begin{center}
\epsfig{file=mescl1.eps,width=10cm}
{\label{Fig.1}}
\end{center}
\end{figure}
The corresponding correction to the nucleon mass, $\Delta M_N = M_N - M_N^o$
was shown to be
\begin{eqnarray}
\label{cp13}
\Delta M_N & = & -\frac{3 g_A^2 m_\pi^3}{32 \pi f_\pi^2} + \cdots \ \ = \ \
-15 MeV + \cdots,
\end{eqnarray}
which makes use of the result
\begin{eqnarray}
\label{cp14}
<\pi^a|\mathcal{H}_m|\pi^b> & = & \delta_{ab} \frac{m_\pi^2}{m} + \cdots.
\end{eqnarray}
The LNAC in the present model of QCD sum rules, after the chiral logs have
been eliminated, are given by processes involving the pion cloud correlator.
The lowest dimensional term is illustrated by the the diagram shown in
Fig. 2
\begin{figure}[htpb]
\begin{center}
\epsfig{file=mescl2.eps,width=10cm}
{\label{Fig.2}}
\end{center}
\end{figure}
In the evaluation of the QCD sum rule diagram the $\pi$-N T-matrix evident in
Fig. 1 is replaced by the traces over the quark propagators. The LNAC to the
nucleon mass is found by equating the phenomenological expression for the
Borel transformed correlator
\begin{eqnarray}
\label{cp15}
\Pi^{p(Phen)}(p) & = & \beta^2 exp[-\frac{M_p^2}{M_B^2}] + continuum,
\end{eqnarray}
with $\beta^2 = (2 \pi)^4 \lambda_p^2/4$ (see Eq.(\ref{eq-etao}),
to the QCD expression with chiral symmetry breaking. Making use of
Eq(\ref{cp14}), the Goldberger-Trieman relation
(g$_{\pi N}$=g$_A$ M$_N$/f$_\pi$), Eq.(\ref{eq-corpim}) and taking the nucleon
and Borel masses M$_p$, M$_B$ = 1 Gev,
we find for the lowest-dimensional LNAC term
\begin{eqnarray}
\label{cp16}
\Delta M_p & = & -\frac{e m_\pi^3 g_A^2}{160 \beta^2 f_\pi^2} \nonumber \\
& \simeq & -20 MeV.
\end{eqnarray}
For the result of a LNAC of about 20 MeV, which is consistent with the chiral
perturbations theory result, we have used a value of $\beta^2$ from
Ref. \cite{is}, where it is pointed out that there is about a 50\%
uncertainty in the value, and have used $\lambda_\pi^2$ = M$_p^2$/g$_{\pi N}$
for the scale factor of the pion cloud model. Note that the gluon condensate
process also contributes to the LNAC, with an opposite sign, cancelling
about 10-20\% of the term shown in Eq. (\ref{cp16}).
Therefore, we have shown that the longstanding puzzle of the absence of the
LNAC m$_\pi^3$ term in the QCD sum rule treatment of the nucleon mass can
be explained in our model, with a correlator composed about equally of
a conventional quark correlator and a meson cloud correlator. The known
value of the LNAC for the nucleon mass can help determine the parameters
of the model.
\section{Conclusions}
We have introduced a model for a nucleon in which Goldstone bosons are
included in a QCD treatment. By only including the boson propagator and
not interior quark-boson interactions we hope to account for long-distance
effects which are difficult to calculate in a pure QCD treatment, and yet
avoid introducing processes which are aleady treated by the nonperturbative
QCD methods of QCD sum rules. With this model the nucleon mass sum rules
are essentially not changed by the meson cloud terms, but from the
treatment of magnetic dipole moments we conclude that within our model
the correlators with and without the pion cloud are about equal. We have
also shown that this model is consistent with chiral perturbation theory,
and that the leading nonanalytic term found in chiral perturbation theory,
but missing in previous treatments of the nucleon mass with QCD sum rules,
is present in our model. The magnetic dipole moments and the LNAC for the
nucleon mass can help determine the parameters of the model.
Our future research with this model will include
studies such as the spin and strangeness content of the proton, as well as
the sea-quark distributions in the nucleon.
The author would like to thank Montaga Aw, Andrew Harey, Ling-fong Li
and Jen-Chieh Peng for helpful discussions. This work was supported in
part by NSF Grant PHY-9722143.
\hspace{.5cm}
| {
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} | 6,181 |
{"url":"https:\/\/cs.stackexchange.com\/questions\/119797\/why-is-the-run-time-with-a-loop-of-this-structure-considered-olog-n\/119799","text":"# Why is the run time with a loop of this structure considered O(log n)\n\nI used the search function and a good amount of google searches, but wasn't able to get a straight answer on how a loop of the form below, is translated to a proper summation where the function derived from the summation is: $$O(\\log n)$$.\n\nExample of the for loop:\n\nint j = 0;\nfor (int i = 2; i <= n; i *= 2) {\nj = j + n * 2;\n}\n\n\nSo I understand within the loop we have 3 operations (multiplication, addition, then assignment).\n\nI understand that the index $$i$$ ranges from $$[1, 2, 4, 8, 16, 32, 64, 128, 256]$$... ($$i$$ is only equal to powers of 2, up to $$n$$).\n\nSo essentially the range of $$i$$ seems to be from $$[2^m, n]$$ and $$m \\in [0, \\log_2n]$$ right?\n\nAlso, $$i^m < n$$ so the loop executes $$\\log_2n - 0 + 1 = \\log_2n + 1$$ times right? How do we go about expressing this in summation notation?\n\nIs it this (just taking a guess, not sure if it's right):\n\n$$\\sum\\limits_{i = 0}^{log_2n + 1} 3$$ since we have 3 operations? If this is the answer, why do we keep the upper bound of the summation to $$\\log_2n$$ instead of $$n$$? Also, I know typically we'd use $$\\log n$$ but just put in the base 2 to help clear things up in my own head.\n\nCould someone please show how the summation of the for loop is properly written?\n\nAssuming the model of computation is RAM(Random Access Machine). Which means the cost of addition, multiplication,division etc is constant. Now your program is\n\nint j = 0;\nfor (int i = 1; i <= n; i *= 2) {\nj = j + n * 2;\n}\n\n\nInside the loop, you are doing addition, multiplication, comparison etc which takes constant time. Let $$k$$ denotes the number of iterations of the loop. Let $$c_i$$ denotes the cost at $$i$$th iteration of loop. The total cost is\n\n$$= c_1+c_2+\\ldots + c_{k}$$ $$= \\sum_{ j =1 \\text{ to } k}c_i$$\n\nIt is easy to see that above summation gives $$\\mathcal{O}(\\log n)$$.\n\n\u2022 Okay, thank you. Yes you are correct in assuming the model of computation is RAM, and the cost of those operations is constant. Sorry, I had $i = 1$ when it should be $i = 2$. I'm going to edit that now. Given that, would it be fair to say that the summation is: $$\\sum\\limits_{i = 0}^{[\\log n]} c_i$$ where I used [ ] to denote floor division (in the event that $n$ is not even) so this shows that the loop runs at most $\\log n$ times? \u2013\u00a0quantitative_ Jan 21 at 17:12","date":"2020-02-20 03:19:21","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 20, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.949303150177002, \"perplexity\": 271.3788923011115}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-10\/segments\/1581875144498.68\/warc\/CC-MAIN-20200220005045-20200220035045-00289.warc.gz\"}"} | null | null |
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"redpajama_set_name": "RedPajamaC4"
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Education Front Page Politics U.S.WND EXCLUSIVE
Harvard punishes students in all-male clubs
Faculty votes to curb constitutional right to assemble
By Bob Unruh
Harvard faculty members have voted to put a limit on the right of students to exercise their constitutionally protected freedom of association.
The policy was imposed last year when the institution approved a politically correct blacklist of students who participate in any "single-sex" social organization.
Such as fraternities and sororities.
It started with a letter signed by Harvard President Drew Gilpin Faust endorsing a policy proposed by university official Rakesh Khurana.
Khurana proposed that any student who belongs to an "unrecognized single-gender social organization" would "not be eligible to hold leadership positions in recognized student organizations or athletic teams."
Scott Greer has released "No Campus for White Men: The Transformation of Higher Education into Hateful Indoctration," now at the WND Superstore.
Violators also would be deprived of any "dean's endorsement letters for those fellowships that require such endorsements."
The education rights group FIRE said at the time the PC policy was a "stunning attack on freedom of association."
Students on the blacklist are barred from Rhodes and Marshall scholarships and from leadership of on-campus organizations or athletic teams, FIRE said.
It's been nearly two years, and the university has had multiple discussions about the issue. A non-discrimination policy that would overrule the blacklist was proposed, and it all came down to a vote this week by faculty.
The motion failed, however, by a vote of 130 to 90.
"The motion's failure represents a significant setback for the state of civil liberties at Harvard, particularly because Harvard faculty had nearly two years to consider it," FIRE said.
The proposal, from Professor Harry R. Lewis, read that Harvard would not "discriminate against students on the basis of organizations they join, political parties with which they affiliate, nor social, political or other affinity groups they join, as long as those organizations, parties, or groups have not been judged to be illegal."
But that was too much for the elite professors.
In a posted statement, Lewis argued for freedom of association.
"It has been said that we need to be idealistic, to create the best possible environment for our students. But idealism is not the same as utopianism. The history of utopian undertakings is not encouraging. Utopias have an official version of social harmony and tend to punish nonconformists. Students come to Harvard not for a social utopia, but for a liberal education in all its tensions and complexity, an education that teaches them how to use the freedom they enjoy, with advice but without coercion," he wrote.
FIRE said that as "discouraging as this development is, the process is not over."
Harvard President Drew Gilpin Faust, an alumna and board member of the proudly and exclusively single-sex Bryn Mawr College, has yet to announce which recommendation she will pursue as policy.
"We hope that she will take the fact that 90 faculty members voted in opposition to any sanctions very seriously," FIRE said.
The Harvard Crimson reported Thomas Dingman, a dean, argued "that the clubs create a toxic and exclusive environment on campus."
He also disclosed that as an undergraduate, he was a member of one of Harvard's all-male final clubs, which date back to the 18th century.
Last year, when the policy was implemented, "FIRE's executive director, Robert Shibley, said "outrageously, Harvard has decided that 2016 is the right time to revive the blacklist."
"This year's undesirables are members of off-campus clubs that don't match Harvard's political preferences. In the 1950s, perhaps communists would have been excluded. I had hoped that universities were past the point of asking people, 'Are you now, or have you ever been, a member of a group we don't like?' Sadly, they are not."
Harvey Silverglate, a Harvard Law alumnus and FIRE's civil liberties lawyer, took up the criticism at the time.
"Harvard's decision simply demonstrates that it is willing to sacrifice students' basic freedom of association to the whims of whoever occupies the administrative suites today," he said.
"Who's to say that Harvard's leaders five years from now won't decide that Catholics or Republicans should be blacklisted because they might not line up with Harvard's preferred values?"
See what American education has become, in "Crimes of the Educators: How Utopians Are Using Government Schools to Destroy America's Children."
Bob Unruh
Bob Unruh joined WND in 2006 after nearly three decades with the Associated Press, as well as several Upper Midwest newspapers, where he covered everything from legislative battles and sports to tornadoes and homicidal survivalists. He is also a photographer whose scenic work has been used commercially.
Democrat who accused GOP of giving rioters 'reconnaissance' tours backs off
Justice Sotomayor adopts pro-life arguments in opinion | {
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{"url":"https:\/\/electronics.stackexchange.com\/questions\/479191\/avrdude-does-not-read-what-it-wrote-correctly","text":"# Avrdude Does not Read What it Wrote Correctly\n\nQuestion\n\nI am getting back into Atmel AVR programming after nearly a decade off. To this end, I am trying to get the usual blinken lights demo working. Unfortunately this does not function, though avrdude reports that it flashed the hex file successfully.\n\nDigging into this a bit more, I find that reading the freshly written flash back yields a different result. The original hex file is:\n\n:100000001DC024C023C022C021C020C01FC01EC0EC\n:100010001DC01CC01BC01AC019C018C017C016C014\n:1000200015C014C013C012C011C010C00FC00EC044\n:100030000DC00CC00BC00AC009C008C011241FBEEF\n:10004000CFEFD1E0DEBFCDBF02D012C0D9CF8FE05D\n:100050008ABB1BBA9BB38BB389278BBB2FEF84E37F\n:100060009CE0215080409040E1F700C00000F2CFBA\n:04007000F894FFCF32\n:00000001FF\n\n\nWhile the read-back hex file comes out as:\n\n:200000001DC024C023C022C021C020C01FC01EC01DC01CC01BC01AC019C018C017C016C010\n:2000200015C014C013C012C011C010C00FC00EC00DC00CC00BC00AC009C008C011241FBE63\n:20004000CFEFD1E0DEBFCDBF02D012C0D9CF8FE08ABB1BBA9BB38BB389278BBB2FEF84E32C\n:140060009CE0215080409040E1F700C00000F2CFF894FFCF5C\n:00000001FF\n\n\nThe key items of note here are the programming addresses at the beginning of each line. In the original, the addresses start at 0x10000000 and increment by 0x1000. In the read hex file the base address is 0x20000000, incrementing by 0x2000. Now, the read hex file's lines are twice as long, which should account for the difference in increment magnitude.\n\nWhat would account for the difference in base address between these two hex files?\n\nI found this question on SO which seems to indicate that the AVR is 16-bit word-addressable instead of 8-bit byte-addressable as is expected by the Intel hex format. That being said, I would have expected avrdude to handle this already since programming hex files to AVR devices is kind of its whole purpose in life.\n\nAdditionally, I dumped the symbols from the elf file. As I would have expected, most of the symbols are referenced to base address 0x00000000 (truncated for brevity):\n\n...\n0000004e T main\n00000070 T _exit\n00000070 W exit\n00000072 t __stop_program\n00000074 T _etext\n000001ff W __stack\n...\n\n\nI would have expected one of the records in the hex file to write to 0x00000000 to set the reset jump offset in the IVT.\n\nWhat is the correct initial offset for program start?\n\nSince neither of these hex files specify a reset vector address there must be an additional mechanism which I am not aware of.\n\nFinally, I have verified that the programmer is actually writing to the chip by erasing the flash and performing a read; I do see the chip return essentially blank. A subsequent program returns the above incorrect hex.\n\nGeneral Information\n\nI am working on Linux using an original STK500v2. Everything is build using a heavily customized makefile based on this post. All the same, the relevant sections are below (please excuse the convoluted variables; this is part of a much larger build system):\n\nAVR_OBJCOPY=@avr-objcopy\nAVRDUDE=@avrdude -c stk500v2 -p t441 -P \/dev\/ttyUSB1\nSREC_CAT=@srec_cat\n\n%.hex: $(APP_TARGETS)$(ECHO) \" MKHEX $*\"$(AVR_OBJCOPY) -j .text -j .data -O ihex $(BUILD_DIR)\/$(ARCH)\/$*$(BINARY_SUFFIX) $(BUILD_DIR)\/$(ARCH)\/$*.flash.hex$(AVR_OBJCOPY) -j .eeprom --set-section-flags=.eeprom=\"alloc,load\" --change-section-lma .eeprom=0 -O ihex $(BUILD_DIR)\/$(ARCH)\/$*$(BINARY_SUFFIX) $(BUILD_DIR)\/$(ARCH)\/$*.eeprom.hex$(AVR_OBJCOPY) -j .fuse -O ihex $(BUILD_DIR)\/$(ARCH)\/$*$(BINARY_SUFFIX) $(BUILD_DIR)\/$(ARCH)\/$*.fuses.hex --change-section-lma .fuse=0$(SREC_CAT) $(BUILD_DIR)\/$(ARCH)\/$*.fuses.hex -Intel -crop 0x00 0x01 -offset 0x00 -O$(BUILD_DIR)\/$(ARCH)\/$*.lfuse.hex -Intel\n$(SREC_CAT)$(BUILD_DIR)\/$(ARCH)\/$*.fuses.hex -Intel -crop 0x01 0x02 -offset -0x01 -O $(BUILD_DIR)\/$(ARCH)\/$*.hfuse.hex -Intel$(SREC_CAT) $(BUILD_DIR)\/$(ARCH)\/$*.fuses.hex -Intel -crop 0x02 0x03 -offset -0x02 -O$(BUILD_DIR)\/$(ARCH)\/$*.efuse.hex -Intel\navr-nm -n $(BUILD_DIR)\/$(ARCH)\/$*$(BINARY_SUFFIX) > $(BUILD_DIR)\/$(ARCH)\/$*.sym read-fuses:$(AVRDUDE) 2>&1 | grep \"Fuses OK\" | sed 's:.*($$.*$$).*:\\n\\1\\n:'\n\nwrite-flash:\n$(AVRDUDE) -U flash:w:$(BUILD_DIR)\/\\$(ARCH)\/firmware.flash.hex\n\n\nI know the STK500 is functional because, infuriatingly, this was working before on this very chunk of silicon.\n\nEdit:\n\nBy request: the source for my test program.\n\n#include <avr\/io.h>\n#include <util\/delay.h>\n\nint main(){\n\nDDRA = 0x0F;\nPORTA = 0x00;\n\nwhile (1)\n{\nPORTA ^= PORTA;\n_delay_ms(500);\n}\n}\n\n\nAlso, for good measure, current fuse settings:\n\navrdude: safemode: Fuses OK (E:FF, H:DF, L:82)\n\n\nEdit 2:\n\nFor any who see this later, the issue with the program was an XOR fail. PORTA ^= PORTA; should have been PORTA ^= 0x0F;. This post just about sums it up. Remember kids, don't try to be too clever.\n\n\u2022 here is the hexfile format description, for anyone doing research ... en.m.wikipedia.org\/wiki\/Intel_HEX \u2013\u00a0jsotola Feb 3 at 4:18\n\u2022 \"I am trying to get the usual blinken lights demo working. Unfortunately this does not function\" - which AVR? Show us your code for blinking lights. \u2013\u00a0Bruce Abbott Feb 3 at 4:44","date":"2020-11-27 10:43:31","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.2438327670097351, \"perplexity\": 8502.842698073608}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-50\/segments\/1606141191692.20\/warc\/CC-MAIN-20201127103102-20201127133102-00077.warc.gz\"}"} | null | null |
Ženski košarkaški turnir na OI 1988. održan je u Seulu od 19. do 29. rujna. Naslov je obranila reprezentacija SAD-a.
Turnir
Skupina A
19. rujna 1988.
22. rujna 1988.
25. rujna 1988.
Skupina B
19. rujna 1988.
22. rujna 1988.
25. rujna 1988.
Izbacivanje
Poluzavršnica je održana 27., utakmica za broncu 28., a utakmica za zlato 29. rujna.
Poluzavršnica
Australija - Jugoslavija 56:57
SAD - SSSR 102:88
Za broncu
Australija - SSSR 53:68
Za zlato
Jugoslavija - SAD 70:77
Ž | {
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\section{Introduction}
By opening the exploration of the new territory of physics at the
Terascale, the CERN Large Hadron Collider (LHC) is likely to shed
light upon the main open puzzle in particle physics, namely the origin
of mass and the nature of electroweak symmetry breaking.
Supersymmetry (SUSY) provides an elegant way of justifying the
electroweak symmetry breaking mechanism in terms of an elementary
Higgs particle, alleviating the so called hierarchy
problem~\cite{Dimopoulos:1981yj}.
The Higgs boson and the existence of supersymmetry therefore stand out
as the main missing pieces in our understanding of fundamental forces,
and a lot of effort has been put into their direct observation.
Indeed the search for the Higgs boson and for supersymmetry constitute
the main topic in the agenda of the LHC. \medskip
In contrast, so far the only established evidence for physics beyond
the standard model (SM) has been the discovery of neutrino masses and
oscillations~\cite{Maltoni:2004ei}, which has culminated decades of
painstaking efforts. \medskip
Here we stress that these two issues may be closely related. Indeed,
low-energy supersymmetry with broken R--parity~\cite{Hall:1983id}
provides a plausible mechanism for the origin for neutrino masses and
mixings. Indeed, as the bilinear model best
illustrates~\cite{Hirsch:2004he}, in contrast to the simplest seesaw
schemes~\cite{Nunokawa:2007qh}, these may be tested at particle
accelerators like the LHC~\footnote{ { Such model has no conventional
neutralino dark matter, though other possible dark matter
candidates may be envisaged such as the
axion~\cite{Peccei:1977hh}, the majoron~\cite{Berezinsky:1993fm},
the axino or the gravitino~\cite{Hirsch:2005ag}.} }.\medskip
Here we consider the simplest ansatz to introduce R--parity breaking
in supersymmetry, characterized by an additional bilinear violating
(BRpV) term in the superpotential~\cite{Hirsch:2000ef}. It provides
the simplest effective description of a more complete picture
containing additional neutral heavy lepton~\cite{Dittmar:1989yg}
superfields whose scalars drive the spontaneous breaking of
R--parity~\cite{Masiero:1990uj}. \medskip
Our focus here is on the specific case of a minimal gravity mediated
supersymmetry breaking model with bilinear R parity violation:
BRpV--mSUGRA model for short. In this model, the lightest
supersymmetric particle (LSP) is no longer stable. Current neutrino
oscillation data indicate that the strength of the BRpV term is
small~\cite{Hirsch:2000ef}, hence the LSP decay length is expected to
be long enough to provide a displaced vertex at the
LHC~\cite{deCampos:2005ri,deCampos:2007bn}. { For a low Higgs mass
the dominant decay is into { $b\bar{b}$}, however at the LHC the
overwhelming QCD background makes this signal irrelevant when the
Higgs is produced in the standard way.
In supersymmetry the Higgs can be produced after the decay chains of
the next-to-lightest supersymmetric particle. In the R--parity
conserving case for specific spectrum and supersymmetric production,
the additional jets and the missing energy can allow the discovery
of the Higgs in the $b$ channel \cite{19}. The same features also
hold in our case, but in addition now the Higgs can be produced from
the lightest neutralino, leading to events with a displaced vertex {
with two large invariant mass b--jets}. The signal of a neutralino
into a Higgs and a neutrino is therefore free of SM backgrounds if
the neutralino decays inside the pixel detector and well outside the
interaction point. Here we show explicitly that this is the
case~\footnote{In fact the LHCb collaboration is considering the
possibility to search for b's originating outside the interaction
point \cite{20}.}.} \medskip
In this work we analyze the potential of the LHC to survey the
existence of the Higgs boson using a novel signal: a b--jet pair
coming from displaced vertices generated by the lightest neutralino
decays within the BRpV--mSUGRA model. We demonstrate that the LHC
reach is capable to uncover a supersymmetric Higgs in a fair region of
the $M_{1/2}\otimes M_0$ parameter plane. \medskip
\section{{ Model description}}
The BRpV model is described by the superpotential
\begin{equation}
W_{\text{BRpV}} = W_{\text{MSSM}} + \varepsilon_{ab}
\epsilon_i \widehat L_i^a\widehat H_u^b \; ,
\end{equation}
in which the standard minimal supersymmetric model (MSSM) is
supplemented by three extra bilinear terms characterized by three new
parameters ($\epsilon_i$), one for each fermion generation. In
addition to these we must also include new soft supersymmetry breaking
terms ($B_i$) in whose presence the bilinears become physical
parameters that can not be rotated away~\cite{Diaz:1997xc}.
\begin{equation}
V_{\text{soft}} = V_{\text{MSSM}} - \varepsilon_{ab}
B_i\epsilon_i\widetilde L_i^aH_u^b
\end{equation}
The new terms in the BRpV Lagrangian ($\epsilon_i$, $B_i$) lead to the
explicit violation of lepton number as well as R--parity. Furthermore,
the sneutrino fields acquire a vacuum expectation value when we
minimize the scalar potential. \medskip
In BRpV models the terms presenting explicit lepton number violation,
as well as, the sneutrino vacuum expectation values generate mixing
among neutrinos and neutralinos giving rise to one tree--level
neutrino mass. The other two neutrino masses are generated through
loop diagrams~\cite{Hirsch:2000ef}. One can show that, indeed, the
resulting neutrino masses and mixings provide a good description of
all current neutrino oscillation data~\cite{Maltoni:2004ei}. \medskip
For the sake of definiteness, we assume mSUGRA as the model of
supersymmetry breaking, implying universality of the soft breaking
terms at unification. In this case, our model depends upon eleven free
parameters, namely
\begin{equation}
M_0\,,\, M_{1/2}\,,\, \tan\beta\,,\, {\mathrm{sign}}(\mu)\,,\,
A_0 \,,\,
\epsilon_i \: {\mathrm{, and}}\,\, \Lambda_i\,,
\end{equation}
where $M_{1/2}$ and $M_0$ are the common gaugino mass and scalar soft
SUSY breaking masses at the unification scale, $A_0$ is the common
trilinear term, and $\tan\beta$ is the ratio between the Higgs field
vev's. For convenience, we trade the soft parameters $B_i$ by
$\Lambda_i=\epsilon_iv_d+\mu v_i$, where $v_i$ is the vacuum
expectation value of the sneutrino fields, since the $\Lambda_i$'s are
more directly related to the neutrino masses; for further details see
~\cite{Hirsch:2000ef}. \medskip
The bilinear R--parity violating interaction gives rise to mixings
between SM and SUSY particles that lead to decay of the LSP into SM
particles. In a large fraction of the parameter space the lightest
neutralino is the LSP and it can decay into leptonic final states $\nu
\ell^+ \ell^{\prime -}$, where $\ell = e$, $\mu$ or $\tau$, as well as
into semi-leptonic final states $ \ell q^\prime \bar{q}$ or $ \nu q
\bar{q}$. For sufficiently heavy neutralinos these decays are
dominated by two--body channels like $\nu Z$, $\ell^\pm W^\mp$ and
$\nu h$ with $h$ being the lightest CP even Higgs boson; for further
details see~\cite{Porod:2000hv,deCampos:2007bn,deCampos:2008re}. In
the region where the stau is the LSP the detached vertex signal
disappears completely since the stau possesses a very small decay
length. \medskip
In contrast, a salient feature of our BRpV model is that neutralino
LSPs exhibit a rather large decay length, ranging from a few
millimeters to tenths of millimeters for $M_{1/2}$ varying from 200
GeV to 1 TeV. Such large decay lengths lead to the production of
detached vertices at the LHC which constitute a smoking gun of this
kind of models. \medskip
In this work, we analyze the two--body lightest neutralino decay into
the lightest Higgs boson $h^0$ as a Higgs discovery channel
\begin{equation}
\tilde{\chi}^0_1 \to h \nu\;\;\;.
\end{equation}
If the lightest neutralino lives long enough it will be detached from
the primary interaction point leaving a displaced vertex as signal at
the LHC. Since the Higgs boson $h$ decays mostly into a b--quark pairs
we expect a displaced vertex with two b--jets as a characteristic
signature for Higgs production. \medskip
\begin{figure}
\begin{center}
\includegraphics[width=0.98\linewidth]{leptongl_higgs}
\end{center}
\vspace{-0.5cm}
\caption{Br$(\tilde\chi_1^0\to h\nu)$ as a function of $M_{1/2}
\otimes M_0$ for $\tan\beta=10$, $A_0=-100$ GeV and $\mu>0$.}
\label{chitohnu}
\end{figure}
We present, in Figure \ref{chitohnu}, the lightest neutralino
branching ratio to $h\nu$ as a function of $M_{1/2} \otimes M_0$ for
$\tan\beta=10$, $A_0=-100$ GeV and $\mu>0$~\footnote{ We note
that in the upper left dark region the stau is the LSP and in what
follows we will not consider this region.}.
Here we focus on the situation where the lightest neutralino is
heavier then $h$, so the neutralino Higgs decay channel opens for
$M_{1/2} \gtrsim {\cal O} (300)$ GeV for our choice of parameters.
The maximum value of the branching ratio for this channel is about
$22\%$; for an illustration of the full behavior of neutralino decays
see, for example,
Ref.~\cite{Porod:2000hv,deCampos:2007bn,deCampos:2008re}. This figure
tells us that, for fixed values of $M_{1/2}$, the LSP branching ratio
into Higgs--neutrino pairs initially grows with increasing $M_0$,
stabilizing for $M_0$ in excess of a few hundred GeV. On the other
hand, the importance of this decay increases with $M_{1/2}$ for
moderate and large values of $M_0$.
\section{Signal and backgrounds}
In order to simulate the Higgs production we calculate all R--parity
violating branching ratios and SUSY spectra using the package
SPheno~\cite{Porod:2003um}. We used PYTHIA version 6.408~\cite{pythia}
to generate events, using the SPheno output in the SLHA
format~\cite{Skands:2003cj}. In order to have a rough simulation of
the detector response we smeared the track energies, but not their
directions, with a Gaussian error given by $\Delta E/E = 0.10/\sqrt{E}
+ 0.01$ (E in GeV) for leptonic tracks and $\Delta E/E = 0.5/\sqrt{E}
+ 0.03$ for all hadronic tracks.\medskip
Displaced vertices at the LHC were identified requiring that the
neutralino decays away from the primary vertex point, that is, outside
an ellipsoid centered at the primary vertex
\begin{equation}
\left ( \frac{x}{{ 5}\delta_{xy}} \right )^2
+ \left ( \frac{y}{{ 5}\delta_{xy}} \right )^2
+ \left ( \frac{z}{{ 5}\delta_{z}} \right )^2 = 1 \; ,
\end{equation}
where the $z$-axis is along the beam direction. To be conservative we
assumed the ellipsoid size to be five times the ATLAS expected
precision in each direction for the semiconductor
tracker~\cite{atlas:2008zzm} which are $\delta_{xy} = 20~\mu$m and
$\delta_z = 500~\mu$m. To reconstruct the vertices we required that
visible tracks coming from neutralino decays must have an intersection
inside a sphere determined by the tracking detector resolution which
we assumed to be $10~\mu$m~\cite{atlas:2008zzm}. Furthermore, we
considered only the charged tracks inside the pseudo--rapidity region
of $|\eta| < 2.5$.\medskip
Since the Higgs production in the LSP decay is characterized by the
presence of two b--tagged jets we looked for events with at least one
displaced vertex containing at least one jet tagged as a b--jet. In
our analyses we considered a b--tagging efficiency up to
$50\%$.\medskip
In order to ensure that the detached vertex events are properly
recorded we accepted only events that pass very simple trigger
requirements.We further required the events to present an isolated
electron (muon) with $p_T>20$ (6) GeV, or the presence of a jet with
$p_T > 100$ GeV, or missing transverse energy in excess of 100 GeV.
\medskip
For our analysis we have fixed $\tan\beta = 10$, $A_0 = -100$ GeV and
$\mu > 0$. For this choice of parameters, the Higgs mass lies in the
range $ 110$ GeV $\raise0.3ex\hbox{$\;<$\kern-0.75em\raise-1.1ex\hbox{$\sim\;$}} M_{h} \raise0.3ex\hbox{$\;<$\kern-0.75em\raise-1.1ex\hbox{$\sim\;$}} 120$ GeV when we vary $M_0$ and
$M_{1/2}$. Since we are only interested in detached jets coming from
Higgs decays, we have further required that the jet--jet invariant
mass is around the Higgs mass value.\medskip
Within the SM framework displaced vertices originate from decays of
long lived particles, like $B$'s and $\tau$'s, and consequently its
visible decay products exhibit a rather small invariant mass. In
contrast, in our BRpV model, the displaced vertices are associated to
the LSP decay and will have in general a large invariant mass
associated to them. Therefore, physical SM processes do not lead to
sizeable backgrounds to the detached Higgs searches due to to large
difference in the invariant mass of the visible products. However,
BRpV LSP decays into $\nu Z$ are a potential source of background for
the Higgs signal.\medskip
As an illustration we show in Figure \ref{wpeak} the jet--jet
invariant mass distribution of all displaced vertices exhibiting
jets. As we can see, a cut on the invariant mass outside the range
$100$ GeV $< M_{inv} < 125$ GeV eliminates a good fraction of
supersymmetric backgrounds coming, for instance, from the neutralino
decay into W and Z bosons as well as the three--body $b\bar{b}\nu$
channel. The physical background can be further suppressed by
requiring that at least one of the jets associated to the displaced
vertex is tagged as a b jet. Moreover, these requirements ensure that
SM backgrounds coming from the decay of long lived particles are also
efficiently eliminated. There remain instrumental
backgrounds~\cite{Strassler:2008fv} which require a full detector
simulation along the lines we have described above; this simulation is
beyond the scope of the present work. \medskip
In Figure~\ref{minv_cut} we show that almost all vertices containing
b--jets come from neutralino decay via Higgs and that our invariant
mass cut will eliminate the $\nu Z$ background, while keeping a large
fraction of the signal events. We checked that the events passing the
LHC triggers and all the above cuts come from the signal events
$\tilde{\chi}^0_1 \to \nu h$ with the physics background being
negligible.\medskip
In order to estimate the LHC reach for Higgs search coming from
displaced vertex signal in BRpV--mSUGRA models we considered a few
scenarios. In the optimistic analysis we assumed that there is no
event coming from instrumental backgrounds or overlapping events and
took the b--tagging efficiency to be 50\%. In this case we required
that the signal must have more than 5 events since no background is
expected and present our result in the $M_{1/2}\otimes M_0$ plane for
integrated luminosities of 10 and 100 fb$^{-1}$. We also considered
three additional scenarios. In the first one we studied the impact of
a lower b--tagging efficiency (30\%) but we still assumed that the
process is background free. In the second case we assumed that there
are 5 backgrounds events originating from instrumental errors and
overlapping events and required a $5\sigma$ signal for a 50\%
b--tagging efficiency. Finally, in the last scenario we assumed the
same background as in the last case, lowering however, the b--tagging
efficiency down to 30\%. \medskip
\begin{figure}[th]
\begin{center}
\includegraphics[width=0.98\linewidth]{higgs1v_minvc}
\end{center}
\vspace*{-8mm}
\caption{Jet pair invariant mass distribution in GeV. The light blue
(greyish) histogram stands for the background where the lightest
neutralino decays via W and Z bosons and the other histogram
stands for the channels where the lightest neutralino decays into
$b\bar{b}$ pairs.}
\label{wpeak}
\end{figure}
\begin{figure}[hb]
\begin{center}
\includegraphics[width=0.98\linewidth]{higgs_part_fullc}
\end{center}
\vspace*{-8mm}
\caption{Invariant mass distribution in GeV of the neutralino decaying into
b-jet pairs separated into its several channels.}
\label{minv_cut}
\end{figure}
\section{Results}
In Figure~\ref{fig:reach} we depict the LHC discovery reach for the
Higgs displaced vertex signal in our most optimistic scenario.
The shaded (yellow) region at the bottom stands for points already
excluded by direct LEP searches while the upper--left corner of the
$M_{1/2}\otimes M_0$ plane, the (red) shaded area, corresponds to the
region where the stau is the
LSP~\cite{deCampos:2007bn}, and hence
is not covered by the present analysis.
The region around $M_{1/2} = 200$ GeV has no signal due to the fact
that the neutralino mass is smaller than the Higgs mass in it,
therefore, being forbidden the two--body LSP decay into
Higgs--neutrino pairs.\medskip
\begin{figure}[b]
\begin{center}
\includegraphics[width=0.98\linewidth]{reach_higgs}
\end{center}
\vspace*{-8mm}
\caption{LHC reach for Higgs search in displaced vertices for the
BRpV--mSUGRA model in the plane $M_{1/2}\otimes M_0$ assuming
$\tan\beta = 10$, $A_0=-100$ GeV, and $\mu > 0$. The yellow stars
(blue squares) represent the reach for an integrated luminosity of
10 (100) fb$^{-1}$ while the hatched region corresponds to the
reach of the LHCb experiment for an integrated luminosity of 10
fb$^{-1}$. The (yellow) shaded region in the bottom stands for
points excluded by direct LEP searches, while the (red)
upper--left area represents a region where the stau is the
LSP. Note that the black lines
delimit different regimes of LSP decay length.}
\label{fig:reach}
\end{figure}
From Fig.~\ref{fig:reach} one can see that the ATLAS and CMS
experiments will be able to look for the signal up to $M_{1/2} \sim
700$ $(900)$ GeV for a LHC integrated luminosity of 10 (100)
fb$^{-1}$.
Notice that the LHC Higgs discovery potential is almost independent of
$M_0$. For a fixed value of $M_{1/2}$ the LSP total production cross
section decreases as $M_0$ increases, however, the LSP branching ratio
into Higgs--neutrino pairs increases with $M_0$, therefore, both
effects tend to cancel and produce the observed behavior.
Moreover, this figure also exhibits the average decay length of the
neutralino, demonstrating that its decay takes place inside the vertex
detector, ensuring a good vertex reconstruction.\medskip
We have also estimated the reach expected at LHCb for our Higgs search
proposal. The hatched region in Fig.~\ref{fig:reach} indicates the
LHCb reach for 10 fb$^{-1}$. Due to the strong cut on the
pseudo--rapidity required by this experiment the reach for 2 fb$^{-1}$
is severely depleted and only a small region of the parameter space is
covered, {\em i.e.}, $300\; \rm{GeV} \leq M_{1/2} \leq 350$ GeV and
$200\; \rm{GeV} \leq M_{0} \leq 500$ GeV.\medskip
Tagging b--jets emanating from a detached vertex is certainly a more
intricate procedure, therefore, we also considered a lower b--tagging
efficiency in our analyses. Figure~\ref{fig:eff30} contains the reach
of LHC for Higgs search using a b--jet reconstruction efficiency of
30$\%$, instead of 50$\%$ used of Fig.~\ref{fig:reach}, however, we
still assumed that the search is background free. Comparing
Figs.~\ref{fig:reach} and \ref{fig:eff30}, one can see that the LHC
reach in this second case is mildly affected by this change for an
integrated luminosity of 10 fb$^{-1}$, while the changes are minute at
higher integrated luminosities.
\medskip
\begin{figure}[t]
\begin{center}
\includegraphics[width=0.98\linewidth]{higgs_eff.eps}
\end{center}
\vspace*{-8mm}
\caption{Same as Fig.~\ref{fig:reach} using a b-jet reconstruction
efficiency of 30$\%$ with no background events. }
\label{fig:eff30}
\end{figure}
A study of the instrumental backgrounds and the effect of overlapping
events does require a full detector simulation, which is beyond the
scope of this work. In order to assess the impact of existence of
non--physical backgrounds we considered that these backgrounds give
rise to 5 background events for both integrated luminosities used in
our studies. In Figure~\ref{fig:5event} we present the $5\sigma$
LHC Higgs discovery potential assuming a b--jet reconstruction
efficiency of 50$\%$ and 5 background events. We can see from this
figure that the existence of background events does lead to a
substantial reduction of the LHC reach for Higgs in displaced
vertices. \medskip
\begin{figure}[t]
\begin{center}
\includegraphics[width=0.98\linewidth]{higgs_5evt.eps}
\end{center}
\vspace*{-8mm}
\caption{Same as Fig.~\ref{fig:reach} using a b--jet reconstruction
efficiency of 50$\%$ and assuming the existence 5 background
events for both integrated luminosities.}
\label{fig:5event}
\end{figure}
In Fig.~\ref{fig:5evt-eff} we present the reach of LHC for Higgs
search in a very pessimistic scenario that exhibits a lower b--jet
reconstruction efficiency of 30$\%$, as well as, the presence of 5
background events. In this case we observe a more severe reduction of
the LHC reach that is reduced to $M_{1/2} = 600$ GeV at most. This
large depletion of the LHC search potential follows from the need of a
large number of signal events to establish the signal given the fast
decrease of the SUSY production cross section with increasing
$M_{1/2}$. In this sense, the 100 fb$^{-1}$ case is more affected
since the production cross section exhibits a steep decrease for
$M_{1/2} \gtrsim 700$ GeV.\medskip
\begin{figure}[thb]
\begin{center}
\includegraphics[width=0.98\linewidth]{higgs_5evt_eff.eps}
\end{center}
\vspace*{-8mm}
\caption{Same as Fig.~\ref{fig:reach} using a b-jet reconstruction
efficiency of 30$\%$ and 5 background events.}
\label{fig:5evt-eff}
\end{figure}
\section{Conclusions}
In summary we have seen how the search for displaced vertices
containing b--tagged jets at the LHC may not only provide evidence for
supersymmetric particles but also lead to the discovery of the Higgs
boson of the electroweak theory. We have given a quantitative analysis
within the simplest minimal supergravity model with bilinear breaking
of R--parity, which accounts for the observed pattern of neutrino
masses and mixings observed in current neutrino oscillation
experiments. Similar variant schemes can be envisaged where, for
example, supersymmetry and/or electroweak breaking is realized
differently.\medskip
In an optimistic background free scenario the Higgs search in LSP
decays can be carried out for LSP masses up to 300 (380) GeV for an
integrated luminosity of 10 (100) fb$^{-1}$. We showed that this
result is robust against variations of the assumed b--tagging
efficiencies. Notwithstanding, the results change drastically if
instrumental backgrounds are present. Assuming the existence of 5
background events reduces the LHC reach to LSP masses of 210 (250) GeV
at the low (high) luminosity run.\medskip
\section*{Acknowledgments}
We thank A. Bartl for careful reading the manuscript. This work was
supported by MEC grant FPA2005-01269, by EC Contracts RTN network
MRTN-CT-2004-503369, by Conselho Nacional de Desenvolvimento
Cient\'{\i}fico e Tecnol\'ogico (CNPq) and by Funda\c{c}\~ao de Amparo
\`a Pesquisa do Estado de S\~ao Paulo (FAPESP) and by Colciencias in
Colombia under contract 1115-333-18740.
\bibliographystyle{h-physrev4}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,562 |
{"url":"https:\/\/www.aimsciences.org\/article\/doi\/10.3934\/cpaa.2004.3.217","text":"# American Institute of Mathematical Sciences\n\nJune\u00a0 2004,\u00a03(2):\u00a0217-235. doi:\u00a010.3934\/cpaa.2004.3.217\n\n## High order product integration methods for a Volterra integral equation with logarithmic singular kernel\n\n 1 Centro de Matematica e Aplic\u0105coes, Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal 2 Laboratorio Interdisciplinar de Computacao Cient\u0131fica, Faculdades COC, 14096-160 Ribeirao Preto - SP, Brazil 3 Centro de Matem\u00e1tica Aplicacoes, Instituto Superior T\u00e9cnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal\n\nReceived\u00a0 June 2003 Revised\u00a0 January 2004 Published\u00a0 March 2004\n\nThis work is concerned with the construction and analysis of high order product integration methods for a class of Volterra integral equations with logarithmic singular kernel. Sufficient conditions for the methods to be convergent are derived and it is shown that optimal convergence orders are attained if the exact solution is sufficiently smooth. The case of non-smooth solutions is dealt with by making suitable transformations so that the new equation possesses smooth solutions. Two particular methods are considered and their convergence proved. A sample of numerical examples is included.\nCitation: T. Diogo, N. B. Franco, P. Lima. High order product integration methods for a Volterra integral equation with logarithmic singular kernel. Communications on Pure & Applied Analysis, 2004, 3 (2) : 217-235. doi: 10.3934\/cpaa.2004.3.217\n [1] Reza Chaharpashlou, Abdon Atangana, Reza Saadati. On the fuzzy stability results for fractional stochastic Volterra integral equation. Discrete & Continuous Dynamical Systems - S, 2020\u00a0 doi: 10.3934\/dcdss.2020432 [2] Bahaaeldin Abdalla, Thabet Abdeljawad. 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Weighted multipolar Hardy inequalities and evolution problems with Kolmogorov operators perturbed by singular potentials. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934\/cpaa.2020274 [16] Susmita Sadhu. Complex oscillatory patterns near singular Hopf bifurcation in a two-timescale ecosystem. Discrete & Continuous Dynamical Systems - B, 2020\u00a0 doi: 10.3934\/dcdsb.2020342 [17] Mokhtar Bouloudene, Manar A. Alqudah, Fahd Jarad, Yassine Adjabi, Thabet Abdeljawad. Nonlinear singular $p$ -Laplacian boundary value problems in the frame of conformable derivative. Discrete & Continuous Dynamical Systems - S, 2020\u00a0 doi: 10.3934\/dcdss.2020442 [18] Hui Lv, Xing'an Wang. Dissipative control for uncertain singular markovian jump systems via hybrid impulsive control. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 127-142. doi: 10.3934\/naco.2020020 [19] Xuefeng Zhang, Yingbo Zhang. Fault-tolerant control against actuator failures for uncertain singular fractional order systems. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 1-12. doi: 10.3934\/naco.2020011 [20] Gunther Uhlmann, Jian Zhai. Inverse problems for nonlinear hyperbolic equations. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 455-469. doi: 10.3934\/dcds.2020380\n\n2019\u00a0Impact Factor:\u00a01.105","date":"2020-11-30 15:06:39","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5941460728645325, \"perplexity\": 10866.526714118485}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-50\/segments\/1606141216175.53\/warc\/CC-MAIN-20201130130840-20201130160840-00547.warc.gz\"}"} | null | null |
Thank you on very personal basis from the whole family for your itinerary and detailed arrangements, for the selection of accommodation, selection of lodges, and the assisted transfers at each travel leg. We met the Bidvest people 3 times at Jo'burg, each occasion a different transfer sequence, and they were very efficient, gaining us priority in queues and taking any confusion away from where to go. Botswana/Zimbabwe border also had the potential of being challenging and the 2 drivers sorted it out easily between them.
You earned our grateful thanks for managing the cancellation of the private flight from Thornybush with the early morning road transfer. The fog was incredibly dense the whole way, and Nelspruit airport had absolutely zero visibility, so it was just as well we did not attempt to fly. The minibus driver, Hermann, was a private guide/driver based in Hoedspruit and was appropriately cautious on a dangerous journey.
If you look into your files you will know that I have been planning this visit for some years, and I'm delighted with how it has turned out. Southern Africa felt very familiar and comfortable to to us despite the 30 year absence. However the greatest joy was seeing it all through the eyes of the children, who continue to enthusiastically relate their experiences back in Sydney. Deborah has cautioned them that they have been spoiled with "Poppy's style of travel" which is not the norm! Congratulations again to you Michelle for judging the standard that we were seeking, not over the top luxurious, but good quality comfort and service.
Thornybush Monwana Lodge was the highlight. The small size suited us perfectly and delivered a very personal experience. "Shared safaris" resulted in only us 4 plus another couple, or sometimes just us. The resident Guide, Doctor, and his tracker were excellent and related incredibly well to the children. When we met other safari vehicles you could tell that the guides related to Doctor with a high degree of respect. He gave us some exciting experiences and set off each day with a purpose, "We are going to find that male lion..". We did a bush walk most days, each one delivering a surprise, with a pair of rhino, a herd of elephants, a lion, and a Cape Buffalo waiting to charge us. We became good friends with Doctor and continued to correspond after we left. The food was bordering on gourmet standard, and the personal attention of the Manageress Tamsyn who one day served lamington cakes in our honour (Australian iconic dish) was special. When you originally booked Thornybush Park for us, I was a little concerned that its finite size was going to present us with a zoo experience rather than wide expanses of African bush. No foundation to my reservations, as with all the fences down the park is connected to Kruger. It was sensational.
Chobe Bakwena Lodge was different and presented its unique experiences. Bakwena is not so upmarket as Monwana, and the gate access is through a dusty African village. The family sized rondavel, (actually an oval) was large and ideal for us. The place is well managed by a group of women, the food wholesome, and willing service. The main lodge building was established, comfortable and practical. We had a guide Jonathan (Jono) who was on contract to Bakwena and was very good. Matthew was a bit put out initially when he discovered that Chobe Reserve would not allow us to go off-road bush-bashing in pursuit of lions as we had just experienced, but in the end that did not limit what we saw.
Chobe overall gave us some fascinating sights, that complemented Monwana, particularly the river trips. We took a private boat one day at 1100am to avoid the flotilla of boats from multiple lodges that are on the river at 3.30pm. Once again our safari vehicle was not overcrowded, most occasions it was just the 4 of us. On the last day, Jonathan took us for a walk through the local village and we visited the junior school. Julia made a presentation of a drawing of a Kookaburra and we left some gifts (30 pen/pencil/ruler sets and notebooks). This was a good educational experience for our children.
Botswana felt safe and well organised.
After the inefficiency of the Zimbabwe border crossing, Vic Falls town also presented a smart prosperous safe environment. It obviously thrives on tourism and influx of USD and is not representative of the rest of Zim. A'Zambezi River Lodge with manicured lawns down to the river was a good hotel selection. The public spaces, restaurant, and bar are all good, fine choice of food, with excellent entertainment at dinner in the evening, Rooms are "holiday inn" style and size; a contrast to the vast sized rondavels we had just enjoyed, but perfectly adequate when combined to the outside sitting area on the lawn. We were impressed that our Guide, Mackson, with his 20 seater bus was at our disposal for the whole time, hence we were not stuck 7km out of town or dependent on hotel minibus schedule.
The helicopter trip was of course the highlight. Thank you for the initiative of including it in the itinerary. We all enjoyed the local craft market, and Deborah especially bought loads of wooden carvings. (No problem at Australian quarantine as hardwood). Just as well it was our last morning. Two nights and one and half days was quite sufficient.
Big picture, we will enthusiastically recommend this itinerary and all the safari locations to everyone, but ideally after Cape Town, reverse the order; start in Zim/Botswana and finish in Thornebush. I know we did not have a choice and you did very well to craft the itinerary so successfully.
Thank you for what you have done for us, particularly sorting out the changed arrangements after Deborah's accident. We greatly appreciate the initiatives you applied and the inspired choices that you made on our behalf. We are enthusiastic ambassadors for Southern Destinations and the service you have delivered. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,616 |
\section{Introduction}
Polarization stabilization and control is a matter of particular interest in the area of quantum communication mainly due to the possibility of encoding qubits in polarization states \cite{GisinRMP02}. Recently, quantum communication protocols based on two-photon interference have been given a lot of attention, specially with the advent of the Measurement Device Independent Quantum Key Distribution Protocol \cite{LoPRL2012}. This protocol, in particular, makes use of the photon-bunching effect in a Bell-State Projection (BSP) which is highly dependent on the indistinguishability between quantum states and, thus, on the aligned polarization states at the BSP \cite{ThiagoPRA2013}. Therefore, polarization stabilization along the quantum channel becomes an important issue.
Recently, a scheme for active polarization stabilization along the optical quantum channel employing current optical fibre technology has been successfully demonstrated \cite{XavierOPEX08,ThiagoQIM12}. Such scheme makes use of a reference laser which is launched in the fiber in a DWDM channel adjacent to that of the quantum communication channel in a counter-propagating manner, such that the transmitter receives the reference signal from the receiver \cite{XavierOPEX08}. A simplified scheme of the proposed system is depicted in Fig.\ref{fig:PolarizationState_Stabilizer}.
\begin{figure}[htbp]
\centering
\includegraphics[width=0.8\linewidth]{PolarizationState_Stabilizer.png}
\caption{Simplified setup for on-time polarization tracking in wavelength multiplexed optical quantum channels.}
\label{fig:PolarizationState_Stabilizer}
\end{figure}
By rotating the received polarization state to match what should be its original state, the transmitter gains access to the optical link transfer function and can produce the inverse transformation on the outgoing optical pulses \cite{XavierOPEX08}. Not only the polarization has been shown to stabilize during long term communication periods but it was also proven that the noise contribution from the adjacent counter-propagating channels was negligible, enabling the use of the technique in quantum communication channels \cite{XavierOPEX08}.
However efficient, the polarization control enforced by the system described above only enables the stabilization of the polarization state rather than its fast switching. As the quantum states must be encoded in the polarization, the rapid switching between polarization states becomes a rather important task, even more when the mathematical security proofs for quantum communication channels rely on the rate of secret key generation \cite{MaPRA05,LutkenhausPRA00}. By associating the polarization stabilization setup proposed in \cite{XavierOPEX08} and an active feedback system based on a sample of the outgoing polarization state, a mixed analog-digital polarization switch is proposed. The scheme is supposed to rapidly switch between arbitrary polarization states whilst protecting the quantum state alignment from fluctuations of the optical channel, a claim supported by the numerical simulation results of each individual system that comprise the main unit.
The paper is divide as follows. In Section II, the mathematical formalism necessary to represent stats of polarization and the lithium-niobate-based polarization controller is presented. In Section III, the individual units are detailed and the complete optoelectronic polarization switch unit is presented. The simulation results and discussions appear in Section IV. Finally, in Section V, the conclusions are drawn and the real implementation of the envisioned system is discussed.
\section{Theoretical Formulation}
\subsection{Mathematical representation of polarization}\label{mathRep}
The state of polarization of light has been represented mathematically as Jones Vectors and Stokes Vectors \cite{saleh1991fundamentals}. Even though the conversion between these two representations require straightforward computations, we shall stick to the Stokes representation since visualization in the Poincar\'e Sphere is direct \cite{saleh1991fundamentals}. Stokes vectors are 4-dimensional vectors that carry information about the State of Polarization (SOP) of light. Since the first component ($S_0$) is associated to the total light intensity, it is common to normalize the Stokes Vector by dividing all of its entries by $S_0$. In the case of polarized light, the 3-dimensional Stokes Vector formed of the remaining three normalized components of the former 4-dimensional vector, has norm $1$. Indeed, the degree of polarization of light is given by the norm of the Stokes vector. Assuming that light is polarized enables one to simplify the representation. The usual representation of the 3-dimensional normalized Stokes vector, assuming polarized light (and, hence norm 1), is a point in the 3-sphere known as the Poincar\'{e} Sphere. Since all SOPs are mapped bijectively in the 3-sphere, we shall treat, from now on, an SOP as a point in the 3-sphere.
SOP changes that do not affect the light intensity can be represented by rotations in 3-space. These rotations are a class of unitary transformations and can be represented by orthonormal matrices \cite{strang09}. The rotation matrix in 3-space has a very interesting characterization via the Spectral Theorem: it always has 3 eigenvalues (since they are normal); all of the eigenvalues have norm 1; one of the eigenvalues is always equal to 1 and its eigenvector is the rotation axis, $e$; the remaining eigenvalues are complex conjugate numbers whose real part correspond to the cosine of the rotation angle, $\theta$, and whose imaginary part correspond to the sine of the rotation angle. A simple and robust way of manipulating 3-space rotation matrices is through the quaternions number system \cite{karlsson2004quaternion,DiasGarciaArXiV2016}. Despite the fact that polarisers affect the light intensity and, as such, cannot be represented by orthonormal matrices, they can be represented by projection matrices.
\subsection{Lithium-Niobate-based Polarization Controller Characteristics}\label{Control}
Literature around polarization control is very rich and diverse techniques were proposed and verified over the last years \cite{heismann1994analysis69, imai1985optical46, noe1988automatic40, heismann1989integrated55}. Our methodology focuses on the electro-optic $LiNbO_3$ EOSpace Polarization Controller Module (PCM) which is available commercially as a multi-stage component to which the input voltage may vary within a $\pm70$ Volts range \cite{saleh1991fundamentals}.
A single stage of the PCM has 3 electrodes \cite{EOSpace} and realizes an arbitrary \textit{Linear Retarder}. A linear retarder is a linear wave-plate capable of inducing a relative phase difference between the two polarization axes. This accomplished through the bi-refringent characteristic of the wave-plate which cause two orthogonal polarization axes to experiment different indexes of refraction while traversing the material. The difference in propagation time is, thus, responsible for enforcing the relative phase shift between polarization axes.
Linear Retarders have a main polarization axis, also known as eigen-mode, $e\in \{v\in\mathbb{R}^3| z=0\}$, and a characteristic phase delay, $\theta\in[0, 2\pi)$. It is possible to show that, by changing the eigen-mode and the phase delay of a linear retarder, one can shift from one SOP to any other SOP \cite{DiasGarciaArXiV2016}. In order to set the eigen-mode to $e=(\cos(\alpha/2), \sin(\alpha/2),0)$ and the phase delay to $\theta = 2\pi\delta$ the electrodes voltages of the lithium-niobate-based PCM must be set to \cite{EOSpace}:
\begin{align}
&V_a=2 V_0 \delta \sin\pars{\alpha} - V_{\pi}\delta \cos\pars{\alpha}+V^b_{a}\label{ds_EOS1} \\
&V_b=0 \label{ds_EOS2} \\
&V_c=2 V_0 \delta \sin\pars{\alpha} - V_{\pi} \delta \cos\pars{\alpha}+V^b_{c}\label{ds_EOS3}
\end{align}
where $V_{\pi}$ is the voltage required to induce a $180^o$ phase shift between the TE and TM modes for a single stage, $V_0$ is the voltage required to rotate all power from the TE to the TM mode, or vice versa, for a single stage, and $V^b_{a}$ and $V^b_{c}$ are the bias voltages required on electrodes A and C, respectively, in order to achieve zero bi-refringence between the TE and TM modes \cite{EOSpace}. Even though the data-sheet of the device provides the voltage range for $V_0$, $V_{\pi}$,$V^b_{a}$ and $V^b_{c}$, their actual values for an arbitrary stage must be determined via a calibration procedure.
Algorithms for both the calibration procedure and for identifying the required rotation in order to achieve a desired polarization state at the output of the polarization controller are presented in \cite{xi2010novel, DiasGarciaArXiV2016}. We shall focus on the hardware implementation of the control system.
\section{Optoelectronic Setup Proposal}
The representation of a polarization state in the Poincar\'{e} Sphere is achieved by measuring the Stokes vector of the incident light, which can be performed in a number of ways with either a set of optical splitters, wave plates and detectors or with a polarization rotator and a polarization state reference \cite{SalehTeichBOOK}. The proposed architecture makes use of the FPGA-based polarimeter for polarization state visualization proposed in \cite{CalliariTCC2014}. The FPGA's internal schematic is presented in Fig.\ref{fig:PolarimeterSchematic}.
\begin{figure}[htbp]
\centering
\includegraphics[width=0.8\linewidth]{PolarimeterSchematic.png}
\caption{Block diagram of the FPGA's internal structure for polarization visualization. The results acquired by the polarimeter are sent to the FPGA and the result is displayed graphically.}
\label{fig:PolarimeterSchematic}
\end{figure}
The polarimeter measures the intensities on each of the three main polarization basis, the rectilinear, diagonal, and circular basis, from which one is capable of determining the corresponding Stokes vector. The measurement is represented by a voltage value which is sent to an Analog-to-Digital Converter (ADC) so the digitized values can be interpreted by the FPGA. Inside the FPGA structure, a series of sub-blocks perform the signal interpretation: the \textit{Int to Float} block is responsible for representing the digitized voltage values as floating point numbers; the \textit{AD to Volts} block converts the digitized values back to their original voltage values represented as a floating point number; the \textit{Calibration Matrix} block permits one to associate the voltage value measured by the polarimeter to each of the four un-normalized entries of the Stokes vector (this block is dependent on the device and on the operating wavelength); up to the \textit{Normalize} block, the digital structure deals with the 4-dimensional Stokes vector, but after they are normalized, we need only to deal with the 3-dimensional vector; the \textit{Isometric Matrix} block enables the 2-dimensional visualization of the Poincar\'{e} Sphere; the remaining \textit{Correct} and \textit{Offset} blocks associate the pixels in the graphic display with the values of the SOP vector.
The goal is to combine the setups of Figs. \ref{fig:PolarizationState_Stabilizer} and \ref{fig:PolarimeterSchematic} in a feedback loop enabling visualization and control of the output SOP \cite{DiasGarciaArXiV2016}. The electronic implementation of the feedback system, depicted in Fig. \ref{fig:ElectronicSetup}, is composed of: an analog polarimeter; an array of analog-to-digital converters (ADC); an FPGA unit; an array digital-to-analog converters (DAC); an electronic driver unit; a Lithium-Niobate-based PCM; and a power supply.
\begin{figure}[htbp]
\centering
\includegraphics[width=0.8\linewidth]{ElectronicSetup.png}
\caption{Mixed analog-digital feedback loop for polarization visualization, selection, and stabilization.}
\label{fig:ElectronicSetup}
\end{figure}
Running in parallel inside the FPGA is the algorithm developed in \cite{DiasGarciaArXiV2016}. The algorithm takes the current state of polarization and the target state of polarization as inputs and attempts to output voltage levels which perform a rotation (according to the equations describing the PCM behavioral) so that the current and target SOPs match each other. The electronic driver that follows the DAC guarantees that the low power signals sent from the FPGA are converted to match the Lithium-Niobate based PCM. Each stage of the PCM demands two electronic drivers capable of reaching an output voltage swing between $\pm70$ Volts for which the full electrical schematic of a single driver stage is presented in Fig. \ref{fig:DriverSchematic}.
\begin{figure}[htbp]
\centering
\includegraphics[width=0.8\linewidth]{DriverSchematic.png}
\caption{Electronic schematic of a single $\pm70$ Volts driver stage of the lithium-niobate-based PCM.}
\label{fig:DriverSchematic}
\end{figure}
The setup presented in Fig.\ref{fig:ElectronicSetup} is suited for classical communication channels since a sample of the output signal can be measured by the polarimeter. When one is interested in transmitting quantum states, as for quantum communication purposes, however, the state cannot be measured without being destroyed. Also, a sample of the quantum state cannot be taken. Thus, a different approach should be considered: the measured polarization state cannot be a sample of the outgoing quantum state so it must be a classical state. It should, however, be polarization-aligned with the outgoing quantum state so, by measuring the classical state, one gains information over the polarization state of the outgoing quantum state. If we suppose the quantum state is generated by an ideal single-photon source (SPS), the block diagram depicted in Fig. \ref{fig:PolarizationState_SelStab_Quantum} should be able to perform its polarization control.
\begin{figure}[htbp]
\centering
\includegraphics[width=0.8\linewidth]{PolarizationState_SelStab_Quantum.png}
\caption{Proposed full polarization stabilization and selection scheme for quantum communication channels. \textbf{SPS}: Single-Photon Source; \textbf{WDM}: Wavelength Division Multiplexer; \textbf{PBS}: Optical Polarizing Beam Splitter; \textbf{APD}: Avalanche Photodiode \textbf{SPAD}: Single-Photon Avalanche Photodiode; \textbf{PC}: Mechanical Polarization Controller.}
\label{fig:PolarizationState_SelStab_Quantum}
\end{figure}
In the input of the polarization control setup, a reference optical signal from a tunable laser diode is directed to a WDM combiner together with the output of the SPS. It is important that each source occupies different WDM channels so they can be multiplexed and later demultiplexed. A polarizing beam splitter (PBS) is then connected to the output of the WDM to act as a polarization aligner. By minimizing the outputs from detectors SPAD$_{adj}$ and APD$_{adj}$, the alignment of the polarization states of both channels at the remaining PBS output arm is enforced \cite{AmaralOL2016}. The polarization-aligned channels are then directed to a PCM where they experiment the same polarization rotation given the wavelengths do not differ greatly \cite{XavierOPEX08}. The polarization-rotated signals are divided by a WDM splitter so $\lambda_Q$ is directed to the output of Bob's station and $\lambda_C$ is directed to the mixed analog-digital feedback system. Combining the information of which polarization state should be keyed at the output and how the optical channel influences the polarization of light, the outgoing state is composed. Note that the quantum state is not measured at any time in the polarization control system and we infer its polarization state taking the measurement over the classical polarization-aligned state as a reference.
\section{Results}
The simulation results were acquired using the Spice simulation tool. All the electronic devices were replaced by their real-parameter model which take into account the supply saturation, frequency response (slew-rate), and gain limitations. In Fig. \ref{fig:OutputVariation}, we depict the simulation results for various digital inputs at the DAC and the corresponding output from both the DAC and the power driver.
\begin{figure}[htbp]
\centering
\includegraphics[width=0.8\linewidth]{OutputVariation.png}
\caption{Voltage swing at the driver output as a function of the DAC output. The FPGA is responsible for configuring the DAC output.}
\label{fig:OutputVariation}
\end{figure}
We observe that the voltage swing is respected by the power driver unit. An important information, however, is the one regarding the switching time between one voltage level to the other since, ultimately, it determines our maximum achievable transmission rate in polarization-encoded quantum communication channels. In Fig. \ref{fig:TransitionTime}, we detail the switching time and show that the proposed system is capable of achieving an up to $125$ KHz transmission rate. It should be noted, however, that the slew-rate of the LTC6090-5 is dependent on its gain. Throughout the simulation runs, we enforced a $14$V/V gain which limits the transition time to $8$kHz. By introducing a pre-amplifier stage with $3$V/V gain before the LTC6090-5, we could operate under a $5$V/V gain achieving a $1$MHz switching rate \cite{LTC6090}.
\begin{figure}[htbp]
\centering
\includegraphics[width=0.8\linewidth]{TransitionTime.png}
\caption{Detailed transition time in the full $\pm70$ voltage swing at the electronic driver's output.}
\label{fig:TransitionTime}
\end{figure}
\section{Conclusion}\label{conclusion}
An optoelectronic unit comprised of a mixed analog-digital control loop and a polarization alignment state is presented. The system's application in polarization-based quantum communication links is studied with respect to the switching rate, usually above $1$MHz. Considering the device's frequency response, we show, through numerical simulations, that the demands are matched. We also show that polarization visualization can be performed throughout the switched operation of the system and a polarization visualization unit is proposed and experimentally demonstrated. Fast and embeddable signal processing tools that permit state of polarization control have been described in the literature and are directly implementable in the proposed scheme.
\section*{Acknowledgment}
The authors would like to thank brazilian agency CNPq for financial support.
\section*{Supplemental Material}
The authors provide digital supplemental material to accompany the article: a video file depicting the simulation run of the polarimeter can be accessed in \cite{YouTubeVideo_Polarimeter}.
\bibliographystyle{IEEEtran}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,595 |
Q: SwiftUI ForEach Nested Struct - Compiler Timing Out and Failing I am having a problem with a nested struct that is populated from a JSON endpoint. I have worked out the decoding and got that all working. I am now having a problem using a nested ForEach function in a SwiftUI View.
Here is the JSON data that comes from my endpoint
{
"success": true,
"message": "Authorized",
"personData": {
"PersonID": 31457,
"Name": "John Johnson Doe",
"Sex": "m",
"Living": 0,
"BirthDate": "28 Dec 1965",
"DeathDate": "22 Dec 1995",
"BirthPlace": "Detroit, Michigan, USA",
"DeathPlace": "Avon, Oakland, Michigan",
"FatherName": "Kenneth William Doe",
"MotherName": "Dorothy Anna Hunter",
"Siblings": [
{
"id": 0,
"SiblingName": "Katrina Ann Doe"
},
{
"id": 1,
"SiblingName": "Iris Marie Doe"
}
],
"Marriages": [
{
"id": 0,
"FamilyID": 10866,
"SpouseID": 31487,
"SpouseName": "Louise Bernadette Timbers",
"MarriageDate": "26 Sep 1985",
"MarriagePlace": "Clark County, Indiana, USA",
"DivorceDate": "27 Oct 1999",
"Children": [
{
"id": 100,
"ChildName": "Timoth Kenneth Doe"
}
]
},
{
"id": 1,
"FamilyID": 10867,
"SpouseID": 31461,
"SpouseName": "Wendy Mae Jackson",
"MarriageDate": "1 May 2001",
"MarriagePlace": "Detroit, Wayne, Michigan, USA",
"DivorceDate": "-",
"Children": [
{
"id": 100,
"ChildName": "Patricia Ann Doe"
},
{
"id": 101,
"ChildName": "Allen Kenneth Doe"
},
{
"id": 102,
"ChildName": "Stephen Patrick Doe"
}
]
}
]
}
}
I have some Observables along with a function which requests the data from the API and decodes it into personData
class NetworkRouter: ObservableObject {
@Published var isPersonLoaded: Bool = false
@Published var personData: PersonData?
func getPersonData(personID: Int) {
let data = KeychainHelper.standard.read(service: "token", account: "blahblah")!
let token = String(data: data, encoding: .utf8)!
Webservice().getPersonData(token: token, personID: personID) { (result) in
switch result {
case .success(let personData):
DispatchQueue.main.async {
self.personData = personData
self.isPersonLoaded = true
}
case .failure(let error):
DispatchQueue.main.async {
print(error.localizedDescription)
}
}
}
}
}
Here are the struct definitions to help decode the JSON
struct PersonResponse: Codable {
let success: Bool
let message: String
let personData: PersonData
}
struct PersonData: Codable {
let personID: Int
let name, sex: String
let living: Int
let birthDate, deathDate, birthPlace, deathPlace: String
let fatherName, motherName: String
let siblings: [Sibling]
let marriages: [Marriage]
enum CodingKeys: String, CodingKey {
case personID = "PersonID"
case name = "Name"
case sex = "Sex"
case living = "Living"
case birthDate = "BirthDate"
case deathDate = "DeathDate"
case birthPlace = "BirthPlace"
case deathPlace = "DeathPlace"
case fatherName = "FatherName"
case motherName = "MotherName"
case siblings = "Siblings"
case marriages = "Marriages"
}
}
struct Marriage: Codable, Identifiable {
let id, familyID, spouseID: Int
let spouseName, marriageDate, marriagePlace, divorceDate: String
let children: [Child]
enum CodingKeys: String, CodingKey {
case id
case familyID = "FamilyID"
case spouseID = "SpouseID"
case spouseName = "SpouseName"
case marriageDate = "MarriageDate"
case marriagePlace = "MarriagePlace"
case divorceDate = "DivorceDate"
case children = "Children"
}
}
struct Child: Codable, Identifiable {
let id: Int
let childName: String
enum CodingKeys: String, CodingKey {
case id
case childName = "ChildName"
}
}
struct Sibling: Codable, Identifiable {
let id: Int
let siblingName: String
enum CodingKeys: String, CodingKey {
case id
case siblingName = "SiblingName"
}
}
I have attempted the following methods for looping through each marriage and displaying the children
struct PersonProfileMarriageView: View {
@EnvironmentObject var networkRouter: NetworkRouter
var body: some View {
VStack {
ForEach(networkRouter.personData!.marriages) { thisMarriage in
HStack(alignment: .top, spacing: 0) {
Text("SPOUSE")
Text("\(thisMarriage.spouseName)")
}
if thisMarriage.marriageDate != "-" {
HStack(alignment: .top, spacing: 0) {
Text("MARRIAGE DATE")
Text("\(thisMarriage.marriageDate)")
}
}
if thisMarriage.children.count > 0 {
HStack(alignment: .top, spacing:0) {
Text("CHILDREN")
VStack(spacing: 0) {
ForEach(thisMarriage.children) { thisChild in
Text("\(thisChild.childName)")
}
}
}
}
}
}
}
}
I have also tried this type of ForEeach
ForEach(networkRouter.personData!.marriages, id: \.id) { thisMarriage in
ForEach(thisMarriage.children) { children in
}
}
And this method
ForEach(networkRouter.personData!.marriages, id: \.id) { thisMarriage in
ForEach(thisMarriage.children, id: \.id) { thisChild in
}
}
All of those produce the dreaded "The compiler is unable to type-check this expression in reasonable time; try breaking up the expression into distinct sub-expressions"
I really have no idea how to "break this up"
The only way I managed to get this to work was by using a List in this manner which seems very hacky.
List(networkRouter.personData!.marriages) { thisMarriage in
ForEach(thisMarriage.children, id: \.id) { thisChild in
}
}
I could very much use some help on this one. I been at it for days with no success. I have tried to make things Identifiable. Made sure the Marriage IDs and Child IDs were unique.
I really dislike using the List as it causes complications with other things I'm trying to do.
Hopefully I have provided all the code necessary to assist. Please let me know if I missed anything.
A: Based on the feedback I was able to "break down" the view a bit more into sub views. Thanks for the tips. The following is working.
import SwiftUI
struct PersonProfileMarriageView: View {
@EnvironmentObject var networkRouter: NetworkRouter
var body: some View {
if networkRouter.personData!.marriages.count > 0 {
VStack {
ForEach(networkRouter.personData!.marriages) { thisMarriage in
PersonProfileMarriageSpouseNameView(marriage: thisMarriage)
PersonProfileMarriageDateView(marriage: thisMarriage)
if thisMarriage.children.count > 0 {
HStack(alignment: .top, spacing:0) {
Text("CHILDREN")
VStack(spacing: 0) {
ForEach(thisMarriage.children) { children in
PersonProfileChildView(child: children)
}
}
}
}
}
}
}
}
}
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 291 |
Cosy apartment with ideal location in Azahara II in the heart of the Golf Valley, situated first line Aloha Golf course. From the Southeast-facing private garden area you will enjoy the sun all day with beautiful views towards Sierra Blanca Mountain and the Mediterranean Sea.
The apartment is well maintained, reformed open plan fully fitted kitchen. Two bedrooms with two reformed bathrooms. Oak floors and open fireplace.
Easy access from the parking to the apartment. | {
"redpajama_set_name": "RedPajamaC4"
} | 5,466 |
Q: Google chrome not opening in ubuntu 16.04 LTS I just installed Ubuntu 16.04 LTS and Google Chrome does not run. I have reinstalled it many times and also restarted my computer, but it still does not run. All it does is just showing the icon and when you click it it will not open.
How to resolve this issue?
A: I had same issue. By running google-chrome from terminal, I found that it needed a new version of NSS:
$ google-chrome
[6999:7036:1113/200616.549496:FATAL:nss_util.cc(632)] NSS_VersionCheck("3.26") failed. NSS >= 3.26 is required. Please upgrade to the latest NSS, and if you still get this error, contact your distribution maintainer.
Aborted (core dumped)
So I installed libnss3:
sudo apt-get install --reinstall libnss3
and it worked for me :)
A: It's worked
I uninstalled it by sudo apt-get purge google-chrome and then rm ~/.config/google-chrome -rf and then installing it back. First, I tried to install it via Google's official website and then downloading .deb file there, but after downloading the installer application of Ubuntu 16.04 stuck, even it isn't working now. Then, I tried to install it via terminal by writing
cd /tmp
wget https://dl.google.com/linux/direct/google-chrome-stable_current_amd64.deb
sudo dpkg -i google-chrome-stable_current_amd64.deb
A: I had a similar issue. Some applications would install OK, and when clicking, they would "Open", or at least they would shake like they were opening, but in effect nothing happened.
It turned out to be because I have a Graphics card, and the system mistakenly thought I had two monitors so the applications were opening on this phantom monitor.
If this is the case for you, go to System Settings > Displays and if there is an extra display, disable it.
I also went on to install the nvidia driver which helped with other problems
A: I also had similar issue in which when I typed command google-chrome on terminal it showed me error of SingletonLock File in /.config/google-chrome/ directory. I deleted that file and then it worked.
To identify the type of error you are facing try to open the program using command line and then analyse error returned back from command-line.
A: you may try Chromuim which is more stable and better for video watching by the way
sudo apt install chromium-browser
A: I had this issue but for me the below worked in terminal.
sed -i -e 's@Exec=/usr/bin/google-chrome-stable %U@Exec=/usr/bin/google-chrome-stable %U --no-sandbox@g' /usr/share/applications/google-chrome.desktop
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,406 |
Il punto o focolaio di Erb, in cardiologia, è il punto in cui è possibile effettuare l'auscultazione della componente aortica del secondo tono cardiaco e di soffi cardiaci causati da alterazioni della valvola aortica.
Eponimo
Prende il nome dal neurologo Wilhelm Heinrich Erb, che nei primi anni dalla sua laurea, si occupò di medicina interna nell'Ospedale di Heidelberg. In realtà il punto di Erb cardiologico è anche noto come punto di Erb II.
Localizzazione
Questo focolaio di auscultazione cardiaca è posto a livello del terzo spazio intercostale sinistro sulla linea marginosternale, immediatamente al di sotto del focolaio dell'arteria polmonare. Alcune fonti lo localizzano a livello del quarto spazio intercostale.
Note
Bibliografia
Voci correlate
Auscultazione
Toni cardiaci
Esame obiettivo
Diagnostica cardiologica | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,250 |
Collins New Naturalist Library
108
# Southern England
### Peter Friend
# Editors
SARAH A. CORBET, ScD
PROF. RICHARD WEST, ScD, FRS, FGS
DAVID STREETER, MBE, FIBIOL
JIM FLEGG, OBE, FIHORT
PROF. JONATHAN SILVERTOWN
The aim of this series is to interest the general reader in the wildlife of Britain by recapturing the enquiring spirit of the old naturalists.
The editors believe that the natural pride of the British public in the native flora and fauna, to which must be added concern for their conservation, is best fostered by maintaining a high standard of accuracy combined with clarity of exposition in presenting the results of modern scientific research.
# Table of Contents
Cover Page
Title Page
Editors
Editor's Preface
Picture Credits
Author's Foreword and Acknowledgements
CHAPTER 1 Looking at Southern England's Landscapes
CHAPTER 2 Time, Process Southern England's Landscapes
CHAPTER 3 Movement of the Earth's Surface from Within
CHAPTER 4 The Southwest Region
CHAPTER 5 The South Coast Region
CHAPTER 6 The Severn Valley Region
CHAPTER 7 London and the Thames Valley Region
CHAPTER 8 The East Anglia Region
CHAPTER 9 The Making of Southern England
Further Reading
Index
The New Naturalist Library
About the Author
Copyright
About the Publisher
# Editor's Preface
L. DUDLEY STAMP'S _Britain's Structure and Scenery_ was one if the earliest books of The New Naturalist Library, published in 1946. Repeated . later editions in the period to 1986 testified to the success of his approach towards providing a geological framework for understanding Britain's landscapes and natural history. He began his account in these words: 'The wealth of a country's fauna and fauna and flora is not to be measured by numbers of species alone. Its wealth lies rather in variety, and to a naturalist in the British Isles, the fascination of the native fauna and flora is in the great variety to be found in a small space.' This variety has its foundation in the underlying geology and the landscapes which are derived from the geology, as Dudley Stamp described so well. For some time, it has been the ambition of the Editors to approach this subject again, since our understanding of the geology and associated landscape evolution has increased so very significantly in the last few decades. The author, Peter Friend, has had long experience of active field research in geology and landscape in many parts of the world, as well as having an intimate knowledge of the subject in the British Isles. He has been able to take full advantage of modern developments in computer mapping and colour printing, making it possible to present the subject in a novel fashion, with great clarity, following the New Naturalist tradition emphasising the importance of illustration. The individual treatment of regions and areas of Southern England brings to the fore the significance of geology and landscape for naturalists who have local or wider interests at heart, giving a necessary basis for relating biodiversity to geodiversity. These two aspects of natural history have come to be seen to be widely significant in understanding plant and animal distribution as well as the problems of conservation. The book is therefore a very ti mely addition to the New Naturalist Library.
# Picture Credits
THE PHOTOGRAPHS and other illustrations that form such a key part of this book have come from many sources, and I am grateful to the following organisations and individuals for kindly allowing me to use their material:
> Aerofilms (Figs 133, 232, 249, 252, 256, 258, 259, 261, 270, 280, 309, 312)
>
> British Geological Survey (Figs 152, 284)
>
> Cambridge News (Fig. 233)
>
> Cambridge University Collection of Air Photographs (Figs 25, 118, 120, 243, 253, 282, 300, 310)
>
> Cassini Publishing (Figs 26, 27)
>
> Sylvia Cordaiy Photo Library (Fig. 141)
>
> Robert Harding Picture Library (Fig. 313)
>
> English Heritage (Figs 83, 308)
>
> Landform Slides – Ken Gardner (Figs 17, 18, 43, 55, 70, 75, 76, 85, 88, 104, 161, 162, 165, 195)
>
> Landform Slides – John L. Roberts (Fig. 69)
>
> Last Refuge Ltd – Adrian Warren, Dae Sasitorn and Will Brett (Figs 41, 42, 46, 47, 53, 54, 56, 58, 60, 62, 63, 67, 68, 71, 72, 73, 74, 82, 86, 89, 90, 91, 101, 102, 103, 108, 110, 111, 112, 119, 121, 122, 125, 130, 132, 134, 135, 142, 144, 146, 148, 158, 163, 164, 169, 171, 175, 176, 185, 191, 192, 193, 194, 196, 216, 217, 218, 219, 220, 222, 254)
>
> London Aerial Photo Library (Figs 23, 199, 205, 207, 235, 257, 277, 297, 298, 303, 314)
>
> Norfolk Museums and Archaeology Service – Nick Arber (Fig. 16)
>
> Norfolk Museums and Archaeology Service – Derek A. Edwards (Figs 1, 287, 293, 301, 302, 306, 307, 315)
>
> Network Rail (Fig. 145)
>
> Peter Oliver, Herefordshire and Worcestershire Heritage Trust (Fig. 172)
>
> Mike Page (Fig. 311)
>
> Science Photo Library (Fig. 2)
>
> Sedgwick Museum, Cambridge (Fig. 239)
>
> R. C. Selley – Petravin Press (Fig. 202)
>
> Sheila Smart (Fig. 131)
>
> Suffolk County Council (Fig. 255)
>
> Victoria & Albert Museum (Fig. 250)
>
>
>
> Illustrations that do not have a source credited in the caption are my own work, or that of the team working with me at the Department of Earth Sciences in Cambridge.
# Author's Foreword and Acknowledgements
MOST PEOPLE ENJOY SCENERY. In my case, an enthusiasm for exploring the countryside was learnt early on from my parents, and my career as a geologist has since allowed me to explore landscapes from the Arctic to tropical deserts and jungles. My hope is that this book will help more people to enjoy the countryside by bringing together some of the exciting recent discoveries about our Earth.
Landscapes are easy to look at, but difficult to describe in words. Recent developments in computer technology offer powerful ways of analysing and presenting landscapes using maps, diagrams and photographs, and it is this imagery that forms the core of this book. Developing the imagery has been the main role of a succession of enthusiastic helpers. Lucinda Edes, Emilie Galley, Liesbeth Renders and Helena Warrington brought their skills and enthusiasm to the early days of the project, working out what could be done best. James Sample has more recently further developed the methods of presentation, and has played a key role in bringing this project to fruition. All have helped to make the project enjoyable as well as productive.
The home for this project has been the Department of Earth Sciences at the University of Cambridge. I walked into the Department as a first-year undergraduate more than 50 years ago and, apart from a period in the Scott Polar Research Institute, I have been based here ever since. I have been teaching and exploring the scenery and geology of many parts of the world, including multiple visits to Spitsbergen, Greenland, Spain, India and Pakistan. This has been an exciting period to be working in geology, particularly in Cambridge, because many key advances have been achieved by the people working here. Apart from the great benefit of being part of this research environment, I have enjoyed the support of six successive Heads of Department and many other colleagues, especially our administrator Margaret Johnston and her team. It has been invaluable to have access to the excellent library run by Ruth Banger and Libby Tilley, and the patient computer support of Jun Aizawa, Aidan Foster, Pete Hill and Pete Wilkins.
I would also like to acknowledge my debt to the Cambridge college system, particularly my own college, Darwin. The College has provided me with the congenial friendship of many people from diverse backgrounds, and their skills have helped me to remain a generalist in my interests.
Any work of this sort on the British Isles owes a fundamental debt to the British Geological Survey (BGS), now based at Keyworth near Nottingham. The numerous Survey maps and reports on this country provide a remarkable source of carefully observed and objective information. The BGS has also readily provided advice and discussion of this project, and helped to determine the sort of coverage and level that would be best.
Many other people have made important contributions by providing ideas and information. These include: John R. L. Allen, Julian Andrews, Muriel Arber, Steve Boreham, Becky Briant, Keith Clayton, Tony Cox, Alan Dawn, Colin Forbes, Brian Funnell, Phillip Gibbard, Steve Jones, Gerald Lucy, Dan Mackenzie, Bob Markham, Charles Notcutt, Bernard O'Connor, Richard Preece, Graham Ward and Richard West.
This book is dedicated to the **Dr John C. Taylor Foundation,** which has provided the financial support for the project, allowing me to work with such a remarkable succession of talented young assistants. More than 40 years ago, John spent two summers exploring the geology of Spitsbergen with me, and we have remained friends ever since. I am extremely grateful for the help of his foundation during the writing of this book.
# [CHAPTER 1
Looking at Southern England's Landscapes](004-toc.html#ch1)
### FIRST APPROACHES
THE WORD **LANDSCAPE** has different meanings for different people, and the best way to illustrate the meaning I have adopted in this book is to look at an example. I have chosen a landscape in the northwest corner of Norfolk, part of our East Anglia Region (Fig. 1).
**FIG 1.** Landscape of the northwest corner of Norfolk. (Copyright Norfolk Museums and Archaeology Service & Derek A. Edwards)
My approach is to focus first on the natural features that we can call landforms, because they have distinctive shapes that directly reflect the processes that formed them. In this Norfolk landscape, coastline landforms are clearly defined but are remarkably varied, ranging from sea cliffs to sandy beaches, gravel spits, wind-blown dunes and salt marshes. Inland, the main features in this photo are the groups of buildings that form the villages and the edge of the town of Hunstanton, and the pattern of fields and woods. All of these are man-made features and are best understood by following the work of _landscape historians._ My interest is primarily in the natural topography on which these man-made features have developed, because even in this rather flat landscape – and not clearly visible on the photograph – there are gentle hills, valleys and streams that I want to try to understand.
Scale and size in landscapes are important considerations that we will return to frequently. The landscapes that we shall be discussing are generally kilometres to tens of kilometres across, and they are often best examined from the air, or by using computer-based maps with exaggerated vertical scale.
Southern England contains many famous and well-loved natural landscapes, ranging from the Chalk Downs, with their unique flora and fauna, to the rocky promontories and bays of Cornwall, Devon and Dorset. In total topographic contrast, the Fens of East Anglia are regarded by some as representing an extreme absence of any scenery at all, but their remarkable flatness is of interest because they are the result of recent sea-level rise, and of engineering on a remarkable scale. These different landscapes are produced by a wide variety of events and processes; exploring these is the theme of this book.
As we have already seen, landscapes have often been extensively modified by people. The early clearance of woodland and the construction of field boundaries have profoundly changed the scenery and, more recently, the construction of buildings, roads, railways, canals and airports has almost completely covered some areas of Southern England. Figure 2 shows night-time lighting in cities, towns and oil platforms, giving a vivid impression of the present extent and distribution of the larger settlements. It is surprising how varied the population density is, even in crowded Britain. Using the figures for 2002, the population density of the UK overall is 244 people per square kilometre, but this conceals a huge variation: 8 people per square kilometre in the Highland Region of Scotland, 143 for Cornwall, 149 for Norfolk and an amazing 13,609 for Kensington and Chelsea in London.
The main focus of this book is the pattern of large scenic features that have resulted from natural episodes that predate human influence. It is not usually difficult to distinguish the natural from the man-made, and the study of the natural can often explain many aspects of the way our ancestors lived in the landscape. It is possible to uncover the reasons why people have chosen to settle with their families in certain places, why villages have grown by the clustering of houses in particular locations, and why some villages have then grown further and turned into towns and eventually cities. Even the roads, railways and airfields have clearly grown using the valley floors, river crossings, better-drained slopes and plateaus that are part of the natural scenery.
**FIG 2.** Satellite image over Britain showing artificial lighting at night. (Copyright Planetary Visions Ltd/Science Photo Library)
There is a further enjoyment that people find in landscapes and scenery that is more difficult to understand. Is it just the physical challenge that causes people to walk and climb to the tops of hills, mountains and other viewpoints? Why do people enjoy the work of landscape painters and photographers? Why do so many tourists in cars choose to take 'scenic' excursions rather than the shortest routes, and why is the preservation of 'unspoilt' or wilderness areas now such a popular cause? It is difficult to understand the various emotions involved, and trying too hard to analyse them may be missing the point. So it seems best to hope simply that this book will help to satisfy some people's curiosity, and at the same time add to their enjoyment of our natural landscapes.
### MAPPING AND ANALYSING SOUTHERN ENGLAND
The detailed discussions of most of the rest of this book have involved dividing Southern England into a number of Areas that form the 'building blocks' for the coverage of Southern England (Fig. 3). Each Area is based on a double-page spread of the size used in many of the larger road atlases available for Britain. In this case I have used the Collins Road Atlas, Britain. This means that total coverage of Southern England is provided, and it is easy for the reader to navigate from place to place. At the beginning of each Area description, a location map of the Area and its neighbours is provided. Ordnance Survey (OS) National Grid References are provided for the edges of the Area, in km east and north of the arbitrary OS Grid origin some 80 km west of the Scilly Isles.
**FIG 3.** Division of Southern England into Regions and Areas.
For convenient reference the Areas – numbered 1 to 16 – are grouped into five **Regions**. Each Region forms a chapter and starts with a general introduction:
CHAPTER | REGION | AREA
---|---|---
**Chapter 4** | Southwest | **1** West Cornwall
**2** East Cornwall and South Devon
**3** North Devon and West Somerset
**Chapter 5** | South Coast | **4** East Devon, Somerset and Dorset
**5** Hampshire and the Isle of Wight
**6** Sussex
**7** East Sussex and Southeast Kent
**Chapter 6** | Severn Valley | **8** Bristol
**9** The Cotswolds and the Middle Severn
**Chapter 7** | London and the Thames Valley | **10** The Cotswolds to Reading
**11** London
**12** The Thames Estuary
**Chapter 8** | East Anglia | **13** Northampton to Cambridge
**14** Suffolk and North Essex
**15** Leicester to the Fens
**16** Norfolk
Even the Area building blocks are relatively large, with arbitrary boundaries, and it has generally been helpful to discuss smaller areas within and across these boundaries that are based on natural features of the scenery (Fig. 4). I have called these smaller areas **Landscapes,** because they are characterised by distinctive features, usually reflecting aspects of the bedrock or distinctive events in their evolution.
These Landscapes correspond closely to area divisions of England that were defined by the Government Countryside Agency (www.countryside.gov.uk). This scheme divides England into 159 'character areas' on the basis of natural features of the scenery along with aspects of its human settlement, past and future development, land use and vegetation and wildlife, so they are likely to be familiar divisions to many readers of the New Naturalist series. Other Government agencies (particularly the Department for Environment, Food and Rural Affairs) that administer the funding of land management use the same character area division.
**FIG 4.** Examples of the three levels of division adopted in the treatment of Southern England.
Maps displaying patterns of elevation of the countryside above sea level are an important part of the discussions. The elevation data on the maps in this book have been compiled and made available as part of the LANDMAP project, which provides a computer-based digital survey of Britain for research and educational use. LANDMAP Digital Elevation Maps (DEMs) are based on satellite radar survey measurements which divide the land surface into a grid of 25 m by 25 m pixels. The average height of each pixel is then measured to produce a terrain model with a vertical accuracy of about ± 5 m. A standard colour shading scale is used to represent heights, ranging from greens for the lowest ground, through yellows and browns, to greys for the highest ground. It is best to use the full range of colours for each map, no matter what numerical range of heights is involved. This makes it possible to convey the fine detail of slopes etc., whether the map is for the Fens or the high moors. To make it possible to compare between maps using this colour scheme, we have quoted the maximum elevation reached in each Area on each map.
I have used ESRI ARC Geographic Information System (GIS) software in the processing and manipulating of the map data. This software makes it possible to present artificial hill-shading, which makes the topography easier to understand, and to provide maps representing slope patterns in certain areas.
In addition, data on roads, railways, coastlines, town boundaries, rivers, etc. suitable for reproduction at a scale of 1: 200,000 has been made available by the Collins Bartholomew mapping agency. For any further details of the areas covered, it is recommended that Ordnance Survey _Landranger_ (1: 50,000) maps are consulted.
### LANDSCAPE CHANGE
We tend to think of rural landscapes as unchanging features of our surroundings, in contrast to the man-made scenery of cities and towns. Yet we all know of local catastrophes, such as a sea cliff collapsing during a storm, or a flooding river removing its bank and wrecking the nearby buildings, and these are the sorts of local events that do result in change. Despite the excitement, individual changes of this sort are small and can usually be regarded as local modifications. However, over time, the accumulated effects of many such modifications can cause whole landscapes to change.
Size and time clearly both play key parts here. The collapsed cliff or eroded river bank will probably be tens to hundreds of metres long at most, while the larger landscape features picked out in this book are tens or even hundreds of kilometres across. Noting the length scales involved in this way is an important way of keeping such differences clearly in mind.
Moreover, while local events such as the destruction of landforms or buildings may be immediately newsworthy, more long-term patterns of change in the natural scenery are rarely apparent during the life spans of people, and even during the hundreds of years of written records. So it becomes necessary to use indirect and circumstantial evidence – to play the detective – to find out what long-term changes have been going on.
An important step in thinking about the natural landscape is to look at it in terms of modifications to complex surfaces defined by the ground. On land, we tend to be most aware of erosional processes removing material, but it is important to realise that the material removed has to end up somewhere – and this will involve its deposition later, on land or in the sea. How much material was removed from the cliff during the storm or from the banks of the river during the flood? Where did the lost material go, and how did it change the landscape when it was deposited at its new destination? Knowledge of these surface modifications can provide a yardstick that allows us to compare different sorts of changes happening over different periods of time and at different scales, and can help us to work out their relative importance, quoting amounts and rates. For example, a flooding river may remove a hundred metres of river bank, modifying the local landscape a little in the process. However, this modification is unlikely to have much impact on the scenery, unless followed many, many times by similar modifications, over centuries to hundreds of thousands of years. In this way a series of such floods can erode and move material that, in the long run, may be of sufficient volume to significantly change the landscape, for example lowering a hill slope or filling a valley bottom.
The majority of- but not all – surface modification processes act to reduce or flatten topography, mainly by eroding the higher features but also by filling in lower ground with sediment. So logically landscapes might always be regarded as tending towards a flat surface. Our understanding of the processes involved suggests that any land area with mountains or hills will be eroded downwards to an increasingly flat surface as time passes, although the rate of erosion will reduce as the topography becomes more and more smooth. Acting against these flattening processes are periodic movements of the ground surface caused by forces within the Earth, producing new mountains and hills, and so creating new landscapes (Fig. 5).
Continuing research into the processes operating within the Earth shows that movements of the Earth's crust are taking place continuously, even though the rates involved are generally too slow to be noticeable. The discovery that the Earth's surface consists of a large number of tectonic plates in continuous relative movement was one of the major breakthroughs in the earth sciences, and has fundamentally changed our understanding of the planet. More on this topic will be considered in Chapter 3, but at this point it is important to realise just how slow the rates of movement are: at most a few centimetres per year on average (often compared to the rate at which fingernails grow). Occasionally, movements of centimetres or metres occur within seconds along faults during earthquakes, but the average rate of movement is still rather slow. Most of us living in stable areas are totally unconscious of any movement at all because we are, ourselves, moving slowly with the landscape that we live on. Slow though the movements may be in a particular landscape, so also are the rates of surface modification, and the balance between the two is a delicate one. In much of Southern England modification by surface processes is dominant, but this has not always been the case.
**FIG 5.** Landscapes are changed by surface modifications (Chapter 2) and solid earth movements (Chapter 3).
Our next chapter deals with the timescales represented in the landscapes of Southern England and the processes that have been modifying them. Chapter 3 deals with the movements from below – from within the Earth's crust – that are ultimately creating major landscape patterns.
# [CHAPTER 2
Time, Process Southern England's Landscapes](004-toc.html#ch2)
### BEDROCK AND SURFACE BLANKET
WALK AROUND THE COUNTRY IN SOUTHERN ENGLAND and the ground beneath your feet is very rarely solid rock. You are walking over soil made of weathered mineral grains and organic debris, along with other relatively soft and granular materials that make up the surface blanket. Beneath the surface blanket lies solid rock, the bedrock of the landscape.
Bedrock forms the bones of the land. From the colour of the soil, to the elevation of the hills, to the types of vegetation present, the landscape is profoundly influenced by the bedrock underlying it. For example, in Southern England the Lower Greensand (a distinctive layer of bedrock of Early Cretaceous age, see page 26) produces soil water with acidic chemical properties. The Lower Greensand was originally deposited as sand over a period of a few million years, more than 100 million years ago. This layer represents a different environment of deposition from the older sediments on which it lies, and was followed by another change of environment which produced the deposits that lie on top of it. Both the preceding and the following bedrock deposits have alkaline chemical properties. In certain regions the bedrock layers have now been brought to the surface of the landscape by erosion and movements within the Earth. The Greensand is harder than the layers above and below it (largely mudstones) and so is generally more resistant to weathering. In some areas the Lower Greensand lies just below the surface blanket and has resisted the general landscape erosion to form a distinct Greensand ridge running across the countryside, characterised by special vegetation adapted to the acidity of the soils.
It is only in cliffs or at man-made excavations such as quarries that we can see bedrock at the surface in most low-lying areas. By using those areas where the bedrock does outcrop at the surface, and the results of drillings (e.g. for wells), we can discover the types and arrangements of rock below any landscape.
### THREE DIFFERENT TIMESCALES
More recent past events tend to be better known and of greater interest than distant past events. Figure 6 is plotted on a logarithmic timescale, so that the most recent times are given more space and greater ages are given less and less space.
**FIG 6.** Three different timescales, plotted to give more space to more recent events.
For the purposes of this book, we can distinguish three overlapping timescales to help us to understand the landscapes of Southern England:
The **bedrock timescale** (extending from 542 million years ago to about 2 million years ago)
The **Ice Age timescale** (covering roughly the last 1 million years)
The **last 30,000 years timescale**
We shall now review each of these, commenting on the sorts of episodes in each that are important in our exploration of Southern England.
### THE BEDROCK TIMESCALE
Figure 7 is a simplified version of a generally accepted geological timescale relevant to the landscapes of Southern England. The names of the divisions are universally accepted in the geological world and, unlike the previous diagram, the passage of time is represented on a uniform (linear) timescale. The divisions have been selected, and sometimes grouped, to help in our analysis of the situation in Southern England, and these have been colour-coded for use in the rest of the book.
**FIG 7.** Bedrock timescale for Southern England.
The rocks at, or just below, the surface of Southern England range in age over hundreds of millions of years, and most of them were formed long before the present scenery began to appear. At the time of their origin, these rocks were deposited in a variety of different environments, mostly when mud or sand materials were transported into and/or around the seas that existed where England is now. Most of the bedrock of Southern England was formed in this way and is said to be of _sedimentary_ origin. The depositional conditions varied from time to time: the climate varied, the geographical pattern of rising and sinking land movements changed, and the supply of mud and sand brought downstream by rivers changed also. Despite these fluctuations, it is possible to generalise the way that sediment has accumulated over an area the size of Southern England, and to offer a succession of layers of different composition, age and average thickness that can provide a general guide. This is shown in Figure 8.
For each of the Regions (and some of the Areas) discussed in Chapters 4 to 8, a rock column, generalised for that particular area, will show the main bedrock layers. Each column will be coloured using the standard colour codes of this book to represent the ages of the layers.
As an example, we will consider another particularly distinctive layer of bedrock, the Chalk, which ranges between 200 and 400 m in thickness. Chalk is visible quite widely at or just below the surface over perhaps a quarter of the area of Southern England (Fig. 9). Chalk is an easily recognised rock because it is made of very small fragments of lime (calcium carbonate) and is usually brilliant white. It formed from fine-grained limey mud deposited on the sea bed, but through many millions of years of burial below other sediments it has been compressed and altered into the hard rock we recognise today. The Chalk is a result of a unique combination of environmental conditions and the presence of particular algal organisms in the history of evolution. It is only found in northwest Europe, and was only formed in Late Cretaceous times.
The presence of Chalk near the surface in Southern England is almost always linked to the presence of hills and slopes in the scenery, clearly showing that Chalk is a tough material that resists landscape erosion more than most of the other rock types available. The Chalk is also noteworthy because it represents the most recent time when most of Southern England was covered uniformly with soft sediment and a shallow sea: in Late Cretaceous times, except for possible islands in the southwest, there was no emergent land across Southern England.
Like all sedimentary bedrock layers, the Chalk initially formed as flat layers or sheets of sediment, extending widely across the floor of the sea. As will be discussed in the next chapter, these sheets of sediment are generally characteristic of stretching movement episodes in the Earth's surface. Such movements produce areas of collapsed and low-lying land that can accommodate large volumes of sediment, if it is available.
**FIG 8.** Generalised succession of the bedrock of Southern England, showing a typical thickness for each layer.
**FIG 9.** The Chalk and its topography. The darker areas represent the chalk uplands.
However, we do not see the Chalk at or near the surface everywhere across Southern England; instead the Chalk forms narrow bands across the land. This is due to later movements affecting the bedrock layers by folding and tilting them, so that some parts were raised (to be later removed by erosion) and other parts were lowered (Fig. 10, A and B). In the millions of years since the sediment layers were laid down, they have been buried, compacted, deformed by various processes, and finally uplifted to form part of the landscape that we know today (deformation processes are treated more fully in Chapter 3). The Chalk layer has been moved and folded as a result of mild compression or convergence, to form a downfold or _syncline_ between the Chilterns and the North Downs, and an upfold or _anticline_ between the North and South Downs (Fig. 10, C). Later, the central part of the anticline was eroded away to produce the bedrock pattern that we recognise today (Fig. 10, D). The vein-like river valleys visible on the elevated Chalk hills of Figure 9 are evidence of this continuing erosion.
**FIG 10.** Deposition and folding of the Chalk.
### LANDSCAPE MODIFICATION BY RIVERS
Weathering of landscape surfaces and the production of soils by the action of rainwater, air and organisms are important factors in shaping landscapes. These processes affect the bedrock when it is very close to the surface, and most of them weaken the material that they work on. This is particularly so when tough silicate rock minerals are altered to soft clay minerals, which are then easily eroded. Freezing and thawing also works to weaken the bedrock as water in cracks freezes and expands, breaking the rocks into fragments.
Whilst weathering is a widespread and general process, most of the other important landscape processes involve the formation of discrete features that we shall call _landforms._ Rivers result in the formation of a number of important landforms that are described below.
The most important landforms resulting from river processes are the channels of rivers and streams (Fig. 11). When rain falls onto a land surface some of it soaks into the land (forming groundwater), whilst the remainder runs along the surface, collecting in topographical lows and producing stream and river channels. Today, many of Southern England's river channels tend to be relatively narrow and shallow – only metres or tens of metres in width and less in depth – so they occupy an extremely small percentage of the area that they drain. However, they are still the dominant agents of landscape change, causing downwards and/or sideways erosion as well as acting as conduits to transport the eroded material out of their catchments.
Most river channels develop a sinuous course, becoming curved (or _meandering_ ) to varying degrees, or developing a number of channels separated by islands of sediment (becoming _braided_ ). The positions of the curves or islands change with time as sediment is shifted downstream, and the position of a river channel will change with time correspondingly.
Because of their ability to erode material and remove the resulting debris, river channels create valleys. The sides of a river valley are referred to as slopes. When a channel cuts downwards the valley sides generally become steeper and slope material (generated by ongoing weathering processes) moves down-slope towards the channel. The material is transported either as small individual fragments or as larger mass flows. Where down-slope movements involve the collapse of large areas of material, the terms _landslip_ or _slump_ are often used. Slope material is then deposited in the channel and removed downstream by the river.
The simplest valleys result from down-cutting by a river or stream to yield a V-shaped profile in cross-section. The gradient of the valley sides depends on the strength of the material that the slopes are composed of in the face of erosion. Stronger materials are more difficult to erode and remove, and so can form steeper slopes than weaker materials. In some areas, the river channel is unable to form valley slopes as the material is too weak to form a noticeable gradient. In the Areas we will be investigating, it is clear that some of the slopes are largely the result of a particularly strong layer in the bedrock resisting erosion as the landscape has developed.
**FIG 11.** Landforms of rivers.
As the valley develops, its profile can become more complex. In some cases, slopes appear to have retreated across a landscape some distance from the position in which they were initially created by river down-cutting. A river with a wide valley floor is one of the most obvious examples of this, in which movements of the channel across the floor have caused the slopes to retreat as the valley floor has become wider. In some cases, slopes appear to have retreated over many kilometres from the original valley as numerous collapses of the slope took place.
Overall, therefore, the valley profile and the channel course reflect variations in the strength of the material being eroded, and in the strength and flood pattern of the river. Climate changes are likely to have a major effect on the strength of the river by altering the volume of water flowing through the channels. Additionally, the lowering or raising of the channel by Earth movement effects (see Chapter 3) can affect the evolution of the landscape by river processes. For example, both climate change and the vertical movement of the river channel can initiate the formation of river terraces. Different examples of all these river geometries will be discussed in greater detail in the Area descriptions in Chapters 4–8.
Over millions of years, river down-cutting, slope erosion and material transport tend to smooth and lower landscapes until they approximate plains, unless they are raised up again ( _rejuvenated_ ) by large-scale Earth movements (Chapter 3) or are attacked by a new episode of channel erosion, perhaps due to climate or sea-level change. Southern England generally has a smoothed and lowered landscape, representing hundreds of thousands of years of this river and slope activity.
The branching, map-view patterns of river channels and valleys are an obvious feature of all landscapes. An approach to understanding how this forms is illustrated by a computer-based experiment (Fig. 12) in which a flat surface (plateau or plain) is uplifted along one of its edges, so that it has a uniform slope towards the edge that forms the bottom of the rectangle shown. Rain is then applied uniformly across the surface, causing the formation and down-cutting of channels that erode backwards from the downstream edge. As the experiment continues, the channels and their valleys extend into the uniform sloping surface by _headward_ erosion, resulting in longer valleys, more branches and a greater dissection of the surface by those valleys.
**FIG 12.** Model showing upstream erosion by tree-like (dendritic) river patterns. (Provided by Dimitri Lague from the work of A. Crave and P. Davy)
As we consider the various Regions and Areas of Southern England, we will summarise the present-day river patterns of each by simplifying the main directions of drainage involved. We will also give an impression of the present-day relative size of the more important rivers by quoting their mean flow rates as estimated in the National River Flow Archive, maintained by the Centre for Ecology and Hydrology at Wallingford.
It seems surprising that today's often sleepy southern English rivers have been the dominant agent in carving the English landscape. However, even today's rivers can become surprisingly violent in what are often described as hundred-or thousand-year floods. Floods in the past were certainly more violent at times than those of today, particularly towards the ends of cold episodes, when melting of ice and snow frequently produced floods that we would now regard as very exceptional.
### THE ICE AGE TIMESCALE AND LANDSCAPE MODIFICATION
The most recent Ice Age began about 2 million years ago, and is still continuing in Arctic areas. At various times during this period ice has thickly covered most of northwest Europe. Recent research, particularly measurements of oxygen isotopes in polar icecaps and oceanic sediment drill cores, has revealed much of the detail of how the climate has changed during the current Ice Age. It has been discovered that long cold periods have alternated with short warm periods in a complex but rather regular rhythm. Looking at the last half-million years, this alternation has occurred about every 100,000 years, and this is now known to have been a response to regular changes in the way the Earth has rotated and moved in its orbit around the sun. A closer look at the last million years (Fig. 13) reveals that for more than 90 per cent of the time conditions have been colder than those of today. Warm ( _interglacial_ ) periods, like our present one, have been unusual and short-lived, though they have often left distinctive deposits and organisms.
**FIG 13.** The last million years of global temperature change.
_*the Oxygen Isotope Stages are an internationally agreed numbering sequence to label the succession of climatic cold (even numbers) and warm (odd numbers) episodes._
One of the most important cold episodes ( _glacials_ ), just under half a million years ago, resulted in the Anglian ice sheet. This was up to several hundreds of metres thick and extended from the north southwards, well into Southern England, covering much of East Anglia and the north London area (Fig. 14). As the ice spread slowly southwards, it was constricted between the Chalk hills of Lincolnshire and those of Norfolk. A wide valley, later to become the Wash and the Fens, was filled with ice to a depth well below that of present sea level. As the ice spread outwards from this valley it dumped the rock material it was carrying, including blocks and boulders up to hundreds of metres across, giving some idea of the tremendous power of the ice sheet. The direct evidence for the presence of an ice sheet is material in the surface blanket called _till_ , or boulder clay (Fig. 15). This often rather chaotic mixture of fragments of rock of all sizes (large boulders mixed with sand and mud) lacks the sorting of the fragments by size that would have occurred in flowing water, and so must have been deposited from the melting of ice sheets.
**FIG 14.** The Anglian ice sheet.
Much of the rest of the surface blanket that accumulated during the last 2 million years was deposited by the rivers that were draining the land or any ice sheets present. As ice sheets have advanced and retreated, so have the rivers changed in their size and in their capacity to carry debris and erode the landscape. Rivers have therefore been much larger in the past as melting winter snow and ice produced torrents of meltwater, laden with sediment, which scoured valleys or dumped large amounts of sediment. The gravel pits scattered along the river valleys and river terraces of Southern England, from which material is removed for building and engineering, are remnants of the beds of old fast-flowing rivers which carried gravel during the cold times.
There are no ice sheets present in the landscape of Figure 16. The scene is typical of most of the Ice Age history (the last 2 million years) of Southern England, in that the ice sheets lie further north. It is summer, snow and ice are lingering, and reindeer, wolves and woolly mammoths are roaming the swampy ground. The river is full of sand and gravel banks, dumped by the violent floods caused by springtime snow-melt. The ground shows ridges of gravel pushed up by freeze-thaw activity, an important process in scenery terms that we discuss below.
**FIG 15.** Boulder clay or till, West Runton, north Norfolk.
The present-day Arctic has much to tell us about conditions and processes in Southern England during the cold episodes of the Ice Age. Much of the present-day Arctic is ice-sheet-free, but is often characterised by permanently frozen ground ( _permafrost_ ). When the ground becomes frozen all the cracks and spaces in the surface-blanket materials and uppermost bedrock become filled by ice, so that normal surface drainage cannot occur. In the summer, ice in the very uppermost material may melt and the landscape surface is likely to be wet and swampy. Ice expands on freezing, and so the continuous change between freezing and thawing conditions, both daily and seasonally, can cause the expansion of cracks and the movement of material, with corresponding movements in the surface of these landscapes. This movement can cause many problems in the present-day Arctic by disturbing the foundations of buildings and other structures.
**FIG 16.** Artist's impression of Southern England, south of the ice sheet, during the Ice Age. (Copyright Norfolk Museums and Archaeology Service & Nick Arber)
Remarkable polygonal patterns, ranging from centimetres to tens of metres across, are distinctive features of flat Arctic landscapes, resulting from volume changes in the surface blanket on freezing and thawing (Fig. 17). In cross-section the polygon cracks and ridges correspond to downward-narrowing wedges (often visible also in the walls of gravel pits in Southern England). Thaw lakes are also a feature of flat areas under conditions of Arctic frozen ground (Fig. 18). They appear to be linked to the formation of the polygonal features, but can amalgamate to become kilometres across and may periodically discharge their muddy soup of disturbed sediments down even very gentle slopes.
Not only can these frozen ground processes be studied in Arctic areas today, but they have left characteristic traces in many of the landscapes of Southern England. Some examples from Norfolk are illustrated in Chapter 8 (Figs 306 and 307), and these provide specific examples of the result of ancient freeze-thaw processes on a small scale. However, the more we examine the wider features of present-day landscapes across Southern England, the more it becomes clear that most have been considerably modified by the general operation of frozen ground processes during the last 2 million years. These processes are likely to have been responsible for the retreat of significant slopes and even for the lowering of surfaces that have almost no perceptible slope.
**FIG 17.** Polygonal frozen ground patterns on the Arctic coastal plain near Barrow, Alaska. (Copyright Landform Slides – Ken Gardner)
**FIG 18.** Thaw lakes, the larger ones several kilometres long, on the Arctic coastal plain near Barrow, Alaska. (Copyright Landform Slides – Ken Gardner)
### THE LAST 30,000 YEARS TIMESCALE AND RECENT MODIFICATION
The timescale shown in Figure 19 covers a period during which various episodes have changed the landscapes of Southern England, creating our present-day world. These episodes include the dramatic rise in sea level and landward movement of the coastline caused by the warming of the climate following the last cold episode of the Ice Age. They also include the progressive changing of the countryside by people, leading up to the domination of some landscapes by man-made features.
**FIG 19.** Time divisions for the last 30,000 years (Late Pleistocene to Holocene).
**Time Division** | **Years Before Present**
---|---
Windermere Interstadial | 13,000–11,000
Loch Lomond Stadial | 11,000–10,000
Flandrian (Holocene) | 10,000-present
Mesolithic | 11,000–7,000
Neolithic | 7,000–4,150
Bronze Age | 4,150–2,750
Iron Age | 2,750–1,950
Roman | 1,950–1,600
The last 30,000 years have been warm, on average, relative to the previous 2 million years of the Ice Age. However, the higher level of detail available in this timescale makes it clear that climate change has not been one of uniform warming during this period. Short periods of colder climate, temporarily involving ice-sheet growth in the north of Britain (sometimes called _stadials_ ) have alternated with short periods of warmer climate (referred to as _interstadials_ ).
### SEA-LEVEL CHANGE
The coastline is the most recently created part of the landscape, and the most changeable. This is due, in large part, to the rise in sea level over the last 20,000 years, since the last main cold episode of the Ice Age (the Devensian). Twenty thousand years ago sea level was 120 m lower than it is today because of the great volumes of water that were locked away on land in the world's ice sheets (Fig. 20). Land extended tens or hundreds of kilometres beyond the present-day coastline, and Southern England was linked to northern France by a large area of land (Fig. 21). Global climate started to warm about 18,000 years ago (Fig. 13) and the world's ice started to melt, raising global sea level. The North Sea and the Channel gradually flooded, and Britain became an island between 10,500 and 10,000 years ago. This flooding by the sea is known as the _Flandrian transgression_ and was a worldwide episode.
**FIG 20.** Graph of sea-level rise over the last 18,000 years.
During the period of most rapid sea-level rise (between 12,000 and 8,000 years ago), areas of low-lying land were swamped and some local features of the coastal scenery moved great distances geographically towards their present positions. The sea cliffs, beach barriers, salt marshes, spits and estuaries that can be seen today have only taken up their present positions over the last few thousand years, as sea-level rise slowed.
In the treatment of the Regions and Areas in the rest of this book, maps are presented that distinguish a _coastal flooding zone_. This presentation is based on the simplifying assumption that the solid Earth movement of Southern England (i.e. any uplift or subsidence, see Chapter 3) has been very small compared with global sea-level changes. The coastal flooding zone is defined as extending between the submarine contour 120 m below present sea level and the contour 20 m above present sea level, and it can be used to identify parts of landscapes which are likely to have been areas of coastline activity in the recent past. Areas of land with an elevation between present sea level and 120 m below sea level correspond to the land submerged during the last 18,000 years of sea-level rise. Areas lying at, or up to, 20 m above present sea level may have been subjected to coastal processes during the highest sea levels of earlier interglacial periods, such as the Ipswichian (see Fig. 13). The coastal flooding zone also defines areas of land that are most likely to become submerged during predicted future rises of sea level.
**FIG 21.** Two episodes (17,000 and 12,000 years ago) in the rise of sea level around the North Sea area. (Redrawn and simplified from _Current Archaeology_ **207** , 2006, Gaffney)
Drowned valleys (Figs 22 and 23) are present on the coastlines of Southern England as a result of recent sea-level rise. Formerly, the rivers draining the majority of these valleys would have transported mud and sand to the sea, where it would have been deposited on the sea bed. However, with the rise in sea level mud and sand are now often deposited in the flooded valleys or estuaries instead, and some have developed carpets of sediment, transported down-valley by rivers or brought up-valley by the sea where tides and storms have been effective.
Coastlines with low seaward slopes and a soft surface blanket and/or bedrock may develop beach barriers when flooded by rising sea level. These barriers are ridges of sand or gravel parallel to the general trend of the coastline (Fig. 24). They are created by the impact of storm waves on the gently sloping and soft landscape. They tend to develop a cap of wind-blown sand which is very vulnerable to storm wave erosion, but may eventually become stabilised by vegetation. Behind the barrier a low-lying area of more sheltered conditions develops and regular flooding at high tide may bring in muddy sediment from the sea that can settle and build up salt marshes.
**FIG 22.** The drowning of a valley by sea-level rise.
**FIG 23.** Drowned valley of the Deben, Suffolk, viewed from above the sea off Felixstowe Ferry. (Copyright London Aerial Photo Library)
**FIG 24.** Cross-section of a beach barrier formed as sea level rises over a very gently sloping landscape.
**FIG 25.** Beach barrier on Scolt Head Island, Norfolk. (Photograph held at Cambridge University Collection of Air Photographs, Unit for Landscape Modelling)
The aerial photograph of part of Scolt Head Island (Fig. 25) in north Norfolk shows the succession of zones parallel to the coastline typical of a recently flooded, gently sloping landscape. On the beach, coast-parallel ridges and hollows (runnels) have been created during recent storms, and are draining water as the photograph was taken at low tide. The crest of the barrier is capped by wind-blown dunes, which have been stabilised by marram grass, but also shows signs of erosion during recent storms. Behind the barrier are salt marshes, generally sheltered from storm waves and developing tidal channels. The salt marshes are forming around the remains of various sand and gravel spits that date from a landscape before the present beach barrier was there. The far side of the salt marsh is marked by a gently curved sea wall built within the last two centuries to reclaim some land by keeping high tides out. Behind that is the boundary between the present flat seaward zone of young sediment and the older terrain, marked by a complex field pattern that is underlain by Chalk bedrock.
### DEVELOPMENT BY PEOPLE
My concern in this book is primarily with natural landscapes, and I will tend to comment on the development by people since the Bronze Age only where this relates to the natural features in an interesting way. However, in reviewing the appearance of the whole of Southern England, I have been struck by an intriguing distinction made by some landscape historians: the distinction between ancient and planned countryside (Figs 26–28). I have based my approach on the discussions offered by Oliver Rackham, ecologist and landscape historian, and these are summarised below.
**Ancient countryside** (Fig. 26) consists of many hamlets, small towns, ancient farms and hedges (of mixed varieties of shrubs and trees), along with roads that are not straight, numerous footpaths and many antiquities.
**Planned countryside** (Fig. 27) has distinct villages, much larger than the hamlets, along with larger eighteenth- and nineteenth-century farms, hedges of hawthorn and straight roads. Footpaths are less common and the few antiquities that are present are generally prehistoric.
I have re-examined the same areas used by Oliver Rackham as examples of these two countryside types, and compared the early Ordnance Survey maps with maps of the same area generated by me using the data and methods used in this book (see Chapter 1). The shading and 'hachured' patterning used in the earlier maps represents the hills and slopes rather clearly – better than the contour representation used in the present-day Ordnance Survey _Landranger_ maps, although these show man-made features much more clearly. My map representation is a compromise in that it represents elevations and slopes using colours and hill-shading, but also allows the patterns of roads and settlements to be seen.
Oliver Rackham's conclusion is that many of the distinctive features of planned countryside were created by the general parliamentary enclosure of land during the eighteenth and nineteenth centuries. This involved the wholesale conversion of commonly held land with open fields into enclosed fields awarded to individuals and institutions. Many landscape historians have claimed earlier origins for the difference between ancient and planned countryside, believing that historical and cultural differences in the people who settled and developed the two areas played an important role. Variations in the bedrock geology also seem to be important here. For example, the ancient countryside shown in Figure 26 is underlain by strongly deformed Variscan bedrock that has been eroded into small hills and valleys (see Chapter 4).
**FIG 26.** Example of ancient countryside at the Devon-Somerset border, near Tiverton, with 1809 and recent mapping compared. (Upper part from Cassini Old Series map 181, copyright Cassini Publishing 2007/www.cassinimaps.co.uk)
**FIG 27.** Example of planned countryside at the Berkshire-Oxfordshire border, around Didcot, with 1830s and recent mapping compared. (Upper part taken from Cassini Old Series maps 164 and 174, copyright Cassini Publishing 2007/www.cassinimaps.co.uk)
**FIG 28.** Generalised map distinguishing ancient and planned countryside across Southern England.
In contrast, the planned countryside covered by Figure 27 consists of only gently tilted Mesozoic bedrock that has formed a much flatter and more open landscape.
# [CHAPTER 3
Movement of the Earth's Surface from Within](004-toc.html#ch3)
### WIDESPREAD MOVEMENTS OF THE EARTH'S SURFACE
TO UNDERSTAND THE CHANGES and movements affecting the appearance of the landscape on large scales we need to review some geological systems, especially _plate tectonics._ Many of the large changes that have created landscapes over long periods of time can now be understood using this discovery.
Knowledge of the processes causing the movement of large (10–1,000 km length-scale) areas of the Earth's surface has been revolutionised by scientific advances made over the last 40 years. During this time, scientists have become convinced that the whole of the Earth's surface consists of a pattern of interlocking _tectonic plates_ (Fig. 29). The word 'tectonic' refers to processes that have built features of the Earth's crust (Greek: _tektōn_ , a builder). The worldwide plate pattern is confusing – particularly when seen on a flat map – and it is easier to visualise the plates in terms of an interlocking arrangement of panels on the Earth's spherical surface, broadly like the panels forming the skin of a football.
Tectonic plates are features of the _lithosphere_ , the name given to the ≈125 km thick outer shell of the Earth, distinguished from the material below by the strength of its materials (Greek: _lithos_ , stone). The strength depends upon the composition of the material and also upon its temperature and pressure, both of which tend to increase with depth below the Earth's surface. In contrast to the mechanically strong lithosphere, the underlying material is weaker and known as the _asthenosphere_ (Greek: _asthenos_ , no-strength). Note that on figure 30 the crustal and outer mantle layers are shown with exaggerated thickness, so that they are visible.
**FIG 29.** World map showing the present pattern of the largest lithosphere plates.
Most of the strength difference between the lithosphere and the asthenosphere depends on the temperature difference between them. The lithosphere plates are cooler than the underlying material, so they behave in a more rigid way when subjected to the forces generated within the Earth. The asthenosphere is hotter and behaves in a more plastic way, capable of deforming without fracturing and, to some extent, of 'flowing'. Because of this difference in mechanical properties and the complex internal forces present, the lithosphere plates can move relative to the material below. To visualise the motion of the plates, we can use the idea of lithospheric plates floating on top of the asthenosphere.
Looking at the surface of the Earth (Fig. 29), the largest plates show up as relatively rigid areas of the lithosphere, with interiors that do not experience as much disturbance as their edges. Plates move relative to each other along _plate boundaries_ , in various ways that will be described below. The plate patterns have been worked out by investigating distinctive markers within the plates and at their edges, allowing the relative rates of movement between neighbouring plates to be calculated. These rates are very slow, rarely exceeding a few centimetres per year, but over the millions of years of geological time they can account for thousands of kilometres of relative movement.
It has proved to be much easier to measure plate movements than to work out what has been causing them. However, the general belief today is that the plates move in response to a number of different forces. Heat-driven circulation (convection) occurs within the mantle, but other forces are also at play. Where plates diverge, warm, new material is formed that is elevated above the rest of the plate, providing a pushing force to move the plate laterally, around the surface of the Earth. At convergent boundaries, cold, older material 'sinks' into the asthenosphere, providing a pulling force which drags the rest of the plate along behind it. Deep within the Earth, the sinking material melts and is ultimately recycled and brought back to the surface to continue the process.
**FIG 30.** Diagram of the internal structure of the Earth.
Knowledge of how tectonic plates interact provides the key to understanding the movement history of the Earth's crust. However, most people are much more familiar with the geographical patterns of land and sea, which do not coincide with the distribution of tectonic plates. From the point of view of landscapes and scenery, coastlines are always going to be key features because they define the limits of the land; we make no attempt in this book to consider submarine scenery in detail.
The upper part of the lithosphere is called the _crust._ Whereas the distinction between the lithosphere and the asthenosphere is based upon mechanical properties related to temperature and pressure (see above), the distinction between the crust and the lower part of the lithosphere is based upon composition. Broadly speaking, there are two types of crust that can form the upper part of the lithosphere: continental and oceanic. An individual tectonic plate may include just one or both kinds of crust.
**Continental crust** underlies land areas and also many of the areas covered by shallow seas. Geophysical work shows that this crust is typically about 35 km thick, but may be 80–90 km thick below some high plateaus and mountain ranges. The highest mountains in Britain are barely noticeable on a scale diagram comparing crustal thicknesses (Fig. 31). Continental crust is made of rather less dense materials than the oceanic crust or the mantle, and this lightness is the reason why land surfaces and shallow sea floors are elevated compared to the deep oceans. Much of the continental crust is very old (up to 3–4 billion years), having formed early in the Earth's life when lighter material separated from denser materials within the Earth and rose to the surface.
**Oceanic crust** forms the floors of the deep oceans, typically 4 or 5 km below sea level. It is generally 5–10 km thick and is distinctly denser than continental crust. Oceanic crust only forms land where volcanic material has been supplied to it in great quantity (as in the case of Iceland), or where other important local forces in the crust have caused it to rise (as is the case in parts of Cyprus). Oceanic crust is generally relatively young (only 0–200 million years old), because its higher density and lower elevation ensures that it is generally _subducted_ and destroyed at plate boundaries that are _convergent_ (see below).
Figure 29 shows the major pattern of tectonic plates on the Earth today. The Mercator projection of this map distorts shapes, particularly in polar regions, but we can see that there are seven very large plates, identified by the main landmasses located on their surfaces. The Pacific plate lacks continental crust entirely, whereas the other six main plates each contain a large continent (Eurasia, North America, Australia, South America, Africa and Antarctica) as well as oceanic crust. There are a number of other middle-sized plates (e.g. Arabia and India) and large numbers of micro-plates, not shown on the world map.
Figures 29 and 32 also identify the different types of plate boundary, which are distinguished according to the relative motion between the two plates. _Convergent_ plate boundaries involve movement of the plates from each side towards the suture (or central zone) of the boundary. Because the plates are moving towards each other, they become squashed together in the boundary zone. Sometimes one plate is pushed below the other in a process called _subduction_ , which often results in a deep ocean trench and a zone of mountains and/or volcanoes, as well as earthquake activity (Fig. 32). The earthquake that happened on the morning of 26 December 2004 under the sea off western Sumatra was the strongest anywhere in the world for some 40 years. It seized world attention particularly because of the horrifying loss of life caused by the tsunami waves that it generated. This earthquake was the result of a sudden lithosphere movement of several metres on a fault in the convergent subduction zone where the Australian plate has been repeatedly moving below the Eurasian plate.
**FIG 31.** Scale diagram comparing average thicknesses of oceanic and continental crust and lithosphere.
In other cases the plate boundary is _divergent_ , where the neighbouring plates move apart and new material from deeper within the Earth rises to fill the space created. The new oceanic crust is created by the arrival and cooling of hot volcanic material from below. The mid-Atlantic ridge running through Iceland, with earthquakes and volcanic activity, is one of the nearest examples to Britain of this sort of plate boundary.
Other plate boundaries mainly involve movement parallel to the plate edges and are sometimes called _transform_ boundaries. The Californian coast zone is the classic example but there are many others, such as the transform boundary between the African and Antarctic plates. In some areas, plate movement is at an oblique angle to the suture and there are components of divergence or convergence as well as movement parallel to the boundary.
Britain today sits in the stable interior of the western Eurasian plate, almost equidistant from the divergent mid-Atlantic ridge boundary to the west and the complex convergent boundary to the south where Spain and northwest Africa are colliding. In its earlier history the crust of Britain has been subjected to very direct plate boundary activity: the results of convergent activity in Devonian and Carboniferous times (between 416 and 299 million years ago) are visible at the surface in southwest England, and in Ordovician to Devonian times (between 490 and 360 million years ago) in Wales, northwest England and Scotland.
**FIG 32.** Diagram illustrating the movement processes of plates (not to scale).
### UNDERSTANDING SURFACE MOVEMENTS
We have been considering the large movement systems that originate within the Earth. There are also more local movement systems operating on the Earth's surface, which are linked to a very variable degree to the large-scale movements of plate tectonics. To explore this complex linkage further, it will be helpful to look now at different processes that may combine to cause particular local movements.
#### **Horizontal movements as part of convergence, divergence or lateral transfer**
Tectonic plates are recognised by their rigidity, so there is relatively little horizontal movement between points within the same plate compared to the deformation seen in plate boundary zones. This extreme deformation may involve folding and fracturing of the rock materials, addition of new material from below, or absorption of material into the interior during subduction.
Nonetheless, deformation is not restricted solely to plate boundaries, and does occur to a lesser extent within the plates. In some cases, major structures that originally formed along a plate boundary can become incorporated into the interior of a plate when prolonged collision causes two plates to join. Southern England includes the remains of a former convergent plate boundary and contains many examples of structures of this sort (particularly around Dorset and the Isle of Wight). These structures have often been reactivated long after they first formed in order to accommodate forces along the new plate boundary via deformation within the plate. Conversely, changes of internal stress patterns can sometimes lead to the splitting of a plate into two, forming a new, initially divergent plate boundary. Many of the oil- and gas-containing features of the North Sea floor originated when a belt of divergent rift faults formed across a previously intact plate.
It needs to be stressed that the patterns of deformation (fracturing and folding) due to these plate motions occur at a wide range of different scales, from centimetres to thousands of kilometres. Sometimes they are visible at the scale of an entire plate boundary, such as the enormous Himalayan mountain chain that marks the collision of India with Asia.
The effects of features as large as plate boundaries on landscapes persist over hundreds of millions of years, long after the most active movement has ceased. For example, parts of southwestern England, Wales and the Scottish Highlands are underlain by bedrocks that were formed in convergent boundary zones of the past. The tin and lead mines of Cornwall owe their existence to a 300-million-year-old convergent plate boundary, where an ocean was destroyed as two plates converged and continents collided. The convergence released molten rock that rose in the crust and gradually cooled to form granite, while metals were precipitated in the surrounding crust as 'lodes' containing tin and lead (see Chapter 4).
Mapping the patterns of bedrock exposed at the surface often reveals folds and faults that provide key information about the movements that have taken place during the past. Figure 33 provides a key to some of the terms commonly used to classify these structures as a step towards understanding the sorts of movement patterns that they represent. In broad terms, folds tend to indicate some form of local convergent movement, though they may be the result of larger movement patterns of a different kind. Normal faults tend to indicate divergent movements, at least locally, whereas reverse and strike-slip faults tend to indicate convergence. Two broad types of fold are distinguished: synclines are u-shaped downfolds, while anticlines are the opposite – n-shaped upfolds.
Further mapping of folds and faults often reveals complex patterns of changing movements. In the example shown in Figure 34, divergent movements in an area of crust produce plastic deformation in the warmer lower crust, and faulting into a number of discrete blocks in the colder, more brittle, upper crust. This is then followed by an episode of convergent movement that results in closing up the upper crustal blocks and further flow in the plastic lower crust, causing crustal thickening and mountain building at the surface.
#### **Vertical crustal movements as part of other crustal movements**
The movement of lithospheric plates is the main cause of convergent and divergent movements affecting thousands of kilometres of the Earth's surface. As shown in Figures 33 and 34, these horizontal movements are generally accompanied by vertical movements that can produce very large scenic features, such as a mountain belt or a rift valley. In this book we are primarily concerned with scenic features at a more local scale, so we now consider various other processes that may be important in creating vertical crustal movements without contributions from large-scale plate interactions.
**FIG 33.** The most important types of folds and faults, and the local patterns of forces responsible.
#### **Vertical changes by erosion or deposition**
Addition or subtraction of material to the surface of the Earth is happening all the time as sediment is deposited or solid material is eroded. The field of _sedimentology_ is concerned with the wide range of different processes that are involved in the erosion, transport and deposition of material, whether the primary agent of movement is water, ice, mud or wind. An important point is that few of these sedimentary processes relate directly to the large tectonic movements of the Earth's crust that we have discussed above. Scenery is often produced by erosion of thick deposits that formed in sedimentary basins where material eroded from the surrounding uplands accumulated. One of the characteristic features of these thick deposits is their layered appearance, which is often visible in the scenery. Layering varies from millimetre-scale laminations produced by very small fluctuations in depositional processes, to sheets hundreds of metres thick that extend across an entire sedimentary basin. These thicker sheets are often so distinctive that they are named and mapped as separate geological units representing significant changes in the local environment at the time they were deposited.
**FIG 34.** Example of a cross-section through the crust, showing how a divergent movement pattern (A) may be modified by later convergent movements (B and C).
#### **Vertical crustal movements resulting from loading or unloading**
In addition to the direct raising or lowering of the surface by erosion or deposition, there is a secondary effect due to the unloading or loading of the crust that may take some thousands of years to produce significant effects. As mentioned above, we can visualise the lithosphere as 'floating' on the asthenosphere like a boat floating in water. Loading or unloading the surface of the Earth by deposition or erosion will therefore lower or raise the scenery, just as a boat will sit lower or higher in the water depending on its load.
An example of this is the lowering of the area around the Mississippi Delta, loaded by sediment eroded from much of the area of the USA. The Delta region, including New Orleans, is doomed to sink continually as the Mississippi river deposits sediment around its mouth, increasing the crustal load there.
A second example of such loading is provided by the build-up of ice sheets during the Ice Age. The weight of these build-ups depressed the Earth's surface in the areas involved, and raised beaches in western Scotland provide evidence of the high local sea-levels due partly to this lowering of the crustal surface.
Unloading of the Earth's surface will cause it to rise. Recent theoretical work on the River Severn suggests that unloading of the crust by erosion may have played a role in raising the Cotswold Hills to the east and an equivalent range of hills in the Welsh Borders (see Chapter 6, Area 9). In western Scotland, as the ice has melted the Earth's surface has been rising again.
#### **Vertical movements by expansion or contraction**
Changing the temperature of the crust and lithosphere is an inevitable result of many of the processes active within the Earth, because they often involve the transfer of heat. In particular, rising plumes of hot material in the Earth's mantle, often independent of the plate boundaries, are now widely recognised as an explanation for various areas of intense volcanic activity (for example beneath Iceland today). These plumes are often referred to as 'hot spots' (see Fig. 32). Heating and cooling leads to expansion or contraction of the lithosphere and can cause the surface to rise or sink, at least locally.
An example of this is the way that Southern England was tilted downwards to the east about 60 million years ago. At about this time, eastern North America moved away from western Europe as the North American and Eurasian plates diverged. The divergence resulted in large volumes of hot material from deep within the Earth being brought to the surface and added to the crust of western Southern England. It is believed that the heating and expansion of the crustal rocks in the west has elevated them above the rocks to the east, giving an eastward tilt to the rock layers and exposing the oldest rocks in the west and the youngest ones in the east. This sequence has important implications for the scenery of England's south coast (see Chapter 5).
### HOW CAN LOCAL SURFACE MOVEMENTS BE DETECTED?
Having just reviewed some of the processes that cause vertical movements of the Earth's surface, it is useful to consider the practical difficulties of how such movements are measured.
For present-day applications, it seems natural to regard sea level as a datum against which vertical landscape movements can be measured, as long as we remember to allow for tidal and storm variations. However, much work has demonstrated that global sea level has changed rapidly and frequently through time, due to climate fluctuations affecting the size of the polar icecaps and changing the total amount of liquid water present in the oceans and seas. It has also been shown that plate tectonic movements have an important effect on global sea level by changing the size and shape of ocean basins.
Attempts have been made to develop charts showing how sea level, generalised for the whole world, has varied through time. However, it has proved very difficult to distinguish a worldwide signal from local variations, and the dating of the changes is often too uncertain to allow confident correlation between areas.
In sedimentary basins, successful estimates of vertical movements have been made using the thicknesses of sediment layers accumulating over different time intervals in different depths of water. In areas of mountain building, amounts of vertical uplift have been estimated using certain indicator minerals that show the rates of cooling that rocks have experienced as they were brought up to the surface. However, both these approaches are only really possible in areas that have been subjected to movements of the Earth's crust that are large and continuous enough to completely dominate other possible sources of error.
Local horizontal movements are also difficult to estimate, although fold and/or fault patterns may allow a simple measure in some cases. Movement of sediment across the Earth's surface by rivers or sea currents can be estimated if mineral grains in the sediment can be tracked back to the areas from which they have come. In the detailed consideration of landscapes in this book, we have to rely on using the widest possible range of types of evidence, carefully distinguishing the times and scales involved. Even then, we are often left with probable movement suggestions rather than certainties.
# [CHAPTER 4
The Southwest Region](004-toc.html#ch4)
### GENERAL INTRODUCTION
MOST OF THE BEDROCK near the surface in the Southwest Region (Fig. 35) is distinctly older than the near-surface bedrock in the rest of Southern England. It therefore provides us with information about earlier episodes, and this is all the more interesting because these episodes involved movements of the crust that created a mountain belt, the only one fully represented in the bedrock story of Southern England. Not only does this add greatly to the interest of the Southwest, but it has resulted in the presence of valuable minerals that have strongly influenced the human history in the Region.
#### Bedrock foundations and early history
##### _Sedimentation and surface movement before the mountain building_
The Southwest Region consists predominantly of bedrock formed between about 415 and 300 million years ago, during Devonian and Carboniferous times. This bedrock records an episode during which some areas of the Earth's crust rose while others sank, as part of a general buckling of the crust that is the first indication of compression and mountain building (Figs 36 and 37). As the rising areas became significantly elevated they were eroded, shedding sediment into the neighbouring sinking areas that became sedimentary basins. It is these basins that preserve most of the evidence of these events (Fig. 38).
In material that has been further and later deformed, it is difficult to work out the shape of the sinking areas, but many of them were probably elongated or trough-shaped, with the troughs separated by rising ridges that ran roughly east-west, parallel to the general trend of the later mountain belt. The troughs and ridges were caused in the early stages of mountain building by the compression and buckling of the crust. The troughs were generally flooded by the sea, or on the margins of relatively narrow seaways. Muds were the commonest materials to accumulate, although sands were also in plentiful supply. Lime-rich sediments, sometimes with corals and other shelly marine animals, were locally important. There were also periodic episodes of igneous activity that contributed volcanic lavas to the sedimentary successions.
**FIG 35.** The Southwest Region, showing Areas 1 to 3.
During these episodes of Devonian and Carboniferous basin and ridge activity, the Southwest Region was just one small part of a larger belt of similar activity that extended to the west into Ireland and Canada. Canada was then very much closer, because the Atlantic Ocean is a younger feature that only started to grow (at this latitude) about 100 million years ago, as divergence and spreading occurred along the mid-Atlantic plate boundary. To the south and east, the same belt of activity continued across northern France and into Germany. This broadly east-west trending belt later became the Variscan mountain belt.
##### _Crustal convergence that created the mountain belt_
The subsidence and sedimentation were sometimes interrupted by, and generally followed by, episodes of convergence of the Earth's crust. This was caused by compression or squeezing, broadly in a north-south direction, so that areas of bedrock were folded and pushed closer together, making the east-west trending Variscan belt narrower, as if between the jaws of a vice. The map (Fig. 39) and cross-section (Fig. 40) show how the folds and faults of the region vary locally in their pattern, but can be explained generally by convergent movements in this north-south direction. These continued over at least 100 million years, and occurred along thousands of kilometres of the belt. Mountain-building events such as this occur when tectonic plates collide (as described in Chapter 3) and always have a profound effect upon the scenery in the vicinity of the collision. The Variscan mountain belt is just one of the great mountain-building episodes that have occurred periodically, throughout the Earth's history.
**FIG 36.** Timeline diagram showing bedrock deposition and emplacement events in the Southwest Region.
Some of the best evidence for the horizontal crustal shortening comes from examining folds that can be seen in the bedrock at many localities (Figs 41 and 42). Folding of the originally flat layers of the bedrock is a spectacular feature of many southwestern sea cliffs, and the direction of the folding gives a clear indication of the direction of the shortening that resulted. Fractures (faults) also frequently cut the bedrock, and careful mapping makes it possible to recognise that, although some of them are very local features, others turn out to have been flat-lying fractures across which many kilometres of movement have taken place.
**FIG 37.** Simplified geological map of the Southwest Region.
**FIG 38.** Typical Devonian sedimentary basin in the Southwest Region.
**FIG 39.** The major bedrock structures of Southwest England and South Wales.
Another feature of the mountain building is that muddy material – the most abundant sediment in the Southwest Region – was often converted into slates that can typically be split into thin sheets and are said to possess a 'slatey cleavage'. These rocks are locally referred to as _killas_ , to distinguish them from other rocks with no cleavage, particularly the granites. The conversion into slates took place during the folding and fracturing of the mountain building, when the original muds, rich in clay minerals, were buried deeply below other sediments and then compressed to produce a new layering (or _cleavage_ ).
One large feature visible in the bedrock is the 'Culm fold belt' or 'synclinorium', a large and complex downfold representing horizontal crustal convergence (Figs 39 and 40). The centre of this feature is a belt of bedrock of Carboniferous age that extends between Bude and Exeter running across the centre and north of the Southwest Region. To the north and south of this, older (Devonian) rocks occur at the bedrock surface, forming the margins of the large downfold or syncline (Fig. 37). _Culm_ is an old term much used by miners and European geologists for Carboniferous sediment, and _synclinorium_ is a name for a downfold (or syncline) which contains numerous smaller folds.
In the Lizard area, much of the bedrock consists of a distinctive group of igneous rocks (Figs 39 and 40). These rocks cooled and solidified earlier than the main mountain building, and were mostly formed by intrusion of hot molten rock in a way that is typical of the floor of an ocean basin. The Lizard area provides one of the best examples now visible on land in Britain of material formed originally as ocean-floor crust. In Late Devonian times, as a result of early Variscan convergence, this large area of oceanic crust was forced northwards over and against sedimentary rocks lying just to the north. This shows how, in a large mountain belt, an area of crust (tens of kilometres across), with a distinctive history as the floor of an ocean basin, can be uplifted and incorporated into a mountain belt as its margins are squeezed together.
**FIG 40.** Schematic cross-section representing major structures of the Variscan mountain belt. The deep structure shown is speculative but shows how crustal shortening seen at the surface may be related to deeper, flat-lying fractures (faults). Located on Figure 39.
**FIG 41.** Zigzag folding due to horizontal convergence during the Variscan mountain building is spectacularly exposed at Hartland Quay (Area 3). (Copyright Will Brett/www.lastrefuge.co.uk)
**FIG 42.** Zigzag folding due to horizontal convergence during the Variscan mountain building, this time at Bude (Area 2). (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
Some of the bedrock of this Lizard Complex is called _serpentinite_ , after the common occurrence of the green mineral serpentine in sinuous cracks and veins. This gives the rocks an attractive colour patterning, and the absence of quartz makes them surprisingly easy to work with steel tools, giving rise to a local industry of carving serpentinite ornaments.
##### _Granites and valuable minerals_
The granites of Southwest England are an important later feature of the Variscan mountain belt. Granites are igneous rocks with coarse (millimetre across) crystals that have grown, interlocking with each other, as the molten material cooled slowly and solidified at some depth in the Earth's crust. The minerals of the granite are most commonly quartz (typically about 30 per cent) and feldspar, generally with some other minerals such as mica (Fig. 43). The granite liquid (often called magma) formed as a result of melting deep within the outer layers of the Earth and was then forced upwards, sometimes pushing aside the overlying bedrock and sometimes replacing it by melting. The granites solidified at depths of several hundred metres or more below the surface and are now at, or near, the surface because of landscape erosion. The main granite areas include the Isles of Scilly in the west, followed by Land's End, Carnmenellis, St Austell, Bodmin Moor and Dartmoor in succession to the east. These distinct granite areas at the surface can be visualised as the tops of fingers extending upwards from a single continuous granite body detectable by gravity surveys at greater depth under the spine of Southwest England (Fig. 44). The deep body extends for some 200 km along the length of the mountain belt.
**FIG 43.** Polished slab cut in the Dartmoor granite showing typical granite texture. Crystals of quartz (light grey), feldspar (white) and biotite (black) have interlocked as the magma (molten rock) solidified on cooling. (Copyright Landform Slides – Ken Gardner)
**FIG 44.** Diagram showing the large granite body below the bedrock of Cornwall and Devon, and the way the granite bosses now visible at the surface are upward extensions of this larger body.
Although there was probably some time range in the arrival of different granite bodies in the upper crust, the main episodes took place at the very end of the Carboniferous and during the earliest Permian, roughly 300 million years ago.
The arrival of the granites from below was only one part of the invasion of the upper levels of the bedrock that took place at this time. Widespread mineralisation around the granites has probably been even more important than the arrival of the granites themselves, in terms of human history. The term mineralisation is used to cover the alteration of the solid granite and the surrounding (older) bedrock that has, in some areas, been caused by the movement of very hot and chemically rich water, using the network of cavities and fractures that existed in the rocks. Because of the chemistry of the rocks deep down, many different chemical elements were brought to the upper levels and crystallized there to form new and valuable minerals, or caused alterations of the earlier solid rocks.
**FIG 45.** Simple diagram of a slice through the Earth's upper levels, showing how the temperature patterns around a granite body have been responsible for the distribution of minerals containing the more important chemical elements.
The granites probably solidified in the Earth at temperatures of about 850 °C, and most of the mineralisation happened at rather lower temperatures as the rocks cooled (Fig. 45). Tin, wolfram, arsenic and copper minerals formed at between 500 and 300 °C, whereas silver, lead, zinc, uranium, nickel and cobalt minerals formed at between 300 and 200 °C, and iron minerals between 200 and 50 °C.
The tin of Cornwall was a major reason why some of the early inhabitants of mainland Europe were interested in Britain. In fact there is evidence that tin minerals were being gathered here more than 3,000 years ago, during the Bronze Age. In those days, much of the material was collected from young sands and gravels derived from the weathering and erosion of the mineral-bearing rock, unlike later times when mining techniques were developed to extract tin directly from the bedrock.
Some granite areas contain much more mineralisation than others, and the range of minerals and chemical elements that are present varies greatly. This depends on the temperature of the granite emplacement and the chemistry of the fluids accompanying and following the granite. The Land's End and Carnmenellis granites are particularly rich in tin, and it is around these granites, in areas near to St Ives, Camborne, Redruth and Helston, that most of the mining has been concentrated. The remains of this mining are often clear to see (Fig. 46), but the presence of the minerals themselves does not generally influence the natural scenery.
**FIG 46.** Tin mine workings near Cape Cornwall, west Cornwall. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
In some of the granites, hot fluids from below altered the mineral feldspar (one of the dominant granite minerals) and turned it into the soft clay mineral kaolinite. The china clay industry has developed round the presence of this mineral, which has usually been extracted from the altered granite by washing it out with powerful water jets. This process has changed the scenery dramatically, particularly around the St Austell granite. For every tonne of useable kaolin, 5 tonnes of waste granite material are produced, and heaps of this waste are obvious scenic features in these areas (Fig. 47). The famous Eden Project at Bodelva, near St Austell, has been constructed inside a large former china clay quarry.
**FIG 47.** China clay excavations at St Austell. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
The older rocks surrounding each of the granite intrusions generally show evidence of alteration that occurred as the mobile granite worked its way upwards from below. This _contact metamorphism_ , often accompanied by the growth of new minerals, is the result of the transfer of heat and introduction of new chemical components from the granite. It has usually resulted in making the rocks more resistant to later erosion at the surface.
#### Younger episodes
##### _Sedimentary markers_
Between 7 and 20 km to the southwest of Exeter, traversed by the A38 and A380 trunk roads, the Great and Little Haldon Hills are capped by a layer of sediments, assigned to the Upper Greensand, and spanning in age the Early/Late Cretaceous boundary (between about 105 and 95 million years ago). These are the westernmost erosional relicts of a continuous sheet of sediment of this age that extended across much of the rest of Southern England. In the Haldon Hills area, the sandy and fossiliferous material seems to have formed near the coastal margin of an extensive Cretaceous sea.
The _Haldon Gravels_ are distinctive deposits that occur above these Cretaceous sediments. They consist largely of flint pebbles and contain sand and mud between the pebbles. Some of the gravels appear to be the result of removal by solution of the calcareous Late Cretaceous Chalk that can no longer be found in its unaltered state so far west. The flint nodules in the Chalk were then left as a layer of much less soluble pebbles. Some of the gravel appears to have been carried to its present position by rivers or the sea, perhaps also with the incorporation of kaolinite clay from the Dartmoor granite. The age of these gravels appears to be early Tertiary, perhaps about 55 million years.
A few kilometres west of the Haldon Hills, northwest of Torquay, the Bovey Formation of early Tertiary age (Eocene and Oligocene, about 45 to 30 million years ago) occurs in a distinct, fault-bounded basin. The formation is more than 1 km in thickness and consists primarily of the clay mineral kaolinite, deposited as mud by local streams, and associated with minor amounts of sand, gravel and peat-like organic deposits of lignite. This sediment fill continues to be a very important material for ceramics, pipes, tiles etc. ranging from high-quality china clay to lower-quality materials. Most of the sediment appears to have been carried into the basin from the area of the Dartmoor granite and its surroundings. The Bovey Basin formed as a result of subsidence along the northwest-to-southeast trending Sticklepath Fault Zone (Fig. 39) which cuts across the whole of the Southwest Region. This fault zone seems to have been active during the accumulation of sediment in the basin and so, at least in this phase of its history, it was much younger than the Variscan structures of the Southwest generally. Further to the northwest along the same fault zone is the smaller Petrockstowe Basin near Great Torrington (see Fig. 38), and, offshore, under the Bristol Channel is the larger Stabley Bank Basin, east of Lundy Island.
About 6 km southeast of St Ives (see Area 1), near the small village of St Erth, a small area is underlain by some soft sands and muds. When first exposed by quarrying, these sediments provided a rich assemblage of fossils that are thought to have lived some 3 million years ago, in latest Tertiary times. The fossils suggest sea depths of between 60 and 100 m, and are now about 30 m above sea level, so they provide a fragment of evidence from a period when the sea was more than 100 m higher than it is now, relative to the land of Cornwall. As will be mentioned below, this deposit is rather similar in its elevation to the most obvious plateau recognised in many of the inland areas, which may also relate to an episode when the sea stood at this level.
##### _Drainage patterns_
On the scale of the whole Southwest Region, the main upland areas are Exmoor in the north and the zone of distinct granite domes in the south, extending from Dartmoor to Land's End.
The highest point of Exmoor is Dunkery Beacon (519 m). Exmoor has been eroded from Devonian bedrock, and may owe some of its elevation to the greater resistance to erosion of this material compared with the Carboniferous material that forms the bedrock further south. Another possible factor is suggested by the remarkable way that many of the river systems of the southwest drain to the south coast, despite their sources being remarkably close to the north coast (Fig. 48). This is the case for the Exe, flowing from Exmoor southwards via Exeter to Exmouth, and, further west, the Tamar, which begins northeast of Bude and flows southwards past Launceston and Tavistock before discharging into Plymouth Sound. It looks as if this part of the Southwest Region has been tilted southwards as these river systems developed on either side of the high ground of Dartmoor, where the granite resisted erosion. A southerly tilt would also be consistent with a preferential uplift of the Exmoor Hills to the north.
**FIG 48.** River pathways, mean flow rates (m 3/s) at some river stations, main drainage divide (red line) and main granites of the Southwest Region.
The southern areas of hills correspond so clearly with the areas of granite outcrops that there can be little doubt that the greater resistance to erosion of the granite explains their higher elevations. But how long has this erosion been taking place? Emplacement of the granites was over by the end of Carboniferous times (about 300 million years ago) and there is evidence of pebbles in the New Red Sandstone from the Dartmoor granite and from the altered bedrock close by. Although the precise age of the earliest New Red Sandstone is uncertain, it does not appear to be much younger than the age of granite emplacement. However, it appears that the granites were not being significantly eroded in quantity much before Cretaceous times, 200 million years later and about 100 million years ago. Since then, the granites have been eroded into the present patterns of local hills and valleys, but at very variable rates as climate, coverage by the sea and rates of river erosion changed.
Each of the main granite bodies corresponds closely to an area of high ground, and their maximum heights tend to be greater towards the east (44 m for the Isles of Scilly, 247 m for Land's End, 252 m for Carnmenellis, 312 m for St Austell, 420 m for Bodmin and 621 m for Dartmoor). This gradient is overall only about 3 m per km. The geophysical data on the large, deep granite body (Fig. 44) recognised below the surface granite bodies do not provide independent evidence for a slope of this sort deep down. Some tilting of the landscape downwards towards the west may have occurred, or the slope may simply reflect the greater proximity of the western granite bodies to the sea and repeated episodes of marine erosion.
##### _Ice Age episodes_
Ice sheets do not appear to have covered the present land of the Southwest Region to any important extent during any of the major cold episodes of the Ice Age. In the Isles of Scilly, material deposited directly from a grounded ice sheet has been recognised and is thought to be Devensian (last cold phase) in age (Fig. 49). Various giant boulders derived from metamorphic sources are a notable feature of some localities on the North Devon coast, some of which appear to have come from Scotland. However, it is not clear whether they were transported to their present locations by a large ice sheet or by floating ice.
In spite of the lack of an actual ice sheet, the repeated cold episodes of the Ice Age must have had a considerable effect upon the weathering style of the bedrock, for example influencing the granite tors, mobilising material to move down slopes and changing drainage patterns and the surface blanket of soft materials.
**FIG 49.** Map showing the greatest extent of the last main (Devensian) ice sheet across England and Wales.
### AREA 1: WEST CORNWALL
A remarkable feature of the peninsula of West Cornwall (Figs 50 and 51), as it narrows towards Land's End, is the contrast between the spectacular coastal scenery and the scenery inland. The rocky coastal cliffs and sharply indented coves reflect West Cornwall's exposure to the prevailing Atlantic storms, and contrast starkly with the inland scenery of rolling – though often rocky -hillsides, carved into a network of small valleys and streams.
The main features of the inland landscape appear to have formed over millions of years, and ultimately reflect the bedrock pattern that has been inherited from the Variscan mountain building that ended 300 million years ago. In contrast, the coastal landscape is clearly much younger, and much of it has been produced by changes in sea level that have occurred since the last main cold phase of the Ice Age, some 10,000 years ago. There is some evidence of earlier sea levels but this is more difficult to evaluate, as it has generally been removed by more recent erosional events.
**FIG 50.** Location map for Area 1.
I have divided West Cornwall into three Landscapes ( **A** to **C** ), each with distinctive bedrock geology (Fig. 52).
#### Landscape A: Granite areas
The Isles of Scilly ( **A1** ; Fig. 53) are formed by the westernmost significant granite bodies of southwestern England. They lie some 45 km southwest of Land's End, scattered over an area approximately 20 km by 15 km. Most of the 150 islands are little more than bare outcrops of granite, sometimes largely submerged at high tide. The landscape is windswept and mainly treeless, with heathlands where the ground has not been cultivated. Historically the islanders eked out a precarious existence from crofting, until the nineteenth century, when shipbuilding and the growing of flowers became economic. Today most of the cultivated land consists of small fields of flowers edged with evergreen hedges, and horticultural work, along with tourism, has become the mainstay of the economy.
The smaller islands are often arranged in rows, separated by 'sounds' (areas of shallow water) that tend to have a northwest-southeast orientation. These sounds must have been valleys before they were drowned by the recent (Flandrian) sea-level rise. Their orientation is similar to that of the valleys and faults of the Land's End granite, discussed more fully below. Numerous sandy bays and beaches reflect the granite weathering and the transport of the weathered sediment, by storms and tides, to more sheltered parts of the island landscape.
**FIG 51.** Natural and man-made features of Area 1.
In the general section of this chapter it has been mentioned that the northern Scillies appear to have been invaded by ice late in the history of the last (Devensian) cold phase of the Ice Age (Fig. 49), and this is surprising in view of their southerly location. It appears that when the Devensian ice sheet had grown to its greatest extent, an elongate tongue of ice, perhaps some 150 km wide, extended for nearly 500 km from the Irish and Welsh ice sheets to the edge of the Atlantic continental shelf. This tongue became so large because it was vigorously fed by ice from the high ground of Ireland to the west, and the Lake District of England and the mountains of Wales to the east. The ice extended across the mouth of the Bristol Channel, well clear of the present north Cornwall coastline, before leaving ice-laid sediment on the northern fringe of the Isles of Scilly. South of the island areas that were covered by ice, the granite has been weathered locally into tors.
**FIG 52.** Area 1, showing Landscapes A to C and specific localities mentioned in the text. Major divisions of Landscape A are identified by **A1, A2, A3** etc., and localities are shown as **a1, a2, a3** etc.
Land's End is the westernmost tip of mainland England. The local cliffs are made of granite and clearly show vertical sets of fractures, probably formed when the granite was cooling and contracting (Figs 54 and 55). Apart from the fractures, the granite is massive compared with the strongly layered and deformed rocks into which the main granites were intruded. Most of the northerly inland areas are exposed and windswept moorland, though arable farming for early vegetables has developed in the valleys to the south. The valleys eroded in the Land's End granite are distinct and often oriented very clearly in a northwest-southeast direction. This orientation is parallel to a large number of faults which appear to have first formed late in the Variscan mountain-building episode. However, they must also have been active much later, after the intrusion of the main granite, because its margin is locally offset by faults with this trend. The movement of superheated water along these fault systems has resulted in mineralisation of the bedrock, altering its resistance to erosion so that valley incision has taken place preferentially in this direction. Tors are largely absent from the Land's End, Godolphin, Carnmenellis and St Austell granite areas, while they are common weathering features on Bodmin Moor and Dartmoor. This probably reflects a difference in the weathering and uplift histories of the different granite bodies.
**FIG 53.** The Isles of Scilly, looking east towards Bryher, Tresco and St Martins. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
The Land's End granite ( **A2** ) forms the bedrock of most of the far southwestern peninsula, which is largely ringed by cliffs. To the east of the granite, St Ives Bay on the north coast and Mount's Bay on the south coast show how much more readily eroded the Devonian killas is in comparison. Along the north coast of the Land's End peninsula, the killas is preserved as a screen of land, rarely more than a kilometre in width, but clearly showing distinctive layering, as seen at Gurnard's Head ( **a3** ; Fig. 56). Present coastal erosion may have been slowed at this point by the greater strength of the Devonian where it has been altered close to the granite. Just north of Land's End point, Whitesands Bay ( **a1** ) is one of the only sandy bays to face the open sea to the west. The bay lacks any significant stream system that could have supplied sand to the beach, so it seems most likely that the sand has been carried into this bay by the storms which so often attack this exposed coast.
**FIG 54.** Land's End peninsula from the air, looking eastwards. Note the lack of clear layering in the granite bedrock and the steep fracture surfaces (joints) that have controlled the form of the cliffs. (Copyright Dae Sasitorn & Adrian Warren / www.lastrefuge.co.uk)
A distinct, though irregular, platform at 100–150 m above sea level rings the area of the Land's End granite, and tends to be followed by local roads. This may have been formed during an early episode of coastal erosion, when sea level was standing at this height relative to the land (Fig. 57). Some evidence for its age is mentioned below. Its irregularity probably reflects local valley erosion that has taken place since its formation.
**FIG 55.** Land's End cliffs, looking westwards. Again, note the vertical jointing. (Copyright Landform Slides – Ken Gardner)
**FIG 56.** Gurnard's Head (Fig. 52, a3), west of St Ives, showing the coastline along the northern edge of the Land's End granite. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
**FIG 57.** Slope map showing the southwestern part of Area 1. Slopes greater than 5 degrees are coloured red, and the main granite areas and the Lizard Complex are outlined. Topographic cross-sections illustrate wave-cut platforms that are presently inland and show the lack of topography on the Lizard Plateau.
The next main granite bedrock area to the east underlies the Carnmenellis area ( **A4** ), although there are other smaller granite areas, such as St Michael's Mount (Fig. 58), across the bay from Penzance, and the intermediate-sized Godolphin granite ( **A3** ), some 8 km to the east. These smaller granite areas show the range in size of 'feeders' that branched off from the major granite body that underlies the whole Southwest Region (Fig. 44). In all cases the granite bedrock corresponds to high ground in the landscape – evidence of the greater resistance of the granite in the face of repeated landscape erosion. Derelict mine engine houses litter the landscape, especially northwards near Camborne and Redruth, once prosperous tin-mining centres. To the south, the landscape is more sheltered and fertile, allowing better farming. Trees are rare because of their past cutting for fuel for the mining industry, as well as because of the general exposure of the landscape to the weather.
**FIG 58.** St Michael's Mount. (Copyright Dae Sasitorn & Adrian Warren/ www.lastrefuge.co.uk)
The same northwest-to-southeast valley pattern that has just been mentioned in the Land's End granite is also apparent in the area around the Carnmenellis granite, and appears to be the result of preferential stream erosion parallel to the faults trending in this direction (Fig. 59).
**FIG 59.** Sketch map showing the orientation of some of the main faults in West Cornwall.
Another similarity to Land's End is the widespread topographic platform at about 140 m above sea level. This platform is particularly clear north of the Carnmenellis granite but is also obvious in the Godolphin granite (Fig. 57). In the Porthmeor and Camborne areas the platform is particularly distinctive, and the continuity of its landward slope is clear on the slope map. It has generally been assumed that these platforms were cut by storm waves when the sea stood at this level about 3 million years ago. At this time, West Cornwall would have consisted of granite islands, like the present Isles of Scilly, while the surrounding Devonian bedrock (killas) was submerged.
The western part of the St Austell granite ( **A5** ) lies within Area 1, and again its resistance to landscape erosion is shown by the high ground that it occupies. The remarkable feature of this granite is the way it has been altered by the circulation of hot fluids. Much of the feldspar in this granite has been altered to the mineral kaolinite, which is a member of the clay mineral group that is the key component of china clay. The result of this is that the St Austell granite has been quarried, particularly in its western part within Area 1. The kaolinite has been extracted from the rotted granite by high-pressure water jets, which leave large volumes of quartz and feldspar grains that are heaped up in enormous and obvious spoil heaps.
Most of the original heathland and moorland on the St Austell granite has been destroyed by the mining industry. More recently, the Eden project redevelopment of one quarry complex (in Area 2) has brought many visitors to the area.
#### Landscape B: The Lizard
Lizard Point is the most southerly headland in Britain, part of a wider Lizard landscape comprising a flat heathland plateau bounded by dramatic cliffs and small coves (Fig. 60). Notice how steep many of the sea cliffs are, and that they show little in the way of well-developed, regular layering or fracturing. Unlike the other upland areas of Cornwall, the Lizard is not underlain by granite. As mentioned in the general section of this chapter, some of the area is underlain by serpentinite, a distinctive, decorative rock that was originally part of the Earth's mantle, below the crust and many kilometres below the surface (see Chapter 3). Other parts of the Lizard bedrock were originally basalt lavas and minor sheet-like intrusions along with small amounts of sediments, all similar to successions elsewhere that appear to have formed in or below the Earth's oceanic crust. During the Variscan mountain building, this mixture of distinctive bedrock types appears to have been squeezed up amongst the strongly compressed Devonian killas. Today, the exceptional bedrock chemistry of the unusual Lizard rocks is the reason why the peninsula has such a variety of rare plant habitats. Much of the peninsula is a National Nature Reserve (NNR) or owned by the National Trust.
As in Carnmenellis and Land's End, a wave-cut platform has been identified on the Lizard, although its level is rather lower. In fact, the platform actually forms the Lizard Plateau and is remarkably flat, the ground surface varying between 60 and 100 m above sea level over large areas. This relative flatness probably reflects the rather uniform composition of the rock materials involved, and their uniform resistance to weathering and erosion.
The coast of the Lizard Peninsula is formed almost entirely of steep cliffs, particularly around its southwestern perimeter. A few small beaches do occur in sheltered locations, such as at Coverack ( **b1** ), and picturesque fishing villages are scattered along the east side of the peninsula around small coves and gullies.
**FIG 60.** The Lizard coastline. Note the contrast between the jagged coastal cliffs and the flat inland landscape. (Copyright Dae Sasitorn & Adrian Warren/ www.lastrefuge.co.uk)
#### Landscape C: Cornish killas
Most of the bedrock of West Cornwall is Devonian sediment, folded, faulted and – locally – altered during the Variscan mountain-building episode (see the general section of this chapter). The Devonian sediments, known to miners and quarrymen as _killas_ , have been less resistant to landscape weathering and erosion than the granites ( **A** ) and the Lizard Complex ( **B** ), and so have been preferentially eroded to form lower landscapes. All the major bays and estuaries of this Area, such as St Ives Bay ( **c4** ) and the Carrick Roads at Falmouth ( **c7** ), are situated in killas areas for this reason. The Variscan folding and faulting that deformed the killas has also locally influenced the directions of valleys and their slopes, which have picked out variations in the killas layering, giving an east-west grain to the landscape (Fig. 61).
**FIG 61.** Slope map of the eastern part of West Cornwall. The main granite bedrock areas are outlined and important boundaries in the Devonian bedrock indicate the direction of the Variscan folding. Note the circular china-clay workings that are visible in the St Austell granite ( **A5** ).
**FIG 62.** Complex landscape of the North Cornwall coast, looking eastwards from Crantock Beach, over the Pentire Ridge towards Newquay (Fig. 52, **c2** ) and Watergate Bay. (Copyright Dae Sasitorn & Adrian Warren/ www.lastrefuge.co.uk)
**FIG 63.** Headlands, bays and beaches of the Newquay area (Fig. 52, **c2** ), looking eastwards from a point 2 km west of Figure 62. Crantock Beach is visible in the middle distance. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
The Flandrian sea-level rise, which ended only 5,000 years ago, has also left its mark on West Cornwall. The most obvious legacy is the extensive array of tidal estuaries at the mouths of the main rivers, which are flooded river valleys or _rias_. The most striking example is the series of branched rias around Falmouth known as the Carrick Roads ( **c7** ). These extend northwards across half of the width of West Cornwall and have had an obvious major influence on the road and rail transport pattern of the area. Major branch rias to the west, north and east around the Carrick Roads divide this part of the Cornish landscape into numerous isolated peninsulas. The inland valleys of the killas areas tend to be deeply incised with little widening, and the branching patterns of these valleys are very clear on the slope map. The rias are obviously the direct result of the drowning of valleys of this form by the Flandrian sea-level rise.
The coastline of the killas landscape of West Cornwall is extremely varied: small, sandy coves alternating with rocky promontories and high cliffs are typical of this part of the north coast (Figs 62 and 63). This irregular coastline is due to local variation in the type and strength of the killas bedrock, with weaker units (often slates) eroding to small bays while the more resistant rocks (often limestones or quartzites) form the headlands.
The sandy bays of north Cornwall ( **c1** , Padstow and the River Camel Estuary; **c2** , Newquay Bay; **c3** , Perranporth and Perran beach; **c4** , St Ives Bay) are famous for surfing, due to the splendid waves that roll in from the Atlantic Ocean. Apart from Padstow Bay ( **c1** ), at the mouth of the River Camel, most of the north Cornwall beaches are not obviously linked to river sources of sand and so must have been filled by sand transported from offshore sources by storm waves. At many famous surfing beaches, such as Perranporth ( **c3** ), sand banks built up by winter storms can be eroded in the summer, resulting in dangerous currents sweeping out to sea. The wind-blown dunes of the Penhale Sands, north of Perranporth, are a spectacular example of the way that gales from the west can move beach sand up to 2 km inland. Because of the variation in the killas bedrock, some headlands are long and the inlets are narrow enough to develop fast tidal flows, capable of forming large, regular ripples as seen in the foreground of Figure 62.
On the south coast, storm-built sandy beaches have also formed, for example at Newlyn ( **c8** ), Praa Sands ( **c5** ) and at the mouth of Helston valley south of Porthleven ( **c6** ). Further east, the coastline is much more sheltered and the scenery is dominated by the drowned valleys and quiet inlets of the Carrick Roads ( **c7** ).
### AREA 2: EAST CORNWALL AND SOUTH DEVON
This Area straddles the boundary between Cornwall and Devon (Fig. 64). In terms of the coastlines of the Southwest, it includes a small stretch of the north coast near Tintagel, and a large section of the south coast from St Austell, via Plymouth and Start Point, to Torquay and Exmouth (Fig. 65).
In the general section of this chapter, the early geological history of the Southwest Region as a whole has been outlined, particularly the evolution of the Variscan mountain belt. Younger episodes in the region have also been discussed, involving river and valley erosion of the landscape, the effects of the Ice Age and the changes in the coastline that have resulted from the most recent (Flandrian) rise in sea level.
In the sections below we shall consider more local features of the scenery in this Area, dividing it into four distinct Landscapes (labelled **A** to **D** ), each underlain by a different kind of bedrock (Fig. 66).
**FIG 64.** Location map for Area 2.
**FIG 65.** Natural and man-made features of Area 2.
**FIG 66.** Area 2, showing Landscape A to D and localities ( **a1, a2** etc.) mentioned in the text.
#### Landscape A: Granite areas
Bodmin Moor ( **A6** ) and Dartmoor ( **A7** ) are the most southerly large upland areas in England and, in each case, the granite bedrock has resisted landscape erosion to produce the high ground. The highest point of elevation in this Landscape is High Willhays ( **a1** ) at 621 m above sea level on Dartmoor. Evidence of the ongoing nature of this landscape erosion is provided by the contrast between the high moorland, with bogs, steep valleys and exposed tors, on one hand, and the surrounding low farmland on the other.
In the general section of this chapter I have outlined some main features of the southwest granites, such as their resistance to erosion and the valuable minerals associated with them. They have also provided excellent strong building stone for the buildings of the Region.
As in the granite areas of West Cornwall (Area 1), mineral mining activities have had a strong impact on the area, and derelict tin mine buildings are scattered over much of the landscape. The china-clay industry has also produced significant changes to the scenery, one of the most remarkable sites being the workings 3 km northeast of St Austell ( **a2** ). These pits now house the famous Eden Project, an educational charity providing a 'Living Theatre of People and Plants' and attracting over a million visitors each year (Fig. 67).
**FIG 67.** The Eden Project is situated in a former china-clay pit. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
The present-day pattern of streams and their valleys has evolved from ancestral streams and valleys that carved most of the inland scenery over millions of years. In the general section of this chapter, we have seen the remarkable way that the drainages of the rivers Tamar and Exe flow southwards across most of the Southwest Region to the sea, divided by the high ground of Dartmoor. A general tilt of the Region to the south, and the resistance of the granite domes to stream and valley erosion, appear to have been important factors. Closer examination of the drainage patterns shows that the streams and valleys of the Bodmin Moor granite tend to radiate out from near its centre, but that the distinctly larger Dartmoor granite has eroded down to form two drainage divides, one in the north and one in the south. This may simply be a matter of the different size of these two granite areas, which has allowed a more complex drainage pattern to develop through time over Dartmoor.
The parallel groups of incised valleys that are common in the granites of Area 1 are not clearly developed on Bodmin Moor and not visible at all on Dartmoor. It is intriguing that the fault system that was responsible for the parallel valleys further to the west is not present in these larger eastern granites. This may tell us something about the greater depth of weathering and erosion experienced by the eastern granites.
There are a number of gorges resulting from the deep incision of rivers and streams into the granites and their surrounding materials. Around the Dartmoor granite, the valleys of the River Dart to the east and the Lydford Gorge to the west ( **a3** ) are examples of these. South of the Bodmin Moor granite, the River Fowey also has a spectacular and well-known gorge at the Golitha Falls ( **a4** ).
Tors are remarkable features of both the Dartmoor and Bodmin Moor granite areas (Fig. 68). They provide a focus for visitors in granite scenery that is often otherwise rather featureless and empty, and there are well over a hundred tors on Dartmoor alone. Tors tend to look like heaps of granite blocks, but a closer inspection shows that they are not jumbled but rather blocks that 'belong' next to their neighbours. These linked blocks are relict volumes of a much larger volume of granite, most of which has disintegrated and been removed by weathering. Tors are very much features of granite weathering, suggesting that the coarse interlocking crystal texture and general lack of layering have caused these remarkable landforms to appear.
Many tors occur on the most elevated parts of the scenery, looking like man-made cairns. Others occur on the slopes of valleys, but it is clear that tors will only form where down-slope processes, driven by gravity, can remove the weathering debris from around them. Cracks in the granite (technically called _joints_ ) give tors much of their distinctive appearance: near-vertical joints produce towers and pillars, while roughly horizontal joints give the rocks a layered, blocky appearance (Fig. 69). Most of the joints seem to have formed during the arrival of the granite material from below (intrusion), either due to contraction from cooling of the newly solid material, or due to other stresses acting shortly after solidification. The flat-lying joints (horizontal on hill tops, and parallel to slopes elsewhere) may also be due to the erosion of the present scenery, allowing the granite to expand and fracture as the weight of the overlying material is removed.
**FIG 68.** Hay Tor, Dartmoor, looking southeast. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
**FIG 69.** Hound Tor, Dartmoor. (Copyright Landform Slides – John L. Roberts)
The slopes round tors tend to be covered with loose granite blocks (often referred to as _clitter_ ), generally angular and obviously derived from the tors (Fig. 70). Finer-grained, crystal-size gravel or sand of quartz and feldspar is another weathering product and is locally called _growan_ or sometimes _head._ It is clear that much of the alteration of the granite that has resulted in the appearance of the tors must have been strongly influenced by the climate, vegetation and soil-forming conditions existing at different times and in different scenic settings. Much of this has been compared to the weathering and down-slope movement that is seen in high-latitude cold climates today, and so is explained as a result of the cold climate conditions experienced repeatedly during the Ice Age. However, weathering of granites is much faster today in the warm, tropical jungle areas of the world, compared to drier, cooler and less vegetated conditions. Early episodes of weathering of the Southwest Region granites may have taken place under the warm, tropical conditions that are indicated by early Tertiary fossil deposits elsewhere in England.
**FIG 70.** Mass-flow terrace, looking westward from Cox Tor, Dartmoor. The terrace is interpreted as being the result of down-slope movement under alternating freeze-thaw conditions. (Copyright Landform Slides – Ken Gardner)
_Rock basins_ are low-lying hollows in the granite topography draped with granite weathering products. Sometimes these are dry and their floors are simply coated with granite weathering materials. In other places the hollows are covered by peat, which is often a feature of the higher and wetter parts of the granite hills. Under very wet conditions, the hollows contain deep bogs or _mires_ , with a reputation for being bottomless! How these low hollows were excavated is a puzzle.
Topographic platforms, cut by storm waves during times of high sea level, have been claimed to be present around the Dartmoor and Bodmin granite areas, although they are not as distinctive as those discussed on the Land's End and Carnmenellis granites of Area 1. The Area 2 platforms are at heights of between 200 and 300 m above sea level, but in the absence of dated deposits similar to the St Erth beds of Area 1, their relevance to sea-level changes is open to doubt. Indeed, as mentioned above, terraces have been recognised around the Dartmoor granite that are thought to be the result of down-slope mass movement under freeze-thaw conditions, rather than due to sea-level changes.
#### Landscape B: _Killas_ and other Devonian bedrock
Apart from the granites, Devonian sediments make up the bedrock of the southern and central part of Area 2. They consist largely of slates and mudstones with some sandstones, and are known generally as _killas_ to distinguish them from the granites and other younger, less altered sediments. In a few localities around Plymouth ( **b1** ) there are Devonian limestones, similar to the well-known limestones around Torquay ( **d1** ) and Chudleigh ( **d9** ). The settings in which these Devonian sediments may have formed are illustrated in Figure 38, in the general section of this chapter.
The youth of the coastal scenery of this Landscape combines with the vigour of many of the processes operating to make it much more distinctive and dramatic than the inland scenery. In the west of Area 2, cliffs characterise the Cornish section of the south coast and often intersect deeply incised valleys that are clearly older features (Fig. 71).
Cornwall and Devon are separated from each other in this Area by the River Tamar, and this meets the south coast in a large drowned valley system around which Plymouth ( **b1** ) has grown (Fig. 72). Plymouth Sound is one of the best natural harbours in the Southwest and the historical naval importance of this city is the result. Similar, but smaller, valley systems (sometimes called _rias_ ) are common all along this stretch of coast, as they are further west in Area 1. Flooded valleys form the estuaries of the River Fowey, east of St Austell, and farther east still at Salcombe ( **b3** ) and Dartmouth ( **b8** ).
**FIG 71.** Polperro, on the south Cornwall coast. (Copyright Dae Sasitorn & Adrian Warren/ www.lastrefuge.co.uk)
**FIG 72.** The Tamar and Brunel Bridges, between Plymouth (Devon), to the right, and Saltash (Cornwall). (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
The headlands from Bolt Tail ( **b2** ) to Start Point ( **b5** ) are made of some of the most highly altered and probably oldest bedrock in Devon, although the age of their deposition as sediments is not known. They have been changed locally to mica-rich and hornblende-rich schists that must have been altered (metamorphosed) several kilometres below the surface, before being pushed upwards during the Variscan mountain-building event. The local resistance of these schists to erosion has led to a particularly intricate pattern of small but sharp headlands and tight small bays. The slope map (Fig. 78) reveals a strong east-west orientation of slopes in this area that must be a reflection of folding in the bedrock. Three separate coast platforms, the highest at about 7 m above present sea level, are very clear at Sharpers Head ( **b4** ). Each platform represents an episode in the retreat and relative lowering of the sea before the latest Flandrian rise.
**FIG 73.** Slapton Sands (Fig. 66, **b7** ). (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
Just north of Start Point ( **b5** ) lies the ruined village of Hallsands ( **b6** ), which vividly illustrates the damage people can unwittingly do in changing features of the coastal zone. From 1897 to 1902 over half a million tonnes of gravel were removed from the bay off Hallsands to construct an extension to the dockyard at Plymouth. Engineers believed that natural storm currents offshore would replenish the material they had taken, but this did not happen. Instead, the removal of the shingle left the beach open to intense storm erosion, and in January 1917, some 15 years later, the lower part of the village and a sizeable section of coastline were removed by a combination of storm and tide conditions.
Further north, the 3.5 km long barrier beach of Slapton Sands ( **b7** ) is another shingle barrier kept active by storm waves from the southeast (Fig. 73). The freshwater lagoon behind it, Slapton Ley, is a nature reserve, home to many rare species of plants and animals. It is under threat from erosion and breaching of the shingle barrier, causing flooding by salt water, and from silting up because of ploughing and deforestation of the inland landscape.
This Landscape of Area 2 also includes a short section of the north Cornish coast around Tintagel ( **b9** ), which was an important trading centre on this difficult coast and became the site of a twelfth-century Norman castle, linked to the legends of King Arthur (Fig. 74). The coastline here is often sheer and rugged, and the bedrock contains sharp folds, fracture surfaces and multiple surfaces of mica-rich cleavage, providing evidence of extreme compression during the Variscan mountain building. Many of the cliffs are flat-topped, because erosion has been controlled by relatively flat-lying surfaces in the bedrock, which contrasts sharply with the hog's-back or whaleback cliffs of other coastal stretches.
#### Landscape C: The Carboniferous Culm of Devon
The northern landscape of Area 2 is underlain by Carboniferous bedrock (locally known as the Culm) which occupies a complex downfold in this part of the eroded Variscan mountain belt. The coastal bedrock here contains many beautiful examples of folding, for example at Boscastle ( **c3** ), famous for the flash flood that did so much damage in August 2004. Spectacular folding is also clearly visible at Millook Haven ( **c2** ; Fig. 75), and at Crackington Haven ( **c1** ; Fig. 76). In both cases, the convergence directions represented by the folds are near vertical, suggesting that the Variscan folding may have involved a later tilting of an earlier fold set.
**FIG 74.** Tintagel Head (Fig. 66, **b9** ). (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
**FIG 75.** Chevron folding of Carboniferous sandstones and mudstones, Millook Haven (Fig. 66, **c2** ). (Copyright Landform Slides – Ken Gardner)
**FIG 76.** Overturned fold in Crackington Formation, Culm Measures, Crackington Haven (Fig. 66, **c1** ). (Copyright Landform Slides – Ken Gardner)
#### Landscape D: New Red Sandstone and younger bedrock
Along the eastern edge of Area 2, relatively unfolded New Red Sandstone of Permian and Triassic age rests on the folded Devonian and Carboniferous sediments of Landscapes **B** and **C**. The junction of the younger material with the older was formed when the younger sediment was deposited on the eroded margins of the Variscan hills. The New Red Sandstone occurs in a wide, north-south trending belt, extending southwards as far as Torquay ( **d1** ) and Paignton, and with fingers extending westwards to the north of Dartmoor (Fig. 37). Along the coast, from Exmouth ( **d4** ) southwards via Dawlish ( **d3** ) and Teignmouth ( **d2** ), the New Red Sandstone has been quarried and penetrated by the tunnels of the main coastal railway to the Southwest. The sandstone forms dramatic red cliffs, and marks the western edge of the World Heritage Site that extends to the east along the coast of Dorset.
The New Red Sandstone consists of sandstones, gravels and mudstones that formed as alluvial fans, desert dunes and in short-lived lakes along the edge of an irregular hilly landscape of older bedrock. The characteristic red colour so typical of many Devon soils has largely been derived from these New Red Sandstone rocks. In the Exeter area ( **d5** ), roads have been spectacularly cut through the New Red sediments, and also through some scattered deposits of volcanic rock, mainly lava. These lavas have been highly altered and have not resisted weathering at the surface any more than the sediments of the succession, so they have not had much influence upon the scenery.
An intriguing feature of the New Red Sandstone is the way the original landscape on which it formed is reappearing as the present landscape erodes. For example, the Crediton Basin ( **d6** ), north of Dartmoor, is now obvious as a remarkably finger-like strip of sediment, only 2–3 km across north to south, but extending almost 40 km west to east (Fig. 37). Detailed examination of the New Red sediment in this basin shows that it was deposited as the fill of a long, narrow valley, with material being derived from north and south as well as along its length from the west. The valley formed parallel to the folds and faults of the earlier Carboniferous bedrock on each side of it, and must have been cut first by river erosion in Permian times, controlled by the earlier folds and faults that were formed during the Variscan mountain convergence. A few kilometres further north, the Tiverton Basin in Area 3 has a similar west-to-east trend, though it is more open and less elongate.
From Exeter ( **d5** ) to Torquay ( **d1** ), the base of the New Red Sandstone reveals topography of hollows eroded westwards into a higher ground of Devonian and Carboniferous bedrock. The New Red Sandstone pattern is of alluvial fans radiating downstream, but generally draining towards the east, and it bears a striking general similarity to the present drainage and scenery of the area (Fig. 77). During Variscan convergence, the Devonian limestones were moved into their present pattern by flat-lying faults, and this was then followed by the intrusion of the Dartmoor granite, which may help to explain why the New Red valleys here were shorter than those preserved as the Crediton ( **d6** ) and Tiverton basins.
**FIG 77.** Reconstruction of the Permian topography and drainage, looking southwards towards the location of present-day Torquay (Fig. 66, **d1** ). The current coastline is indicated purely for reference; there is no evidence for a sea in Permian times where the sea now is.
I have already described the importance of the Devonian limestones in creating topography in the Torquay area ( **d1** ) and around Torbay generally. This material is an important part of the bedrock in its own right, and has been quarried widely as a building stone. It was a popular stone for ornaments and furniture, particularly in Victorian times, when cut and polished fossil corals featured in many of the washstands that were produced in the period.
In Torquay the Kent's Cavern complex of caves, formed by solution of Devonian limestones, is an important archeological site, preserving evidence of Heidelberg and Neanderthal man from deposits about 450,000 years old. These were deposited during the Anglian cold phase of the Ice Age, when ice sheets spread across East Anglia and into the Thames valley, though not into the Southwest. The remains of cave bears, hyenas and sabre-tooth cats have also been found in the cave complex, as well as those of modern humans.
The Haldon Hills ( **d7** ), about 10 km south of Exeter, are clearly erosional relicts of the young valley systems of the Rivers Exe and Teign. Their higher ground retains fragments of the Late Cretaceous and Early Tertiary bedrock record and provides information about the history and environments in this key area. The Haldon Hills formed the boundary between the high ground that existed at the time in most of Cornwall and Devon, and the areas of thicker sedimentation that developed since Permian times to the east (Areas 4 to 7). To an extent, the presence of the Late Cretaceous and Early Tertiary material has provided a resistant cap to the Haldon Hills.
The youngest bedrock in Area 2 is the clay, sand and lignite near Bovey ( **d8** ), between Dartmoor and the New Red Sandstone area. Bovey and Petrockstowe in Area 3 lie on the Sticklepath Fault that runs northwest to southeast across the whole of Devon (Fig. 78). The fault was active about 40 million years ago, at the same time as the Alps were forming as a major mountain belt much further south. It seems likely that this fault formed along the direction of earlier fractures in the bedrock left by the Variscan mountain building and described more fully in Area 1. The Bovey and Petrockstowe basins must have grown as areas of surface subsidence linked to movements of the Sticklepath Fault, and sediment must have been carried into the newly subsiding low ground by streams. The basin sediment is now mined for ball clay, which has been an important source of clay for pottery and many other purposes. There are also layers of lignite and sand which have been used as a fuel and in the making of glass.
**FIG 78.** Slope map of the eastern part of Area 2, showing the distribution of slopes greater than 5 degrees (coloured red). The Dartmoor granite bedrock area is indicated (orange), as are the Bovey Basin (green) and the Sticklepath Fault (dashed line).
### AREA 3: NORTH DEVON AND WEST SOMERSET
This Area (Figs 79 and 80) divides neatly between the high ground of Exmoor in the north, where the bedrock consists of sediments of Devonian age, and an area of Carboniferous bedrock to the south (Fig. 37). The bedding slopes generally southwards, forming the northern part of a large downfold or trough (often called the _Culm synclinorium_ or fold-belt in Fig. 39) that forms the central feature of the Variscan mountain belt of the Southwest.
I have selected four Landscapes ( **A** to **D** ), loosely following the Countryside Commission's character area scheme, with each Landscape being shown in Figure 81.
#### Landscape A: Exmoor's Devonian bedrock
Exmoor is a hilly plateau ranging in summit elevation between 250 m and about 500 m above sea level. The central parts consist of a treeless, heather- and grass-moorland landscape, which is well seen from the highest point, Dunkery Beacon, at 519 m ( **a1** ; Fig. 82). Exmoor ponies and red deer roam this landscape.
**FIG 79.** Location map for Area 3.
**FIG 80.** Natural and man-made features of Area 3.
**FIG 81.** Area 3, showing Landscapes **A** to **D** and localities ( **a1, a2** etc.) mentioned in the text.
**FIG 82.** Dunkery Beacon (Fig. 81, **a1** ). (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
However, there is much variation in landscape within Exmoor. To the east of the main hilly plateaus and flat-topped ridges are the Brendon Hills ( **a2** ), a region of rolling countryside with a large proportion of Exmoor's ancient oak woodland. Though the upper ground of the rest of Exmoor is largely treeless, Exmoor's combes and valleys are quite densely wooded with conifer plantations and broadleaved woodland (Fig. 83). Much of Exmoor is a patchwork of fields claimed from the moor in the nineteenth century. The moorland becomes wetter and more broken into hills and valleys towards the south, approaching Landscape **B**.
Exmoor is the only large upland area in the Southwest Region that is made of sedimentary bedrock, rather than granite. The bedrock consists of Devonian sediments, folded and altered during the Variscan convergence and of similar composition to the Cornish killas in Areas 1 and 2. Mudstones and sandstones are the commonest types of sedimentary bedrocks in the Exmoor landscape, originally formed in the Devonian basinal setting illustrated in Figure 38.
Exmoor was never glaciated, and the upland plateau surface may be as much as 200 million years old, formed in the Early Jurassic. Gently rounded hillsides and gentle valleys are typical of most of the higher ground, suggesting that the surface was developed over a long period of stream action. A more recent valley incision is also apparent and probably relates to steady upward movement of the ground relative to the sea during Tertiary times.
**FIG 83.** Heddon's Mouth, Exmoor, 5 km west of Lynton. (Copyright National Monuments Record, English Heritage)
As the slope map (Fig. 84) shows, local slope patterns in both Exmoor and the Culm area of Landscape **B** have a tendency to run broadly west to east. This is the result of the direction of the folding that formed during the Variscan convergence. Local erosion of tilted sedimentary layers and their fold axes has produced ridges and hillcrests with this orientation. The most obvious east-west slope is the 'Exmoor line', running eastwards from Barnstaple and South Molton (Fig. 80), which marks the join of the more easily eroded Carboniferous sediments (Landscape **B** ) and the underlying Devonian sediments.
The coast of Exmoor has some of the highest cliffs in England, formed where the old hilly plateau of Exmoor, with tops locally over 300 m in elevation, has been cut into and removed by young coastal erosion. There is so much interest along this coastline that I will comment on it locality by locality, from east to west (Fig. 81).
Westwards from Minehead, the Bluff is the northernmost point of an isolated hill range that reaches elevations of more than 300 m and runs for some 7 km along the coast. There is a marked change of slope at 200 m, above which the topography is gently hilly, whereas below it descends steeply in numerous landslides towards small cliffs of bedrock being actively eroded by the sea. There are many small folds in the bedrock, but generally the coastal slope is of the hog's-back type (Fig. 85). Views from this hill range extend northwards across the Bristol Channel and southwestwards across a wide valley, eroded preferentially in New Red Sandstone and with a capping of Early Jurassic sediment. It is clear that an early topography of valleys was partially filled with New Red Sandstone (strictly part of our Landscape **C** ), which has later been modified by faulting. The faulting makes interpretation of this area difficult, so the details of the early topography are not as clear as they are to the south and north, along this same important unconformity.
**FIG 84.** Slope map of Area 3, with slopes greater than 5 degrees shown in red.
Porlock Bay ( **a3** ) occupies the mouth of this valley, and has been the site of an interesting recent planning decision. Until 1996, the bay was protected by a natural barrier of gravel that had been accumulating under storm conditions and moving landwards to its present position as the Flandrian sea level rose. Behind the barrier, farm land had been drained, using tidal gates along with periodic engineering work to maintain the level of the barrier. In 1996 the barrier was breached by storm waves at a time of high tide, and it has now been decided to let the farmland 'go', returning it to salt marsh. After centuries of attempting to defend the land against the seas, it is difficult to convince people that it is sensible to let some land go, particularly if they have a special interest in it.
**FIG 85.** The typical hog's-back cliff profile of the Devonian bedrock of Exmoor, looking eastwards towards Foreland Point (Fig. 81, **a5** ). (Copyright Landform Slides – Ken Gardner)
The section of the coast from the Culbone Hills ( **a4** ) to Foreland Point ( **a5** ) illustrates well the contrast between the actively eroding coast and inland areas with an older ground surface. Whereas the coastal slope is wooded and steep, descending from a line of hills some 350 m high, the other side of the hillcrest contains the sinuous and well-developed valley of the East Lyn, flowing parallel to the coast. The mature inland landscape has been transected by vigorous coastal processes of erosion (Fig. 86).
The long coastal section from Foreland Point ( **a5** ) to Combe Martin ( **a7** ), Ilfracombe and round the corner to Morte Point ( **a8** ) and Baggy Point ( **a10** ) contains classic examples of different forms of cliff profiles seen in southwest England. The 'corner' at Morte Point ( **a8** ) marks a change from bedding-parallel erosion along the north-facing coastline to the east, to erosion that cuts across the folding and layering of the bedrock to the south. This has produced the distinctive finger headlands of Morte and Baggy Points. _Hog's-back_ cliffs have small, steep cliffs near sea level that pass upwards into a distinct slope inclined at 30–40 degrees towards the sea (Fig. 87). These slopes become gentler towards their summits and may continue into an inland-facing slope, producing a convex-upward, hog's-back form. Contrasting _flat-topped_ cliffs are present at Morte Point, further west ( **a8** ), and result from horizontal or poorly layered bedrock that produces a near-vertical cliff with a flat top. _Bevelled_ cliffs appear to form when rising sea level meets terrain which already has a smooth convex-upwards slope profile.
**FIG 86.** Aerial view eastwards from Elwill Bay towards Foreland Point (Fig. 81, **a5** ), showing cliffs with south-dipping strata and hog's-back profiles. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
Lynton and Lynmouth ( **a6** ) are twin villages, with Lynton situated on the Exmoor upland some 200 m above Lynmouth, which sits at the head of the deeply incised valley of the Lyn. Lynmouth made headlines in 1952, when heavy rains on Exmoor led to a massive flood, sweeping away many houses in the valley floor and sadly killing 34 people. A similar flash flood at Boscastle (Area 2) in 2004 fortunately did not kill any people, but again illustrates the danger of flooding in the deeply incised young valleys of the northern coast of the Southwest.
The Valley of the Rocks, just west of Lynton, is a further striking example of an old, uplifted landscape under attack from active coastal erosion (Fig. 88). This 'dry valley' contains remarkable weathered Devonian sandstone outcrops, with names like Castle Rock, Rugged Jack and the Devil's Cheesewring. At its lower (western) end, the valley turns towards the sea, and is then abruptly truncated by the actively eroding coastal cliff. The valley was probably last actively evolving during the last (Devensian) cold phase of the Ice Age, before sea-level rise caused the coast to invade and remove its lower end.
**FIG 87.** Terminology used to describe different cliff profiles.
Much of the Exmoor coast consists of inaccessible cliffs with steep wooded slopes, but there is a 3 km long bay ( **a9** ) filled by Woolacombe Sand, between Morte Point ( **a8** ) and Baggy Point ( **a10** ). The bay appears to be the result of a bedrock change from the strong Hangman Grits in the north to weaker Ilfracombe Slates which have been more readily eroded by streams and coastal processes. Like Croyde Bay, just south of Baggy Point, the beach is popular with surfers since it catches the Atlantic swell waves from the west. Woolacombe Beach is backed by sand dunes which appear to cover an old wave-cut platform eroded during an earlier episode of high sea level.
**FIG 88.** The Valley of the Rocks, west of Lynton. (Copyright Landform Slides – Ken Gardner)
The raised beaches at Baggy Point ( **a10** ) and 3 km to the south at Saunton Down provide further evidence of a higher sea level in the past. They are clearly defined and run for about 4 km at a level about 15 m above today's sea. Several deposits of sands and gravels are preserved, cross-cutting the layering of the bedrock beneath. These beaches must have formed before the ice sheet of the last (Devensian) cold phase of the Ice Age reached its maximum extent (Fig. 49). Associated with these beaches is a remarkable range of boulders and pebbles from igneous and metamorphic sources much further north. The growth and decay of ice sheets along with variations in sea level provide an extraordinary range of possible episodes in which these boulders might have been transported.
#### Landscape B: The Culm (Carboniferous) bedrock area
Culm bedrock underlies the southern part of Area 3 and also the northern part of Area 2. Together these two parts form the Culm fold belt (Fig. 39), which is the Variscan downfold between the older rocks of Exmoor and the Dartmoor-Bodmin Moor uplands. The Culm rocks have not resisted landscape erosion as much as the older rocks to north and south, and so have formed a lower landscape, not exceeding 250 m above sea level. The area is rural and sparsely settled, with an economy relying predominantly upon dairy farming.
**FIG 89.** The Torridge-Taw Estuary. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
Several large rivers run through this Landscape. In the centre, the valleys of the Torridge ( **b2** ) and the Taw ( **b3** ) wind northwards from headwaters on the northern margin of Dartmoor, draining the west and northeast before emptying into Bideford Bay ( **b9** ), also sometimes called Barnstaple Bay) on the north coast (Fig. 89).
It is the rest of the drainage of this Area that is so remarkable, as has been pointed out in the introduction to this chapter. It is extraordinary that the other main rivers – the Tamar ( **b1** ) and the Exe ( **b4** ) – join the sea along the south coast, yet drain southerly even quite close to the north coast. This has been taken to suggest that the Southwest Region has been tilted southwards, causing the southerly-flowing rivers to erode their headwaters, thus extending their areas to the north.
Landscape erosion of the Variscan folds has picked out sandstone layers to form ridges and valleys, trending west to east, and this is very clearly shown on the slope map (Fig. 84). The southern coastal section of this Landscape runs from Bude ( **b5** ) to Hartland Point ( **b6** ), and is almost entirely formed of flat-topped cliffs displaying beautiful zigzag folds, clearly visible at Hartland Quay, 3 km south of the Point (Fig. 90).
**FIG 90.** Zigzag folding at Hartland Quay. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
From Hartland Point ( **b6** ) to Clovelly ( **b7** ), the coast trends parallel to the general direction of the Variscan folding, and many of the cliffs are of bevelled type. This probably reflects the way the coastline runs parallel to the Variscan fold direction, so that a less dramatic cliff is generated. Low cliffs run from Clovelly to Westward Ho! ( **b8** ), where there is an extensive wave-cut platform which must date from the last episodes of Flandrian transgression (rise in sea level). This platform provides an almost continuous cross-section through the generally steeply dipping bedrock strata which have provided valuable insights into the details of the large deltas in which the Carboniferous rivers deposited sands and muds. At low water mark along this coast, the remains of much younger trees are sometimes visible, providing striking evidence of a much more recent relative rise of sea level.
#### Landscape C: New Red Sandstone and younger bedrock
The belt of New Red Sandstone and younger sediments that skirts the older deformed Variscan bedrocks of the Southwest Region continues northwards from Area 2 into Area 3 (Fig. 37). In the discussion of Area 2, we saw that this arrangement of the New Red Sandstone marks its contact with the distinct Permian landscape of hills and valleys that formed an edge running across the Variscan mountain belt. The same is true further north in Area 3, where the Crediton ( **c1** ) and Tiverton ( **c2** ) basins represent remarkably complete relicts of this very old landscape. Further north, in the Minehead area, other valleys of this Permian landscape are visible in the present-day landscape.
The present-day landscape that has been eroded in the Permian and younger sediments is generally flatter and lower than that of the older bedrocks, because the younger rocks are relatively weak in the face of stream erosion.
The Early Tertiary Petrockstowe Basin ( **c3** ), some 7 km south of Great Torrington, formed along the Sticklepath Fault (Fig. 39) as a result of sinking movements associated with fracturing and movement along the fault. Streams carried clays into this basin, from which they have been extracted commercially, as with the Bovey Basin in Area 2.
Along the north coast for several kilometres from Minehead, southeasterly to Blue Anchor Bay, much of the actual coastline is backed by a flat platform with its upper surface 5–8 m above sea level. Low water reveals a shore of boulder-strewn sand, except in Minehead itself, where the Strand consists of relatively well-sorted sand. This reflects the way that this northeast-facing part of the coast is sheltered from the storm waves that sweep in from the west. Behind the platform, slopes rise abruptly to the main inland hills, and a number of valley mouths and isolated hills were carved during New Red Sandstone times, and perhaps as late as the early Jurassic. This ancient landscape has much more recently been filled with river sediments, which have then, in turn, been covered by seashore deposits, probably reflecting an interglacial high-stand of the sea. This interesting succession of sediments is now being overlain by younger coastal deposits formed during the recent Flandrian (postglacial) rise of sea level.
#### Landscape D: Lundy Island
I have defined a separate Landscape for this island because it is so distinctive, not only in form, but also in its location.
Lundy Island (Fig. 91) measures approximately 5 km north to south and only about 1 km in width. The highest hill top is 142 m above sea level, but the island is generally flat-topped and surrounded by steep cliffs that provide homes to many seabirds. The northern part of the island comprises desolate heathland, while the main settlement is in the southern part, where the land is divided into small fields and pastures. Most visitors are attracted to Lundy by a natural sense of curiosity, stimulated by its isolated setting.
Most of the island is granite, the same type of igneous rock as many other areas in the Southwest, but the Lundy granite was emplaced in the crust much more recently: about 65 million years ago, compared with some 300 million years ago for the other Southwest granites. The Lundy granite was intruded relatively recently into Devonian sediments that had been deformed into slates during the Variscan mountain-building episode, some of which can be seen in the southeast of the island, near to the landing beach. The Lundy granite formed as the core of a volcano, being the southernmost visible Tertiary volcanic feature in a volcanic province that included Northern Ireland and much of western Scotland. This activity is now understood to have been linked to divergent plate movements that resulted in the growth of the Atlantic Ocean and created important land movements, raising much of the west of Britain.
**FIG 91.** Lundy Island from the south. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
# [CHAPTER 5
The South Coast Region](004-toc.html#ch5)
### GENERAL INTRODUCTION
AS DESCRIBED IN the previous chapter, the Southwest Region records the history of part of the Variscan mountain belt, resulting from movements before 300 million years ago. In contrast, the South Coast Region records a younger history of episodes largely involving downward movements and the accumulation of sediment in a Southeast England Basin.
In Areas 2 and 3 of the Southwest Region (Chapter 4), the New Red Sandstone rests on and against a landscape that had been eroded in the earlier Devonian and Carboniferous bedrock. This contact is an _unconformity_ , created when an area of hills formed by erosion along the eastern fringe of the folded Variscan mountains was covered by New Red Sandstone sediments.
The East Devon and West Dorset Area (Area 4) provides valuable information about the movement between the subsiding Southeast England Basin and the uplifting crust of the Southwest. Careful tracing of layers within the basin reveals another, younger unconformity, often called the _Western Unconformity._ This has resulted from the upward movement of the New Red Sandstone, Jurassic and Early Cretaceous layers in the west, followed by an episode of erosion before they were submerged again and covered by the Upper Greensand deposits. The younger Western Unconformity therefore represents a time gap in the depositional record of the western part of the basin, equal to the time represented by the Wealden and Lower Greensand deposits that are missing here but visible further east (Fig. 94). Note how the Upper Greensand lies parallel to ( _conformable with_ ) the top of the Lower Greensand and earlier layers in the east, but cross-cuts (is _unconformable on_ ) the tilted Jurassic and New Red Sandstone layers in the west. Note also that the Jurassic, Wealden and Upper Greensand layers are thicker in the east than in the west, providing further support for the idea that eastern areas were moving downwards more than those in the west.
The oldest bedrock visible in this region occurs in the Brendon and Quantock Hills of Somerset (northwest of Taunton), which are the eastward continuation of the Exmoor hills of north Devon (Fig. 95). The bedrock here consists of Devonian sandstones and mudstones, formed during an episode when sands, muds and thin limestones accumulated in environments that varied from fresh water (rivers and alluvial flats) to brackish and salt water (shallow sea and coastal). The area was sinking during Devonian times, allowing sediment to accumulate along a broad swathe as the coastline moved progressively inland. During the convergent movements that caused the Variscan mountain building, the Devonian sediments were moved into folds and sliced by fractures, and the mudstones were cleaved to form slates.
The next bedrock episode represented is the New Red Sandstone. This was deposited after the Variscan mountains had grown as a result of the plate convergence and compression of the crust. The New Red Sandstone was deposited on and against the eroded surface of the deformed older material, as outlined in Chapter 4, and was itself the product of erosion of the higher areas of the Variscan mountains. The New Red Sandstone consists of distinct layers of sandstone, conglomerate and mudstone, and there is an overall trend towards finer-grained material in the younger layers (for example, the very fine-grained Mercia Mudstones of Triassic age). This finer material indicates a trend towards less vigorous river transport of debris as the high ground of the Variscan mountains was being carved and lowered by erosion, leading to gentler river channel gradients. Much of the New Red Sandstone was deposited by rivers and in lakes on land, though in later times the area was sometimes submerged by the sea.
Lying on top of the New Red Sandstone, the Jurassic bedrock succession in the west outcrops most dramatically along the _Jurassic Coast_ , a World Heritage Site considered in more detail in Area 4. For now, it is enough to note that the full succession represents most of the 50 million years of Jurassic time, and consists mainly of mudstones, thin limestones and some sandstones that accumulated in the seas of the Southeast England Basin. Many types of fossils have been found in these rocks, and in some localities they are extremely abundant. The Jurassic ammonites are particularly famous, and form the basis for dating this succession, while fossil vertebrates – including dinosaurs – have played an important role in the early days of geological science and are still being studied today. The layers in the Jurassic that have resulted in extensive topographic features are primarily the Bridport Sand (from the Early Jurassic) and the limestones, especially the Purbeck and Portland limestones from the very latest Jurassic.
**FIG 92.** Western half of the South Coast Region, showing Areas 4 and 5, with natural and man-made features of the landscape (above), and bedrock and other natural features (below).
**FIG 93.** Eastern half of South Coast Region, showing Areas 6 and 7, with natural and man-made features of the landscape (above), and bedrock and other natural features (below).
The Late Jurassic materials were formed in an arm of the sea that became increasingly shallow and coastal as time passed. By the Early Cretaceous, the local environments were changing and the Wealden deposits were formed in lakes that were clearly separated from the sea and were periodically invaded from the north by sand-carrying rivers. Eventually the sea invaded again from the south, and in younger Early Cretaceous times sands (later forming the Greensands) and muds accumulated in shallow coastal seas. Eventually these coastal environments became the remarkably uniform seas of the Late Cretaceous in which algal calcareous muds formed, ultimately turning into the Chalk after burial and compression by further sediments.
**FIG 94.** Sketch section showing the Western Unconformity visible in the layers across the Southeast England Basin. The zigzag lines represent the unconformities.
Above the Chalk, the succession contains a distinct time gap of about 20 million years in the record of sedimentation, during which the already deposited Jurassic and Cretaceous bedrock was subjected to crustal movements, and the pattern of sediment accumulation was interrupted. When the record starts again in Early Tertiary times, the material deposited was being formed in seas that extended only over an area now represented by the Hampshire and London basins. The succession of Tertiary layers preserved in the Hampshire Basin (located on Fig. 92) is beautifully visible in some localities, for example Alum Bay at the western end of the Isle of Wight. The succession in the Hampshire Basin spans the time from about 58 million years ago to 28 million years ago (mid Paleocene to mid Oligocene). The layers vary from about 200 to 700 m in total thickness from west to east, and the proportion of sediment that was deposited in the sea rather than on land also increases eastwards, confirming the idea that the eastern part of the Southeast England Basin was the most strongly subsiding.
**FIG 95.** Generalised bedrock succession for the South Coast region.
#### Bedrock movement, uplift and erosion by rivers
The overall geographical arrangement of the bedrock layers is largely the result of gentle folding, which took place after the Tertiary sedimentation described above. The distinctive Late Cretaceous Chalk layer acts as a clear marker for this late episode of large-scale movement (Fig. 96). From northwest to southeast the Chalk marker curves round the broad Weald uplift (or _anticline_ ), is buried by Tertiary clays in the Hampshire Basin downfold (or _syncline_ ), and arrives at the surface again at the Isle of Wight stepfold (or _monocline_ ), which extends across Areas 4 and 5. There are also other gentle fold structures in the area, and it is clear that they are the surface expression of a series of west-to-east trending faults deeper in the crust which formed after the end of Tertiary sedimentation (Figs 92 and 96). An early phase of extension or stretching, particularly in the Jurassic, appears to have generated a series of normal faults, which became inactive and were buried by continuing sediment deposition. A later phase of mid-Tertiary compression and convergence reactivated these faults but in the opposite direction, pushing the sediment layers above into gentle folds. This model of crustal deformation seems a more likely explanation of the South Coast mid-Tertiary folds than one linking them to the severe plate boundary convergence that generated the Alps and the Pyrenees many hundreds of kilometres to the south, over the same period of time.
The absence, on land, of bedrock of later Tertiary age suggests that the land surface of Southern England was uplifted at this time (beginning about 20 million years ago), allowing river and stream erosion to begin to carve the scenery. Indeed, some features of the present-day scenery are thought to date from mid-Tertiary times, and the local evidence for this is covered in detail in the Area discussions that follow.
**FIG 96.** Dorset cross-section from the northwest to the southeast, located on Figure 92. Note the Hampshire Basin and the Isle of Wight monocline.
#### Modification under Ice Age conditions
The whole of the South Coast Region lies south of the areas covered by ice sheets during the Ice Age. However, there is no doubt that surface conditions during much of the Ice Age must have been periglacial (near-glacial), similar to those of Arctic Canada and Russia at the moment. The subsoil and upper bedrock would have been permanently frozen (forming the _permafrost_ layer), while the upper layer of the soil thawed during spring and summer and froze in the winter. Weathering processes such as the freeze-thaw shattering of rocks and down-slope mass movement, due to the unfrozen top layer of soil slowly sliding over the permafrost layer, began to shape the landscape.
These Ice Age conditions also help to explain the dry valleys that are such a feature of some local scenery, particularly where Chalk forms the bedrock, for example in the North and South Downs. The dry valleys were initially carved by seasonal water flow and slope movement when the ground was frozen at depth, preventing the water from seeping away into the usually permeable Chalk. When the Ice Age ended, the disappearance of the permafrost layer allowed water to percolate down through fractures in the bedrock, leaving the valley floors dry. Some Chalk streams today are _winter-borne_ , only flowing when the water in the Chalk is at a high level, and then becoming dry in the summer and autumn.
#### Coastal shape and location
The spectacular 100 km long coastline is the defining feature of this South Coast Region. As outlined in Chapter 2, worldwide sea level was around 120 m lower than at present only 18,000 years ago, and has been at or near its current level for only 5,000 years, at the most (Fig. 20). This means that the impressive coastal features that can be examined along the South Coast today have formed within a very short space of time, though some of them almost certainly involve relicts of earlier scenic features created by previous high sea levels (for example during the Ipswichian, 130,000 years ago; Fig. 13).
The overall east-west trend of the coastline is parallel to the folding that formed during the mid Tertiary (see above). This is particularly so in the west, where these folds have locally controlled the arrangement of the resistant Jurassic limestones and the Late Cretaceous Chalk to produce spectacular, narrow headlands that dominate the scenery. In the east of the Region, the coastline of Areas 6 and 7 swings northwards and cross-cuts the mid-Tertiary folds, which themselves curve to the southeast and link up with similar folds in the bedrock of northern France. This northwards curve of the coastline was produced during low-sea-level conditions when a river flowed where the English Channel is now, carving a wide valley through the bedrock structures. At the end of the Ice Age cold episodes, the sea flooded this valley to create the English Channel (Fig. 21).
Another feature of the present coastline that strongly influences its local shape is the presence of large accumulations of gravel in the form of active gravel spits. Examples of these are Chesil Beach, Hurst Spit (5 km south of Lymington) and Dungeness. In all these cases, the gravel accumulations appear to have been transported into this area by powerful rivers during Ice Age times, and are now being reworked and reshaped by modern-day wave action.
### AREA 4: EAST DEVON, SOMERSET AND DORSET
This area (Figs 97 and 98) includes most of the Jurassic Coast, a stretch of the coastline that became a World Heritage Site in 2001. This coast holds a special place in the history of geological discovery, providing a beautifully varied and colourful range of bedrocks that cover some 250 million years of the Earth's history. It is famous for Jurassic fossil collecting and also provides a laboratory for studying coastal erosion, land-slipping and sedimentation processes, as well as for exploring the natural history of the coastal zone. Oil-producing rocks are also visible along the coast and oil is currently being extracted from parts of southeast Dorset (at Wytch Farm – see Area 5).
**FIG 97.** Location map for Area 4.
**FIG 98.** Natural and man-made features of Area 4.
As well as most of Dorset, Area 4 includes parts of Devon, Somerset and Wiltshire. It is a topographically complex Area with many different landscapes (Fig. 99). I have divided the area into nine Landscapes, labelled **A** to **I** , simplifying the Countryside Agency's character area scheme (Fig. 100).
#### Landscape A: The Brendon and Quantock Hills, Vale of Taunton and East Devon Redlands
The Vale of Taunton and Quantock Fringes consist generally of low-lying, flat farmland that extends to the north coast of Somerset in Area 8, and separates the upland areas of the Brendon and Quantock Hills. The Brendon hills ( **a1** ) are a continuation of the North Devon hills, while the Quantock hills ( **a2** ) form a high ridge covered by well-drained heathland, giving breathtaking views across to Exmoor in the west and the Blackdown Hills to the south in Landscape C. The hills here owe their height to the resistance to weathering and river erosion offered by their Devonian bedrock, in clear contrast to the surrounding lowlands that are underlain by the easily eroded Mercia Mudstone (part of the New Red Sandstone). Further west, however, the New Red Sandstone bedrock also contains sandstones, pebble beds and breccias that have resisted erosion more successfully and formed hills. The presence of these coarser-grained sediments represents the more vigorous erosion and transport that occurred in early New Red Sandstone times along the fringes of the Variscan mountains.
**FIG 99.** Area 4, showing river pathways, coastal flooding zone, Landscapes **A** to **I** and localities ( **a1, a2** etc.) mentioned in the text.
North of the Tone valley, the Brendon Hills are separated from the Quantock Hills by a distinct valley, occupied by the Taunton to Minehead road and the West Somerset railway line. The bedrock in this valley is again New Red Sandstone, and its detailed mapping shows that the layers have been much cut by faulting since they were first deposited. The southwestern edge of the Quantock Hills is straight, steep and often reaches 200 m in height above the valley floor (Fig. 99). This edge may be an eroded fault scarp, but it could also be an ancient topographic feature, perhaps a slope dating from New Red Sandstone times that was excavated again during the Tertiary.
**FIG 100.** Geology and hillshade map of Area 4, with Landscapes marked.
The New Red Sandstone extends down the western edge of Area 4 and continues into Areas 2 and 3 (Fig. 100). The most characteristic features of the East Devon Redlands are the red soils and buildings, both of which have been made from the New Red Sandstone. The bedrock is largely Mercia Mudstone, but there are earlier Triassic sandstones and coarser pebble beds in the west, because the Triassic rivers tended to deposit their coarsest material closest to their sources in the hills of the Southwest Region.
The Redlands extend down the valleys of the Exe and the Otter, which drain to the south coast. Beautiful cliffs of gently eastward-sloping red sediments of Triassic age are striking features of this part of the coastal scenery, particularly between Ladram Bay ( **a3** ) with its sea stacks and Peak Hill ( **a4** ). These Triassic sediments can be seen in Figure 101.
**FIG 101.** Looking northeastwards across Ladram Bay (Fig. 99, **a3** ) towards Sidmouth, showing the gently sloping layers of Triassic age in the New Red Sandstone. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
To the west of Budleigh Salterton ( **a5** ) are cliff exposures, including the Budleigh Salterton Pebble Beds, which are evidence for a Triassic episode of transport of unusually coarse-grained gravels in very vigorous floods. The material forming many of these pebbles seems to have been carried by the rivers from source areas similar to those presently exposed in Brittany in northwest France, which were also part of the Variscan mountain belt.
#### Landscape B: The Somerset Levels and Moors and the Mid-Somerset Hills
The Somerset Levels and Moors are low and very flat fingers of land that extend southeastwards from the coast of the Bristol Channel. Although the whole area is commonly known as the Somerset Levels, more precisely the Levels are the coastal areas underlain by clay, while the inland peat areas are called the Moors. Low ridges and isolated hills of higher ground, such as the Polden Hills ( **b1** ) and Glastonbury Tor ( **b2** ), extend into the Levels. Further north, Landscape B extends into Area 8 in the direction of the Mendip hills.
Before the concerted drainage efforts of the eighteenth and nineteenth centuries, the Levels and Moors were wetland areas frequently flooded by the rivers or the sea. Drainage and agriculture created today's characteristic Somerset Levels landscape: flat straight-sided fields of lush pasture, bounded by artificial streams (called _rhynes_ ), willows and occasional poplar trees. The rhynes augment the natural drainage provided by the rivers Parrett and Brue.
The bedrock of this Landscape varies considerably. The hills and ridges of higher ground are formed mainly of Triassic and Jurassic clays and limestones that have resisted erosion by the ancestors of the present-day rivers and streams. Much younger sediment has accumulated in the lower ground, particularly during the later stages of the Flandrian transgression that followed the last cold episode of the Ice Age. In the inland areas, the clay is buried under a surface blanket of peat, the youngest sediment in the region, which formed between 7,000 and 2,000 years ago.
The low but often distinctive Mid-Somerset Hills are due to the resistance to erosion offered by thin limestones in the lowermost part of the Blue Lias, which forms the oldest layer of Jurassic bedrock. The sharpness of the toes of the slopes just above the flat ground of the Levels suggests that the hills may have been eroded not only during the Flandrian sea level rise, but also during the earlier (Ipswichian) high-stand of the sea, about 130,000 years ago.
Glastonbury Tor ( **b2** ) and the Pennard Hills ( **b3** ) are very clearly defined features of the Mid-Somerset Hills, both of which have been eroded from layers within the Early Jurassic Lias group. The distinctively shaped Tor of Glastonbury is capped by Bridport/Yeovil Sand and owes its well-defined form to the resistance of this material to erosion (Fig. 102). The lower slopes of Glastonbury Tor and most of the Pennard Hills are composed of earlier Jurassic silts that also appear to have resisted erosion more than the surrounding mudstones. One possible explanation for this is that mineralisation from hot water migrating up faults has strengthened the surrounding bedrock: the Pennard Hills, Glastonbury Tor and Brent Knoll (in Area 8) are all associated with northeast-southwest trending faults.
**FIG 102.** Glastonbury Tor (Fig. 99, **b2** ) and some of the Somerset Levels. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
#### Landscape C: The Blackdown Hills and Sidmouth to Lyme Bay
This Landscape consists of flat-topped hills dissected by numerous valleys, extending from the Blackdown Hills ( **c7** ) on the Devon-Somerset border to Sidmouth and Lyme Regis ( **c6** ) on the Jurassic Coast.
The extensive flat caps of these hills are made of a resistant sheet of Early Cretaceous Gault (marine silts and clays) and Upper Greensand (marine sands and silica-rich, flint-like cherts), and the geological map shows that every ridge is underlain by a finger of this bedrock. In the general introduction to this chapter I described the Western Unconformity that forms the western edge of the Southeast England Basin (Fig. 94). The resistant cover of Early Cretaceous sediments forms the upper cap of this unconformity.
**FIG 103.** Looking northeastwards over Lyme Regis, with Golden Cap in the right background (Fig. 99, **c6** ). (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
Locally, the Early Cretaceous layer is covered by patches of Late Cretaceous Chalk, and there is also often a widespread soil cover known as _Clay-with-flints._ This is interpreted as an ancient (possibly early Tertiary) weathering product, involving solution of the underlying Chalk bedrock to yield a concentrate of less soluble flint and chert materials.
The surface of the Western Unconformity is visible in this Landscape over an area approximately 30 km by 30 km, and it slopes very gently to the southeast, from an elevation of 230 m inland to just 70 m around Lyme Regis (Fig. 103). As the unconformity was originally formed by erosion at sea level about 100 million years ago, it provides an indication of land movements since that time, relative to present-day sea level. The net uplift of ≈250 m inland and ≈100 m around present-day Lyme Regis may have included several downward movements, but it is unlikely that any significant horizontal movement has taken place.
The coastline of this Landscape is famous for its spectacular cliffs and abundant fossils. From Sidmouth to Beer Head ( **c1** ), red Triassic sandstones are capped by Cretaceous Upper Greensand that slopes gently eastwards, occupying more and more of the coastal cliff face. About 1.5 km west of Beer Head the base of the Cretaceous bedrock passes below sea level and the New Red Sandstone disappears from view, until it is brought back to the surface by a north-trending fault at Seaton Bay. The Late Cretaceous Chalk is also present in the upper parts of the cliffs in this area, forming spectacular near-horizontal layers picked out by flints. The flints have been used as building materials in Beer along with a distinctive form of Chalk known as 'Beer Stone', which was quarried in a remarkable system of caves and tunnels.
From Seaton ( **c2** ) to Charmouth ( **c3** ), the coastal hill plateau consists largely of Cretaceous bedrock, showing up as a yellow cap in the distance on the right of Figure 104 and resting upon gently sloping layers of New Red Sandstone and Jurassic materials. Because much of this older material is made of mudstone, which tends to slip when wet, there are numerous examples of land-slipping in this area. The Bindon landslide of 1839 attracted widespread contemporary interest, and movements at Goat Island and Black Ven in 1995 have greatly changed the look of the coastline.
Whereas the New Red Sandstone formed in river and lake environments and generally lacks fossils, the Lias of the Early Jurassic is marine and contains abundant fossils that can be seen in the museums and fossil shops of Lyme Regis and Charmouth. Ammonites are among the commonest of these fossils, but marine reptiles such as plesiosaurs and ichthyosaurs are probably the most famous.
**FIG 104.** Black Ven landslip with Charmouth (Fig. 99, **c3** ) in the foreground, and Lyme Regis ( **c6** ) beyond. (Copyright Landform Slides – Ken Gardner)
The Marshwood ( **c4** ) and Powerstock ( **c5** ) vales are drained southwards by the Char and Brit rivers and are surrounded by typical flat-topped hills and ridges capped by Cretaceous Upper Greensand, as in the Blackdowns. Gentle folding in this area has elevated the rocks into a dome structure (called a _pericline_ ), bringing soft Jurassic mudstones to the surface in the centre of the dome and leaving younger, less easily eroded Cretaceous sediments around the edges. Erosion has had the greatest impact on the mudstones, so flat and low-lying topography has formed within the vales, which are surrounded by ridges and hills made of the tougher Cretaceous sediments.
Golden Cap, 6 km east of Lyme Regis, is the highest cliff on the South Coast and owes its name to the yellow colour of the Upper Greensand that forms its crest. The permeable Greensand sits on top of impermeable Gault and Lias clays, and landslides are therefore common along this stretch of coastline. Rainwater percolates readily through the Greensand but cannot penetrate the clays so easily, resulting in a build-up of fluid pressure at the interface between the two layers. This pressure works to destabilise the cliff face and, combined with erosion of the cliff base by waves, can result in large and dangerous landslides as the Greensand slides over the underlying Jurassic clays.
#### Landscape D: The Yeovil Scarplands
The northward-draining Yeovil Scarplands are underlain entirely by bedrock of Jurassic age, so the pattern of hills and valleys is not easily explained by the simplified geological map in Figure 100. Moreover, the Jurassic bedrock here is extremely variable, not only between its layers but also within a single layer, from one place to the next. Discrete layers of resistant sandstones and limestones, picked out by erosion in one area, often die out laterally to be replaced by more recessive mudstones and clays. The diversity of the Jurassic rocks is due to highly variable local environments in Jurassic times, when the sediments were accumulating. For example, the Ham Hill Stone is a famous calcareous building stone much used in Dorset, but it is only found at a small number of locations, such as at Ham Hill ( **d1** ). This is because the stone originally formed in a ≈5 km wide Jurassic tidal channel, bounded on either side by islands of less calcareous Bridport/Yeovil sand.
Another reason why the pattern of hills and valleys in this Landscape is unclear is that the bedrock has been cut by large numbers of faults that were active after the Jurassic sediments had been deposited. It is difficult to see any simple pattern in the fault directions: groups of faults trend roughly north-south, but east-west faults are also important. The faults influence the scenery because they sometimes juxtapose very different bedrock materials at the surface, and these differences are quickly picked out by erosion to form a complex landscape.
Despite the complexity of much of this Landscape, some of the most spectacular scenery is easily understood. For example, the local topography of north Dorset is due to the presence of particular layers in the bedrock that have resisted erosion, such as the Blue Lias limestones, the Bridport/Yeovil Sands and the Inferior Oolite. In contrast to the Cotswold Hills to the north, many of the other Middle Jurassic layers that produce striking topography are much less important or absent in this Landscape.
#### Landscape E: Blackmoor Vale and the Vale of Wardour
This Landscape also does not define itself easily in terms of its pattern of hills and valleys. It occupies the area of hills and vales between the main northward-draining catchment of the Parrett and Brue (Landscapes **B** and **D** ) and the Chalk Downs (Landscape **F** ) to the south (Fig. 99). The Landscape drains largely southeastwards via the River Stour, breaking through the main Chalk rim near Blandford Forum ( **f1** ). The Vale of Wardour ( **e1** ) lies between the Wiltshire Downs and Cranborne Chase, while Blackmoor Vale ( **e2** ) is largely defined by the catchment of the River Stour before it enters the Dorset Chalk. The landscape is of typical 'wooded clay vale' with rich pastureland underlain by soft Jurassic clays, similar to Marshwood Vale ( **c4** ), described on page 137.
Although the topography of the area is complex (Fig. 105), the map pattern of the bedrock geology and its effects on the local scenery are easier to understand. In the Vale of Wardour ( **e1** ), detailed mapping of the bedrock has revealed that the margins of the Vale are bounded by high ground underlain by Upper Greensand and Chalk, forming the Wiltshire Downs to the north and Cranborne Chase to the south (Fig. 106). The low ground of the Vale of Wardour is underlain by Jurassic clays, and this has made it the natural route for railways and roads: the main southerly railway loop between London and Exeter and the main A30 Salisbury-Yeovil road both run through the Vale.
More detailed examination of the Vale of Wardour bedrock allows the reconstruction of a scenically important sequence of events. Firstly, a variety of bedrock layers was deposited during the Middle and Late Jurassic, including the Portlandian limestones, which are resistant enough to produce slopes today in the east of the Area. The deposition of these layers was followed by a general stretching of the crust across the whole South Coast Region, resulting in normal faulting and mild folding of the bedrock layers. The rocks were then subject to erosion as the sea flooded the Region, followed by the deposition in the Cretaceous of the Gault clays, the Greensand and the Chalk. In mid-Tertiary times the crust of the area was deformed under horizontal compression to produce reverse faulting and some localised folding in the fault zones. The uplift associated with this compression exposed the surface rocks to erosion, removing the Early Tertiary deposits from everywhere except the Hampshire Basin. The northern edge of the Vale of Wardour also formed at this time.
**FIG 105.** Vale of Wardour slope (greater than 3 degrees) and hillshade map. Located on Figure 100.
**FIG 106.** Cross-section through the Wiltshire Downs, Vale of Wardour and Dorset Downs, showing both normal and reverse faulting. Located on Figure 105.
Erosion of the land surface has continued since, and more resistant levels in the bedrock have been picked out while valley slopes have formed as sediment is transported down the streams and rivers. One of the layers that has been picked out during this ongoing erosion process is the Chilmark Stone, a well-known building material used in the construction of Salisbury Cathedral. It was quarried from the Chilmark Oolite, a unit of the Portland Limestone Formation brought to the surface by compression and subsequent erosion in the Vale of Wardour.
To the west of the Vale of Wardour is the area round Sherborne and Blackmoor Vale. Here the scenery of hills and valleys reflects the presence of various resistant layers of the Middle and Late Jurassic, particularly the limestones of the Corallian, Forest Marble, Inferior Oolite and Fuller's Earth Rock, and the sandstones of the Yeovil Formation. The pattern is complicated, partly by the lack of continuity of some of these resistant layers (reflecting lateral changes in Jurassic environments of deposition), but also due to local faulting (Figs 105 and 106).
#### Landscape F: The Wiltshire and Dorset Downs and Cranborne Chase
In the north of Area 4, this Chalk landscape includes part of the Wiltshire Downs ( **f2** ), forming the northern margin of the Vale of Wardour. Compared with the large area of Chalk Downs that makes up Salisbury Plain further to the northeast (see Area 10), these Chalk hills are high and deeply dissected, particularly along the indented western margin of the Chalk, where Brimsdown Hill ( **f3** ) reaches 284 m in elevation. Large valleys here generally tend to have a valley floor consisting of mass-flow deposits, called head, and river deposits, called _alluvium_ , which usually consist of mass-flow deposits that have been eroded, locally transported and deposited by streams.
More centrally within Area 4, the Dorset Downs ( **f4** ) are the westernmost chalk uplands in England. They form the northern and western edges of the Hampshire Basin, which extends towards the east across Areas 5 and 6. The Chalk layer slopes gently southeastwards from the escarpments around the northern and western edges of the basin towards its centre, which is filled by sediments of early Tertiary age (see Landscape **G** ). Although Chalk slopes also bound the southern edge of the basin, they are much narrower because the Chalk layer here dips much more steeply. In fact, it is almost vertical in some localities, for example the narrow Chalk ridge of the Purbeck Hills (see Landscape **I** ). This difference between the northern and southern structures is due to the mid-Tertiary compressional movements discussed above.
**FIG 107.** Slope (greater than 3 degrees) and hillshade map of the Hampshire Basin. Located on Figure 100.
The Dorset Downs are a classic area for studying features of Chalk scenery. The typical rolling, grass-covered tops and the steep-sided valleys, sometimes with flat bottoms, show up beautifully on the slope map in Figure 107. Many small valleys and hollows in the faces of the Chalk hills are dry, having been formed by slope failure and stream flow during the Ice Age when the subsurface was frozen (see the general introduction to this chapter for more detail).
The present drainage of this Landscape takes place to the east and south, towards the centre of the Hampshire Basin. Major rivers are the Frome, through Dorchester, and the Stour, which cuts through the Downs at Blandford Forum ( **f1** ).
#### Landscape G: The Dorset Heaths
This Landscape, lying between the Dorset Downs and the Purbeck Chalk ridge, is underlain by flat-lying bedrock of Early Tertiary age. This bedrock occurs in a shallow basin centred on Poole Harbour that also contains the large conurbation of Poole and Bournemouth (see Area 5).
Although there are layers in the Early Tertiary succession that are assigned to the London Clay, other layers below and above this are more prominent and much richer in sand. This gives rise to the widespread acid-soil heathland with a vegetation cover of heather, bracken and gorse, though much of this habitat has now been converted to farmland or conifer woodland. The hills and slopes of the area are low and poorly defined, sometimes marking sandy layers in the Early Tertiary bedrock. There are also patches of gravel and alluvial terraces forming a surface blanket, representing episodes in the much younger Quaternary development of the landscape.
#### Landscape H: The Weymouth Lowlands and the Isle of Portland
The Weymouth Lowlands stretch along the coast from Burton Bradstock ( **h1** ) to Weymouth, bounded to the north by the Chalk ridge that forms the edge of the Dorset Downs. The bedrock of the area is Jurassic in age and consists of east-west trending limestone ridges interspersed with clay vales.
The Weymouth Lowlands have been eroded downwards to reveal a very broad upward fold in the bedrock – the Weymouth Anticline – which has an east-west trending axis and gentle slopes, steepest in the north where the slope reaches 10 degrees. The oldest layers, exposed by erosion in the central part of the anticline, are of Middle Jurassic age, but a full succession of younger Jurassic strata is also visible. Many faults have been discovered in these strata by drilling and seismic work aimed at the detailed exploration of possible oil-bearing reservoirs. Most of the faults are normal faults, suggesting that they formed during a period of extension or stretching of the crust, though the gentle folding of the Weymouth Anticline implies a later period of crustal compression. Some 5 km east of Weymouth, a tighter upfold (the Poxwell Anticline) runs east to west, parallel to but inland from the coast, and contains Early and Late Cretaceous layers to both north and south. Inclinations of up to 65 degrees have been measured on the very steep north slope of this fold, contrasting with the gentle southern slope, which confirms that the overturning movement during this late compressional phase was in the same northward direction as occurred in other late movements in this area.
The Isle of Portland ( **h3** ) is a limestone plateau which slopes southwards, from high northern cliffs to barely 10 m above the sea. This slope and the layers visible in the northern cliffs of Portland are part of the southern limb of the Weymouth Anticline. The Isle is famous for its bedrock, the Portland Stone, a shelly, often oolitic, limestone that has been widely used as an ornamental stone in important British building projects such as St Paul's Cathedral in London. The Portland Stone has been quarried since Roman times and the Isle is extensively scarred by old quarries and spoil heaps.
**FIG 108.** Looking southeastwards along Chesil Beach (Fig. 99, **h2** ) to the Isle of Portland ( **h3** ). (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
The Isle of Portland is connected to the mainland by Chesil Beach ( **h2** ), a remarkable coastal feature (Fig. 108). It is a coast-parallel gravel barrier some 28 km long, and for most of its length it is separated from the mainland by the tidal lagoon known as the Fleet. The pebbles are roughly pea-sized at the northwestern end of the beach at West Bay, and potato-sized at the Portland end. The larger pebbles are thought to be transported the longest distances along the beach because of the impact of the prevailing storm waves on their larger surface area. Local folklore has it that smugglers could tell exactly where along the beach they had landed just by looking at the size of the pebbles.
Chesil Beach is one of several large gravel landforms that occur along the South Coast. During the last (Ipswichian) interglacial, about 125,000 years ago, sea level was slightly higher than now, and the coastal slope was eroded by storms and landslips just as today. During the subsequent cold phases of the Ice Age, the former coastal debris would have been spread widely by river action over the areas now covered by the sea, and was then transported inland again by the rising sea during the most recent (Flandrian) sea-level rise. Chesil Beach was formed about 10,000 years ago, but is constantly being reshaped by the waves. It seems that the beach is currently moving inland over the tidal muds of the Fleet, as its outer face often reveals peats that appear to have formed in the Fleet and then been over-run by the gravel ridge migrating landwards.
#### Landscape I: South Purbeck
This Landscape consists of a narrow strip of coastline, never more than 7 km wide, running along the coast from Lulworth ( **i1** ) to Swanage on the Isle of Purbeck. The area is defined topographically by the dramatic, west-to-east trending stepfold (or _monocline_ ) in the bedrock. To the north, the stepfold is expressed at the surface by steeply dipping Chalk and older layers immediately south of the Dorset Heaths (see Landscape **G** ). Typically, the Chalk has resisted erosion to form a narrow ridge known as the Purbeck Hills ( **i2** ), running inland from just north of Swanage and crossing the Isle of Purbeck before reaching the coast again at Lulworth. East of Lulworth ( **i1** ) and south of the Chalk, the layers at the surface span the full local succession from Early Cretaceous to Late Jurassic, though they are flat-lying by the time the south coast is reached.
**FIG 109.** Cross-section running north-south through St Alban's Head (Fig. 99, **i4** ), South Purbeck.
The Purbeck Ridge is breached by the northward-draining Corfe River, which flows into Poole Harbour. Corfe Castle and its small town have grown in this breach, which acts as the gateway to the low-lying Corfe Vale, underlain by Early Cretaceous Wealden sandstones and mudstones. To the south of this is a plateau, carved at an elevation of 120–140 m above sea level, and underlain by Late Jurassic Kimmeridge Clay and limestones and mudstones of the Portland and Purbeck groups. The Portland Stone Formation is particularly resistant to weathering, and its historic importance as a building stone is shown by the remarkable number of abandoned quarries on this plateau.
**FIG 110.** Looking westwards along the coast towards the Isle of Portland. Lulworth Cove (Fig. 99, **i1** ) is in the foreground. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
**FIG 111.** Durdle Door, 2 km west of Lulworth Cove (Fig. 99, **i1** ). (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
The structure of the Isle of Purbeck area is well illustrated by a cross-section through St Alban's Head ( **i4** ), as shown in Figure 109. Further west, Lulworth Cove ( **i1** ) is one of the most famous features of this stretch of coast, demonstrating the control of the coastal geometry by the folding of the bedrock (Fig. 110). The outer coastal wall of the Cove is formed by steeply layered, erosion-resistant Portland limestone, which has been breached by wave action during storms. The breach probably first occurred at the mouth of a former stream flowing into the sea where the entrance to the Cove is now, allowing waves to erode the softer sediments behind the limestone barrier. The Cove was then excavated in relatively weak Wealden mudstone, and has now cut back far enough to expose the tougher Late Cretaceous Chalk as a steep-sided cliff at the back of the bay. The remarkably regular, circular form of the Cove seems to be a response to the diffraction (or bending) of the crests of storm waves as they enter the mouth of the Cove, fanning out and causing longshore transport of the available debris.
**FIG 112.** Cliffs at Kimmeridge Bay (Fig. 99, **i3** ) showing the typical bedrock layering, often cut by faults. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
Just west of Lulworth Cove, Stair Hole displays a beautiful example of a small fold called the Lulworth Crumple.
About 2 km west of Lulworth Cove is Durdle Door, another famous feature of the Jurassic Coast. In this case, a steeply sloping limb of the Purbeck Stepfold (or _monocline_ – Fig. 109) is exposed in the Portland Stone, where it has been eroded into a spectacular doorframe-like arch.
Just east of Lulworth Cove is a famous locality where a 'fossil forest' may be seen. It is on the coastal footpath just within the boundary of a large military firing range, so access is not permitted at certain times. Tree trunks of large conifers and ferns that flourished in the Late Jurassic were preserved here when the Jurassic sea level rose and the trunks became surrounded by mats of primitive plant material, preventing their decay.
The steep bedrock layers of Chalk and limestone that cause the spectacular scenery of Durdle Door and Lulworth Cove continue eastwards along the coast, before striking inland to form the Purbeck hills. Along the coast, they are replaced by increasingly flat-lying layers of clay and limestone. Land-slipping is common in this area, where the cliffs have permeable, resistant tops overlying soft, easily eroded Kimmeridge Clay.
Kimmeridge Bay ( **i3** ; Fig. 112) is much visited by scientists. This is partly because its name has been adopted for one of the worldwide subdivisions of Jurassic time, but it is also of interest because it is the original locality that gave its name to the Kimmeridge Clay, a layer that provides a high proportion of the oil wealth of the North Sea. The grey mudstones exposed in Kimmeridge Bay are rich in fine-grained organic material generally referred to as _kerogen_. If this material has been buried deeply enough, and subjected to high temperatures, for long enough, the kerogen becomes altered, releasing oil that can migrate along and through any permeable layers in the bedrock. The oil can either seep out at the surface or become trapped by folds, faults or loss of permeability to form a natural reservoir, which may then be exploited as an oil field. The contribution of the Late Jurassic Kimmeridge Clay to the economy of Britain has been enormous.
### AREA 5: HAMPSHIRE AND THE ISLE OF WIGHT
This area includes the striking coastal scenery of the Isle of Wight, as well as the seaside cities of Bournemouth and Portsmouth. Southampton sits in the centre of the area within the low-lying Hampshire Basin, while to the north Salisbury and Winchester lie within Chalk hills (Figs 113 and 114).
The bedrock succession of this Area records a variety of episodes starting in the Late Jurassic, through the Cretaceous and into the early Tertiary, representing 150 million years of Earth history. Although the total thickness of the bedrock layers shown in Figure 115 is around 2 km, this figure is misleading because it does not represent subsidence of the Earth's surface by this amount at any one place. In fact, some of the layers (e.g. the Early Cretaceous Wealden and the Tertiary) accumulated in certain parts of the Area while crustal movements uplifted other parts, causing them to be eroded and to supply- rather than receive – sediment. A general review of the changing environments of sedimentation for the whole Region is included in the general introduction to this chapter.
**FIG 113.** Location map for Area 5.
**FIG 114.** Natural and man-made features of Area 5.
The pattern of the Late Cretaceous Chalk on the geological map (Fig. 116) provides a useful marker in this Area, as it does for most of Southern England. It records well the broad movement pattern that developed after the main bedrock succession had formed, and explains the distribution of hills and downs on the one hand, and basins on the other. The large northern areas of Chalk that form Salisbury Plain, the Hampshire Downs and the South Downs are replaced southwards by the Early Tertiary sediments that fill the Hampshire Basin. South of these sediments, the Chalk reappears at the surface in the Portsdown Ridge, and in the northward-facing stepfold (monocline) that extends across the Isle of Wight and South Purbeck (Figs 116 and 117).
As Figure 116 shows, I have divided this Area into seven Landscapes ( **A** to **G** ), which are treated separately below.
**FIG 115.** Generalised bedrock succession for Area 5.
**FIG 116.** Geology and hillshade map of Area 5, showing Landscapes **A** to **G** and localities ( **a1, a2** etc.) mentioned in the text.
#### Landscape A: The Isle of Purbeck
A description of the westward continuation of this Landscape is given in Area 4. Here it is enough to note that, as in Area 4, the Isle of Purbeck is defined by two distinctive ridges. The northernmost of these is the Chalk ridge north of Swanage, which has been formed by the erosion of the stepfold that also runs through the Isle of Wight (Fig. 117). Figure 118 shows the cliffs around Old Harry ( **a1** ), where the near-horizontal Chalk has been eroded by storm waves to create numerous small bays. The remarkable feature of this erosion is the way that the waves swing round to attack both sides of the main headland, resulting in well-defined, almost parallel-sided 'bites' in the cliff line. The southernmost distinctive ridge is formed by the Late Jurassic/Early Cretaceous Portland and Purbeck limestones, which form a high plateau ( **a2** ) south of Swanage. Jurassic Kimmeridge Clay forms the base of the cliffs along the south coast of Purbeck, and its preferential erosion by storms has undermined the cliffs in many places, causing frequent land-slipping (Fig. 119). Swanage itself lies in the low ground of the Corfe Valley, on soft Wealden mudrock.
**FIG 117.** Oblique block view of the crustal geology, starting 10 km west of the eastern edge of Area 5 and looking westwards.
The cross-section in Area 4 (Fig. 109), a few kilometres west of the boundary with Area 5, is relevant to this area, since the same bedrock pattern continues eastwards through this Landscape. The Triassic, Jurassic and Early Cretaceous layers in this section have been cut by a number of normal faults, indicating stretching movement of the crust in a north-south direction, linked to subsidence and increasing amounts of sediment accumulation to the south. This contrasts with the folding and faulting that is visible in the Purbeck Stepfold or Monocline, with reverse faulting that indicates convergence of the crust and increased sedimentation to the north in mid-Tertiary times. The same patterns, involving two distinct phases of movement, are also visible where the stepfold crosses the Isle of Wight.
**FIG 118.** Looking southwestwards across the eastern Isle of Purbeck. Note the embay-ments and sea stacks cut into the Chalk, including Old Harry and Old Harry's wife (Fig. 116, **a1** ). (Copyright reserved Cambridge University Collection of Air Photographs)
**FIG 119.** Looking eastwards over Dancing Ledge, South Purbeck. (Copyright Dae Sasitorn & Adrian Warren/ www.lastrefuge.co.uk)
#### Landscape B: The Isle of Wight
The variety of landscapes and relative ease of access have added greatly to the popularity of the Isle of Wight. The mild climate and long hours of summer sunshine have brought large numbers of tourists to the island since Victorian times.
The landscapes here range from the lush pastures and creeks of the north, particularly in the area west of Cowes ( **b3** ), across the windswept downs and cliffs of the central belt, to the open fields and wooded 'chines' (narrow, deep ravines) of the south. All these features have formed during the long history of erosion of the underlying bedrock geology. The most dramatic geological structure is the spectacular, northward-facing stepfold in the Chalk known as the Isle of Wight Monocline, running east-west through the centre of the island (Fig. 117). The steep layers of the Chalk form the Needles ( **b1** ) at the western end of the island and extend eastwards across the island as a high ridge, although the steeply-dipping layers temporarily flatten out near Newport, where another fold crosses the stepfold. Culver Cliff ( **b4** ) marks the eastern end of the Chalk ridge.
**FIG 120.** The Needles (Fig. 116, **b1** ) and Alum Bay, western Isle of Wight. (Copyright reserved Cambridge University Collection of Air Photographs)
North of the central belt and its stepfold, the Isle of Wight is underlain by soft-weathering early Tertiary materials that have been dissected by local stream and river erosion. The multicoloured cliffs of Alum Bay (Fig. 120) are formed of steeply tilted (locally vertical) early Tertiary sediments that have been folded along with the Chalk. The colours of the sandstones and mudstones in the cliffs are exceptionally bright and varied, and collections of multicoloured sand samples in transparent tubes are carried home from Alum Bay by holidaying families every year. White sands are made of pure quartz, whose grains lack the thin coating of iron oxide that colours the Bay's red to yellow sands. Green sands have been coloured by the iron-bearing mineral _glauconite_ , preserved when reducing conditions are generated by organic material in the sediment. Dark layers of _lignite_ (a coal-like material) were formed by the burial of ancient vegetation. These striking bands of colour were formed during deposition, when the layers were in their original near-horizontal orientation, before they were tilted to near-vertical by folding and faulting as the stepfold was created.
South of the Isle of Wight central belt, the bedrock consists of Early Cretaceous Wealden strata, which form the core of the southern Isle of Wight Anticline or upfold. The elevated area near the south coast is a remnant of Chalk grassland lying above the Wealden. The southern face of the coast ( **b2** ), between St Catherine's Point and Dunnose, has cliffs that tower above terraces stepping down to the shore. This coastal strip is one of the largest areas of land-slipping in western Europe, because overlying materials have slipped down the coastal slopes created by storm erosion, lubricated by underlying muddy layers after prolonged periods of rain.
#### Landscape C: The Dorset Heaths
This Landscape passes westwards into Landscape **G** of Area 4. In Area 5, it is covered largely by Poole Harbour and the City of Bournemouth, so its typical heath landscape is only developed over rather small areas, where the Early Tertiary sandstones produce acid-soil vegetation. Although the landscape here is very subdued, there are small hilly features created by erosion of the varying materials in the bedrock, or by unsteady erosion of the rivers Stour, Avon and their tributaries. In fact, the southern part of this Landscape is covered with many levels of unconsolidated surface materials, consisting mainly of gravels brought down by ancestral versions of the rivers draining the Chalk terrain to the north.
Just on the western edge of Area 5, below this young spread of Early Tertiary and Quaternary sediment, is the Wytch Farm oil field ( **c1** ), the largest oil field in Europe that has been drilled from land. The field was developed by BP and taps porous New Red Sandstones of Triassic age which have been tilted and faulted into a valuable reservoir pattern. The oil itself appears to have come from Jurassic source sediments.
#### Landscape D: The New Forest
The New Forest became the newest National Park in Britain when an official Park Authority was designated in April 2005. It occupies the distinctive part of the Hampshire Basin between the Hampshire Avon to the west and Southampton Water and the River Test to the east.
The New Forest has had special status for over 1,000 years, initially as a royal hunting ground. The grazing and hunting of deer were particularly favoured by the balance of open and mixed woodland cover, resulting from the generally acid soils that have formed on the Tertiary bedrock and the younger cover of Quaternary sediments, particularly gravels. To maintain the mix of open ground and woodland cover, grazing by ponies, donkeys, cattle and pigs has been actively encouraged for centuries by laws defining the rights of local Commoners. At the same time, large-scale settlement has been discouraged.
Detailed mapping of the Early Tertiary bedrock and the surface blanket of the area has shown that the bedrock here has only loosely controlled the gently hilly topography. One of the most obvious patterns is visible in the area east of Fordingbridge ( **d1** ), where distinct ridges and valleys have been carved into the Early Tertiary strata, draining southwestwards into the Hampshire River Avon. The ridges are capped by what were, at one stage, defined as the 'Plateau Gravels', though these are now regarded simply as the earliest of a very large number of river terraces that are preserved across much of the New Forest. The gravels are very largely composed of flints, originally derived by erosion of the Chalk, although material derived from _Sarsen Stones_ (hard sandstones of Tertiary age) is also present. In the absence of fossil evidence it is very difficult to be sure whether these gravels represent stages in the history of the rivers draining this area, or evidence for episodes of deposition from high-stands of sea level.
#### Landscape E: The South Hampshire Lowlands and the western South Coast Plain
The South Hampshire Lowlands form the ground between the South Downs to the north and Southampton Water and the Gosport-Portsmouth coast to the south. The bedrock is predominantly Tertiary mudrock and sandstone, except just north of Portsmouth where the Portsdown Ridge has formed by erosion of the Tertiary material, revealing an east-west trending upfold of Late Cretaceous Chalk (Fig. 116). This ridge rises some 130 m above sea level and is clearly visible north of the M27 motorway, just north of Portsmouth. Since Napoleonic times, the Portsdown Ridge has repeatedly been used as a site for fortifications (for example, Palmerston's Follies) to oversee the important harbour and settlement centres of Portsmouth to the south.
**FIG 121.** Looking northwards across Portsmouth Harbour, with Gosport to the left and the Hampshire Downs in the distance. (Copyright Dae Sasitorn & Adrian Warren/ www.lastrefuge.co.uk)
The coastal stretch south of the Portsdown Ridge marks the western end of the South Coast Plain. The bedrock consists entirely of gently folded Early Tertiary mudrocks and sandstones, but there is a widespread cover blanket of younger river-terrace sediment, including much fine-grained material often referred to as _brickearth._ The highly indented coastline around Portsmouth Harbour (Fig. 121) was formed at the end of the last cold phase of the Ice Age, as the rising water flooded the low-lying land and created broad expanses of sheltered water, edged by a mix of mudflats, marshes, wetland scrub, low-lying fields and the occasional creek.
**FIG 122.** Hurst Castle Spit (Fig. 116, **e2** ). (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
The sea-level rise also created drowned valleys such as Southampton Water ( **e1** ). Today this body of sea water receives water from the rivers Test, Itchen and Hamble, but during the last cold spell of the Ice Age, Southampton Water was the trunk river valley into which the present rivers flowed as tributaries. When it filled with the rising sea water it became the estuary on which Southampton grew to become one of Britain's premier ports for international shipping.
The gravel beds of southward-draining rivers provided much of the material that now forms the large number of gravel spits, bars and ridges that are such a feature of this area (e.g. Calshot Spit, Hurst Castle Spit ( **e2** ) and Poole Harbour ( **c1** )). These coastal features have been shaped by storm waves and the strong tidal flows that are active in these coastal waters.
Hurst Castle Spit (Fig. 122) extends into the western Solent towards the Isle of Wight, leaving a channel less than 1.5 km wide. This gives the spit great strategic importance, and a castle was first built on it by Henry VIII in 1544. The spit was last manned for defence during the World War II.
#### Landscape F: The southern Salisbury Plain, Hampshire Downs and western South Downs
In the northern half of Area 5, the Hampshire Downs form part of the broad belt of Chalk linking Salisbury Plain in the west with the South Downs in the east. To the south, the Chalk dips gently under the Early Tertiary sandstones and mudstones of the Hampshire Basin.
The scenery of the Hampshire Downs has the open and exposed character typical of most regions with Chalk bedrock, with rolling downland scarps, hill tops and valley walls. Chalk grassland covers steep scarps and is a particular feature of the South Downs. Most of the smaller valleys are dry, except in winter, and have a distinctive branching pattern.
The uniformity of much of the Chalk bedrock is one of its most distinctive features, although the presence of a ≈5 m thick hard band (the Stockbridge Rock Member) about two-thirds of the way up the Chalk succession has influenced the local shape of many of the ridges and slopes in this area.
In the area around Salisbury, the Chalk bedrock is strongly dissected by the upper valley of the Avon and its various tributaries. The scenery of wide valley floors, with floodplains and river terraces between steep valley-side slopes, is very typical of the area and provides a fine setting for Salisbury Cathedral. This section of the Chalk is quite well populated, in contrast to the high plains further north in Area 10.
About 10 km west of Salisbury, erosion of the fault and fold structure of the Vale of Wardour has brought Early Cretaceous Gault and Upper Greensand bedrock to the surface (see Area 4 for more detail). Unlike Area 4, where it is more fully developed, the Vale of Wardour is not well defined in Area 5.
The Test and Itchen river valleys (Fig. 123) have cut particularly clearly across this typical downland scenery, providing the trunk drainage of the area southwards towards Southampton Water. Some 3 km south of Winchester, the large and controversial excavation made for the M3 motorway through Twyford Down demonstrates very clearly the way the erosion of the Itchen valley has cut into the Chalk. Water meadows are a traditional feature of many of the larger valley floors, being flooded early in the season to keep off frosts and provide fresh vegetation for stock. The Watercress Line, a steam railway running from Alresford to Alton, takes its name from the crop grown in these water meadows.
The northeastern edge of the Hampshire Downs is an undulating plateau covered by Clay-with-flints, a surface blanket of material that appears to have formed by weathering of the Chalk under very variable climates, leaving a residue of flints and clay. This surface blanket has formed on different layers within the upper part of the Late Cretaceous Chalk, but has distinct margins with slopes facing eastwards over the Weald uplift in Landscape **G** ( **g1** ) and westwards over the upstream branches of the River Itchen ( **f2** ). These Clay-with-flints deposits often support small patches of woodland, unlike the thin, dry Chalk soils elsewhere that are covered by grassland and pastureland.
The high ridge of the South Downs ( **f1** ) rises out of the Hampshire Downs south of Winchester, gaining definition as it runs east towards Sussex. In Area 5, the South Downs occupy only a thin sliver of country about 10 km wide, extending from the Itchen valley near Winchester in the west to a few kilometres east of the A3 trunk-road between Havant and Petersfield. Along the whole of this stretch, a remarkable plan-view pattern of arrowhead-like Vs can be seen on the south side of the ridge pointing northwards (see Fig. 123, for example). Both this pattern and the narrowness of the Chalk belt are the direct result of the regional tilting of the Chalk layers, which steadily slope southwards at between 2 and 6 degrees.
#### Landscape G: The western outcrop area of the Wealden Greensand
In the northeastern corner of Area 5, the Chalk is replaced by older (Early Cretaceous) bedrock that has been brought to the surface by erosion of numerous gentle, open folds. Together they produce the Weald uplift, a regional-scale structure that dominates the bedrock geology of southeastern England south of the Thames, described more fully in Area 6.
The youngest of the Early Cretaceous layers is the Upper Greensand. This 5 m thick sandstone and siltstone, often richly cemented with iron, forms a clear series of ridges round the western end of the Weald uplift, particularly near Selborne ( **g1** ). The Upper Greensand ridges change sharply in direction around the town of Petersfield, from a broadly southwesterly direction to an easterly direction, running approximately parallel to the escarpment of the South Downs.
Below the Upper Greensand is the mudstone-rich Gault and, below that, the alternating sandstones and mudstones that make up the thick Lower Greensand. In Area 5, the Gault lies east of the Upper Greensand, and has generally been eroded into low-lying, featureless country, whereas the Lower Greensand sandstones further east have resisted erosion. To the northeast of Petersfield the topography reflects the way that river erosion has picked out fault displacements of these Lower Greensand layers.
#### Review of the landscape history
Most of the inland slopes and valleys have been created during the evolution of the river and stream systems that occupy the valley bottoms. These systems have not only drained the landscapes, but they have also generated sediment as they have eroded and carried it away, causing an overall lowering of the ground surface.
**FIG 123.** Main river pathways and coastal flooding zone for Area 5.
The present-day drainage provides a template for this key aspect of the landscape evolution, though the exact locations of the rivers will have changed considerably over time. We can simplify the pattern by selecting the main valleys and labelling them as the 'main river pathways', as in Figure 123. This general pattern is likely to be over 20 million years old.
The coastline of this area has taken up its familiar form and position only in the last few thousand years. During the previous 12,000 years, the coastline has advanced inland great distances because of a rise in sea level of about 120 m, due to the melting of the ice sheets formed during the last cold episode of the Ice Age.
At the time of the Devensian Glacial, about 20,000 years ago, a continuous belt of hilly ground underlain by Chalk extended across most of the southern part of Area 5 (now largely covered by the sea), from an area south and east of the present Isle of Wight to the present Isle of Purbeck. The headland of Culver Cliff at the eastern end of the present-day Isle of Wight marks the stump of this Chalk belt left by wave erosion today. West of the present Isle, the wave erosion eventually broke through what must have been a continuous line of Chalk hills (Fig. 124), exposing the softer Tertiary rocks to the north to intense wave erosion and creating the broad concave coastline around Bournemouth. All that remains of the Chalk ridge today are the headlands of Ballard Point with Old Harry on the Isle of Purbeck, and the Chalk Downs stretching from the Needles to Culver Cliff on the Isle of Wight.
We can visualise further the effect of this 120 m sea-level change by considering the present Isle of Wight and its surroundings. At the time of low sea level 20,000 years ago, the area now occupied by the Isle of Wight was simply an area of higher ground surrounded on all sides by lower land. To the north, a large Solent River flowed eastwards along a valley where the Solent seaway is today (Fig. 124). The river transported water and sediment from much of Dorset and all the main rivers of Hampshire, as well as from the south, where the higher ground of the present Isle of Wight was continuous with Chalk hills now covered by the waters of the English Channel, as described above. The rivers of Southern England and northern France drained into this plain, eventually flowing into the Atlantic west of Cornwall (Fig. 21). This involved a change in direction from eastwards to westwards for the waters of the Solent river as it negotiated the topography and bedrock contrasts generated by the fold and fault movements of the Purbeck-Isle of Wight stepfold.
Some 20,000 years ago the view shown in Figure 125 would have looked across the open valley of the Solent river, with no sea visible. The Flandrian sea-level rise has flooded a large valley, creating the present Solent and making the distant Chalk hills into the Isle of Wight. In the foreground, the rising sea has also flooded the mouth of the Lymington tributary of the former Solent river, and storms and tides have mobilised sediment to produce the pattern of river-mouth islands.
**FIG 124.** The ancient Solent River drainage before the Flandrian sea-level rise.
Flint tools and ancient trees dating from before the Flandrian rise in sea level have been found towards the middle of the Solent, providing evidence to support the ideas described above. However, worldwide sea level largely stopped rising about 6,000 years ago, yet much younger artefacts have also been found submerged below the present sea. For example, Saxon sheep pens, perhaps 1,000 years old, have been found offshore between the Isle of Wight and the English mainland. The main Flandrian global sea-level rise due to ice-sheet melting cannot account for this, because most of it was over long before Saxon times. This implies that some younger downward movement of the bedrock, due to changes within the Earth, must have taken place very recently in some local areas.
**FIG 125.** Lymington river, looking southeastwards towards the Isle of Wight. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
Some scientists now believe that during the last few thousand years sea level was briefly higher than it is today, though this is far from certain, and estimates of sea level during earlier interglacials are even less clear. Figure 123 attempts to show the effects of a 20 m rise in sea level, ignoring any of the effects of local bedrock rising or sinking that may have taken place. This is relevant to today's worries over rising sea level, although the extent of the contribution made by our own species to the undoubted present warming is not clear.
### AREA 6: SUSSEX
A north-south traverse through the centre of this Area runs from Crawley through Haywards Heath to the coast at Brighton. The western edge of the Area adjoins Area 5, and runs from Haslemere via Midhurst to Chichester and Selsey Bill on the coast. The eastern edge adjoins Area 7, and runs from Royal Tunbridge Wells via Hailsham to Beachy Head and Eastbourne on the coast (Figs 126 and 127).
Area 6 extends across the central and southern part of the Weald of southeastern England, an area neatly defined by the presence of the Early Cretaceous bedrock known as the Wealden (Fig. 128). The name _Weald_ derives from Old English, and refers to the woodland cover that is still an obvious feature of this area, particularly when looking across from the escarpments of younger Chalk or Greensand that form its border to the north, west and south. This rim acts as the frame of the broad and gentle _Weald uplift_ in the bedrock, formed by a phase of compression and upward movement in the crust about 30 million years ago. The neat map pattern of concentric layers of bedrock (Fig. 129) and scenery is the direct result of the way the Wealden structure has been bevelled downwards as river and stream erosion has lowered the ground surface over those last few tens of millions of years. Figure 129 also shows that some of the mapped boundaries between the main layers are locally quite jagged; a result of the presence of much smaller local faults and folds, often trending, very approximately, east-west. These small features have probably formed as a result of the movement of larger faults at greater depth.
**FIG 126.** Location map for Area 6.
Six distinctive Landscapes can be identified in Area 6, labelled **A** to **F** in Figure 129. These are discussed in turn below.
#### Landscape A: The High Weald
This Landscape forms the northeastern corner of the Area. It is framed to the south, west and north by Landscape **B** , the Low Weald. The scenery of the High Weald is typically one of small wooded hills and valleys distributed in a weakly radial pattern, so that some of the High Weald drainage is to the west and the north, draining via the Medway into the Thames estuary. The rest of the drainage is southerly, via the headwaters of the Adur, Ouse and Cuckmere to the south coast, along valleys carved through the South Downs (Fig. 136).
The hills of the High Weald range in elevation between about 50 m and 250 m, whereas the Low Weald is generally much lower and flatter. Erosion in the High Weald to the west of Mountfield has exposed bedrock of latest Jurassic age identified as the lower part of the Purbeck beds ( **a2** ). In addition to mudstones and thin limestones, these Purbeck deposits contain gypsum (calcium sulphate) which has been mined commercially for plasterboard. All the rest of the bedrock at the surface of the High Weald is Early Cretaceous in age and assigned to the Hastings Beds that make up the greatest thickness and lower part of the Wealden Series (Fig. 128).
**FIG 127.** Natural and man-made features of Area 6.
**FIG 128.** Bedrock succession for Area 6.
**FIG 129.** Geology and hillshade map of Area 6, showing Landscapes **A** to **F** and localities ( **a1, a2** etc.) mentioned in the text.
In Early Cretaceous times the material that now forms the Wealden Series was deposited in a low-lying, subsiding basin that extended southwards from a flat upland area where London is now. This Wealden Basin was occupied by lakes and extensive mud flats that were invaded from the north by rivers flowing and shifting across plains with channels and sandbars. The sediments deposited in these mud- and sand-flats became mudstones and sandstones as they were buried by more sediment as the area continued to subside. The sandstone sheets have now been eroded to form slopes, and locally even form distinctive areas of cliffs that provide challenges for rock climbers, particularly in the Tunbridge Wells area.
In mid-Tertiary times, the surface of the Wealden area began to move upwards, and erosion by rivers and streams began to cut downwards into the Wealden bedrock, eventually creating the topography of hills and valleys that we see today (Fig. 130). The crude radial pattern of this drainage (described above) reflects the erosion of the rising, dome-like Weald uplift. In addition, local geological mapping has shown that many of the sandstone sheets have been cut by faults that often trend approximately east-west, particularly in the lower parts of the Hastings Beds. These faults have often provided bedrock contrasts that have influenced the local directions of the young valley systems.
The High Weald was the focus of a remarkable iron industry from the fifteenth to the seventeenth centuries. The source of the iron was siderite, an iron carbonate mineral that grew as a precipitate in the wet muds of the Wealden lakes. The small valley networks of the High Weald were ideal for the construction of dams and ponds (known as 'hammerponds'), and these in turn powered bellows for the smelting of the iron and forge hammers for working it. The forges were fuelled using charcoal from valley and slope woodlands, and the industry eventually died because the northern British coalfields became recognised as a more efficient source of heat and power.
**FIG 130.** Typical High Weald landscape, looking eastwards over Bewl Lake (Fig. 129, **a1** ). Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
#### Landscape B: The Low Weald
In Area 6, the Low Weald extends in a belt to the south and west of the High Weald, from Haslemere in the west, past Horsham and Haywards Heath, and on towards the sea between Eastbourne and Hailsham, where it passes into the Pevensey Levels (Landscape **F** ).
This rather flat and featureless Landscape owes its lack of topography to the uniformity of its bedrock, which is the upper division of the Wealden beds known as the Weald Clay (Fig. 128). There is an obvious contrast in elevation and the presence of slopes between this Weald Clay landscape and the higher and more hilly topography seen in Landscapes **A** and **C**. In a few locations, the Weald Clay does contain thin sandstones and freshwater limestones which create some topography, but they are much less common here than in the Greensand below and the Hastings Beds above.
The Vale of Fernhurst ( **b1** ) at the western edge of Area 6 has a floor of Weald Clay sandwiched between scarps cut in the Lower Greensand. In some places, these scarps are due to the presence of an important, erosion-resistant sandstone (the Hythe Beds) in the lower part of the Lower Greensand. In other places, distinct slopes seem to have been carved in the Wealden below the actual Lower Greensand boundary.
#### Landscape C: The Wealden Greensand
Much of the sediment that accumulated in Area 6 during the later part of the Early Cretaceous has been assigned to the Lower Greensand. This unit consists of alternations of mudstones and sandstones, ranging up to a maximum total thickness of about 400 m. The sediments seem to have formed in a shallow sea, and shelly fossils found in them have allowed a fairly precise age for the rocks to be worked out. The deposits vary from place to place, depending on their position in the succession, and this reflects the changing patterns of the Early Cretaceous shallow marine environment and the variable way that sandy material was being supplied to the sea floor by rivers.
In the western third of this Landscape, the lowest thick sandstone layer of the Lower Greensand (the Hythe Beds) has resisted stream and river erosion to produce an escarpment that is particularly clear between Midhurst and Haslemere. Here the Vale of Fernhurst ( **b1** ) has been eroded down into the Low Weald by what is now a small stream flowing along the line of a gentle west-to-east trending upfold. The small stream runs parallel to the much larger River Rother, which flows about 10 km further to the south, under the shadow of the South Downs Chalk escarpment (Figs 129 and 136). Valley-slope processes in the Vale of Fernhurst have resulted in escarpments to the north and south that are steep enough to have collapsed by land-slipping.
Further east in this Landscape, the bedrock has not produced any clear slope features in the Wealden Greensand belt.
#### Landscape D: The South Downs
The South Downs provide a classic example of a linear range of hills that have been formed by the erosion of a bedrock succession containing a sloping, more resistant, layer, in this case the Chalk. In Area 6, the slope is typically southwards at only a few degrees, although gentle and open folds with higher slopes are present locally.
The most famous scenery of this Landscape occurs where the sea has cut the spectacular coastal cliffs between Eastbourne, Beachy Head ( **d1** ), the Seven Sisters ( **d2** ) and Seaford Head ( **d3** ). The Beachy Head photograph (Fig. 131) shows how a recent rock fall produced a lobe of debris extending outwards towards the lighthouse. Further to the west, the Seven Sisters provide a beautiful example of the way that receding coastal cliffs can reveal a perfect cross-section through a pre-existing landscape of parallel ridges and valleys (Fig. 132). Beyond is the valley of the Cuckmere, where an artificial channel has been used to bypass the highly meandering lower stretch of the river (Fig. 133). The object of this was to improve drainage to make the floodplain less liable to flooding.
The special properties of the Chalk give its scenery the classic features seen in most other Chalk bedrock areas in Southern England. Chalk is a remarkably homogeneous and fine-grained sediment, generally giving rise to hills that are smoothly rounded and separated by distinct valleys. However, the lack of clear bedding or layering also means that it has responded to the inevitable stresses within the Earth's crust by fracturing, where many other rock types would have responded by slipping along layers. This fracturing makes much of the Chalk permeable to rainwater, so most Chalk valleys now are dry for much – if not all – of the year. Chalk valleys, therefore, were probably excavated mainly during the cold episodes of the Ice Age, when frozen ground conditions sealed the bedrock and made it impermeable, and surface erosion could remove material in the short summers.
The northward-facing escarpment is the most striking feature of the scenery of the South Downs, and corresponds directly to the position of the base of the Chalk layer. The escarpment shows up very clearly, for example, in Figure 127, reflecting the contrast in erosional resistance of the Chalk compared with that of the underlying Early Cretaceous Gault or Upper Greensand. Looking at the form of the line marking the base of the Chalk in Figure 129, a number of deflections mark distinct departures from a simple straight line. These are due to local folds that have deformed the Chalk layer. Another feature of the escarpment is that it consists of large numbers of _coombes_ or hollows, usually less than 1 km across, which appear to have formed by local slope collapse of the Chalk under Ice Age conditions of thawing and freezing. Other evidence of the effects of this slope collapse is the jumbled deposits of Chalk mud and fragments (known as _head_ ) resulting from flows of debris into the floors of many of the valleys.
**FIG 131.** Beachy Head (Fig. 129, **d1** ) seen from the west. (Copyright Sheila Smart)
**FIG 132.** The Seven Sisters (Fig. 129, **d2** ) from above, showing the parallel valleys intercepted by the cliff line. (Copyright Dae Sasitorn & Adrian Warren/ www.lastrefuge.co.uk)
**FIG 133.** Looking northwestwards over the western Seven Sisters and the Cuckmere valley. (Copyright Aerofilms)
Many scientists have considered the way that the river and stream drainage pattern of the Weald may have developed. A focus of this interest has been the way that a rather regular series of large valleys cuts right through the South Downs, carrying water southwards from Landscapes **A, B** and **C** (Fig. 136). From west to east, the Arun, Adur, Ouse and Cuckmere pass through clear valleys sometimes called water gaps, and it has been concluded that they are the descendants of rivers that originated early in the history of the Weald uplift as the bedrock layers became tilted. On the high ridge of the South Downs, between these cross-cutting _water gaps_ , a similar number of _wind gaps_ or low points have been identified. It has been suggested that they may represent early valleys that were abandoned by their rivers as the drainage pattern evolved and tributaries cut back to deflect or capture other streams.
#### Landscape E: The South Coastal Plain
This remarkable coastal-plain Landscape stretches all the way from Southampton Water and Portsmouth in the west (see Area 5) eastwards, via Selsey Bill (Fig. 134), as far as Brighton (Fig. 135). It provides clear evidence of the way that coastal processes, coupled with sea-level changes, have created a zone where bedrock structures have been planed down by storm-wave action and covered by a thin veneer of gravel and wind-blown _brickearth_ (a fine-grained sand).
The bedrock structure here involves the folding of the Chalk and Early Tertiary sediments (the London Clay and Bracklesham Beds; Fig. 128) into the distinctive _Chichester downfold_ ( **e1** ), the _Portsdown upfold_ ( **e2** ) and the _Littlehampton upfold_ ( **e3** ).
Boxgrove ( **e4** ), about 4 km northeast of central Chichester, has attracted a lot of interest because of the remarkable information it has provided on the conditions at the northern edge of the coastal plain here during the middle Pleistocene. A number of gravel pits have revealed an ancient cliff line cut into the Chalk forming the toe of the South Downs. Marine sediments rest on a wave-cut platform in the Chalk bedrock and are covered by layers formed by periodic slumping of Chalk debris that alternate with lagoonal sediments, soils and freshwater deposits. The special interest of this situation is that fossil bones of early humans have been found here, along with stone artefacts and the remains of rhinoceros, horse and red deer that appear to have been butchered by the humans. These people appear to have been an archaic form of _Homo sapiens_ , referred to by some as Heidelberg man, rather than Neanderthal. The deposits probably date from episodes before the Anglian cold episode, perhaps 500,000 years ago.
**FIG 134.** Selsey Bill (Fig. 129, **e5** ), looking northwestward. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
**FIG 135.** Hove and Brighton, looking eastwards. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
#### Landscape F: The Pevensey Levels
The Pevensey Levels, between Eastbourne and Hailsham, are a distinctive low-lying Landscape formed by recent coastal processes of erosion and deposition. The Levels consist largely of gravels deposited by storms on beaches fringing an embayment that has existed periodically just north of the South Downs (Landscape D) during times of high sea level. Salt-marsh and river deposits have also been added to this gravel material in some areas.
#### Review of the landscape history
The present-day scenery of this Area started to develop about 30 million years ago, when the Weald uplift began to form in response to stresses generated within the Earth's crust. Although in country-wide terms this is a large structure (approximately 150 km by 80 km), it is simply one part of a much larger pattern of gently tilted layers that resulted from continental movements during mid-Tertiary times. More locally, 1 km scale folds and faults formed as part of the same movement episode, and are clearly apparent in the pattern of mapped geological boundaries. Many of these local effects were due to the presence of earlier faults in the bedrock that moved again during the later episode, often in the opposite direction.
As soon as the Weald uplift produced high ground, patterns of local river and stream drainage started to develop, particularly by cutting valleys back from the coastlines into the areas of newly formed high ground to produce a generally radial drainage pattern. The variable resistance of the bedrock to erosion has strongly influenced the landscape, creating some of the most spectacular scenic features. The other variable in this valley erosion was the climate, which influenced the amount of rainfall and the occurrence of the floods that do much of the work in eroding and removing material from the landscape. Valley slopes are also critically affected by climate changes, which determine vegetational cover and, during cold episodes of the Ice Age, the permeability and stability of the bedrock. It seems likely that the dry valleys visible today on the South Downs formed during cold phases when the ground was frozen.
Sea-level change, particularly in response to vigorous changes of climate during the Ice Age, is the other major factor that has influenced the scenery. It is now understood that, about 20,000 years ago, sea level was some 120 m lower than at present. Since then it has invaded the land, rising to within 10 m of its present level approximately 6,000 years ago, although minor fluctuations more recently have been important in local coastal development, both natural and man-made. Over the previous 2.6 million years of Pleistocene time, sea-level changes between about 100 m below and 10 m above present sea level have occurred many times, at approximately regular intervals (see discussion of this under Area 7).
Figure 136 shows the present coastline of Area 6, and the present land up to an elevation of 20 m above sea level as the 'coastal flooding zone'. Sea level may not have reached as high as this 20 m level, but river and stream systems of the past would certainly have been influenced by invading seas, causing ponding-up of their flow to about this level at some earlier times. The whole of the South Coastal Plain (Landscape **E** ) and the Pevensey Levels (Landscape **F** ) are clearly within this coastal flood zone, and it is also interesting to note how the 'water gaps' of the rivers Arun, Adur, Ouse and Cuckmere allow the flooding zone to extend inland, to invade Landscapes **B** and **C** and even parts of Landscape **A**. One conclusion is that anywhere within this zone will have been influenced by coastal advance and retreat processes over the past few million years of the Ice Age. Another conclusion is that anywhere within this zone is liable to be influenced by future rise of sea level.
**FIG 136.** Main river pathways and coastal flooding zone of Area 6.
### AREA 7: EAST SUSSEX AND SOUTHEAST KENT
More than half of this Area rectangle is occupied by the sea (Figs 137 and 138). The coastline extends from Bexhill in the west, where the sea is eroding cliffs in the Early Cretaceous High Weald bedrock, to Folkestone in the northeast, where the cliffs have been formed by erosion of the Early Cretaceous Lower Greensand and Gault and the Late Cretaceous Chalk. Between these two sections of coastal cliffs is a large area of young surface blanket forming Dungeness and Romney Marsh.
**FIG 137.** Location map for Area 7.
**FIG 138.** Natural and man-made features of Area 7.
**FIG 139.** Bedrock succession and surface blanket of Area 7.
Almost all of the land of Area 7 is underlain by bedrock of Cretaceous age. The only exception to this is a small area of bedrock in the High Weald, just north of Battle, which is of Late Jurassic (Purbeck) age (Fig. 139).
Five distinctive Landscapes can be identified in Area 7, labelled **A** to **E** in Figure 140. The first four of these are defined by their successively younger bedrock, while the last one is defined by its surface blanket of young material.
**FIG 140.** Geology and hillshade map of Area 7, showing the boundaries of important bedrock layers, Landscapes **A** to **E** and localities ( **a1, b1** etc.) mentioned in the text.
#### Landscape A: The High Weald
Most of the land of Area 7 is underlain by the Early Cretaceous Hastings Beds, though in the centre of the Area this is covered by the surface blanket of younger sediment that forms the Dungeness and Romney Marshes. The hilly ground to the west of the Area is therefore a continuation of the High Weald Landscape of Area 6, and many aspects of its history are discussed more fully under that Area.
Only rarely do the hills of this part of the High Weald exceed 100 m in elevation, but the topography consists generally of many small valleys and ridges, so there are very few substantial areas of flat ground. The small size of the topographic features made this Landscape ideal for damming streams to provide local sources of power, and so, as in Area 6, an iron-smelting industry flourished here between the fifteenth and seventeenth centuries.
**FIG 141.** Hastings Castle, foreshore and cliff (Fig. 140, **a1** ). (Copyright Sylvia Cordaiy Photo Library Ltd)
The layering of the Hastings Beds in this Landscape is generally near to horizontal, and consists of alternations of sandstones and mudstones on many scales. The sandstones were mainly deposited in Early Cretaceous river channels and at river mouths, while the mudstones were formed in lakes or on river floodplains. Two groups of sandstone layers are particularly important: an early, lower group called the Ashdown Sand and a later, upper group called the Tunbridge Wells Sand. They are separated by a mud-rich interval known as the Wadhurst Clay (Fig. 139). These changes of rock type have locally influenced the slopes that have formed during the erosion of much of the topography. At Hastings ( **a1** ), the castle was constructed on a prominent sandstone layer within the Wadhurst interval, which has been eroded by coastal storms to produce a distinctive cliff feature (Fig. 141).
The bedrock was cut by faults that became active during the movement of the crust in mid-Tertiary times, when the Weald uplift was forming. Displacements along these faults have disrupted the regular layer pattern of the bedrock, which has, in turn, caused variation in local slope erosion. The commonest fault direction is WNW-ESE, and some of the main valleys, such as those of the Rother and Brede, locally trend parallel to particular faults (Fig. 149, page 192).
#### Landscape B: The Low Weald
The Low Weald is defined by the presence of the Early Cretaceous Weald Clay just below any surface blanket that happens to be present locally. It forms a wide and rather featureless belt of scenery along the northern margin of Area 7.
To the east of this Landscape, the Weald Clay bedrock forms an irregular but generally linear slope feature that was eroded in the Bilsington area ( **b1** ) before the coastal-zone deposition of Dungeness and Romney Marsh began. The irregularities of this slope may reflect the way the weak mud material of the Weald Clay has tended to collapse and flow down-slope.
As the coastal town of Hythe is approached, the Weald Clay bedrock becomes covered up by the surface blanket of Romney Marsh. The area underlain by the Weald Clay generally becomes much narrower in Area 7, at least partly because the total thickness of the Clay in the bedrock succession decreases here to just over 100 m, compared with some 500 m near Guildford in Area 11. Changes of thickness of this sort usually reflect variations in the downward movements of the Earth's crust during the accumulation of the sediment, but may also reflect variations in the amount of sediment supplied to the environment in which the Weald Clay accumulated.
#### Landscape C: The Wealden Greensand
Coastal erosion in the Hythe and Folkestone area has produced vegetated cliffs cut into Early Cretaceous Lower Greensand and Gault bedrocks (Fig. 142). These units have a combined thickness of about 150 m in the Folkestone area and consist largely of mudstones, except for a lower sandstone layer (the Hythe Beds) and an upper sandstone layer (the Folkestone Beds). The sandstones have preferentially resisted erosion to produce slopes in the local scenery, particularly in the case of the Hythe Beds, which contain thin, hard limestone layers inter-bedded with sandstones containing grains of the dark green, iron-bearing mineral glauconite. These alternations of hard and soft bands were known as 'rag and hassock' by local quarrymen in earlier times, and 'Kentish Rag' is still a source of road stone and concrete aggregate.
The Hythe beds have been eroded into a distinct scarp for some 10 km along the northern margin ( **c1** ) of Romney Marsh, west of Hythe. In more recent times, the margin of this scarp has been made less distinct by land-slipping and surface modification, as the Hythe Bed sandstones have collapsed downwards over the underlying softer mudstones.
**FIG 142.** Looking northeastwards past Hythe (in the foreground) to Folkestone (with the pier) and the White Cliffs of Dover (in the distance). (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
#### Landscape D: The North Downs
Area 7 contains a very small area of Late Cretaceous Chalk bedrock along its northeastern margin, which can be identified as Landscape D. The Chalk continues northwards into Area 11, where it forms the North Downs, extending from Dover northwestwards via Chatham, and on westwards south of London. All three subdivisions of the Chalk are present in the Folkestone area, the Lower and Middle each about 70 m thick, and the Upper about 200 m thick.
**FIG 143.** Diagram showing the way the Channel Tunnel was excavated within the Chalk Marl, the lowest layer in the Late Cretaceous Chalk. (Redrawn from drawing by Nigel Woodcock)
The design of the Channel Tunnel (completed in 1994) involves three tunnels, one for each of the two traffic directions, and a smaller one for emergency and maintenance work. The tunnels are excavated as far as possible within the lowest unit of the lower Chalk, known as the Chalk Marl (Fig. 143). This material consists of a mixture of clay minerals and fine-grained calcium carbonate, making it largely impermeable to water flow, yet plastic enough to suit the tunnelling machinery. It is also not so brittle that it contains cracks and fractures that would cause collapse and flooding by groundwater.
Excavation took place simultaneously from both France and England and took about three years. Spoil from the tunnels on the English side was used to construct a 1 km by 300 m extension to the coastline just west of Shakespeare Cliff ( **d1** ), most of which is now used as the Samphire Way Country Park.
The decision was also taken to locate the tunnel mouths very well inland, some 2.5 km north of the coast in central Folkestone (Fig. 144). The route of the tunnels crosses the coastline below Shakespeare Cliff ( **d1** ), some 2 km from the Western Docks of Dover and almost 10 km from the tunnel mouths north of Folkestone. This 10 km of tunnelling below land was felt to be preferable to locating the tunnels closer to the coastal cliffs, which had proved to be extremely unstable in the past, particularly along the 3 km coastal stretch just northeast of Folkestone known as the Warren ( **d2** ). Cliff erosion of the soft Early Cretaceous Gault overlain by the Late Cretaceous Chalk in this area has caused continuous land-slipping here. The decision to construct the first railway line to Dover across the Warren required frequent movement and re-cutting of the line, culminating in a major landslip in 1915 which carried away a complete train (Fig. 145).
**FIG 144.** Aerial view eastwards, looking at the mouth of the Channel Tunnel. To the right is Folkestone and to the left is the edge of the Late Cretaceous Chalk. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
**FIG 145.** The Folkestone Warren landslip, 1915. Note the train in the foreground. (Photo from British Railways, Southern Region)
The dry valleys and steep slopes that are developed so clearly in many areas of Chalk downland in Southern England are very clear in the Downs to the north and northwest of Folkestone and Dover. A detailed investigation of the landscape history has been carried out in Holywell Coombe, north of Folkestone and just south of the A20 tunnel mouth a few hundred metres from the Channel Tunnel portal. This showed that the Chalk slopes were actively retreating because of freeze-thaw collapse during the Dimlington and Loch Lomond cold periods (see Chapter 2, Fig. 19), providing clear evidence that this Chalk landscape was actively evolving in very recent geological terms.
#### Landscape E: The Dungeness and Romney Marshes
Dungeness is one of the largest beach-gravel promontories of the whole coastline of Britain. It adds a highly distinctive shape to the coast of the Strait of Dover, the narrowest section of the English Channel.
**FIG 146.** Photograph looking northwestwards over Dungeness and the nuclear power stations (Fig. 140, **e1** ). The lines or ridges on the surface of the promontory mark the positions of former coastlines. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
The surface of the main Dungeness promontory is only lightly vegetated, and very clearly shows large numbers of distinct lines or ridges, locally called 'fulls' and visible in Figure 146. Groups of these ridges trend in different directions, and excavations made during the construction of the power station show that they mark the tops of sedimentary layers, sloping downwards towards the sea at about 9 degrees. These layers were formed during storms when gravel was deposited on the sloping surfaces of old beaches. This means that the pattern of lines provides a record of the positions of active beaches over time, making it possible to plot the way the promontory has grown and changed in the past (Fig. 147). Where the lines have been truncated by the present coast, an earlier episode of deposition by storms must have been followed by a later episode of net removal, causing the movement of the coast landward.
As Figure 147 shows, analysis of these lines provides evidence for an early episode of build-out of the coastline in the southwest of this Landscape, near Rye. The building of the large promontory of present-day Dungeness, further to the east, has occurred more recently, and has been accompanied by large amounts of erosion south of Rye (Fig. 148), as well as some lesser erosion to the northeast, about 5 km southwest of Hythe, where a wall has been constructed to protect the coastline.
**FIG 147.** Diagram illustrating the evolution of the Dungeness promontory.
**FIG 148.** Looking southeastwards down the River Rother, with Rye in the foreground. The gravel beaches of the present coastline of Rye Bay extend further to the left into Dungeness. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
Inland from the shingle-covered areas are large areas of flat-lying, open, agricultural land with distinctive dykes and marshes. Although there are many local names, these flat-lying areas are often grouped under the general name of the Romney Marshes.
Muds and sands are widespread just below the surface of the Marshes, and peats are common a few metres down. It is possible to date these peats using radiocarbon methods, and it is also possible to use related fossils to determine whether the peats formed in wetlands that were freshwater or becoming salty because of flooding due to sea-level rise. This work has confirmed that all the Marsh deposits have been formed during the last period of the Flandrian transgression (rise) of the sea. Some 6,000–7,000 years ago, sea level was about 10 m lower than at present and it rose progressively to reach its present level within the last few hundreds of years. However, it is also clear that horizontal movement of features such as tidal channels, beach barriers, wetlands and salt marshes can be responsible for local vertical changes, without requiring any change of overall sea level.
There is no question that the global rise of sea level since the last (Devensian) cold spell has been the major factor controlling the arrival and deposition of all the sediment in the Dungeness and the Romney Marshes. However, on a more local scale, it seems that small-scale variations in the climate have also been important, controlling both the supply of sediment to the marshes and the power and frequency of storms.
One regional feature that needs to be stressed is the special location and geometry of Dungeness in relation to the geography of land and sea. The Dungeness promontory is situated in an exposed position, at the mercy of prevailing Atlantic storms driven from the southwest up the English Channel, and also from winter storms caused by depressions passing over the northern North Sea. Both of these processes act to transport sediment into and around the Dungeness promontory. At the same time, the proximity of the promontory to the coast of France means that winds from the southeast, which are unusual anyway, do not have sufficient reach to cause erosion that would counteract the tendency for Dungeness to grow.
Another striking feature of this Landscape is the _degraded cliff_ that marks the boundary between the areas of bedrock control, to the north and west, and the flat-lying area of the Marshes covered with surface blanket, to the south and east (Fig. 147). This cliff feature runs on the landward side of the Royal Military Canal, which was constructed for communication and defence purposes under threat of a Napoleonic invasion. As the 'degraded cliff' name implies, this distinctive slope feature is regarded as a cliff line eroded by the sea before deposition of the young Marsh. Although it is generally assumed that it formed just before the Marsh sediments themselves, within the last 7,000 years or so, it is also possible that it is much older. For example, in some areas along the coast of East Anglia, cliff-forming erosion took place during the last (Ipswichian) interglacial, about 125,000 years ago, when sea level was a few metres higher than it is at present. It is possible that the Romney Marsh cliffs formed by similar processes, and that their degradation took place over the 125,000 years that followed.
#### Review of the landscape history
The oldest features of the scenery of Area 7 must be the major river valleys of the Rother, Tillingham and Brede, which started to erode downwards into the rising land surface when the Weald uplift began some 30 million years ago. These rivers have excavated the intricate valley patterns of the High Weald, the low and subtle drainage patterns of the Low Weald, and the more marked scarps and valleys of the Wealden Greensands and Chalk.
The second group of landscape features are those that reflect changes in sea level. There is no clear dating evidence for high-stands of the sea earlier within the Tertiary, but the evidence for Holocene flooding by postglacial sea-level rise is abundant and has been discussed above. So also has the possibility that the Romney Marshes degraded cliff line may date from the high sea level associated with the Ipswichian interglacial, some 125,000 years ago. The evidence for this is based not on direct dating, but on the configuration of the land as represented by the 'coastal flood zone' shown in Figure 149. This figure highlights the inland valley patterns, and also identifies the large proportion of the Area sensitive to fairly small changes in sea level.
**FIG 149.** Main river pathways and coastal flooding zone of Area 7.
# [CHAPTER 6
The Severn Valley Region](004-toc.html#ch6)
### GENERAL INTRODUCTION
IHAVE LINKED AREAS 8 AND 9 together to form the Severn Valley Region (Fig. 150). This is because the Bristol Channel and the Severn and Avon valleys form one of the most important landscape features of this part of Southern England. Another dominant feature of this Region is the Cotswold Hills, extending from Bath northeastwards through Banbury.
The generalised bedrock succession for this Region (Fig. 151) contains a major unconformity or time gap. At this gap, the scale used to represent the thickness of the rock successions shown in Figure 151 has been changed, because the Carboniferous and older bedrock generally involves much greater thicknesses than the younger bedrock. This provides evidence for a slowing in the rate of sediment accumulation in this Region towards the end of the Carboniferous, which suggests that Earth movements were more active in earlier times, when the raising and lowering of the Earth's surface resulted in vigorous production of sediment and its trapping in subsiding basins.
The time gap in the succession can be mapped across the Region and is known as the _Variscan Unconformity._ Figure 151 shows this gap spanning the time between 305 and 299 million years ago, but this is misleading because 305 million years is the youngest age found in the underlying layers, while 299 million years is the oldest age found in the overlying layers. In most localities in the Region the time gap is much longer in duration.
The Variscan Unconformity is spectacularly exposed along the coastline at Woodhill Bay, Portishead, some 10 km west of central Bristol (Fig. 152).
**FIG 150.** The Severn Valley Region (Areas 8 and 9).
The lower part of the unconformity here consists of Devonian rocks of the Lower Old Red Sandstone, deposited as more-or-less flat beds about 400 million years ago. These beds were tilted and then eroded to form a flat surface during the Variscan mountain building, before being covered by layers of Triassic dolomitic conglomerate about 270 million years ago. These rocks provide a vivid record of the Variscan mountain building in this Region: the Devonian strata were tilted by folding, moved upwards and then eroded, before being covered by sediment derived, at least partly, from Variscan mountains that still existed nearby.
The Severn Valley Region contains an unusual diversity of scenery and bedrock because it straddles an important boundary represented by the Variscan Unconformity, dividing the older and newer bedrock successions of England and Wales (Fig. 153). Carboniferous and older bedrock geology underlies most of the Southwest, Wales, northwestern England and some parts of the English West Midlands. New Red Sandstone and younger bedrock dominates most of the rest of Southern England and the eastern part of northern England. The map in Figure 153 shows the trend of Variscan folds generated during the plate convergence that caused the Variscan mountain building. South of the line marked 'Variscan Front' the main fold trends run east-west, representing convergence in a roughly north-south direction. North of the Variscan Front, in Areas 8, 9 and 10, folds of similar age trend generally north-south and result from a different pattern of movement.
**FIG 151.** Generalised bedrock succession for the Severn Valley Region.
**FIG 152.** The Variscan Unconformity spectacularly exposed at Woodhill Bay, Portishead. The upper rocks are dolomitic conglomerates of Triassic age, resting upon the tilted Lower Old Red Sandstones of the Devonian. (Copyright British Geological Survey)
The other landscape feature of Regional interest here is the valley system of the River Severn and Bristol Channel. Figure 153 shows the extent of the Bristol Channel Basin, outlined by the pre-New Red Sandstone unconformity and filled mainly with New Red Sandstone sediment. This basin formed as an area of persistent downward movement during the latest stages of the Variscan mountain building. The soft sediment fill of the basin made it more susceptible to erosion than the surrounding older, harder rocks, allowing the Bristol Channel to form as it is now.
East of the Basin, the Bristol Channel narrows and becomes an estuary, until it ceases to be tidal near Gloucester. This northeasterly reach, largely in Area 8, is characterised by the change in fold and fault trends referred to above, from east-west in the south, to northeast-southwest, and then north-south in the north. It seems likely that the change in direction of the estuary and the river has resulted from erosional topography controlled by the presence of these structures.
Further north, the eastern edge of the Severn-Avon catchment is formed by the watershed of the Cotswold Hills. We shall see in Area 9 how the drainage divide here is controlled by various resistant layers in the Jurassic bedrock, which slope regionally and very gently to the southeast. In this Region, the gentle tilting movements appear to have been influenced partly by uplift of the Atlantic margin in the west and partly by the lowering of the North Sea to the east. Area 9 also contains evidence of possible late-stage uplift of the Cotswolds in response to erosional unloading of the Severn Valley. The River Severn itself flows generally southerly through Area 9, much of it near parallel to the north-south trending Malvern Line to the west. In contrast, in its upper reaches, it flows generally easterly and southeasterly, from headwaters that are less than 20 km from the sea at Cardigan Bay. In our consideration of Area 9, we shall review evidence that this highest section of the Severn began as the headwaters of an ancestor of the River Thames and flowed eastwards all the way across Southern England to the ancestral North Sea.
**FIG 153.** Map of western England and Wales showing the main Variscan fold trends and the Variscan Front. The surface cover of younger rocks (from Permian New Red Sandstone to Early Cretaceous age) is also shown, along with the catchment area of the Severn-Avon river system.
### AREA 8: BRISTOL
The boundary of this area runs along the coast of the Bristol Channel, up the Severn Estuary and along the banks of the River Severn (Figs 154 and 155). Bristol and Bath are the most important cities. We shall consider the origins of the complex pattern of hill areas and the landscapes of gorges (Avon) and caves (Cheddar, Wookey Hole etc.). In contrast, we shall also examine the origins of the low and very flat Somerset Levels.
The following detailed discussion of the scenery of Area 8 is organised into six Landscapes, labelled **A** to **F** in Figure 156. The main river pathways and coastal flooding zone are shown in Figure 157.
#### Landscape A: The Quantock Hills and Fringes
The patch of higher land in the southwest corner of Area 8 is the northern tip of the Quantock Hills, which rise to an elevation of 310 m at Beacon Hill ( **a1** ), some 3 km from the coast of the Bristol Channel. The bedrock underlying the Quantocks is hard-wearing Devonian sandstone and slate, similar to the bedrock of Exmoor in the west. The resistance of this bedrock to landscape weathering and erosion is the reason for the high ground in both cases.
**FIG 154.** Location map for Area 8.
As in the rest of Area 8, the Variscan Unconformity marks the important end-of-Variscan episode when the Triassic and Jurassic layers surrounding the Quantocks were deposited on folded Devonian bedrock (Fig. 152). Much of the younger, overlying material is mudstone, which has been eroded preferentially over the last few million years to form small hills and valleys at a lower level than the Quantocks themselves (the Quantock Fringes landscape). Geological mapping of the unconformity reveals the ancient landscape of the Variscan mountains, carved into the Devonian and older bedrock between 300 and 200 million years ago, and subsequently buried by Triassic and Jurassic sediments.
**FIG 155.** Natural and man-made features of Area 8.
**FIG 156.** Map showing the main fold trends and faults of Area 8, and the areas underlain by bedrock of Carboniferous age or older. Landscapes **A** to **F** are also marked, along with localities ( **a1, a2** etc.) mentioned in the text.
This Landscape's Bristol Channel coastline runs approximately from west to east and is a continuation of the Exmoor coast (see Area 3). Both run parallel to – and have been controlled by – the main Variscan folds. Hinkley Point ( **a2** ) is notable as the site of two nuclear power stations, one of which is in the process of being decommissioned. The intertidal zone of this stretch of coastline consists largely of a wave-cut bedrock platform, exposed to view at low water on medium tides. Most of the bedrock is Early Jurassic in age and consists of grey mudstone with a clear, regular layering of thin limestones. Examination of the layering shows that this bedrock has been folded locally and fractured by numerous faults that trend east-west. Because these movements have deformed the Jurassic bedrock, they must have occurred distinctly later than the mountain-building episode represented by the Variscan Unconformity, and may have formed during the creation of the Bristol Channel Basin (Fig. 153).
**FIG 157.** Main river pathways and coastal flooding zone of Area 8.
A narrow beach of sand and mud is present along much of this coastline at the upper limit reached by normal high tides. Inland from this, there is generally a small cliff line that is only reached by storms during high tides. It seems likely that this cliff line was created by storm action relatively recently, after the sea rose to within about 10 m of its present level some 6,000 years ago. However, as along many other stretches of the coast of Southern England, initial erosion may have taken place some 130,000 years ago during the Ipswichian, when the sea was last as high as it is today.
#### Landscape B: The Somerset Levels and Moors and the Mid-Somerset Hills
The flatness of this Landscape is one of its most remarkable features. In Southern England, the only other flat area of comparable size is the Fens of East Anglia (Area 15). Both the Fens and the Somerset Levels owe their flatness to the presence of easily eroded mudstone bedrock in areas that have experienced repeated invasions and retreats of the sea during the last 2 million years. These repeated invasions have resulted in large flat surfaces of eroded bedrock covered by young, surface-blanket sediments, deposited by low-lying rivers along the coasts or washed inland by the sea. In the Somerset Levels, the flat areas are underlain by the soft mudstones of the lower Lias (Early Jurassic), which are often covered by a surface blanket of Quaternary muds, formed during the late stages of the Flandrian sea-level rise. Some areas, locally called moors, are peat-rich and were formed in wetland landscapes.
The hills, although low, often present abrupt slopes overlooking the flat lands. Brent Knoll ( **b1** ) is a striking conical hill rising over 100 m above the surrounding Levels, and best visible to people travelling southwards along the M5 motorway. It consists of flat layers of Early Jurassic mudstones capped by a small patch of Middle Jurassic limestone and a prehistoric fort. Brent Knoll owes its existence to its cap of limestone, which is a more resistant bedrock layer than the mudstones underneath it. Erosion of the slopes of the Knoll was active both during times of warm climate and high sea level, and during cold episodes, when freeze-thaw action led to slumping of bedrock material and soil down-slope to produce the conical form we see today.
To the east, the Wedmore to Wookey ridge ( **b2** and **b3** ) is another distinctive feature of the northern part of the Somerset Levels. The zigzag plan shape of the ridge follows the pattern of a number of faults that cut limestones of Late Triassic and Early Jurassic age. This is another example of deformation (in this case faulting) that has taken place since the Early Jurassic, changing the pattern of resistant bedrock and resulting in a distinctive present-day geometry in the scenery.
The stretch of coastline bordering Landscape **B** has a low-lying hinterland because it marks the area in which the main Severn Valley is joined by the River Parrett ( **b4** ; Fig. 158). The Parrett is one of the main tributaries of the Severn, bringing water and sediment from much of Somerset. At the maximum of the last cold episode of the Ice Age, some 20,000 years ago, the entire Bristol Channel was dry land at least as far as Land's End and westernmost Wales. Since then the sea has advanced to its present position by flooding this landscape of rivers, valleys and hills. The River Parrett flows into Bridgwater Bay (Fig. 157) where an array of channels and bars is covered and modified twice a day by the exceptionally large tides of the Severn Estuary. These tides have the greatest range of anywhere on the British coast: up to 15 m between low and high tide. This remarkable range is a result of the unique interaction between the orientation, shape and location of the Bristol Channel, and the patterns of tides that move around this part of the eastern Atlantic margin.
**FIG 158.** Meandering lower reaches of the River Parrett (Fig. 156, **b4** ), near Burnham-on-Sea. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
Away from the channels and bars of the river mouth, the intertidal zone is unusually extensive, with 2–4 km of land exposed at low tide. Much of the exposed material is mud, although it tends to be sandy and locally gravel-rich near the high water mark, where stronger wave action (especially under storm conditions) has sorted and moved the sediment. Although there is obviously a large amount of sediment movement offshore along this coast (as shown by the muddy waters), it is not known whether the sediment predominantly comes from the land via rivers, or from the floor of the recently flooded Bristol Channel.
Above the high water mark there is commonly a belt of wind-deposited dunes, up to 1 km wide. The dune belt was built largely under storm conditions after the sea stabilised at its present position. Low islands of bedrock appear locally from beneath this spread of young sediment and, as at the mouth of the Parrett, they have sometimes become incorporated into the coastal bars and spits of the present-day coastline.
#### Landscape C: The Mendip Hills
The Mendip Hills extend across the Somerset-Gloucestershire border, from Weston-super-Mare in the west to Frome, some 40 km to the east. They rise to over 300 m above sea level, and their landscape of limestone cliffs, plateaus and gorges provides a striking contrast with the surrounding lowlands.
The Mendips are defined by a number of anticlines (upfolds) that have brought Devonian Old Red Sandstone and Carboniferous Limestone to the surface. These older rocks have resisted erosion to form uplands distinctly higher than the surrounding softer and younger bedrocks. The pattern of anticlines and small faults was created during the Variscan mountain-building episode some 300 million years ago.
A cross-section through the North Hill upfold (Fig. 159), just north of Wells, illustrates some of the features found in many of the Mendip anticlines: a core of Devonian sandstone is flanked by layers of Carboniferous Limestone that are steeply tilted (to about 40 degrees) and cut by small faults. The Devonian and Carboniferous bedrocks have resisted erosion and form rolling upland plateaus, possibly relicts of some earlier erosion event. Perhaps they are wave-cut platforms, recording a time in the past when sea level was very high and/or the land was lower, similar to the wave-cut platforms identified in the Southwest granites. The highest elevation of the cross-section is in the Devonian bedrock, at 305 m.
Another cross-section (Fig. 160) reconstructs the wider Variscan fold and fault pattern in a north-to-south direction across much of Area 8. We can picture a geometry of this sort forming by using an analogy: imagine a weak paper tablecloth violently pushed over the table-top. The paper will fold and tear as it is bunched up. Similarly, the upper layers of bedrock have folded and faulted as they slid northwards over a flat-lying surface (the table-top) and over each other. The flat-lying surface must have formed by fracturing along some weak layer deep in the ancient (Silurian or older) bedrock.
**FIG 159.** 5 km cross-section through the North Hill upfold in the Mendip Hills. Located as line W-E in Figure 156.
During the Variscan deformation, the rock now forming the Mendips was part of a massive convergent mountain belt. The intense heat and pressure created by the convergence led to metal ores being deposited in the rocks by hot-water (hydrothermal) circulation, similar to the circulation which deposited tin and lead in the granites of Cornwall. As in Cornwall, the Mendips have been mined for their metal ores, particularly those containing lead and zinc. The Romans were the first to exploit these ores, and the industry reached its peak in activity during the seventeenth century, but continued until much more recently. Mining activity has left considerable evidence of surface working in local landscapes, particularly in the areas around Charterhouse ( **c1** ) and Shipham ( **c2** ).
**FIG 160.** 20 km cross-section suggesting the fracture and fold structure at depth that would explain the surface pattern. Located as line N-S in Figure 156.
The Mendips are also known for their cave complexes, resulting from moving water dissolving and enlarging crack systems in the limestone bedrock. A famous example is Wookey Hole ( **c3** ), just north of Wells. In some areas, most famously Cheddar Gorge ( **c4** ; Fig. 161) and Burrington Coombe ( **c5** ), roof collapse of large cave systems has generated spectacular landscapes that attract large numbers of visitors. Large limestone quarries are a man-made feature of the Mendip scenery, often of similar size to the famous natural collapses.
One particularly interesting feature of Area 8 is the relationship between the folded and faulted Variscan bedrock, as exemplified in the Mendips by the bedrocks of Devonian and Carboniferous age, and the overlying New Red Sandstone of Triassic age. Careful examination of the contact between these rocks reveals episodes when hilly scenery was being 'drowned' in Triassic times by angular conglomerates ( _breccias_ ), sandstones and mudstones. These, of course, are further examples of the Variscan Unconformity (Fig. 152). In some localities, kilometre-scale valleys have been eroded into Carboniferous bedrock and then plugged up by sediment. It seems clear that much of this sediment must have been transported from source areas some distance away from the valleys themselves. Figure 159 presents an example of this situation, where, at the western end of the cross-section, around We stbury, the Carboniferous Limestone has been tilted and fractured, and then eroded to produce a distinct valley almost 1 km across. This valley was then plugged by Triassic sediments consisting of angular coarse blocks (breccias) derived from the nearby valley walls and sandstones derived from nearer the valley centre. Local hollows in the hills are preserved in the same section on the Mendip upland east of Priddy, and on the northern Mendip flank near Chewton Mendip.
**FIG 161.** Cheddar Gorge seen from the Heights of Abraham (Fig. 156, **c4** ). (Copyright Landform Slides – Ken Gardner)
#### Landscape D: The Bristol and Avon Valleys and Ridges
This Landscape lies north of the Mendips and west of the Cotswolds, and includes the city of Bristol and the coastline from Weston-super-Mare to Avonmouth. North of Avonmouth the landscape merges into that of the Severn Vale. The region is hilly but does not reach the heights of the Mendips. The main river is the Avon, which runs northwest towards the Severn, passing through Bath and Bristol on the way.
Like the Mendip Hills to the south, the discrete hill features of this scenery are the result of Variscan fold structures in the bedrock. However, the folds are less regular and continuous in their arrangement than in the Mendips, because the Bristol Landscape appears to have developed across the transitional zone of the Variscan Front. Here the east-west trends of the main Variscan mountain belt give way northwards to a more open arrangement with a general north-south trend.
In spite of this important difference in the regularity and trend of the folds, the basic bedrock components are very similar to those of the Mendips. Carboniferous Limestone is the most distinctive feature of the folds, and one of its most famous features is the Avon Gorge ( **d1** ; Figs 162 and 163) at Bristol. The cliffs of the gorge are up to 100 m high, and have been formed partly by rainwater dissolving the rock and partly by gravitational collapse of the highly fractured limestone.
Away from the hills, the surrounding landscape is often underlain by a sequence of Late Carboniferous sediments broadly grouped as the Coal Measures. The Coal Measures are predominantly mudstone, but also contain coals and sandstones. Being mostly mudstone, the coalfields have tended to be preferentially eroded by younger rivers and streams, resulting in rather lower landscapes. This was also the case during Triassic times, because the distribution of Triassic sediment in many of the coalfield areas provides evidence that these areas were low-lying when sediment was accumulating. The large volume of Triassic sediment present indicates that much of it was not simply being derived from local sources, but was being transported over longer distances, probably from the central peaks of the Variscan mountain range to the south.
**FIG 162.** The Avon Gorge, looking downstream from the Clifton Suspension Bridge (Fig. 156, **d1** ). (Copyright Landform Slides – Ken Gardner)
**FIG 163.** Looking eastwards over Bristol with the Avon Gorge and Clifton Suspension Bridge in the foreground (Fig. 156, **d1** ). (Copyright Dae Sasitorn & Adrian Warren/ www.lastrefuge.co.uk)
A number of small areas of Jurassic sediment occur in the western part of Area 8. The most prominent of these forms Dundry Hill ( **d2** ) on the southern edge of Bristol. Dundry, rising to 233 m above sea level, is a flat upland made of limestones of the Middle Jurassic Inferior Oolite. It is ringed by a broad zone where the limestones have landslipped downwards on slopes of Early Jurassic (Lias) mudstones. In the eastern part of Area 8, the surface is underlain by Early Jurassic mudstones occupying relatively low ground, rising eastwards towards a scarp of the Middle Jurassic limestones that define Landscape **F** , the Cotswolds.
**FIG 164.** Looking northeastwards across Weston-super-Mare, with the headlands of Weston Woods (Fig. 156, **d4** ) and Sand Point ( **d5** ) behind. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
The striking features of the stretch of coastline around Weston-super-Mare are the isolated sections of Carboniferous bedrock that form the strongly projecting headlands of Brean Down ( **d3** ), Weston Woods ( **d4** ) and Sand Point ( **d5** ). The combination of hilly headlands with wide bays provides attractive views (Fig. 164), though the strong tides and abundant availability of muddy sediment make many of the beaches too muddy to attract many visitors. The headlands, along with the offshore islands of Flat Holm ( **d6** ) and Steep Holm ( **d7** ), are the tops of ridges that are the relicts of faulted folds made largely of Carboniferous Limestone, deformed during the Variscan mountain building and then eroded and draped with Triassic sediments. More recent river erosion has subsequently modified the hill form of the Carboniferous features. Finally, Flandrian sea-level rise has deposited yet another layer of sediment on the low-lying land (now beaches) between these old hill features.
Between Clevedon and Portishead the coast displays another example of a Variscan faulted fold, although in this case it runs northeasterly, forming a ridge parallel to the coast. Inland from the ridge is the Gordano Valley, with the M5 motorway running along its southeasterly slope. The low ground of the Gordano Valley was probably carved out by an episode of erosion when the main River Severn occupied this part of its valley slope. Mapping of the bedrock in this area shows that the present-day coastal ridge was also a ridge in Triassic times, a relict of the early Variscan landscape similar to the Weston-super-Mare headlands and Westbury Valley in the Mendips.
#### Landscape E: The Severn Vale
This Landscape consists of the flat areas lying between the hills of folded Devonian and Carboniferous bedrock of Landscape D and the coast of the Severn Estuary, north of Avonmouth. Locally, these flat areas are interrupted by hills underlain by folded ancient bedrock typical of the Bristol area. The largest of these is near Berkeley ( **e1** ), where a major bedrock structure of tilted and faulted Carboniferous, Devonian, Silurian and Cambrian bedrock runs northward across the estuary. As in the Bristol Landscape ( **D** ), the older bedrock was folded by the Variscan episode, then covered by more-or-less flat-lying Triassic New Red Sandstone, which was then covered by Jurassic bedrock. These flat-lying strata can be seen below both of the Severn Road Bridges, at Severn Beach ( **e2** ) and Aust ( **e3** ).
As explained in greater detail in Area 9, it seems clear that an important episode in the erosion of the Severn Valley has taken place during the last 500,000 years. The removal of soft Triassic and Early Jurassic mudstones from the valley floor unearthed discrete hills made of the folded Carboniferous and earlier bedrock and left patches of relict Triassic and Early Jurassic rock. During this time, the river channel of the Severn has moved laterally across its floodplain, widening the floor of the valley and resulting in the deposition of a surface blanket of even younger river and estuarine sediments.
This Region is bounded to the northwest by the estuary of the River Severn. The river is notable for its tidal _bore_ , a surge involving several waves up to 3 m in height that moves upstream in the uppermost tidal reaches of the Severn at high tide. People now compete to surf the longest upstream distance on the best bores. The largest bores occur when a particularly high tide is combined with critical values of freshwater inflow from the River Severn, atmospheric pressure and wind direction. Predictions and information on locations from which to observe the bore (such as at Minsterworth, **e4** ) are posted on numerous Severn Bore websites. This is the only location in Britain where this phenomenon occurs so clearly and so often, and indicates the special nature of the tidal regime and the shape of the Severn Estuary and Bristol Channel.
#### Landscape F: The Cotswolds
The Cotswold Hills form the eastern margin of Area 8 and consist of erosion-resistant oolitic limestone of Middle Jurassic age. These hills were extensively explored and understood by William Smith (often referred to as 'the Father of English Geology') between 1794 and 1799. Working as a canal and coal-mine engineer, he was able to demonstrate clearly for the first time, by careful examination of the landscape, that individual layers of characteristic appearance and fossil content can be followed from one place to another. He was also a pioneer in demonstrating how these layer arrangements can be presented in diagrammatic form, preparing and publishing the first systematic geological map of England and Wales in 1815.
**FIG 165.** The Cotswold Edge near Wooton-under-Edge, looking northwestwards towards Wortley. (Copyright Landform Slides – Ken Gardner)
The hill ridges stand up above the nearest valleys because of the way that their limestones have resisted erosion better than the surrounding softer rocks (Fig. 165). A remarkable point is that this erosion may have contributed to further upward movement of the landscape: parts of the Cotswolds crust may have been uplifted (or rebounded) by about 30–40 m when the Severn Valley was eroded, removing the weight of 100 m of sediment and producing a compensating flow in the deep crust. This process is discussed further under Area 9.
The Cotswold Hills are generally capped by limestone layers of Middle Jurassic age, but it is remarkable how many of the valley slopes below these caps are also underlain by blocks of limestone – many tens of metres or more across – that have moved down the slopes over the underlying mudstones as the valleys have been carved. This is particularly clear north of Bath, where, apart from isolated ridges capped by limestones that are still in place, local geological mapping has shown that the intervening valley slopes and floors are underlain largely by detached limestone blocks, producing areas of _foundered strata._
In the area between Frome and Bath the bedrock pattern changes. Near Frome the Early Jurassic succession is very thin, apparently because it was a shallow-water shoal in the Jurassic sea. Sediment tended to be moved by wave action off the shoal and into surrounding areas, where greater thicknesses accumulated in deeper water. In this same area, the Middle Jurassic Inferior Oolite is also thin and unusually sandy, while the equivalent of the Great Oolite is a largely mudstone layer known as the Forest Marble. Much of this bedrock succession is interrupted by southwest-northeast running faults that locally run parallel to the directions of the sloping layers in the Carboniferous strata of the Mendip Hills. In the Bath area itself, the topography is dominated by the meandering and incised valley of the Avon. Ten kilometres north of Bath, the main layer capping the Cotswold Hills is the Great Oolite, which is more resistant than its southerly equivalent, the Forest Marble. The narrow valleys carved with an ESE-WNW trend into this Cotswold Landscape give it a particularly distinct form in the area around Marshfield ( **f1** ).
### AREA 9: THE COTSWOLDS AND THE MIDDLE SEVERN
The landscapes of Area 9 (Figs 166 and 167) are dominated by the Cotswold Hills, stretching from the southwest near Gloucester to the northeast near Rugby. They separate the drainage that flows down the Avon and Severn valleys into the Bristol Channel from the drainage of the smaller rivers that flow eastwards and southwards, eventually to the North Sea. Area 9 therefore occupies a central position in the landscape of England and Wales, and the fact that it sends stream and river drainage in such different directions reflects this position.
We shall be considering why the Cotswold Hills exist, why they are located and oriented the way they are, and why they have such a clearly defined edge south of Evesham. We shall also consider why the River Severn flows southwards down the western edge of the Area, and why the large cities of Birmingham and Coventry have developed along the northern edge of the Area. On their eastern and southern flanks, the Cotswold Hills generally lack a well-defined margin, although important cross-cutting valleys there have provided routes for the roads, railways and canals that run between London and the Welsh Borders.
**FIG 166.** Location map for Area 9.
**FIG 167.** Natural and man-made features of Area 9.
The general introduction to this chapter provides an overview of the bedrock geology of the Severn Valley Region as a whole. It also includes a generalised succession for the bedrock layers below the surface blanket (Fig. 151). Although, like the rest of Southern England, this Area has much bedrock of Jurassic and Cretaceous age, it also includes older layers more typically seen further north and west. In terms of the bedrock near the surface, this Area is on the border between the newer and older bedrock regions of Britain.
For the more detailed discussion of the influence of the bedrock on the scenery the Area can be divided into four Landscapes, labelled **A** to **D** on Figure 168. I have simplified the bedrock succession, representing it as a succession of layers of rock ranging in thickness between a few metres to over a kilometre. Each of the layers was formed over a period of time in the distant past when totally different landscape patterns prevailed in the Area. Each consists of sedimentary rock (most commonly mudstone) that was deposited in the sea or by rivers over a period of millions of years. The layers are distinguished from the older and younger layers below and above them by the types of rocks present, their arrangement and, in most cases, by characteristic fossils.
**FIG 168.** Slope map showing the main divisions of the bedrock by age. Landscapes **A** to **D** and localities ( **c1, c2** etc.) mentioned in the text are also marked.
During and after the formation of this succession of layers there were distinct episodes of local movement of the Earth, now recorded in the rocks by gentle differences in the slope or tilt of the layers. The last of the episodes left even the youngest of the bedrock layers with a gentle southeasterly tilt. This episode appears to be linked to a general rising of western Britain due to the emplacement of hot, molten rock at depth, linked to the opening of the Atlantic Ocean. The North Sea was also sinking at this time, causing a lowering of eastern Britain and adding to the southeasterly tilt. For Area 9, the important point is that the tilting of the bedrock means that the oldest and lowest material is exposed in the northwest of the Area (the Carboniferous rocks of Landscape **A** ), while the youngest and highest material is exposed in a very small patch in the far southeast (the Cretaceous rocks of Landscape **D** ).
#### Landscape A: Carboniferous and earlier bedrock
The northern edge of Area 9 contains the southern ends of two areas distinguished by bedrock of Carboniferous and earlier age. The presence of Carboniferous material near the surface here has strongly influenced the ways in which settlement has occurred in these areas: the presence of coal at depth resulted in the development of the South Staffordshire and Warwickshire coalfields, which in turn brought widespread industrial activity to the Birmingham and Coventry areas (Fig. 169).
**FIG 169.** Old and new cathedral buildings in the city centre of Coventry mark its bombing during World War II, reflecting the industrial importance of the city. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
The two examples of the Carboniferous Landscape represented in Area 9 have rather different geology. In the case of the westernmost, South Staffordshire area ( **A1** ), the structure is dominated by an upfold. The core of this upfold is a fault-bounded strip of Ordovician Lickey Quartzite that has been eroded into the distinctive narrow ridge of the Lickey Hills (Fig. 170). This quartzite consists of quartz sand grains, themselves strongly cemented together by later growths of quartz, which make it very resistant to the processes of weathering. The quartzite is the result of an Ordovician episode (roughly 480 million years ago) when the sea flooded across central England, which had, at that time, been weathered and eroded into a very flat landscape. Repeated storm wave activity during this flooding resulted in sand that was unusually rich in pure quartz grains. These grains later became a tough, erosion-resistant quartzite upon burial by further sediment and cementation.
**FIG 170.** Diagrammatic cross-section across the top edge of Area 9 (located on Fig. 168).
The easternmost (Warwickshire) part of this Landscape ( **A2** ) has not created distinctive present-day scenery, probably because rather weak Carboniferous mudstones dominate the near-surface materials. Unlike Landscape **A1** , this area corresponds to a gentle downfold in the Carboniferous layers, although its subsequent movement history has tended to raise the central area of Carboniferous bedrock while lowering its margins, giving something of an upfolded appearance in Figure 170. This movement pattern has included the formation of a southeastern boundary where the earlier bedrock has been eroded and then covered by gently tilted Triassic and Jurassic bedrock. In contrast, the western boundary consists of the steep Warwick Fault (shown in Fig. 170).
#### Landscape B: New Red Sandstone bedrock
The two areas of Landscape **A** described above are surrounded by areas of New Red Sandstone, which constitute Landscape **B**. It is convenient to divide this Landscape geographically into **B1** , the Worcester Basin; **B2** , the Knowle Basin, and **B3** , the Avon Valley Basin.
The New Red Sandstone provides the red (iron oxide) pigment that colours many of the soils and cliffs of the West Midlands. Detailed mapping shows that it consists of a lower (earlier) division called the Sherwood Sandstone Group, made largely of sandstones but also containing coarser-grained conglomerates and breccias (with rounded and angular pebbles, respectively). This is overlain by an upper (later) division called the Mercia Mudstone Group, made up largely of mudstones. In older maps and reports these two divisions are often labelled as _Bunter_ and _Keuper_ , using the terminology first invented for the excellent outcrops of the New Red Sandstone in Germany.
The red (oxidised) colour of the New Red Sandstone, together with the absence of fossils that are typical of seawater deposits, suggests that it was originally deposited from fresh water, particularly in rivers on land. The lower Sandstone Group appears to be largely Triassic in age but may contain some Permian material. The coarse grain size of these deposits suggests they were deposited by relatively fast-flowing, vigorous rivers. The upper Mudstone Group is entirely Triassic in age, and its relatively fine grain size suggests that it formed on the floodplains of more gentle rivers, although distinct sandstone horizons (often referred to as Arden Sandstone) may mark episodes of more vigorous flow. The minerals gypsum and rock salt occur in distinct layers in the Mudstone Group and have been extracted commercially in some localities. These sulphate and chloride minerals formed by precipitation from the waters of saline lakes or coastal lagoons and reflect arid climatic conditions, rather like those of the present-day Dead Sea.
From the present landscape point of view, the coarser deposits of the Sherwood Sandstone Group have locally resulted in hills and slopes. In contrast, the Mercia Mudstone Group tends to have been eroded to form lower ground, except where more resistant sandstone layers (the Arden Sandstone) have produced small scarps.
The New Red Sandstone sediments of the Worcester Basin ( **B1** ) have been gently moved into a downfold, with the younger Mudstone Group bedrock preserved in its centre below Worcester and Droitwich. The older Sandstone Group forms the flanks of this downfold, closer to the older bedrock of Carboniferous age ( **A1** ). The scenery locally reflects this change in bedrock type: in the east a number of northwest-southeast ridges reflect landscape erosion of distinct sandstone layers, sometimes further picked out by the presence of northwest-southeast trending faults. In the centre, slopes cut into the mudstone are small, largely reflecting episodes in valley erosion by relatively small tributaries of the River Severn. In the Kidderminster area, valley slopes have been cut by the River Severn and its major east-bank tributary, the Stour. These have cut into the sandstones, and local variations in sandstone erosional behaviour and in-valley down-cutting histories have resulted in distinct sandstone ridges.
In the Knowle Basin ( **B2** ), the upper (younger) Mercia Mudstone is the bedrock nearest to the surface, so the only slope features tend to be small and due either to Arden Sandstone layers or to features of the surface blanket.
The Avon Valley Basin ( **B3** ) extends from Warwick via Leamington Spa towards Rugby. There is a layer (up to 50 m thick) of Sherwood Sandstone along its northwestern edge, resting on the Carboniferous area of **A2**. Apart from that, the local bedrock is the Mercia Mudstone Group and the scenery is dominated by a surface blanket of ice-laid and river deposits that are discussed below.
#### Landscape C: Jurassic bedrock
Younger than the New Red Sandstone bedrock – and above it in the succession – are distinctive layers of Jurassic age found extensively in the southeastern parts of this Area and beyond. This reflects a widespread change of environment, from the deposition of New Red Sandstone in lakes and rivers during the Triassic to deposition in shallow seas during the Jurassic. In the seas, subtle changes in environment may produce widespread and distinctive changes in the resulting bedrock. Because of this, the Jurassic succession contains many distinct marker layers, and can be divided up and traced like a layer-cake much more readily than the New Red Sandstone. There are five marker layers that have been resistant enough to produce distinct erosional topography in Area 9 (see Fig. 151 for their place in the bedrock succession).
#### (1) _The Rhaetic (labelled R on Figs 151 and 168)_
Although most of the Early Jurassic rocks (historically known as the Lias) consist of soft mudstones that have not generally produced features in the scenery, they are underlain by a group of distinctive beds that, together, have produced steep slopes where the landscape has been carved out by erosion. We use the label _Rhaetic_ , borrowed from central European geological usage, to refer to this layer (also called the Penarth Group). This group of beds is now regarded as partly latest Triassic and partly earliest Jurassic in age. It contains at least one surface representing a relatively short time gap in the deposition and includes mudstones, limestones and fossil beds, up to and including material called the Blue Lias. These beds represent the arrival of coastal and lagoonal conditions after a long period of New Red Sandstone river and lake sedimentation. There are numerous small scarps, particularly in the lowlands of the Avon valley around Evesham and Leamington Spa, which mark the resistance to erosion of this Rhaetic material.
#### (2) _The Marlstone Rock Bed (labelled M on Figs 151 and 168)_
In the middle part of the Early Jurassic succession, the Marlstone Rock Bed tends to form distinct slopes because it contains limestones and iron-rich materials, making it a valuable resource that has been extensively quarried. At Edge Hill ( **c3** ; see also Fig. 173) the Rock Bed caps a 100 m escarpment, straddling the A422 between Stratford-upon-Avon and Banbury, some 5 km southwest of the M40 motorway. This escarpment results from the resistance to local river erosion of the Marlstone Rock Bed, but is more famous as the setting for the Battle of Edge Hill (Fig. 171). The area below the scarp of Edge Hill is still often called the Vale of the Red Horse, although the carvings that once gave it this name are no longer visible. The Vale gained fame because the colour of its rocks was so spectacular, due to the red iron oxide of the Marlstone Rock Bed.
**FIG 171.** Radway Village and the gently undulating flatlands of the battlefield below the Edge Hill scarp (covered with trees at the right of the photograph) (Fig. 168, **c3** ). (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
We allow ourselves to be diverted here to outline the way the Battle of Edge Hill was influenced by this feature of the landscape. The battle, the first large engagement of the English Civil Wars, took place on 23 October 1642. King Charles I was the commander of the Royalist army and the Parliamentarians were commanded by Robert Devereux, Earl of Essex. The troops and the field commanders on both sides were generally inexperienced and unsure, and there was no clear winner in the battle. The king decided that the strategic advantage offered by the Edge Hill scarp was such that he chose to position his army of some 15,000 infantry and cavalry there. Because of the steepness of the upper slopes, the Royalists moved some of their cavalry to the toe of the escarpment before making their charge down onto the similar-sized Parliamentarian army, which had been drawn up on the ground below (now occupied by a large Ministry of Defence munitions depot!). In spite of this move, the charge by the Royalist cavalry was so vigorous that it not only scattered the Parliamentarian cavalry, but overran the infantry lines in its pursuit and became disorganised. Some 3,000 men, including some influential figures of the time, were killed or wounded in the chaos that followed, but the armies then disengaged and regrouped. Over the next days and weeks, the Royalists established themselves in Oxford, while the Parliamentarians consolidated their hold on the London area.
#### (3) _The Northampton Sand (labelled N on Figs 151 and 168)_
In the northeast of Area 9, the Northampton Sand at the base of the Middle Jurassic is important not only as a hard material that resisted erosion during the creation of the present landscape, but also because it has been quarried widely as an economically important source of iron.
#### (4) _The Middle Jurassic oolitic limestones (labelled O on Figs 151 and 168_ )
The Middle Jurassic of this Area was one of the earliest successions anywhere in the world to be analysed in detail and traced from place to place. This pioneering work was carried out by William Smith, as described in the treatment of Area 8. He divided this limestone-dominated, fossil-rich part of the Jurassic succession into two major subdivisions, the Inferior Oolite (lower and older) and the Great Oolite (higher and younger), and was able to trace and map them over many tens of kilometres, although the two divisions together are normally no more than 100 m thick. Although these Middle Jurassic sediments also include mudstones, sandstones and ironstones, a wide variety of limestones is present which dominate the local landscapes, forming the Cotswold Hills, one of the main scenic features of Southern England. Most of these layers of sediment were deposited in the shallow tropical seas that covered Southern England during the Middle Jurassic. The variation in the sediment layers reflects changes in the environments of sedimentation, including periodic invasions of muddy material brought in by rivers. Much of the limestone is honey-coloured, and its wide use as a building stone is one of the most attractive features of the villages and towns of the Cotswolds (Fig. 172).
**FIG 172.** The Lygon Arms Hotel in the village of Broadway (Fig. 168, **c5** ), 8 km southeast of Evesham. The hotel is typical of many traditional Cotswolds buildings and is made using Middle Jurassic oolitic limestones. (Copyright Peter Oliver, Herefordshire and Worcestershire Heritage Trust)
Ebrington Hill ( **c2** ), 5 km northeast of Chipping Camden, is the northernmost point on the well-defined section of the Cotswold Edge, where the scarp is capped by Middle Jurassic oolites. This hill reaches an elevation of 259 m and looks out over the floor of the Avon Valley some 200 m below. The lower slopes are formed in the Marlstone Rock Bed (marked **M** in Fig. 168), while the top is made of the resistant limestones of the Oolite layer.
Bredon Hill ( **c1** ) dominates the low ground where the Rivers Severn and Avon meet. It has a similar structure of resistant layers to Ebrington Hill, though many of the steeper slopes have been covered by blocks of limestone that have collapsed from the edge of the outcrop and slipped down the slopes. The isolation of Bredon Hill from the main Cotswold Edge is due to vigorous back-cutting by the headwaters of eroding streams. These streams must have increasingly encircled and detached this prominent-but previously attached-point on the Edge.
The position and direction of trend of the Cotswold Hills, particularly the well-defined Cotswold Front, is a direct result of the level to which the landscape of the Area has been eroded at the moment. As erosion continues to lower the landscape the Front will move to the southeast, because that is the direction in which the layers slope.
The slope pattern of the Cotswold Hills (Fig. 168) reflects directly the distribution of these Jurassic marker layers. The well-defined Cotswold Edge that extends southwesterly from Ebrington Hill ( **c2** ) corresponds to the thickest development of the oolitic limestones, due to environmental conditions or gentle tilting by Earth movements in Jurassic times. Similarly, the replacement of the prominent Oolite scarp further to the northeast by a more widespread array of lesser scarps (due to the Marlstone Rock Bed, Northampton Sand and a thinner Oolite scarp) is an erosional response to changes in the layer pattern that reflect variations in Jurassic environments and movements (Fig. 173).
**FIG 173.** Comparison of topographic profiles across the northwestern edge of the Cotswold Hills, contrasting the northeastern, multi-scarp sector at Edge Hill (a) with the higher, single-scarp sector at Fish Hill (b). The sections are located on Figure 168.
#### (5) _The Portlandian (labelled P on Figs 151 and 168)_
The layers above the Oolites are of Late Jurassic age and generally consist of mudstones. Most of this younger Jurassic bedrock has not produced distinct topography on erosion, except in the southeast of the Area, east of Oxford, where limestones of latest Jurassic age ('Portlandian') cap some well-formed hills.
#### Landscape D: Early Cretaceous bedrock
The tops of some of the distinct hills in the southeast corner of Area 9 contain small areas with thin layers of Early Cretaceous material. This situation is discussed more fully in the treatment of Areas 10, 11 and 13; in Area 9 these are very small features of the landscape.
#### Younger drainage and erosion patterns
The discussion of this Area concludes with a review of the present drainage systems (Fig. 174) and their Tertiary and Quaternary evolution, because it is largely the rivers that have been responsible for the shape of the present landscape.
**FIG 174.** Main river pathways and coastal flooding zone of Area 9.
The National River Flow Archive gives us insights into the present drainage pattern by providing estimates of mean flow rates (in m3/s) for the main rivers, together with figures for the upstream areas (in km2) being drained by the rivers in question. Here I have selected some of these flow data to demonstrate the present-day important role of the River Severn and its major tributary, the Avon. The very largest mean river flow rate is 106 m3/s at the downstream end of the Severn-Avon system. This station has a catchment area of 9,900 km2, which reflects its drainage of large parts of central Wales and the Midlands. For comparison, the Thames at Kingston has a mean river flow rate of 66 m3/s from a catchment of very similar size (9,948 km2), reflecting lower general rainfall and different groundwater conditions. The gauging stations on the south and east side of the Cotswold drainage divide are the sources and upper reaches of the Nene, Great Ouse, Cherwell and Windrush, with catchment areas in Area 9 of no more than a few hundred square kilometres, and mean river flows of no more than 4 m3/s.
#### _Drainage to the Severn Estuary_
As described above, the Severn and Avon river systems have by far the largest catchments and river flows in Area 9. Where the River Severn flows into Area 9, it has generally incised a few tens of metres into a landscape underlain by New Red Sandstone. **A** distinct floodplain, typically half a kilometre in width, has been built by river sedimentation during the Holocene (postglacial) rise of sea level, but there are often small patches of river terraces at higher levels representing earlier floodplains. Along the rest of its downstream course across Area 9, the Severn continues to display similar features (Fig. 175). However, increases in the width of the young floodplain, the extent of ancient river terraces, and the size of meander bends all correspond to the steady increase in mean flow downstream as the catchment area and number of tributaries increase.
The River Avon is the largest tributary of the Severn, joining it near Tewkesbury after flowing parallel to the Cotswold drainage divide. The tributaries of the Avon that join it from the southeast have been the main agent in eroding the northwestern slopes of the Cotswolds (Fig. 174). The River Avon itself is incised into landscapes made largely of impermeable mudstones of Triassic and Early Jurassic age (Fig. 176). Its young floodplain is locally more than 2 km across, and it has particularly well-developed large meanders (several kilometres in wavelength) in the reach just above and below Evesham. The meanders become smaller – though they are still well developed – in the reach upstream towards Stratford-on-Avon, as the mean flow becomes less. In the area between Coventry and Rugby, large areas of the valley slopes are occupied by surface-blanket deposits, particularly ice-laid materials and water laid muds, sands and gravels. The most important of these, from a landscape point of view, are the Dunsmore Gravels, which form a distinct plateau southeast of the Avon, between Stratford-upon-Avon and Leamington Spa. Here they provide a clear scarp to the river Leam, a southern tributary of the Avon. The age of these gravels is not clear, but they represent a major episode of river deposition that was probably linked to one of the Ice Age cold phases. Whether this was the Anglian cold episode, about 450,000 years ago (oxygen isotope stage 12), or one of the later cold episodes is still uncertain.
**FIG 175.** The River Severn flows towards us past the cathedral in Worcester. The wide floodplain contains the cricket ground (to the left of the river) and the racecourse (to the right of the river), both flooded when the photograph was taken. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
**FIG 176.** Looking westwards over Warwick Castle and the River Avon, which flows to the left on its way to join the Severn near Tewkesbury. (Copyright Dae Sasitorn & Adrian Warren/ www.lastrefuge.co.uk)
The important development of surface-blanket sediment in this Area provides an excellent example of how difficult it can be to separate and distinguish events in the history of the Ice Age. Wolston Quarry ( **c4** ), between Coventry and Rugby, has given its name to the _Wolstonian_ , which was claimed to be a distinct episode of ice advance and retreat later than the Anglian but before the Devensian (see Chapter 2, Fig. 13). Recent detailed interpretation of the Wolstonian surface-blanket succession recognises an early phase of near-ice-sheet river sediments, followed by ice-laid deposits and then the deposits of a lake that was probably ice-dammed and extensive enough to be given a local name: Lake Harrison. These deposits are followed by further ice-laid sediments, and finally by the river-laid deposits referred to above as the Dunsmore Gravels. Although a vivid story of environmental change has emerged from this locality, it is still not clear which of the Ice Age cold episodes is represented.
**FIG 177.** Former rivers of Area 9.
Some of the early surface-blanket, water-laid deposits of the Avon valley have been interpreted as the deposits of a now extinct river that has been called the Bytham (Castle Bytham is 10 km north of Stamford in Area 15). In Area 9, this river has been reconstructed as flowing northeastwards, roughly parallel to the present Avon, before turning eastwards near Leicester (Fig. 177). It is then supposed to have continued to flow eastwards across the present Fens before turning southwards. Along with the ancestral Thames, the River Bytham is thought to have been drastically re-routed by the arrival of the major ice sheet of the Anglian cold episode, about 450,000 years ago.
Other recent work on the landscape history of this catchment is based partly on the recognition that pebbles in old surface-blanket gravels near Oxford have been derived from New Red Sandstone outcrops to the northwest of the River Severn, and could not have been carried by rivers over the present Cotswold Hills drainage divide. Indeed, the gravels lack pebbles of material that would prove that the Cotswolds were available for erosion at that time. The suggestion is that very active erosion of the weak mudstones of the younger New Red Sandstone and Early Jurassic caused the lower River Severn to cut backwards and northwards up the Bristol Channel. This erosion was focused along the valley of the Bristol Channel, decreasing the load on the local crust and causing deep movements in the 'solid' Earth that produced regional-scale uplift (Fig. 178).
This remarkable effect has already been commented on in Chapter 3. It is now realised that loading (for example, by the arrival of an ice sheet) or unloading (for example, by erosion) of the Earth's surface can cause Earth movements that result in the surface moving upwards or downwards, like the response of a wooden boat floating in a bath. The 'floating' in this geological situation is of the upper, relatively light layers of the crust floating on deeper, denser material in the Earth. This sort of raising or lowering of the Earth's crust can happen over timescales that mean northwest England and western Scotland are still rising today, some 20,000 years after the thickest ice sheets there started to melt.
Theoretical models suggest that the margins of the Severn-Avon valley (the Welsh Borders to the northwest and the Cotswolds to the southeast) might be expected to have risen approximately 50 m due to the erosional unloading of the Severn-Avon river system. This raising of the Cotswolds could have caused the diversion of the upper former Thames to become the Welsh headwaters of the Severn, leaving the middle section of the former Thames to become the new headwaters, draining only the southeasterly flanks of the Cotswolds.
**FIG 178.** After valley erosion (1), the unloading of the crust resulted in deep movements within the 'solid' Earth that generated a bulge of movement near the surface of the crust (2). The two effects combined (3) produced scarp edges that may have contributed to the height of the Cotswold and Welsh Border hills.
#### _Drainage towards the Wash on the east coast_
In the northeast of Area 9, some 20 km of the headwaters of the River Nene flow eastwards from a drainage divide near Watford Gap towards Northampton in Area 13. In this westernmost part of the catchment, the Nene and its small tributaries are very gently incised – at most a few tens of metres – and the most clearly defined hills are capped by Northampton Sandstone. The area of the drainage divide is marked by flat hill tops covered with ice-laid deposits, often associated with river sediments thought to have been deposited by rivers flowing from the ice sheets. These ancient river deposits are very much concentrated along the Nene Valley, where a buried channel has been identified, demonstrating the early existence of an ancestral Nene. As in the case of the Avon Valley discussed above, the ice sheet involved may have been the Anglian, but there is some uncertainty about this. Whichever cold episode was responsible, most of the present gentle landscape topography has been created by river erosion since the ice melted.
The headwaters of the Great Ouse flow eastwards from near Brackley to Buckingham, on the edge of Area 9, and then further on towards the northern edge of Milton Keynes. This part of the catchment lacks important scarps and slopes, though it has cut gently into the Middle Jurassic Oolite. There is a surface layer of ice-laid material over much of the higher ground here, and this may have discouraged more widespread down-cutting. The River Tove, a tributary from the west and north, has cut into the Early Jurassic mudstones, but steep slopes are again not a feature. Upstream from Buckingham, well-marked meanders are a striking feature of the river scenery, though with a small wavelength to match the low average flow rates. As with the Nene, it is still uncertain which cold episode of the Ice Age resulted in the deposition of the ice-laid material, but it appears likely that the valley and hill pattern has been eroded since the ice sheet melted. River terrace deposits in the immediate Buckingham area and in the Tove tributary suggest considerable variability in the river evolution histories.
#### _Drainage towards the Thames and the southeast coast_
These tributaries drain generally southwards down the slope of the tilted bedrock layers. The headwaters of the western tributaries have cut downwards into the Early Jurassic mudstones and then, in the downstream direction, cut across the more resistant Middle Jurassic Oolite layer before flowing over the Late Jurassic mudstones. These produce distinctive valley wall slopes in the Windrush (Oxford-Cheltenham road), Evenlode (Oxford-Worcester railway) and Cherwell valleys, where the Great Oolite layer particularly tends to cap the valley wall slopes. These rivers all have low mean flow figures and minor floodplains with young alluvium, but no significant areas of ancient river terraces. Ice-laid material is present in small patches left on some of the high ground during later landscape erosion.
East of the Cherwell, the low ground drained by the River Ray is mainly underlain by Late Jurassic mudstones (quarried for brick-making east of Bicester) and is generally very flat, particularly south of Bicester and the M40 motorway. Here, Ot Moor is a remarkable local area of Fen-like appearance where faulting has brought a strip of Middle Jurassic Oolite material to the surface, and the topography and drainage reflect this. Southeast of Bicester, river erosion has picked out a number of discrete hills with caps of Portlandian (latest Jurassic) limestones and Early Cretaceous material. Between these hills and Bicester itself are two dome-like hills which have been much quarried, but lack resistant caps. These may be relicts of features formed when the resistant Portlandian extended as far to the northwest as this.
# [CHAPTER 7
London and the Thames Valley Region](004-toc.html#ch7)
### GENERAL INTRODUCTION
THE LONDON AND THAMES VALLEY REGION includes the western watershed between the Severn and Thames valleys in Gloucestershire and Wiltshire, one of the main drainage divides in Southern England. It also extends eastwards, through Oxfordshire, Berkshire and Buckinghamshire to London, Essex, Kent and the sea. Travelling from west to east, I have divided it into Areas 10, 11 and 12 (Figs 179 and 180).
I shall start by examining the bedrock geology, and how it relates to the general river-valley and hill pattern of the Region (Fig. 181).
The central feature of this Region is the London Basin, bounded to the north and south by hills of Late Cretaceous Chalk. The folding of the Chalk has formed the London Basin downfold to the north and the Weald uplift to the south (Fig. 182). This is a classic example of how gentle folding of the bedrock can influence landscapes and topography on a Regional scale.
Earlier chapters, particularly Chapters 5 and 6, have shown how important the Variscan mountain building has been in the landscape evolution of Southern England. This mountain-building episode culminated about 300 million years ago and was followed by New Red Sandstone sedimentation during the Permian and Triassic. Southern England then entered a period of relative stability, although gentle regional tilting did occur, along with important variations in sediment accumulation and minor faulting of the crust.
One important effect of the faulting has been to produce differences in the bedrock successions to the north and south of the London Basin in layers of sediment of Early Cretaceous age or older. Most of this faulting was normal (see Chapter 3, Fig. 33), caused by stretching of the crust that fractured it into discrete blocks, some rising and some subsiding. The stretching was a local response to larger movements of western Europe, linked to the opening of the Atlantic Ocean to the west and the sinking of the North Sea area to the east. In the Thames Valley area, the result of this new pattern was that a relatively stable London crustal block (often called a _platform_ ) became separated by fracturing from a subsiding Wessex Basin to the south (Figs 183 and 184). The Wessex Basin is now represented near the surface by the thick succession of Early Cretaceous bedrock in the Weald area to the south of the North Downs.
**FIG 179.** London and Thames Valley Region.
**FIG 180.** Elevation and drainage map of the Thames Valley Region, including the areas of Chalk outcrop.
**FIG 181.** General bedrock succession for the Thames Valley Region.
**FIG 182.** Block diagram, looking westwards, to show how the Chalk outcrop pattern at the surface results from erosion of the fold pattern in the bedrock.
Later, in the Early Cretaceous, sea level rose substantially, flooding the previously river-dominated Wessex Basin and depositing the shallow marine sands of the Lower Greensand, which are often seen to infill ancient river valleys cut earlier into the Wealden bedrock. Later still, by the mid Cretaceous, the deeper marine Gault Clay and Upper Greensand were deposited (Fig. 181). By the Late Cretaceous, rising sea levels progressively inundated most of northwest Europe. The Thames Valley Region was submerged beneath a sea several hundred metres deep, and pure white chalk was deposited over much of Southern England.
During Early Tertiary times, the whole of Southern England was subjected to crustal convergence, causing further movements along faults and local folding of the bedrock. This occurred at roughly the same time as the major convergence that caused the tectonic-plate-related mountain building of the Alps and Pyrenees to the south. Some old faults relating to the lowering of the Wessex Basin relative to the London area were reactivated, but this time in the opposite direction: the Wessex Basin was uplifted and the London Platform subsided. The uplifted Wessex Basin was further compressed to form the Weald uplift or anticline, while in the London region a broad, eastward-opening downfold (syncline) developed, creating the impressive arcuate bedrock pattern that is clearly picked out by the Chalk today (Figs 180 and 182).
**FIG 183.** Bedrock cross-section through the London area, showing the bedrock structure.
As the formation of the London Basin progressed, its northern and southern edges became elevated, while its central portion was depressed, creating a shallow hollow some 80 km wide and about 500 m deep. River networks developed and began to erode the higher ground, transporting sediments inwards towards the centre of the basin. This erosion quickly picked out the strong layer of Chalk in the bedrock succession and produced the distinctive Chalk hills that mark the edges of the London Basin today.
Later in the Tertiary, sea level was rising once more, flooding the newly formed basin as far as Newbury and depositing a thick sequence of marine muds (particularly the London Clay) over a wide area. The London Clay is one of the best-known and most extensive Tertiary deposits in England, forming the bedrock beneath most of Greater London. The properties of the London Clay make it an excellent rock for excavation and tunnelling, and in 1863 the world's first underground railway was opened. Today the London Clay beneath London is riddled with tunnels, and the Underground has become a huge enterprise, used by some 3 million passengers, on average, each day.
Overlying the London Clay are the pale yellow sands of the Bagshot Formation, deposited in a shallow marine or estuarine environment as the sea retreated from the Region once again. The main outcrops are found on Bagshot Heath, an area of elevated ground around Camberley.
**FIG 184.** Structural setting of the London platform.
The most recent deposits in this Region are the extensive Quaternary terrace deposits of the modern-day Thames, predominantly sands and gravels that have been extensively quarried. In the north of the Region there are also deposits ( _till_ ) left behind by the Anglian ice sheet 450,000 years ago.
The evolution of the London Basin downfold and the Weald uplift (see also Chapter 2, Fig. 10) can be summarised as follows:
1. Prior to about 60 million years ago, the Thames Valley Region was covered by the sea, allowing Chalk and Earliest Tertiary sediments to accumulate in approximately horizontal layers. By about 60 million years ago, sea level had dropped and/or the Region had been uplifted to expose dry land.
2. Between 60 and 45 million years ago, crustal compression began to move the bedrock units to create the London Basin downfold and the Weald uplift. The London Basin subsided along an approximately east-west trending axis and the rocks to the north and south of this axis were tilted gently inwards by about 1 degree. The sea flooded the newly created basin from the east and sediments began to accumulate.
3. Continuing compression between 45 and 40 million years ago gradually increased the tilts of the rocks forming the fold limbs. Erosion of the uplifted ground to the north and south of the London Basin exposed the Chalk that now forms the Chilterns and North Downs respectively. Between about 40 million years ago and the present day, river networks became established on the high ground and the sea repeatedly advanced into and retreated from the London Basin. Erosion continued and intensified, lowering the landscape generally and causing the Chalk scarps to retreat inwards towards the centre of the basin.
4. Today, the landscape has been eroded to expose Early Cretaceous sediments in the core of the Weald uplift, bounded to the north and south by the Chalk scarps of the North and South Downs. Tertiary sediments are preserved within the London Basin, while to the north, at its northern margin, another Chalk scarp marks the Chiltern Hills.
#### Modification under Ice Age conditions
The Thames Valley Region was only rarely invaded by ice sheets during the Quaternary. The most widespread invasion of the past few million years occurred during the Anglian cold phase 450,000 years ago, when ice reached the London Basin and diverted the course of the ancestral River Thames. The more local effects of the Anglian glaciation on the London Basin are discussed further in the Area accounts.
Although most of the Region has not been covered by ice sheets, it has still been severely affected by the periglacial (near-glacial) climate. For most of the time the land was treeless tundra, with a permanently frozen subsurface layer of soil and bedrock. At the surface, soil and bedrock were frozen in winter but thawed every summer, an effect which, combined with the snow-fed spring meltwater, created fast-flowing and highly erosive rivers. The 'dry valleys' of the Chalk were carved at this time: chalk is naturally porous because it is highly fractured, but the frozen subsurface blocked the fractures and prevented water from draining away through the chalk as it did during warmer times. Instead the water flowed across the surface, carving valleys that are visible today.
Other cold-climate effects on the scenery were land-slumping and land-slipping, accelerated by freeze-thaw cycles. These created characteristic indents in hill ranges (see Areas 10 and 12) and concentrated Sarsen Stones in valley floors (see Area 10). Glacial processes also modified the earlier, river-created landscape, for example in south Essex in Area 12.
The River Thames was severely affected by the Ice Ages. Before the great Anglian glaciation the Thames entered the London basin from the west approximately where it does now, but then flowed northeastwards along the Vale of St Albans, some 30 km north of its present course. It then turned northwards in the Chelmsford area and flowed across north Essex and Suffolk, eventually joining the Rhine somewhere in the area now covered by the southernmost North Sea (see Area 11). Just under half a million years ago, the advance of the Anglian ice from the north extended across the course of this ancestral Thames, locally damming the river and deflecting it progressively southwards to finally take up its present path. The hill ridges of south Essex, the Valley of Romford and the estuaries of the Blackwater and Crouch are all likely to have been shaped during episodes when the Thames or its immediate tributaries flowed in that direction.
#### Coastlines and sea-level rise
The coastline of the Thames Valley area is one of the youngest features of the landscape, since it has been profoundly affected by the dramatic rise in sea level over the last 10,000 years. At the end of the most recent cold phase of the Ice Age, the River Thames and its tributaries flooded seasonally over wide, braided floodplains. The rise in sea level flooded the Channel, turning the lower river valleys of the Thames and its tributaries into tidal estuaries. The sea level did not rise continuously, however, and small drops in sea level are marked by layers of peat in the sediment. The peat layers are the remains of plants which colonised the exposed mud flats when sea level dropped, only to be buried by silt and clay when the sea level resumed its rise once more. The last peat layer dates from the third or fourth century AD, when sea-level rise destroyed several Roman forts built on the coast.
Away from the estuaries, most of the coastline consists of large expanses of mud flats and salt marshes, although much of the original marsh has been drained for agriculture. The coast between Southend-on-Sea and Dengie (30 km to the northeast) is typical: salt marsh is separated from intertidal mud flats by _chenier ridges._ These are raised ridges almost totally composed of seashells, which can be up to 3 m high and 25 m wide. They mark the transition between land and shore, since they are formed when shells are thrown up onto the salt marshes by storm-whipped waves. The ridges are moving landward at up to 8 mm a year due to continuing sea-level rise in this area.
Sea-level rise poses an important problem for the London area. Due to a combination of subsidence and global sea-level rise (estimated at ≈1–2 mm a year since 1900), levels are rising in the Thames estuary by about 60 cm a century, relative to the land.
After the 1953 flood of the east coast and Thames Estuary, when some 300 people were killed, it was decided to build the Thames Barrier (Fig. 185). This is situated at Woolwich and has six moveable gates which can be raised in minutes if needed. It was built between 1972 and 1984, and was designed to be effective until at least 2030. Many longer-term solutions to protect London are also being considered. One recent proposal is for a 16 km ("ten-mile") barrier from Sheerness in Kent to Southend in Essex, in order to protect a much more extensive section of the Thames Estuary (Fig. 180).
**FIG 185.** The Thames Barrier. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
### AREA 10: THE COTSWOLDS TO READING
Area 10 straddles the main topographic and drainage divide of Southern England (Figs 186 and 187). About half of it is part of the Thames catchment and drains eastwards, via London, to the North Sea, while its western areas form parts of the Bristol Avon and Severn catchments, which drain into the Bristol Channel, and its southern part (Salisbury Plain) drains southwards towards the South Coast (Fig. 188).
The Area can be divided into four Landscapes based upon the presence of particular bedrocks immediately below the surface blanket (Figs 189 and 190). The large-scale features of the bedrock pattern, as shown by the locations of the Chalk hills, have already been explained in the general introduction to this Region. The more detailed pattern has been created largely by river erosion, which has modified the gently sloping limbs of the London Downfold and transported material to the east. In particular, the locations of the Chalk Edges are entirely due to the interaction of earth movements and landscape erosion over the past 60 million years, influenced especially by climate change.
**FIG 186.** Location map for Area 10.
**FIG 187.** Natural and man-made features of Area 10.
The bedrock of Area 10 ranges from Jurassic to Early Tertiary in age (Fig. 189), and the distinctive patterns of hills and valleys in each of the four Landscapes correspond directly to the different bedrocks that underlie them. Each Landscape is considered in turn below.
#### Landscape A: The Cotswold Hills of Middle Jurassic limestone
The upper Thames and Avon valleys are bordered in the northwest by the Cotswold Hills, which trend roughly northeast from Bath (see Area 8), across the corner of Area 10 towards Northamptonshire (see Area 9). The Cotswolds are formed of Middle Jurassic layers, often oolitic and shelly limestones with an average thickness of about 100 m. They dip very gently southeast, forming a series of rolling plateaus or 'wolds' dissected by narrow, wooded valleys. To the southeast the valleys widen and the landscape becomes gentler as the limestone layers slope very gently beneath the clays of Landscape **B**. In Area 10, Stroud and Cirencester are the main Cotswolds towns, and they were important centres of the wool industry during the Middle Ages. The fine, honey-coloured Cotswold Stone houses can still be seen in town centres today, along with fine 'wool churches', built in the late Middle Ages when the economy of the region was very strong.
**FIG 188.** Main river pathways and flow rates for Area 10.
Around Stroud it is remarkable how much of the highly sloping landscape of the Cotswold Edge appears to conceal large masses of limestone that have become displaced and moved down-slope, under gravity, as the slopes have been evolving by erosion. The most vigorous of these collapse movements are likely to have taken place during the Ice Age under periglacial conditions, when freeze-thaw processes were most active.
#### Landscape B: The Mudstone Lowlands of Late Jurassic to Early Cretaceous bedrock
The Wiltshire and Oxfordshire Clay Vales form much of the northernmost part of Area 10, extending roughly from Trowbridge, via Cirencester ( **b1** ), to Oxford ( **b3** ) along the path of the Thames. The Vales consist of a broad belt of open, relatively low-lying, gently undulating farmland underlain by blue-grey Oxford and Kimmeridge Clays of Late Jurassic age They are part of a larger belt of clay-dominated lowlands that link eastwards with the Cambridgeshire Late Jurassic-Early Cretaceous Greensand-Gault belt (Landscape B of Area 13). The clays of the Vales weather into heavy, wet, slightly calcareous soils which support wide expanses of hedge-lined pasture.
**FIG 189.** Slope map of Area 10, showing important bedrock boundaries and Landscapes **A** to **D**.
The centre of the Oxfordshire Clay Vale is dominated by the valley of the River Thames, flanked by Quaternary gravel deposits derived from the Cotswolds. The largest towns tend to have grown on these free-draining gravels. The surrounding floodplain consists of Jurassic clay mantled by a substantial layer of more recent river sediments, providing excellent arable farmland. Over the past few hundred years farmers have planted hedges and pollarded willows to divide the area into a very distinctive patchwork pattern of fields, thought to have inspired Lewis Carroll's 'chessboard' landscape in _Through the Looking-Glass._
**FIG 190.** Landscapes, Downs, Vales and localities ( **b1, b2** etc.) of Area 10.
As well as offering ideal ground for building, the Quaternary gravel deposits have also been exploited as a ready source of aggregate for road building and the construction industry. In the regions south of Cirencester ( **b1** ), southeast of Whitney ( **b2** ) and north of Oxford ( **b3** ), active gravel workings and flooded former gravel pits have become locally extensive features of the landscape. These gravel pits are clearly visible on the maps, particularly south of Cirencester, where an area some 7 km across has been designated as the Cotswold Water Park. Many of these areas of man-made lakes are now being managed as nature reserves, or have been turned into lakeside housing developments.
The character of the River Thames has changed dramatically over the last 2.6 million years of Quaternary time. Like all rivers that are only constrained by resistant bedrock in a few localities, it has changed its course many times, switching back and forth across a floodplain that is also continually changing. By studying the record of these changes preserved in the Thames terrace gravels, geologists have been able to reconstruct the later drainage history and climate of the Quaternary for much of Southern England. The evidence shows that the Thames was a much greater river at times in the past than it is today. There are also indications that, prior to the uplift of the Cotswolds, its headwaters may once have drained wider areas of the West Midlands and even north Wales (see Chapter 6). During cold episodes of the Ice Age, when sea level was much lower than it is today, the river also extended eastwards over what is now the floor of the North Sea, following the axis of the London downfold to join the Rhine, before flowing southwards and westwards along the valley of what is now the English Channel (see Chapter 2).
At least nine distinct gravel terraces, each at a different height above sea level, have been identified in the Thames Valley generally (see Area 11), and attempts have been made to link these terraces to the climate record inferred from oxygen isotope data (see Chapter 2, Fig. 13). The dating of individual terraces remains controversial, but a recurrent cycle of climate change and terrace formation is generally assumed, consisting of alternating cold and warm episodes:
> **Cold episodes:** High river flow rates, at least during spring melts, lead to down-river transport of coarse gravel sediment and channels with high erosive power. The river is able to build up gravel on its floodplain or cut downwards into its floodplain, depending on elevation, which is determined by the sea level at the time.
>
> **Warm episodes:** Lower flow rates and less powerful rivers, associated with temperate climates, deposit finer-grade sediments. A relative rise in sea level, due to the warming climate and melting of ice sheets, results in flooding of the lower parts of river valleys and the deposition of estuarine and marine sediments. The lower reaches of the river become clogged up with silt. As the next cold phase begins, there is an increase in river discharge and erosion, and the river begins to cut down into its floodplain.
In addition to the vertical movements of the river and floodplain surface described above, the upper Thames has also switched its course back and forth across the Vale of Oxfordshire, constrained by the Cotswold Hills to the north and the Midvale Ridge to the south. The gravel terraces are therefore widespread, distributed horizontally as well as vertically, and their ages vary.
The River Thames now drains eastwards along the Oxfordshire Clay Vale before turning north and then south as it cuts through the Midvale Ridge at Oxford, entering the Vales of White Horse and Aylesbury. In this area, the patchy nature of the oldest (and highest) Quaternary gravels has, in places, protected the underlying Oxford Clay from further erosion, resulting in a series of scattered tabular hillocks rising above the present-day floodplain. The Thames then cuts through the Chalk Downs at Goring Gap ( **c1** ; Fig. 191), which was probably initiated when a tributary of the middle section of the Thames cut through the northern Chalk rim and intercepted the drainage of the ancestral northern clay vales. It is generally believed that the Thames was constrained within the Goring Gap half a million years ago, when its course much further downstream in the St Albans area was deflected southwards to its present position by the arrival of the Anglian ice sheets.
**FIG 191.** The Goring Gap (Fig. 190, **c1** ), looking north (upstream) along the Thames from near Pangbourne. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
In the west of Area 10, the Wiltshire Clay Vale occurs between the dip slope of the Cotswolds to the west and the Marlborough Downs to the east. To the south the Vale extends past Trowbridge and Fro me (Area 8) to join with the clays of Blackmoor Vale and the Vale of Wardour, described in Area 4.
The Wiltshire Clay Vale is primarily underlain by the Late Jurassic Oxford Clay, which gives the area a subdued, undulating topography and heavy, wet soils. In the west, substantial outcrops of rather older sandy bedrock (called _Kellaways Sand_ ) produce rich, free-draining soils that are highly valued as arable farmland. The centre of the Vale is dominated by the wide, level floodplain of the Bristol Avon, which, despite modern agricultural development, still retains traces of an ancient pattern of flood meadows. Surface sediments include river deposits of fine-grained alluvium and terrace gravels. The eastern margin of the Vale is marked by a resistant band of Late Jurassic Corallian Limestone and Early Cretaceous Greensand – equivalent to the Midvale Ridge of Oxfordshire – which is backed by the Late Cretaceous Chalk scarp of the Marlborough Downs.
The market towns and villages of the area are particularly distinctive. A number of valuable building stones are available locally, from the warm, yellow Middle Jurassic Cotswold Stone in the northwest to the rough, brown Late Jurassic Corallian Rag from the east. Ancient towns such as Malmesbury, Chippenham, Melksham and Trowbridge, all of which became wealthy due to the thriving post-medieval wool trade, have made full use of these attractive stones, and their town centres are filled with beautiful historic buildings.
At Wootton Bassett ( **b4** ), south of the M4 motorway and just southwest of Swindon, the clays of the Wiltshire Clay Vale region have produced a geological phenomenon that is extremely rare in Britain – a series of mud-springs. The springs are situated in a small wood called Templar's Firs, and were first described as three domed 'blisters' some 10 m long by 5 m wide by 1 m high. The skin of the blisters was formed by matted vegetation and contained a core of liquid mud which oozed out of any fissure in the skin and into a nearby brook. The blisters have since been burst by inquisitive visitors, but the springs themselves remain. Surveys have shown that the vents contain liquid mud down to a depth of at least 6 m, and that the volume of the underlying mud chamber is much larger than originally anticipated: local farmers have stories of cattle drowning in the springs and, in 1990, in an attempt to block up the main spring for safety reasons, a local contractor dumped 100 tonnes of quarry rubble into the main vent. Within half an hour the stone had disappeared without a trace and the displaced mud spilled out over the surrounding countryside, blocking a nearby stream. The area has since been fenced off and warning signs posted.
The exact cause of the Wootton Bassett springs is controversial, but they appear to result from a combination of local bedrock structure and particular rock types. The springs emerge through the Late Jurassic Ampthill Clay Formation. Underlying this clay is a layer of permeable Corallian Limestone, which acts as an aquifer in which water migrates to the lowest part of a local downfold, where it escapes upwards when the water pressure is sufficient. When the water emerges at the surface it moves the surrounding muddy material upwards with it.
Further east, the Midvale Ridge forms a southern limit to the Oxfordshire Clay Vale. It can be traced from southwest to northeast, running from Chippenham, through Swindon and on towards Oxford. The ridge is formed mainly of sandy Corallian Limestone of early Late Jurassic age, although locally there are also patches of latest Late Jurassic Portlandian sandstones and limestones. These hills are in places capped by a layer of Early Cretaceous Lower Greensand, which has prevented the weathering and erosion of the limestone below, forming prominent sandy knolls. Broadly speaking, the ridge has a tabular profile and, in contrast to the surrounding clay vales, the soils are sandy, light and free-draining, home to scattered woodlands interspersed with sandy pastures.
The Midvale Ridge has a long history of human settlement, and there are a number of important Roman sites located on prominent areas of higher ground. More recently, the small villages and hamlets typical of this region have been built upon spurs and subsidiary low ridges, using locally occurring Corallian Limestone as the main construction material. The area is attractive and offers fine, commanding views over the clay vales to the north and south.
To the south of the Midvale Ridge is the Vale of White Horse. As with much of Area 10, the rocks here dip gently to the southeast, exposing Late Jurassic Kimmeridge Clays along the northern sides of the Vale, followed by Early Cretaceous Gault Clay a little to the south. These rock types produce typical low-lying clay-vale scenery, though this is punctuated in places by prominent-weathering outcrops of Portland limestone. The southern margin of the Vale, immediately north of the Chalk scarp of the Lambourn Downs, is underlain by Early Cretaceous Upper Greensand (mudstones and sandstones), which supports rich orchards in the vicinity of Harwell ( **b5** ).
The Vale of White Horse drains generally eastwards to join the Thames at Abingdon. Like that of the Thames, this floodplain offers fertile arable farmland and frequent gravel deposits, upon which many of the area's towns were first settled. Buildings in the Vales of the Upper Thames are often brick-built, reflecting the widespread use of local clay as a building material. This contrasts with the Wiltshire Vale to the west (see page 248), where local limestones were extensively used as building stones.
The City of Oxford (Fig. 192) probably started to grow because of the strength of the local farming economy and its role as a transport hub, located where the River Thames cuts through the Midvale Ridge. Its ancient heart rests on a tongue of Quaternary gravels that have formed terraces where the Thames and its tributary the Cherwell run parallel to each other before joining.
It is interesting to compare landscape features of Oxford with those of England's other ancient university town, Cambridge (see Area 13). Oxford's large eastern and southern extension from Headington to Cowley is relatively new, and reflects major industrial development in the early twentieth century that largely passed Cambridge by. There is also a considerable difference in the scale of the development of the ancient parts of the two cities, perhaps due to the importance of the river link with London in the case of Oxford. However, it also seems to reflect the difference in scale of the rivers and the terraces that have provided the frameworks for growth. The Thames some kilometres north of Oxford has a mean flow rate of 15.4 m3/s, draining 1,609 km2 of catchment (Fig. 188), whereas the Cam in Cambridge has a much smaller mean flow rate of only 2.8 m3/s from 762 km2 of catchment (see Chapter 8, Fig. 230). So the altogether smaller size of the Cam, both in flow rate and in the size of its catchment, has strongly influenced the size and number of branch water courses constructed, and the scale of the terrace and bedrock hill topography.
**FIG 192.** Looking northwards across the City of Oxford, with the Thames (or Isis) flowing from left to right across the foreground. Beyond that is the ancient centre of the city, with Christ Church Great Quad acting as a landmark, with grass in the quad and Tom Tower on its left side. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
The Vale of Pewsey ( **b7** ) separates the Marlborough and Lambourn Chalk Downs from the Chalk of Salisbury Plain to the south. The Vale is characterised by lush orchards and meadows and gently undulating lowlands, in contrast to the Chalk scarps and uplands to north and south. The Vale is aligned roughly parallel to a broad upfold or anticline running from Trowbridge ( **b6** ) eastwards, formed during the mid Tertiary. Following this crustal movement, the Chalk at the crest of the anticline has been eroded away, exposing the Early Cretaceous Upper Greensand. Subsequent erosion has focused on the relatively softer Greensand, carving a broad, gentle valley with fertile, sandy soils.
#### .Landscape C: The Downs of Late Cretaceous Chalk
The Marlborough and Lambourn Downs, stretching across north Wiltshire and Berkshire, are a region of high, rolling hills underlain by Late Cretaceous Chalk. The Chalk dips gently to the south and southeast and has a dramatic northern edge overlooking the Vale of White Horse. In most cases along this northern edge the upper Chalk appears to have provided more resistance to erosion than the lower Chalk materials, so that it forms the lip of the steep slopes. However, particularly in the Marlborough Downs and just south of Harwell ( **b5** ), hill features of intermediate height have also been eroded into the lower Chalk levels.
Within the Chalk hills, a complex network of dry valleys or 'coombes' seems to have formed during glacial times, when the subsurface was permanently frozen to a depth of several metres. The ice sealed the fractures that normally make the Chalk such a permeable bedrock, resulting in poor surface drainage, slope collapse and erosive surface streams. The dry valleys may be divided into two types: _edge valleys_ that cut into or across the Chalk edge itself, and _dip-slope valleys_ that dissect the Chalk down-slope, away from the edge. Edge valleys show the greatest variability in size and shape, ranging from shallow depressions to deeply incised cuts. They are generally aligned approximately perpendicular to the Chalk edge, and their morphology is controlled principally by the width of the escarpment. Complex, multi-branching systems tend to develop where the zone is broad, while straight, simple coombes tend to be found where the scarp is high, straight and steep. Dip-slope coombes are typically longer than those on the scarp face and often form well-developed, branching valley networks. Near the edge, the dip-slope valleys are shallow and gentle, and the resulting landscape smooth and rounded. Further down dip, as the streams on frozen ground increased in volume and power, the valleys became deep coombes with steep sides. Both classes of dry valley have a broadly U-shaped cross-section.
**FIG 193.** The Manger (Fig. 190, **c2** ), a dry valley in the Chalk scarp at Uffington. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
**FIG 194.** The White Horse (Fig. 190, **c2** ) at Uffington. (Copyright Dae Sasitorn & Adrian Warren/ www.lastrefuge.co.uk)
When the ground thawed after the last (Devensian) cold phase of the Ice Age, the streams that carved these valleys soaked away into the permeable Chalk bedrock and the valleys were left dry. The lower portions of many of these valleys are considered too steep to be worth farming, and it is here that the last remnants of the original chalk grassland can be found, sometimes supporting several species of rare orchids. Perhaps the most famous dry valley in this area is the Manger ( **c2** ), with distinctive flutes on its slopes where the chalk has slumped downwards (Fig. 193). The White Horse at Uffington (Fig. 194) is nearby, and according to local folklore the Manger is the spiritual abode of the white horse, which on moonlit nights would travel here to feed. Up until recently, the steep valley sides were also the venue for local cheese-rolling competitions, held during a two-day festival once every seven years called the 'Scouring of the White Horse'. The floor of the Manger contains thick deposits of Chalk rubble and silt that slumped and washed down-slope under freeze-thaw climate conditions. Careful dating of similar sediments elsewhere in Southern England (see Area 7) has shown that steep Chalk slopes like these were last active during the warming times after the Devensian cold episode.
In general, the Chalk produces light, free-draining, thin soils supporting wide expanses of open chalk grassland. This helps to explain why the area around Lambourn in the Berkshire Downs has become one of England's main centres for race-horse training, with exercise 'gallops' and stables scattered over much of the Landscape.
Over much of the dip-slope of the Chalk, the surface is underlain by a layer of Clay-with-flints, an insoluble, clayey residue with flints left behind after the upper layers of the Chalk had been dissolved by chemical erosion. Clay-with-flints gives richer, more acidic soils than the surrounding chalk grassland and is capable of supporting large tracts of woodland. An example is Savernake Forest ( **c3** ), to the southeast of Marlborough, which is believed to be very ancient.
Another common feature of these Downs are the scattered sarsen stones or _greyweathers_ (Fig. 195). It has been suggested that the sarsen blocks are relicts of local patches of Early Tertiary sandstone which developed a hard silica cement and so resisted erosion while the surrounding, less-cemented and softer sandstones were worn away. These isolated blocks of weathered Tertiary sandstone are often found incorporated into ancient burial mounds or into the foundations of the area's oldest houses. Glacial _solifluction_ processes have transported these blocks downhill, and they are often seen to be concentrated in lines at the bottoms of dry valleys. The sarsens are thought to have come from the Tertiary Reading Formation, a greyweathering sandstone which outcrops as bedrock in a narrow band in the east of Area 10. The wide distribution of sarsen stones across the Chalk Downs suggests that Tertiary sediments used to be much more widespread than they are today across Area 10, but have since been eroded away.
**FIG 195.** Sarsen stones on Fyfield Down (Fig. 190, **c5** ). (Copyright Landform Slides – Ken Gardner)
Area 10 has a long and archeologically important history of human settlement, often strongly influenced by the bedrock geology. The Marlborough Downs region includes many of the most spectacular ancient sites (such as Avebury, **c4** ) linked together by the Ridgeway, an ancient travellers' route from Dorset to the Wash running along the top of the northern Chalk escarpment. This route has been in more or less constant use since at least Neolithic times, around 5,000 years ago, and was presumably chosen because the permeable and well-drained Chalk offered a more direct and reliable all-weather route than the neighbouring clay vales, which were probably densely wooded and marshy. Today the Ridgeway is maintained as a popular long-distance walking path running from Avebury to the northeast, providing an excellent route through some of the most spectacular chalk downland scenery in Southern England.
North of the village of Pewsey, on the southern edge of the Marlborough Downs, is Fyfield Down ( **c5** ), an easily accessible area of chalk downland with one of the highest concentrations of sarsen stones in the country (Fig. 195). Stones from this area have been used in the construction of Avebury stone circle ( **c4** ) and in megalithic monuments at the famous Stonehenge ( **c6** ).
To the south of the Vale of Pewsey is Salisbury Plain, the largest single piece of unimproved chalk grassland left in northern Europe. Since the early part of the twentieth century, much of the Plain has been reserved by the Ministry of Defence for military training purposes, while the surrounding downlands have been extensively modified by agricultural intensification. The downland landscape is of vast, rolling arable fields and unimproved chalk grassland, punctuated by small hill-top woodlands of beech and conifer. The northern and western margins of the Plain are clearly marked by a steep, near-continuous edge overlooking the Upper Greensand of the Vale of Pewsey and the clay vales of the River Avon. As with the Marlborough Downs, a patchy blanket of Clay-with-flints mantles the Chalk in places, often supporting scattered stands of woodland. The Late Cretaceous Chalk slopes very gradually (slightly more than 1 degree) to the southeast, away from the upfold in which the Vale of Pewsey has been eroded.
For the most part, Salisbury Plain is without surface water, providing the typical open scenery associated with the Stonehenge area ( **c6** ). There are, however, a few streams, such as the Hampshire Avon, that drain the plateau. These streams are often deeply incised into the Chalk, with valley bottoms that are lined with gravels and alluvium sourced from the Plain and large numbers of regular side valleys, giving a distinctive branching pattern on the slope map (Fig. 189). Trees have taken advantage of the nutrient-rich soils along these valleys, and the contrast between open chalk grasslands and occasional wooded river valleys is a striking characteristic of this region.
North of Andover and east of Salisbury Plain, the further continuation of the Chalk hills is called the Hampshire Downs. Their northern margin forms a very clearly defined edge that includes Walbury Hill ( **c7** ), which, at 297 m, provides clear views to the north across the Early Tertiary bedrock of Landscape D. Close to the edge of this Tertiary material, local upfolds at Shalbourne ( **c8** ) and Kingsclere ( **c9** ) have brought Early Cretaceous bedrock upwards to be level with the Late Cretaceous Chalk. These upfolds can be regarded as a continuation of the Vale of Pewsey structure further west.
**FIG 196.** The River Thames just upstream from Reading and downstream from Pangbourne. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
Watership Down, made famous as the title of Richard Adams' 1972 book, is a north-facing Chalk edge south of Newbury, on the southerly-sloping (at about 3 degrees) fold limb of the Kinsclere Upfold ( **c9** ). The northern limb of the upfold slopes more steeply, at about 25 degrees to the north, showing that the general movement there was down towards the north. This sense of local movement is consistent with the movement that might be expected on the northern edge of the large London Basin downfold (Fig. 182).
#### Landscape D: The Kennet Valley with Early Tertiary bedrock
The final Landscape of Area 10 is defined by its bedrock of Early Tertiary sediments, marking the western end of the London Basin downfold (Figs 180 and 182). The town of Reading has grown where the River Thames emerges from its valley incised into the Chalk to the north and first meets these Tertiary sediments (Fig. 196). The sediments are largely flat-lying except locally, along the southern margin of the Basin, where they have been tilted by folding in the Kingsclere upfold ( **c9** ). The River Kennet is the central drainage feature of most of this Landscape, although further west its headwaters and tributaries (particularly the Lambourn) drain large valleys with numerous dry side branches in the Chalk Downs.
The Early Tertiary sediments consist of between 100 and 200 m of muddy and sandy sediment. Some of this was deposited by streams and in swamps, but most of it, particularly the London Clay, accumulated in what appears to have been an arm of the sea occupying the London Basin.
To the south, topographic surfaces in the Chalk Downs have been suggested to represent coastal erosion _peneplains_ formed at about 200 m above sea level about 5 million years ago (Late Miocene or Pliocene), but the definition of the surfaces, and their age, are very speculative.
Many of the slopes visible in the slope map (Fig. 189) on the valley floors in this Landscape are clearly the result of river erosion into Early Tertiary or Chalk bedrock. In some cases they may be fragments of earlier river floodplains now represented as terraces. These have been mapped and correlated with the 'staircases' of terraces identified in the middle and upper Thames (see Fig. 192 and Landscape **B** respectively). It is relatively easy to distinguish some of the higher floodplains as dating from the Anglian glacial (about 470,000 years old), and lower ones as post-Anglian, representing episodes in the Late Pleistocene history, although local correlations are difficult to confirm in many cases. Despite the difficulties, the way the River Kennet has generally cut downwards through time and climate cycles is clear.
### AREA 11: LONDON
One hundred years ago, more people lived in London (Figs 197 and 198) than in any other city on Earth. Although London now rates as only fifteenth in a recent survey of the populations of the world's cities, it is indisputably still one of the greatest in terms of its historical and economic importance. In fact, a recent report based on the 2001 British census suggests that, in economic and social terms at least, the whole of Southern England can be regarded as fringing Greater London!
The proportion of the ground covered by buildings, roads and railways in London is so great that it often obscures the local landscape (Fig. 199). It is therefore necessary, in the maps, to take away the layers of man-made 'cover', in order to see the natural features beneath.
**FIG 197.** Location map for Area 11.
As Figures 200 and 201 show, London has grown in the natural basin created by the Chiltern Hills to the northwest and the North Downs to the south. The centre of this basin, including most of Greater London, is dominated by the River Thames and its floodplain, along with a number of isolated hills. In spite of the remarkable growth of Greater London, the river still dominates the scenery at its heart, and has created most of the local slopes and hilly viewpoints. Towards the west end of the basin, around Bracknell, are the Thames Basin Heaths, while to the east the River Thames broadens out into a wide estuary (Area 12). The Thames and its estuary have been key factors in London's remarkable growth and development.
I have divided this Region into seven Landscapes, indicated by the letters **A** to **G** on Figure 201.
#### Landscape A: The Vale of Aylesbury
This Landscape is defined largely by its low elevation relative to the Chiltern Hills to the southeast. The bedrock consists of largely Late Jurassic mudstone (mainly Kimmeridge Clay and Portland Beds) covered by mudstones of the Early Cretaceous Gault Clay, so it is not surprising that the land is relatively low-lying and lacks obvious topographic features. This Landscape links with more mudstone lowlands to the west (Landscape **B** of Area 10) and with the Clay-Greensand-Gault belt to the northeast (Landscape **B** of Area 13).
**FIG 198.** Natural and man-made features of Area 11.
#### Landscape B: The Wealden margin
South of the spectacular Chalk hills of the North Downs, there is a distinct belt of hills formed because of the resistance to erosion of the Lower Greensand of Early Cretaceous age. The Greensand is rich in quartz grains held together by mineral cement, and seems to have resisted erosion more effectively than the overlying and underlying mudstones. In fact, the Greensand has resisted erosion so well in this Area that Leith Hill ( **b1** ) has an elevation of about 290 m – distinctly higher than the Chalk hills of the North Downs (Landscape **D** ), which reach a height of only 173 m at Box Hill ( **d4** ). The Greensand has again resisted erosion to the east of the River Mole, south of the M25 and M26 motorways, and the resultant hills reach over 200 m in elevation south of Sevenoaks.
**FIG 199.** View from Westminster over central and eastern London, looking along the Thames towards the sea. (Copyright London Aerial Photo Library)
**FIG 200.** Main river pathways, flow rates and coastal flooding zone for Area 11.
South of the Lower Greensand ridge, earlier Cretaceous bedrock has again influenced the topography, particularly towards the centre of the Weald Uplift. Here the tough, sandstone-rich Hastings Beds create more hilly topography, surrounded by the more readily eroded Weald Clay. As described more fully in Area 6, the hills here are prominent, but lack the linear pattern of the Lower Greensand ridge to the north.
#### Landscape C: The Chiltern Hills
The Chilterns are the northeasterly continuation of the Marlborough and Berkshire Downs (Landscape C of Area 10). The Chalk bedrock that has produced the Chilterns slopes gently downwards to the southeast beneath the London Basin and has been eroded to produce distinctive features in the Chiltern scenery. The first of these is the Chiltern Edge ( **c1** ), which faces to the northwest and results directly from the greater strength of the chalk material, in the face of river erosion, compared with the older and weaker underlying mudrocks. Southeast of the scarp, the Chiltern plateau ( **c2** and **c3** ) dips very gently to the southeast and is divided into distinct sectors by a remarkable series of branching, largely dry valleys, picked out beautifully in Figures 201 and 208. These dry valleys were formed during Ice Age times when freezing of the ground mobilised the near-surface Chalk and prevented water from soaking away, creating surface streams that cut downwards into the plateau. Railways and roads heading northwest from London make good use of these valleys to take travellers across the Chilterns, avoiding the steepest slopes and highest ground.
**FIG 201.** Map of Area 11, showing Landscapes **A** to **G** and localities ( **b1, c1** etc.) mentioned in the text.
The Chiltern plateau is unlike other Chalk uplands in that it is often very heavily wooded, lacking the airy, open character of the Berkshire Downs a short distance to the southwest. Indeed, the region supports the most extensive beech woodland in the country, including examples of 'hanging woodlands' where trees thrive even on the steep slopes of dry valleys. This difference is due to a combination of natural and human factors. Firstly, ice sheets never extended from the north to cover the Chiltern plateau, although further east they did extend well into the London Basin. This means that the Chilterns were able to develop and preserve a thick weathering blanket of Clay-with-flints, covering the plateau with soils that have encouraged vegetation more actively than the typically thin Chalk soils in other areas. Secondly, during the eighteenth and nineteenth centuries, beech trees were planted and managed here in order to supply the rapidly growing furniture industry then developing in London. This contrast between thick forests and more typical Chalk grassland gives the Chilterns a very distinctive charm.
#### Landscape D: The North Downs, Hog's Back and Greensand
The North Downs form the southern limb of the London Basin Syncline or downfold (Fig. 202). Here the upper surface of the Chalk slopes gently to the northwest, just as the Chilterns form the northern limb and slope to the southeast. Otherwise the Chalk hills of the North Downs have much in common with the Chilterns, though there are some important differences. In the east they are broad – similar in width to the Chilterns – extending further east into Area 12 and ultimately reaching the coast between Folkestone and Deal. To the west, the hills narrow dramatically, and there is a very distinctive scarp facing southwards (e.g. at Botley Hill, **d1** ). These features reflect the form and position of the Chalk bedrock layer that underlies the Downs, influenced by its long history of folding and faulting.
**FIG 202.** The Chalk scarp of the North Downs, as seen from Box Hill near Dorking (Fig. 201, **d4** ). Denbies Vineyard is on the south-facing slope beneath. (Copyright R. C. Selley, 2004. _The Winelands of Britain_ , Petravin Press)
The clearly branched dry valley patterns cut into the Chalk hills are similar to those of the Chilterns. Two very clear examples are the valley that provides the main railway and road route across the scarp between Croydon ( **d2** ) and Reigate, and, further east, the large valley of the River Darent ( **d3** ), now paralleled by the M25.
A very distinct difference compared with the Chilterns is the presence of a second clear scarp to the south of the Chalk scarp, due to erosion of a bedrock layer lower than the Chalk in the bedrock succession. This Lower Greensand layer is part of Landscape **B** , just described above.
In the western part of the area, particularly west of the centre of Guildford, is the Hog's Back ( **d5** ), a remarkably straight Chalk ridge that separates the Thames Basin in the north from the Wealden area in the south. The crest of the ridge rises up to 70 m above the ground to the north and is capped by the A31 road. The ridge is an eroded stepfold or monocline that represents the transition between two major asymmetric folds: the London Basin downfold or syncline to the north, and the Weald Uplift or anticline to the south (Fig. 203). The reason for the narrowness and the straightness of the Hog's Back ridge is the presence of large faults beneath this region, separating the London Basin from the Wessex Basin (see the general introduction to this chapter). Movement along these faults, combined with compressional folding, has rotated the strong Chalk layer so that, in places, it is now sloping at up to 55 degrees to the north. As a result of this, the Chalk outcrops at the surface in a long, narrow band cut by straight fracture surfaces. Because the Chalk is strong, and sloping in this way, it has resisted river erosion more successfully than the softer material to the north and south, so producing this prominent ridge.
**FIG 203.** Sketch sections showing (A) the location of the Hog's Back monocline in the overall fold pattern and (B) more detailed pattern of folding and faulting around the Hog's Back.
#### Landscape E: The Thames Valley and the London hills
In the Early Tertiary, sands and marine muds were deposited over the Chalk in the centre of the London Basin downfold, forming bedrock deposits such as the London Clay and Bagshot Beds that underlie much of London. Later crustal compression in Middle Tertiary times involved further gentle movements of the downfold, along with steep folding over a few localised faults, which produced structures such as the Hog's Back.
Landscape erosion then picked out the harder Chalk on the north and south edges of the basin, creating the Chilterns and North Downs. This created a drainage network that focused river erosion on the central part of the basin. In time, the ancestors of the Thames, Colne and Lea developed to form the main stems of today's branching river pattern (Fig. 200). These rivers have cut progressively downwards into the Tertiary bedrock, forming floodplains with alluvial sediment at a variety of different levels, often described as a 'staircase' of river terraces. The staircases provide a record of the river history of the London Basin over the past million years or so.
The terraces form much of the flat land upon which Greater London is built. Slough ( **e12** ), for example, has been constructed upon the ancient Boyn Hill Terrace and sits above the level of the present-day floodplain. The terraces also contain extensive deposits of sand and gravel that have long been worked and used as a source of aggregate. The abandoned gravel pits ( **e1** ) have often filled with water and in time become valuable wetland habitats, recreational parks and water treatment works, such as those in the vicinity of Heathrow Airport ( **e1** ), and between Windsor ( **e8** ) and Richmond Hill ( **e4** ). The Quaternary terraces of the Thames Valley are amongst the best studied in the country and provide an excellent record of the switching of the River Thames back and forth across its floodplain. In addition, the terraces in the lower reaches of the Thames record the most recent rise in sea level associated with the end of the last (Devensian) cold episode, which flooded the lower Thames Valley to form the Thames Estuary.
Each terrace deposit is the remains of a sheet of old floodplain material that formed when the river was flowing at the level of the terrace. Each step of the staircase reflects an episode of downward cutting by the local river channel, while the succession of steps, from highest and oldest down to lowest and youngest, shows how the rivers have cut downwards into the landscape as time has passed (Fig. 204). It has sometimes been possible to suggest ages for the terraces in terms of the stages of the oxygen isotope timescale (see Chapter 2, Fig. 13). The youngest and lowest terrace material was deposited during the rise of sea level that has occurred over the last few thousand years.
Figures 201 and 208 help to pick out the scattered, isolated hills that are distinctive features of the London Basin. Examples include Parliament Hill on Hampstead Heath ( **e2** ; Fig. 205) and Highgate Cemetery ( **e3** ) to the north of the Thames. To the south of the present Thames are Richmond Hill ( **e4** ), Wimbledon Common ( **e5** ), Shooter's Hill ( **e6** ) and Crystal Palace ( **e7** ). Most of these hills are features that became isolated and left behind as the staircase of river terraces was being formed. The importance of these upstanding river-terrace hills is enormous in providing present-day Londoners with a sense of natural landscape, wildlife and recreation.
**FIG 204.** Diagram representing the terraces in the middle (Nettlebed to Slough) and lower (Area 12) parts of the Thames valley, with their ages in terms of oxygen isotope stages.
**FIG 205.** Looking eastwards over Highgate Ponds and Parliament Hill on Hampstead Heath (Fig. 201, **e2** ). (Copyright London Aerial Photo Library)
At the western end of the Thames Valley Basin, northeast of Bagshot Heath ( **f1** ), the present-day Thames flows past another isolated hill. This one is crowned spectacularly by Windsor Castle ( **e8** ), the largest fortified castle in the world that is still inhabited by the (royal) family that owns it. This hill owes its existence to the presence of strong Chalk that was raised up as a small anticline or upfold above faults in the bedrock, probably during the Middle Tertiary (Fig. 206). The fold is relatively narrow and angular, meaning that the Chalk outcrops at the surface over an area only about 1 km across, creating a prominent, isolated hill and an ideal location for a castle (Fig. 207).
About 470,000 years ago, the Anglian cold episode resulted in ice sheets reaching their furthest southern position, leaving a distinctive mark on the London area. It was the only cold episode in the last 2 million years when ice extended as far south as London. As the ice advanced, it deposited a glacial _till_ of boulders, sand and clay. In places, this till is closely associated with river-deposited gravels, showing that material was often transported locally by meltwater streams that ran beneath and in front of the ice. It is the presence of the till that indicates how far south the ice sheets came.
**FIG 206.** The geological structure under Windsor Castle (Fig. 201, **e8** ).
**FIG 207.** Looking westwards over Windsor Castle (Fig. 201, **e8** ) and the River Thames. (Copyright London Aerial Photo Library)
Investigations of Quaternary deposits in the Vale of St Albans ( **e9** ) have identified glacial till overlying gravel deposits that appear to have been laid down by an ancestor of the River Thames. This suggests that, rather than flowing generally eastwards as it does today, the early River Thames used to flow in a generally northeasterly direction towards Essex and Suffolk. When the Anglian ice later advanced into the area from the northeast, the path of the original Thames was deflected to approximately its present-day position some 30–40 km to the south, creating two glacial lakes at the ice front as it did so (Fig. 208). The evidence for these lakes is found in a series of finely laminated silts and clays in the Ware and Watford ( **e10** ) areas north of London. The laminations in these sediments are known as varves, and they are typically formed by annual freeze-thaw cycles experienced by large lakes in cold regions. By counting the number of cycles, sedimentologists have been able to establish that the lakes must have existed for several hundred years.
**FIG 208.** Slope map showing the limit of the Anglian Ice, routes of the past and present Thames and the ice front lakes at Ware and Watford.
With the Thames diverted to the south, a number of large outwash streams developed at the ice front, flowing southwards into the new Thames. As the climate became milder at the start of the next interglacial, these rivers became charged with large volumes of meltwater, cutting valleys to eventually form the rivers Colne and Lea as we know them today. Flow rates in the Thames itself also increased and a number of very coarse gravel deposits date from this time, carried into position by the fast-flowing waters. Examples include the coarse gravel beds of the Black Park terrace (Fig. 204).
As the climate warmed further and the ice retreated, large blocks of ice buried within the till melted, causing subsidence and eventually creating a number of small lakes known as _kettle holes_ (Fig. 209). Over the course of the subsequent interglacial, these small lakes were filled with peat and silt, as well as pollen from the surrounding vegetation. They therefore provide an excellent record of climatic conditions during the warm phase, and so are often of considerable interest to climatologists. A number of kettle holes were discovered during construction work at Hatfield north of London ( **e11** ) where they appear as isolated patches of interglacial sediment set within the surrounding glacial till.
#### Landscape F: The Thames Basin Western Heaths
The Tertiary fill of the London Basin has influenced the landscapes mainly in the areas surrounding Landscape **C** , with its river floodplains and their terraces. The Bagshot Beds (Fig. 181) are sandy deposits which overlie the London Clay in parts of the Basin, especially in the southwest, where they define Landscape F. The sand content of the bedrock here gives rise to nutrient-poor, acidic soils that favour heathland vegetation and pasture, and are of little use for agriculture. The Bagshot Beds mostly outcrop around the Reading-Aldershot-Woking area, also known as the Thames Basin Heaths. The area has been widely taken over for military training purposes, particularly around the Sandhurst and Aldershot military centres, in the valley of the Blackwater river. The waters of the Blackwater flow northwards into the River Loddon beside the hills of Bagshot Heath ( **f1** ) and enter the Thames to the east of Reading.
**FIG 209.** Diagram illustrating the processes of kettle-hole formation.
To the south, where the Chalk scarp of the Hog's Back meets the lower-lying Heaths, water stored within the higher Chalk strata escapes to the surface in a series of freshwater springs. These springs are commonly associated with ecologically important natural habitats, and also seem to have had an influence upon early human settlement patterns in this area.
The Bagshot Beds also outcrop on Hampstead Heath in north London, and around Brentwood and Rayleigh in south Essex (see Area 12).
#### Landscape G: The Hertfordshire Plateau
The Hertfordshire Plateau, between the rivers Colne and Lea, extends northwards into the southern part of Area 13. It is underlain by Tertiary bedrock, most widely the London Clay, with a cover of Quaternary alluvium. Historically it was heavily cultivated, growing a variety of crops including hops and wheat to sustain London, making Hertfordshire famous as the best corn county in England. Over the last 50 years urbanisation has crept north from London, and the area is now a zone of commuter homes and new towns.
As with other Landscapes in this Area, the scenery in Landscape G has been strongly influenced by an episode when the pre-Anglian Thames flowed through it, leaving spreads of gravel at high levels on the Hertfordshire Plateau. The arrival of the edge of the Anglian ice sheet, with lobes extending down the Vale of St Albans and as far as Finchley and Hornchurch (Fig. 208), must have modified the landscape considerably, and the subsequent history of ice-sheet front lakes and kettle holes has been mentioned already.
### AREA 12: THE THAMES ESTUARY
The general introduction to this Region has explained how Greater London occupies the centre of a wide and gentle downfold in the bedrock. The formation of this downfold began more or less at the same time as this Area (Figs 210 and 211) first emerged from the sea, after a long episode of Chalk accumulation. In Early Tertiary times, marine sediments started to accumulate in the Area once again, though this time they were limited to the large embayment of the sea formed by the continuing downfolding of the basin. This sedimentation ceased in mid-Tertiary times, and was followed by a long episode of erosion by rivers that has created much of the present-day landscape of low-lying ground intersected by estuaries (Fig. 212). The River Thames has been the central feature of this erosion, and has also been the main reason for London's remarkable growth to become the commercial hub of England.
This Area, centred on the Thames Estuary, represents a continuation of the London Basin downfold that we have examined in Areas 10 and 11, although its geometry changes eastwards from the simple downfold structure that cradles Greater London. The southern margin of the downfold is still clearly defined in Area 12 by the North Downs, but the northerly Chalk margin curves off first to the northeast and then to the north as it crosses East Anglia (see Chapter 2, Fig. 9). As a result, the northern half of Area 12 is underlain by Early Tertiary bedrock, marking the centre of the London Basin downfold. This pattern in the bedrock (Figs 213 and 214) provides the best division for more detailed examination of local scenery, and forms the basis for dividing the Area into four Landscapes, marked **A** to **D** in Figure 215. Whereas the main features of the Landscapes in the southern part of Area 12 reflect the different resistance to river erosion of the Greensand and Chalk bedrock, the features of the northern parts directly reflect the recent history of river and coastal movement.
**FIG 210.** Location map for Area 12.
#### Landscape A: The Northern Weald
At the beginning of this chapter I introduced the Weald as being exposed within a large uplift, created by upward movement of the Cretaceous bedrock. In the area around Maidstone, the northern Weald succession can be seen ranging southwards from Late Cretaceous Chalk in the North Downs, to the Early Cretaceous Hastings Beds around Royal Tunbridge Wells.
**FIG 211.** Natural and man-made features of Area 12.
**FIG 212.** Main drainage pathways, flow rates and coastal flooding zone for Area 12.
South of the North Downs Chalk hills (see Landscape **B** ), there are a number of hills and valleys that correspond to Early Cretaceous resistant sandstones and weaker mudstones respectively. Moving southwards corresponds to working downwards in the rock succession because of the gentle northward slope of the bedrock. The following features can be observed:
1. A low-lying linear bench that tends to have been eroded in the Early Cretaceous Gault Clay, south of the North Downs scarp. Some parts of the M26 and M20 motorways follow this feature. The low ground has been eroded at least partly by the River Len, a tributary that joins the Medway in Maidstone ( **a1** ), and by the Great Stour upstream of the valley it has carved through the North Downs.
2. A ridge of hills eroded from the Early Cretaceous Lower Greensand, which is about 100 m thick in the Maidstone area but thins easterly, resulting in lower elevations of the hills. At locality **a2** , 5 km south of Maidstone, the Lower Greensand scarp has a particularly distinctive relief of about 100 m.
3. A further belt of low ground ( **a3** ) that has been eroded preferentially in the relatively weak Weald Clay by the upper Medway and its tributary the River Beult.
4. A general area of hilly country around Royal Tunbridge Wells ( **a4** ). Here the bedrock is the more erosion-resistant Tunbridge Wells Sandstone, which forms part of the Hastings Beds (see Area 6). Unusual sandstone bluffs have weathered out to produce features similar in form to the granite tors of Southwest England, which are much prized by outdoor groups and rock climbers.
**FIG 213.** Bedrock succession for Area 12.
**FIG 214.** Oblique hill-shaded map of Area 12 showing bedrock geology.
The Weald Uplift continues south and west of this Area, and is examined in more detail in Areas 6, 7 and 11. The origin of the Wealden bedrock as a southerly-building Early Cretaceous delta is discussed in Chapter 5, Area 6.
#### Landscape B: The North Downs and Isle of Thanet
The North Downs are the most clearly defined and easily followed topographic feature of this Area. The Downs rise to heights of over 190 m above sea level and have the typical shape of a hill range formed by erosion of a tilted layer of resistant bedrock: the north slope of the Downs is relatively gentle, following the northerly dip of the Chalk layers, while the southerly slope is a steep scarp, because here the Chalk has tended to collapse along internal fracture surfaces, which are often steeply inclined.
**FIG 215.** Map of Area 12, showing Landscapes **A** to **D** and localities ( **a1, a2** etc.) mentioned in the text.
Another feature of the North Downs, clearly seen in Figure 215, is the way that the northerly slope is covered with distinct valleys running directly down-dip. In some areas, for example at locality **b1** , just north of Dover, the regularity and parallel trend of the valleys is remarkable, even though the down-slope dip is only about 1 degree. Figure 216 looks northwestwards up the well-defined large valley that cross-cuts the linear valleys developed on the high Chalk ground that it has traversed. This suggests that the main valley has been carved very vigorously compared with the linear, parallel, higher valley features, and this may have been caused by pulses of sea-level lowering. The White Cliffs of Dover are also shown in the photograph, but represent a much younger episode of erosion: the way in which they spectacularly cut across the fortifications of the castle shows just how recently the carving of the cliff has been active.
**FIG 216.** The White Cliffs of Dover (Fig. 215, **b2** ) with their fortifications, castle and Roman lighthouse. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
Further west in the North Downs, the Chalk valleys are more branched and appear to have formed by backwards erosion of upper valley ends, which were shaped by multiple collapse events creating the branches. All the valleys appear to have been carved and enlarged under Ice Age conditions when the subsurface was permanently frozen, as today most of the valleys are dry and so could not have been carved under modern climatic conditions. Many of the valleys contain _head_ , the name given to a mixture of Chalk blocks and chalky mud produced by Ice Age slumping and land-slipping of the bedrock down-slope.
Only two rivers cut right across the North Downs in Area 12. To the west, the Medway flows through Maidstone before passing through the Medway Gap and entering its extensive estuary (see Landscape **C** ). To the east, another breach in the North Downs has been cut by the Great Stour branch of the Stour, flowing through the Downs and then on to Canterbury and the sea south of Ramsgate.
The resistant Chalk ridge of the North Downs has, throughout history, provided a key transport route between London and the shortest sea crossing to continental Europe. The shortest crossing, only some 30 km in length, runs from the resistant Chalk cliffs of Dover ( **b2** ) and Folkestone (Area 7) on the English side, to the similar landscape of Calais and Boulogne on the French side. On the English side, the North Downs have provided the obvious inland routes because they separate the flat lands and estuaries of the south shore of the Thames from the heavily wooded and often wet country of the Weald (Landscape **A** ) to the south.
For example, the Pilgrim's Way from Winchester to Canterbury (Fig. 217) is a historically important route that runs along the southern slopes of the North Downs, avoiding the highest plateau edge. King Henry II is sometimes regarded as the first to undertake the pilgrimage to Canterbury, after hearing of the murder there of Archbishop Thomas Beckett in 1170.
North of the main North Downs lies the Isle of Thanet ( **b3** ; Fig. 218), an isolated and distinctive Chalk landscape feature of the East Kent coastline. Here the Chalk layers have been moved into an upfold that has been eroded and now forms a gentle range of hills up to 50 m in elevation. The layering in the Chalk slopes at almost 10 degrees along the southern margin of the Isle. Between the North Downs and Thanet, the Chalk has been downfolded, and is buried under soft-weathering Tertiary sediments, forming the low-lying lands of the Sandwich-Pegwell Bay area.
The Isle of Thanet was a true island up until very recently. In Roman times the Wantsum Channel ( **b4** ) separating it from the mainland to the west was up to 3 km wide, and the Vikings were able to sail into Canterbury in the eighth century. Over time, the channel has silted up, aided by the land reclamation efforts of the Church in the twelfth and thirteenth centuries, and by the sixteenth century the channel had ceased to be navigable. The Great and Little Stour now flow out to the sea eastwards to the south of the Isle of Thanet (Fig. 212).
**FIG 217.** Canterbury Cathedral, with Roman and medieval city and walls. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
**FIG 218.** Looking northwestwards across the Isle of Thanet (Fig. 215, **b3** ) and Ramsgate on the Chalk cliffs. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
#### Landscape C: The Thames and tributary estuaries
The intricate pattern of tidal channels and islands that is so typical of this Landscape extends from the Blackwater Estuary in Essex (Fig. 219) to the Medway and the Isle of Sheppey in Kent. The Landscape has formed by the flooding of river valleys by the recent (Flandrian) rise in sea level. The bedrock of the estuary is London Clay, but this is buried under large thicknesses of recent marine, estuarine and freshwater muds.
Sea level has risen by over 100 m worldwide in the last 20,000 years, since the end of the last (Devensian) cold episode of the Ice Age. Sea-level rise relative to the local land surface may have been even higher in this particular area, due to a seesaw effect between the northwest and the southeast of Britain: northern and western Britain have been rising since they are no longer being depressed by the weight of the ice sheets; meanwhile, south and east England, on the other end of the 'seesaw', have been gradually subsiding.
**FIG 219.** Maldon (Fig. 215, **c1** ) on the upper Blackwater estuary. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
The idea that this area may recently have been tilted eastwards at the same time as worldwide sea level was rising is supported by the sedimentation pattern of the region. Over the last 10,000 years, more than 30 m of marine and estuarine sediment has accumulated where Canvey Island ( **c2** ) now is, whereas at Tilbury ( **c3** ), 20 km further up the Thames, only 10 m of sediment has accumulated. During the last 10,000 years, a number of peat beds formed further up the Thames, representing distinct phases of swampy river conditions. Similar beds have not been found further downstream, suggesting that downward movement and marine conditions were more continuous there.
One fascinating feature of the shoreline of this Landscape is the Medway Estuary, which is remarkable for its width and its large number of islands. Most of the islands appear to have grown recently as mud and sand have been brought into the estuary by the tides, creating isolated salt marshes and other expanses of intertidal sediment. The width of the estuary suggests that it formed under Ice Age conditions, prior to the recent rise in sea level, as an extensive, flat-lying lowland. This lowland area may have grown in size through freeze-thaw slumping of its hilly margins, similar to the areas of south Essex described below (Landscape **D** ). In the aerial photograph (Fig. 220), Rochester's Norman castle and cathedral can be seen in the foreground, overlooking the River Medway.
**FIG 220.** The Medway river and estuary, with Rochester castle and cathedral. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
The rising sea level did not just flood valleys and streams. Sea storms moved large quantities of soft sand and mud, which were then deposited against the new coastlines. The ancestral Thames and its associated tributaries also supplied large quantities of mud and sand to the coastline, transported from further upstream. Plants stabilised the sediment, and eventually it developed into wide expanses of salt marsh and estuarine mud flats.
The efforts of humankind have also had a large impact on the estuary: man-made sea walls encourage the deposition of sand and mud, accelerating the growth of the salt marshes and mud flats. The new land is reclaimed from the sea and new sea walls are built further seaward as the process of reclamation continues. The Romans were the first to drain the wetlands for agriculture, although the fields largely returned to marshland when the empire crumbled. Since the early Middle Ages, land has been systematically reclaimed from the sea and protected by sea banks. Historically the land was used for farmland, especially wet pasture. During the last century, the land has been further used for oil-storage depots, military training ranges and tourism (yachting, marinas, water and jet-skiing) as well as for intensive arable farming on the fertile loamy soils.
#### Landscape D: South Essex and the Northern Thames Basin
Most of South Essex is underlain by flat-lying horizontal layers, mainly mudstones of Tertiary age. Patches of the sandy Bagshot Beds underlie Ice Age deposits in the northwest corner ( **d1** ), but most of the region is underlain by London Clay that is covered by Quaternary river and ice-laid deposits. Around Tilbury ( **c3** ), near the River Thames, the older Chalk layer is exposed at the surface, as shown in Figure 214.
Much of the landscape of Essex does not directly reflect contrasts in the erosional strength of the underlying bedrock. It has a distinctive topography that reflects most obviously the variety of processes that have shaped it over the last few million years. The River Thames has been the primary influence on the shape of this Landscape, accounting for much of the erosion of south Essex, although deposition by the Anglian ice has also played an important role. Consideration of the landforms can help to work out which processes have been involved.
An undulating plateau (Fig 215 **d1** ), sometimes reaching 100 m above sea level, forms the corner of this Landscape, northwest of the Brentwood-Chelmsford A12 trunk road. Much of this plateau is underlain by Anglian ice-laid material, and the undulations may reflect surface-blanket topography left by the melting ice, although it must have also been modified later by small stream systems.
To the southeast of the plateau there are more distinctive ridges and slope features, mostly trending southwest-northeast. The first of these hilly features is a knoll centred on Danbury ( **d2** ), which is linked to a ridge continuing northeast towards Tiptree in Area 14. The slopes and ridges were carved by the Thames or one of its branches before the arrival of Anglian ice, which seems to have extended southeastwards only as far as this Danbury-Tiptree Ridge.
Southeast of the Danbury-Tiptree Ridge, the next distinct topographic feature is a series of lowlands that extend all the way from Thurrock ( **d3** ), near the Thames in the southwest, to Maldon ( **c1** ) in the northeast. This is the Valley of Romford, another old course of the River Thames, with very distinct margins to the northwest and southeast (Fig. 221). The northwest margin is a strongly indented southeast-facing scarp which forms the edge of the Hanningfield Plateau ( **d7** ), whereas the southeastern margin is the Rayleigh-Dengie Ridge. The lowlands are also crossed by distinctive smaller ridges at Purleigh (northwest of **d6** ) and the Langdon Hills ( **d4** ). The northwestern margin of these lowlands contains a series of arcuate hollows which probably formed when freeze-thaw processes in the largely clay bedrock triggered land-slipping down slopes. On a more general scale, the lowlands appear to have encroached on the surrounding hills by a combination of Ice Age land-slipping processes and removal of the slumped mud by river action.
**FIG 221.** Slope map of Area 12, showing the extent of Anglian ice, along with former and present drainage pathways.
To the southeast of the Valley of Romford, erosion has picked out slopes that are often capped by the more sandy Claygate Member, which forms the uppermost part of the Early Tertiary London Clay Formation. Hadleigh Castle ( **d5** ), shown in Figure 222, has been built on a particularly distinctive point of the 70 m high Southend scarp. It is from here that John Constable captured remarkable light effects in his views towards the mouth of the Thames Estuary (see Area 14).
An interesting insight into more recent landscape development comes from the flat Dengie and Rochford peninsulas, north and south of the Crouch Estuary ( **d6** ). Field boundary patterns, apparently dating from Iron Age times, about 2,000 years before the present, show a remarkably parallel alignment on the two sides of the tidal Crouch Estuary. This observation, along with evidence of early bridging and fording of the channel, confirms that a very recent rise in sea level must have taken place, drowning ancient fields and crossing places to form today's 400 m wide estuary.
**FIG 222.** Hadleigh Castle (Fig. 215, **d5** ), 7 km west of Southend-on-Sea. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
# [CHAPTER 8
The East Anglia Region](004-toc.html#ch8)
### GENERAL INTRODUCTION
EAST ANGLIA (Fig. 223) is famous for its spectacular skies, partly because they often lack the distractions of horizons dominated by mountains or hills. Indeed, one of the most intriguing features of East Anglian scenery is its general flatness.
The East Anglian Region as a whole shows remarkably little variation in topography, being some 200 km from west to east and 150 km from north to south, but with the highest hill top lying only 256 m above sea level. Furthermore, within the Region are landscapes such as the East Anglian Fens and the Broads, which are flat to the extent that traverses of many kilometres often contain no changes in surface elevation of more than 2 m. These areas represent the extremes of flatness in Southern England.
Why is the landscape of this Region so flat compared with other British regions? The bedrock and surface-blanket history help us to answer this question.
#### Bedrock structure and early history
Most cross-sections prepared to represent the Earth's uppermost crust in detail show very little unless their vertical scale is greatly exaggerated. In Figure 224 we can compare the same cross-section of East Anglia with no exaggeration, and with the vertical scale exaggerated ten times and 100 times. Exaggeration gives a false impression of the angles of slopes or tilts in the bedrock, but it does help us to understand the relationships between different rock units.
**FIG 223.** The East Anglia Region.
Beneath the near-surface layers of the bedrock of East Anglia, there is older bedrock that can be examined only in boreholes, and by remote geophysical methods. This has revealed evidence for an important geological episode some 300 million years ago, during latest Carboniferous or earliest Permian times. Before this, the geography of the Region was very different to that of the present, with sediments accumulating in some areas while hills had formed elsewhere due to movements of the crust. Approximately 300 million years ago, the whole Region became a land area of general erosion, and part of the area was uplifted to become what we now call the London Platform.
Since that time, younger sediments have been deposited and turned into bedrock. Initially they only accumulated in the northwest of the Region but then, in Jurassic and Early Cretaceous times, the area of deposition extended further southeast towards the London Platform. Eventually, in Late Cretaceous times, the whole Region was submerged and covered by accumulating Chalk. After this, during the Tertiary, the surface was moved upwards and tilted, so that sediment accumulation became confined to the southeast of the Region.
Although none of these sedimentary layers is uniform across the Region, the fact that the 300-million-year-old landscape (labelled pre-Triassic in Fig. 224) is still so close to the present surface shows that little vertical movement of the crust (less than ≈500 m) has taken place since that time. Its younger bedrock cover provides key information about the environments in which the sediments formed, and these are all consistent with unusual stability and lack of crustal movement.
**FIG 224.** Sketch cross-section of the uppermost crust across East Anglia. Located on Figure 226.
The type of bedrock appearing near the surface in different parts of the Region has a major influence upon the scenery, at least locally. The succession shown in Figure 225 generalises the thickness of the main layers and the time of their deposition over the last 230 million years.
The earliest information comes from the northwest of the Region, where the bedrock, of Triassic age, consists largely of red mudstones deposited by rivers and streams in low-lying ground between low hills (Fig. 226). At this time, the area to the southeast consisted of a landscape of uplands made of London Platform bedrock, more than 300 million years old, where sediments did not accumulate. This same platform feature can be traced below the surface under the southern North Sea and the Low Countries, and is often referred to as the London-Brabant Landmass (Brabant is an old name applied to the land roughly equivalent to present-day Belgium.
**FIG 225.** Generalised near-surface bedrock succession for the East Anglian Region.
**FIG 226.** Bedrock map of the East Anglian Region with hillshade.
About 200 million years ago, as Jurassic times began, the sea invaded East Anglia and established a marine gulf between the London Platform to the southeast and other areas of low hills in Wales and the West Country to the north and west (Fig. 227). The position of this Jurassic gulf is now marked by the presence of bedrock of Jurassic age extending from the North York Moors, across the East Midlands and East Anglia, to the Cotswolds, Hampshire, Dorset and the South Coast. Most of the marine sediments are mudstones, but there are limestones of mid-Jurassic age that are particularly important in terms of the scenery. When these limestones were later uplifted and eroded, they proved to be more resistant than the mudstones and so have produced distinctive limestone topography. It is also because of their toughness that these Middle Jurassic limestones became a common building material in the west of this Region, from Northampton towards Peterborough and up to Grantham. This building stone gives villages and towns an attractive appearance that is better known further southwest, in and around the Cotswold Hills. The Late Jurassic mudstones have also proved to be nationally important as sources of oil and materials for brick-making.
**FIG 227.** The land and sea pattern during the Middle Jurassic, with Areas 13–16 outlined.
Early Cretaceous sediments were again largely limited in their deposition to a gulf similar in its position to the Jurassic gulf, though there were episodes of no sedimentation and sedimentation by streams and rivers rather than the sea. The thickness of the sands deposited varies from place to place, as represented by the present bedrock of the Lower Greensand (very obvious in Bedfordshire), and the Carstone (in West Norfolk), but the variations still involved very low slopes. Subsequent erosion has picked out the relative strength of these sandstones enough to form local hill features. In some areas the sandstones have been valued as local building stones, particularly where they have been hardened by the addition of iron minerals (often now rust-coloured) formed in the sands after they were deposited.
In Late Cretaceous times, a distinctive episode began in which the entire London Platform became submerged and unusually uniform marine sedimentation extended across it. The sediment deposited at this time was to become the particularly pure, fine-grained, white limestone known as Chalk. This unique material, made largely of the very small plates of floating microscopic plants, was deposited widely across the floor of a shallow sea (perhaps 200 m in depth) that extended over most of the British Isles. The compact and homogeneous nature of the Chalk has yielded the scenery of steep escarpments, rounded hills and dry valleys that are typical of the Chalk hills of East Anglia. The white Chalk has been an important local building material, particularly when certain unusually hard bands have been quarried. It has also been an important source of the generally black and very strong flint nodules that have grown within it, by precipitation of silica dissolved in the groundwater. Flints have been quarried locally from the Chalk, but more commonly collected from coastal beaches and river gravels for use in buildings and as tools by early humans.
There is a time gap in the bedrock succession representing an episode in the lower Cretaceous from which no deposits have been preserved. In the East Anglian Region, this episode involved uplift and eventual abandonment of the Late Cretaceous Chalk sea. Rather later, deposition began again in the London area, which started to subside to form the London Basin or downfold. This Early Tertiary deposition culminated in the deposition of the London Clay.
In mid-Tertiary times faulting and folding of the Earth's crust became quite widespread across the southern parts of Southern England, although only gentle tilting of bedrock layers occurred in East Anglia. By this time, some 25 million years ago, the East Anglian Region was largely land and subject to widespread river erosion. Indeed, this time saw an important change from general sinking of the East Anglian surface as sediment accumulated, to general uplift and erosion of the surface due to tectonic processes. This was the time when the main pattern of the present-day bedrock map started to form.
In general terms the bedrock pattern consists of a simple series of slightly curved belts (Fig. 226), each providing outcrops of one of the main layers of the bedrock succession. This map pattern is very simple compared with the pattern of other parts of Britain, because it is the result of the erosion of a gently tilted succession that was broadly uniform across the whole Region. The curvature of the zones is due to a change in the tilt direction of the rocks, from easterly in the north of the Region, to southeasterly in the south of the Region, where the rocks slope towards the London downfold. Over the extent of the whole Region (between 200 and 150 km depending on the direction) the bedrock has been tilted downwards – relative to its original position – by about 700 m, so a quick calculation shows that the overall amount of the tilt is less than 1 degree.
In latest Tertiary times, further downward movement taking place in the southern North Sea caused the eastern edge of East Anglia to sink slightly once again, depositing a thin veneer of sandstones and limestones. The general term _Crag_ has been given to these deposits.
#### Surface blanket and more recent history
The surface blanket of softer material that rests upon the bedrock contains evidence for episodes that have occurred during the Quaternary (the last 2.6 million years at most). There is debate about the number, the timing and the areas covered by the ice-sheet invasions associated with this time period, but it is generally agreed that the most extensive glaciation was due to the advance of the Anglian Ice Sheet about 450,000 years ago (see Chapter 2, Figs 13 and 14). At this greatest extent, ice covered the whole Region except for the area of the higher Chalk hills southwest of Luton.
Both before and after this Anglian cold episode, East Anglia lacked ice-sheet cover and was subjected to very varied but predominantly cold conditions. There is evidence that the ground was often frozen, and that seasonal melting created conditions of widespread river erosion and deposition, along with highly active slumping of slopes and melt-induced movements of the soils.
Much more recently, the worldwide sea-level rise that has followed the melting of the last ice sheet (see Chapter 2, Fig. 13) has been responsible for much of the sedimentation in the very flat areas of the Fens and the Broads, as well as widespread sedimentation in most of the main river valleys. Local features that are the results of these episodes will be picked out in the Area discussions that follow.
#### East Anglia's flatness
Although a plot of the bedrock succession, generalised for the whole of the East Anglian Region (Fig. 225), shows some 800 m of bedrock, it must not be thought that layers accumulated to this total thickness at any one place. Indeed, as described above, the succession shows that gentle movements of the Earth's surface caused the thickest accumulations of each of the main layers to move through time from the northwest to the southeast (Fig. 224), so that the layers rest on the ancient London Platform foundation rather like overlapping plates in a plate rack.
The presence of the London Platform foundation only a few hundred metres below the East Anglian landscape, and its relatively uniform cover by sediments since, is evidence that movements of the Earth in this Region have been very limited compared to those taking place in other regions. Most of the near-surface bedrock has therefore avoided the deep burial within the Earth that causes rocks to harden, so it has remained soft enough to be readily eroded by rivers, ice sheets and the sea. With this in mind, it is perhaps not so surprising that East Anglia lacks high ground to such an unusual degree.
The erosion of the East Anglian landscape has worked to create large areas of very little topography at or close to present-day sea level, and ready to receive sediment from the very recent (Flandrian) sea-level rise. These sediments have filled what few hollows there were in an already flat landscape to produce areas of extreme flatness such as the Fens and the Broads.
### AREA 13: NORTHAMPTON TO CAMBRIDGE
In the general introduction to this chapter we saw how movements of the Earth's crust in the East Anglian Region over the last 300 million years have been limited to very gentle tilting (less than 1 degree across the Region as a whole). In terms of the present scenery, this means that most of the natural features of Area 13 (Figs 228 and 229) are predominantly due to surface processes (driven by rivers, ice, tides and storms) that have progressively modified the landscape since these minor crustal movements took place.
**FIG 228.** Location map for Area 13.
**FIG 229.** Natural and man-made features of Area 13.
We will examine Area 13 by considering firstly the present-day river and coastal systems and then, secondly, the way in which the bedrock pattern has influenced them.
Comparison of the main valley pattern of the Area with the bedrock pattern makes it clear that the drainage divide provided by the Chalk hills is one of the most important scenic features. The largest valleys tend to be parallel to the bedrock belts of different ages, with tributaries and lesser valleys perpendicular to this trend, most obviously on the southeastern slope of the Chalk hills (Fig. 230). Northwest of the Chalk hills the main rivers flow northeasterly, towards the coastal zone represented by the edges of the Fens.
I have chosen five Landscapes as convenient divisions for the discussion of this Area (Fig. 231). Landscapes **A** to **D** are defined by their underlying bedrock and form a series of southwest-to-northeast trending zones, each reflecting the persistent, though very gentle, tilt of the bedrock layers downwards towards the southeast. Landscape **E** is a feature of the surface blanket, rather than the bedrock, and reflects recent coastal flooding of the lowest areas. For the sake of more detailed examination of certain aspects of Landscape **B** and C, I have introduced three sub-areas, labelled in Figure 231 as I, II and III.
**FIG 230.** Main drainage valleys and coastal flooding zone in Area 13.
#### Landscape A: Jurassic limestone hills
Landscape A extends across the northwestern part of Area 13, from the northern edge of Milton Keynes, via Northampton to Rushden. It is underlain by bedrock ranging from Triassic to Middle Jurassic in age, though the Middle Jurassic limestones provide most of its distinctive hill scenery. It is drained by the River Nene, which has a mean flow of only 1.3 m3/s near the western edge of Area 13, but then increases in flow northeastwards as its tributaries converge and it enters the Fens in Area 15. Large gravel workings from Northampton downstream reflect the Nene's much greater activity during the Ice Age, when its spring melt flow rate was sufficient to deposit large floodplains of gravel.
**FIG 231.** Hillshade map for Area 13, showing bedrock, Landscapes **A** to **E** and localities ( **a1, b1** etc.) mentioned in the text. For more detailed maps of sub-areas I, II and III, see Figures 237, 240 and 241.
The Early Jurassic mudstones (the Lias, Fig. 225) contain a thin occurrence of the Marlstone Rock Bed – although, compared to Area 9 further west, this bed has little importance in Area 13, either topographically or economically. The Early Jurassic is overlain by Middle Jurassic sandstones, mudstones and limestones belonging to the Inferior and Great Oolite Series. These Jurassic strata slope very gradually downwards to the southeast, at much less than 1 degree overall, although there are local variations in tilt and small faults, often due to the settling of the bedrock as the edges of valleys have been eroded.
The present scenery in the northwest of Area 13 consists of valleys eroded into these Triassic and Jurassic materials, with Middle Jurassic sandstones and limestones capping hills between valleys that are floored by earlier mudstones. On top of many of the hills are sheets of Anglian glacial deposits, often with river sands and gravels that may have been closely linked to ice sheets. Much of the 100 m relief of the valley topography has been created since the glaciation by erosion into and through this surface blanket. A plateau of this material forms the Yardley-Whittlewood Ridge ( **a1** ) between the Nene and Great Ouse valleys (Landscape **B** ). An important conclusion is that much of the scenery of this Landscape has been formed since the departure of the Anglian ice, some 400,000 years ago. In this erosional work, the main agents have been the rivers and their tributaries: reaches of the Nene tend to have a wide valley- often over 1 km across – and are typically fringed by river terraces, representing episodes in the evolution of the river during the varied climatic fluctuations since the Anglian cold episode.
#### Landscape B: Clay-Greensand-Gault belt
This belt extends diagonally across Area 13, containing Milton Keynes, Bedford ( **b5** ), Huntingdon ( **b2** ) and Cambridge ( **b3** ). It is underlain by mudstones of Late Jurassic age (e.g. Oxford, Ampthill and Kimmeridge Clays), as well as sandstones (Lower Greensand) and mudstones of Early Cretaceous age (Gault). Because the local topography is complicated by these bedrock variations and by the patchy presence of large amounts of Anglian ice-laid sediment, it is worth selecting some parts of this Landscape for more detailed treatment. I shall first outline some of the features of the Great Ouse and Cam drainage system, and then examine more closely the patterns of hill slopes in the three sub-areas (I, II and III) marked in Figure 231, from northeast to southwest along the Clay-Greensand-Gault belt.
The Great Ouse is the largest river of the Area, and it is interesting to examine information on its flow rate. The Great Ouse has a mean flow of only 10.4 m3/s at Bedford, where it is draining an upstream catchment of 1,460 km2. Further downstream at Brownshill Staunch (about 8 km from St Ives, **b6** ) and just before the Great Ouse becomes tidal, its mean flow rate is 14.4 m3/s from a catchment of 3,030 km2, reflecting its drainage of much of Area 13 and some of Area 9. For comparison, the mean flow in a downstream reach of the largest river of Southern England, the River Severn, is 106 m3/s from a wetter catchment of 9,900 km2.
**FIG 232.** Looking northwards over the Great Ouse and Bedford (Fig. 231, **b5** ; see Fig. 240 for a better idea of the location). (Copyright Aerofilms)
The photograph over Bedford (Fig. 232) shows a relatively wide reach of the Great Ouse, but this is the result of the raising of the local river level by engineering structures. The medieval town lay north of the river, but new roads have been created to allow for modern traffic. More recent development has greatly extended the city, and has created radial patterns of development north and south of the Great Ouse.
Considerably downstream from Bedford at St Ives ( **b6** ; Fig. 233), the medieval markets and lanes are beautifully preserved, as well as the ancient bridge incorporating a chapel. In the further distance the numerous lakes are the result of flooding gravel pits that mark the deposits of the ancestral Great Ouse, which deposited large quantities of gravel at the end of the last (Devensian) glaciation.
**FIG 233.** Looking eastwards across the Great Ouse and the town of St Ives (Fig. 231, **b6** ; see Fig. 237 for a better idea of the location). (Copyright Cambridge News)
Not far downstream from St Ives, the Great Ouse enters an area that may be called the Cottenham Flatlands. They appear to have been formed where the River Cam emerges from the valley that parallels the front of the Chalk hills, and joins the Great Ouse (Fig. 230). In the surroundings of Cambridge, the alluvial terraces of the Cam have been studied and their ages have been estimated using their fossil content. The sketch map (Fig. 234) shows the radial arrangement of the successive pathways of the river over the last 300,000 years of great climate fluctuation, using a simplified scheme in which three episodes of river activity are recognised, each with its distinct pathway and climatic signature.
The fan arrangement reflects the freedom of the river to shift laterally once it reached the open country downstream from the confining higher ground to the west and east. The deposits of each of these main phases of Cam activity occur at progressively lower elevations as the river continued to lower the local landscape. Indeed, old river deposits of sand and gravel appear to have resisted erosion to form high ground that was then avoided by later floods, diverting younger rivers to new courses.
**FIG 234.** Former courses of the River Cam.
Red arrows mark former river pathways
1) 300, 000 years ago (upper terrace level). Cold
2) 150, 000 years ago (middle terrace level). Cold, then warm.
3) 30, 000 years ago (lower terrace level). Cold.
The River Cam and its upstream tributary, the Rhee, flow some 50 km northeast to join the Great Ouse a few kilometres south of Ely, running parallel to (and draining) the northwestern face of the Chalk hills. During the general lowering by erosion of the landscape, this face of the Chalk hills must have migrated southeastwards, down the direction of the gentle tilt. This will not have been a steady process and, particularly during the Anglian glaciation, the presence of ice (and meltwater) will have influenced the pattern of erosion by the rivers. An example of this is the way the Rhee-Cam river flows generally on Early Cretaceous (Gault) bedrock, except for some areas near Cambridge where it crosses the earliest Late Cretaceous (lower Chalk) that now extends across its valley to the Harlton ( **b10** ) and Madingley ( **b11** ) ridges. In this area, interglacial (Ipswichian) gravels have provided evidence that valley erosion was active just south of the Harlton ridge some 120,000 years ago. The width of the valley of the Rhee and Cam here is evidence for the erosional effectiveness in the past of what now seems to be a minor river: the present mean flow rate of ≈1.2 m3/s from a catchment of 30 km2 would not be sufficient to produce a valley of this size. It seems likely that periglacial processes of slope erosion, as outlined in Chapter 2, also played an important role in the southeastern migration of the Chalk hills. As an aside, the Ipswichian gravels from this area have also yielded some remarkable fossils, including the Barrington Hippo now in the Sedgwick Museum, Cambridge.
In the foreground of Figure 235, the River Cam (yellow arrow) flows away from the camera across its floodplain, which can be picked out as a curving belt of college gardens and parks, swinging to the left and then following the large bend in the river to the second yellow arrow, where the river leaves the right-hand edge of the view. The only place where the floodplain has been built over – repeatedly- is the area beside the earliest bridge over the Cam (now Magdalene Bridge), in the top left of the photo (starred). This area, where Chalk bedrock has been preserved and the curve in the River Cam has been constrained, saw development and fortification by the Romans and the construction of the older colleges and churches of medieval Cambridge. Away from the present-day floodplain, slopes lead upwards to flat terraces that are fragments of older floodplains formed as the river carved its valley downwards to its present level.
A recent reversal of the general down-cutting of the River Cam is represented in Figure 236, a cross-section of the river and its floodplain in the grounds of King's College, at the centre of Cambridge. Shallow drillings in this area show that the present channel is flowing at a higher level than an earlier channel, which appears to have cut a small valley when sea level was low during the Devensian cold phase (≈20,000 years ago). This valley was subsequently filled with sediment as the Devensian ice melted and sea level rose, and the present-day channel has been cut into this sediment infill. The filling with sediment of a previously incised valley is a common result of the recent Flandrian sea-level rise around Southern England.
**FIG 235.** Looking northeastwards across Cambridge. (Copyright London Aerial Photo Library)
Having looked at aspects of the histories of the main rivers, we now consider the pattern of slopes in the three sub-areas identified in Figure 231, all of which include this Landscape.
Southeast of the valleys of the rivers Rhee (or Ashwell Cam) and the lower Cam, the slopes of the Chalk hills are well defined, particularly west of the Royston area (Fig. 237, **c1** ). Most of the steeper slopes in the outer or northwestern face of the Chalk hills are the direct result of the presence of erosionally resistant (hard) layers in the Chalk succession (see Landscape C for further details).
Southeast of these outer Chalk hills, the tops of the inner hills are largely underlain by upper (younger) levels in the Chalk, and they tend to have the form of a tilted plateau sloping very gently to the southeast. Much of this tilted plateau has a cover of Quaternary deposits, mainly those left by the Anglian ice. Many of the local valley slopes are capped by this material. The slopes, therefore, have probably been eroded during the last 400,000 years since the deposits were left by the Anglian ice sheets.
**FIG 236.** The Cambridge Backs and the River Cam, with Clare and King's Colleges in the foreground.
In the northern half of sub-area I, between Grafham Water ( **b1** ) and Harlton ( **b10** ), the scenery eroded into the mudstone bedrock consists of well-developed tributary valleys separated by narrow, often near-parallel ridges. The ridges are generally capped by a sheet of Quaternary (Anglian) ice-laid material. Similar uplands, with clearly defined tributaries and valley slopes carved into Anglian ice-laid material and Late Jurassic mudstones, occur north of the Ouse near Huntingdon ( **b2** ) and east of the Ouse near St Neots ( **b6** ), where they make up part of the 'Western Plateau' of Cambridge. Central parts of the plateau are about 70 m above sea level. Below its surface, its cover of Anglian ice-laid deposits has filled earlier valleys, and new patterns of slopes have been eroded, completely changing the shape of the earlier scenery. Parts of the plateau margin display incised valleys that have been cut into the ice-laid deposits since the Anglian. They have been further eroded when their slopes collapsed due to freeze-thaw mobilisation during subsequent cold spells. Iron-rich concretions in the Lower Greensand of Cambridge's Western Plateau have given rise to a surprisingly long history of local iron smelting.
The Greensand ridge behind Sandy ( **b9** ) overlooks the River Ivel valley, and the typical rusty-weathering of the sandstones is visible in a number of quarries. The ridge extends more widely across Area 13, forming the northwestern edge of the Early Cretaceous, though it varies from under a few metres in thickness in the northeast of the Area to a much more important 70 m in thickness in the southwest, near Leighton Buzzard (Fig. 240, **b8** ). In this thicker development in the southwest, the Lower Greensand has been quarried extensively as a source of sand, which has been most prized where the iron minerals that are often present have been removed by solution in the groundwater to yield a pure quartz sand. In some localities the quarries reveal stratification patterns typical of sandbars that ranged up to several metres in height, migrating under the action of the Early Cretaceous tides (Fig. 238). The variation in thickness of the Lower Greensand is probably due to episodes of non-deposition and very gentle movement of the Earth's surface, before and after deposition on the floor of the Early Cretaceous sea.
**FIG 237.** Slope and hillshade map of the Sandy-Cambridge sub-area (I) of Area 13 (located on Fig. 231), showing localities ( **b1, b2** etc.) and, towards the southeast, two hard layers within the Chalk (see under Landscape **C** , below): **2** , Melbourn Rock; **4** , base of upper Chalk.
**FIG 238.** Old quarry face near Sandy Warren, showing stratification formed by migrating sandbars. (Copyright Peter Friend)
A Greensand Ridge Walk has been established along the length of this feature, linking a number of estates and nature reserves where the acid-soil vegetation and fauna are distinctive.
Northeast of Sandy, under the Cambridge Western Plateau, and further northeast across the rest of Area 13, the Lower Greensand below the surface blanket becomes thinner and has only rarely produced low ridges, being generally completely obscured by Anglian ice-laid material or younger alluvium.
The rest of the Early Cretaceous succession, above the Lower Greensand, consists of mudstones of the Gault, about 75 m in thickness. The Gault tends to be a uniform, relatively soft material, so topographic slopes that occur within the area underlain by Gault bedrock are generally due to valley incision or slope retreat, rather than to the picking out of bedrock material contrasts.
Phosphate-rich _coprolites_ caused an economic boom in Cambridgeshire, particularly in the nineteenth century, when they were extracted from the Cretaceous rock at a number of different levels. One of these, labelled the Cambridge Greensand, occurs at the junction between the Gault and the Chalk, where a few metres of chalky material contain a scatter of black and grey fossils, pebbles and nodules that are enriched in phosphate and valuable as agricultural fertilisers. Some of the phosphate is the result of mineralisation in the groundwater of the excreta of Cretaceous organisms, particularly fish. This phosphate-rich material was named coprolite, for polite purposes, using a word from classical Greek ( _kopros_ , faeces). Areas of low-lying Cambridgeshire, wherever the Cambridge Greensand, Gault or Lower Greensand were found to be rich in coprolites, were subjected to a coprolite 'rush' (Fig. 239). Open-cast digging and washing of the coprolites involved large numbers of local and imported workers.
**FIG 239.** Coprolite digging in the late nineteenth century, between Orwell and Barrington, 11 km southwest of Cambridge. (Photo held at the Sedgwick Museum, Cambridge)
The Great Ouse upstream from Bedford (Fig. 240, **b5** ) has a particularly sinuous course which must have developed before it cut down into the Jurassic bedrock, incising and fixing the meanders.
Southwest of Bedford is a remarkable topographic feature that I refer to here as the 'Bedford Bite' ( **b4** ), though it is also sometimes referred to as the Marston Moretaine Basin. The floor of this feature is underlain by Late Jurassic Oxford Clay that has been extracted in large amounts for brick-making around Marston Moretaine and Stewartby. The slope map shows small slopes edging some of the rectangular brick pits, but also the much larger curved slopes that face into the Bite as a continuous edge to the southeast, south, west and northwest. Some of the southern sector of this edge is capped by Early Cretaceous sandstone (Lower Greensand), but the rest of it, to the east and west, is made of slopes capped by Anglian ice-laid material, which has draped the Early Cretaceous or Late and Middle Jurassic bedrock. The clear definition and curved shape of the bounding edges of this Bite, along with the flatness of its floor, suggest that the edges have retreated backwards as they slumped under the very varied climatic conditions since the Anglian. The slumped material may then have been cleared from the floor of this large feature by freeze-thaw processes, before finally being carried downstream by the ancestors of the Great Ouse.
**FIG 240.** Slope and hillshade map of the Bedford sub-area (II) of Area 13 (located on Fig. 231), showing localities and hard Chalk layers **1, 2** and **4** (see Landscape **C** ).
**FIG 241.** Slope and hillshade map of the Aylesbury sub-area (III) of Area 13 (located on Fig. 231).
Southwest of the Bedford Bite, the next extensive slopes are in the Brickhill area ( **b8** ), where they have been carved into the Lower Greensand and look out over the valley of the River Ouzel to the west.
In the southwest corner of Area 13, west of Aylesbury (Fig. 241, **b7** ), is an area of flat-topped hills with well-marked marginal slopes (sub-area III). These hills and slopes have been carved from the youngest Jurassic sediments visible in the whole of East Anglia, which consist of several metres of sediment dominated by the limestones of the Portland Formation. These are the time equivalent of the limestones that form the famous building stone that is quarried on the Isle of Portland in Dorset (Area 4). The hills in Area 13 are clear examples of the way that the general lowering of a landscape underlain largely by mudstone can produce distinctive hills simply because of the presence of a few metres of erosionally strong limestone.
#### Landscape C: Chalk hills and valleys
The Chalk hills stand out on the map (Fig. 230) as the largest and most clearly defined topographic feature of the southern part of Area 13. They are highest and most clearly defined in the southwest, around Luton, but extend northeast via Hitchin, Stevenage, Royston and Saffron Walden. These hills are the relicts left behind as erosion acted on the gently tilted, 250 m thick Chalk layer. The orientation of the Chalk hills is the result of their tilt to the southeast, and their present location is due to the level presently reached by the processes of landscape erosion.
Even though the tilt is so gentle, it still gives rise to a contrast between the northwestern flank of the Chalk hills, where erosion has cut through successive levels within the Chalk, and the southeastern flank, where well-defined valleys have been eroded a few tens of metres into the tilted upper surface of the Chalk (Fig. 230).
The greatest elevations in the Chalk hills of Area 13 are in the southwest, near to Luton and Whipsnade, where elevations of 250 m occur. In this area the Chalk edge is unusually distinct, making it a very popular launch site for paragliders keen to explore the lower ground to the north. Elevations tend to decrease southeastwards, following the tilt of the upper surface of the Chalk layer. Further northeast in Area 13, Chalk hill elevations rarely exceed 100 m and the Chalk edge facing northwestwards is much less distinct. In this area, the Rhee branch of the Cam is joined by the Cam and Granta streams just upstream from Cambridge. These drain the Saffron Walden and Linton valleys in the Chalk Hills, where the Chalk edge is particularly far to the southeast. These lower elevations may reflect erosion by Anglian ice in this eastern area, because it appears that the higher edge in the Luton area ( **c2** ) was never surmounted by the Anglian ice sheets.
The lowest part of the Chalk is often called the Chalk Marl, because it is richer in clay than more normal Chalk, which is almost entirely calcite. During the erosion of the landscape the Chalk Marl has tended to behave in a similar way to the underlying Gault mudstones: both usually form rather low ground, in contrast to the rest of the Chalk, and may have been subject to widespread periglacial mobilisation of near-surface material, producing low, rounded hills and hollows that are typical at this level.
Within the main Chalk layer there are a number of hard bands (Fig. 225), each a few metres thick, which have often resisted general landscape erosion to produce distinct escarpments in the topography (Figs 237 and 240). The hard bands tend to vary from place to place, and they rarely all produce slope features in the same area, but the following number system is used to refer to the most distinctive: ( **1** ) Tottenhoe or Burwell Rock; ( **2** ) Melbourn Rock; ( **3** ) Middle Chalk; ( **4** ) Base of Upper Chalk. The hardness of the bands appears to reflect changes in the environment of the original Chalk seas, but it may also reflect differences in the precipitation of calcite within small pores in the Chalk after its burial. Spring lines are also features of the landscape caused by these hard bands, for example at Ashwell, where the Cam (Rhee) rises.
In the southeastern corner of sub-area II (Fig. 240) the slope map shows two different slope features forming the northwest face of the Chalk hills. The Chalk hard bands (1, 2 and 4) have produced the steeper slopes as well as the gently sloping surface to the southeast, where valleys have eroded parallel to the tilt of the Chalk bedrock through a cap of several metres of Clay-with-flints and Upper Chalk bedrock. The Clay-with-flints is a soil-like deposit resulting from solution and weathering of Chalk. It forms a capping layer rich in the flints that were present as nodules in the original Chalk. More generally, this special material has Anglian ice-laid material on top of it in places, and must therefore have formed at least partly before the ice sheet arrived some 450,000 years ago. The solution and weathering probably took place under the warmer climatic conditions that existed in the millions of years before the Ice Age.
The upper, southeasterly surface of the Chalk Hills has a cover of Anglian ice-laid material, except southwest of Luton ( **c2** ), where the hills do not seem to have been overwhelmed by the ice. Another area lacking ice-laid material is the intriguing northwesterly face of the Chalk hills, which seems to have had an important influence on the location of historic travel and trade routes. It seems most likely that ice-laid deposits did cover this face when the Anglian ice sheet melted, but that they have been stripped off by river and slope erosion over the subsequent 400,000 years.
One of the greatest environmental changes in the Chalk hills landscape was the arrival of the Anglian ice sheet. Southwest of the upper Lea Valley ( **c3** ) and Luton ( **c2** ), the lack of ice-laid deposits is evidence that the elevation of the Chalk topography was sufficient to prevent the further spread of the ice sheet in that direction. Northeast of this ice margin, ice-laid material was deposited over the whole of the southeasterly surface of the Chalk Hills and influenced the form of the valleys later eroded into it.
The patterns of southeasterly- and southerly-flowing river valleys eroded into the Chalk are striking, particularly on the slope maps, where the paired valley margins are picked out, clearly contrasting with the flatter valley floors (Figs 230 and 237). Most of these Chalk valleys now lack a permanent stream, because rainfall runoff percolates through fractures in the Chalk instead of flowing over the ground surface. It is believed that these valleys were eroded under Ice Age conditions, when rivers flowed vigorously for at least part of the year because their water could not percolate through the near-surface zone of permanently frozen bedrock.
The Hitchin-Stevenage gap ( **c4** ) is a funnel-shaped hollow in the face of the Chalk hills, some 10 km wide in the north and narrowing southwards. It contains the A1 trunk road and the main East Coast railway line from London (King's Cross) to Scotland. The development of Hitchin, Baldock, Letchworth and Stevenage is further evidence of the importance of these transport routes to local settlement.
The floor of the gap is underlain by a complex of Anglian ice-laid material with sands and gravels deposited by rivers. An unusual feature of these surface-blanket sediments is that they have often been deposited as material plugging a system of branching valleys up to 100 m deep (Fig. 242). Valleys that have been almost completely filled with glacial and later sediment are an intriguing feature of many areas of Chalk hills. Some of the present open valleys may have been cut under similar conditions, then plugged with material, and then emptied again by later river action. It is now believed that much of the erosion of these valleys took place by meltwater flow active under the Anglian ice sheets. Most of the buried valley floors slope southwards, indicating drainage flow in that direction, but local reversals in valley slope do occur. These northward-sloping valleys seem to result from situations where the rivers were forced to flow up local gradients under the ice sheet, like water in an enclosed pipe.
**FIG 242.** Cross-section showing buried valleys near Hitchin (Fig. 231, **c4** ).
Some of the southeastern Chalk-slope valleys have eroded into the Upper Chalk, but not cut deeply enough to expose hard band 4. Much of the erosion of these shallow valleys is relatively young and has taken place into Anglian ice-laid material since it was deposited about 400,000 years ago. The valleys often show beautiful branching patterns of their tributaries, which probably result from the distinctive behaviour of the muddy ice-laid material when the heads of the tributaries cutback into it. Good examples of these patterns are the valleys that flow from the north into the Lea trunk river on the southern edge of Area 13 ( **c5** ).
#### Landscape D: Bishop's Stortford Clay hills
This Landscape occupies the southeastern corner of Area 13, where it is defined by the occurrence of Early Tertiary sediments below the surface blanket. Up to 17 m of sandy Woolwich and Reading Beds are overlain by some 65 m of London Clay, all deposited in an arm of the sea during Early Tertiary times.
Above the bedrock, the surface blanket contains river sands and gravels which are thought to have been deposited by an ancestor of the River Thames (Areas 10 and 11).
Some 450,000 years ago, the Anglian ice sheet covered – at its maximum extent- the whole of this Landscape, deflecting the ancestral Thames to its present more southerly route. When the Anglian ice sheet melted, it left up to 30 m of ice-laid deposits. Most of the natural topography of the present-day Landscape is the result of river erosion, which has cut shallow valleys through this and into the Early Tertiary mudstones.
#### Landscape E: The Fen edge
In the northeast corner of Area 13, the wide, shallow valleys of the Great Ouse and Cam slope very gently towards the sea. The covering of the lower parts of these valleys with mud and peat during the recent Flandrian rise of sea level has produced local arms of very flat Fenland that is more fully described in Area 15.
The Fens surround the Isle of Ely ( **e1** ), a low upland that has been carved in Late Jurassic mudstones capped by Early Cretaceous Lower Greensand, an extension of our Landscape **B**. Other local fenland features in the Cam valley are due to a patch of Late Jurassic limestones a few kilometres across near the village of Upware ( **e2** ), and a ridge of Anglian ice-laid material on which the village of Wicken ( **e3** ) stands.
**FIG 243.** Former area of Soham Mere, just southeast of Ely (Fig. 237, **e4** ). (Photography held at Cambridge University Collection of Air Photographs, Unit for Landscape Modelling)
Wicken Fen ( **e3** ) is a nature reserve famous as one of the first places in the country where determined efforts were made to preserve a rapidly disappearing natural environment. It was purchased as a small sample of Fen wetland environment at a time when aggressive draining of the surrounding farmland was threatening its existence. The present development plan for the Fen involves the enlargement of the reserve to include some surrounding farmland, which will then be allowed to revert to natural wet land, acting as a recreational 'green lung' for the highly developed Cambridge area.
Before the engineered drainage of the Fens, more-or-less permanent lakes were local features, particularly around the edges of the Fenland, where groundwater tends to flow from the neighbouring uplands. Soham Mere was a good example of one of these lakes, and the outline of the drained lake is still clearly visible in aerial photographs (Fig. 243). The extent of the former mere is now marked by a patch of lighter soil that contrasts strongly with the surrounding fields of darker peaty soils. The lightness is the result of chalk-like limey deposits made by single-celled plants that lived in the lake. The plants made use of the 'hard' water which emerged as springs through the limestone and chalk of the surrounding uplands, producing calcium carbonate that then collected on the bottom of the lake as the plants died and sank.
### AREA 14: SUFFOLK AND NORTH ESSEX
In the general introduction to the East Anglian Region, I stressed the open feel of the scenery and the absence of high hills, explaining these to be the result of the unusual lack of movement of the Earth's surface in this Region over the last 300 million years. Other results of this lack of movement are that the bedrock succession formed during this time varies only slightly across the Region, so that a single, generalised bedrock succession (Fig. 225) is adequate to represent the bedrock pattern across all four Areas of the Region (Fig. 226), and the bedrock layers have a very gentle tilt and simple pattern.
The scenery of Area 14 (Figs 244 and 245) is largely the result of relatively recent river and coastal processes acting upon earlier landscapes. In broad terms, the valleys of the Area consist of a small northwesterly-flowing group draining to the Fenland coastal zone, and a more extensive southeasterly group draining towards the coasts of north Essex and Suffolk (Fig. 246). These rivers have fairly small catchments, with their headwaters in the nearby Chalk hills, an area which receives relatively little rainfall compared to other areas of Southern England. Consequently the mean flow rates for these rivers are rather small.
**FIG 244.** Location map for Area 14.
**FIG 245.** Natural and man-made features of Area 14.
**FIG 246.** Main valley pathways and coastal flooding zone in Area 14.
Apart from the erosion pattern of the drainage valleys, the other major factor in determining the local scenery is the distribution of the underlying bedrock. This reflects movements of the Earth's surface which, although very minor, have still caused some areas to rise and others to subside, exposing bedrock of different ages near the surface across the Area (Fig. 247).
I have divided Area 14 into four Landscapes, labelled **A** to **D** (Fig. 247). This division is based largely on the bedrock that underlies the surface blanket, and it may be helpful that these four Landscapes are similar to the 'character areas' used by the Countryside Agency.
#### Landscape A: The Fen-edge Claylands (Late Jurassic and Early Cretaceous)
This Landscape in the northwest corner of Area 14 is defined by its bedrock of Late Jurassic age (Kimmeridge Clay) and Early Cretaceous age (Lower Greensand and Gault). The scenery carved into this bedrock has been formed by the Fenland rivers more fully described under Areas 13 and 15, where this landscape is more extensive.
**FIG 247.** Bedrock pattern, structure, Landscapes A to D and localities ( **b1, b2** etc.) in Area 14.
The tilt of the bedrock layers in this area is uniformly less than 1 degree to the southeast; there is no measurable difference between the Late Jurassic and the Early Cretaceous tilt, despite a time gap of some 16 million years. This implies an absence of tilting movement during this period, before the formation of the thin (up to 20 m thick) Lower Greensand and the thicker Gault. In scenery terms, the Lower Greensand has often produced slightly higher ground than the mudstones below and above, demonstrating its greater resistance as the landscape was being eroded.
#### Landscape B: The Chalk Hills (Late Cretaceous)
This Landscape is defined by the near-surface presence of Late Cretaceous Chalk. The erosion of the Chalk hills is being carried out now by rivers flowing in two very different directions. In the north and northwest of Area 14, the River Lark drains northwestwards towards the Fens (Area 15). However, the vast majority of the Chalk hills are drained to the east coast by rivers such as the Waveney, Deben and Stour.
In the northwestern part of this Landscape, because of the southeasterly tilt of the Chalk, the surface is underlain by the lowest layer of the Chalk, which has produced generally low ground with gentle slopes. This reflects the mud content of the lowest layers of the Chalk succession, which makes them easy to erode compared with the higher Chalk to the southeast. Views around the Cambridgeshire Fen-edge villages (for example Burwell, **b1** ) and Newmarket ( **b3** ) provide good examples of this low-lying, but undulating, Chalk-edge landscape. They lie centrally in a distinctive belt of country that runs along the north and west edge of the Chalk hills right across East Anglia. The belt is several kilometres across and runs between the higher Chalk hills to the southeast, with their surface blanket of Anglian ice-laid material, and the low wetlands of the Fens to the northwest. Why the Chalk-edge belt lacks ice-laid material is a puzzling question, but may simply reflect the way river erosion has stripped cover from the edge of the Chalk hills, leaving the main Chalk landscape still covered with ice-laid material. It may also reflect the way this mud-rich bedrock has been particularly prone to mobilisation under freeze-thaw Ice Age conditions, perhaps even involving thaw-lake processes (see Chapter 2). The muddy ice-laid material mantling the higher Chalk to the southeast has made it very difficult to farm, leading to a history of thick tree cover in contrast to the open character of the Chalk-edge belt to the northwest. Because of this, the Chalk-edge belt became important in prehistoric times as an area for settlement and a pathway for long-distance travel. The name Icknield Way has been applied for centuries to the series of ancient roads linking settlements along the Chalk-edge belt, in recognition of the regional importance of a through-route here.
Several Anglo-Saxon boundary markers extend across the Chalk-edge belt, perpendicular to its length. The Devil's Dyke ( **b2** ) near Newmarket is the most completely preserved of these. On the July Racecourse, the horses race up a gentle but steady incline underlain by the lower part of the Late Cretaceous Chalk and forming the Chalk-edge hills (Fig. 248).
**FIG 248.** The Devil's Dyke in the foreground, with the July Racecourse (Fig. 247, **b2** ), near Newmarket, behind.
Between Haverhill, Newmarket and Bury St Edmunds, the Chalk hills reach their greatest elevations in Area 14 at about 120 m above sea level. South and east of Newmarket ( **b3** ), north-facing scarps are the result of hard bands in the Chalk resisting erosion. In the rest of this higher area of the Chalk hills, the slopes are the sides of valleys carved in the surface blanket of Anglian ice-laid material, and so must have formed during the last half-million years since that glaciation.
The town of Bury St Edmunds was laid out in the early 1100s around the precinct of the great Abbey Church and shrine to St Edmund, which owes its location to the River Lark (Fig. 249) and stands on a terrace with a gentle slope facing the floodplain of the river.
In contrast to the Lark, most of the seaward-draining valleys in the Chalk hills landscape flow generally towards the southeast, but some show distinct doglegs, which seem to parallel the mapped boundary with the Early Tertiary landscape (Landscape **C** ) to the south (Fig. 246). These doglegs may have formed when the downward-eroding rivers met changes of erosional strength at the boundary between the Early Tertiary bedrock and the underlying Chalk. As the landscape subsequently eroded downwards, the valleys may have maintained their dogleg plan, following the boundary between bedrock units by moving several kilometres southwards, down the gentle tilt of the bedrock layers.
**FIG 249.** The Abbey precinct in Bury St Edmunds (Fig. 247, **b4** ). The River Lark flows just in front of the red-roofed building. In the lower right corner is St Edmundsbury Cathedral, to which a magnificent Millennium tower has been added since the photograph was taken. (Copyright Aerofilms)
One of the most obvious doglegs is in the upper reaches of the Stour valley ( **b5** ), which links the famous Suffolk villages of Clare, Cavendish and Long Melford. These villages are famous for the preservation of large numbers of beautiful houses and churches, reflecting the fifteenth-century peak of prosperity in the wool and textile trade in this area. Flints from the Chalk have been widely used in building here, and the timber frames, often painted and ornamented into surface patterns (pargetting), along with their Chalk-based plaster work, are particularly attractive.
Northeastward of the A14 trunk road and the Bury St Edmunds to Ipswich railway (Fig. 245), the Chalk hills landscape of north-central Suffolk ( **b6** ) is a southern extension of the Breckland, discussed further under Area 16. The landscape here is lower than the Chalk hills to the southwest, and is widely covered by a gently undulating sheet of Anglian ice-laid material, locally eroded by valleys that penetrate to the Chalk bedrock.
#### Landscape C: The Essex Claylands (Early Tertiary)
This Landscape is defined by the Early Tertiary age of the bedrock underlying it. The hill-shaded elevation maps (Figs 245 and 246) make it clear that the size and form of the hills and valleys is remarkably little influenced by the change of bedrock, which continues to be capped widely by Anglian ice-laid material.
As with the southern part of the Chalk hills (Landscape **B** ), present-day erosion of this Landscape is being carried out by a number of rivers draining southwards and eastwards towards the sea. At locality **c1** in Figure 247 there is a second major dogleg on the River Stour, in one of the most clearly developed of these widened valley systems. It has steep valley walls, cut through Anglian ice-laid material resting on Early Tertiary mudstone bedrock. In the case of both materials, undermining by the river will have tended to cause collapse, which has produced the steep slopes that form the valley walls. Another feature is the presence of small, steep-sided branch valleys, often with their own branches. These are probably due to local collapses of the valley heads under the freezing and thawing conditions that existed during much of the Ice Age.
Figure 250 shows an early pen and watercolour drawing made by John Constable in 1800, when he was only 24. It is a beautifully careful representation of the coach road leading across the flat floodplain of the Stour valley, the distinct northern wall of which is visible in the background. The present view from this locality is obscured by large trees, and the entire valley crossing at this point has now been heavily engineered to reduce gradients on the busy A12 trunk road running between Colchester and Ipswich. Constable's drawing shows very clearly the distinctive slopes of the valley walls to north and south compared to the flatness of the floodplain floor (Fig. 251), although he probably had no idea that the flat valley floor is the result of recent (Flandrian) sea-level rise.
John Constable (1776–1837) was born in East Bergholt ( **c2** ), a village 3 km downstream from Stratford St Mary on the Stour, near to the present crossing of the A12 trunk road. He was the fourth child in a family whose successful milling and river transport business on the Stour dominated John's early years, providing the basis for his life as an artist. His delight in the challenge of portraying river-bank scenery and activities – often under highly variable light and changing skies \- was highly original. Most previous artists had tended to invent landscapes as incidental backgrounds to portraits of individuals, or to historical or religious scenes. Much of his work shows scenes in the 20 km stretch of the lower Stour valley that is now known as Constable Country, and he built much of his reputation on this work. Remarkably, Thomas Gainsborough (1727–88) came from further up the same Stour valley of Suffolk, though he was born some 50 years earlier, and is most famous for his portraits.
**FIG 250.** The Valley of the Stour with Stratford St Mary in the distance. (Copyright J. Constable/V&A Images/Victoria and Albert Museum)
Over the whole of the southern part of this Landscape, the gently hilly scenery is dominated by the presence of the coastline. There are two rather distinct kinds of coastal scenery here, each reflecting a different response to the Flandrian rise in sea level that has taken place since the last important cold episode of the Ice Age. The first of these consists of cliffs where low hills (now 10–30 m above sea level) have been attacked by storm waves. These cliffs occur from the Naze ( **c3** ), via Walton, to Frinton-on-Sea ( **c4** ) and Clacton ( **c5** ) and, to a minor extent, at Jaywick ( **c6** ). Most of these cliffs have been cut in material of the Early Tertiary London Clay, but small amounts of Late Tertiary Crag deposits exist on top of this at, for instance, the Naze. Surface-blanket layers of younger sand and gravel have also locally been cut into small cliffs.
The second kind of coast scenery has formed where the rising sea level has invaded a flat and low-lying land surface, causing the sea to deposit mud on a tide-dominated coast with mud flats and tidal channels. Good examples of this second type are around Brightlingsea ( **c7** ) and Mersea Island ( **c8** ), with the Colne tidal estuary between. The River Colne estuary extends across the whole of the view shown in Figure 252, its drowned valley running inland towards Colchester. The mud flats in the foreground of the photograph show very beautifully the winding patterns formed by small tidal flood-and-ebb channels on muddy foreshores.
**FIG 251.** Slope map of the Stour and neighbouring valleys, also showing the location and direction of Constable's drawing (Fig. 250).
#### Landscape D: Suffolk Coast and Heaths (Late Tertiary)
The presence of the Late Tertiary Crag bedrock is used to define the extent of this Landscape, which is dominated by the coast and the estuaries that have been formed by the Flandrian flooding of valleys draining the inland parts of Area 14. The Orwell Bridge (Fig. 253) spans one such drowned valley.
**FIG 252.** Looking westwards from Brightlingsea Creek (Fig. 247, **c7** ) to Mersea Island ( **c8** ) in the distance. Cindery Island is visible in the foreground and, in the bottom right-hand corner of the picture, the mud flats just east of Brightlingsea can be seen. (Copyright Aerofilms)
Harwich Harbour ( **d1** ) is a remarkable natural haven where the Stour and Orwell valleys join, sheltered behind the coastal ridge that extends through Felixstowe to Landguard Point (Fig. 254). Both of the main valleys have been carved, over long periods of changing conditions, by freshwater streams, and have been flooded recently by the Flandrian rise in sea level since the last cold episode of the Ice Age.
Over the last 30 years, the Port of Felixstowe (north of **d1** ; Fig. 255) has been built on the flat ground behind the main coastal gravel barrier. The port is one of the largest commercial developments in Southern England over the last few years, and has been specifically engineered to handle international container transport.
**FIG 253.** Looking northwestwards up the tidal estuary of the Lower Orwell (Fig. 247, **d1** ). The Orwell Bridge spans the estuary in the distance, carrying the **A14** trunk road to connect the industrial Midlands with Felixstowe container port, and some of the buildings of Ipswich can be seen beyond the bridge on the right-hand side of the picture. Orwell Park House is in the middle distance on the right, on one of the steep 20–30 m high shoulders typical of the drowned valleys of Suffolk, and the marina near Pin Mill is visible rather further away on the left. (Photography held at Cambridge University Collection of Air Photographs, Unit for Landscape Modelling)
It is interesting to note that the Early Tertiary layer just below the surface between Felixstowe and Ipswich yields phosphate mineral material (generally in the form of coprolites) that has been commercially important in the past, and helped to develop the fertiliser industry in this area. These coprolites are younger than the Early Cretaceous coprolites of Cambridgeshire (Area 13), which also strongly influenced local commercial development. The Early Tertiary London Clay has also yielded valuable materials that have given rise to local industries. _The Harwich Cement Stone_ came from one bed – less than a metre thick – that occurs on the foreshore. On heating, this stone was found to produce excellent Portland cement able to set strongly even in the presence of water. The Harwich _Copperas Stones_ , also collected from the foreshore, and often originating as fossil wood, provided a source of sulphate important in tanning and the dyeing of textiles.
**FIG 254.** Landguard Point and the Port of Felixstowe. (Copyright Dae Sasitorn & Adrian Warren/www.lastrefuge.co.uk)
**FIG 255.** Felixstowe container quay. (Copyright Suffolk County Council)
**FIG 256.** Looking southeastward from Ipswich down the Orwell estuary. Medieval Ipswich is to the left of the river, in the middle distance. Two more geometrically planned suburban areas have been built on high plateaus that form the shoulders of the valley: California and Rosewell (left, middle distance) and Chantry (right, foreground). (Copyright Aerofilms)
Ipswich (Fig. 256) developed in the first area upstream from the open estuary of the Orwell where a river crossing was relatively easy. So the position of Ipswich is a direct result of the last great (Flandrian) rise of sea level, which flooded the Orwell valley up to this point. Three kilometres downstream, the Orwell Bridge (completed in 1982) was built to allow the A14 trunk road from the Midlands and northern England to bypass Ipswich, taking container and other traffic to and from Felixstowe Port.
Excavations in the Ipswich area ( **d2** ) reveal bedrock of Late Cretaceous Chalk, Early Tertiary mudstones (mainly London Clay) and Late Tertiary Crag deposits. Rivers must have been eroding valleys during the time between the formation of these layers, but the evidence of these rivers is largely missing. The surface layer above the bedrock, however, tells us quite a lot about the conditions in the Ice Age. Deeply eroded valleys – many of them tens of metres deep – were cut into the Chalk before being filled with Ice Age sediment. The load-bearing properties of such sediment infills are generally poor, and one of these valleys caused engineering problems during construction of the Orwell Bridge. Some of the valleys were cut more than 50 m below present-day sea level, confirming that the sea must have been much lower when the valleys were eroded. Anglian river sands and gravels representing the ancestral Thames were spread widely over this area, covering the flat plateau picked out in the aerial photograph (Fig. 256). The Anglian ice-laid material was then deposited, marking the farthest extent of these ice sheets. In the 400,000 years since this cold spell, the present valley system of the Gipping and Orwell has been eroded and partly filled with sediment, most obviously related to the Flandrian rise of sea level since the end of the Devensian glacial.
**FIG 257.** Felixstowe Ferry crossing over the River Deben, between Felixstowe Ferry, in the foreground, and Bawdsey Manor, on the far side (Fig. 247, **d3** ). The coast continues to the northeast, where Orford Ness ( **d5** ) forms the prominent bulge in the far distance. (Copyright London Aerial Photo Library)
At the mouth of the River Deben (Fig. 257) the passenger ferry crossing is only about 200 m wide between Felixstowe Ferry and Bawdsey Manor ( **d3** ), famous as a key site for radar experimentation during World War II. On the outer coast near the woods of Bawdsey Manor, outcrops of Early Tertiary London Clay and Late Tertiary Crag form low cliffs that have been cut since sea level rose following the last glacial.
The estuary of the River Deben extends inland for some 12 km from Felixstowe Ferry and the sea to Martlesham Creek (the right branch in the photo, Fig. 258) and the town of Woodbridge ( **d4** ). The tidal reach of the Deben, up to 1 km wide, is a marvellous example of a river valley with well-developed bends that has been drowned by the rise of sea level since the Devensian. The 10–20 m shoulders of the valley define its edges clearly, even though mud has been gathering along the inside of many of the river's bends, which have sometimes been embanked and drained. At Sutton Hoo, on the slopes of the Deben Valley opposite Woodbridge, the body of the Anglo-Saxon warrior King Raedwald was buried in about AD 625, along with a ship and one of the most remarkable treasures so far found in Britain. The site and visitor centre have been developed by the National Trust.
**FIG 258.** Looking southeastwards from Woodbridge (Fig. 247, **d4** ) down the River Deben to Felixstowe Ferry and the sea. (Copyright Aerofilms)
**FIG 259.** Northeastward view from the settlement of Shingle Street, along Orford Beach to Orford Ness, the outward bulge some 10 km away from the end of the spit, in the far distance (Fig. 247, **d5** ). (Copyright Aerofilms)
Further north along the coast, the long, finger-like spit of Orford Beach (Fig. 259) has been constructed by storm waves and has grown several kilometres from Orford Ness ( **d5** ). At the southern end of the spit, a complicated pattern of linear ridges records former outlines of the spit as it has changed its position and shape with time.
Orford Beach and Orford Ness together form one of the largest coastal accumulations of gravel on the east coast. Although the exact timing of the growth episodes of the Orford Beach spit is not known, it is clearly the result of powerful waves from the northeast driving sand and gravel southwards along the coast (Fig. 260). The growth of the gravel and sand barrier has created a back-barrier of salt marshes and flats, which have accumulated muds in waters that are still strongly tidal, but sheltered from storm waves. Valleys entering this sheltered back-barrier have been topped up with fine mud-flat sediments, as is the case in the Norfolk Broads (Area 16) or the Fens (Area 15). The Butley River can be seen in the middle distance in Figure 259, joining the River Ore to flow parallel to and behind the spit.
**FIG 260.** Episodes in the evolution of the coast from Aldeburgh (Fig. 247, **d6** ) southward, past Orford Ness ( **d5** ).
**FIG 261.** Looking southwards across Southwold (Fig. 247, **d7** ) towards Walberswick. (Copyright Aerofilms)
At the northeastern corner of Area 13, Southwold (Fig. 261) is attractively located on small cliffs carved into Crag deposits of the Late Tertiary. This material is preserved in a plateau between the low ground of the River Blyth valley to the south, and the low ground immediately to the north, where Buss Creek enters the sea at Sole Bay.
Southwold ( **d7** ) and Dunwich ( **d8** ) provide another beautiful example of the way natural coastal processes, in this case storm wave activity, can change the shape of the coastline on a historical timescale (Figs 262 and 263). Over the last 1,600 years, since the end of the Roman period, the position of the outer coast at Southwold has moved inland by more than 1 km. This coastal retreat simply measures the success of storm wave attack in removing Late Tertiary Crag material from the landscape during this recent period, which was long after the sea reached approximately its present level as a result of the Flandrian sea-level rise. Some of the sand and gravel moved by the storm waves at Southwold must have contributed to the filling-in of the large bay that existed at the end of Roman times between Southwold and Dunwich.
**FIG 262.** Episodes in the evolution of the coastal scenery of Southwold (Fig. 247, **d7** ) to Dunwich ( **d8** ).
**FIG 263.** Street map of ancient Dunwich, showing the retreat of the coastline.
The history of Dunwich during this time is dramatic and famous. By the year 1300, Dunwich was one of the most important ports in eastern England, with many parishes and churches, an extensive merchant shipping trade and two members in Parliament. However, it was already suffering from the problem of cliff erosion, and the filling-up of its north-facing harbour with sand and gravel driven southwards along the coast during storms. The average rate of cliff erosion in this area has been well over 1 m per year for at least the past 1,000 years, but this figure gives a misleading impression of steady movement: in practice, retreats take place suddenly as responses to infrequent and particularly violent storms. Until recently, gravestones from the churchyard of All Saints' were visible on the cliff top, but now even these have gone (Fig. 264).
**FIG 264.** Destruction of All Saints' Church, Dunwich, over the last 250 years.
### AREA 15: LEICESTER TO THE FENS
In the west of Area 15 (Figs 265 and 266) the scenery consists of low hills and open valleys in Leicestershire and Nottinghamshire, whereas the eastern scenery is dominated by the spectacular flatness of the Fens. We shall be considering why the scenery is so different in these two parts of the Area.
The bedrock history of Area 15 is similar to that of the other three Areas of the East Anglian Region, so the general bedrock succession (Fig. 225) and distribution map (Fig. 226) provide a perfectly good introduction.
The coastal zone and the inland river system are the active sites of present-day change to the scenery, so it is useful to start by summarising their map pattern (Fig. 267). The ways these coasts and valleys are related now, and how they have interacted with the bedrock, will help us to understand the long-term development of the scenery.
The coastal zone of this Area- defined as the ground lying less than 20 m above sea level – is mostly part of the Fenland Basin (Fig. 268, Landscape **C** ), which owes its exceptional flatness to the thin cover of sediment that has accumulated on the flat bedrock surface during the last few thousand years of Flandrian sea-level rise. Knowledge of this and earlier sea-level changes suggests that some of the present-day slopes at the edges of the Fens have been carved into the bedrock at times when they formed the shoreline of the sea or short-lived lakes.
**FIG 265.** Location map for Area 15.
The drainage pattern of the Area is complicated, and not immediately obvious to the casual traveller because of the gentleness of the slopes and the open nature of the landscape (Fig. 267). In the extreme southwest corner of the Area, southwest of Market Harborough, small streams drain westwards to eventually join the Avon and Severn and flow into the Bristol Channel. Ground elevations here are only 170 m above sea level – remarkably low for one of the main drainage divides in the whole of Southern England.
Further north, the River Trent, one of the main rivers of central England, drains the hilly northwestern corner of Area 15. Considerably to the west of this Area, the Trent flows southeasterly through Stoke-on-Trent in the Potteries, then past the Burton-on-Trent breweries before passing the Trent Bridge cricket ground in Nottingham, just beyond the western boundary of this Area. Further downstream, to the north of Area 15, the Trent runs through Newark-on-Trent (90.5 m3/s mean flow) before joining the Humber estuary some 70 km north of this Area. In the west of this Area, the Melton Mowbray hills drain westwards, ultimately into the Trent, via the Rivers Eye and Wreake.
**FIG 266.** Natural and man-made features of Area 15.
**FIG 267.** River pathways and coastal flooding zone in Area 15.
All of the other rivers in this Area drain into the Wash via the Fenland, where they have been considerably rearranged by centuries of engineering work. From southeast to northwest, the main rivers are the Great Ouse (10.9 m3/s), Nene (9.3 m3/s) and Welland (3.9 m3/s), where the mean flows have been measured at the stations marked on Figure 267.
Along with the present-day pattern of rivers and coasts, the other major factor determining the local scenery is the underlying bedrock. I have divided Area 15 into four Landscapes (labelled **A** to **D** in Fig. 268), basing the division largely on the bedrock or its surface blanket.
#### Landscape A: Triassic bedrock and the River Trent
This Landscape is defined by the presence of Triassic bedrock below the surface blanket in two small patches in Area 15 (Fig 268). This bedrock consists of layers of red mudstone that were deposited in an inland basin supplied with mud and occasional sand by rivers over 200 million years ago (Fig. 225). Thin gypsum layers were deposited periodically in lakes or arms of the sea when they dried out in the arid climate of that time. The landscape here has been shaped by recent erosion into a gently undulating surface, except where the thin bedrock sandstones have resisted recent river erosion to produce low escarpments.
**FIG 268.** Bedrock distribution and structure of Area 15, showing Landscapes **A** to **D** and two sub-areas (Vale of Belvoir, sub-area I, Fig. 269; and Oakham, sub-area II, Fig. 272).
The River Trent flows across this corner of Area 15 within a distinct floodplain, which is 2–3 km wide, remarkably straight and constrained between steep valley walls that are generally about 50 m high. The last events in the retreat of these valley walls probably eroded the Triassic bedrock during times of low sea level since the Anglian glaciation, and some of the floodplain has been constructed during the recent Flandrian sea-level rise. However, the Trent has a well-developed series of river terraces (see Chapter 2, Fig. 11), and this suggests a long and varied early life from pre-Anglian times.
The northerly part of Landscape **A** only contains small relict patches of Anglian ice-laid material, probably because the rest of the cover has been removed by the Trent as it shifted its course widely during its early history. The southern part of Landscape A, near Leicester, has a more extensive cover of Anglian material, along with distinctive incised valleys that have been carved in the 400,000 years since it was deposited.
#### Landscape B: Jurassic hills and valleys
This Landscape encompasses the area of low hills immediately west of the Fens. Its Jurassic bedrock is reviewed first.
The closing episode of Triassic times was marked by the flooding of this landscape by the sea and the deposition of the Rhaetic layer of distinctive limestones. This flooding heralded the opening of the Jurassic and Cretaceous seaway (Fig. 227), which lasted for more than 100 million years. These Rhaetic limestones have locally resisted recent erosion to produce small escarpments in the scenery. The limestones were followed by a general accumulation of Early Jurassic sediments, mostly the mudstones and thin limestones collectively known as the Lias. These do not usually produce distinctive scenery, except in the case of the Marlstone Rock Bed. This remarkable layer – never more than 10 m thick – consists of iron-rich limestones and sandstones that have been widely quarried across the western parts of Area 15, often using a network of local railways. Its unusual materials, formed in a distinctive chemical episode during the life of the Jurassic seaway, have made it resistant to recent landscape erosion, so that it forms a clear escarpment in the western part of Area 15 (Fig. 268).
**FIG 269.** Map of slopes in the Vale of Belvoir, sub-area I, showing localities mentioned in the text ( **b1, b2** etc.), Marlstone Rock Bed of the Early Jurassic ( **mr** ) and Middle Jurassic bedrock ( **mj** ). Located on Figure 268.
The Marlstone Rock Bed (Fig. 269, **mr** ) underlies the eastern edge of the Vale of Belvoir, the largest and most distinctive scenic feature in the northwest of Area 15. In contrast, the less well-defined southern and western edges of the Vale are carved in Anglian ice-deposited material.
Above the Marlstone Rock Bed, the Jurassic succession includes more of the Early Jurassic (Lias) mudstones, carved into hilly terrain. However, the next major slopes in the scenery are the result of resistant bedrock materials, particularly limestones, of the Middle Jurassic. Because of the generally uniform tilt of the bedrock layers at less than 1 degree to the east-southeast, the slopes in the scenery due to the Middle Jurassic units (Fig. 269, **mj** ) generally lie to the east of those due to Late Triassic and Early Jurassic units. In the early days of geological exploration, the Middle Jurassic succession was divided by William Smith (Chapter 6, Area 9) into an Inferior Oolite unit and a Great Oolite unit. The Inferior Oolite lies below the Great Oolite, but there is much variation from place to place in the detailed nature of these bedrock materials. Limestones, of particular importance in producing steep slopes in the scenery, alternate in the successions with mudstones and sandstones. Special mention should also be made of the Northampton Sandstone layer (forming the local base of the Middle Jurassic), in which ironstones have been of great importance economically, particularly in the southwest of Area 15 around Market Harborough and Corby. This variable package of Middle Jurassic bedrock, rarely more than 50 m thick in total, has been eroded into isolated hills in the west but forms whole valley sides further east, where the tilt has brought it down to lower elevations. Many of these incised valleys have rather parallel sides and trend roughly east-west, a pattern that may indicate that the early streams formed on easterly sloping surfaces.
Rutland Water, near Oakham, was created in 1977 by the construction of a dam across two such easterly-trending branches of the River Gwash. The Gwash has eroded downwards through the Middle Jurassic limestones into the underlying Northampton Sandstone and Early Jurassic mudstones. The limestone has been used in building the older houses in the village of Edith Weston, shown in the foreground of Figure 270.
The Middle Jurassic limestone has also provided stone for many of the buildings throughout Landscape **B** , whether in villages or stately mansions. The building of Burghley House (Fig. 271) was begun in 1555, largely using the locally quarried Lincolnshire Limestone of Middle Jurassic age. It has been the home of the Cecil family ever since.
**FIG 270.** Northwesterly view across Rutland Water from the village of Edith Weston. (Copyright Aerofilms)
North of Stamford, between Bourne and Sleaford, a number of low hills are underlain by Late Jurassic Oxford Clay, often capped by Anglian ice-laid material. Erosion here has carved numerous 30–40 m deep valleys, cut through the Anglian material and into the Oxford Clay beneath. These valleys must have formed since the end of the Anglian glaciation about 400,000 years ago.
In pre-Anglian times, perhaps 600,000 years ago, a large eastward-draining 'Bytham River' is thought by some to have flowed across this Area (Fig. 267). The evidence comes from sediment grains found in the far east of Area 15, which appear to have originally come from bedrocks in the West Midlands and Wales. This river must have flowed at a higher level than most of the present surface, because its course bears little relationship to present valleys or to the flow directions of present rivers.
**FIG 271.** Burghley House, near Stamford.
The slope map of sub-area I, around the Vale of Belvoir (Fig. 269), helps us recognise some further episodes in the formation of the landscape. The key to this is the realisation that some parts of the local area are characterised by slopes that are capped by – and largely cut into – the bedrock, whereas in other parts the capping material is largely sediment left by the Anglian ice sheets. These deposits cover large parts of the landscape, capping some of the highest elevations and carpeting some of the low areas in the southwest. The western edge of the Vale of Belvoir ( **b1** ) consists of Anglian material, still not removed by later erosion. The southern section of the southeastern edge is largely capped by Early Jurassic lithologies, except for two places ( **b2** and **b3** ) where pre-Anglian valleys, plugged by ice-laid deposits, have been cut across by later erosion. To the north of this, Early and Middle Jurassic layers form the double edge of the Vale, and have been stripped of Anglian material. To the east of the Vale of Belvoir is the Ancaster Gap ( **b4** ), now used for road and rail transport (via Sleaford) through the Middle Jurassic scarps. It appears to be large enough to have been carved by early ancestors of the River Trent, which may have been the agents for the general removal of the Anglian cover from the floor of the Vale and its southeastern edge.
In the southeast of Figure 269, the pattern of shallow valleys of the Witham ( **b5** ) and the West and East Glen ( **b6** and **b7** ) is remarkably rectangular, suggesting some fracture pattern in the bedrock, perhaps due to stresses linked to earth movements.
Similar ideas, based on the distribution of Anglian material, can be applied to sub-area II, around Oakham (Fig. 272). Here the cover of Anglian material is general except for a large part of the northeast, where the larger rivers (for example the ancestral Welland and Nene) have eroded widened valleys and may be largely responsible for the removal of the cover of Anglian ice-laid material.
Local slopes must have been modified and moved by slumping and collapse under Ice Age conditions of frequent freezing and thawing. Some of the flatter surfaces in this Landscape may have formed during cold, but not ice-covered, periods of the Ice Age via the removal of sediment by meltwater streams.
On the edge of the Fens south of Peterborough, the slope bounding the Fens may have been formed, at least partly, by coastal erosion during high-stands of the sea, perhaps during the Ipswichian interglacial just over 100,000 years ago. Another suggestion that has been made is that a Fenland lake existed here when the Devensian ice was melting, and that shoreline erosion at the margins of this lake may have been responsible for the Fen-edge slope line.
**FIG 272.** Map of slopes in the Oakham area, sub-area II. Located on Figure 268.
Recent examination of the shapes of some of the depressions in the Jurassic upland bedrock surface, to the west and south of this Fen edge, has suggested that the depressions may have formed as thaw lakes that grew on the surface when the ground was frozen (Fig. 273). These features, generally 1 km or so in diameter, have been recognised as the probable products of _thermokarst_ processes (because of the key roles of heat and ice-melting – see Chapter 2), and they provide a valuable insight into the mechanisms that have led to the lowering of these clay flat-lands.
#### Landscape C: The Fens
The Fenland Landscape is defined by the presence of a remarkably flat and extensive surface blanket of silts and peats that date from the last few thousand years (Fig. 274). This surface blanket was deposited during the Flandrian rise of sea level following the worldwide melting of ice that marked the end of the last cold phase of the Ice Age. Below this cover of surface blanket is Late Jurassic bedrock (Fig. 268). The Oxford Clay and the Kimmeridge Clay are the best-known layers in the Late Jurassic succession, which consists primarily of mudstone. The relative ease with which this mudstone has been eroded during the late Tertiary and Quaternary, particularly by rivers but also by the Anglian ice, explains why this Fenland Landscape is never more than a few metres above or below sea level. In the south, islands of marginally more resistant bedrock are surrounded by younger Fen deposits, for example at Ely.
**FIG 273.** Slope map of sub-area III, showing the Fen edge and thermokarst hollows south of Peterborough. Located on Figure 275.
**FIG 274.** The Fenland.
**FIG 275.** Central Fenland, showing locations ( **c1, c2** etc.) mentioned in the text.
Numerous gravel pits in the surface blanket of the Fens near Peterborough (Fig. 275, **c1** ) and Stamford ( **c2** ) mark the location of fans of gravel brought into the Fenland basin by the ancestral Nene and Welland, as they carved the hill and valley landscape to the west. Some of the gravel was deposited simply because the rivers were slowing as they emerged from their valleys and flowed into the flat lands of the Fens. In other cases, the gravel was moved around by storm waves at times when the sea – or perhaps a lake – was standing several metres higher than the present water level.
The Fens are the largest expanse of really flat land in Britain. The remarkable flatness of their present-day surface is the result of a very young infilling or 'topping-up' process illustrated in Figure 276. In a situation where the sea level is rising, low-lying areas are increasingly prone to flooding because they are drowned repeatedly by high river or storm waters. Each flood leaves deposits of muddy particles behind, topping up the surface towards the level reached by the highest floods.
The parts of the Fens nearest to the sea are known as the Silt Fens (Fig. 274). Their sediment has been deposited largely by wave and tidal action in the coastal zone as the land was built upwards and outwards into the embayment known as the Wash. Former coastlines (back to the Middle Ages) can be seen on the 1:50,000 Ordnance Survey maps (e.g. _Landranger_ 131), where they are marked by former sea walls, now more than 1 km inland from the present sea defences. This retreat of the sea has been encouraged by the building work undertaken by people, because the construction of walls helps to pond up tidal waters, leading to the deposition of fine coastal muds. This man-made build-out of the coastline over the past few hundred years is a reversal of the drowning of the Wash-Fenland Basin caused by Ice Age melting over many thousands of years (see Chapter 2, Figs 20 and 21).
The Silt Fens have been farmed since medieval times. With their ancient churches and intricate pattern of tracks, roads and field boundaries, they provide an isolated example of the 'ancient countryside' described in Chapter 2 (Fig. 26). It is also interesting to realise that the early concentration of farming activity here will tend to increase the supply of mud to rivers and storms, thus accelerating the recent retreat of the sea.
**FIG 276.** Infilling of hollows in the already quite flat Fenland bedrock, to produce the flattest landscape in Southern England.
In contrast to the Silt Fens, the young soils of the Peat Fens have formed under wetland conditions that developed where the main rivers have flowed from hilly Landscape **B** into the flat Fens. Under these wetland conditions, swamps developed behind the coast and the Silt Fens, and vegetation has been preserved as black, organic-rich peats. The Peat Fens began to lose their wetland character when major engineering works began in the early seventeenth century, at which point the characteristic rectangular pattern of field boundaries, roads and drains appeared. It is typical of the Peat Fens that they lack the network of ancient roads and buildings that occur in the Silt Fens.
Figure 277 shows a typical view of the southern Peat Fens, with a sugar-beet refinery steaming away in the middle distance. The peat soils, open fields and straight drainage and road boundaries in the foreground contrast with the more ancient field-boundary pattern behind. The black soils are being lost rapidly, because their drainage and cultivation are leading to the destruction of the peat.
Before the seventeenth century, the southern Peat Fens were low-lying marshes with meandering rivers, and the few inhabitants tended to live on local 'islands'. Fen and marsh people made a living from hunting wildfowl, fishing and harvesting reed, sedge and willow. Life was not easy because of frequent flooding and the lack of well-drained land.
**FIG 277.** The Peat Fens, looking northwards towards Methwold (Fig. 275, **c3** ). (Copyright London Aerial Photo Library)
**FIG 278.** Small Fenland drainage windmill, restored at Wicken Fen in the northeast of Area 13.
The major drainage work that converted much of the Fens to farmland was planned and managed by Cornelius Vermuyden (1595–1683). He was born in the Netherlands and died in London, having introduced Dutch land reclamation methods to the flatlands of England. His first major drainage projects were primarily funded by Charles I and the Earl of Bedford, along with a group of other English and Dutch investors (then known as Adventurers). His first campaign in the Fens involved the digging of the Old Bedford River ( **c4** ) and the Forty Foot Drain ( **c5** ), completed in 1637. During the Civil War, Parliament ordered the dykes to be broken in order to hinder the royalist advance. After the war, work continued, using the labour of prisoners of war, and the New Bedford Level was cut by 1652, completing the remarkably long and straight dual-river stretch of the Great Ouse that is so obvious on maps.
Vermuyden's strategy was to straighten the large rivers in order to speed up the water flow, resulting in the rapid passing of floods and avoiding the plugging of the channels by silt. In more recent times, attention has also been paid to widening and deepening rivers for navigation, and gates have been installed to help control river depth and flooding.
Water was initially lifted from low-lying areas by large numbers of windmills (Fig. 278). Later more efficient drainage was achieved by a succession of different types of drainage engines, firstly powered by steam, then diesel and now electricity. The Fens have rapidly become the most engineered landscape in Britain. This increasingly vigorous drainage of the Fenland fields has caused the surface blanket to shrink and its surface to be lowered. Intensive ploughing of the land has also caused lowering of the surface due to oxidation of carbon-rich peats (generating carbon dioxide), and the removal of the dry soil by the wind during storms.
Because of this general lowering of the ground surface, Fenland rivers now run between flood embankments that are generally much higher than the river surface. This may often be several metres above the level of the surrounding fields, which may lie well below sea level. Rainwater on the fields seeps downwards into their drains. The water is then pumped up into rivers, and the water of these is eventually released into the sea at low tide (Fig. 279).
After disastrous flooding of the Fens in 1947, it was decided to construct yet more components that would improve the major drainage scheme. Part of this involved digging the Flood Relief Channel, the larger and straighter of the channels shown in Figure 280. This greatly increased the floodwater storage capacity in this area, which had previously consisted only of the tidal Great Ouse channel (seen to the left of the Relief Channel in the photograph, winding its way towards King's Lynn and the sea). Through the last 50 years, the engineering of the Fen rivers has successfully avoided any serious flooding. There are current proposals to carry out more engineering work on this river system, and one of these is to allow better recreational navigation between the Fenland rivers and those of the Thames and the Midlands.
**FIG 279.** Drainage from low-lying Fenland fields is pumped into a Fenland river.
**FIG 280.** The Great Ouse (left) and Flood Relief Channel (right) at Downham Market (Fig. 275, **c6** ). (Copyright Aerofilms)
The engineering of the Fenland rivers has changed the river pattern completely. Before the drainage work there was a complicated network of winding rivers with many branches, reflecting the freedom of the flooding rivers to change their courses over the very flat landscape. This has now been changed to a network of straight, restrained rivers (Fig. 281).
But traces of the old network remain. In Figure 282 the Little Ouse rodden shows up beautifully as a ribbon of pale silt meandering across fields of darker peat soils. Many smaller silt-filled ancient channels are also visible, depending on the state of ploughing and crop-growth in the fields. The straight course of the A1102 road, running between Littleport and Shippea Hill, can be seen crossing the winding rodden, which is marked in red on the natural rivers map in Figure 281. Houses have been built where the road crosses the rodden, to take advantage of the silt, which makes for better foundations than the shrinking and wasting peat soils. This rodden is clearly shown on Ordnance Survey _Landranger_ Sheet 143 (Ely and Wisbech).
**FIG 281.** Natural river courses of the Fens, contrasted with the present engineered straight courses.
**FIG 282.** The Little Ouse rodden (Fig. 275, **c7** ), a silt-filled ancient channel. (Copyright reserved Cambridge University Collection of Air Photographs)
Before their general drainage, the Fens contained not only numerous winding rivers, but also many lakes, often called _meres._ The conversion of the Fen wetlands to the valuable arable 'prairies' that exist today means that all of these meres are now dry and often generally forgotten. Some of the best known were those at Soham (see Area 13, Fig. 243), Ramsay and Whittlesey.
Whittlesey Mere ( **c8** ) was not drained until 1851. Before that, it was some 4 km across and was claimed to be the second largest lake in England, after Windermere. It was famous for its fishing, for its recreational sailing, and for the size of waves that would form on its surface under stormy conditions. It was also known for the exploits of the speed skaters who competed there under the fierce freezing winter conditions common in the eighteenth and nineteenth centuries.
The limestone blocks shown in Figure 283, the smallest weighing over a tonne, provide unusual evidence for the former presence of Whittlesey Mere. They are thought to have arrived here when the mere was open water, as they were being transported on a raft which foundered during stormy weather. They appear to have originated in one of the Middle Jurassic limestone quarries in the west, and had been destined for a building site – probably one of the religious settlements on the Fenland 'islands' to the east. They were marked out as a navigational hazard before the mere was drained and they again became visible.
**FIG 283.** Engine Farm limestone blocks (Fig. 275, **c8** ), 9 km southeast of Peterborough.
**FIG 284.** The Holme Post (Fig. 275, **c8** ), 9 km south of Peterborough. The red and white rule is 1 m in length. (Copyright British Geological Survey)
**FIG 285.** Woodwalton Fen.
The shrinking and wasting away of the Fenland soils has been mentioned above. The Holme Post (Fig. 284) provides an impressive indication of the lowering of the surface since the draining of Whittlesey Mere. This post was buried in 1848 in a vertical shaft dug into the ground not far from the edge of the mere. When it was buried, the base of the post was fixed into the underlying mudstone bedrock, and its top was fixed level with the ground surface. The soil (much of it peaty) has shrunk 4 m in just over 150 years (almost 3 cm/year), leaving the post projecting by that amount into the air. It is interesting to see that the shrinkage was greatest in the early years, when the ground was drying out particularly rapidly after the drainage of the mere in 1851.
At Woodwalton, Wicken and Lakenheath Fens, campaigns are being directed towards preserving relicts of the early Fen wetland environment (Fig. 285). This has been made more difficult by the recent drainage of the surrounding landscapes, but it now looks as if the trend towards ever more efficient drainage is being reversed. The increasing concern to protect threatened wildlife and provide people with recreational space is encouraging long-term plans to re-flood and greatly extend the wetlands in these preserved areas. The Fen wetland nature reserves are generally designed to be maintained with a high water table, in contrast to the drained fens elsewhere. This favours a range of different ecological environments, controlled by the degree of drainage. Reed and sedge form at the edge of open water, followed by a scrub of willow and alder as drainage becomes better.
**FIG 286.** 'Bog oak' at Wicken Fen.
The Peat Fens have often yielded large pieces of timber on ploughing, and heaps of this material can sometimes be seen at the edges of fields (Fig. 286). This timber reflects a period when the Fens were drained well enough to allow the growth of woodland with trees of this size.
#### Landscape D: Early Cretaceous Fenland foothills
Bedrock of Early Cretaceous age rests upon Late Jurassic bedrock along the eastern margin of Area 15 (Fig. 268), where it is sometimes covered with a surface blanket of Fenland deposits. This Landscape is more fully developed in Area 16, but it is logical to consider some aspects of the development of King's Lynn at this point.
King's Lynn ( **d1** ) has a long history as a transfer point between sea-borne ships and smaller, river-borne craft. The waterfront in King's Lynn shows the remarkably preserved pattern of medieval warehouses and unloading quays constructed on the tidal margin of the Great Ouse (Figs 287 and 288). Because of the presence of a number of side creeks at right angles to the waterfront, the medieval centre of King's Lynn was divided to an unusual degree.
Its position on the banks of the Great Ouse has obviously governed the growth of King's Lynn. So also has the presence of a number of drainage channels rising in the nearby hills, which form the eastern margin to the Fens, and draining westwards into the Great Ouse. These channels bring water from the Early Cretaceous hills (Carstone and Sandringham Sands), but also provide excellent sheltered channel mouths which have been developed for the unloading, loading and repair of shipping.
**FIG 287.** Part of the King's Lynn waterfront (Fig. 275, **d1** ). At the left-hand margin is the large Tuesday market place, with numerous stalls. To the right of the obvious Purfleet channel, near the right-hand margin, is the Saturday market place. (Copyright Norfolk Museums and Archaeology Service & Derek A. Edwards)
**FIG 288.** Simple sketch map of medieval King's Lynn.
### AREA 16: NORFOLK
Although Norfolk was famously described by Noel Coward in _Private Lives_ as 'very flat', it generally has a much more varied topography than, for example, the Fenland of Area 15 to the west. It is true that the hills barely exceed 100 m in height, but there are open valleys between the hills, and undulating plateaus are extensive.
The only part of Area 16 (Figs 289 and 290) that approaches the extensive flatness of the Fens is the Broads area of east Norfolk, and both of these landscapes result directly from the recent (Flandrian) rise of sea level that has followed the melting of ice since the last (Devensian) cold episode of the Ice Age.
The most obviously recent landscape changes are those we can see taking place in the coastal zone, arbitrarily defined here as ground less than 20 m above sea level. These changes have been taking place over the last 6,000 years, since the rising Flandrian sea reached approximately its present level. This general map of areas of recent landscape change picks out the extent of the coastal zone, and also shows the general pathways of the main present-day rivers, where the change of inland landscape tends to be concentrated (Fig. 291).
**FIG 289.** Location map for Area 16.
**FIG 290.** Natural and man-made features of Area 16.
The drainage of the Norfolk landscape depends on low-gradient rivers in open valleys draining to the west, north and east from the Chalk high ground of west Norfolk. The main westerly rivers flow into the Fens over relatively short courses, and are comparatively small. They are, from south to north, the Little Ouse (3.0 m3/s), Wissey (1.8 m3/s) and Nar (1.2 m3/s), where the mean flow figures have been measured at the stations shown in Figure 291. In contrast, the main rivers flowing to the east coast are distinctly longer, although water extraction leaves some of them with low mean flows. From south to north, mean flow figures measured at the stations shown are: Waveney, 0.6 m3/s; Yare, 1.4 m3/s; Wensum, 4.0 m3/s and Bure, 2.2 m3/s. The overall drainage divide within the Chalk hills runs from the northwestern part of the Area, inland from Hunstanton, in a southeasterly direction to the Lopham Gap, between the Little Ouse and the Waveney. Here, remarkably, the divide between the westerly-flowing Little Ouse and the easterly-flowing Waveney is less than 25 m above sea level.
Some of the examples of recent changes are so clear that they merit discussing in unusual detail below. In much earlier times, during brief periods of warmer climate and higher sea level over the last million years or so, coastal processes are likely also to have influenced the scenery along the edge of the Fens in west Norfolk.
**FIG 291.** Valley pathways and coastal flooding zone for Area 16.
The general introduction to East Anglia at the start of this chapter summarises the bedrock distribution (Fig. 226) and succession (Fig. 225), and this sets the scene for consideration of the Landscapes of Area 16 (Fig. 292).
The tilting of the bedrock layers to the east is very gentle, but enough to take the base of the Chalk (Late Cretaceous) from a few metres above sea level at Hunstanton to a depth of 550 m below sea level under Great Yarmouth, 80 km to the east. This amounts to an overall slope downwards to the east of less than 1 degree. The gentle tilting took place during the Tertiary period, and can be regarded as part of the general lowering of the Earth's surface that has caused great thicknesses of sediment to accumulate in the area now covered by the southern North Sea. The tilting may also have been linked to the volcanic activity and uplift of western Britain that occurred during earliest Tertiary times, as the Atlantic Ocean continued to open with the movement of its underlying plates.
**FIG 292.** Bedrock pattern and structure of Area 16.
The hilly landscape created by the Late Cretaceous Chalk and Late Tertiary Crag contrasts markedly with the flat landscape to the west, underlain by Jurassic mudstones (Area 15).
The gentle bedrock tilt to the east that is the main feature of the structure of Norfolk is visible in the Hunstanton cliffs (Fig. 293), where the contact between the white Chalk and the underlying brown Carstone slopes down to the left in the cliff line. These cliffs are shown in more detail in Figure 297.
I have divided Area 16 into four Landscapes, labelled A to D in Figures 292 and 294, basing the division on the bedrock that underlies the surface blanket. In general the Landscapes recognised in this book, though based on bedrock differences, are similar to the character areas recognised by the Countryside Agency, which are based largely on land-use patterns.
#### Landscape A: Late Jurassic mudstones of the Fens
There are only very small parts of Area 16 where the surface blanket is underlain by the Late Jurassic mudstones of the Kimmeridge Clay. These occur along the western edge of Area 16 and, in topographic terms, they form part of the main Fenland that is discussed under Area 15.
**FIG 293.** Looking northeastwards over the Hunstanton cliffs. (Copyright Norfolk Museums and Archaeology Service & Derek A. Edwards)
**FIG 294.** Area 16, showing Landscapes **A** to **D** and localities ( **b1, b2** etc.) mentioned in the text.
#### Landscape B: Early Cretaceous foothills
The Early Cretaceous bedrock succession that underlies the surface blanket in west Norfolk consists largely of Gault mudstones in the south of Area 16. However, to the north, in the areas east of Downham Market and King's Lynn, increasing thicknesses of sand are present, forming the Sandringham Sands and the Carstone. Through much of this northern area, the Carstone has been used as a distinctive local building stone: a red, brown or orange sandstone looking rather like gingerbread. The slabs or blocks are irregular, and have generally been used to face walls, requiring brick or limestone piers or frames to give strength and form to windows and doors. The photograph (Fig. 295) is of a new wall in Hunstanton.
The sandstone materials of the Early Cretaceous have resisted landscape erosion more than the underlying Late Jurassic mudstones of Landscape **A** , producing low hills often covered with acid-soil heathland vegetation. Bracken and mixed forestry, particularly extensive around the royal Sandringham estate ( **b1** ), have been developed for countryside shooting activity. East of King's Lynn, around Leziate ( **b2** ) and Roydon Heath, this heathland also contains an array of sand-pits, where the Sandringham Sands have been quarried as a source of pure quartz sand.
The variety of deposits in the Nar Valley ( **b3** ) shows how valley pathways have been used repeatedly as the landscape has evolved. The earliest surface-blanket deposits are of Anglian ice-laid material, some 450,000 years old. These are followed by Hoxnian deposits (about 400,000 years old) that include evidence of flooding by the sea up to a level 25 m above the present sea level. The next episode recorded in the sequence represents the deposition of gravels, sands and muds in a river delta that built outwards into a lake. It seems that the Nar Valley was dammed at this time by Wolstonian ice sheets (180,000 years old), which must have entered the Fenland basin from the northwest, creating a lake.
A final dramatic episode in the history of this Landscape is marked by the Hunstanton ice-laid till, which was deposited just inland of the present coast of northwest Norfolk during late Devensian times, about 20,000 years ago. The topography of the landscape in these recent times must have been quite similar to that of today, because the Devensian ice sheets that spread across the North Sea basin were stopped by slopes similar to those that currently face the Fenland Basin and the North Sea.
#### Landscape C: North Norfolk coast and the Late Cretaceous Chalk hills
The Chalk hills of Norfolk form more than half of the land area of Area 16, forming a broad belt trending roughly north-south, with the chalk strata tilted to the east by less than 1 degree. Most of the Landscape is covered by a thick surface blanket, so the easiest way of looking at samples of the Chalk is to look at the local buildings that are made from it. White Chalk is often used as a building stone and is generally quarried from the particularly resistant layers known as 'clunch'. Flints from the Chalk (Fig. 296) are also commonly used as a facing material.
**FIG 295.** Wall faced with blocks of gingerbread Carstone bedrock.
**FIG 296.** Flint nodules in Chalk at West Runton, 2 km east of Sheringham.
Flints are a common feature in the upper layers of the Chalk, and are the major component of the river and beach gravels of Norfolk. They have been abundantly used in the building of many walls and houses. The flints formed in the first place by mineral growth within the soft muddy sediment that was later to become the Chalk. They grew when silica was precipitated from the water in the minute spaces and cracks that are always present in young sediment, replacing the calcium carbonate that was present before. In areas close to the coast, flint walls often show the flints with their rounded, sometimes white exterior crusts, whereas elsewhere flint walls consist of 'knapped' flints with a flatter, black face outwards, created by cracking open the flint before mounting it in the wall.
The scenery of the coastal zone of northwest Norfolk is much younger than the valleys and slopes visible inland. This is because the sea has only arrived at its present position within the last few thousand years, since the general melting of the Earth's ice cover that took place at the end of the Devensian, about 20,000 years ago (see Chapter 2).
Hunstanton ( **c1** ) is the only place in the whole of East Anglia where tough, overhanging sea cliffs occur. This is because there are no other localities where hard bedrock has become directly exposed to the attack of storm waves.
Hunstanton is also famous for the three differently coloured layers of bedrock in its cliffs: a layer of Late Cretaceous white Chalk overlies an Early Cretaceous layer of brown sandstone (Carstone), with a thin layer of red Chalk between them (Fig. 297). The detached and fallen blocks of white chalk at the base of the cliff show that the cliffs are collapsing and moving inland all the time. The regular rows of weed-covered Carstone blocks in the lower part of the beach show how the storm waves have created a wave-cut platform with a regular system of _joints_ (cracks). These joints were formed during an early and widespread phase of stressing of the bedrock.
East of Hunstanton the coastline is characterised by spits, beach ridges and barriers, often with salt marshes divided up by the tidal channels that are typical of this coastal stretch. The Burnham Flats are an offshore area of unusually shallow sea, north of Scolt Head ( **c2** ), that produce the special coastal scenery of this area. The Flats extend some 25 km out to sea before the depth at low tide becomes greater than 10 m. This means that when the sea level was rising due to melting of the Devensian ice, the sea must have flooded over this area of land extremely rapidly. More importantly, the flatness and shallowness of the Burnham Flats has allowed vigorous attack on the sea bed by storm waves, moving considerable quantities of sediment and constructing beach barriers with their associated salt marshes.
**FIG 297.** The sea cliffs at Hunstanton (Fig. 294, **c1** ). (Copyright London Aerial Photo Library)
Scolt Head Island (Fig. 298) is a beautiful example of a beach barrier island: 'beach' because it is made of sand and gravel pushed into place by storm waves, and 'barrier' because it protects the land behind it from these waves. The beach barrier forms the north rim of the island, and protected back-barrier features have formed behind it. At the western end of the island (the foreground in Figure 298), advancing storm waves have curved around as they moved up the deep tidal channel in the right of the picture. This has, in turn, curved the beaches that form the end of the island. A number of old curved beaches are visible in the foreground of the photograph, where successive storms over recent centuries have added more sand and gravel to the island.
**FIG 298.** Looking eastwards along Scolt Head Island (Fig. 294, **c2** ). (Copyright London Aerial Photo Library)
Since the Flandrian sea-level rise, global sea level has changed relatively little over the last 6,000 years, and the Norfolk coastline itself has stayed in more or less the same position. However, the plentiful supply of gravel, sand and mud moved around by sea storms means that beach barriers such as Scolt Head Island are continually changing their shape. People who revisit stretches of the coast are always spotting year-to-year changes in the barrier's shape, the positions of the tidal channels and the build-up of mud in sheltered areas.
Wells-next-the-Sea ( **c3** ) is the only settlement on the north Norfolk coast that is still used by commercial shipping. For about 1 km north of Wells, the construction of a sea wall west of the main tidal channel has allowed drainage of the western back-barrier areas. A road running behind this sea wall provides easy car, pedestrian and railway access to a wide range of beach-barrier and shore environments (Figs 299 and 300).
In Figure 300, the tidal channel is the straight, light-coloured feature running inland towards Wells-next-the-Sea. The channel has been straightened by the building of a sea wall along the near side of it. The large, dark, tree-covered ridge directly behind the beach in the foreground is the main storm-built barrier, stabilised in the 1850s by planting pine trees on its wind-blown dunes. The beach itself shows at least four distinct, slightly sinuous ridges of sand, more or less parallel to the tree-covered barrier. These ridges tend to be driven landwards during storms and may eventually be added to the barrier. The ridge closest to the tree-covered barrier is the lightest in colour because it has been capped by dry, wind-blown dunes formed within the last 20 years. Behind the main barrier, Wells Caravan Site can be seen, built upon meadows formed by draining ground that was previously salt marsh. These drained meadows were flooded when the sea wall was breached during a storm in 1978. This whole array of coastal features has been constructed and altered during the last 6,000 years, since the sea rose and flooded the land up to its current level.
**FIG 299.** Pattern of coastal sediment near Wells-next-the-Sea (Fig. 294, **c3** ).
Figure 301 shows the large barrier feature of Blakeney Spit ( **c4** ) in the far distance, along with a number of smaller barrier ridges forming a discontinuous, sandy strip in the middle distance, on the seaward side. Behind these barriers, in the centre of the photograph, is a large area of back-barrier salt marsh, completely covered by the highest tides and supplied with sea water and sediment by a complex network of channels. The sharp southern edge of the coastal strip (on the right-hand side of the picture) is marked by a clear, straight line that truncates fields on the hilly ground to the south. This edge is thought to mark an old cliff line formed during the Ipswichian (about 130,000 years ago), when the sea was at a slightly higher level than it is today. Between the Ipswichian warm episode and today, the sea retreated for hundreds of kilometres as ice advanced into this area. When the ice melted, the sea advanced back to its present position.
**FIG 300.** Looking southeastwards across the tidal channel that leads into Wells-next-the-Sea (Fig. 294, **c3** ), whose buildings cluster round the quay in the middle distance at the right-hand edge of the photograph. (Copyright reserved Cambridge University Collection of Air Photographs)
The photograph in Figure 302 was taken when the gravel barrier ridge was under attack from a severe winter storm in February 1996. A light powdering of snow has fallen on the brown winter landscape. The storm has sent waves over the top of the barrier, flooding the low-lying marshes behind and creating small gravel fans from the barrier material in this temporary lagoon.
An even more severe storm in 1953 caused loss of life in the village of Salthouse, on the left side of the flooded marshes in Figure 302. This area has been chosen for an engineering programme of 'managed retreat', where the present barrier will be left to be modified by future storms, and a new barrier will be built further inland as a second line of defence.
The presence of ripples as large as those shown in Figures 303 and 304 is evidence of high flow speeds in the tidal channels, providing enough energy and turbulence to form these remarkable and distinctive shapes. Walking over beaches, you will often see much smaller ripples (20–30 cm between crests) that have been formed in the same way, but under less rapid flows in minor channels. Similar – but more symmetrical – small ripples can also be formed by the to-and-fro action of waves, as opposed to one-directional flows.
**FIG 301.** Looking eastwards over the young coastal sediment from a point 1 km east of the Wells tidal channel. (Copyright Norfolk Museums and Archaeology Service & Derek A. Edwards)
Figure 305 shows the flow patterns that create such ripples and lead to their migration. If water speed is increasing over a flat bed, turbulent eddies will come and go, always varying in size, speed and direction, but tending to form at regular intervals in a mass of flowing water. Eddies can also be initiated as water flows over an irregular surface and, once set up, they often scour the bed, having enough energy to pick up loose material. In this way, sand grains can be picked up by the flow of water and carried along the bed into ridges or ripples, separated by hollows scoured out by the eddies. Since pockets of turbulence tend to occur at regular intervals, regularly spaced ridges soon form in the sandy bed. These ridges take on the shape of ripples, with gentle upstream and steep downstream faces, and they start to migrate downstream. Eddies now become amplified in the troughs between ridges, excavating sand which is then pushed up the upstream side of the next ridge, before avalanching down the downstream face. This transfer of material, from the upstream side of the ripple to the downstream side, allows the ripple to be continuously rebuilt in a downstream direction whilst maintaining its size and shape.
**FIG 302.** Looking west over the eastern stem of Blakeney Spit (Fig. 294, **c4** ). (Copyright Norfolk Museums and Archaeology Service & Derek A. Edwards)
**FIG 303.** Large ripples (5–15 m from crest to crest) on a sand bar in the tidal channel behind Blakeney Spit, near the village of Morston (Fig. 294, **c5** ). (Copyright London Aerial Photo Library)
The inland parts of Landscape C have a surface blanket of river and ice-laid material, often producing a gently undulating plateau surface. Much of this material is Anglian in age, so the open and gentle valleys that have been eroded in the cover of this inland plateau have largely formed over the last half-million years. The details of the Anglian events, and of earlier episodes in the Pleistocene, are the subject of much interest and research at the moment. This will be reviewed briefly in the section on Landscape **D** that follows this.
Since the Anglian cold phase, the Earth has experienced four more major cold episodes, the last of which was drawing to a close only about 18,000 years ago. During this last (Devensian) cold episode, ice from the north extended as far south as the position of the present north Norfolk coast. Most of the land to the south, though probably not covered by ice since the Anglian glaciation, had for much of the time been subjected to viciously cold temperatures, which created a layer of ice within the ground. The northern latitudes of Canada and Russia provide vivid present-day examples of ground-freezing processes, and of the ways in which freezing in winter and thawing in summer can cause damage to the foundations of buildings and roads. East Anglia contains many examples of processes of this sort, preserved since this last cold episode.
**FIG 304.** Sandbank in the tidal channel at Wells-next-the-Sea (Fig. 294, **c3** ). The large ripples have a wavelength of about 10 m and become active only when covered by a tide high enough to flow outwards (to the left) at speeds greater than ≈0.6 m/s (≈2.1 km/h).
The field shown in Figure 306 has been photographed under ideal conditions of crop growth to show a regular honeycomb pattern in the ground. Similar patterned effects are often to be seen in the present-day Arctic (see Chapter 2, Fig. 17), where areas of ground are subjected to alternations of fierce winter freezing and summer melting. When the ground freezes, the first ice tends to form at a large number of ice nucleation points scattered below the soil surface. Once some ice crystals have formed it is easier for more to grow on these than to grow on their own, so small pockets of frozen ground form and grow outwards until they meet neighbouring pockets. Here they push against each other, creating straight edges. Another important effect is that when the water in the ground freezes it expands, shifting the soil outwards slightly. Where they meet, neighbouring pockets of frozen ground cannot shift the soil outwards and so force it upwards to the surface, forming ridges which define the edges of the pockets and producing the honeycomb pattern.
**FIG 305.** Movement patterns during the migration of ripples. Movement at three levels in the water (blue) becomes increasingly marked by eddies as the floor of sand (yellow) is approached. On the surface of the sandy bed, sand is carried up the upstream side of the ripples and deposited on the downstream side, building downstream-dipping layers in the sand. As these movements continue, the ripples will migrate downstream, and this may be a steady movement if the water continues to flow in a steady way.
The name _pingo_ has been borrowed from northern native ('Eskimo') languages and applied to hillocks typical of some Arctic areas, formed when lenses of ice grow within the soil. These lenses may grow until the ice core breaks through to the surface, forming a hollow like the crater of a volcano which may contain water during the summer. At Thompson Common ( **c7** ), on the A1075 between Thetford and East Dereham, a Pingo Trail has been arranged, where visitors can see irregular hillocks and hollows with ponds, believed to have been formed in this way during Devensian cold episodes. These features, also seen at East Walton ( **c9** ; Fig. 307), are further examples of the effects of soil movements generated by ice growth and melting.
Over the southwestern part of this Landscape the surface blanket contains light sandy soils, in contrast to the heavy clay soils on the thicker ice-laid material further east. The name Breckland is used for this area of light soils, which tend to dry out quickly and lack the nutrients needed to produce good crops. The area has never been valued for farming and has, even in recent historical times, resembled an arid desert, subject to widespread dust storms and removal of soil and seeds by the wind.
**FIG 306.** Patterned ground, 2 km northwest of Oxburgh Hall (Fig. 294, **c6** ), very like the present-day Arctic pattern shown in Figure 17. (Copyright Norfolk Museums and Archaeology Service & Derek A. Edwards)
**FIG 307.** Pingo remains near East Walton (Fig. 294, **c9** ), 10 km east of King's Lynn. (Copyright Norfolk Museums and Archaeology Service & Derek A. Edwards)
The photograph of the Grimes Graves area (Fig. 308) shows, in the background, the forest cover now typical of much of the Breckland. In the foreground, large numbers of craters are the relicts of the Neolithic flint mining for which Grimes Graves is famous. English Heritage provides access to some of these small mines, where the flints can be examined in the position in which they originally grew in the Chalk. The flints were used by Neolithic people to make knives, axe heads and spear heads by careful chipping ('knapping'). At Grimes Graves there are about 500 mines spread over an area of 6 hectares, many of them reaching a special seam of flints in the Chalk where the miners cut horizontal galleries from the main vertical shafts. Deer antlers were used to hammer, lever and rake the flints from the rock, before hauling them to the surface in baskets. Flint knapping is still carried out today by a few experts and there is still a small demand for flint chips for reproduction flint-lock firearms.
Much of the forestry in the Breckland was planted by the Forestry Commission in the 1920s to add value to the ground and to limit soil erosion by the wind. Parts of Thetford Forest have also been used for many years for military training. In earlier times, this empty country was used for hunting by royalty, and today it is once again becoming popular for recreation: Center Parcs is just one of the many tourist developments of recent years.
**FIG 308.** Grimes Graves (Fig. 294, **c8** ), 4 km northeast of Brandon. (Copyright Skyscan Balloon Photography, English Heritage Photo Library)
A gravel quarry near Lynford ( **c8** ) has revealed, in recent years, a vivid picture of life some 60,000 years ago on the floodplain of the ancestral River Wissey. At that time the Devensian cold episode of the Ice Age was in full force, and local January/February temperatures are estimated to have averaged -10°C or lower. Neanderthal man lived in the area and it appears that they used an abandoned river channel loop as a location for shepherding, trapping and butchering of mammoths, woolly rhinos, horses and bison.
Thetford has grown around a crossing of the westward-flowing Little Ouse, just below the point where it is joined by the River Thet. An ancient road here, known as the Icknield Way, followed a belt of open country marking the western edge of the Chalk bedrock and our Landscape **C**. Thetford embarked on a programme of major expansion in the 1960s, with the construction of large areas of housing and industrial development, often in conjunction with London housing authorities.
The Wensum and Yare form the longest river in the Norfolk area (Fig. 291). It is probably the latest version of a much longer easterly-flowing river that developed when the bedrock of the area first began to tilt eastwards. Near Fakenham, the headwaters of the Wensum lie in an area of very gentle hills ranging in elevation between 50 and 80 m above sea level. Much of this rather flat area is underlain by ice-laid material, and the Wensum has cut a small, open valley into this with only a narrow floodplain and a limited valley floor. Beside the river are patches of gravel moved from the local slopes when spring floods were more vigorous, probably during and immediately after the Devensian glacial.
Further downstream towards Norwich ( **c10** ) the river increases in size as it gathers water from its branches and gradually drops in altitude. The locality map (Fig. 294) shows how it develops a series of meanders downstream of Norwich, approximately 2–3 km from bend to bend. Gravel pits close to the Yare provide further evidence that the river carried much coarser materials under the vigorous flooding conditions following the Devensian glacial. In this area the whole shape of the valley (slopes and floor) has a meandering form cut into Anglian ice-laid material, Late Tertiary Crag and Late Cretaceous Chalk. This tells us that since the Anglian cold spell, the river has firstly formed meanders by side-cutting and only later cut downwards to produce its valley.
Although much redeveloped, it is still possible to see many features of medieval Norwich in Figure 309. To the left, the River Wensum flows generally southeast, and its first large meander became the site of the cathedral (with the spire) and the castle (on the obvious mound to the right). The River Wensum formed the early northern boundary of the city, which was surrounded on the other three sides by curtain walls that still exist in some areas.
**FIG 309.** Medieval centre of Norwich (Fig. 294, **c10** ). (Copyright Aerofilms)
The location of Norwich represents a balance between the relative ease of bridging rivers where they are smaller above a confluence, and the advantage of being able to bring cargo further up a river when it is still tidal.
Norwich Castle and museum perch above the medieval city centre, and when the shopping centre was built nearby the excavations penetrated deeply into the Chalk. Elsewhere under Norwich, tunnels have been dug to extract chalk (for lime) and flint (also for building), as well as to create storage. These tunnels are prone to collapse and, in one incident a few years ago, trapped a double-decker bus.
Early work on Norwich Cathedral was began late in the eleventh century. It is situated lower than the castle, close to the valley floor but on a terrace of old gravels. The lack of good building stone in the north and east of East Anglia means that the stone for the cathedral was brought over from Caen in France. Barges carried the blocks via the English Channel and the North Sea to Great Yarmouth, then up the rivers Yare and Wensum to a short length of canal that ran to the cathedral.
For most of their courses, the rivers of Norwich have wide valleys with sides that are relatively low (often less than 20 m) and gentle. One exception is the slope where Mousehole Heath has been cut into by the Wensum, immediately northeast of the city-centre bend. Mousehole Heath is underlain by an extensive sheet of gravel and sand that seems to have been left there by northward-flowing rivers draining from a tongue of ice that existed to the south at some time during the Anglian cold spell. Ice-laid material to the south of Norwich, particularly near Poringland, reaches an elevation of 75 m, which is high for this area.
#### Landscape D: Late Tertiary Crag hills and the Broads
This Landscape is defined by the presence of Late Tertiary bedrock, generally known as the Crag, resting upon the Late Cretaceous Chalk. Chalk is exposed on the shore at West Runton near Sheringham ( **d1** ), but the Late Tertiary Crag is exposed above this over most of eastern Norfolk and Suffolk. Of special interest are coastal exposures of the Cromer Forest Bed, which forms a very important and remarkably extensive layer sporadically visible for more than 60 km from Cromer ( **d2** ) in the north to Happisburgh ( **d3** ) and as far south as Pakefield ( **d4** ). The Cromer Forest Bed consists of a variety of mudstones and sandstones, often carbonate-rich and full of fossil remains. The fossils represent temperate climatic conditions and are overlain by distinctive glacial deposits representing a return to a much colder climate. Understandably, great interest has followed the recent discovery of flint artefacts, convincingly made by early people, both at Happisburgh and at Pakefield. These are thought by some to represent the oldest evidence of early humans so far found in lands north of the Alps. However, the Cromer Forest Bed deposits and the overlying glacial deposits are complicated, involving many local episodes, and their dating is still open to doubt and expert disagreement. Some workers believe that the glacial deposits represent a pre-Anglian glaciation, and that the flint implements beneath them must therefore be some 700,000 years old. Others feel that the glacial deposits are of Anglian age and that the flint implements are more likely to be ≈500,000 years old, an age more consistent with the currently accepted date of settlement at these latitudes.
The cliffs in the foreground of Figure 310 are actively collapsing by land-slipping under the attack of North Sea winter storms. They provide a cross-section through the Cromer Ridge, one of the highest hill features in Norfolk, reaching 90 m above sea level just inland of Sheringham ( **d1** ), and extending more than 10 km towards the southwest. The ridge is thought to have been deposited by ice sheets and contains gravel and sand, along with contorted blocks of mixed sediment tens of metres across. Much of this appears to have been dumped, folded and fractured by ice sheets of the Anglian cold episode, which came from a northerly direction some 450,000 years ago (see Chapter 2). The deformation of the material suggests that the ice margin repeatedly advanced and retreated, scraping up and bulldozing its earlier deposits in front of it. In this respect, and because the material forms such a clear ridge, it may be that the Cromer Ridge is the remains of a moraine similar to those found at the fronts of many present-day glaciers and ice sheets.
The coastal scenery of northeast Norfolk consists of a narrow beach backed by cliffs, varying in height from a few metres in some places to over 70 m just east of Cromer. The cliffs are made of soft, clayey sediments, consisting sometimes of ice-laid material and sometimes of Late Tertiary Crag sands, muds and gravels.
When attacked by waves, these soft cliffs slump and slide down onto the beach before being washed away by storms. This contrasts with the much older and harder bedrock cliffs seen at Hunstanton, which collapse as large, hard blocks. More dramatic, however, is the contrast between these soft cliffs and the landscape of wide beaches, beach-barriers and salt marshes of the northern coast. The beach-barriers are continually being built up with new material brought in by the sea, whereas the cliffs of the northeast undergo a general regime of erosion and removal (Fig. 311).
Why is there this important change in the type of coastline around Norfolk? It may be that the facing direction of the northeast coast exposes it to more vigorous storm waves, or perhaps the shallowness of the offshore area of northern Norfolk removes energy from the waves, reducing their erosive power.
**FIG 310.** Looking northwestwards towards Overstrand (Fig. 294, **d5** ) and Cromer ( **d2** ). (Copyright reserved Cambridge University Collection of Air Photographs)
The east-facing coastline of south Norfolk and north Suffolk has a continuous, narrow beach zone along its length which is locally backed by cliffs. These cliffs, though made of the same ice-laid material as those in the northeast of Norfolk, are rarely greater than 10 m in height. This stretch of coastline is under a general regime of erosion by the sea, similar to that of northeast Norfolk. In this case, however, the sea has not only removed sand and gravel material from the coastline but it has then churned it up and dumped it back on the land to produce local exceptions to the regime, where sediment has built up.
Great Yarmouth ( **d6** ) and Lowestoft ( **d7** ) have grown where important rivers flow into the sea. In each case, former river valleys have been plugged by coastal sediment over the last 6,000 years. Further north, at Sea Palling ( **d8** ), a successful attempt to locally combat the erosive action of the sea involved the construction of nine offshore sea-defence islands, spaced along 3 km of coast. These islands have helped to trap sediment that would otherwise have been washed along the shore by waves, resulting in a build-up of the beach in this area over the last 20 years.
In Lowestoft (Fig. 312), the muddy water of Oulton Broad (in the foreground) and the blue water of Lake Lothing (nearer the sea) make up an eastward-extending waterway around which the town has grown. Lake Lothing, surrounded by large buildings, leads to the sea and the harbour and quay of Lowestoft – the easternmost point of mainland England. To the northwest, Oulton Broad is linked to the River Waveney system, which drains a large lowland area further inland. It seems clear that the River Waveney originally entered the sea down this waterway. However, at times when this route was blocked by coastal sand and gravel, the main flow of the Waveney would drain to the sea near Great Yarmouth, some 20 km to the north.
**FIG 311.** Happisburgh coastline (Fig. 294, **d3** ) phot ographed in 2004. The red line marks the position of the cliff in 1994. (Copyright Mike Page/www.mike-page.co.uk)
**FIG 312.** Lowestoft (Fig. 294, **d7** ), looking east over the town towards the North Sea. (Copyright Aerofilms)
The Norfolk Broads authority is responsible for the Wensum and the Yare from Norwich downstream almost as far as Great Yarmouth and Lowestoft, and also for some way up the northern tributaries of the Bure and Ant. The Broads are England's largest low-lying area of undrained wetlands and are home to many rare species of plants and animals.
The Broads contain many shallow lakes, providing marvellous habitats for wildlife and a great deal of boating pleasure for a large number of human visitors. Until the 1960s most people believed that the lakes were natural, on account of their size, but in fact the Broads are largely man-made. They are the result of medieval diggings for peat which formed in this swampy ground on the ancient river floodplains. The peat became an important fuel as an increasing scarcity of firewood coincided with growing demands for cooking, heating and evaporating sea water to produce salt for food preservation.
The peat diggings were usually 2–3 m deep. Deeper diggings were more likely to have flooding problems, but the peat cut at greater depths was usually more compact and, when dried out, provided a more efficient fuel. During the thirteenth and fourteenth centuries, flooding of the peat diggings became an increasing problem, perhaps due to climate change and rising sea level. The year 1287 saw particularly severe flooding, and the Broads were largely abandoned as sources of peat, becoming more important as sources of fish, wildfowl and reeds for thatching.
**FIG 313.** Looking southeastward towards Heigham Sound from a point above Hickling Broad (Fig. 294, **d9** ). (Copyright Robert Harding Picture Library Ltd)
**FIG 314.** Looking northwestward over Hickling Broad (Fig. 294, **d9** ). (Copyright London Aerial Photo Library)
**FIG 315.** Looking southeastwards across the Halvergate Marshes (Fig. 294, **d10** ) towards Great Yarmouth on the coast. (Copyright Norfolk Museums and Archaeology Service & Derek A. Edwards)
Figures 313 and 314 show the typical pattern of lakes and channels, most of which have been created and/or modified by excavations. Particularly characteristic are the long, narrow islands that were left as the margins of some of the excavations. These Broads are the result of excavating a swamped wetland area on one side of the River Thurne, which terminates in the young beach deposits and the present-day coastline only 5 km away.
The straightness of the railway and road in Figure 315 contrasts strongly with the meandering form of the River Bure. The flatness of the Halvergate Marshes and the position of the coastline both reflect the level reached by the sea during its last Flandrian rise.
Surrounding the very flat valley floors occupied by the Broads are large areas of slightly higher ground with soils that are particularly productive. The 'island' of Flegg ( **d10** ), just north of Great Yarmouth, is very largely within our definition of the coastal flooding zone, and must certainly have been an island at former times of high sea level.
# [CHAPTER 9
The Making of Southern England](004-toc.html#ch9)
OUR SURVEY BY REGIONS AND AREAS is now complete, so we can conclude the journey by contemplating the broader patterns across Southern England as a whole, and why it has its present form and location.
In Chapters 1 to 3 I developed the idea that all landscapes are the result of a variety of processes, operating, sometimes spasmodically, over long periods of time. I also concluded that two distinctive groups of processes can be involved:
1. **Surface modification,** largely caused by moving water (rivers, mudflows, waves, tides and sometimes ice). All of these water-based processes are strongly influenced by climatic variations in temperature, rainfall and storm intensity.
2. **2. Solid Earth movement,** resulting from processes originating and operating within the Earth, rather than on its surface. Although most solid Earth movement is difficult to detect, except where earthquakes or volcanoes are involved, it is likely that such movement plays a key role in landscape development. Without movement of this sort, surface modification would, over millions of years, turn hilly landscapes into flat plains.
In this final chapter we shall examine a time-sequence of three major episodes that have resulted in many of the distinctive landscape features of Southern England, both locally and regionally. We start with the Variscan mountain-building episode, an example of solid Earth movement, and end with river erosion and the Flandrian rise of sea level, a remarkable example of surface modification.
### EPISODE 1: THE VARISCAN MOUNTAIN BUILDING
The Variscan mountain building occurred over many millions of years, but was particularly active between 400 and 300 million years ago. It was the result of Earth movement between a tectonic plate that included the crust of northern Europe (from central Wales northward) and a southern plate, or plates. The movement and detailed shape of the plates is not clear, and there were probably a number of small plates involved in the generally convergent boundary. However, the convergence must have had a major component of north-south shortening, because there is much evidence of folding and fracturing of the bedrock that is consistent with this shortening direction.
Northern Europe, including most of Scandinavia, is made of large (100–1,000 km scale) areas of bedrock that were last intensively moved during mountain-building episodes older than the Variscan. In contrast, the bedrock of central Europe was intensively moved in Variscan times, and then developed a very different movement pattern involving local rising uplands and intervening subsiding basins. The Southwest Region of Southern England is typical of one of the uplands, and others are visible in northern France, Belgium and Germany. These uplands were separated from each other by areas that subsided, filling with sediments, and the Southeast England Basin is one of these.
**FIG 316.** Southern England and surroundings, showing fold trends in the Variscan mountain belt, and the position of its northern Front.
In Southern England, the Southwest Region bedrock was given a pronounced 'grain' by its Variscan folding and fracturing. Our Area-by-Area review has picked out many cases where variations in bedrock resistance to erosion have produced local landscape features with this orientation. There are also local changes in this orientation, suggesting that the convergent movement was not consistent, and that local resistant crustal blocks, or small plates, may have been present. We have noted the great importance of the major zone of late Variscan granites that dominate some Areas in the Southwest. The northern margin of the broad Variscan belt is recognisable in south Wales, southern Ireland and the Bristol area, where the west-to-east grain in the bedrock has strongly influenced the local landscapes (Fig. 316).
East of the Southwest Region, Southern England is covered by younger bedrock that formed in the Southeast England Basin, and the effects of this on the landscapes are discussed in the next section. Here it is important to note that the Variscan bedrock, with its west-to-east grain, is present at depth below this cover. The obvious sign of this is the presence of various often rather isolated fold and fracture belts, now visible at the surface of the cover. Spectacular examples of these are the Purbeck-Isle of Wight fold monocline, and the Hog's Back structure near Guildford, but there are many other localised structures with a similar trend. Although the structures have moved sediments of Late Cretaceous and younger ages, they appear to have been localised by older Variscan structures, deeper in the crust, that became active again when later crustal forces were sufficient.
In terms of the making of Southern England, it can be claimed that the convergent movements of the Variscan mountain building have given local and regional features of the Southwest and South Coast their orientation.
### EPISODE 2: THE SOUTHEAST ENGLAND BASIN
The Variscan mountain-building episode was followed by an episode, almost 300 million years long, in which the crust of southeast England subsided, and sediments accumulated in the resulting basin. For this overview, I pick out three levels in the Permian, Mesozoic and Tertiary sedimentary succession. Each of these levels (Fig. 317) contains particularly resistant bedrock, so has tended to produce hills of regional landscape importance. Each level has also acted as an indicator of the net extent of earth movement since it formed as a relatively flat layer.
**FIG 317.** Southern England and surroundings, showing the cover of sediment (Permian, Mesozoic and Tertiary in age) formed during Episode 2. On land, the outcrop locations of the three levels in this bedrock cover are mapped: (A) lower New Red Sandstone; (B) Middle Jurassic; (C) Late Cretaceous Chalk.
Although this selection of the three levels picks out erosion-resistant, hill-forming sediments in the succession, it is important to realise that the Southeast England basin-fill consists predominantly of mudstones that are easily eroded. This is one reason why the present-day landscapes are generally so low and gentle.
#### A: Lower New Red Sandstone level
We have already explored numerous local situations, particularly in Areas 2, 3, 8 and 9, where the contact between the Variscan-deformed Devonian and Carboniferous rocks and the overlying New Red Sandstone is very distinctive. This contact provides vivid evidence of the transition from erosional hills and valleys, at the margin of the Variscan uplands, to the basins of sediment deposition further east. Much local evidence shows that the post-Variscan landscapes contained features oriented by variations in resistance to erosion of the Variscan bedrock.
Close to places where this important surface can be examined today, the level low in the New Red Sandstone often contains gravels and sands that, on subsequent burial and cementing, have become strong enough to resist later erosion at the surface. There are, therefore, many hills today resulting from the presence of strong New Red Sandstone sediments. These hills mimic the New Red Sandstone alluvial fans that earlier extended into the basin.
Looking more widely around and across Southern England, the mapping of this level allows us to pick out some broader features of the landscape not seen before. Along the south coast of the Southwest this level has been traced below the sea, closely following the present coastline, and then, in East Devon and Somerset, the general trend of the surface turns abruptly northwards until it turns again to run westerly, forming the floor of the Bristol Channel Basin. Subsiding movements represented by this level show therefore that the Southwest Region was becoming a distinct upland in early New Red Sandstone times.
Further north, the position of the basal New Red Sandstone level shows that subsiding movements were already starting to define not only the Bristol Channel but also St George's Channel, the Worcester and Cheshire Basins and the uplifting Pennines ridge, with the South Staffordshire and Warwickshire upfolds at its southern end (Fig. 316). This pattern makes it clear that the east-west trends south of the Variscan Front are replaced by a very different movement pattern in the north.
Further east, in the East Anglian and Thames Valley Regions, the New Red Sandstone level is present below the surface, and helps to define the Midlands-London platform below the later Mesozoic and Tertiary cover. The fact that the platform surface is flat-lying, and generally at depths of only hundreds of metres, demonstrates the lack of major vertical movements in this eastern part of Southern England since Permian and Triassic times.
#### B: Middle Jurassic level
This is a very different sort of level, selected because it marks a widespread change to limestone-accumulating conditions (most famously producing sediments that became the Inferior Oolite) on the floor of the Middle Jurassic sea. This is important, in present-day landscape terms, because the limestones form one of the main escarpment features across the Southeast England Basin, particularly in the Severn Valley Region, where they form the Cotswolds, and in the west of the East Anglian Region.
The gentleness of the tilt of this level across Southern England, away from the localised belts of remobilisation of deep Variscan structures, is evidence of the gentleness of later deep Earth movements. The gentleness of the tilt also means that the scarp created by its surface modification, mainly by rivers, will have resulted in important migration of the scarp, down-slope, as the generalised topography was lowered.
#### C: Late Cretaceous Chalk level
This level marks the very widespread change in conditions that resulted in the deposition of the Late Cretaceous Chalk. The important role of the resistant Chalk bedrock in giving the landscapes of Southern England their high downlands and Chalk cliffs has been stressed in most of the chapters of this book.
The Chalk also serves as a remarkable marker for movement patterns since the Late Cretaceous, when it was formed. The mapped distribution of the outcrop of this level picks out major structures such as the London Basin downfold and the Weald uplift, as well as many more local features that have resulted from the remobilisation of deep Variscan structures. The very gentle eastward tilt of the Chalk also records downward movements that have occurred in the southern North Sea area, possibly linked to the uplift of western Britain at this time. This western uplift is believed to be due to volcanic activity and molten rock emplacement at depth related to the opening of the Atlantic Ocean.
### EPISODE 3: RIVER EROSION, FREEZING CLIMATES AND SEA-LEVEL MOVEMENTS
From mid-Tertiary times (around 20–30 million years ago), two elements of the shape of Southern England started to emerge as distinct land areas. The southern element, formed by the strong Variscan convergent plate movements, was covered by the Southeast England Basin. The northern element was covered by other basins, principally centred on the North Sea and Irish Sea areas and separated by an upward-moving region along the Pennine axis. This sets the scene for the surface modification by rivers, ice and sea-level change that has resulted in the final episode of the making of Southern England. Figure 318 shows a simplified version of the pattern of rivers that have been eroding Southern England since at least mid-Tertiary times. I have extended these below present sea level to indicate broadly where they must have run during the long periods when sea level was much lower than it is today. It is clear that the shape of the coastline, particularly the drowning of valleys, is a direct result of sea-level rise.
It is also clear that the orientation and location of the coastal zones and the submarine topography must reflect the erosional activity of these rivers. The way that the southern coast runs slightly oblique to the east-west Variscan trend must reflect this erosional history. The erosion of the Bristol Channel, Severn Estuary and Severn Valley appears to be related to the river erosion of the soft sediments of the Bristol Channel and Worcester Basin, and may have caused late-stage uplift of the Cotswolds. In the east, the coastline of the Thames Estuary and the other associated estuaries must reflect stages in this river's erosion, probably localised, to an extent, by the downward movement of the London downfold. Its form is very different from that of the Wash on the other side of East Anglia, which is likely to reflect a combination of the stability of the Midlands Platform and erosion by the Great Ouse and other Midlands rivers.
**FIG 318.** Southern England and surroundings, showing main river valleys and approximate continuations at times of low sea level.
### THE SHAPE, FORM AND LOCATION OF SOUTHERN ENGLAND
#### What has given Southern England its 100-km-scale inland landscape features?
The presence of the resistant and deformed Variscan bedrock in the Southwest Region has given it many distinctive landscape features, including the deformed killas slates, the major granite bodies and the Lizard Complex, that were all formed during Episode 1 (the Variscan mountain building). However, on the 100 km scale, the present-day shape and form of the western part of Southern England was defined during Episode 2, and it is marked particularly by the pattern of basins defined by the Lower New Red Sandstone level.
I have to admit to having no real explanation for this pattern, except that it must have formed as a movement response to the very varied patterns of materials in the Earth's crust at this point. The second, the Middle Jurassic level, has given rise to a relatively simple scarp pattern extending from the north to the south coast, and the third, Late Cretaceous Chalk level, has been eroded into the Chalk Downs, which have since been gently folded and locally faulted by Earth movements.
We began this book by wondering why it is that Southern England has such gentle and generally rather low-lying landscapes. The answer seems to be that relatively little Earth movement has taken place since the end of the Variscan plate convergence and the onset of the New Red Sandstone pattern of movements. There has been gentle uplift in the west, probably linked in part to the divergence of the American and European plates, and the growth of the Atlantic Ocean, but also probably linked to the growth and sinking of the North Sea basin. But another important factor has been that much of the sediment accumulating in the Southeast England Basin turned into soft mudstones that have been relatively efficiently eroded by river action, with the exception of the resistant levels of sandstone or limestone. These same mudstones have also been particularly prone to erosion by slope movement during the long cold episodes of the Ice Age, when much of Southern England, though not glaciated, became frozen ground.
#### What has given the coastline of Southern England its 100-km-scale location and shape?
We have seen how the coastline has retreated actively over the last 20,000 years as sea level has risen due to the melting of the ice of the last cold episode of the Ice Age. The shape of the present coastline depends primarily on the shape of the topography invaded by this rising sea, although in many places significant erosion by the arrival of storm waves has caused further retreat.
The pattern of river valleys (Fig. 318) has been responsible for the major features of the invaded topography. These valleys include the English Channel and the Irish Channel/Bristol Channel valleys that had earlier been eroded from the Atlantic Ocean side, and the southern North Sea (Dogger Hills) valleys eroded from the North Sea side. The shape of these valleys was already apparent in the pattern of downward Earth movements that started in Permian and Triassic times when the movement patterns of the convergent Variscan deformed belt, changed into the pattern of basins and uplands of New Red Sandstone times (Fig. 317).
The existence of the Variscan deformed belt near the surface in the Southwest Region, and its continuation under our South Coast Region, has provided a persistent west-to-east element of erosionally resistant bedrock that has given the coastline its greatest extent, north of which the British coastlines tend to converge to give Great Britain its triangular form (Fig. 316).
#### Why is Southern England where it is?
Southern England has been reduced in size and changed in local detail by surface modification. But its location depends on the solid Earth movements that have influenced this area of the Earth's lithosphere. The lithosphere plate movements that were responsible for the growth of a convergent boundary through this area in Variscan times produced the land of Southern England, attaching it also to crustal material further north with a very different history. Later movements, initiated in New Red Sandstone times, started to form other elements that are recognisable in the western and eastern margins of Southern England.
As we saw in Chapter 3, the Earth's surface is made up of lithosphere plates that have been continuously moving and changing their configuration for 2–4 billion years. By focusing on Southern England we have examined in detail the surface history of one small area of the Earth's crust. Although small relative to most plates, it has nonetheless seen an episode (1) of plate margin activity, followed by an episode (2) of basin movement unrelated to a plate margin, and then finally an episode (3) of surface modification, strongly influenced by climate change. During these episodes, Southern England moved from equatorial latitudes to its present northern position, as shown by measurements of rock magnetism.
Research on deep crustal and mantle structure is developing all the time, and is now starting to detect the presence of rock volumes possessing distinctive physical properties at these considerable depths. So the onion-skin model (as shown in Fig. 30) is likely to be a gross oversimplification. Some of the distinctive deep rock volumes appear to have a similar lateral extent to Southern England or the British Isles, and it is likely to be at these great depths within the Earth that the reason for the existence of such features of the Earth's natural landscape must be sought.
# Further Reading
The material that I have used in this book ranges very widely. It includes leaflets and local guides available at visitor centres, general accounts for a wide readership, systematic scientific reviews and technical original research papers. I have arranged suggestions for further reading in sections that follow the order of the chapters of this book, starting with the general introduction (Chapters 1–3), proceeding through the regional accounts (Chapters 4–8) and ending with the overview (Chapter 9).
Internet search engines will also provide valuable leads on almost all the topics raised in this book.
### SOURCES (REGIONAL GUIDES, LOCAL GUIDES, BOOKS AND MAPS)
British Geological Survey Sales Desk, Keyworth, Nottingham NG12 5GG (0115 936 3241), sales@bgs.ac.uk, shop.bgs.ac.uk.
BGS London Information Office, Natural History Museum, Earth Galleries, Exhibition Road, London SW7 2DE (020 7589 4090), bgslondon@bgs.ac.uk.
Geo Supplies Ltd, 49 Station Road, Chapeltown, Sheffield S35 2XE (0114 245 5746), www.geosupplies.co.uk.
### CHAPTERS 1–3, GENERAL INTRODUCTION
**Allen, P. A.** (1997) _Earth Surface Processes._ Blackwell, Oxford.
**French, H. M.** (2007) _The Periglacial Environment_ , 3rd edn. John Wiley and Sons.
**Gradstein, F. M., Ogg, J. G. and Smith, A. G.,** eds (2004) _A Geologic Timescale 2004._ Cambridge University Press, Cambridge. (Timescales generally on the International Commission on Stratigraphy website at www.stratigraphy.org.)
**Holmes, A. and Duff, D.** (1994) _Holmes' Principles of Physical Geology_ , 4th edn. Chapman and Hall, London.
**Leeder, M. R.** (1999) _Sedimentology and Sedimentary Basins: from Turbulence to Tectonics._ Blackwell, Oxford.
**Office for National Statistics.** _Population Statistics._ www.statistics.gov.uk.
**Press, F. and Siever, R.** (1986) _Earth_ , 4th edn: Freeman, New York.
**Rackham, O.** (1986) _The History of the Countryside._ London, Dent.
**Rackham, O.** (2006) _Woodlands._ New Naturalist 100. Collins, London.
**Skinner, B. J., Porter, S. C. and Park, J.** (2004) _Dynamic Earth: an Introduction to Physical Geology_ , 5th edn. Wiley, Cichester.
**Stringer, C.** (2006) _Homo Britannicus: the Incredible story of Human Life in Britain._ Allen Lane, London.
**Van Andel, T. H.** (1994) _New Views on an Old Planet: a History of Global Change_ , 2nd edn. Cambridge University Press, Cambridge.
#### General coverage of Southern England
**Ballantyne, C. K. and Harris,** C. (1994) _The Periglaciation of Great Britain._ Cambridge University Press, Cambridge.
**Brenchley, P. J. and Rawson, P. F.,** eds (2006) _The Geology of England and Wales_ , 2nd edn. Geological Society of London.
**Centre for Ecology and Hydrology:** the National River Flow Archive, including river flow data and maps of the UK Gauging Station Network, is at www.ceh.ac.uk/data/nrfa.
**Countryside Agency:** the Character Area reports produced by this agency provide valuable summaries of local geology, geomorphology and historical development. This function of the Agency has been the responsibility of Natural England since October 2006. Most of the reports are available as downloads from www.naturalengland.org.uk or enquiries@naturalengland.org.uk.
**Fortey, R.A.** (1993) _The Hidden Landscape: a Journey into the Geological Past._ Cape, London.
**Gibbard, P. L. and Lewin,** J. (2001) Climate and related controls on interglacial fluvial sedimentation in lowland Britain. _Sedimentary Geology_ 15: 187–210.
**Gibbard, P. L. and Lewin, J.** (2003) The history of the major rivers of southern Britain during the Tertiary. _Journal of the Geological Society of London_ 160: 829–45.
**Jones, D. C. K.** (1981) _The Geomorphology of the British Isles: Southeast and Southern England._ Methuen, London.
**Miller, T. G.** (1953) _Geology and Scenery in Britain._ Batsford, London.
**Rose, J.** (1994) Major river systems of central and southern Britain during the Early and Middle Pleistocene. _Terra Nova_ 6: 435–43.
**Stamp, L. D.** (1949) _Britain's Structure and Scenery_ , 3rd edn. New Naturalist 4. Collins, London.
**Straw, A. and Clayton, K.C.** (1979) _The Geomorphology of the British Isles: Eastern and Central England._ Methuen, London.
**Toghill, P.** (2000) _The Geology of Britain: an Introduction._ Swan Hill Press, Shrewsbury.
**West, R. G.** (1977) _Pleistocene Geology and Biology, with Especial Reference to the British Isles_ , 2nd edn. Longman, London.
**Winchester, S.** (2001) _The Map that Changed the World: the Tale of William Smith and the Birth of a Science._ Viking, London.
**Woodcock, N. H. and Strachan, R.,** eds (2000) _Geological History of Britain and Ireland._ Blackwell, Oxford.
#### Geological maps
British Geological Survey detailed maps are available for the whole of Southern England, which is covered by approximately 170 sheets (of which 33 are currently out of print). The currently available sheets are on the 1:50,000 scale.
**British Geological Survey** (2007) _Bedrock Geology of the UK: South Map._ 1:625,000 scale.
**British Geological Survey** (2007) _Bedrock Geology of the UK: South Booklet._
**British Geological Survey** (1977) _Quaternary Geology Map of the UK: South Sheet._ 1:625,000 scale.
**British Geological Survey** (1991) _Geology of the United Kingdom, Ireland and Continental Shelf: South Sheet._ 1:1,000,000 solid (bedrock) geology.
**British Geological Survey** (1996) _Tectonic Map of Britain, Ireland and Adjacent Areas._ 1:1,500,000 scale.
#### Detailed stratigraphic reviews across Southern England
The Geological Society of London has published Special Reports dealing with the correlation (time and layering relationships) as follows:
_Permian_ , No. 5.
_Triassic_ , No. 13.
_Jurassic_ , Nos 14 and 15.
_Cretaceous_ , No. 9.
_Tertiary_ , No. 12.
_Quaternary_ , revised edition, No. 23.
#### British Geological Survey Regional Guides
These guides systematically survey in detail the geological foundations of their regions. Seven of the series cover Southern England, and details of the relevant guide are given under each region, below.
### CHAPTER 4, THE SOUTHWEST REGION
**Durrance, E. M. and Laming, D. J. C.,** eds (1982) _The Geology of Devon._ University of Exeter Press, Exeter.
**Edmonds, E. A., McKeown, M. C. and Williams, M.** (1975) _British Regional Geology: South-West England_ , 4th edn. British Geological Survey, London.
**Keene, P.** (1996) _Classic Landforms of the North Devon Coast_ , 2nd edn. Geographical Association, Sheffield.
**Mottershead, D.** (1997) _Classic Landforms of the South Devon Coast_ , 2nd edn. Geographical Association, Sheffield.
**Parslow, R.** (2007) _The Isles of Scilly._ New Naturalist 103. Collins, London.
**Selwood, E. B., Durrance, E. M. and Bristow, C. M.,** eds (1998) _The Geology of Cornwall and the Isles of Scilly._ University of Exeter Press, Exeter.
### CHAPTER 5, THE SOUTH COAST REGION
**Brunsden, D.,** ed. (2003) _The Official Guide to the Jurassic Coast: Dorset and East Devon's World Heritage Coast._ Coastal Publishing, Wareham.
**Bird,** E. C. **F.** (1995) _Geology and Scenery of Dorset._ Ex Libris Press, Bradford on Avon.
**Ensom, P.** (1998) _Discover Dorset: Geology._ Dovecote Press, Wimborne.
**Gallois, R. W.** (1965) _British Regional Geology: the Wealden District_ , 4th edn. British Geological Survey, London.
**Gibbons, W.** (1981) _The Weald._ Unwin, London.
**Melville, R. V. and Freshney,** E. C. (1982) _British Regional Geology: the Hampshire Basin and Adjoining Areas_ , 4th edn. Institute of Geological Sciences [now British Geological Survey], London.
**Preece, R. C. and Bridgeland, D. R.** (1999) Holywell Coombe, Folkestone: a 13,000 year history of an English chalkland valley. _Quaternary Science Reviews_ 18:1075–125.
### CHAPTER 6, THE SEVERN VALLEY REGION
**Goudie, A. and Parker, A.** (1996) _The Geomorphology of the Cotswolds._ Cotteswold Naturalists' Field Club, Oxford.
**Green, G. W.** (1992) _British Regional Geology: Bristol and Gloucester Region_ , 3rd edn. British Geological Survey, London.
**Hains, B. A. and Horton, A.** (1969) _British Regional Geology: Central England_ , 3rd edn. British Geological Survey, London.
**Lane, N. F., Watts, A. B. and Farrant, A. R.** (2008) An analysis of Cotswold topography: insight into the landscape response to denudational isostasy. _Journal of the Geological Society of London_ **165:** 85–104.
**Smurthwaite, D.** (1993) _Complete Guide to the Battlefields of Britain, with Ordnance Survey Maps_ , new edn. Mermaid, London.
**Watts, A. B., McKerrow, W. S. and Richards, K.** (2005) Localized Quaternary uplift of south-central England. _Journal of the Geological Society of London_ , 162:13–24.
**Watts, A. B., McKerrow, W. S. and Fielding, E.** (2000) Lithospheric flexure, uplift, and landscape evolution in south-central England. _Journal of the Geological Society of London_ 157:1169–77.
**Williams, G. D. and Chapman, T. J.** (1986) The Bristol-Mendip foreland thrust belt. _Journal of the Geological Society of London_ **143:** 63–73.
### CHAPTER 7, LONDON AND THE THAMES VALLEY REGION
**Essex RIGS Group / Essex Wildlife Trust.** _The Geology of Essex._ www.essexwt.org.uk/Geology/geology.htm.
**Lucy, G.** (1999) _Essex Rock: a Look Beneath the Essex Landscape._ Essex Rock and Mineral Society.
**Powell, P.** (2005) _The Geology of Oxfordshire._ Dovecote Press, Wimborne.
**Selley, R. C.** (2004) _The Winelands of Britain: Past, Present and Prospective._ Petravin, Dorking.
**Sumbler, M. G.** (1996) _British Regional Geology: London and Thames Valley_ , 4th edn. British Geological Survey, London.
### CHAPTER 8, THE EAST ANGLIA REGION
**Brand, D., Booth, S. J. and Rose, J.** (2002) Late Devensian glaciation, ice-dammed lake and river diversion, Stiffkey, north Norfolk, England. _Proceedings of the Yorkshire Geological Society_ 54: 35–46.
**Chatwin, C. P.** (1961) _British Regional Geology: East Anglia and Adjoining Areas_ , 4th edn. British Geological Survey, London.
**Essex RIGS Group / Essex Wildlife Trust**. _The Geology of Essex._ www.essexwt.org.uk/Geology/geology.htm.
**Hains, B. A. and Horton, A.** (1969) _British Regional Geology: Central England_ , 3rd edn. British Geological Survey, London.
**Jermyn, S. T.** (1974) _Flora of Essex._ Essex Naturalists' Trust, Colchester.
**Lucy, G.** (1999) _Essex Rock: a Look Beneath the Essex Landscape._ Essex Rock and Mineral Society.
**Reed, F. R. C.** (1897) _A Handbook to the Geology of Cambridgeshire._ Cambridge University Press, Cambridge.
**Rose, J., Lee, J. R., Candy, I. and Lewis, S. G.** (1999) Early and Middle Pleistocene river systems in eastern England: evidence from Leet Hill, southern Norfolk. _Journal of Quaternary Science_ 14: 347–60.
### CHAPTER 9, THE MAKING OF SOUTHERN ENGLAND
**Shaw-Champion, M., White, N. J., Jones, S. and Priestley, K. F.** (2006) Crustal velocity structure of the British Isles: a comparison of receiver functions and wide-angle data. _Geophysical Journal International_ **166:** 795–813.
**Jackson, J., McKenzie, D., Priestley, K. and Emmerson, B.** (2008) New views on the structure and rheology of the lithosphere. _Journal of the Geological Society of London_ **165:** 453–66.
# Index
The pagination of this electronic edition does not match the edition from which it was created. To locate a specific passage, please use the search feature of your e-book reader.
ancient countryside 46–7, 49
Anglian cold phase 238–9
Anglian ice sheet 35, 36
_anticline_ 30
Ashdown Sand 183
_asthenosphere_ 50
Avon Gorge 207
Avon Valley 207–10
Baggy Point 112, 115
Bagshot Beds 265, 271, 284
Bagshot Formation 236
Bawdsey Manor 331
Beachy Head 173
'Bedford Bite' 308–11,
bedrock
Chalk 27–30
influence 24
_sedimentary_ origin 27
timescale 25, 26–30
'Beer Stone' 136
Beult, River 276
_bevelled_ cliffs 113
bibliography 401–6
Bishop's Stortford Clay hills 314–15
Black Ven landslip 136
Blackdown Hills 134–7
Blackmoor Vale 138–40
Blackwater Estuary 281–2
Blakeney Spit 372–3, 375
Bluff, the 110–11
Bodmin Moor 94
Boscastle flood 101
boulder clay 35, 37
Bournemouth 156
Bovey Basin 74, 105
Box Hill 259
Boxgrove 175–6
_braided_ rivers 31
_breccias_ 206
Brendon Hills 108, 121, 129–33
Brent Knoll 202
_brickearth_ 158, 175
Bridport Sand 123
Brighton 177
Bristol 198–212
Bristol Channel Basin 196, 198–202
Bristol Valley 207–10
Broadway 222
Budleigh Salterton Pebble Beds 133
Burghley House 343, 345
Burnham Flats 369–70
Burrington Coombe 206
Burwell 320
Bury St Edmunds 321–2
'Bytham River' 344
Cam, River 299–303
Cambridge 250–1, 303–5
Cambridge's Western Plateau 305–7
Canterbury 279–80
Carnmenellis granite 86, 85
Carrick Roads 88, 91
Carstone bedrock 292, 368
cave complexes 206
Cavendish 322
Chalk bedrock 27–30
Chalk Marl 186, 312
Chalk properties 172
Channel Tunnel 186–7
'character areas' 19–20
Cheddar Gorge 206
Chesil Beach 128, 143–4
Chilmark Stone 140
Chiltern Edge 261–2
Chiltern Hills 261–3
Chiltern plateau 262–3
china clay industry 72–3
Clare 322
clay-with-flints 161
Claygate Member 286
cliff profiles terminology 113
cliffs, highest 110
_clitter_ 97
Coal Measures 207, 209
coast parallel ridges 45
_coastal flooding zone_ 41–3
Colne, River 269
Constable, John 323–4
_contact metamorphism_ 73
_coprolites_ 307–8, 327
Cornwall, West 77–91
faults 86
granite areas 78–87
_killas_ 88–91
Lizard, The 87–8
Cornwall _see also_ East
Cornwall and South
Devon
Cotswold Hills of Middle
Jurassic limestone 242–3
Cotswold Water Park 245
Cotswolds 211–12
Cotswolds and the Middle
Severn 213–31
Carboniferous and
earlier bedrock 216–17
Early Cretaceous
bedrock 225
Jurassic bedrock 219–24
New Red Sandstone
bedrock 218–19
overview 213–16
younger drainage and
erosion patterns 225–31
Cotswolds to Reading area 241–57
overview 241–2
Crackington Haven 101
Cranborne Chase 140–1
Crediton Basin 104
Cromer Forest Bed 383–4
Crystal Palace 266
Cuckmere valley 174
Culm 101
'Culm fold belt' 67
_Culm synclinorium_ 107
Culver Cliff 155
Dartmoor 94
Deben, River 44, 331
_degraded cliff_ 191
Devensian ice sheet 77
Devils Dyke 320
Devon _see_ East Cornwall and South Devon
Devonian basin 63, 65
Devonian limestone 105
divergent plate boundary 55
Dorset Downs 140–1
Dorset Heaths 142, 156–7
Dorset _see_ East Devon, Somerset and Dorset
Downs of Late Cretaceous
Chalk 251–6
drowned valleys 43–4
dry valleys 127
Dundry Hill 209
Dungeness 128, 188–91
Dunkery Beacon 75, 109
Dunwich 334–7
Durdle Door 146
Early Tertiary
Petrockstowe Basin 118
Earth's crust movements 22
Earth's surface
anticline faults 57
continental crust 53
convergent plate
boundaries 54
_crust_ 53
detecting local surface
movements 61
folds 57, 58
horizontal movements 56–7
lower crust 57
normal faults 57, 58
oceanic crust 53–4
reverse faults 57, 58
strike-slip faults 57, 58
surface movements 56–60
syncline folds 57
upper crust 57
vertical changes by deposition 58–9
vertical changes by erosion 58–9
vertical crustal
movement resulting
from loading or unloading 59–60
vertical crustal movements 57–60
vertical movements by expansion or contraction 60
widespread movements 50–6
East Anglia Region 287–390
bedrock structure 287–94
flatness 294–5
introduction 287–95
surface blanket 294
East Cornwall and South
Devon 92–105
Carboniferous Culm of Devon 101–3
granite areas 94–8
_killas_ and other
Devonian bedrock 98–101
New Red Sandstone and younger bedrock 103–5
East Devon Redlands 129–33
East Devon, Somerset and Dorset 128–48
East Sussex and Southeast
Kent 179–92
landscape history 192
overview 179–82
Eden Project 72, 94
Edge Hill 220–21
enclosure of land 46
erosional process 22
ESRI ARC Geographic
Information System 21
Essex Claylands 323–5
Essex, South 284–6
Essex _see_ Suffolk and
North Essex
Exe, River 75
Exmoor 75–6, 107–15, 109–11
'Exmoor line' 110
Falmouth 88–9
fault types 57
feldspar 70, 72
Felixstowe 326–8
Felixstowe Ferry 331
Fen edge 315–16
Fen-edge Claylands 318–20
Fenland foothills 360–1
Fens, The 347–60
_Flandrian transgression_ 41
flat land 350
_flat-topped_ cliffs 113
flatness of East Anglia 294–5
Flegg 390
Flood Relief Channel 53–4
fold-belt 107
Folkestone Warren
landslip 186–7
Forest Marble 212
Forty Foot Drain 353
'fossil forest' 148
_foundered strata_ 212
freeze-thaw process 38
further reading 401–6
Fyfield Down 255
Gainsborough, Thomas 324
gault 161
_glacial_ periods 35
Glastonbury Tor 133–4
_glauconite_ 156
Godolphin granite 81, 84, 86
Golden Cap 135, 137
Golitha Falls 95
Goring Gap 247
Government Countryside
Agency 19–20
Grafham Water 305
Granta, River 311–12
gravel spits 128
Great Oolite 212
Great Oolite unit 343
Great Ouse, River 299–302, 353
Great Stour, River 274, 279, 281
Great Yarmouth 385–7
Greensand Ridge Walk 307
_grey-weathers_ 253–4
Grimes Graves 380
_growan_ 97
Gurnards' Head 83
Hadleigh Castle 286
_Haldon Gravels_ 73–4
Haldon Hills 73, 105
Hallsands 101
Ham Hill Stone 137
Hampshire and the Isle of Wight 149–65
landscape history 162–5
overview 149–52
Hampshire Basin 124, 140
Hampshire Downs 160–1, 255–6
Hampshire, South
Lowlands 157–60
Hampstead Heath 266–7
Happisburgh 383, 386
Harlton 305
Harlton Ridge 303
_Harwich Cement Stone_ 328
_Harwich Copperas Stones_ 328
Harwich Harbour 326
Hastings Beds 169–70, 183, 261
_head_ 97, 140, 279
headlands, projecting 210
_headward_ erosion 34
Heddon's Mouth 110
Hertfordshire Plateau 271
High Weald 167–71, 182–3
Highgate Cemetery 266
Highgate Ponds 267
Hog's Back 263–5
_Hog's-back_ cliffs 112–13
Holme Post 358–9 'hot spots' 60
Hove 177
Hunstanton 369–70
Hunstanton ice-laid till 367
Hurst Castle 159–60
Hurst Spit 128
Hythe 185
Hythe Beds 171–2, 184
Ice Age timescale 25, 34–9
Icknield Way 320, 381
Inferior Oolite 212
Inferior Oolite unit 343
_interglacial_ periods 35
_interstadials_ 41
Ipswich 329–30
Ipswichian interglacial 144
iron ore 305
Isle of Portland 142–4
Isle of Purbeck 152–4
Isle of Thanet 276–81
Isle of Wight 155–6
Isle of Wight Monocline 155
Isle of Wight stepfold 126
Isle of Wight _see also_
Hampshire and the Isle of Wight
Isles of Scilly 76, 78–80, 81
Itchen, River 160
Jurassic Coast 121–3, 128
kaolinite 72, 74
Kellaways Sand 248
Kennet Valley 256–7
Kent _see_ East Sussex and Southeast Kent
Kent's Cavern caves 105
_kerogen_ 148
kettle holes 270
_killas_ 67, 81, 88–91, 101
Kimmeridge Bay 147–8
Kimmeridge Clay 148, 153
King's Lynn 360–1
'knapped' flints 369
Lambourn Downs 251
Land's End 77, 80, 81–3
_landforms_ 16, 31
landforms of rivers 32
LANDMAP project 20 _Landranger_ OS maps 21
landscape
change 21–3
meaning 15–16
modification by people 16
modification by rivers 31–4
modifications 34–9
_rejuvenated_ 33
scale 16
size 16
word used to name
small areas 19
_landslip_ 31
Lark, River 320
last 30,000 years timescale 25, 40–1
Late Cretaceous Chalk 135
Late Cretaceous seas 124–5
Lea, River 269
lead 206
Leicester to the Fens area 338–61
Fenland foothills 360–1
Fens, The 347–60
Jurassic hills and valleys 342–7
overview 338–40
Triassic bedrock 340–1
Leith Hill 259
Len, River 274
lighting, artificial 16, 17
_lignite_ 156
lithosphere 50–2
Little Ouse rodden 355–6
Little Stour, River 281
Lizard area 67, 69
Lizard, The 87–8
Loddon, River 271
London 257–71
overview 257–8
London and the Thames
Valley Region 232–86
coastlines and sea-level
rise 239–40
Downs of Late
Cretaceous Chalk 251–6
Ice Age modifications 238–9
introduction 232–40
Kennet Valley 256–7
Mudstone Lowlands 243–52
London Basin 266
London Basin downfold 237–8
London-Brabant
Landmass 291
London Clay 236, 265
London hills 265–70
London Platform 235, 288–94
Long Melford 322
Low Weald 171, 184
Lower Greensand 24
Lowestoft 385–7
Lulworth Cove 145–6
Lulworth Crumple 148
Lundy Island 118–19
Lymington, River 165
Lynmouth 113
Lynton 113
Madingley Ridge 303
magma 70
Manger, The 252–3
Marlborough Downs 248, 251, 254
Marlstone Rock Bed 220–1, 298, 342–3
Marston Moretaine Basin 308–11
_meandering_ rivers 31
Medway Estuary 282–3
Medway Gap 279
Medway, River 279
Mendip caves complex 206
Mendip Hills 204–7
_meres_ 357
metal ores 70–1, 205–6
Mid-Somerset Hills 133–4, 202–4
Middle Jurassic Oolitic
limestones 221–4
Midvale Ridge 249
Millook Haven 101
mineralisation 70–1, 205–6
_monocline_ 126, 144, 155
Morte Point 112–13
mud-springs 248–9
Mudstone Lowlands 243–52
National River Flow
Archive 34
Nene, River 297–9
New Bedford Level 353
New Forest 157
Newmarket 320
Norfolk 362–90
Early Cretaceous
foothills 367
late Cretaceous Chalk
hills 367–83
Late Jurassic
mudstones 365
Late Tertiary Crag hills 383–90
Norfolk Broads, The 383–90
North Norfolk Coast 367–83
overview 362–5
Norfolk Broads, The 383–90, 387–90
normal fault 139
North Devon and West
Somerset 107–19
Culm (Carboniferous)
bedrock area 115–17
drainage 116
Exmoor's Devonian
bedrock 107–15
Lundy Island 118–19
New Red Sandstone and younger bedrock 118
North Downs 185–8, 263–5, 276–81
Northampton Sand 221
Northampton to Cambridge area 295–316
Bishop's Stortford Clay
hills 314–15
chalk hills and valleys 311–14
Clay-Greensand-Gault
belt 299–311
Fen edge 315–16
Jurassic limestone hills 297–9
overview 295–7
Northern Weald 273–6
Norwich 381–3
Oakham 346
oil 128, 148
Old Bedford River 353
Orford Beach 332–3
Orwell Bridge 325, 327, 329
Oxford 250–1
Oxfordshire Clay Vales 243–5
Pakefield 383
Palmerston's Follies 158
Parliament Hill 266–7
Parrett, River 203
patterned ground 378
peat diggings 388
Peat Fens 348, 351
Pennard Hills 133–4
people related
development 46–9
_permafrost_ 37
Petrockstowe Basin 74, 105, 118
Pevensey Levels 177
Pilgrim's Way 279
_pingo_ 178–9,378–9
Pingo Trail 378–9
planned countryside 46, 48–9
_plate boundaries_ 52
_plate tectonics_ 50
Plymouth Sound 98
Polden Hills 133
polygonal patterns 38, 39
Poole Harbour 156
Porlock Bay 111–12
Portland Formation 311
Portlandian 225
Portsdown Ridge 158
Poxwell Anticline 142
Purbeck Hills 141, 144
Purbeck Ridge 145
Purbeck stepfold 153
Quantock Fringes 198–202
Quantock Hills 121, 129–33, 198–202
quartz 70
Quaternary terrace
deposits 237
Radway Village 220
Raedwell, King 331
reversed fault 139
_Rhaetic_ 219–20
Rhee, River 303, 311–12
_rias 89_ , 98, 100
Richmond Hill 266
_Ridgeway, The_ 254
ripples 373–7
rising plumes 60
river channels 31
river terraces 33
river landforms 32
_rock basins_ 98
rodden 356
Romney Marsh 184, 188–91
runnels 45
Rutland Water 343–4
St Austell granite 81, 86–7
St Ives Bay 88
St Michael's Mount 85
Salisbury Plain 160–1, 255
Salthouse 375
Samphire Way Country
Park 186
_Sarsen Stones_ 157, 239, 253–4, 255
Scolt Head Island 81, 370–1
sea-level change 41–5
sedimentology 58–9
Selsey Bill 176
serpentinite bedrock 69
Seven Sisters 174
Severn Estuary
drainage 226–9
drainage towards the
Thames 231
drainage towards the
Wash 230–1
Severn, River _see also_
Cotswolds and the
Middle Severn
Severn Vale 210–11
Severn Valley Region 192–231
introduction 193–7
Shooter's Hill 266
Silt Fens 348. 350
Slapton Sands 101
'slatey cleavage' 67
_slump_ 31
Smith, William 212, 343
Soham Mere 315–16
Solent, River 164
Somerset Levels 133–4, 202–4
Somerset Moors 133–4, 202–4
Somerset _see_ East Devon,
Somerset and Dorset
Somerset _see_ North Devon
and West Somerset
South Coast Plain,
Western 157–60
South Coast Region 120–92
bedrock movement,
uplift and erosion by rivers 125–6
coastal shape and location 127–8
Ice Age modification 127
introduction 120–8
South Coastal Plain 175–7
South Downs 160–1, 172–5
South Purbeck 144–8
Southampton Water 159
Southeast England Basin 120–21, 124, 393–6
Late Cretaceous Chalk
level 396
Lower New Red
Sandstone level 395
Middle Jurassic level 396
Southern England
analysing 18–21
coastline location and shape 399
freezing climates 396–8
inland landscape
features 398–9
litho sphere plate
movements 399–400
mapping 18–21
river erosion 396–8
sea-level movements 396–8
shape, form and location 398–400
solid earth movement 391
Southeast England
Basin 393–6
surface modification
process 391
Variscan Mountain
Building 392–3
Southwest Region 62–119
bedrock foundations 62–73
crustal convergence 63–9
drainage patterns 75–6
granites and other
minerals 69–73
Ice Age episodes 76–7
introduction 62–77
_sedimentary_ markers 73–5
sedimentation 62–3
surface movements
before mountain
building 62–3
Southwold 334–7
Stabley Bank Basin 74
_stadials_ 41
Sticklepath Fault 105, 118
Sticklepath Fault Zone 74
Stockbridge Rock Member 160
Stonehenge 255
straight river 353
_subduction_ 54–5
Suffolk and North Essex 316–37
Chalk Hills 320–3
Essex Claylands 323–5
Fen-edge Claylands 318–20
overview 316–18
Suffolk Coast and Heaths 325–37
Suffolk Coast and Heaths 325–37
surface modification
process 22, 23
Sussex 166–79
landscape history 178–9
overview 166–7
_see also_ East Sussex and
Southeast Kent
Sutton Hoo 331
_syncline_ 30
'synclinorium' 67
Tamar, River 75
tectonic plate movements 22
Test, River 160
Thames Barrier 240
Thames Basin Heaths 258
Thames Basin Western Heaths 270–1
Thames Estuary 258, 272–95
overview 272–3
Thames Northern Basin 284–6
Thames tributary estuaries 281–4
Thames Valley 265–70
_see also_ London and the
Thames Valley Region Thames, River
changes 245–7
Thames, River, ancestral 238–9, 265, 268–9, 271, 285
_Through the Looking-Glass_ 245
_till_ 35, 37
timescales 25
tin 71–2
topographic platforms 98
tors 81, 95–7
transform plate boundary 55
Trent, River 339–41
Tunbridge Wells
Sandstone 183, 276
Uffington White Horse 252–3
upstream erosion 34
Vale of Aylesbury 258–9
Vale ofBelvoir 342, 345
Vale of Fernhurst 171–2
Vale of Pewsey 251
Vale of St Albans 268
Vale of Taunton 129–33
Vale ofWardour 138–40
Vale of White Horse 249
Valley of Romford 285–6
Valley of the Rocks 113–14
'Variscan Front' 195, 197
Variscan Mountain
Building 63–9, 392–3
Variscan Unconformity 193, 196, 199
Vermuyden, Cornelius 353
Wantsum Channel 279–81
_water gaps_ 175
Watercress Railway 161
Watership Down 256
wave-cut platform 87
Waveney, River 387
Weald Clay 261
Weald uplift 161, 237–8
Wealden Beds 171
Wealden Greensand 161–2, 171–2, 184
Wealden Margin 259–61
Wealden Series 169
Wells-next-the-Sea 371–3, 376
Wensum, River 381, 387
Wessex Basin 235
West Cornwall 77–91
faults 86
granite areas 78–87
_killas_ 88–91
Lizard, The 87–8
Western Unconformity 120–1, 134–5
Weymouth Lowlands 142–4
White Cliffs of Dover 277–8
Whitesands Bay 82
Whittlesey Mere 357
Wicken Fen 315–17, 352
Wiltshire Clay Vales 243–5, 248
Wiltshire Downs 140–1
Wimbledon Common 266
windmill 352
Windsor Castle 267–8
Woodhill Bay 193–4
Wookey Hole 206
Wootton Bassett 248–9
Wootton-under-Edge 211
Worcester 227
Yare, River 381, 387
Yeovil Formation 140
Yeovil Scarplands 137–8
zigzag folding 68, 117
zinc 206
# The New Naturalist Library
1. _Butterflies_ —E. B. Ford
2. _British Game_ —B. Vesey-Fitzgerald
3. _London's Natural History_ —R. S. R. Fitter
4. _Britain's Structure and Scenery_ —L. Dudley Stamp
5. _Wild Flowers_ —J. Gilmour & M. Walters
6. _The Highlands & Islands_—F. Fraser Darling & J. M. Boyd
7. _Mushrooms & Toadstools_—J. Ramsbottom
8. _Insect Natural History_ —A. D. Imms
9. _A Country Parish_ —A. W. Boyd
10. _British Plant Life_ —W. B. Turrill
11. _Mountains & Moorlands_—W. H. Pearsall
12. _The Sea Shore_ —C. M. Yonge
13. _Snowdonia_ —F. J. North, B. Campbell & R. Scott
14. _The Art of Botanical Illustration_ —W. Blunt
15. _Life in Lakes & Rivers_—T. T. Macan & E. B. Worthington
16. _Wild Flowers of Chalk & Limestone_—J. E. Lousley
17. _Birds & Men_—E. M. Nicholson
18. _A Natural History of Man in Britain_ —H. J. Fleure & M. Davies
19. _Wild Orchids of Britain_ —V. S. Summerhayes
20. _The British Amphibians & Reptiles_—M. Smith
21. _British Mammals_ —L. Harrison Matthews
22. _Climate and the British Scene_ —G. Manley
23. _An Angler's Entomology_ —J. R. Harris
24. _Flowers of the Coast_ —I. Hepburn
25. _The Sea Coast_ —J. A. Steers
26. _The Weald_ —S. W. Wooldridge & F. Goldring
27. _Dartmoor_ —L. A. Harvey & D. St. Leger Gordon
28. _Sea Birds_ —J. Fisher & R. M. Lockley
29. _The World of the Honeybee_ —C. G. Butler
30. _Moths_ —E. B. Ford
31. _Man and the Land_ —L. Dudley Stamp
32. _Trees, Woods and Man_ —H. L. Edlin
33. _Mountain Flowers_ —J. Raven & M. Walters
34. _The Open Sea: I. The World of Plankton_ —A. Hardy
35. _The World of the Soil_ —E. J. Russell
36. _Insect Migration_ —C. B. Williams
37. _The Open Sea: II. Fish & Fisheries_—A. Hardy
38. _The World of Spiders_ —W. S. Bristowe
39. _The Folklore of Birds_ —E. A. Armstrong
40. _Bumblebees_ —J. B. Free & C. G. Butler
41. _Dragonflies_ —P. S. Corbet, C. Longfield & N. W. Moore
42. _Fossils_ —H. H. Swinnerton
43. _Weeds & Aliens_—E. Salisbury
44. _The Peak District_ —K. C. Edwards
45. _The Common Lands of England & Wales_—L. Dudley Stamp & W. G. Hoskins
46. _The Broads_ —E. A. Ellis
47. _The Snowdonia National Park_ —W. M. Condry
48. _Grass and Grasslands_ —I. Moore
49. _Nature Conservation in Britain_ —L. Dudley Stamp
50. _Pesticides and Pollution_ —K. Mellanby
51. _Man & Birds_—R. K. Murton
52. _Woodland Birds_ —E. Simms
53. _The Lake District_ —W. H. Pearsall & W. Pennington
54. _The Pollination of Flowers_ —M. Proctor & P. Yeo
55. _Finches_ —I. Newton
56. _Pedigree: Words from Nature_ —S. Potter & L. Sargent
57. _British Seals_ —H. R. Hewer
58. _Hedges_ —E. Pollard, M. D. Hooper & N. W. Moore
59. _Ants_ —M. V. Brian
60. _British Birds of Prey_ —L. Brown
61. _Inheritance and Natural History_ —R. J. Berry
62. _British Tits_ —C. Perrins
63. _British Thrushes_ —E. Simms
64. _The Natural History of Shetland_ —R. J. Berry & J. L. Johnston
65. _Waders_ —W. G. Hale
66. _The Natural History of Wales_ —W. M. Condry
67. _Farming and Wildlife_ —K. Mellanby
68. _Mammals in the British Isles_ —L. Harrison Matthews
69. _Reptiles and Amphibians in Britain_ —D. Frazer
70. _The Natural History of Orkney_ —R. J. Berry
71. _British Warblers_ —E. Simms
72. _Heathlands_ —N. R. Webb
73. _The New Forest_ —C. R. Tubbs
74. _Ferns_ —C. N. Page
75. _Freshwater Fish_ —P. S. Maitland & R. N. Campbell
76. _The Hebrides_ —J. M. Boyd & I. L. Boyd
77. _The Soil_ —B. Davis, N. Walker, D. Ball & A. Fitter
78. _British Larks, Pipits & Wagtails_—E. Simms
79. _Caves & Cave Life_—P. Chapman
80. _Wild & Garden Plants_—M. Walters
81. _Ladybirds_ —M. E. N. Majerus
82. _The New Naturalists_ —P. Marren
83. _The Natural History of Pollination_ —M. Proctor, P. Yeo & A. Lack
84. _Ireland: A Natural History_ —D. Cabot
85. _Plant Disease_ —D. Ingram & N. Robertson
86. _Lichens_ —Oliver Gilbert
87. _Amphibians and Reptiles_ —T. Beebee & R. Griffiths
88. _Loch Lomondside_ —J. Mitchell
89. _The Broads_ —B. Moss
90. _Moths_ —M. Majerus
91. _Nature Conservation_ —P. Marren
92. _Lakeland_ —D. Ratcliffe
93. _British Bats_ —John Altringham
94. _Seashore_ —Peter Hayward
95. _Northumberland_ —Angus Lunn
96. _Fungi_ —Brian Spooner & Peter Roberts
97. _Mosses & Liverworts_—Nick Hodgetts & Ron Porley
98. _Bumblebees_ —Ted Benton
99. _Gower_ —Jonathan Mullard
100. _Woodlands_ —Oliver Rackham
101. _Galloway and the Borders_ —Derek Ratcliffe
102. _Garden Natural History_ —Stefan Buczacki
103. _The Isles of Scilly_ —Rosemary Parslow
104. _A History of Ornithology_ —Peter Bircham
105. _Wye Valley_ —George Peterken
106. _Dragonflies_ —Philip Corbet & Stephen Brooks
107. _Grouse_ —Adam Watson & Robert Moss
# About the Author
**Peter Friend** retired in 2001 after a career spent teaching and researching in the Department of Earth Sciences at the University of Cambridge. His boyhood was spent in Scotland, where he became fascinated by the variety and beauty of the natural landscapes. From his base in Cambridge, he carried out research programmes in Spitsbergen, Greenland, Spain, Pakistan and India, and became increasingly aware of the importance of rivers in shaping landscapes. He is currently Chairman of the Friends of the Sedgwick Museum of Earth Sciences and Emeritus Fellow of Darwin College, Cambridge
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# Copyright
This edition published in 2008 by Collins,
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First published 2008
© Peter Friend, 2008
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EPub Edition © JULY 2010 ISBN: 978-0-007-40592-3
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{"url":"https:\/\/www.physicsforums.com\/threads\/probability-of-observing-e-for-particle-in-a-box.803116\/","text":"# Homework Help: Probability of observing E for particle in a box\n\n1. Mar 14, 2015\n\n### Maylis\n\n1. The problem statement, all variables and given\/known data\n\n2. Relevant equations\n\n3. The attempt at a solution\nSince this is discrete, I know the probability is equal to $|a_{n}|^{2}$, hence the probability of observing $E_{1}$, $P(E_{1}) = \\frac {9}{25}$, and $P(E_{2}) = \\frac {16}{25}$. However, I just sort of remembered this fact, I am not sure how to prove that the probability is equal to the square of the absolute value of the coefficient.\n\nFor the second part, they pose a very good question, what in the heck is $f$? I don't see any $f$ anywhere.\n\nFor the third question, shouldn't it just be $|q_{7}|^{2}$?\n\n2. Mar 14, 2015\n\n### Staff: Mentor\n\nThere nothing to prove. This is simply the Born rule.\n\nI see two possibilities: a typo, and its supposed to be $|\\psi\\rangle$. Or its any state $|f\\rangle$, and you have to prove a general statement.\n\nWhat is $q_7$ in the problem?\n\n3. Mar 14, 2015\n\n### Maylis\n\nI'll just assume its for any state $|f \\rangle$,\n\nThen $$\\langle f|f \\rangle = \\int_{-\\infty}^{\\infty} f^{*}f \\hspace{0.02 in} dx$$\n\nAnd for question 3, I suppose $q_{7}$ is the operator $\\hat {Q}$\n\n4. Mar 14, 2015\n\n### Staff: Mentor\n\nI guess that the question is asking you to push this further, considering that you have a particle in a box.\n\nThat's not correct. You have\n$$\\hat{Q} | g_7 \\rangle = q_7 | g_7 \\rangle$$\nCan you identify all the elements in that equation?\n\n5. Mar 14, 2015\n\n### vela\n\nStaff Emeritus\nDid you post the actual, complete problem statement as given to you? I'm thinking not because of the word eigenstuff. If you are, you should ask your instructor for clarification on what's being asked.\n\nThe general idea is that if a system is in state $\\lvert \\psi \\rangle$ and you want to calculate the probability you'll find it in the state $\\lvert \\phi \\rangle$, you calculate the overlap of the two states, $\\langle \\phi \\vert \\psi \\rangle$, which is called the probability amplitude. The probability is then given by the square of the modulus of the probability amplitude. Knowing this, you should be able to answer part (c).\n\nBy the way, $q_7$ is a number. It's definitely not the operator $\\hat{Q}$. What is its relation to $\\hat{Q}$? That's what DrClaude wants you to understand.\n\n6. Mar 15, 2015\n\n### Maylis\n\nThis is the question statement, I just copied it off a youtube video.\n\nAssuming $|g_{7} \\rangle$ is nonzero, they should cancel on both sides, hence $q_{7} = \\hat {Q}$. I know $q_{7}$ is an eigenvalue and $\\hat {Q}$ is the operator, but I don't know what to make of it.\n\nFor question 2, I will revert to @DrClaude other idea, to replace $f$ with $\\psi$\n\nThen\n$$\\langle \\psi | \\psi \\rangle = \\int_{-\\infty}^{\\infty} (\\frac {3}{5} | \\psi_{1} \\rangle + \\frac {4i}{5} | \\psi_{2} \\rangle)(\\frac {3}{5} | \\psi_{1} \\rangle + \\frac {-4i}{5} | \\psi_{2} \\rangle) dx$$\n\n$$= \\int_{-\\infty}^{\\infty} \\frac {9}{25} + \\frac {16}{25} dx$$\n$$= \\int_{-\\infty}^{\\infty} 1 dx$$\n$$= ???$$\nApparently this does not make sense.\n\nLast edited: Mar 15, 2015\n7. Mar 15, 2015\n\n### Staff: Mentor\n\nYou can't do that. Since one is an operator and the other a scalar, they can't be equal. If you want to calculate things in QM, you need to understand how eigenequations work. With the equation $\\hat{Q} | g_7 \\rangle = q_7 | g_7 \\rangle$, you are being told that there is an operator $\\hat{Q}$, of which one eigenvector is $| g_7 \\rangle$, with eigenvalue $q_7$.\n\nThe question is not very well posed. Let me rephrase it: you have a system in state $|\\psi\\rangle$. You measure Q, which corresponds to the observable (operator) $\\hat{Q}$. Write an expression for the probability of measuring $Q = q_7$.\n\nYou are mixing two notations. If you have functions $\\phi(x)$ and $\\psi(x)$, then you can calculate the scalar product as\n$$\\int_{-\\infty}^\\infty \\phi(x)^* \\psi(x) dx$$\nIn the Dirac notation, that scalar product is simply written $\\langle \\phi | \\psi \\rangle$. The product of a bra and a ket is already an integration, and you can't have a ket as a function of position. Bras and kets are abstract representation of states.\n\n8. Mar 15, 2015\n\n### Maylis\n\nHow can a ket not be a function of position? Certainly $\\psi = f(x)$, hence what Vela said the \"probability amplitude\" $\\langle \\phi | \\psi \\rangle$ would have a ket as a function of position. If what I wrote is not right, I have no clue what I am supposed to do to evaluate.\n\nLast edited: Mar 15, 2015\n9. Mar 15, 2015\n\n### Staff: Mentor\n\nBecause it is an abstract state vector, that lives in a Hilbert space. To get a function of position, you need to calculate\n$$\\psi(x) = \\langle x | \\psi \\rangle$$\n\nIf you know the position representation of the bras and kets, you can use that to calculate inner products, e.g., for the 1D harmonic oscillator eigenfunctions $\\phi_i$\n$$\\langle \\phi_i | \\phi_j \\rangle = \\int_{-\\infty}^\\infty \\phi_i^*(x) \\phi_j(x) dx$$\nBut you don't need to know that function representation, because since the eigenfunctions are othonormal, you get directly\n$$\\langle \\phi_i | \\phi_j \\rangle =\\delta_{ij}$$\nIn other words, you can (and should here) manipulate the kets as abstract state vectors.\n\n10. Mar 15, 2015\n\n### Maylis\n\nSo then the inner product $\\langle \\psi | \\psi \\rangle$ actually means $\\psi(\\psi)$? Since you can't have a function with an argument of a function, so that makes no sense.\n\n11. Mar 15, 2015\n\n### Staff: Mentor\n\nThe notation does not mean $\\langle a | b \\rangle = b(a)$. I was referring to position eigenstates\n$$\\hat{x} | x \\rangle = x | x \\rangle$$\nwhich have the property\n$$\\langle x | x' \\rangle = \\delta(x - x')$$\nYou need to understand Dirac notation better to progress with these exercises. The document http:\/\/www.hep.manchester.ac.uk\/u\/stevew\/teaching\/dirac.pdf might be a good start.\n\n12. Mar 15, 2015\n\n### Maylis\n\nNo wonder I have no idea what you are talking about, I'm still on section 3.5 of Griffiths, and \"Dirac notation\" does not appear until 3.6. However, I still don't see the consistency in what you are saying.\n\nIf the inner producted is defined for $f(x)$ and $g(x)$\n$$\\langle f|g \\rangle = \\int_{-\\infty}^{\\infty} f^{*}(x)g(x) \\hspace {0.03 in} dx$$\n\nThen what is wrong with\n$$\\langle \\psi |\\psi \\rangle = \\int_{-\\infty}^{\\infty} \\psi^{*}(x) \\psi(x) \\hspace {0.03 in} dx$$\n\nA side note, it seems like the author is using Dirac notation before formally introducing it as the section in chapter 3...\n\nLast edited: Mar 15, 2015\n13. Mar 15, 2015\n\n### vela\n\nStaff Emeritus\nNothing, but that's not what you wrote before.\n\nIt may help to connect the new notation to what you've learned before. Suppose you have a vector $\\vec{a}$. In the new notation, you'd write $\\lvert a \\rangle$. To keep things simple and familiar, let's say it lives in three-dimensional space. Now you decide how you're going to orient the x, y, and z axes. In linear algebra speak, you're choosing a basis. Once you've done this, it makes sense to talk about the x-component of $\\vec{a}$ and so on, and you can now write\n$$\\vec{a} = a_1 \\hat{e}_1 + a_2 \\hat{e}_2 + a_3 \\hat{e}_3 = \\sum_{i=1}^3 a_i \\hat{e}_i$$ where the $\\hat{e}_i$'s correspond to the unit vectors (basis vectors) pointing along the various axes. In the new notation, you'd write\n$$\\lvert a \\rangle = a_1 \\lvert 1 \\rangle + a_2 \\lvert 2 \\rangle + a_3 \\lvert 3 \\rangle = \\sum_{i=1}^3 a_i \\lvert i \\rangle.$$ To find $a_i$, you'd calculate $a_i = \\hat{e}_i \\cdot \\vec{a}$. In Dirac notation, you have $a_i = \\langle i \\vert a \\rangle$. So finally we can write\n\\begin{align*}\n\\vec{a} &= \\sum_{i=1}^3 \\hat{e}_i (\\hat{e}_i \\cdot \\vec{a}) \\\\\n\\lvert a \\rangle &= \\sum_{i=1}^3 \\lvert i \\rangle\\langle i \\vert a\\rangle\n\\end{align*}\n\nNow let's go back to quantum mechanics\u2026 You have the state vector $\\lvert \\psi \\rangle$. The set of vectors {$\\lvert x \\rangle$} form a basis; they correspond to {$\\lvert i \\rangle$} in the previous example where $x$ acts as a label as $i$ did earlier. $x$ is continuous, so we replace the summation by an integral\n$$\\lvert \\psi \\rangle = \\int \\lvert x \\rangle \\langle x \\vert \\psi \\rangle\\,dx.$$ Just as each $a_i = \\langle i \\vert a \\rangle$ is a number, $\\langle x \\vert \\psi \\rangle$ is a number. It's equal to the wave function $\\psi$ evaluated at $x$. That is, $\\psi(x) = \\langle x \\vert \\psi \\rangle$. You need to distinguish between the state vector $\\lvert \\psi \\rangle$, the wave function $\\psi$, and $\\psi(x)$, the value of the wave function maps $x$ to.\n\nNow consider the dot product of two vectors $\\vec{a}$ and $\\vec{b}$. Once we choose a basis, we can write\n\\begin{align*}\n\\vec{a}\\cdot\\vec{b} &= \\sum_{i=1}^3 a_i b_i = \\sum_{i=1}^3 (\\vec{a}\\cdot\\hat{e}_i)(\\hat{e}_i \\cdot \\vec{b}) \\\\\n\\langle a \\vert b \\rangle &= \\sum_{i=1}^3 a_i b_i = \\sum_{i=1}^3 \\langle a \\vert i \\rangle \\langle i \\vert b \\rangle\n\\end{align*} In the continuous (and complex-valued) case, we have\n$$\\langle f \\vert g \\rangle = \\int f^*(x)g(x)\\,dx = \\int \\langle f \\vert x \\rangle \\langle x \\vert g \\rangle.$$ In what you wrote back in post 6, you didn't put $\\psi(x)$ in the integral; you used $\\lvert \\psi \\rangle$. That's why you got a non-sensical expression. It was analogous to saying\n$$\\vec{a}\\cdot\\vec{a} = \\sum_{i=1}^3 \\vec{a}\\cdot\\vec{a} = \\sum_{i=1}^3 (a_1^2+a_2^2+a_3^2) = 3(a_1^2+a_2^2+a_3^2).$$ In the very first step, instead of correctly using $a_i$ and regular scalar multiplication, I inserted $\\vec{a}$ and used vector multiplication, which leads to an erroneous result.","date":"2018-07-22 07:14:51","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9614102244377136, \"perplexity\": 359.76672442010727}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-30\/segments\/1531676593051.79\/warc\/CC-MAIN-20180722061341-20180722081341-00598.warc.gz\"}"} | null | null |
//!file
//! \brief floating-point comparison from Boost.Test
// Copyright Paul A. Bristow 2015.
// Copyright John Maddock 2015.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt
// or copy at http://www.boost.org/LICENSE_1_0.txt)
// Note that this file contains Quickbook mark-up as well as code
// and comments, don't change any of the special comment mark-ups!
#include <boost/math/special_functions/relative_difference.hpp>
#include <boost/math/special_functions/next.hpp>
#include <iostream>
#include <limits> // for std::numeric_limits<T>::epsilon().
int main()
{
std::cout << "Compare floats using Boost.Math functions/classes" << std::endl;
//[compare_floats_using
/*`Some using statements will ensure that the functions we need are accessible.
*/
using namespace boost::math;
//`or
using boost::math::relative_difference;
using boost::math::epsilon_difference;
using boost::math::float_next;
using boost::math::float_prior;
//] [/compare_floats_using]
//[compare_floats_example_1
/*`The following examples display values with all possibly significant digits.
Newer compilers should provide `std::numeric_limitsFPT>::max_digits10`
for this purpose, and here we use `float` precision where `max_digits10` = 9
to avoid displaying a distracting number of decimal digits.
[note Older compilers can use this formula to calculate `max_digits10`
from `std::numeric_limits<FPT>::digits10`:[br]
__spaces `int max_digits10 = 2 + std::numeric_limits<FPT>::digits10 * 3010/10000;`
] [/note]
One can set the display including all trailing zeros
(helpful for this example to show all potentially significant digits),
and also to display `bool` values as words rather than integers:
*/
std::cout.precision(std::numeric_limits<float>::max_digits10);
std::cout << std::boolalpha << std::showpoint << std::endl;
//] [/compare_floats_example_1]
//[compare_floats_example_2]
/*`
When comparing values that are ['quite close] or ['approximately equal],
we could use either `float_distance` or `relative_difference`/`epsilon_difference`, for example
with type `float`, these two values are adjacent to each other:
*/
float a = 1;
float b = 1 + std::numeric_limits<float>::epsilon();
std::cout << "a = " << a << std::endl;
std::cout << "b = " << b << std::endl;
std::cout << "float_distance = " << float_distance(a, b) << std::endl;
std::cout << "relative_difference = " << relative_difference(a, b) << std::endl;
std::cout << "epsilon_difference = " << epsilon_difference(a, b) << std::endl;
/*`
Which produces the output:
[pre
a = 1.00000000
b = 1.00000012
float_distance = 1.00000000
relative_difference = 1.19209290e-007
epsilon_difference = 1.00000000
]
*/
//] [/compare_floats_example_2]
//[compare_floats_example_3]
/*`
In the example above, it just so happens that the edit distance as measured by `float_distance`, and the
difference measured in units of epsilon were equal. However, due to the way floating point
values are represented, that is not always the case:*/
a = 2.0f / 3.0f; // 2/3 inexactly represented as a float
b = float_next(float_next(float_next(a))); // 3 floating point values above a
std::cout << "a = " << a << std::endl;
std::cout << "b = " << b << std::endl;
std::cout << "float_distance = " << float_distance(a, b) << std::endl;
std::cout << "relative_difference = " << relative_difference(a, b) << std::endl;
std::cout << "epsilon_difference = " << epsilon_difference(a, b) << std::endl;
/*`
Which produces the output:
[pre
a = 0.666666687
b = 0.666666865
float_distance = 3.00000000
relative_difference = 2.68220901e-007
epsilon_difference = 2.25000000
]
There is another important difference between `float_distance` and the
`relative_difference/epsilon_difference` functions in that `float_distance`
returns a signed result that reflects which argument is larger in magnitude,
where as `relative_difference/epsilon_difference` simply return an unsigned
value that represents how far apart the values are. For example if we swap
the order of the arguments:
*/
std::cout << "float_distance = " << float_distance(b, a) << std::endl;
std::cout << "relative_difference = " << relative_difference(b, a) << std::endl;
std::cout << "epsilon_difference = " << epsilon_difference(b, a) << std::endl;
/*`
The output is now:
[pre
float_distance = -3.00000000
relative_difference = 2.68220901e-007
epsilon_difference = 2.25000000
]
*/
//] [/compare_floats_example_3]
//[compare_floats_example_4]
/*`
Zeros are always treated as equal, as are infinities as long as they have the same sign:*/
a = 0;
b = -0; // signed zero
std::cout << "relative_difference = " << relative_difference(a, b) << std::endl;
a = b = std::numeric_limits<float>::infinity();
std::cout << "relative_difference = " << relative_difference(a, b) << std::endl;
std::cout << "relative_difference = " << relative_difference(a, -b) << std::endl;
/*`
Which produces the output:
[pre
relative_difference = 0.000000000
relative_difference = 0.000000000
relative_difference = 3.40282347e+038
]
*/
//] [/compare_floats_example_4]
//[compare_floats_example_5]
/*`
Note that finite values are always infinitely far away from infinities even if those finite values are very large:*/
a = (std::numeric_limits<float>::max)();
b = std::numeric_limits<float>::infinity();
std::cout << "a = " << a << std::endl;
std::cout << "b = " << b << std::endl;
std::cout << "relative_difference = " << relative_difference(a, b) << std::endl;
std::cout << "epsilon_difference = " << epsilon_difference(a, b) << std::endl;
/*`
Which produces the output:
[pre
a = 3.40282347e+038
b = 1.#INF0000
relative_difference = 3.40282347e+038
epsilon_difference = 3.40282347e+038
]
*/
//] [/compare_floats_example_5]
//[compare_floats_example_6]
/*`
Finally, all denormalized values and zeros are treated as being effectively equal:*/
a = std::numeric_limits<float>::denorm_min();
b = a * 2;
std::cout << "a = " << a << std::endl;
std::cout << "b = " << b << std::endl;
std::cout << "float_distance = " << float_distance(a, b) << std::endl;
std::cout << "relative_difference = " << relative_difference(a, b) << std::endl;
std::cout << "epsilon_difference = " << epsilon_difference(a, b) << std::endl;
a = 0;
std::cout << "a = " << a << std::endl;
std::cout << "b = " << b << std::endl;
std::cout << "float_distance = " << float_distance(a, b) << std::endl;
std::cout << "relative_difference = " << relative_difference(a, b) << std::endl;
std::cout << "epsilon_difference = " << epsilon_difference(a, b) << std::endl;
/*`
Which produces the output:
[pre
a = 1.40129846e-045
b = 2.80259693e-045
float_distance = 1.00000000
relative_difference = 0.000000000
epsilon_difference = 0.000000000
a = 0.000000000
b = 2.80259693e-045
float_distance = 2.00000000
relative_difference = 0.000000000
epsilon_difference = 0.000000000]
Notice how, in the above example, two denormalized values that are a factor of 2 apart are
none the less only one representation apart!
*/
//] [/compare_floats_example_6]
#if 0
//[old_compare_floats_example_3
//`The simplest use is to compare two values with a tolerance thus:
bool is_close = is_close_to(1.F, 1.F + epsilon, epsilon); // One epsilon apart is close enough.
std::cout << "is_close_to(1.F, 1.F + epsilon, epsilon); is " << is_close << std::endl; // true
is_close = is_close_to(1.F, 1.F + 2 * epsilon, epsilon); // Two epsilon apart isn't close enough.
std::cout << "is_close_to(1.F, 1.F + epsilon, epsilon); is " << is_close << std::endl; // false
/*`
[note The type FPT of the tolerance and the type of the values [*must match].
So `is_close(0.1F, 1., 1.)` will fail to compile because "template parameter 'FPT' is ambiguous".
Always provide the same type, using `static_cast<FPT>` if necessary.]
*/
/*`An instance of class `close_at_tolerance` is more convenient
when multiple tests with the same conditions are planned.
A class that stores a tolerance of three epsilon (and the default ['strong] test) is:
*/
close_at_tolerance<float> three_rounds(3 * epsilon); // 'strong' by default.
//`and we can confirm these settings:
std::cout << "fraction_tolerance = "
<< three_rounds.fraction_tolerance()
<< std::endl; // +3.57627869e-007
std::cout << "strength = "
<< (three_rounds.strength() == FPC_STRONG ? "strong" : "weak")
<< std::endl; // strong
//`To start, let us use two values that are truly equal (having identical bit patterns)
float a = 1.23456789F;
float b = 1.23456789F;
//`and make a comparison using our 3*epsilon `three_rounds` functor:
bool close = three_rounds(a, b);
std::cout << "three_rounds(a, b) = " << close << std::endl; // true
//`Unsurprisingly, the result is true, and the failed fraction is zero.
std::cout << "failed_fraction = " << three_rounds.failed_fraction() << std::endl;
/*`To get some nearby values, it is convenient to use the Boost.Math __next_float functions,
for which we need an include
#include <boost/math/special_functions/next.hpp>
and some using declarations:
*/
using boost::math::float_next;
using boost::math::float_prior;
using boost::math::nextafter;
using boost::math::float_distance;
//`To add a few __ulp to one value:
b = float_next(a); // Add just one ULP to a.
b = float_next(b); // Add another one ULP.
b = float_next(b); // Add another one ULP.
// 3 epsilon would pass.
b = float_next(b); // Add another one ULP.
//`and repeat our comparison:
close = three_rounds(a, b);
std::cout << "three_rounds(a, b) = " << close << std::endl; // false
std::cout << "failed_fraction = " << three_rounds.failed_fraction()
<< std::endl; // abs(u-v) / abs(v) = 3.86237957e-007
//`We can also 'measure' the number of bits different using the `float_distance` function:
std::cout << "float_distance = " << float_distance(a, b) << std::endl; // 4
/*`Now consider two values that are much further apart
than one might expect from ['computational noise],
perhaps the result of two measurements of some physical property like length
where an uncertainty of a percent or so might be expected.
*/
float fp1 = 0.01000F;
float fp2 = 0.01001F; // Slightly different.
float tolerance = 0.0001F;
close_at_tolerance<float> strong(epsilon); // Default is strong.
bool rs = strong(fp1, fp2);
std::cout << "strong(fp1, fp2) is " << rs << std::endl;
//`Or we could contrast using the ['weak] criterion:
close_at_tolerance<float> weak(epsilon, FPC_WEAK); // Explicitly weak.
bool rw = weak(fp1, fp2); //
std::cout << "weak(fp1, fp2) is " << rw << std::endl;
//`We can also construct, setting tolerance and strength, and compare in one statement:
std::cout << a << " #= " << b << " is "
<< close_at_tolerance<float>(epsilon, FPC_STRONG)(a, b) << std::endl;
std::cout << a << " ~= " << b << " is "
<< close_at_tolerance<float>(epsilon, FPC_WEAK)(a, b) << std::endl;
//`but this has little advantage over using function `is_close_to` directly.
//] [/old_compare_floats_example_3]
/*When the floating-point values become very small and near zero, using
//a relative test becomes unhelpful because one is dividing by zero or tiny,
//Instead, an absolute test is needed, comparing one (or usually both) values with zero,
//using a tolerance.
//This is provided by the `small_with_tolerance` class and `is_small` function.
namespace boost {
namespace math {
namespace fpc {
template<typename FPT>
class small_with_tolerance
{
public:
// Public typedefs.
typedef bool result_type;
// Constructor.
explicit small_with_tolerance(FPT tolerance); // tolerance >= 0
// Functor
bool operator()(FPT value) const; // return true if <= absolute tolerance (near zero).
};
template<typename FPT>
bool
is_small(FPT value, FPT tolerance); // return true if value <= absolute tolerance (near zero).
}}} // namespaces.
/*`
[note The type FPT of the tolerance and the type of the value [*must match].
So `is_small(0.1F, 0.000001)` will fail to compile because "template parameter 'FPT' is ambiguous".
Always provide the same type, using `static_cast<FPT>` if necessary.]
A few values near zero are tested with varying tolerance below.
*/
//[compare_floats_small_1
float c = 0;
std::cout << "0 is_small " << is_small(c, epsilon) << std::endl; // true
c = std::numeric_limits<float>::denorm_min(); // 1.40129846e-045
std::cout << "denorm_ min =" << c << ", is_small is " << is_small(c, epsilon) << std::endl; // true
c = (std::numeric_limits<float>::min)(); // 1.17549435e-038
std::cout << "min = " << c << ", is_small is " << is_small(c, epsilon) << std::endl; // true
c = 1 * epsilon; // 1.19209290e-007
std::cout << "epsilon = " << c << ", is_small is " << is_small(c, epsilon) << std::endl; // false
c = 1 * epsilon; // 1.19209290e-007
std::cout << "2 epsilon = " << c << ", is_small is " << is_small(c, 2 * epsilon) << std::endl; // true
c = 2 * epsilon; //2.38418579e-007
std::cout << "4 epsilon = " << c << ", is_small is " << is_small(c, 2 * epsilon) << std::endl; // false
c = 0.00001F;
std::cout << "0.00001 = " << c << ", is_small is " << is_small(c, 0.0001F) << std::endl; // true
c = -0.00001F;
std::cout << "0.00001 = " << c << ", is_small is " << is_small(c, 0.0001F) << std::endl; // true
/*`Using the class `small_with_tolerance` allows storage of the tolerance,
convenient if you make repeated tests with the same tolerance.
*/
small_with_tolerance<float>my_test(0.01F);
std::cout << "my_test(0.001F) is " << my_test(0.001F) << std::endl; // true
std::cout << "my_test(0.001F) is " << my_test(0.01F) << std::endl; // false
//] [/compare_floats_small_1]
#endif
return 0;
} // int main()
/*
Example output is:
//[compare_floats_output
Compare floats using Boost.Test functions/classes
float epsilon = 1.19209290e-007
is_close_to(1.F, 1.F + epsilon, epsilon); is true
is_close_to(1.F, 1.F + epsilon, epsilon); is false
fraction_tolerance = 3.57627869e-007
strength = strong
three_rounds(a, b) = true
failed_fraction = 0.000000000
three_rounds(a, b) = false
failed_fraction = 3.86237957e-007
float_distance = 4.00000000
strong(fp1, fp2) is false
weak(fp1, fp2) is false
1.23456788 #= 1.23456836 is false
1.23456788 ~= 1.23456836 is false
0 is_small true
denorm_ min =1.40129846e-045, is_small is true
min = 1.17549435e-038, is_small is true
epsilon = 1.19209290e-007, is_small is false
2 epsilon = 1.19209290e-007, is_small is true
4 epsilon = 2.38418579e-007, is_small is false
0.00001 = 9.99999975e-006, is_small is true
0.00001 = -9.99999975e-006, is_small is true
my_test(0.001F) is true
my_test(0.001F) is false//] [/compare_floats_output]
*/
| {
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} | 3,485 |
Entrepreneur Guest
Want better ROI? Come to Chicago
Mark Tebbe, ChicagoNEXT September 10, 2017 10:25 AM
Image Credit: f11photo / Shutterstock
[Updated 9/26 to correct the spelling of Eric Lefkofsky's name and to correct the number of companies Lightbank has founded (14, not seven).]
Unlike many cities across the country, Chicago has no intention of trying to become the next Silicon Valley. The Windy City is happy doing what it does best: nurturing startups to leverage abundant opportunities amidst the nation's most diverse economy.
Yet, in one key measure important to venture capitalists, Chicago already surpasses Silicon Valley: return on investment (ROI). Nearly half of Chicago tech investments (45 percent) have provided a 10-times return on investment compared to 25 percent ROI in Silicon Valley, according to a recent analysis of figures from Pitchbook and government reports by Hyde Park Angels.
Chicago is already a tech powerhouse, and its maturing ecosystem of investors, mentors, and successes continues to blossom. If 2017 remains at its current pace, this will mark the fifth straight year of record-setting tech investments. Chicago's tech scene isn't a typical overnight success story; rather, it is the result of long-term sustainability, committed re-investment, and truly diverse startup opportunities across a breadth of industries.
Consider these recent Chicago successes:
Cleversafe, a data-storage firm, was purchased in 2015 for $1.3 billion by IBM and is now the backbone of IBM Cloud Object Storage. Chris Gladwin, Cleversafe's founder, has now launched his fourth Chicago software startup, Ocient.
Fieldglass, a cloud-based vendor-management system, was acquired by SAP in 2014 for more than $1 billion.
GrubHub, the fast-growing food delivery service that handled nearly $3 billion in food orders last year, recently paid $287.5 million to buy Eat24 from Yelp.
Outcome Health, a digital media firm focused on serving healthcare facilities, is now valued at $5 billion, thanks in part to a $500 million investment by Goldman Sachs Investment Partners earlier this year.
Similarly, Goldman Sachs invested $150 million in 2016 in SMS Assist, a maintenance scheduling business, leading a valuation north of $1 billion.
Uptake is a predictive analytics firm that monitors industrial assets in more than 94 countries and is valued at $2 billion. Uptake is one of 14 companies founded by Chicago-based Lightbank's Brad Keywell and Eric Lefkofsky, with five of them going public, including Groupon.
Explaining why Goldman Sachs has invested heavily in Chicago startups, partner Topher Dawe told Crain's Chicago Business, "While these businesses aren't necessarily the household names as some of our other companies, like Spotify or Uber, these are incredible businesses tackling large addressable markets. We're actively looking for more Chicago deals."
Chicago tech is particularly strong in B2B sectors, including healthcare, fintech, food, software, and service industries. That breadth of opportunity is directly tied to the strength and resiliency of Chicago's overall economy, where no single industry employs more than 14 percent of the total workforce. Also, the notion that Chicago is simply a fly-over city is false: Chicago is the heartbeat of the country's transportation industry. Fifty percent of U.S. rail freight passes through the city, while our two airports – O'Hare and Midway – are among the nation's busiest.
So why doesn't Chicago garner more national credibility as a dynamic startup hub?
For one, Chicago's startups aren't that sexy. They focus on logistics, data storage, back-office efficiencies, and in the case of SMS Assist, maintenance. Unless you have skin in the game – and by that, I mean investment dollars – these businesses aren't ones that grab consumer attention.
Second, investors here are more conservative than their coastal counterparts. We like to see some success before we invest: customers, a product, and a positive cash flow. That's the opposite of Silicon Valley, where investors tend to bet on promising ideas more than established returns.
Third, startups are just one part of a sprawling economy. Tech gets more or less the same amount of press as any other industry here. As far as Chicagoans are concerned, that's fine. This diverse economy is reflected even within the tech ecosystem, where there are more than 15 Innovation Hubs each specializing in a different sector of technology, from food innovation and manufacturing to healthcare.
The Chicago tech economy continues to expand. Chicago's 2016 direct technology GRP was $23.76 billion; and while that only comprised 3.9 percent of the area's overall GRP, it represents an almost 40 percent increase since 2011.
Another huge advantage for Chicago is a ready talent pool. Apart from Boston, Chicago has more four-year universities than any other U.S. city. Chicago is also a magnet for graduates of other top Midwestern universities, such as Indiana, Michigan, Michigan State, Purdue, Northwestern, Wisconsin, and Illinois. We have more graduates from those universities than any other city in the world. And the lower cost-of-living, compared to similar U.S. cities and particularly Silicon Valley, keeps those graduates here.
Recognizing this wealth of talent, well-known tech companies from the coasts, such as Uber, Google, and PayPal, have extended their operations to include Chicago. The result is over 143,000 people working for Chicago tech companies in 2016, 32.8 percent more than 2011.
Mark Tebbe is Chairman of ChicagoNEXT, the technology arm of World Business Chicago and organizer of this month's Chicago Venture Summit. He has more than 30 years of entrepreneurial and startup experience, included the founding of two NASDAQ-listed publicly-traded corporations. | {
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{"url":"https:\/\/byjus.com\/question-answer\/a-certain-gas-takes-three-times-as-long-to-effuse-out-as-helium-its-molecular-1\/","text":"Question\n\n# A certain gas takes three times as long to effuse out as helium. Its molecular mass will be:\n\nA\n36u\nB\n64u\nC\n9u\nD\n27u\n\nSolution\n\n## The correct option is B $$36u$$A certain gas takes three times as long to effuse out as helium. The rate of effusion is inversely proportional to the molecular mass.$$\\cfrac { { r }_{ 1 } }{ { r }_{ 2 } } =\\sqrt { \\cfrac { { M }_{ { w }_{ 2 } } }{ { M }_{ { w }_{ 1 } } } }$$The rate of effusion is the ratio of the volume effused to the time taken$$\\cfrac { { V }_{ 1 } }{ { t }_{ 1 } } \\times \\cfrac { { t }_{ 2 } }{ { V }_{ 2 } } =\\sqrt { \\cfrac { { M }_{ { w }_{ 2 } } }{ { M }_{ { w }_{ 1 } } } }$$Volume is same, so\u00a0 $$\\cfrac { 3 }{ 1 } =\\sqrt { \\cfrac { { M }_{ { w }_{ 2 } } }{ 4 } }$$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 $$9=\\cfrac { { M }_{ { w }_{ 2 } } }{ 4 }$$$$\\therefore { M }_{ { w }_{ 2 } }=36$$The molecular mass of the gas is $$36 u$$. So, the correct option is $$A$$Chemistry\n\nSuggest Corrections\n\n0\n\nSimilar questions\nView More\n\nPeople also searched for\nView More","date":"2022-01-18 02:13:15","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8480678200721741, \"perplexity\": 2372.1476303929594}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-05\/segments\/1642320300658.84\/warc\/CC-MAIN-20220118002226-20220118032226-00533.warc.gz\"}"} | null | null |
\section{Introduction}
In recent years, the scientific interest in the study of noninertial effects
on physical systems has been renewed and many systems have been studied \cite%
{Castro1,Castro2,inercial9,inercial10,inercial7}. For instance, in \cite%
{Castro1} it was shown that the noninertial effect breaks the symmetrical of
the energy spectrum about $E=0$. In this way, it was shown that the energy
spectrum associated with scalar bosons in a rotating reference frame is
different from the one obtained in a usual inertial reference frame, in
other words, the energy levels are shifted by the effects of the rotating
frame.
Another kind of noninertial system that may be investigated with this
purpose are the uniformly accelerated observers in Minkowski spacetime, the
so-called Rindler spacetime. In order to investigate the energy states of
any quantized field in a accelerated reference frame it was suggested that a
uniformly accelerated detector in vacuum measures blackbody radiation, i.e,
an observer who undergoes a acceleration apparently sees a fixed surface
radiate \cite{uru1,uru2,uru3}.
Parallel to this, gravitational effects on quantum mechanical systems have
been studied intensively over the last few years \cite%
{parker1,parker2,parker3,parker4,parker5,hcurvo1,Barros1,chandrasekharansatz,cohen,neutrino1,santos1}%
. A fundamental question in physics is how quantum systems are affected by
the structure of the spacetime, and if exists some significant effect. In
order to study these gravitational effects, systematic studies \ are being
carried out \cite{santos1,santos2}. For example, in \cite{santos1} where the
effects of very intense magnetic fields in the energy levels, as intense as
the ones expected to be produced in ultra-relativistic heavy-ion collisions,
are investigated, in \cite{santos2} where bosons inside cosmic strings are
considered.
In this paper, a single particle solution of the Dirac equation in an
accelerated reference frame is discussed. The motivation for this work
besides the ones pointed out above is the understanding of the physical
consequences of the Dirac equation in noninertial systems of reference that
undergo translational acceleration.
The paper is organized as follows: section 2 contains a brief review about
the wave equation for spin 1/2 particles in curved spacetimes where the
basic formulation and the equations that will be needed in the next sections
will be shown. In section 3, we will present an equation for spin 1/2
fermions in the Rindler spacetime, i.e., the Dirac equation in an
accelerated reference frame. In section 4, we will see that the energy
spectrum associated with the Dirac equation in Rindler space is discrete and
depends on $a$, the acceleration of the reference frame. Finally, section 5
presents our conclusions. In this work, we use natural units, $\hbar =c=1.$
\section{Fermions in curved spacetimes}
A essential characteristic of the Dirac operator in flat spacetimes is its
invariance under Lorentz transformations, so when these particles are
studied in curved spacetimes, it is necessary to preserve this aspect
(locally). It can be written by using the tetrads $e_{\text{ \ \ \ }\mu
}^{\left( a\right) }$ that may be defined in order to satisfy the expression
\begin{equation}
g_{\eta \lambda }=e_{\text{ \ \ \ }\eta }^{\left( a\right) }e_{\text{ \ \ \ }%
\lambda }^{\left( b\right) }\eta _{\left( a\right) \left( b\right) },
\label{eq1}
\end{equation}
\noindent here $\eta _{\left( a\right) \left( b\right) }$ is the Minkowski
tensor, and $g_{\eta \lambda }$ the general metric tensor. We use $\left(
a\right) ,\left( b\right) ,\left( c\right) ,...$ to denote the local Lorentz
spacetime and $\alpha ,\beta ,\gamma ,...$ to denote the general spacetime
coordinate \cite{tetrada1,tetrada2,tetrada3}. From eq. $\left( \ref{eq1}%
\right) $, we can see that the tetrads may be used in order to project
vectors from the curved spacetime in the flat spacetime with the equation $%
A_{\mu }=e_{\text{ \ \ \ }\mu }^{\left( a\right) }A_{\left( a\right) }$
\noindent that relates the form of a vector in different spacetimes.
Now we study the behavior of the elements of the Dirac equation under
transformations that preserve the Lorentz symmetry. We note that a spinor
transforms according to $\psi \rightarrow \rho \left( \Lambda \right) \psi $%
, with $\rho \left( \Lambda \right) =1+\frac{1}{2}i\varepsilon ^{\left(
a\right) \left( b\right) }\Sigma _{\left( a\right) \left( b\right) }$, and $%
\Sigma _{\left( a\right) \left( b\right) }$ is the spinoral representation
of the generators of the Lorentz transformation, written in terms of the $%
\gamma ^{\left( c\right) }$ matrices, $\Sigma _{\left( a\right) \left(
b\right) }\equiv \frac{1}{4}i\left[ \gamma _{\left( a\right) },\gamma
_{\left( b\right) }\right] $ \cite{nakahara}. The first task is to construct
a covariant derivative $\nabla _{\left( a\right) }\psi $ that is locally
Lorentz invariant, for this purpose we impose the transformation condition
\begin{equation}
\nabla _{\left( a\right) }\psi \rightarrow \rho \Lambda _{\left( a\right) }^{%
\text{ \ \ }\left( b\right) }\nabla _{\left( b\right) }\psi . \label{eq3}
\end{equation}
\noindent The common way to obtain the explicit form of the covariant
derivative operator is by supposing the combination of terms
\begin{equation}
\nabla _{\left( a\right) }\psi =e_{\left( a\right) }^{\text{ \ \ \ }\mu
}\left( \partial _{\mu }+\Omega _{\mu }\right) \psi ,\text{ } \label{eq4}
\end{equation}
\noindent we note that the operator $\Omega _{\mu }$ transforms according
\begin{equation}
\Omega _{\mu }\rightarrow \rho \Omega _{\mu }\rho ^{-1}+\partial _{\mu }\rho
\rho ^{-1}. \label{eq5}
\end{equation}
The next step is to find the explicit form of the operator $\Omega _{\mu }$.
\noindent If we consider the combination of terms
\begin{equation}
\Omega _{\mu }\equiv \frac{1}{2}i\Gamma _{\text{ }(a)\mu (b)}\Sigma
^{(a)(b)}=\frac{1}{2}ie_{\text{ \ }\nu }^{\left( a\right) }\nabla _{\mu }e_{%
\text{ \ }}^{\left( b\right) \nu }\Sigma _{\left( a\right) \left( b\right) },
\label{eq6}
\end{equation}
\noindent\ the eq. $\left( \ref{eq5}\right) $ and $\left( \ref{eq3}\right) $
are satisfied, where the term $\Gamma _{\text{ }(a)\mu (b)}$ is given by
\begin{equation}
\Gamma _{\text{ }(a)\mu (b)}=e_{(a)\nu }\left( \partial _{\mu }e_{(b)}^{%
\text{ \ \ }\nu }+\Gamma _{\text{ \ }\mu \lambda }^{\nu }e_{(b)}^{\text{ \ \
}\lambda }\right) ,
\end{equation}
\noindent where $\Gamma _{\text{ \ }\mu \lambda }^{\nu }$ are the
Christoffel symbols. As a result, we obtain the final form of the covariant
derivative operator
\begin{equation}
\nabla _{\left( c\right) }\psi =e_{\left( c\right) }^{\text{ \ \ \ }\mu
}\left( \partial _{\mu }+\frac{1}{2}ie_{\text{ \ \ \ }\nu }^{\left( a\right)
}\nabla _{\mu }e_{\text{ \ }}^{\left( b\right) \nu }\Sigma _{\left( a\right)
\left( b\right) }\right) \psi . \label{eq7}
\end{equation}
\noindent By replacing the conventional derivative operator of the Dirac
equation in a flat spacetime by the one obtained in $\left( \ref{eq7}\right)
$ we obtain the final form of the wave equation for fermions particles in a
curved spacetime
\begin{equation}
ie_{\left( a\right) }^{\text{ \ \ \ }\mu }\gamma ^{\left( a\right) }\left(
\partial _{\mu }+\Omega _{\mu }\right) \psi -m\psi =0. \label{eq8}
\end{equation}%
It is common to define the term $\gamma ^{\mu }=e_{\left( a\right) }^{\text{
\ \ \ }\mu }\gamma ^{\left( a\right) }$ as a Dirac matrix in a given curved
spacetime and it is easy to see that it satisfies the Clifford algebra
\begin{equation}
\gamma ^{\mu }\gamma ^{\nu }+\gamma ^{\nu }\gamma ^{\mu }=g^{\mu \nu }%
\mathbf{1}. \label{eq10}
\end{equation}
\noindent If the spinor $\psi $ is coupled to the gauge field $A_{\mu }$, we
may introduce this effect by a minimal coupling
\begin{equation}
ie_{\left( a\right) }^{\text{ \ \ \ }\mu }\gamma ^{\left( a\right) }\left(
\partial _{\mu }+\Omega _{\mu }+ieA_{\mu }\right) \psi -m\psi =0.
\label{eq8b}
\end{equation}
\section*{Wave equation in the Rindler spacetime}
The Rindler metric represents an accelerated reference frame in the
Minkowski spacetime where the line element may be written in the form%
\begin{equation}
ds^{2}=\left( 1+a\xi \right) ^{2}d\tau ^{2}-d\xi ^{2}, \label{eq11}
\end{equation}%
where $\xi $ and $\tau $ are the proper coordinates of the accelerated
frame, and $a$ is the acceleration \cite{qft}. The coordinate of distance $%
\xi $ is constrained by $\xi >-\frac{1}{a}$ while the proper time $\tau $
varies in the interval $-\infty <\tau <\infty $. We shall now\ rewrite the
metric $\left( \ref{eq11}\right) $ in a conformally flat form. The usual way
to obtain the conformal form of eq. $\left( \ref{eq11}\right) $ is by making
the transformation%
\begin{align}
\bar{\tau}& =\tau , \notag \\
x& =\frac{1}{a}\ln \left( 1+a\xi \right) . \label{eq12}
\end{align}%
In this way, we obtain the line element%
\begin{equation}
ds^{2}=e^{2ax}\left( d\bar{\tau}^{2}-dx^{2}\right) . \label{eq13}
\end{equation}%
Now the conformal coordinates $x$, $\bar{\tau}$ vary in the interval $%
-\infty <\bar{\tau}<\infty ,$ and $-\infty <x<\infty $, that means an
extension of the spacetime metric. From \ eq. $\left( \ref{eq13}\right) $ we
can see that the metric is conformally flat because the conformal factor $%
e^{2ax}$ is multiplied by the Minkowski line element. In addition, the
spacetime metric $\left( \ref{eq13}\right) $ represents a flat spacetime
since it is related to the Minkowski line element by a coordinate
transformation.
Thus, the next step is to choose the tetrad basis for the line element $%
\left( \ref{eq13}\right) $. The diagonal form of $\left( \ref{eq13}\right) $
suggests the following tetrad basis
\begin{align}
e_{\nu }^{\text{ \ }\left( a\right) }& =\left(
\begin{array}{c}
e^{\frac{\sigma \left( x\right) }{2}} \\
0%
\end{array}%
\begin{array}{c}
0 \\
e^{\frac{\sigma \left( x\right) }{2}}%
\end{array}%
\right) , \label{eq15} \\
e_{\text{ \ }\left( a\right) }^{\nu }& =\left(
\begin{array}{c}
e^{-\frac{\sigma \left( x\right) }{2}} \\
0%
\end{array}%
\begin{array}{c}
0 \\
e^{-\frac{\sigma \left( x\right) }{2}}%
\end{array}%
\right) , \label{eq16}
\end{align}%
where $\sigma \left( x\right) \equiv 2ax$. It is easy to verify that it
satisfies the equation%
\begin{equation*}
g_{\mu \nu }=e_{\text{ \ \ \ }\mu }^{\left( a\right) }e_{\text{ \ \ \ }\nu
}^{\left( b\right) }\eta _{\left( a\right) \left( b\right) }.
\end{equation*}%
Observing that the only non-zero term $\Omega _{0}$ in the wave equation,
relative to the tetrad (\ref{eq15}) is given by%
\begin{equation}
\Omega _{0}=\frac{i\gamma ^{0}\cdot \gamma ^{1}}{4}\frac{d\sigma }{dx},
\label{eq17}
\end{equation}%
equation (\ref{eq8}) becomes%
\begin{equation}
\left[ i\gamma ^{\left( 0\right) }\frac{\partial }{\partial \bar{\tau}}%
+i\gamma ^{\left( 1\right) }\frac{\partial }{\partial x}+\frac{i\gamma
^{\left( 1\right) }}{4}\frac{d\sigma \left( x\right) }{dx}-me^{\frac{1}{2}%
\sigma \left( x\right) }\right] \psi \left( \bar{\tau},x\right) =0,
\label{eq18}
\end{equation}%
where the usual representation for the gamma matrices in $1+1$ dimensions is
considered%
\begin{equation}
\gamma ^{\left( 0\right) }=\left(
\begin{array}{c}
0 \\
1%
\end{array}%
\begin{array}{c}
1 \\
0%
\end{array}%
\right) ,\text{ }\gamma ^{\left( 1\right) }=\left(
\begin{array}{c}
i \\
0%
\end{array}%
\begin{array}{c}
0 \\
-i%
\end{array}%
\right) . \label{eq19}
\end{equation}%
In eq.$\left( \ref{eq18}\right) ,$ we will suppose a solution of the form%
\begin{equation}
\psi \left( t,x\right) =e^{-i\varepsilon \bar{\tau}}\left[
\begin{array}{c}
\bar{g}\left( x\right) \\
\bar{f}\left( x\right)
\end{array}%
\right] , \label{eq22}
\end{equation}%
where $\varepsilon $ is the energy of particle. So, equation (\ref{eq18})
may be written in an explicit form%
\begin{align}
\left[ \frac{d}{dx}+\frac{1}{4}\frac{d\sigma \left( x\right) }{dx}+me^{\frac{%
1}{2}\sigma \left( x\right) }\right] \bar{g}\left( x\right) & =\varepsilon
\bar{f}\left( x\right) , \label{eq23} \\
\left[ -\frac{d}{dx}-\frac{1}{4}\frac{d\sigma \left( x\right) }{dx}+me^{%
\frac{1}{2}\sigma \left( x\right) }\right] \bar{f}\left( x\right) &
=\varepsilon \bar{g}\left( x\right) . \label{eq24}
\end{align}%
Making a unitary transformation \cite{diraco14} in the system of equations%
\begin{equation}
U\left( x\right) =\left[
\begin{array}{c}
e^{\frac{1}{4}\sigma \left( x\right) } \\
0%
\end{array}%
\begin{array}{c}
0 \\
e^{\frac{1}{4}\sigma \left( x\right) }%
\end{array}%
\right] , \label{eq25}
\end{equation}%
we obtain a simplified form%
\begin{align}
\left[ \frac{d}{dx}+z\left( x\right) \right] g\left( x\right) & =\varepsilon
f\left( x\right) , \label{eq26} \\
\left[ -\frac{d}{dx}+z\left( x\right) \right] f\left( x\right) &
=\varepsilon g\left( x\right) , \label{eq27}
\end{align}%
where $z\left( x\right) =me^{\frac{1}{2}\sigma \left( x\right) }$ and%
\begin{equation}
\bar{\psi}=U\psi =U\left[
\begin{array}{c}
\bar{g}\left( x\right) \\
\bar{f}\left( x\right)
\end{array}%
\right] =\left[
\begin{array}{c}
g\left( x\right) \\
f\left( x\right)
\end{array}%
\right] . \label{eq28}
\end{equation}%
In order to investigate the solutions of the system of equations, we will
consider that the set of equations $\left( \ref{eq26}\right) $ and $\left( %
\ref{eq27}\right) $ may be decoupled. The function $f$ \ can be isolated in
eq. $\left( \ref{eq26}\right) $ and then, using $\left( \ref{eq26}\right) $
to eliminate the terms containing the $g$. The result is%
\begin{equation}
\frac{d^{2}f}{dx^{2}}-\frac{dz}{dx}f-z^{2}f+\varepsilon ^{2}f=0,
\label{eq29}
\end{equation}%
in a similar way, we derive the equation for $g$%
\begin{equation}
\frac{d^{2}g}{dx^{2}}+\frac{dz}{dx}g-z^{2}g+\varepsilon ^{2}g=0,
\label{eq30}
\end{equation}%
that may be resumed in the form%
\begin{equation}
\frac{d^{2}F}{dx^{2}}-s\frac{dz}{dx}F-z^{2}F+\varepsilon ^{2}F=0,
\label{eq31}
\end{equation}%
where $F=f$ when $s=1$ and $F=g$ when $s=-1$. For the case of the Rindler
metric, we have $\sigma =2ax$ so that%
\begin{equation}
g_{\mu \eta }=\exp \left( 2ax\right) \left(
\begin{array}{cc}
1 & 0 \\
0 & -1%
\end{array}%
\right) . \label{eq32}
\end{equation}%
If we consider small values of the acceleration $a$, we may solve eq. $%
\left( \ref{eq31}\right) $ neglecting terms in higher orders, and then $%
z\left( x\right) $ can be expanded as%
\begin{equation}
z\left( x\right) =m\left( 1+\frac{ax}{2}+...\right) . \label{eq33}
\end{equation}%
So, substituting this equation into Eq. (\ref{eq31}) we obtain the following
expression%
\begin{equation}
\frac{d^{2}F}{dx^{2}}-s\frac{ma}{2}F-\frac{a^{2}m^{2}}{4}\left( \frac{2}{a}%
+x\right) ^{2}F+\varepsilon ^{2}F=0. \label{eq34}
\end{equation}%
In order to investigate the solutions of the Eq. (\ref{eq34}), we will
consider the transformation
\begin{equation}
y=\sqrt{\frac{am}{2}}\left( x+\frac{2}{a}\right) , \label{eq35}
\end{equation}%
and as a result, the equation will take the form%
\begin{equation}
\frac{d^{2}F}{dy^{2}}+\left( \eta -V_{ef}\right) =0, \label{eq36}
\end{equation}%
here we have defined $\eta =\frac{2\varepsilon ^{2}}{am}$ end $%
V_{ef}=y^{2}+s.$ In the next section we will obtain two classes of solutions
of the Dirac equation in the Rindler spacetime. Indeed, eq. $\left( \ref%
{eq36}\right) $ may be mapped into a Sturm--Liouville problem of a Schr\"{o}%
dinger-like equation.
\section{Bound-state solutions}
As we may observe, equation (\ref{eq36}) is similar to the Schr\"{o}dinger
equation, and the term $V_{ef}=y^{2}+s$ may be identified as an effective
potential and as we can see, the system has the form of a harmonic
oscillator. In fact, the solution of the equation (\ref{eq36}) may be mapped
into a 2-dimensional harmonic oscillator-like, and then the
\begin{figure}[tbp]
\includegraphics[scale=1]{img1.eps}\newline
\caption{The plots of the energy spectrum for $a=0.01,a=0.02$ and $a=0.03.$
The energy is symmetrical about $\protect\varepsilon =0.$}
\label{fig1}
\end{figure}
solutions are given in terms of the Hermite polynomials
\begin{equation}
\bar{\psi}=\left(
\begin{array}{c}
B_{1}^{\prime }\exp \left( -y^{2}\right) H_{n+1}\left( y\right) \\
B_{\substack{ 2 \\ }}^{\prime }\exp \left( -y^{2}\right) H_{n}\left(
y\right)%
\end{array}%
\right) , \label{eq37}
\end{equation}%
where $B_{1}^{\prime }$ and $B_{2}^{\prime }$ are normalization constants.
The Hermite polynomials satisfy the recurrence relation%
\begin{equation}
a_{j+2}=\frac{2j+1-\eta }{\left( j+2\right) \left( j+1\right) }a_{j},
\label{eq38}
\end{equation}%
as the series must be finite in order for our solution to have physical
meaning, we suppose that there exists some $n$ such that when $j=n$, the
numerator is $2j+1-\eta =0$. In this way, we obtain the energy spectrum%
\begin{equation}
\varepsilon =\pm \sqrt{am\left( n+\frac{1+s}{2}\right) .} \label{eq39}
\end{equation}
\begin{figure}[p]
\includegraphics[scale=0.55]{img2.eps}\newline
\caption{The lower spinor component $g\left( x\right) $ as the function of $%
x $ for three fixed values of $a,$ Up: left and right the figures are plots
for $n=0$ and $n=1$. Down: left and right the figures are plots for $n=2$
and $n=3.$}
\label{fig2}
\end{figure}
We can see that the energy spectrum associated with the Dirac equation in
the Rindler space is discrete and depends on $a$, the acceleration of the
reference frame. This is a interesting feature of the system because the
noninertial effect mimics an external potential in the Dirac equation. From
Fig. 1, we can see that the discrete set of energies are symmetrical about $%
\varepsilon =0$, that means the particle and antiparticle have the same
energy. As it may be seen in Fig. 2, the solution $g\left( x\right) $
decreases with the coordinate $x$ and becomes negligible as $x\rightarrow
\pm \infty $.
\section{Conclusions}
In this work a brief review about the wave equation for spin 1/2 particles
in curved spaces is done. We have determined a single particle solution of
the Dirac equation in an accelerated reference frame, and as result, a
compact expression for the energy spectrum associated with the Dirac
equation in an accelerated reference frame has been obtained.
It was shown that the noninertial effect mimics an external potential in the
Dirac equation and, moreover, allows the formation of bound states. We also
have shown that the energy spectrum associated with fermions in this kind
spacetime is discrete. The solution is obtained by adopting the limit $a\ll
1 $, that means a not so fast acceleration.
With these results it is possible to have an idea about the general aspects
of the behavior of spin 1/2 particles in the Rindler space. Potential
applications of our work include physical systems with conformally flat
metrics, i.e, invariant under conformal transformations. For instance, in
applications of the AdS/CFT correspondence \cite{adscft1} to the study of
strongly coupled QCD, we look for solutions of the wave equations where the
conformal symmetry plays a pivotal role \cite{adscft2}.
It is interesting to observe that the results obtained above, in addition to
previous ones \cite{santos1,santos2}, for example, show many important
aspects of quantum systems studied in spacetimes with different structures.
However, these results rather than being considered as final, may be
considered as a motivation for future works in order to obtain a deeper
understanding of this fundamental theme of physics.
\section{Acknowledgments}
This work was supported in part by means of funds provided by CAPES%
\begin{equation*}
\end{equation*}%
\bigskip
\bigskip
\bibliographystyle{model1-num-names}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,001 |
{"url":"http:\/\/www.vositaly.org\/x6nw\/wewe.php?ra=geometry-calculator-circle","text":"# Geometry Calculator Circle\n\nThe following links are to calculators which will calculate the Section Area Moment of Inertia Properties of common shapes. First, a circle is a shape that is formed by tracing a continuous line the same distance from a single point (a circle's center point). Texas School for the Blind and Visually Impaired. Area of semi-circle formula is derived from the formula of a circle. To get the coordinates: Enter the radius of the circle, orient X and Y-Axes with the \"Switch\" buttons, enter the degrees that the coordinate points are to be at on the. To find the circumference of a circle, use the formula pi x diameter = circumference. There are a number of geometric constructions using a circle which produce phi relationships, as described below. Calculate the area of a circular ring when outer and inner radii are known. This calculator estimates how many circles of radius r can be placed inside another circle of radius R. \u2013 arc whose measure is less than a semi-circle or 180 degree. How to Find the Perimeter of a Shape. Symbolab: equation search and math solver - solves algebra, trigonometry and calculus problems step by step. The standard form of a circle is plus equals the radius squared. Page 1 of13 O levels. Notes: Trigonometric functions are evaluated in Radian Mode. Radius of a circle from circumference: The terms radius, diameter and circumference are related to two-dimensional geometric shape named circle. - Sacred Geometry in the Great Pyramid. Circle is a two dimensional closed shape with curved edges. Area of a Circle Calculator. The calculator will generate a step by step explanations and circle graph. If you wish to calculate the properties of a three-dimensional solid, such as a sphere, cylinder or cone, it's best to use our volume calculator. They're all free to watch! \u2193. The arc is smaller than 360\u00b0(or $2\\pi$) because that is the whole circle. ) In the figure at right, the lines and are tangent to both circles. This page will show you how to calculate various things that pertain to a circle. The standard form of a circle is plus equals the radius squared. Instructions: Enter the radius $$r$$ of a circle and the unit (cm, mt, ft, etc) and the solver will compute the corresponding area and perimeter. Geometry Help - Definitions, lessons, examples, practice questions and other resources in geometry for learning and teaching geometry. My exercise asks me to write a program (geometry. Welcome to the calculator section of Pi Day, we are constantly working on new math calculators so if you have any suggestions please get in touch. Examples: sinc exp dome. Graphing circles is a fairly simple process once we know the radius and center. Four different types of angles are: central, inscribed, interior, and exterior. A free interactive math textbook, including circles and arcs, from mathopenref. This Measurement Worksheet may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to help someone learn math. 14159 for pie. Round your answer to the nearest Infinite Geometry - Geometry Circle Review. Geometry - Topics. Our site offers geodesic dome plans, geodesic dome cover patterns, our dome calculator and geodesic dome formulas. it cost $40 to produce each canoe. The arc is smaller than 360\u00b0(or$2\\pi$) because that is the whole circle. Instructions: Enter the radius $$r$$ of a circle and the unit (cm, mt, ft, etc) and the solver will compute the corresponding area and perimeter. How to use the calculator to find the area or the circumfernce of a circle. We are more than happy to answer any math specific question you may have about this problem. 142 in simpler calculations, in the equation circumference equals. In trigonometry, it provides a convenient way to learn about lengths and angles. 1 yd 11 yd 19) circumference = 12. com's Area of a Circle Calculator \u2013 Provides the area of a circle formula as a reference. TN0032814 13 RSV \u2219 UST Select the two statements that must be true. Summary of circle geometry theorems Calculate the value of r if the radius of the circle is 5 cm. calculate the area of a triangle 4. Circles Geometry 3. A circle's circumference is the measurement of its entire border, and its diameter is a straight measurement that goes through the circle's origin between two points on the circumference. The diameter of the holes that are equally distributed around the bolt circle diameter Bolt circle diameter: the diameter of the circle on which the holes will be evenly distributed. Equations of Straight Lines. Equation of a circle passing through 3 points (x 1, y 1) (x 2, y 2) and (x 3, y 3) The equation of the circle is described by the equation: After substituting the three given points which lies on the circle we get the set of equations that can be described by the determinant:. This Resource Center supports users of the award-winning Dynamic Geometry \u00ae mathematics visualization software, The Geometer's Sketchpad. Provided at this site are worksheets, objective explanations, vocabulary, textbook connections, a geometry gloossary, lesson notes, assessment items, videos, links and much much more. Definition sketch for Geometry of a circular culvert: Equations Used in the Calculation of Circular Culvert Geometry: Where: d = Diameter of culvert. That distance is called a radius. Please enter a function, starting point, ending point, and how many divisions with which you want to use Trapezoidal Rule to evaluate. Use our circumference calculator to determine the area of a circle. Calculated out this gives an area of 28. Graph a Circle - powered by WebMath. In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. A circle is a simple shape of Euclidean geometry consisting of those points in a plane which are equidistant from a given point, called the centre. Given any one variable A, C, r or d of a circle you can calculate the other three unknowns. Enter any single value and the other three will be calculated. Calculations at a circular segment. How to calculate the angles and sides of a triangle? A triangle is determined by 3 of the 6 free values, with at least one side. Mathway currently does not support this subject. Hamilton-Wenham Regional School District. HWRHS Common Core Standards Geometry. This Account has been suspended. Use this GeoGebra applet to see the (x, y) coordinates that correspond to different angles on the unit circle. \" In trigonometry, it provides a convenient way to learn about lengths and angles. Recall that the formula to get the circumference of a circle is 2 \u00d7pi\u00d7r with pi = 3. This calculator will find either the equation of the circle from the given parameters or the center, radius, diameter, area, circumference (perimeter), eccentricity, linear eccentricity, x-intercepts, y-intercepts, domain, and range of the entered circle. Free Geometry calculator - Calculate properties of planes, coordinates and 3d shapes step-by-step. Taxicab geometry is a form of geometry, where the distance between two points A and B is not the length of the line segment AB as in the Euclidean geometry, but the sum of the absolute differences of their coordinates. 21) area = 201. Trigonometric functions calculator. Calculate the Area of a Rectangle 3. Therefore, in spherical geometry, a great circle is comparable to a line. To calculate the area, you just need to enter a positive numeric value in one of the 3 fields of the calculator. A circle is a simple shape of Euclidean geometry consisting of those points in a plane which are equidistant from a given point, called the centre. Read on and enjoy our circle facts and trivia before taking a look at all our other interesting information devoted to the wonderful world of geometry. DOC Author: default Created Date: 4\/24\/2003 3:32:56 PM. Namaste Maker's Geometry Zip Mini - Our Maker's Geometry Zip Mini Trio is mindfully designed with the organized crafter in mind. The picture, drawn from the calculated values, witnesses that the computations are correct. The area of a circle is given by the formula A= 2. Calculate the Area of a Rectangle 3. Geometry is a branch of mathematics that pertains the the location and attributes of a point, line, shape or solid. There are also some other important distances on a circle, called the radius (r) and diameter (d) We will need these to calculate the circumference. Calculate the radius r of the circle and the length of the diagonals of the rhombus. 25) circumference = 6\u03c0 yd 26) circumference = 22 \u03c0 in. The Guidelines link to examples of common errors, and demonstrate techniques that your instructors will love!. Summary of circle geometry theorems Calculate the value of r if the radius of the circle is 5 cm. Page 1 of13 O levels. Improve your math knowledge with free questions in \"Calculate radius, diameter, and circumference\" and thousands of other math skills. Central angle of a circle \u2013 angle whose vertex is the center of the circle and whose rays are radii of the circle. Calculate the area of a circle 2. A Shaft Keyway Depth Calculator and More handy Calculators can be found by clicking the Shop Aides menu item!. The activities may involve very simple things like colouring, ticking, drawing a line to match items etc. Provided at this site are worksheets, objective explanations, vocabulary, textbook connections, a geometry gloossary, lesson notes, assessment items, videos, links and much much more. If you're behind a web filter, please make sure that the domains *. The Lesson: We show circle O below. This calculator can find the center and radius of a circle given its equation in standard or general form. The distance between the center of the circle and any point on the circle is always same. In spherical geometry, there are no parallel lines. Notes: Trigonometric functions are evaluated in Radian Mode. txt) or read online for free. The following circumference calculator is easy to use. Online arctan(x) calculator. Parallel, twisted, ribbon. Therefore, in spherical geometry, a great circle is comparable to a line. Title: Microsoft Word - Stand Alone GEOMETRY2002 Blueprint. calculate the area of a triangle 4. Trigonometry calculator Right triangle calculator. Examples with step by step solutions, Angles, triangles, polygons, circles, circle theorems, solid geometry, geometric formulas, coordinate geometry and graphs, geometric constructions, geometric transformations, geometric proofs, Graphing Calculator. Cosine calculator. Simply enter the desired value in the relevant box. 1 yd 11 yd 19) circumference = 12. Degrees = Tan-1 (Slope Percent\/100) Example: With a slope percentage of 43%, degrees would be: Degrees = Tan-1 (. Investigate the relationships among the angles of intersection of the two lines and the intercepted arcs using positive and negative angle and arc measures. This is the height (or depth) of the arc. How to Find the Perimeter of a Shape. Take away the carpenters Framing Square, CMC calculator, and circular saw to show you what they really know about cutting rafters. Math Antics has a brand new look! Find out why: \u2193 Scroll down to check out our Video Lessons. 1 yd 11 yd 19) circumference = 12. Revised 2011. Get the exact online tutoring and homework help you need. Area of plane shapes. Mathematics. For these two solid shapes, the volume formula is the same: it's one-third of the area of the base times the height. Fill in 3 of the 6 fields, with at least one side, and press the 'Calculate' button. The circle is a simple closed curve ,where the distance between the center of the images and the circumference is called as radius. A line that \"just touches\" the circle as it passes by is called a Tangent. Circle is a two dimensional closed shape with curved edges. r = radius d = diameter C = circumference A = area \u03c0 = pi = 3. , Austin, TX 78756 - (512) 454-8631. Improve your math knowledge with free questions in \"Write equations of circles in standard form from graphs\" and thousands of other math skills. OUR GOAL: To find the standard form of the given circle equation by factoring. Enter the input values in the circle calculator to calculate area, diameter, circumference and sector. A circle's diameter is the length of a line segment whose endpoints lie on the circle and which passes through the centre. Contemporary geometry has many subfields: Euclidean geometry is geometry in its classical sense. Central Angle Calculator Calculates a Circle's Central Angle, Radius or Arc Length. So, by carrying out either of the two foregoing operations, the user will be able to find the Arc of a Circle quickly and without any difficulties. Our circumference calculator provides circumference of a circle by entering its radius. Recall that the formula to get the circumference of a circle. Please enter a function, starting point, ending point, and how many divisions with which you want to use Trapezoidal Rule to evaluate. Choose the number of decimal places, then click Calculate. You can also see at the bottom of the calculator, the step-by-step solution. Please use only numbers (e. Calculate the area of a circle 2. person_outline Timur schedule 2017-10-20 13:35:16 This calculator estimates the maximum number of smaller circles of radius r that fits into a larger circle of radius R. Calculating a circle's diameter is easy if you know any of the other dimensions of the circle: the radius, the circumference, or the area. For background and to contact me with comments see my blog. However, as it turns out, not. Measuring Large Bolt Circle Geometry Equations Calculators. Math lessons, videos, online tutoring, and more for free. calculate the area of a triangle 4. Circle Sector, Segment, RETURN TO GEOMETRY INDEX. calculate the area of a rectangular 3. Valid input formats are at the bottom of this page. Knowledge Precise rafter layout can only be accomplished with knowledge of the geometry that develops the parallelogram in the compound joint. person_outline Timur schedule 2017-10-20 13:35:16 This calculator estimates the maximum number of smaller circles of radius r that fits into a larger circle of radius R. We know the formula to calculate area of a circle is \u03c0r^2, by dividing this by 2 we will get the area of a semicircle. The activities may involve very simple things like colouring, ticking, drawing a line to match items etc. The segment OA is a radius of the circle. It would be the border of an area or the outline. Geometry is used to find volume, area, and other properties of shapes. In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. Calculate the radius of the circle and size of central angle. The height of the circular segment becomes one of the segments of the second imaginary cord. Practice, practice, practice. Geometry calculator solving for circle arc length given radius and central angle. So, by carrying out either of the two foregoing operations, the user will be able to find the Arc of a Circle quickly and without any difficulties. Calculator for Adjusting Concentration of Ethanol in water Solution; Calculator for Combining Ethanol in water Solutions of Different Concentration. Enter the radius, diameter, circumference or area of a Circle to find the other three. Circle Calculator. This calculator can find the center and radius of a circle given its equation in standard or general form. The perpendicular bisectors of (at least) 2 chords always meet at one point: the center. In simple terms it looks like a slice of pie. The program is a great tool! Not only does it give you the answers but it also shows you how and why you come up with those answers. Circle Calculator. In the following section we will show that the Great Pyramid squares the circle with a better approximation than the one obtained from Kepler triangle. The name comes from Greek words \u1f15\u03be (hex) meaning six, and \u03b3\u03c9\u03bd\u03af\u03b1 (gonia) meaning a corner, an angle. ) In the figure at right, \ud835\udc5a \u0302=91\u00b0 and. How to calculate the angles and sides of a triangle? A triangle is determined by 3 of the 6 free values, with at least one side. 23) area = 64 \u03c0 mi\u00b2 24) area = 16 \u03c0 in\u00b2 Find the area of each. These calculators are best used to check your work, or to compute a complicated problem. Many different professions use slope in describing an angle. calculate the area of a rectangular 3. The following links are to calculators which will calculate the Section Area Moment of Inertia Properties of common shapes. Area of Sectors and Segments MathBitsNotebook. volume of rectangular pyramid end cube formula. This is a free online math calculator together with a variety of other free math calculators that compute standard deviation, percentage, fractions, and time, along with hundreds of other calculators addressing finance, fitness, health, and more. Unit circle \u2013 be able to fill-in a blank unit circle chart (exactly like one attached here) WITHOUT a calculator, evaluate trig and inverse trig values (know your unit circle!!) Solve trig equations for given intervals Practice Questions: 1) Evaluate the six trigonometric functions of the angle \u03b8. How to Calculate the Area of a Circle. That is going to wrap up Part 1 of the HP Prime Geometry App Tutorial. Contact your hosting provider for more information. Trigonometric functions calculator. This calculator will find either the equation of the circle from the given parameters or the center, radius, diameter, area, circumference (perimeter), eccentricity, linear eccentricity, x-intercepts, y-intercepts, domain, and range of the entered circle. Use your calculator's value of \u03c0\u03c0\u03c0. The arc is smaller than 360\u00b0(or$2\\pi\\$) because that is the whole circle. Help & Settings Printing Help (new window). GEOMETRY, a MATLAB library which carries out geometric calculations in 2, 3 and N space. How to Use the Calculator. The critical knowledge needed to do the calculation is knowing about the value of Pi and the radius of the circle. Result will be displayed. Texas School for the Blind and Visually Impaired. Finding a Circle's Center. There are also some other important distances on a circle, called the radius (r) and diameter (d) We will need these to calculate the circumference. volume of rectangular pyramid end cube formula. We get many questions asking us to calculate the volume of topsoil, gravel, water, concrete, etc. In geometry, an ellipse is a regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant, or resulting when a cone is cut by an oblique plane that does. The radius of the circle is the length of a straight line stretching from the center of the circle to the line of circumference. Calculate the intersection area of two circles July 14th, 2016. Taxi Cab Geometry with Technology: Some Exploration Materials. Distance across the circle passing through the center is called as diameter. Circle: Convert General Form to Standard Form. We could formulate cases to step through the same as in the other article, but I will do it a little shorter this time. Geometry Calculator: 1. person_outline Timur schedule 2017-10-20 13:35:16 This calculator estimates the maximum number of smaller circles of radius r that fits into a larger circle of radius R. Circle Calculator. Circles activity for Geometry students. Finding a Circle's Center. How do the area and circumference of a circle compare to its radius and diameter? This activity allows you to investigate these relationships in the Intro and Investigation sections and then hone your skills in the Problems section. I would like to ask how to create a circle with radius=4km. Let us consider 3 scenarios to calculate the area of a circle. Radius of Circumscribed Circle - Geometry Calculator. Taxi Cab Geometry has the following distance function between points A(x 1,y 1) and B(x 2,y 2):. Our site offers geodesic dome plans, geodesic dome cover patterns, our dome calculator and geodesic dome formulas. CAS calculations. spherical namespace. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and. Circles, Triangles, parallelograms and many more. This Measurement Worksheet may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to help someone learn math. Free online apps bundle from GeoGebra: get graphing, geometry, algebra, 3D, statistics, probability, all in one tool!. Geometry Circle Review Find the area of each. Consult your favourite Calculus book for more details. Pearson \/ Prentice Hall Textbooks SEARCH SEARCHStep-by-step solutions to all your Geometry homework questions - Slader4 days ago \u00b7 hypothesis testing homework help. A line is said to have a positive gradient if the slope goes up from the left hand side to the right hand side. Although the educational system presents numerous opportunities for students to enjoy developing new skills, excelling at sports, and practicing public speaking, it seems that nothing is working when it comes to mathematics. Use this circle calculator to find the area, circumference, radius or diameter of a circle. This is one of the most useful calculations in all of math. Use your calculator's value of p. quit Enter your choice (1-4)-if the user enters 1, then the program should ask for the radius of the circle and then should display the area. This geometry calculator will take one known circle measurement (area, circumference, diameter, or radius) and calculate the other three. Geometryx: Geometry - Calculator 2. A line segment from one point on the circle to another point on the circle that passes through the center is twice the radius in length. An inscribed quadrilateral is any four sided figure whose vertices all lie on a circle. Round your answer to the nearest tenth. Formula for the lateral surface area of a cylinder. Area of semi-circle formula is derived from the formula of a circle. Circle Solver Calculator Enter the circle area, diameter, or circumference and it will solve for the other two. Compasses draw up to a 10\" diameter circle Rulers, Triangles & Protractor feature a name plate for easy identification along with Inch & Metric graduations Comes packed in a reusable shatter-proof carrying case The perfect geometry kit for more advanced students!. Mathway currently does not support tutoring in Chemistry. If the two lines are formed at a 180 degree angle then the sector is often referred to as a semi-circle. The perimeter formula is one of the easier formulas to remember in math! The perimeter of a shape is the distance around the outside of the shape. An interesting topic in 3-dimensional geometry is Earth geometry. Texas School for the Blind and Visually Impaired. Calculator for Adjusting Concentration of Ethanol in water Solution; Calculator for Combining Ethanol in water Solutions of Different Concentration. Properties of Spherical Geometry. It also features a labeled circle diagram. Formula for area of circular ring. com for more Free math videos and additional subscription based content!. To calculate the area, you just need to enter a positive numeric value in one of the 3 fields of the calculator. Welcome to The Calculate Circumference and Area of Circles (A) Math Worksheet from the Measurement Worksheets Page at Math-Drills. Water Chlorination Calculators. 21) area = 201. Measuring or determining distances for a bolt circle geometry can be facilitated using the following equations and methods. Math Our free online math calculators can calculate everything from simple math problems all the way up to complex and in depth mathematical functions. cpp) that displays the following menu: Geometry Calculator: 1. All the geometry help you need right here, all free. Distance across the circle passing through the center is called as diameter. Area of a sector calculator Given the radius and the angle, use this calculator to find the area of any sector. Area of a Semicircle Calculator A semicircle is nothing but half of the circle. It can be also used to calculate other parameters of a circle such as diameter, radius and area. prism: (lateral area) = perimeter(b) L (total area) = perimeter(b) L + 2bsphere = 4 r 2. How to use the calculator Enter the sides a, b and c of the triangle as positive real numbers and press \"enter\". The Earth is very close to a sphere (ball) shape, with an average radius of 6371\\ \"km\". The distance around the edge of the circle is called the circumference. Calculations at a circle. Use your calculator's value of \u03c0\u03c0\u03c0. Quit Enter your choice (1 \u2013 4): If the user enters 1, the program should ask for the radius of the circle and then display its area. For these two solid shapes, the volume formula is the same: it's one-third of the area of the base times the height. CIRCLE Calculator for Radius, Central Angle, Chord, Segment Height, Apothem, Arc Length and Chord Length. These calculations include angles, areas, containment, distances, intersections, lengths, and volumes. volume of rectangular pyramid end cube formula. In terms of circumference, the diameter can be computed using the equation d = c\/pi, where \"c\" represents the circumference and pi is approximately equivalent to 3. This work is derived from Euclid's Elements starting at Book III Proposition 1. This calculator uses the formula r = sqrt [ (s - a)(s - b)(s - c) \/ s ] where s = (a + b + c) \/ 2. Lines of longitude and the equator of the Earth are examples of great circles. This is possible if and only if the sum of opposite angles is 180\u00b0. The earlier worksheets in this section require calculating the area and the circumference given either a radius or a diameter. Use thie step-by-step help information to code\u2026. Similarly to the article about intersection points of two circles we're now interested in the area that is formed by the intersection of two overlapping circles. This is the height (or depth) of the arc. OUR GOAL: To find the standard form of the given circle equation by factoring. Getting Started: Make math and science easier (and more fun) with free graphing calculator programs and games from calculatorti. Circular Segment Calculator. TN0032814 13 RSV \u2219 UST Select the two statements that must be true. Enter two values of radius of the circle, the height of the segment and its angle. Methanol and Water Solution Calculator Density and Concentration Calculator for Mixtures of Methanol and Water. We can use this idea to find a circle's center: draw a right angle from anywhere on the circle's circumference, then draw the diameter where the two legs hit the circle; do that again but for a different diameter; Where the diameters cross is the center! Cyclic Quadrilateral. The perpendicular bisectors of (at least) 2 chords always meet at one point: the center. Pythagorean theorem was proven by an acient Greek named Pythagoras and says that for a right triangle with legs A and B, and hypothenuse C See this lesson on Pythagorean Theorem, animated proof See How to generate triples of sizes that are natural See In Depth Wikipedia article on Pythagorean theorem. The name comes from Greek words \u1f15\u03be (hex) meaning six, and \u03b3\u03c9\u03bd\u03af\u03b1 (gonia) meaning a corner, an angle. Pre Algebra Practice By Circle Team Issuu Exercises Connections Answers Multiplying Algebraic Terms Worksheet Get To Math Word Problems For Free Expressions Calculator College Students Easy. This diagram shows the circumference of a circle. 1 ft 4 ft Find the diameter of each circle. Check out our wide variety of mathematic calculators that can do everything from calculate the area of a circle to calculate the volume of a pyramid to calculate standard deviations. There are two ways to do this: 1) With user interaction: Program will prompt user to enter the radius of the circle. : Cob Web Plot \u2013 Change variables and observe patterns from this graphing simulation. Calculate the radius of a circle inscribed inside a triangle of sides a, b and c. In this lesson, you'll how to calculate the area of a circle by knowing only its radius or diameter. For a complete analysis of a circular arc please check out The Complete Circular Arc Calculator. An inscribed quadrilateral is any four sided figure whose vertices all lie on a circle. How to find the length of a line segment in a circle? Additional Topics in Math Calculator: Not Permitted Circle Geometry The semicircle above has a radius of r inches, and chord CD is parallel to the diameter AB. Properties of Spherical Geometry. Texas School for the Blind and Visually Impaired. A line is said to have a positive gradient if the slope goes up from the left hand side to the right hand side. No matter your proficiency in the geometry of a circle, the equation of the circle may still make your head spin. For complete tests and break downs of each section, please check out web site listed below. Just enter the value of the radius and hit calculate button. Practice calculating the area, radius, diameter and circumference of a circle. How it works: Just type numbers into the boxes below and the calculator will automatically calculate the distance between those 2 points. Learn more about pi, or explore hundreds of other calculators addressing finance, math, fitness, health, and more. How do the area and circumference of a circle compare to its radius and diameter? This activity allows you to investigate these relationships in the Intro and Investigation sections and then hone your skills in the Problems section. Enter the radius, diameter, circumference or area of a Circle to find the other three. Formulas, explanations, and graphs for each calculation. Perimeter of a triangle calculation using all different rules: SSS, ASA, SAS, SSA, etc. Classify the steps involved in the formation of a solution as being endothermic or exothermic. We will look at the one-dimensional distance around the figure and the two-dimensional space covered by the figure. Enter the radius. Round your answer to the nearest tenth. Compasses draw up to a 10\" diameter circle Rulers, Triangles & Protractor feature a name plate for easy identification along with Inch & Metric graduations Comes packed in a reusable shatter-proof carrying case The perfect geometry kit for more advanced students!. AB is the diameter of a semi-circle. Use the this circle area calculator below to find the area of a circle given its radius, or other parameters. Enter the actual pinhole diameter and press calculate for the fstop 4. The degrees shown around the circle only show the orientation. It is therefore assumed that students studying The Circle have an adequate working knowledge of the ideas from The Line, the first of the co-ordinate geometry topics. 3 Computer algebra system (CAS) CAS view 53. Geometry Calculator. in a circle ( , N), until the intersection with the circle passing through the peaks of a square circumscribed to the circle ( , N). Formulas, explanations, and graphs for each calculation. All possible solutions are calculated in your coordinates and units. com explains, a unit circle is \u201ca circle with a radius of 1. Explore math with desmos. It includes some tutorial information as well as circle formulas and examples. You can also see at the bottom of the calculator, the step-by-step solution. Calculate the area of a circle 2. Plots & Geometry - powered by WebMath. Quit Enter your choice (1 \u2013 4): If the user enters 1, the program should ask for the radius of the circle and then display its area. 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Q: Contract requires Session, but Binding 'BasicHttpBinding' doesn't support it or isn't configured properly to support it When i'm using SessionMode = SessionMode.Required in servicecontract then i get this error
Contract requires Session, but Binding 'BasicHttpBinding' doesn't
support it or isn't configured properly to support it.
anyone tell me a solution?
A: This error message is seldom clear. Here the answer goes like this, basichttpbinding doesn't support session. So you have to use the below property if you want to use it.
[ServiceContract(SessionMode = SessionMode.Allowed)]
This means, If you are trying to configure multiple bindings like basichttp, wshttp, net.tcp, WCF will automatically enable session for other than basichttp binding. so if you put SessionMode.Required instead of Allowed, then you are forced not to use basichttpbinding.
That said, solving this issue usually would require something like this:
<system.serviceModel>
<protocolMapping>
<add scheme="http" binding="wsHttpBinding" bindingConfiguration="wsHttpBindingConfiguration" />
</protocolMapping>
<bindings>
<wsHttpBinding>
<binding name="wsHttpBindingConfiguration" transactionFlow="true" />
</wsHttpBinding>
.......
A: As it's listed here, choose wsHttpBinding or NetTcpBinding.WSHttpBinding binding.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 9,793 |
{"url":"https:\/\/www.physicsforums.com\/threads\/simple-algebra-calculus-question.392214\/","text":"# Simple algebra-calculus question\n\n1. Homework Statement , and relevant equations\n\nHow is A6 arrived at and *how* did they get the \"Q\" in A6?\n\n## Homework Equations\n\nSee above\n\n3. The Attempt at a Solution\n\nObjective: Rid A1 of L. They simply substituted \"C\" in A2 into A1. But how did they get rid of the L? I don't quite get the algebraic manipulation...please help","date":"2021-05-14 11:10:10","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8464547991752625, \"perplexity\": 5448.513424801018}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-21\/segments\/1620243990449.41\/warc\/CC-MAIN-20210514091252-20210514121252-00049.warc.gz\"}"} | null | null |
Munt la Schera är en bergstopp i Schweiz. Den ligger i regionen Engiadina Bassa/Val Müstair och kantonen Graubünden, i den östra delen av landet, km öster om huvudstaden Bern. Toppen på Munt la Schera är meter över havet, eller meter över den omgivande terrängen. Bredden vid basen är km.
Terrängen runt Munt la Schera är bergig åt nordväst, men åt sydost är den kuperad. Den högsta punkten i närheten är Piz dal Fuorn, meter över havet, km norr om Munt la Schera. Runt Munt la Schera är det glesbefolkat, med invånare per kvadratkilometer.. Närmaste större samhälle är Scuol, km norr om Munt la Schera.
Trakten runt Munt la Schera består i huvudsak av gräsmarker.
Kommentarer
Källor
Berg i Graubünden
Berg i Schweiz 2000 meter över havet eller högre | {
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Q: First you throw away my outside and cook the inside. Then you eat my outside and throw away my inside. What am I?
A: Corn on the cob. Because you throw away the husk, cook the corn. Then you eat the kernels, and throw away the cob.
Q: What runs, but never walks. Murmurs, but never talks. Has a bed, but never sleeps. And has a mouth, but never eats?
A: A river.
Q: What bird can lift the most weight?
A: A crane.
Q: What goes up as soon as the rain comes down?
A: An umbrella.
Q: The more you take, the more you leave behind. What am I?
A: Footprints.
Q: I have all the knowledge you have. But I'm so small, you can hold me in your fist. What am I?
A: Your brain.
Q: How much dirt is there in a hole that's 5 feet wide and 5 feet deep?
A: None. | {
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{"url":"http:\/\/kb.osu.edu\/dspace\/handle\/1811\/21475","text":"# CONTROL OF COHERENT LIGHT AND ITS APPLICATIONS TO MOLECULAR SPECTROSCOPY\n\nPlease use this identifier to cite or link to this item: http:\/\/hdl.handle.net\/1811\/21475\n\nFiles Size Format View\n2004-WA-02.jpg 579.1Kb JPEG image\n\n Title: CONTROL OF COHERENT LIGHT AND ITS APPLICATIONS TO MOLECULAR SPECTROSCOPY Creators: Ye, Jun Issue Date: 2004 Publisher: Ohio State University Abstract: Recent progress in precise phase control of ultrafast lasers has led to a wide range of applications in both frequency and time domains, including measurement of optical frequencies, precision laser spectroscopy, optical atomic clocks, optical frequency synthesis, as well as pulse timing stabilization, coherent synthesis of optical pulses, and phase-sensitive extreme nonlinear optics. New capabilities for atomic and molecular spectroscopy are emerging. The combination of precision femtosecond lasers and ultracold atoms have enabled us to enter a qualitatively new regime of ultrahigh resolution spectroscopy. We utilize a phase-coherent wide-bandwidth optical comb to induce the desired multipath quantum interference effect for the resonantly enhanced two-photon transition (from 5S to 5D states) in the cold Rb atoms. The large bandwidth of the femtosecond laser comb allows us to recover high precision information on hyperfine intervals (RF) and optical transition frequencies among all related states. In addition to structural information, we can also obtain information regarding dynamic population transfer among all hyperfine states by varying the interaction time between the femtosecond laser pulses and the cold atoms. Understanding of molecular structure and dynamics often involves detailed spectral analysis over a broad wavelength range. Such a task can now be accomplished with a desired level of accuracy uniformly across all relevant spectral windows, allowing precise investigations of minute changes in the molecular structure over a large dynamic range. Furthermore, molecular samples can now be prepared in a well-controlled environment and in a well-defined internal state. In our current experiments we accelerate\/decelerate a supersonic beam of the Hydroxyl free radicals (OH) to a mean speed adjustable between 500 m\/s to rest, with a translational temperature tunable from 1mK to 1K. These velocity-manipulated stable bunches'' contain $10^{6-9}$ molecules (depending on the translational temperature) at a density of $\\approx 10^{7-10} cm^{-3}$ in the beam and $\\approx 10^{9} cm^{-3}$ in the trap. These cold samples can be held in an electrostatic trap for precise measurements. Simultaneous control of timing jitter and carrier-envelope phase is used to phase coherently superpose a collection of successive pulses from a mode-locked laser. Such a passive pulse amplifier'', along with the synchronization technique we developed for pulse synthesis, has led to significant improvements in experimental sensitivity and spatial resolution for nonlinear-optics based spectroscopy and imaging of bio-molecular systems. URI: http:\/\/hdl.handle.net\/1811\/21475 Other Identifiers: 2004-WA-02","date":"2014-08-30 10:12:22","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5222691893577576, \"perplexity\": 2225.301695480427}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2014-35\/segments\/1408500834883.60\/warc\/CC-MAIN-20140820021354-00391-ip-10-180-136-8.ec2.internal.warc.gz\"}"} | null | null |
Commentary: Yuri!!! On Ice
By mayu - Wednesday, December 21, 2016 - No Comments
(This post contains spoilers from the anime.)
An anime series which started airing towards the end of the year, Yuri!!! On Ice (YOI) is now widely acclaimed in many parts of the world. Fans have taken to many of the characters in the show; the story revolves mainly around a competitive figure skating environment and its participants.
Since the premise is skating, it is considered a sports anime, like Kuroko No Basuke, Haikyuu!!, Free!, All Out!!, Ace of Diamond, just to name a few. But for a couple of reasons, it differs from the typical sports anime trope in many ways.
1. Competitors being of a wider age range
Shounen sports anime are often set in a high school premise, which often results the casting of high school competitors aged around 15-18. For YOI, we have a 15 year old Yuri Plisetsky (Yurio) and also a 27 year old Viktor Nikiforov and everyone else somewhere in between or close, and most had been participating or are participating in world skating championships at the time of the story.
Personally I love the high energy of the typical shounen sports anime, it does make me feel more motivated and wanting to do my best in my life. YOI also does motivate, but in a different way; it subtly pushes messages to the audience such as believing in oneself is the first step to bringing out an individual's potential, as most significantly seen in Yuri's growth throughout the story.
Also this gives rise to the so-called more mature premise, where the environment is ever-changing due to the competitions being held in many different countries, which then introduces more international characters as well. As a result it does make the show more relatable for a wider group of audience; even the skaters in real life are catching on to this series and loving it!
2. Relationships
Shounen anime in general is mostly just nakama power!!!! or the likes of it; YOI does something like that as well, in the form exploring different kinds of relationships, mostly via the characters' thoughts during their routine, in which there is often a purpose or a particular audience they are skating for.
The main relationship in the series is Yuri forming a bond with Viktor as they eye gold medal of the Grand Prix Final together.
I like how their relationship is portrayed here; where their love for each other is mostly shown via simple day-to-day activities; through training together, through sightseeing together, through planning things and travelling together. Though truthfully, not many people will meet at high-profile events and fall in love, but it is how Yuri and Viktor stay by each other and treat each other that tugs at the heartstrings.
Also, Yurio's "Agape" performance, showcases another kind of relationship; of Yurio receiving and accepting unconditional love and care he has encountered, and once he realises he could skate to that thought, he was able to showcase his full ability in skating the theme.
After episode 11: So far, so good?
Last week's episode ended on a cliffhanger, with Yuri declaring to Viktor that he wanted to end all of this after the current competition.
But what does Yuri want to end exactly? My head had been swimming with all the possibilities, but my first response to what Yuri said was probably a little bit of shock and worry. Very likely something he observed, or feel all this time, caused him to say this; there were a few theories/metas thrown around the past week by a few observers, but a few words from the director, Kubo-sensei, on what we can expect!
YOI finale episode 12 synopsis and preview #yurionice pic.twitter.com/BQ6wjSmQI3
— ji@勇ヴィク結婚!!💍✨⛸⛸ (@soukatsu_) December 14, 2016
Whatever the outcome, Yuri!!! On Ice have outdone the expectations of many and as the opening song aptly puts it, true "history makers" in many aspects. I also like the animation and OSTs, they are quite exceptional in my opinion. If I ever do get the chance I would love to buy the blurays and soundtracks when they release it.
The last episode (episode 12) airs in about half an hour and many fans are eagerly anticipating it at this point in time. 2016 may not be a good year for many people, but this anime is cheering up the hearts of many in different ways.
Have a great rest of the year, all!
Within the first week airing the first episode of YOI, a huge amount of fanarts based on the series have been created. Below are just some of the ones I like:
Mafia!AU
Yuri and Viktor as Waiters + Artist's loots from Japan's YOI-themed cafe
You are a nice coach! - from Kubo-sensei herself
ritsu
Posted by mayu at 8:58 AM
No Comment to " Commentary: Yuri!!! On Ice " | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,262 |
\section{Introduction}
Varying speed of light (VSL) cosmologies have recently received
considerable attention as alternatives to cosmological inflation
to provide a different basis for resolving the problems of the
standard model (see for example \cite{magu} and refs. therein).
Instead of adopting the inflationary idea that the very early
universe experienced a period of superluminar expansion, in these
universes one assumes that light travelled faster in the early
universe. In such cosmological models the known puzzles of the
standard early universe cosmology are absent at the cost of
breaking the general covariance of the underlined gravity theory.
We do not enter here into a discussion on the foundations of VSL
theories and the conceptual problems arising from the very meaning
of varying the speed of light (see \cite{magu} for a discussion).
In this paper we report on some preliminary results of our
on-going work \cite{cm07} on the application of the method of
asymptotic splittings introduced in \cite{cb06} to study the
singularities that may arise in VSL cosmologies. In particular, we
focus here on the VSL model proposed in \cite{alma} and further
investigated in \cite{barr}. An important characteristic of this
model is that one assumes minimal coupling at the level of the
Einstein equations so that a time-variable $c$ should not
introduce changes in the curvature terms in Einstein's equations
in the cosmological frame, Einstein's equations must still hold.
As Barrow points out \cite{barr}, $c$ changes in the local
Lorentzian frames associated with the cosmological expansion, a
special-relativistic effect, so that the resulting theory is not
covariant and one has to make a specific choice of time
coordinate. Choosing that specific time to be comoving proper time
the Friedman equations retain their form with $c(t)$ and $G(t)$
varying.
We assume an equation of state of the form $p=(\gamma-1)\rho c^{2},$ with $%
0<\gamma \leq2$ and we write the Friedman equations with varying
$c\left( t\right) $ and $G\left( t\right) $ as follows:
\begin{equation}
\left( \frac{\dot{a}}{a}\right) ^{2}+\frac{kc^{2}}{a^{2}}=\frac{8\pi G}{3}%
\rho, \label{frie}
\end{equation}%
\begin{equation}
\frac{\ddot{a}}{a}=-\frac{8\pi G}{6}\left( 3\gamma-2\right) \rho .
\label{rayc}
\end{equation}
Here $a$ is the scale factor, $k=0,+1,$ or $-1.$ Differentiating
the first and using the second equation above we obtain the
conservation equation
\begin{equation}
\dot{\rho}+3\gamma \rho \frac{\dot{a}}{a}=-\rho \frac{\dot{G}}{G}+3\frac{k}{%
a^{2}}\frac{c\dot{c}}{4\pi G}, \label{cons}
\end{equation}
and setting $a=x,$ $\dot{x}=y$ we obtain the non-autonomous system%
\begin{eqnarray}
\dot{x} & =&y, \nonumber \\
\dot{y} & =&-\frac{8\pi G\left( t\right) }{6}\left( 3\gamma-2\right) x\rho,
\label{nona} \\
\dot{\rho} & =&-3\gamma \frac{y}{x}\rho-\rho \frac{\dot{G}\left( t\right) }{%
G\left( t\right) }+3\frac{k}{x^{2}}\frac{c\left( t\right) \dot{c}\left(
t\right) }{4\pi G\left( t\right) }, \nonumber
\end{eqnarray}
subject to the constraint
\[
\frac{y^{2}}{x^{2}}+\frac{kc^{2}\left( t\right) }{x^{2}}=\frac{8\pi G\left(
t\right) }{3}\rho.
\]
\section{The flat case}
For flat ($k=0$) models we set $z=G\rho$ and the system
(\ref{nona}) becomes
\begin{eqnarray}
\dot{x} & =&y, \nonumber \\
\dot{y} & =&-\frac{8\pi}{6}\left( 3\gamma-2\right) xz, \nonumber\\
\dot{z}+3\gamma\frac{y}{x}z&=&0,\label{flat}\end{eqnarray}
subject to the constraint%
\[
\frac{y^{2}}{x^{2}}=\frac{8\pi}{3}z.
\]
This system is exactly that which was analyzed using the method of
asymptotic splittings in \cite{cb06}, and we rewrite their
result. Putting
\[
x=\alpha \tau^{p},\ y=\beta \tau^{q},\ z=\delta \tau^{r},
\]
we find the balance
\begin{equation}
p=\frac{2}{3\gamma},\ q=p-1,\ r=-2,\ \
\beta=\frac{2}{3\gamma}\alpha ,\delta=\frac{1}{6\pi \gamma^{2}},\
\alpha=\mathrm{arbitrary.} \label{bala}
\end{equation}
Computation of the eigenvalues of the Kovalevskaya matrix
$K=D\mathbf{f} \left( \mathbf{\alpha}\right) -diag\left(
\mathbf{p}\right) $ yields the values $-1,0,\frac{2\left(
3\gamma-2\right) }{3\gamma}.$ Applying the constraint to the
second equation we obtain an integrable system with general
solution
\begin{equation}
x =(At+C)^{2/3\gamma},\quad y
={\frac{2A}{3\gamma}}(At+C)^{2/3\gamma-1}, \quad z
={\frac{A^{2}}{6\pi \gamma^{2}}}(At+C)^{-2},\label{exact}
\end{equation}
where $A$ and $C$ are constants of integration. We see that the
density function always has a finite time singularity. On the
other hand, the Hubble parameter blows up in finite time only for
$\gamma<2/3.$ It is interesting that the leading-order terms
(\ref{bala}) obtained from the calculation of the dominant balance
already contain all the information provided by the exact solution
(\ref{exact}), an effect due to the fact that the system is
weight-homogeneous. We will report on the details of the full
analysis of this system elsewhere.
\section{Reduction to two dimensions}
We assume a power-law dependence of the function $c,$
\[
c=c_{0}a^{n},\ \ \ n\in \mathbb{R},\ \ G=\mathrm{constant},
\]%
and use a system of units with $8\pi G=1=c_{0}^{2}.$ We can avoid
having to deal with denominators if we
set $x=1/a,$ $H=\dot{a}/a.$ Then the system (\ref{frie}), (\ref{rayc}), (\ref%
{cons}) becomes
\begin{eqnarray}
\dot{x} &=&-xH, \nonumber \\
\dot{H} &=&-H^{2}-\frac{\left( 3\gamma -2\right) }{6}\rho , \label{3-d} \\
\dot{\rho} &=&-3\gamma \rho H+6knu^{2-2n}H, \nonumber
\end{eqnarray}%
and the constraint reads
\begin{equation}
H^{2}+ku^{2-2n}=\frac{1}{3}\rho . \label{const}
\end{equation}%
We use the constraint to eliminate $x,$ and write the system in
the form
\begin{eqnarray}
\dot{H} &=&-H^{2}-\frac{\left( 3\gamma -2\right) }{6}\rho , \nonumber \\
\dot{\rho} &=&-\left( 3\gamma -2n\right) \rho H-6nH^{3}. \label{2-dim}
\end{eqnarray}%
From Eq. (\ref{const}) it follows that the phase space of
(\ref{2-dim}) is the set $ \left\{ \left( H,\rho \right) \in
\mathbb{R}^{2}:\rho \geq 0,\rho -3H^{2}>0\right\} $ for closed
models, and $\left\{ \left( H,\rho \right) \in \mathbb{R}^{2}:\rho
\geq 0,\rho -3H^{2}<0\right\} $ for the open ones. Note that the
corresponding equations in general relativity have the feature
that the conservation equation corresponding to the second equation in (\ref%
{2-dim}) is just $\dot{\rho}=-3\gamma \rho H,$ which implies that the line $%
\rho=0 $ is invariant, i.e., the trajectories of the system cannot
cross the line $\rho=0.$ On the other hand, here equations
(\ref{2-dim}) without further assumptions do not guarantee that a
solution curve starting at a point with $\rho>0$ will not
eventually enter the region with $\rho<0,$ which of course is
unphysical.
A first task of the method of asymptotic splittings is to find all
possible asymptotic forms $ H=\alpha \tau ^{p},\, \rho =\beta \tau
^{q} $ admitted by the system (\ref{2-dim}). One balance gives
$ p=-1,q=-\left( 3\gamma -2n\right) $ with $\alpha =1,\,\beta =\mathrm{arbitrary}.$
This has K-exponents $(-1,0)$. A second interesting balance is for
$p=-1,q=-2$ with coefficients given by
\[
\left( \alpha =\frac{2}{3\gamma },\beta =\frac{4}{3\gamma ^{2}}\right)
,\left( \alpha =\frac{1}{1-n},\beta =-\frac{6n}{\left( 3\gamma -2\right)
\left( 1-n\right) ^{2}}\right) .
\]%
The K-exponents are in this case given by the forms
\[
\left( -1,\frac{2}{3\gamma}\left( 3\gamma+2n-2\right) \right) ,\left( -1,%
\frac{3\gamma+2n-2}{n-1}\right) .
\]
These results lead to formal series expansions of the solutions in
a suitable neighborhood of the finite time singularity, they will
be presented elsewhere, \cite{cm07}. It is interesting that a
phase space analysis shows that only closed models run into a
finite time future singularity. In fact the phase portrait of
(\ref{2-dim}) with $n=-1/2,\gamma =1$ is shown in Figure 1.
\begin{figure}[htb]
\begin{center}
\includegraphics{2-d.eps}
\end{center}
\caption{The phase portrait of (\protect\ref{2-dim})}
\label{fig1}
\end{figure}
The dashed line in this Figure separates the closed from the open
models. We see that every initially expanding universe starting
below this line eventually approaches the origin which corresponds
to zero density and expansion rate. On the other hand, initially
expanding universes starting above the dashed line eventually
contract and $H\rightarrow -\infty ,$ $\rho \rightarrow \infty $
in a finite time. Numerical experiments confirm the above
analysis.
\section{The general case}
The reduction of the three dimensional dynamical system
(\ref{3-d}) to the two-dimensional system (\ref{2-dim}) is not
unique. We can use the constraint (\ref{const}) to eliminate $\rho
$ instead of $u.$ However, we shall see that assuming a power-law
dependence for $G$ as well, we can handle both cases at once. In
this Section we assume that
\[
c=c_{0}a^{n},\ \ \ G=G_{0}a^{m},\ \ \ n,m\in \mathbb{R},
\]%
and use a system of units with $8\pi G_{0}=1=c_{0}^{2}.$ Setting
again $x=1/a,$ $H=\dot{a}/a,$ the system (\ref{frie}), (\ref{rayc}), (\ref%
{cons}) can be written as
\begin{eqnarray}
\dot{x} &=&-xH, \\
\dot{H} &=&-H^{2}-\frac{1}{6}\left( 3\gamma -2\right) \rho x^{-m}, \nonumber
\\
\dot{\rho} &=&-3\gamma \rho H-m\rho H+6knx^{2+m-2n}H, \nonumber
\end{eqnarray}%
subject to the constraint%
\begin{equation}
H^{2}+kx^{2-2n}=\frac{1}{3}\rho x^{-m}. \label{constr}
\end{equation}%
We use the constraint to eliminate $\rho ,$ and arrive at the
two-dimensional system
\begin{eqnarray}
\dot{x} &=&-xH, \nonumber \\
\dot{H} &=&-\frac{3\gamma }{2}H^{2}-\frac{\left( 3\gamma -2\right) }{2}%
kx^{2-2n}. \label{2-di}
\end{eqnarray}%
Note that from (\ref{constr}) the phase space of (\ref{2-di}) is the set
\begin{equation}
\left\{ \left( x,H\right) \in \mathbb{R}^{2}:x\geq 0,\
H^{2}+kx^{2-2n}>0.\right\} \newline
\label{phsp}
\end{equation}
This system is now in a form suitable for both a dynamical systems
analysis and an application of the method of asymptotic
splittings. Full details will be given elsewhere but we report
here on some partial results to give a flavor of the analysis.
Putting $x=\alpha \tau ^{p},\, H=\beta \tau ^{q}$ we find a
possible balance with $q=-1,p=-2/3\gamma $ and $\beta =2/3\gamma
=1,\alpha =\mathrm{arbitrary},$ acceptable for $n<0$. The
Kovalevskaya eigenvalues for this balance are at $-1,0,$
compatible with the arbitrariness of $\alpha .$
In the case where all terms are dominant, the vector field is
\[
\mathbf{f}^{(0)}=\left[
\begin{array}{c}
-xH \\
-\frac{3\gamma }{2}H^{2}-\left( \frac{3\gamma }{2}-1\right)
kx^{2-2n}
\end{array}
\right]
\]%
and we find the balance (disregarding the case $\alpha =0,\beta
=0,$)
\[
\left( q=-1,\ p=\frac{1}{n-1}\right) ,\ \ \left( \beta
=\frac{1}{1-n},\ \ \alpha ^{2-2n}=\frac{2-2n-3\gamma }{\left(
3\gamma -2\right) k\left( 1-n\right) ^{2}}\right),
\]
with K-exponents given by
\[
-1,\frac{2-2n-3\gamma}{1-n}.
\]
Note that if $n=-1/2$ and $\gamma=1$ (dust), or if $n=-1$ and
$\gamma=4/3$ (radiation) the second eigenvalue is equal to $0$.
We may proceed to analyze the system (\ref{2-di}) in phase space.
First, we write the system it as a single differential equation,
\begin{equation}
\frac{dH}{dx}=\frac{3\gamma H^{2}+\left( 3\gamma -2\right) kx^{2-2n}}{2xH},
\label{de}
\end{equation}
and we set $H^{2}=z$ to obtain a linear differential equation for
$z$ which is easily integrable. We find that (\ref{de}) has the
general solution
\begin{eqnarray}
H^{2} &=&\frac{\left( 3\gamma -2\right) k}{2-3\gamma -2n}x^{2-2n}+Cx^{3%
\gamma }\ \ \ \textrm{if\ \ }3\gamma +2n\neq 2, \label{gens} \\
H^{2} &=&\left( 3\gamma -2\right) k\,x^{3\gamma }\ln x+Cx^{3\gamma
}\ \ \ \textrm{if\ \ }3\gamma +2n=2, \nonumber
\end{eqnarray}%
where $C$ is a constant of integration. Suppose that $3\gamma +2n\neq 2.$ We
observe that the leading-order terms of the first decomposition, namely
\[
x=\alpha \tau ^{-2/3\gamma },\ \ \ H^{2}=\frac{4}{9\gamma
^{2}}\tau ^{-2},
\]%
reproduce the $Cx^{3\gamma }$ part of the solution (\ref{gens}). The
leading-order behavior of the last decomposition,
\[
x\sim \tau ^{1/\left( n-1\right) },\ \ \ H^{2}\sim \tau ^{-2},
\]%
recovers the $\frac{\left( 3\gamma -2\right) k}{2-3\gamma -2n}x^{2-2n}$ part
of the solution.
\begin{figure}[htb]
\begin{center}
\includegraphics{g43b.eps}
\end{center}
\caption{The phase portrait of (\protect\ref{2-di})}
\label{fig2}
\end{figure}
The integral curves of (\ref{gens}) allow us to sketch the phase
portrait of (\ref{2-di}). Let us assume for concreteness that
$n=-1,$ $\gamma=4/3$ (radiation). There are two cases to consider:
\begin{itemize}
\item Closed models. The phase space (see (\ref{phsp})) is the half-plane $%
x\geq 0.$ Equation (\ref{gens}) yields $H^{2}=-2x^{3}+Cx^{4},$
which implies that $C>0.$ Any orbit starting in the first quadrant
satisfies $x\geq 2/C,$ i.e., there are no solutions approaching
the origin. For $C>0,$ any orbit of (\ref{2-di}) starting in the
first quadrant crosses the $x-$axis at $2/C$ and remains in the
fourth quadrant. We conclude that any initially expanding closed
universe reaches maximum expansion at some finite time and then
recollapse begins, i.e. $H$ approaches $-\infty $ in a finite
time. The phase portrait is shown in Figure 2.
\item Open models. From (\ref{phsp}) we see that the phase space is the set $%
x\geq 0,\ H^{2}>x^{3}$. In the first quadrant this set is represented as the
area above the dashed line in Figure 2 B. Eq. (\ref{gens}) yields $%
H^{2}=+2x^{3}+Cx^{4},$ which implies that for $C>0$ any orbit
starting in the first quadrant asymptotically approaches the
origin. For $C<0,$ there are homoclinic curves connecting the
origin with itself. However, we must remember that the allowed
initial conditions for expanding universes lie above the dashed
line in Figure 2. It can be shown that these trajectories also
asymptotically approach $\left( 0,0\right) .$ We conclude that any
initially expanding open universe remains ever-expanding.
\end{itemize}
In all, we find that VSL cosmological models may share many
interesting dynamical characteristics not fully present in the
more conventional models so that a more detailed study of the
singularities in these universes is worthwhile as a future
challenge.
\section*{References}
| {
"redpajama_set_name": "RedPajamaArXiv"
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{"url":"https:\/\/stats.stackexchange.com\/questions\/317081\/regression-with-variables-that-are-dependent-off-another","text":"# Regression with variables that are dependent off another\n\nSay I am running a regression to predict race time in an upcoming race. For each runner, I have a demographic information and one past race performance. For some subset of runners, I have another race performance.\n\nMy model would therefore look like:\n\nFuture Race ~ Demographic Info + Past Race1 + Past Race2\n\n\nHowever, for many modelling packages in r, the regression simply drops incomplete data rows.\n\nI could present a simpler model of simply:\n\nFuture Race ~ Demographic Info + Past Race1\n\n\nThis seems to drop useful information. Are there modelling approaches to dealing with this incomplete data beyond simple deletion or imputation (generating random values from the distribution)?\n\n\u2022 Note that imputation need not generate random values: multiple imputation uses correlations with other independent variables (such as the demographic info) to generate meaningful guesses for the distribution of values, ultimately generating a number of bootstrap datasets. The variation across datasets captures the uncertainty in these correlations.\n\u2013\u00a0mkt\nDec 4, 2017 at 17:41\n\u2022 Possibly too simple to mention, but why not use (a) model including past race data for the subset for which it is available (b) model for other predictors only for the same subset (c) model for other predictors for all data. That is perhaps as complex as most researchers would want to be. It's hard to be optimistic about imputing past race performance from demographic data. Dec 4, 2017 at 18:25","date":"2022-08-14 17:56:23","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.1715092658996582, \"perplexity\": 2393.2708679072257}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-33\/segments\/1659882572063.65\/warc\/CC-MAIN-20220814173832-20220814203832-00534.warc.gz\"}"} | null | null |
DEDICATION
For Ana
You are going to do so many great things. And I can't wait to witness them.
And to the #TeamGarrick street team
I pretty much adore you all. And I hope the universe gifts you each with a gorgeous guy with a lovely accent.
CONTENTS
Dedication
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
An Excerpt from Finding It
Chapter 1
An Excerpt from Losing It
Chapter 1
An Excerpt from Faking It
Chapter 1
Chapter 2
About the Author
Books by Cora Carmack
Back Ads
Copyright
About the Publisher
Garrick
THE ALARM SOUNDED too early.
I smacked it into silence, and then reached for Bliss. I found only rumpled sheets and empty space. My eyelids felt like they'd been weighted down by sandbags, but I sat up and pried them open.
My voice was graveled with sleep when I called out, "Love? Where are you?" Something clanged in the kitchen in response. I sat up, fatigue wiped away by the realization that Bliss was up. And she was cooking.
That couldn't be a good sign.
I threw back the covers, and cool morning air assaulted my bare skin. I pulled on a pair of pajama bottoms and a T-shirt before padding down the hallway to the kitchen.
"Bliss?"
Another clang.
A muttered curse word.
Then I rounded the corner into a war zone.
Her wide eyes met mine. Her face, her hair, our tiny nook of a kitchen was covered in flour. Some kind of batter was smudged across her cheek and the countertops.
"Love?"
"I'm making pancakes." She said it the way one might say, "I didn't do it" when held at gunpoint by policemen. I cast my eyes down to keep from laughing, only to be devastated by the bare legs stretching out from the oversize T-shirt she wore. My T-shirt. Damn.
I'd loved her legs from the moment I'd first seen them while helping her with a burn she'd received on my motorcycle. They drove me to distraction just as much now as they did then.
I could have studied for hours the shape of her thighs and the way they flared out toward her hips. I could have been swept away by the feeling of possession that swelled in me at seeing her wear my clothing. There were dozens of things that I wanted to do in that moment, but an acrid smell tickled my nostrils, and a few tendrils of smoke began to creep around Bliss from the stove at her back. I lurched for the pan, where I found a blackening, misshapen lump of something. I pulled the pan off the stove, and heard a slight hitch in Bliss's breath behind me.
Another bad sign.
As quickly as I could, I tossed the "pancake" into the trash, and deposited the pan in the sink. I said, "Why don't we go out for breakfast?"
Bliss smiled, but it was one of those watery, wavering kinds of smiles that made every man want to run for the hills. I'd become well accustomed to Bliss's panic freak-outs. But crying . . . that was still a terrifyingly unfamiliar territory.
She collapsed into a nearby chair, and her head thumped down onto the table. I stood there, clenching and unclenching my fists, trying to decide on the best course of action. She turned her head to the side, pressing her cheek against the table, and looked at me. Her hair stuck up in every direction, her bottom lip suffered under her teeth, and the look in her eyes pulled at something in my chest. Like an itch at my heart. All I knew was that something was wrong, and I wanted to fix it. The how was the question.
I moved forward and knelt beside her chair. Red lined her eyes, and her skin was a shade paler than normal. I asked, "How long have you been awake?"
She shrugged. "Since around four. Maybe closer to three."
I sighed and ran a hand over her unruly hair.
"Bliss . . ."
"I read and did some laundry and cleaned the kitchen." She looked around. "It was clean. I swear."
I laughed and leaned up to press a kiss to her forehead. I pulled another chair around, and took a seat beside her. I laid my head down beside hers, but she closed her eyes and flipped her head around to face the other direction.
She said, "Don't look at me. I'm a mess."
I wasn't about to let her get away with that. I slipped an arm underneath her knees and tugged her into my lap. She whined my name, and then buried her head into my neck. I took hold of her jaw, and made her meet my gaze. It couldn't be a coincidence that this was happening on the day we were set to leave for London to meet my parents. She'd been remarkably calm about it until now. "Everything is going to be fine, love. I swear it."
"What if she hates me?"
That's what this was about. My mother. Bliss could barely handle her own overbearing mother; it seemed cruel that the universe had seen fit to give us two. But I was far more worried about what Bliss would think than what my mother would think. Bliss was honest and sweet and genuine, and my family . . . well, not so much.
I forced a smile and said, "Impossible."
"Garrick, I've overheard enough phone calls with your mother to know she's very . . . opinionated. I'd be stupid not to worry about what she'll think of me."
"You'd be stupid to think that anything my mother could say would matter." And it wouldn't matter to me. But it would matter to Bliss. Late at night when our apartment got quiet, the image of my mum as predator and Bliss as prey kept popping into my head. One week. We just had to survive one week. I stroked my thumb across her jaw and added, "I love you."
So much that it terrified me. And I didn't scare easy.
"I know . . . I just—"
"Want her to like you. I know. And she will." Please God, let my mother like her. "She'll like you because I love you. She might be a bit abrasive, but like any mother she wants me to be happy."
Or at least I hoped that was how she would see things.
Bliss's chin tipped up slightly, bringing her lips closer to mine. I felt her breath across my mouth, and my body reacted almost instantly. My spine straightened, and I became acutely aware of the bare legs draped across my lap. She said, "And you are? Happy?"
God, sometimes I just wanted to shake her. In many ways, she'd overcome the worst of her insecurities, but in moments of stress they seemed to all come rushing back. Rather than wasting my breath answering, I stood with her cradled in my arms, and headed for the hallway.
"What are you doing?" she asked.
I stopped for a moment to press a hard kiss to her mouth. Her fingers laced around my neck, but I pulled back before she could distract me from making my point. "I'm showing you how happy I am."
I nudged the bathroom door open, and leaned past the shower curtain. Bliss squealed and held tighter to my neck, as I turned the shower knobs with her still in my arms. She raised an eyebrow, a sly grin sneaking across her lips. "Our shower makes you happy?"
"You make me happy. The shower is just multitasking."
"How very responsible of you."
I kissed a smudge of pancake batter off her cheek, and smiled.
"Yes, that's the word."
I set her down on her feet, but her arms stayed tucked around my neck. When she smiled at me like that, I forgot all about the flour on her face or her wild bed head. That smile went straight through me and settled somewhere in my bones.
I kissed her on the forehead and said, "Let's get you cleaned up."
I found the hem of her oversize T-shirt, and began pulling it over her head. I'm not sure where the T-shirt ended up because when I realized she was wearing nothing underneath it, my vision narrowed to encompass only her.
God, she was gorgeous.
If you would have told me two years ago that I'd be getting married to a girl that I'd met just over a year ago, I would have called you mental. My romantic history was so horrendous, I'd never really thought of myself as the marrying type. Until her.
Bliss cleared her throat, and my eyes went back to her. To her mouth. Her chest. The small of her waist that seemed perfectly sculpted to fit in my hands.
She was the ultimate game changer. I hadn't known what it was like to meet a person so full of joy that just by being near her, I was elevated to a happier place. I'd never been with someone who was able to captivate every part of me—mind, body, and soul.
Body, of course, being my primary focus at the moment.
Her bottom lip stuck out, calling to me, and she said, "How long are you going to make me stand here naked while you're fully clothed?"
I took a seat on the toilet, and smiled cheekily up at her. I leaned back, laying one leg across my other knee, and said, "I could do this all day."
And I wasn't lying. I wanted to study her, to memorize her, to be able to close my eyes and see her perfectly as she was.
She rolled her eyes. "Yes, well, it might be a little awkward if I were to stay naked all day. Though it would make going through airport security much simpler."
I barked a laugh, and she added, "Wasn't your goal to distract me and make me less self-conscious? You're falling down on the job, Mr. Taylor."
Well, I couldn't have that, now could I?
I gripped her waist and pulled her forward until my chin brushed the skin just below her belly button. She shivered in my arms, and the reaction sent my blood screaming through my veins. I let my lips graze her just slightly and said, "You have nothing to be self-conscious about."
Her hands laced into my hair, and she looked down at me with glazed eyes. Firmer this time, I dragged my lips over her belly button and up to the valley made by her ribs. I tasted flour on her skin even here, and smothered a laugh.
Above me, she sighed and said, "You're back on track with that distracting thing."
Suddenly impatient, I stood and pulled my shirt over my head. I was rewarded with a breathy sigh and a bitten lip that made it incredibly hard not to be cocky. And not to take her right then.
She swallowed, drawing my eyes to her neck. God, I didn't know what it was about her neck, but it was constantly my undoing. I felt like a teenage boy, wanting to mark that pale, unblemished skin as mine again and again. I brushed a thumb over her pulse point, and she swallowed again, her eyes wide. I laced my fingers through her sleep-addled curls, and tilted her head back.
"How about now?" I asked.
If she was even half as distracted as I was, I'd say I'd done my job. Her eyes pulled away from my bare chest and she said, "Uh . . . what?"
I laughed, but the sound stuck in my throat when her slim fingers smoothed from my chest down to the waist of my pajama bottoms. Her fingers curled around the band, and I swallowed. Looking down, I could see the way her curves reached out toward my body, and I wanted nothing more that to seal our bodies together.
Before I completely lost my train of thought, I said, "No more worrying about my mother, right?"
For either of us.
She gave me a half-glazed glare.
I used one hand to pull her closer, and the other to cup her breast. Then I repeated, "No more worrying."
"Do you promise to do this every time I do worry?"
I gave a quick pinch to the tip of the breast in my hand. She flinched, and then moaned. Her eyes fluttered closed and her body swayed toward mine.
She breathed, "No worrying."
And I thought, Thank God.
Because I couldn't wait another second.
I crushed my lips against hers, wishing for the hundredth time that I could just permanently affix our mouths together. Every part of her tasted divine, but her mouth was my favorite. It was so easy to lose myself in kissing her, mostly because I could tell she was doing the same. Her body pressed against mine, and her fingernails dug into my shoulders like she was dangling off a cliff, and that was the only thing holding her up. The harder I kissed her, the harder her nails bit into my skin. I trailed a hand from her neck down the line of her spine, and her mouth broke away from mine. She shivered in my arms, her eyes closed.
I leaned my forehead against hers, and pulled her bare chest to mine. Between the shower steam and her skin, our tiny bathroom felt like a furnace. I never would have thought I could feel such peace while my heart hammered and my skin burned, but that's what she brought me. I'd always thought love was this complicated, messy, frankly ugly thing. Possibly because, growing up, I'd not had much of an example for what a relationship should be. I didn't know it could be any other way. But Bliss chased away the gray and made everything seem black and white. No matter the question, she was the answer.
She was my everything—the lungs that allowed me to breathe, the heart that had to beat, the eyes that let me see. She'd become a part of me, and all that was left was a piece of paper to tell the world we were as inseparable as I already felt we were.
It was just a piece of paper. The feeling mattered so much more, but a part of me sang with nervous energy demanding we make it official. Soon. It was the same part of me that worried about how Bliss would react to my family . . . to the way I grew up.
She stepped out of my arms, biting down on her already red and swollen bottom lip. Then she pulled back the shower curtain and stepped into the tub.
I hated the fear that chased the heels of my love for her.
Despite the fact that our relationship had begun in the most troubling and impossible situation—between teacher and student—things had been almost perfect since then. A rose-tinted world.
But it couldn't stay that way. Logic, reality, and a lifetime knowledge of my mother made me certain of that. The feeling always came out of nowhere. I'd be watching her, touching her, kissing her, and then suddenly, for one infinitesimal moment I'd feel like it was all about to come crashing down. Like we were balanced on a precipice, it felt inevitable that eventually we would fall. I didn't know how it would happen. Her insecurities. My stubbornness. The interfering hand of fate (or family). But for a few seconds, I could feel it coming.
Then always, she would pull me back. Those seconds of inevitability and uncertainty would dissolve in the sheer magnitude of my feelings for her. The doubt would be erased by the touch of a hand or the quirk of a smile, and I would feel like we could hold off that fall for forever and a day.
She did it again, peeking one last time around the shower curtain wearing nothing but a smile. I heard the water pattern change and knew she'd stepped under the stream of the shower. So I pushed my worries away in favor of a much more pleasant use of my time.
I kicked off the last of my clothing and joined her in the steam. We weren't in London yet, and I wasn't going to let fear steal another second of perfection from my grasp.
As long as we both kept pulling each other back, we'd make it. We'd keep our rose-tinted world.
Bliss
OUR MORNING IN the shower turned into a morning back in bed, and that miraculous man loved every ounce of stress from my body. Seriously. I think his tongue had some kind of special ability to melt my bones because I felt so relaxed that I was practically liquid. Just call me Alex Mack.
"That, Mr. Taylor, was a very good answer to my question."
His fingertips tickled the back of my knee and his mouth moved lazily across my shoulder. I shivered as he said, "What was the question again?" The hand on my knee trailed up the sensitive skin on the inside of my thigh. "I got distracted."
I swallowed.
We did distraction so well.
"I asked if you were happy."
His hand continued farther up until his touch made my back bow and my head fall back.
"Right. That was a stupid question."
I wanted to swat him, but I had an unsurprising lack of control over my limbs thanks to his very focused ministrations.
"It's not stupid," I squeezed out through clenched teeth. "I can't read your mind. Sometimes I just need to hear it."
He leaned over me, his hair mussed, but his eyes thoughtful. "And I'm bad at saying it."
"Only sometimes." Or sometimes I just needed to hear it more. I told myself that I was being stupid, but hating my insecurities didn't make them go away.
He shifted over me and settled into the crux of my thighs. Still sensitive from our last go, I whimpered when his body pressed into mine.
"In that case, you should know that every time I do this"—his hips shifted—"I am incredibly happy."
Somehow through all the sensation I managed to roll my eyes.
"We're talking about two different kinds of happiness."
He shook his head, and lowered his lips to my ear. "There's only one kind. Whether I'm inside you or lying beside you or touching your hair or listening to you laugh, it all means the same thing. If I'm with you, I'm happy."
God, he was good. At everything.
He hit a sensitive spot inside me, and the word good tumbled from my mouth by accident.
He chuckled darkly. "Are you grading me? I thought I was the teacher here."
I pulled his mouth to mine to shut him up, and then wrapped my legs around his waist.
"I'm not grading you. Your ego is big enough already."
He laughed and continued distracting me through the morning and a good portion of the afternoon.
It worked for a little while, okay maybe a long while. But when we boarded the flight late that night, no amount of flirting or touching or whispers in my ear could get my mind off the plethora of potential disasters that awaited me in London.
I knew almost nothing about his family. Except that his mother terrified me. She scared me by proxy, just based on the look on Garrick's face while he talked to her on the phone and the sound of her voice leaking from the speaker. When I saw her name on the caller ID, it was like seeing the Dark Mark hovering above my apartment.
What if she took one look at me and confirmed what I already knew to be true? Garrick was too good for me.
Don't get me wrong. I wasn't awash in self-pity about it because . . . hello, I got the guy. No complaints here. But that didn't mean I was too stupid to know that he could have someone prettier or taller or with less frizzy hair.
But he was with me. As long as I didn't screw it up, of course.
And God knows I was good at screwing things up.
So I sat in my seat on the plane as everyone else around me slept, including Garrick, and I drove myself crazy with worry.
If the weight of my stress were real, there was no way this plane could have stayed in the air. We'd start plummeting and spinning and then some brave soul would throw me out the side door for the good of everyone and scream, "Lighten up!" as I fell to my death.
That was another thing that could go wrong. I could fall to my death on the stairs at Garrick's house. Wait . . . did they have stairs? I should have made him detail it all for me. Maybe I should wake him up and ask him now about the stairs. And for a description of the entire house. And backgrounds on his parents and everyone he had ever met. Maybe he could just keep talking, so that I could stop listening to my own thoughts.
I started to reach for him, but then brought that same hand back to thump against my forehead.
Seriously, Bliss. Chill out.
That was my mantra for the rest of the trip. I repeated it in my head (and possibly out loud) as I pressed my forehead against the cool glass of the airplane window, and tried to get some sleep.
The mantra worked about as much as my attempts to sleep. Fitfully I moved between the window, the seatback tray, and Garrick's shoulder, trying to find a place to lean my head that didn't feel horrendously uncomfortable. I didn't get how I could sleep on Garrick's shoulder anytime at home, and now when it was my best option for slumber, it was like trying to rest my head on a pillow of glass shards covered in ants dusted with anthrax.
I'd switched back to the seatback tray, folding myself over onto it, when Garrick sat up and unbuckled his seat belt.
I woke him up.
Girlfriend Fail.
"I'm sorry," I whispered.
He reached between me and my current resting place, found the metal fastener of my seat belt, and clicked it open.
"What are you doing?" I asked.
He didn't even talk, just gestured with his hand for me to stand.
I fumbled to put up the tray and stand in the low space. My head craned to the side to fit under the overhead bins, and he pulled up the armrest and slid over into my spot. With his hands on my hips, he deposited me in his old seat, and then he turned toward me and leaned his back against the window. He opened his arms to me with a sleepy half smile, and I fell gratefully into his arms. With my head perched atop his chest, I sighed in relief.
"Better?" he asked, his voice raspy with sleep.
"Perfect."
His lips brushed my temple, and then sleep was almost as irresistible as he was.
I WOKE A few hours later to find light peeking through the plane windows. Two women were whispering quietly a few rows behind us in a familiar lilting accent. And it hit me. We were almost in London.
I was going to be in London.
God, all those months of seeing Kelsey's pictures and hearing about her travels, and I had been raging with jealousy. And now it was my turn.
I wanted to mind the gap at the tube station and eat fish and chips and try to make the Queen's guards laugh. I wanted to see Big Ben and the Globe and the London Bridge and Dame Judi Dench. Or Maggie Smith. Or Alan Rickman. Or Sir Ian McKellen. Or anybody famous and British, really.
Holy crap. This was really happening.
And I wasn't just a tourist. I was visiting with someone who'd grown up in the city. With my fiancé.
Take that, world.
"You look happier."
I pulled my head away from the window to find Garrick awake and staring at me. I gave a small squeal and launched myself at him. I locked our mouths together, and for a moment he sat still and shocked beneath me. Then his eyes closed, his hand cupped the back of my neck, and he kissed me so thoroughly that I almost forgot about London. Almost.
I broke away, grinning, and he said, "Not that I will ever complain about moments like that, but what's gotten into you? You waited a little late if your goal was to join the mile-high club."
I swatted his shoulder playfully, and then placed another quick kiss on his mouth because I couldn't resist. I said, "You're English."
He smiled and blinked a few times. "Yes. Yes, I am."
"And we're about to be in England."
He nodded slowly, and I knew I sounded crazy, but I didn't care.
"Yes. We've only been planning this visit for a month."
"I know . . . I just . . . it didn't hit me until now that we're in London. Or about to be, anyway. I've been worrying so much about your mother that I hadn't really thought about it. I'm going to London! Eeep!"
He chuckled, small and quiet, and brushed his fingers across my lips to quiet me. Right. People were sleeping. Then, like he couldn't contain it, he laughed louder, completely disregarding his own warning to be quiet.
"What's so funny?" I asked.
Slowly smothering his laughter, he used the hand hooked around my neck to pull my forehead against his. Our lips brushed just barely when he said, "You make me happy." I smiled my approval, and he added, "Marry me?"
My heart flip-flopped, like my unsuccessful pancakes from this morning were supposed to.
"You've already asked me that, and I already said yes."
"I know. It's unfair that I only get to ask you that once, though."
Melting. So much melting.
I reached up and brushed my fingertips along his jaw. He hadn't shaved in a few days, so the hair there was rough and masculine and unbelievably sexy. He closed his eyes and leaned into my hand the way that Hamlet did when anyone but me was playing with her. Stupid cat.
I said, "Yes. The answer will always be yes."
He took my hand from his jaw and brushed his lips across my knuckles. My insides went as gooey as the nearly congealed breakfast the flight attendants had passed out. He kissed the ring on my third finger, and who knew the engagement ring was an erogenous zone?
"I'm going to hold you to that. I know how much you love accents, and I'm going to have much more competition in that arena here."
I laughed. "I hadn't even thought of that! Just think, a whole country full of British men! I could—"
He tugged me forward and silenced me in my favorite way.
"That's not funny," he said. "It's bad enough that I'm about to have to share you with my family."
Ugh. I was going to ignore that whole family thing. I'd been enough of a Debbie Downer already to last the rest of the trip.
"Remember that time we met and you said you weren't the jealous type? Remember the time that was a big fat lie?"
Ah well. Jealousy looked really good on him.
"It wasn't a lie. I just hadn't ever met anyone worth getting jealous over until you."
I slid my arms around his waist. "Are all British men such smooth talkers?"
"No. Just me."
"And James Bond."
"Right. Of course."
"Fine. I guess since James is fictional, I'll have to keep you."
"You couldn't get rid of me if you tried."
"I'm not trying."
A flight attendant tapped me on the shoulder and asked us to please prepare for landing. I guessed what she really meant was to stop molesting my boyfriend in public.
God, airlines. Stingy with the peanuts and the fun.
I wasn't sorry, but I blushed anyway because that's the only thing my traitorous body was good for. I faced forward, but noticed a woman sitting across the aisle staring at us. She had her elbow on the armrest and her cheek propped up on her hand, gawking at us like we were her in-flight entertainment. My small blush spread like a wildfire across my whole face and down my neck.
Maybe we had been making a bit of a scene.
Garrick didn't seem to mind the attention, his chest bouncing with silent laughter. I flicked his arm, and tried to ignore the woman, who was still staring.
Garrick said again, "Marry me."
Oh, now he was just showing off.
I heard the woman aww next to us, and I swear to God I expected her to pull out a bag of popcorn or something.
I flicked his arm again, and he just laughed. I leaned my head back against the seat as the plane began to slow and dip, and I tried to get my blush under control.
Garrick stayed smug beside me as we landed and taxied to the gate. I was glad we were near the front of the plane, so that we could grab our things and get away from our audience. I pulled my purse from under the seat in front of me, and moved to flee.
"Wait," the woman said. "Aren't you going to answer him?"
Garrick chuckled and added, "Yes, aren't you going to answer me?"
My chin dropped, and I floundered like, well, a flounder.
He was really going to make me do this with that woman watching. And now that she'd said something, a few others were paying attention, too. I pressed my lips together, and glared at him. As an actor, I should be better at handling attention, but it was different when I was playing a part. I got to turn off my brain and think like someone else.
Reluctantly, I said, "Yes."
"What was that, love? I couldn't quite hear you."
Cue eye roll. "I said yes."
Garrick turned to the people surrounding us and practically yelled, "She said yes!"
Gradually, the cabin broke out into applause, and I threw him a look that was one part I'm-going-to-murder-you and three parts get-me-out-of-here-now-kthxbye.
Garrick soaked up the applause with a charming smile while I looked on, probably barely more attractive than a radish. I turned to flee and tripped over something. I couldn't actually see anything, but I swear there was something.
I power-walked off the plane and resisted the urge to run down the walkway and into the terminal. Garrick caught up to me just as I passed through the door, and looped an arm around my neck.
"You know I love it when you blush."
"And you know I hate it."
"It reminds me of your face the second time we met, that morning in my classroom. The most inappropriate time and place to ever be turned on, but you've got a take-no-prisoners kind of blush. My body didn't give me much of a choice."
He was only saying that to make me blush more. You would think that I'd be a bit more comfortable talking about sex, now that I'd had it and all. You would also think that at my age I would be able to successfully insert the straw into a Capri Sun juice pouch. I was 0–2 there.
So I let him enjoy my embarrassment. And I enjoyed the way his side was pressed against mine. Fair trade.
Garrick
I WAS STILL a bit bleary-eyed as we waited through the long line for immigration, then picked up our bags, and passed through customs. Bliss vaulted between exuberance and silence, more of the latter, as we got closer to our final destination.
Outside the airport, I tucked Bliss under my arm, needing to feel her, to feel some sort of control as her panic began to bleed into me. I was halfheartedly trying to flag down a taxi to take us to my parents' place in Kensington when I heard someone shout, "Taylor! Garrick Taylor! Look over here, you prat!"
Bliss had already stopped and was staring at two idiots down the pavement, yelling and waving their arms. The first idiot had dark skin and a buzzed head that had been covered in dreads the last time I'd seen him. That would be Rowland. And paired with the second idiot, Graham, who looked enough like me to pass for my brother (a scam we'd used more than once when we were kids), they meant trouble.
I passed a hand through my hair and smiled. "Bloody hell."
What in the world were they doing here?
"Friends of yours?" Bliss asked.
"Very old friends."
Bliss and I turned around our luggage and barely made it a few meters before Rowland was tackling me.
"Ricky!" he yelled, messing with my hair.
I heard Bliss say, "Ricky?" over my shoulder before I shoved Rowland off. Glaring, I said, "That nickname wasn't okay in secondary, and it isn't okay now."
Graham said, "Oh, come on, brother. At least let him have a little fun. You've not visited in ages. Though I can see why."
I didn't have to look to know he was staring at Bliss. Not only did Graham and I look alike—tall, blond hair, blue eyes—but we had the same taste in women. I had mostly been joking with her earlier about finding another guy, but now it wasn't so funny. I shook my head at him and pulled her closer to me.
"Bliss, these two gits are my old mates, Rowland and Graham. We came up together. And this is my fiancée, Bliss."
God, it felt good saying that.
"Her name is Bliss? Or is that your nickname for her because she's really good in—"
"Rowland," I warned.
He shrugged and shot Bliss a cheeky smile. She was grinning at both of them, her cheeks a brilliant red. And as good as it was to see them, I was not even remotely keen on sharing her.
I asked, "What are you lot doing here?"
Rowland said, "We phoned your dad and told him to tell your mum that your flight had been delayed by a few hours."
"Why would you do that?"
Graham grinned in Bliss's direction and said, "Because we wanted to meet your girl . . . before your mum tore her to pieces."
I saw the blood drain from her face, and she went from red to white in seconds. Well, there went the last of her calm.
"Garrick!" Her hand connected with my arm, and then again with my chest.
Throwing a glare at Graham, I caught her hands and pulled her close.
"He's joking, love. It's all going to be fine."
Please let it be fine.
"Or after a few pints with us, it will be, anyway," Rowland cut in.
"It's the middle of the day," I said.
Rowland shrugged. "We'll make sure there's some food had somewhere in there."
Bliss had her arms crossed over her chest, glaring at me. She looked so bloody hot when she was angry that I almost didn't mind.
I said, "Thank you both for coming. And for managing to piss my future bride off in record time. But it was a long flight. I should probably just get Bliss home."
When I reached, her hand flitted out of my range and then came back to poke me in the chest. "Oh no you don't, Mr. Taylor." I heard Rowland laugh behind me. She continued, "You are not depriving me of the chance to gather some much needed liquid courage or to question your friends."
Graham whistled. "I like this one."
That much was uncomfortably clear.
I met her eyes, and she wasn't backing down. I pressed my lips together into a thin line, but her eyebrows just rose in answer.
"Fine. Okay." I turned to my old friends and added, "One drink. With food. One hour. That's it." They held up innocent hands in surrender, and started leading us down the pavement.
Over his shoulder, Graham said, "Damn, Taylor. Did teaching suck all the fun out of you?"
"Something got sucked while he was teaching."
I shoved Rowland from behind, and he launched forward several feet, cackling.
"What?" Bliss asked. "What did he say?"
"Nothing. Just being a prick."
Rowland kept his distance as he led us to the same old Peugeot he'd been driving the last time I'd lived in London nearly eight years ago. It was funny how little some things and some people changed.
I'd changed . . . that much was for sure. In turns, I'd been just as elitist and judgmental as my parents or I'd rebelled and battled that with tremendous levels of stupidity and trouble. It was only in the last two years that I'd started to feel like I'd finally found a reasonable middle ground. I could only pray to find something similar today with my parents. I could only pray that this whole trip wouldn't blow up in my face.
I helped Bliss into the backseat, and then turned to Graham before sliding in after her. He didn't just look like a brother to me; he'd felt like one for most of my life, too. And when I left this city, I'd left that friendship, too. I'd only just recently reached out to him to reconnect.
I said, "It's really good to see you, mate. Sorry that I've done a botch job of keeping in touch."
He clapped me on the back and shook his head. "Don't worry about it. I get why you stayed away. And things seemed to have worked themselves out just fine." I peeked into the car, where Bliss was smiling and listening to some no doubt filthy story that Rowland was telling her from the driver's seat. I smiled. "Yeah, things have worked out perfectly."
I climbed into the backseat and pulled Bliss over to meet me in the middle. My old mates might have been troublemakers of the highest order, but they did have one thing going for them; Bliss was the most relaxed I'd seen her in the last week.
Maybe it was a good idea to just let loose for a little while. We both needed it.
I brought her head close to mine, pressing my nose into her curls as she laughed at the ridiculous voice Rowland was doing in imitation of his mother. Her warmth, her scent calmed me. And she made me see London in a new light. She made me see it how it was before my parents and all their pressure and manipulation had made me want to leave.
Again and again, Bliss seemed to be my new beginning, the thing to help me let go of the past and move forward.
She rested a hand on my thigh and looked up at me. I must have been tuned out for longer than I realized because she asked, "You okay?"
I laid my hand over hers and said, "Just glad to be home and to have you with me."
She turned her hand over and laced her fingers with mine, and Rowland made gagging noises in the front seat.
"Oh shut it, Row. You're just jealous because you haven't yet managed to hold on to a woman for more than one night."
"Managed? Managed? I should win an award for that. It's harder than you think."
Bliss snuggled into my side and asked, "So how long have you known Garrick?"
Rowland answered, "I've only known him since secondary."
"High school," I translated for Bliss.
"But Graham and Garrick have been attached at the hip since they were in nappies."
"Diapers," I added.
"Hey, she gets the gist of it. No need to translate every bleeding thing I say. I'm speaking English."
"So what you're saying," Bliss began, leaning forward between the two front seats, "is that Graham is the one to go to for the embarrassing stories?"
"Excuse me." I poked her in the side, and she squirmed away from me.
"Oh come on. Like you don't know enough embarrassing things about me. You've been there for too many of them."
"Do tell," Rowland said, his eyebrows waggling at us through the rearview mirror.
"Don't. You. Dare." It was her turn to poke me.
"Wait." Graham turned in his seat to face us. "Are you talking about being all hot for teacher?"
"Garrick!" I had a feeling I was going to be hearing my name in that tone all too often on this trip. "You told them?"
"I told Graham. Since Rowland doesn't seem too surprised, I'm guessing he's been filled in."
Bliss bent and buried her face in her hands. "Oh my God, I'm so embarrassed."
"Why would you be embarrassed?" Rowland asked. "You can't get much hotter than a schoolgirl fantasy. After Graham told me, I had dreams for a week featuring girls in our old school uniforms."
Bliss gave a garbled groan and sank even further until her face rested against her knees. I was still learning the intricacies of speaking Bliss, but I was fairly certain that groan meant that she thought she was dying of mortification.
I leveled a stare at him and said, "Thanks a lot, mate."
Then I ran a hand across the curve of Bliss's back and said, "There's no reason to be embarrassed, because we didn't do anything wrong. I don't ever want to have to lie about us again."
Call it an issue. Call it baggage. But I really hated lies. They're ugly things, festering like wounds, spreading like disease. They're winner-less crimes that hurt everybody in the end.
I felt her back rise and fall in a heaving breath beneath my hand. "You're right." She sat up, and I kept my hand between her and the seat. "I'm not sorry, and I'm done being scared of it."
"Thatta girl," Rowland said.
"That's my girl," I said into her ear.
"You hold on to that thick skin, sweetheart. Let Graham and I treat you to a few pints and you'll have armor by the time you're standing in the Taylors' grand foyer."
"You have a grand foyer?" She paled.
I scratched at my neck and said, "It's really only slightly grand."
"What about stairs? Do you have stairs?"
I nodded.
She threw her hands up. "That's it. I'm gonna die. I knew it."
I saw Rowland and Graham glance at each other in confusion, then look at me. I shook my head because I had no idea. Maybe I could be a bit lenient about that one-drink rule.
"I don't know what you're talking about, but you're not going to die. It's just a house. Nothing to worry about."
It really was just a house. I'd not ever really thought of it as a home.
She took a breath and nodded. Sitting up taller, she gave me a determined look.
Stairs. Cats. I loved the woman, but God knows I didn't always understand her. She was so afraid of little things—mothers and fancy houses—but when she set her mind to something, she tackled it with such ferocity. Big things. Scary things.
Her career in Philly. Life after college. Falling in love with me.
I was the one that struggled with the big picture. I never quite knew what I wanted until it had already slapped me around a bit.
Or until she walked into my life with an imaginary cat.
"SHE DOESN'T NEED another one, Rowland. She's good."
We were both good. If I drank any more, I wouldn't have a filter by the time we met my parents, which was a bit like not having a life raft on the Titanic.
"Oh, come on. What's the point of working in a pub if I can't get my friends completely sloshed?"
There was something terribly wrong about being in a near-empty pub midday and having as much alcohol as we had.
"I don't know . . . gainful employment? Saving up to finally stop living with your parents?"
"Ssh!" He waved a forceful hand at me, like the two people in a booth across the bar were going to hear.
"First of all, that was cold, mate. And second, I have my own flat. It just happens to be above my parents' garage. That doesn't count as living with my parents."
"Whatever helps you sleep at night, Row."
"Just for that . . ." He poured another glass and slid it in Bliss's direction.
I snatched it away as she reached for it, and pulled it away from her.
"Hey!" Her bottom lip curled into a pout. An almost irresistible pout.
"Sweetheart, I think you're fine without it."
She teetered toward me on her stool, wrapping a hand around my neck. Her fingers tangled in the hair at the base of my neck and she said, "Well, if I can't have it, you should drink it."
Rowland cut in, "Now, that is a plan. Maybe another drink will make you less of a bore."
"I'm not boring."
Graham gave a loud snore, pretending to sleep with his head balanced on the top of his mug.
Bliss laughed raucously, and the only thing that kept her from toppling off her seat was my hand at her waist. Graham's eyes opened, and he winked at her before giving another overdramatic snore.
That did it.
I took hold of Bliss's stool and dragged it over right next to mine. She squealed and fell into me. I tried to not to look too obviously annoyed at Graham as I draped my arm over her shoulder and took a swig of beer.
Rowland cheered, Bliss hummed against the skin of my neck, and I told myself one drink wouldn't hurt.
Famous last words.
Bliss
"OKAY, NOW WE'RE really done," Garrick said, his voice deep and hypnotic.
I didn't want to be done. This was so much more fun than meeting his parents. I rested my chin on his shoulder and said, "Just one more."
He glanced down at me and said, "Trust me, love. You're going to want to stop now. Otherwise you'll be making up songs and talking about how good I smell and getting inappropriately touchy."
I laid my cheek down on his shoulder and slipped my fingers just below the collar of his shirt. "I thought you liked it when I was inappropriately touchy."
Garrick stilled my hand at his neck and said, "Not when we're about to meet my mother."
Oh God. His mother. It shouldn't be funny, but I found myself laughing anyway. I had to laugh . . . or I might cry. I know he said that Rowland and Graham were joking, but I was fairly certain he was just trying to keep me from running.
Rowland said, "Your mum will understand. The two of you are practically on a honeymoon already. It's pretty nauseating."
Graham added, "Of course she'll understand. I mean, she's your mom. It's not like she hasn't had sex before."
Oh God. Now I was going to laugh and cry.
Graham leaned around me to look at Garrick, whose face was scrunched up in possibly the only unattractive expression I had ever seen on his face. Taunting Garrick further, he said, "I bet your parents are doing it right now. Sneaking in a quick shag while your flight is 'delayed.' "
Garrick slid off his stool. "And . . . that's our cue to call it a night."
"And call a therapist." Graham smiled.
"And get coffee," I added. Definitely coffee.
Garrick stood behind me, and his warm hands gripped my shoulders. I leaned back and tilted my head until my head rested against his stomach, and I was looking at him upside down. I blinked. Or I meant to, anyway. Instead, my eyes stayed closed, and the dark swirled with color, and I had the sensation that I was tumbling down a long black hole. I peeled my lids open, and then had to squint against the light of the bar. Between being upside down and being two drinks past the point of caring, the world was horrendously disoriented. "I think . . ." I looked up at Garrick. "That I drank too much."
Garrick nodded, and if his heavy-lidded eyes were any indication, he wasn't exactly sober, either. Or he was turned on. Or both . . . hopefully.
He said, "I think I'm friends with a couple pricks."
Graham stood, leaving his half-empty beer on the bar. "Take it easy on the mushy stuff, Taylor. We know how much you love us. No need to make a spectacle."
"Let's just get out of here," Garrick said.
I agreed by looping my arms around his waist and laying my head against his chest.
Rowland said, "At least she's relaxed now. I did you a favor."
I was gloriously relaxed, in fact. And I figured . . . maybe we could stretch out this fake plane delay for a little longer, get a little time on our own in the city before I had to walk the plank. I slid my hands down to the leather belt that wrapped around his hips, and lifted up on my tiptoes. Humming, I found the warm crux where the muscles of his shoulder flowed into his neck. This was the perfect part of him. When I took a deep breath, I could almost imagine we were alone, and I was surrounded by him.
Garrick cleared his throat. "Maybe a little too relaxed."
I opened my lips and tasted perfection, too. A small noise of satisfaction rolled from my lips, and somewhere behind me I heard, "Rowland really did do you a favor."
Gently, Garrick pushed me down until my feet were flat on the ground, and I could no longer reach his neck.
He held up his middle finger toward his friends. Graham raised his eyebrows, and Garrick seemed to realize we weren't in the States anymore. He blinked and shook his head, and then added a second finger. It looked like a backward peace sign, but I knew it didn't mean that. Not here.
Graham shook his head. "Damn it. The Americans got to you."
Garrick flipped him off with two fingers again, this time with a bit more conviction. I watched on, only vaguely aware of what was happening, until the both of them burst into laughter.
I rolled my eyes.
Men.
Garrick kept a tight hold on my hand as we left the pub, and then we headed back to the car we'd arrived in. Garrick lowered me into the backseat first, and then climbed in after me.
I neglected the seat belt in favor of wrapping myself around Garrick. I found that spot on his neck again and sighed. "You really do smell so good."
He laughed. "You always say that, especially when you've been drinking."
That's because it was true. I'd never really gotten scent as a turn-on. When I'd bought cologne for previous boyfriends, it kind of all smelled the same to me. I usually made someone in the store pick for me. But with Garrick . . . God, I just wanted to be surrounded by his smell all the time. If I couldn't be near him, I wanted to wear his clothes or sleep on his side of the bed.
I was a creeper. I could accept that.
Maybe it was the alcohol or being in a foreign city or the fact that this was the first time we'd really been out drinking together since the night we met; Whatever it was, I wanted him, so bad that my skin itched to touch his. I fiddled with one of the buttons on his shirt, trying to act as innocent as possible. And then ever so slowly, I slipped his top button open. His head didn't move, so I went for a second button.
Apparently one button was my stealth limit because he totally caught me. I smiled up at him as sweetly as I could and slid my fingers under his shirt to the bare skin of his chest. His chin dipped, and he stared at me in warning, but he didn't stop me. I trailed my fingers across his collarbone and from his shoulder back down to his chest. He watched me with dark eyes, and the arm draped over the seat behind me came down around me. His fingertips slid under my shirt to curve over my shoulder.
Shifting, I faced him, leaning my other shoulder against the seat and draping my legs over his lap. Immediately, his other hand curved around my calf.
I might be clueless about a lot of things, but I knew my fiancé. He was definitely a leg man.
Between his touch and the alcohol, I felt light-headed.
That might have been mostly the alcohol, considering how heavy my head felt and the way the world in my peripheral vision kept swooping and spinning. His fingertips found the back of my knee, and I giggled at his touch.
"Aw, man." Rowland said from the front. "You two are like a bunch of randy teenagers."
I felt like a teenager. I hadn't been this drunk in ages. I was too busy working and working and then working some more.
Being an adult blows.
I tilted my head up to Garrick and said, "I can't feel my lips."
"Here, let me check." His mouth slanted over mine, his tongue dipping between my lips, tangling with mine. He tasted like beer and himself, and I realized that he'd had almost as much to drink as me. He pulled back. "Nope, they're still there."
He grinned playfully, and that was when I knew he'd had plenty to drink. Laughing, I hooked my arms around his neck, and lay back against the seat cushion, pulling him with me.
"Hey, hey now!" Rowland called. "No sex while I'm driving. That's a public hazard."
Garrick's lips ran down my neck, and I couldn't seem to make myself stop giggling. I called back to Rowland, "So pull over."
"Are you seriously going to have sex in my car? Because that's hot. Can she be on top?"
Garrick said, "Eyes on the road, Rowland! No one is having sex."
I frowned, and he kissed my puckered bottom lip. He muttered, "You are a public hazard."
Graham leaned around his seat to look at us. "You two don't need coffee. You need a fucking tranquilizer."
Groaning, Garrick's hands slipped off my body to brace against the seat. He pushed himself back into a sitting position, and I whined at the distance.
Whined. I would have been embarrassed if I wasn't so turned on.
He clenched his fists and tilted his head back against the seat.
Of all the times for him to practice restraint. I was going to burn up in my skin here.
Staring up at the ceiling, he spoke, his voice strained. "Sorry about that."
"Sorry?" I asked. "Who's sorry?"
"I'm not!" Rowland said.
I trailed my fingers over his arm. "I'm sorry you stopped."
Garrick glared at Rowland in the rearview mirror until his eyes focused back on the road. Then he turned to me and pointed at his friend. "That's why I'm sorry."
Somewhere in my body, I was fairly certain I still had a brain. And it had probably been shouting at me for a while. But my hormones must have had fucking megaphones because that's all I could hear. I sat up, my arms and legs shaky with pent-up need. My shirt was twisted, and you could see the blue lace of my bra and the swell of my chest peeking out from the neckline of my shirt. I adjusted it quickly, glancing to see if Rowland or Graham had seen, but luckily they were still looking ahead. My eyes skipped to Garrick's dark gaze. Yeah, he definitely hadn't missed it.
A bolt of electricity shot through me, and I pressed my thighs together, trying to relieve something, anything. Garrick leaned over and his lips brushed my ear. So not helping the situation. As I tried to keep from squirming, he said, "As much as I'm dying to have you right now, you're mine. And I don't share."
I swallowed, and squeezed my legs tighter. This was somehow the worst and best moment of my life. In fact, most of our relationship fell into those categories. Best boyfriend. Worst embarrassing moment. Best kiss. Worst excuse ever. Best (well . . . only) sex. Worst timing. But I could take all the worsts, if the best always followed.
His nose brushed my jaw and his breath fanned across my neck, and I swear my body shook in response. You would think with the morning he'd spent distracting me before our flight, I wouldn't be so desperate for him now, but I was always desperate for him.
Plus, even though we lived together, I never saw him enough. Between plays and the additional jobs it took to pay our rent in Center City, it felt like we were always on the go. I couldn't remember the last time we'd gone out for a night together, at least not when we hadn't just finished a show and weren't exhausted.
All those years of making up excuses not to have sex, and now I was busy trying to think of an excuse to ditch his friends and his parents and keep him all to myself.
His lips brushed against my ear again, and I dropped a hand to his thigh and squeezed. I wasn't sure whether I was signaling him to stop or to give me more; I just knew I was dying from his proximity alone. A low rumble spilled from his throat, and I glanced up front to make sure his friends weren't watching. They weren't, so I took a chance and slid my hand a little higher.
I didn't get but an inch before his hand clamped down on mine. Against my ear, he growled, "You really are a hazard to my health." I just squeezed his leg again, and leaned my head to offer him more of my neck. He nipped my skin there and then whispered, "We're going to meet my parents. We'll smile and talk long enough that they feel like they've met you, then we're finding a place to be alone. My bedroom, the bathroom, the kitchen, I don't care where. The only thing I care about is fucking you so hard you can't see straight."
Annnd . . . aneurysm.
The air fled my lungs like I'd been punched in the chest, and I blushed so hard I felt like my blood was boiling. Seriously. It had turned so hot in this backseat, I was going to have a freaking heatstroke. And I had to bite down hard on my lip to keep in the string of unintelligible noises building on my tongue.
Garrick and I had sex. Often. Good sex. But in the spectrum of intercourse (oh God, only my brain would think spectrum of intercourse at a time like this), we made love. It was intense and sweet and perfect. I don't know if it was the alcohol or my actions that pushed him to the other side of the spectrum, but I knew I was wound tight enough that another minute of him whispering in my ear could probably send me over the edge. That was probably why my arms and legs felt like Jell-O when we stood in front of his parents' door, and he rang the bell. Though I'm sure the alcohol and the stress and the traveling didn't help.
"This is going to be okay, right?" I asked. "You can't tell I'm drunk, right?"
And would his parents be able to tell that I'd just been dying to screw their son in the backseat of a car like a high school prom date? That I was still dying to?
I could picture it now.
Hi Mom and Dad, this is my girlfriend—
HARLOT!
Then they would make me sew a red A on all of my clothing, and I did not look good in red, what with all the blushing. Plus I'd barely passed my costuming class in college. Needles and me don't mix.
A hand came down on my shoulder, and I jumped. Rowland smiled, "You're good, Bliss. You're going to be a smash. Just wait."
Right. I was going to be fine.
Garrick rang the doorbell a second time, and when no one answered, Graham said, "Told you they were shagging."
Throwing a glare over his shoulder, Garrick took a deep breath and squared his shoulders. I stared, and for the first time realized that he was as nervous as I was. Oh hell, if he was nervous I was doomed. My odds were looking about as good as a main character in Game of Thrones.
He turned the knob. It gave way in his hand, and the door swung open to reveal a darkened entryway. My footsteps echoed as we stepped inside.
"That's strange," he said, his voice echoing, too.
Did this mean we could just go straight to his bedroom? Because oh my yes, thank you.
The open door let in just enough late afternoon light to reveal a strip of empty . . . well, foyer. Never thought I would have the need to actually use that word in real life. The windows were covered by heavy curtains, draping the rest of the place in darkness. I reached for the wall beside the door, running my hands along it looking for a switch.
I wasn't sure which of my many issues to blame when my forearm collided with something cool and smooth and vase-shaped, knocking it sideways. When I tried to catch it and missed, I was blaming my sex-distracted thoughts. When I heard it crash and shatter against the floor, I was blaming the alcohol. When the light flipped on revealing a seriously grand foyer, a large group of people streaming into the entryway holding champagne flutes, and an elegant and terrifying woman that could only be Garrick's mother staring in horror . . . well, that's when I knew it wasn't any of those things.
It was just me . . . failing at life again.
Behind me, Rowland broke the silence with a tentative "Surprise?"
No . . . me being a disaster of awkward proportions was the least surprising thing ever. I'd made a smash all right. Like I was the Hulk's cousin.
Bliss SMASH.
Garrick
THE CRASH OF the vase echoed through the foyer for several seconds afterward, and each reverberation seemed to cause my mother's expression to contort further.
I'd always thought I was fairly good at thinking on my feet and reacting in a crisis (and looking at my mother, this definitely counted as a crisis). For the life of me though, I couldn't think of a single thing to say. Maybe I was out of practice or maybe there still wasn't enough blood flowing through my brain, but either way only one word was going through my mind.
Fuck.
And not the kind I'd had in mind.
Luckily, my father, ever the composed businessman, covered for us all.
"Well . . . wasn't that quite the entrance?"
The crowd laughed, and I could almost feel the heat of Bliss's blush from here. The entire downstairs was brimming with what seemed like every person I had ever met, and plenty that I hadn't. And I hadn't the foggiest clue about what they were doing here.
Dad crossed to Bliss, and she looked queasy enough to pass out. He was immaculate in a dark suit that contrasted with his silvering hair. He picked up her hand and kissed the back of it. Her eyes flicked to mine, surprised.
Dad said, his voice loud enough for everyone to hear, "Don't you worry about it for one second, sweetheart. I'm sure at some point in his life Garrick had already broken that old thing and glued it back together."
Mum would have flayed me. She loved that vase. But the people laughed, and the room collectively sighed in relief. Dad was good at that kind of stuff. He could charm any conference room, any party, any seminar. It was the one-on-one things he couldn't do.
Dad helped Bliss step over the glass shards, and that made me spring into action. We crossed to each other, but Dad stayed in between us. Still holding one of her hands, he clapped me on the shoulder and looked out at the crowd.
"Well, we wanted a surprise engagement party, and we certainly got a surprise." Everyone laughed again. Dad squeezed my shoulder and said, "You all know my son, Garrick." I spotted a few business types in the crowd—salt and pepper hair, pristine suits, impeccable ties. I sure as hell didn't know them. Mixing business with family as always.
"He graduated at the top of his class, and his mother and I were ready for him to go to Oxford like all the other Taylor men." Here we go. Time for the not-so-sly insults about how I'd ruined our family legacy. "But children have to make their own way, or they'll only pretend to grow up. I'm proud to look at him and see the man he has become."
I tried not to gape. My mother and I spoke often enough, but I couldn't even recall the last time Dad and I had actually spoken. He'd been furious when I left, and certain that I'd ruined my life. Was it possible that my parents had done some changing of their own? This new leaf threw me off balance, and suddenly all I could think about was the scent of beer on my breath and how disheveled I probably looked. "He left us to make his own way and moved to America, where he's already managed to become a university professor at his young age."
Okay, so his storytelling was a bit selective considering I was no longer a professor. But it was a compliment nonetheless.
"He's become a fine man and has now brought home this lovely, unpredictable young woman to join our family." He turned to Bliss, holding up her hand. "We're so happy to have you here, Bliss." Then he turned out to the crowd. "We're happy to have all of you here to celebrate their engagement with us. Please, eat, drink, enjoy yourselves. Though perhaps keep an eye on the decor." He winked, and Bliss laughed, completely charmed.
He presented her hand to me as people around the house clapped, and then without actually saying a private word to either of us, retreated to a group of men in suits.
I wanted to punch myself. People laughed and aww'd at his performance, and I'd been sucked in just like the rest of them. Like I was sixteen all over again, I churned with rage and wanted to storm out of the door.
So much for that new leaf.
He'd thrown this stupid party to impress people, and he'd made it a surprise so that I couldn't object. Just once I would love to see my father try to do something important without an audience.
I schooled my face into a blank expression, and then concentrated on Bliss. I placed a kiss on her temple. She hugged me, and against my chest, I heard her say, "Kill me. Just put me out of my misery, please."
"And leave me to be miserable without you? Never."
"So selfish."
"When it comes to you? Absolutely." Already I wanted to just take her away, to just be the two of us again. I sighed and looked around. Some people were staying in the foyer, others were streaming into other parts of the house, laughing and drinking, and grabbing hors d'oeuvres from passing waiters.
I said, "I guess our odds of finding somewhere to be alone just got significantly smaller."
She looked up at me and frowned. She looked so disappointed that my stomach clenched with desire all over again.
Just a few hours. This thing couldn't last forever.
"I'm so sorry about the vase. And for making such a scene." Her face scrunched up like she was going to cry, and my method of dealing with her tears yesterday morning probably wasn't going to fly in this room full of people. I smoothed a hand over her hair and said the only thing I could.
"Marry me?"
Her eyes turned sad.
"Garrick, not now."
My heart twisted. It was another one of those moments. "Yes, now, love. Marry me."
"Still? You know I'm just going to keep breaking things."
"And you know I'm just going to keep loving you anyway." Her frown twitched, and I added, "Besides . . . not marrying you would break me."
The frown softened, and she blinked away the film of tears in her eyes. "Me too."
"It's settled then. You're stuck with me forever."
She shook her head and made a noise that sounded like disbelief.
My biggest fear was that someday she would talk herself out of our relationship. That she would shake her head and listen more to her own poisonous thoughts than the words coming out of my mouth.
I kissed her cheek and whispered in her ear, "We are forever. If you don't believe me, I'll have to make you. As soon as we find that place to be alone."
I only got a faint pink in her cheeks as she looked down at her feet, but I'd take it. After a second, she tipped her head back and groaned, a sound that went straight through me.
She said, "I'm wearing jeans."
I nodded. I loved those jeans. They fit her perfectly.
"And by the looks of it, I'm in a room filled with people in designer dresses. And you're crazy if you think this foyer is only slightly grand. There's a freaking chandelier."
"Luckily that can't be knocked over." Mum's voice was like whiskey, it came off smooth, but ended with a burn.
"Mum." It was halfway between a greeting and a warning.
"Hi sweetheart." She leaned up and kissed my cheek before turning to Bliss.
"Mum, this is Bliss. Bliss, my mother."
She smiled. "What a name."
Bliss knotted her fingers together. "Um . . . thank you?"
Mum's smile was all red lips, white teeth, and sugared kindness. It was the razor-sharp tongue behind those teeth that I was worried about.
"Mrs. Taylor," Bliss began. "I am so sorry about the vase. I don't even know how to begin apologizing."
"Then don't." God, my mother's voice should be listed on WebMD as a cause of frostbite. "It was just an accident after all."
"I am so very sorry though. And so thankful that you've welcomed me into your home. It's so nice to meet you. And I'm just so, so happy to be here."
"So you are. And we're happy that our Garrick has come home. And brought you along, of course."
"Yes, I'm so happy to be here."
"You've already said that much." She turned to me then. "She's very sweet, Garrick. Is it just the clumsiness she's overcompensating for? Or something worse?"
And so it began.
I laughed like she was joking. Because that's how you have to handle my mother. She wants a reaction, and humor is the safest one. I kept laughing, and after a few moments, Bliss's uneasy laugh joined mine.
I changed the subject before Mum could point out that she wasn't, in fact, joking.
"Was this party your idea, Mother?"
She gave me a look before rolling her eyes toward Dad. "Your father wanted to make sure you and your fiancée had the best welcome possible."
Read: He wanted to take advantage of the opportunity to show off. The "best welcome" was just the company line. And though my mother certainly had her issues, I loved her for not even pretending to go along with it.
"Right. Thanks for that."
She gave a single, solitary chuckle and took a long drink from her champagne. Mum hated events like this. I suppose that was at least one thing that she and Bliss had in common.
I saw Bliss fidgeting with her shirt and shifting her feet.
"Mum, would you excuse us for a moment? Since we had no warning, we're not quite dressed for a party. We'll get changed and then come back down."
"Of course, dear. That's definitely a good idea. Just casual party attire will do fine."
As we turned to grab our luggage, Bliss said, "In what world is this casual?"
My world, unfortunately. Or my old one anyway.
I took her bag for her, and said, "We're upstairs. I'm right behind you."
I didn't have to tell her twice. At the speed she went, I'm sure she was tempted to take it two stairs at a time.
I directed her toward my old room. She breezed through the door, and didn't stop until she had thrown herself facedown on the bed with a groan.
"I'm never going back out there. I'll climb out the window."
I parked our luggage just inside the room, and then shut the door behind me. I took a seat beside her and laid a hand on her back. "Look on the bright side, we've got some alone time after all."
She rolled over, putting herself farther away from me.
"Sorry, but I'm not exactly in the mood anymore."
I winced.
"Bliss, I—"
She pushed herself up and off the bed and began pacing. "Why couldn't you just tell me that she was going to hate me? Why tell me again and again that I was worrying over nothing when I clearly wasn't?"
"I didn't want you to worry. I thought things would go smoother if you were calm."
"Have you met me? Smooth is not an option I come with. If you're looking for smooth, maybe you should look elsewhere."
Mid-pace, I caught her by the elbows and made her face me.
"Don't do that. Don't push me away."
She covered her hands with her hands and took a deep breath. "I'm sorry. I didn't mean that. I just . . . I didn't expect it to be like this."
"What does that mean?"
She shook her head, and dropped her hands to look up at the ceiling instead. "Nothing. It's . . . nothing."
She pulled away and went to her suitcase. She went to put it up on the bed, took a long look at the white bedding, and then laid it on the floor.
"Bliss, talk to me."
"Do you think this is okay? It's the best I have." She stood, pulling a simple blue cotton dress from her bag.
"Bliss, you can wear whatever you want down there. I only said we were going to change to give us a break."
"Right. Maybe I can find some decent jewelry. Just give me a couple minutes." She took the dress and a few other items, and disappeared into the bathroom. The door closed behind her with a click, and it was my turn to throw myself back on my bed.
I stared up at the ceiling and cursed under my breath.
Maybe my fears were warranted after all.
Bliss
THIS WAS A joke. A massively unfunny joke.
I'd fixed my hair, retouched my makeup, donned my best outfit, thrown on my best jewelry, and I was fairly certain that their toilet bowl scrubber still cost more than my entire outfit.
Why hadn't he told me?
I got that he didn't talk about his family much. They clearly weren't close. God knows I didn't talk about mine much, either, except to complain. But you'd think he could have just taken half a second to drop a quick "By the way, my family is loaded" into conversation.
If I was worried that Mrs. Taylor might think I wasn't good enough for her son before, it was pretty much a solidified fact now.
I didn't fit here. At all. Not even almost. One of these things is really not like the others.
And to make matters worse, Garrick looked perfect when I exited the bathroom. He'd donned a button-up shirt and tie to go with his khaki pants, and he looked effortless. Unlike me, he fit.
And a small, niggling voice in my mind asked how it was possible then that we fitted together? I shook my head to clear my thoughts, and Garrick crossed the room to place a kiss on my forehead.
"You look lovely."
I smiled, but I didn't feel it. "Thanks. So do you."
"Everything is going to be fine."
He'd said that so many times that it didn't mean anything anymore. Like when you say a word too much and it stops sounding like itself and feels alien and foreign in your head.
"Let's go then," I said.
His hands cupped my jaw, and he leaned in for a kiss. I tilted my head back away from him.
"You'll get lipstick on you."
"I don't care, love. The only thing I care about right now in this entire house is you."
My resolve melted, and he brushed a feather-light kiss across my lips, somehow coming out lipstick-free. He laced our fingers together and planted another kiss on the back of my hand.
I wanted the gesture to be comforting, but it only made me more unsettled. It only made me wonder more what he could possibly see in me.
Together, we descended the stairs back into the jungle of champagne flutes and designer handbags and outfits that put mine to shame. It was a forest of self-esteem issues waiting to happen, and I was smack-dab in the middle of it.
We'd barely made it two feet past the base of the stairs before we were intercepted by a group of people.
"Garrick! So good to see you!"
He let go of my hand to greet a guy about Garrick's age. He had dark hair, combed perfectly, and wore a suit. Again, I say, in what world is a suit casual?
"John, it's good to see you, too. This is my fiancée, Bliss."
John turned to the side and a woman stepped up beside him. She, too, had dark hair, fixed into a perfect bun at the nape of her neck. I concentrated on not touching my out-of-control curls in response.
"Lovely to meet you, Bliss. This is my wife, Amy."
I smiled. "It's nice to meet you."
God, this was repetitive.
She laughed. "Oh no, the pleasure is all mine."
I was probably supposed to say something more, but all that came to mind was insisting that the pleasure was actually mine, like a freaking tug of war. But that would have been a lie anyway, so I just stayed silent.
After a few painful seconds, Garrick added, "John and I went to school together."
John nodded, his smile plastic. "I loved your father's reminder that you were first in our class. Still can't get away from coming in second even all these years later."
Garrick laughed, and I could tell he was uncomfortable by the stiffness of his hand when he laced our fingers together again. But you would never know it from his face.
Maybe that's what I needed to do to get through this. I needed to act. I needed to turn off Bliss and become someone else, someone who fit in this place and knew what to say and what not to say. If I became that someone else, I could separate my thoughts from my own worries and maybe get through this night intact. The stage was the only place I ever really felt confident, and I could use a bit of confidence at the moment. So that's what I did. I played a part.
"So John," I asked. "What have you been doing since the last time you and Garrick saw each other? Catch us up."
"Well"—he kissed the back of Amy's hand—"I got married. Beat you on that front, at least." God, this guy was a prick. No wonder Garrick was so stiff. "I'm now working as a software designer."
"A software designer? That's interesting. I bet that's challenging."
"Oh, not really. It's a bit boring really. Though I'm sure in comparison to what Taylor over here is doing these days, it probably looks like brain surgery."
I laughed, thinking with each little chuckle how satisfying it would be to punch him in the face.
"Well, some of us are blessed to have careers that we love and are simple because we love them. Others get jobs that are, what did you say? Boring? But maybe someday you'll grow to love it."
Garrick lowered his head and gave a cough that was suspiciously laugh-like and said, "It's was nice chatting with you John, Amy. But we should probably make the rounds. Lots of people to see."
Once he'd led me a few feet away, his shoulders began to bounce in laughter.
He said, "I realize I'm being redundant now, but I just can't help it. Marry me?"
"You're going to make me wear out the word yes."
"Nah. I'm saving that goal for our wedding night."
Miraculously, I managed to keep my blush to a minimum. I had a pretty tight rein on my reactions at the moment.
He walked me through the rest of the room talking to more old classmates, friends of the family, and neighbors. They were old, young, male, female, and I held my own. I wasn't quite as charming as Garrick. That wasn't humanly possible for me. Or most people, really. But I did okay. I watched people's expressions change as they talked to me. They went from wary or amused (probably due to my entrance) to smiling and accepting.
I took a deep breath, and felt proud.
Garrick brushed a kiss against my cheek, and said, "You're doing wonderfully. See? Nothing to worry about."
I smiled, but there was a sour taste on my tongue. It was a good thing . . . that I could force myself to fit here in his life. I just wished I hadn't had to be someone else to do it.
Almost as if she could sense my vulnerability, his mother made her reappearance then. She kissed Garrick's cheek, and surveyed his outfit. "Better. Much better."
She glanced briefly at my dress, but didn't say anything.
"Everything going okay? I saw you talking to Mrs. Everheart. Is she well?"
"When is she not well?" Garrick asked. "How old is she now, a century?"
Ah. I nodded, remembering who they were talking about now.
His mom shrugged. "Who knows? I wouldn't be surprised if she outlasted me just to spite all those grabby children of hers, dying for her inheritance."
I took a deep breath, and tried not to let it show how disgusting I found this whole thing. That old woman, Margaret was her name, had been so sweet. She reminded me of Cade's grandma, and the time he'd introduced us during college. She was kind, but you could definitely tell she was a firecracker underneath. That her own children would just see her as dollar signs was terrible. And that Garrick's mum and even Garrick didn't seem appalled by it . . . that was even worse.
Mrs. Taylor turned her eyes on me then, and said coolly, "So, Bliss, tell me about yourself?"
Not such a difficult question. But did I answer genuinely? Or did I tell her what she wanted to hear?
Garrick
BLISS HESITATED, THEN opened her mouth to speak. But she was interrupted by a bellowing voice calling my name.
"Garrick! Son!"
We both turned to look. My father called my name a second time. He waved me over and said, "Come here for a second."
I sighed.
"Just go," Mum said. "You know he won't let it go until you do."
"He's just going to drag me into some conversation about business. I don't want to subject myself to that, and I certainly don't want to subject Bliss to that."
"So leave her with me."
I tried not to look too alarmed by that. "Oh no, Mum. That's okay. Bliss and I would rather stay together, since it is our engagement party."
"Nonsense. I'm sure Bliss could use a break from you anyway. If you're anything like your father, you're nauseatingly cheerful." That might be one of the nicer things I'd ever heard her say about him. "Besides, if you're only giving me a week with my future daughter-in-law, I'm going to need all the time I can get with her."
She spoke like a trainer trying to break in a horse, or an interrogator trying to break a witness. And from the look on Bliss's face, you'd think she was going to be waterboarded instead of subjected to conversation with my mother.
I stared into Bliss's wide eyes. I didn't want to leave her alone with my mother, but she had been holding her own since we came downstairs. And Mum had on her business smile, and I knew I wasn't going to win this one. Truthfully, there was no arguing with either of my parents. If my dad wanted me to go talk to him, I would have to. And if Mum wanted Bliss to stay with her, she'd get her way. That's why I hadn't bothered with telling them when I decided to leave London. God knows we'd spent enough time arguing about a thousand other things. Like a pendulum swing, the more I grew up, the farther I swung from my parents' beliefs and habits in every respect. So I'd waited to tell them I was leaving until I was already in the States and called from a pay phone.
My last year before uni, life just started moving so fast. Things were unraveling quicker than I could take hold of them, and it felt like trying to stop a boulder from rolling down a hill. My life was falling into these predetermined paths, and it didn't even really feel like I was living as much as reacting. I hated it, but I didn't know how to stop it, other than to leave. Clean slate.
My father called my name again, and I sighed. "Fine. But I'm not spending all night talking to clients or business prospects or whoever he's playing tonight.
"I'll be quick," I promised Bliss. Her expression was blank, and I couldn't tell now how she was feeling, but her frequently flushed skin looked a wee bit pale. I kissed her forehead, and then did the same to my mother.
"Be nice," I murmured.
Mum gave a single, solitary chuckle. That was either a very good or a very bad sign.
Two minutes. I'll be back in two minutes.
I gave Bliss one more parting kiss, and then feeling like the worst fiancé ever, I left her to fend off her shark while I faced mine.
Already eager for the conversation to be over, I stepped up to my father's group and said, "Yes, Dad?"
"Oh, good. Garrick, you remember Mr. Woods. You did that summer internship at his firm."
Advertising, I think? Honestly, I couldn't remember. Dad pushed me into so many internships, they all ran together.
"Of course, Mr. Woods. It's nice to see you again."
Mr. Woods was old, in his sixties or seventies maybe. He wore large glasses and his hair was a pale white. His smile made all the wrinkles around his mouth more pronounced, and his skin was worn and wrinkled like old leather as I shook his hand.
"And you as well. That's a lovely fiancée you have there."
I smiled. "Thank you. I love her very much, and she keeps my life interesting."
He barked a laugh, his wrinkles almost disappearing for a second as he did.
"You're just as spirited as I remember you. Your father has been filling me in on your life in the States. Quite impressive."
I resisted the urge to roll my eyes. My father had no doubt embellished to the point that I'd probably become the youngest tenured professor at Harvard or some other nonsense.
I shrugged. "I wouldn't say it was all that impressive."
"Not easily satisfied. I like that. You'll be outdoing your father in no time, I'm sure."
Dad laughed and hooked an arm around my neck like we were wrestling, "Not without a fight he won't."
It was all so staged, so forced. And I couldn't tell if everyone else felt it, or if they were so accustomed to it that they didn't even notice it anymore.
The men and women gathered around us laughed, and I followed out of habit.
Eight years.
It had been over eight years since I'd moved away, and in less than an hour, I was already getting pulled back into the lifestyle I hated. Fancy parties, nice things, expensive clothes, all covered by a layer of fake so thick that it choked out every real emotion.
It had to have been two minutes by now. And even that felt like two minutes too many.
"It was so nice seeing you again, Mr. Woods, but I should get back to my fiancée." I nodded at the rest of the people in the group and said, "Ladies. Gentlemen."
"Just one second before you run off, Garrick."
I stopped short, and tried not to look aggravated.
"Yes, Mr. Woods?"
Gradually, the others around us began to break off until it was just my old boss and my father.
"I wanted to talk to you about a job opening—"
Jesus. Not even a decent night's sleep before it started.
"Oh, sir, I—"
"Now hear me out. I have a PR position open, the same division where you did your internship actually. And I've been through half a dozen men in the last three years for this position. They're all smart enough, but they're just missing that special quality that attracts people, that makes clients feel at ease. They're not like you or your father." I tried not to bristle at being compared to my father and the quality I despised most in him. "I remember you doing fantastic work in your internship. And by the sound of what your father has told me, you're quick to adapt and learn." He pulled out a business card from his pocket and held it out to me. "Just think about it. Give me a call, and we'll talk it all through. It doesn't hurt to just consider it."
I looked at the card, but didn't take it.
"That's very kind, Mr. Woods. But Bliss and I have no plans to move to London." I directed my last few words to my father, as firmly as I could without seeming angry.
For the first time, my dad cut in and said, "Maybe it's something you should think about, Garrick. It's a good job."
I'm sure it was a fine job. But it wasn't a coincidence that this interest was coming now with my father watching on. He was a puppeteer pulling strings, but I'd cut mine a long time ago.
Mr. Woods added, "If it makes a difference, I'm sure it would be a significant step-up in pay from teaching, and we'd cover your relocation."
If it were a significant step-up from teaching, it would be about three or four steps up from what I was doing now. It had been difficult segueing back into part-time work and small contracts from my comfortable job at the university. But we were making it.
I took the card just to end the ambush and said, "I'll think about it. But I really am happy where I'm at."
I could feel my father's stare, but I didn't meet his gaze.
I nodded at Mr. Woods. "It was nice seeing you again. Thank you for coming. Enjoy the party."
Then I turned, and stuffed the card into my pocket. I made it just a few feet before my father stopped me for our first private conversation of the night. In years, really.
"I know what you're thinking, Garrick, but you should give this job a fair shot."
"I have a job, Dad." Several, actually.
"But this is a job that could really lead somewhere. If you keep doing what you're doing, you'll be forty and working at a restaurant to make ends meet. These kinds of opportunities won't be around then."
"Thanks for the confidence, Dad."
"Don't give me that. You're an adult. You don't need me in the stands cheering you on and lying to you. You're about to have a wife, a new life. What you need is to grow up and get a real job. Something with real benefits."
Oh, the irony of him lecturing me on what was real.
"Thanks for the talk, Dad. But I need to go find Bliss and Mum."
I maneuvered around him and left before he could drag me back into the argument. I was halfway across the room before I really looked around.
Bliss wasn't where I'd left her. And neither was my mother.
Bliss
GOD, HIS MOM should have been a lawyer instead of working in finance. Just her stare was like a fishing hook, luring all my secrets out of me. And I was the poor fish, dangling on the line, a rusty piece of metal tearing me open. An hour alone with her on the stand, and I would be in the fetal position, reciting the traumas of my childhood, like that time Jimmy pantsed me at the top of the slide during recess in third grade.
"And have you two set a date yet?"
I almost asked her if she would prefer to choose for us.
"Well . . . we're not set on anything yet. But we were thinking maybe June. Or August."
"Of next year? Oh, that could definitely work."
"This year, actually . . . ma'am."
"This year? But that's only a couple months from now."
"I know, but we weren't thinking of anything big. Just a small ceremony for close friends and family."
"But you won't have even been engaged for a year at that point."
This was one thing I wouldn't submit to her on. There was no way in hell that I was waiting over a year to get married. Garrick and I had had enough waiting for a lifetime.
"Yes, but we've been together over a year."
"No, you—" His mother stopped, her brows furrowed and one finger in the air. "Wait, you've been together over a year?"
I nodded, and then immediately wished I hadn't. Her eyes narrowed, and she fixed me with a look that was more sledgehammer than fishhook.
"I was under the impression that the two of you met in Philadelphia. But Garrick would have been teaching in Texas a year ago."
I swallowed. God, please don't tell me that Garrick hadn't told them about how we'd met. After he told Graham and his big speech about not lying or being ashamed, I had just assumed that he'd told them, the basics anyway.
Based on the calculating look on his mother's face, I was going to say that was a big, fat no. "So the two of you met in Texas?"
I tried to say yes, but really I just made noises and nodded.
"How old are you, Bliss?"
I could have narcolepsy! That would get me out of this question, right? I could just pretend to pass out. Or maybe I could really pass out?
My non-answer must have been enough to confirm things for her because she spun on her heel and started in Garrick's direction.
I darted around her and held my hands up.
"Mrs. Taylor, wait. We didn't do anything wrong. I promise."
"Oh, sweetheart." Her smile gave me chills. "I don't think you did anything wrong."
"You don't?" I was shocked into silence.
"No, dear. My son is the one who has done something wrong."
I flinched back like she'd slapped me. I had enough doubts about Garrick being with me in my head, all of which seemed to have compounded in the hours since we'd arrived. I didn't need her adding any more to that. I stood up taller, and in my plain clearance dress, I faced off against her immaculate, no doubt heinously expensive cocktail dress.
"With all due respect, Mrs. Taylor. You're wrong. Your son loves me. And I love him. We're both adults, as we were when we met. If you make a big deal out of this now, you'll only ruin this party and possibly the already unstable relationship you have with your son. He's twenty-six, almost twenty-seven years old. He has a career and a fiancée, and you're not going to win any battles by treating him like he's a kid again. He's an adult," I reiterated, though that was another word that had been said and thought so many times it was beginning to lose its meaning. "We both are. How we met doesn't matter."
Her red lips flattened into a line, and her gaze felt sharp enough to slice bread. She made this sound in her throat, not quite a laugh, more like a noise of surprise. "You have a head on your shoulders after all."
Hey there, backhanded compliment. We've been seeing a lot of each other.
She was the one missing vital organs . . . like a heart. She stared at me for a few moments longer, and then smoothly turned her back to where Garrick was standing.
"Two questions, Bliss."
Did I really just talk her down? Holy crap.
"Yes, ma'am."
She clicked her nails together and looked away from me as she asked, "Would you like to have lunch on Thursday?"
I was so shocked, I nearly choked on my saliva, which would have totally ruined the whole head-on-your-shoulders moment from a few seconds ago.
I forced myself not to say, "Um," and continued, "Yes. Lunch. I would like that."
"Fantastic. And the last thing. You want to get married soon?"
"Yes, ma'am, we do."
"Are you pregnant?"
I blanched and said firmly, "No. Absolutely not. I'm not . . . we're not . . ."
I stopped. Full stop. Screeching-tires-stopped. I resisted the urge to reach for my day planner. I didn't have it anyway. I'd left it back in Philly. But I have a vague recollection of jotting down a note to get my birth control prescription refilled.
How long ago had that been? I'd been finishing up that run of Peter Pan and we were doing the maximum number of shows a week because it was selling so well. Things had been so busy, and . . . damn it.
"I—"
I closed my gaping mouth and gave her a tight smile. I shook my head and said, "No. Nothing like that."
Shit. Why was my memory such a blur? This is what happened when you worked multiple jobs with no consistency, and you did the same shows day in and day out. It became really fucking hard to distinguish one day from another.
Mrs. Taylor said, "Okay then. I'll let you get back to my son."
I nodded, already a thousand miles away.
"And Bliss?"
I lifted my head and met her cool gaze again.
"No more breaking things, okay?"
"Right." I gave a pained laugh. "Of course."
She walked away, her heels clicking against the marble floor, and I should have felt relieved to see her go. I should have been glad when Graham and Rowland came over to check on me, but I wasn't either of those things.
Because if I was remembering correctly, I was late.
And I was going to be sick.
"DIDN'T REALIZE YOU were that pissed. You must be a real lightweight."
Rowland and Graham were waiting when I got out of the bathroom, and I didn't know whether I wanted to find Garrick or avoid him, whether I wanted to scream or cry or throw up some more.
"I just . . . I need to sit down for a bit."
"We'll go in the sitting room," Graham said.
Damn it. This place would have a fucking sitting room. My parents were proud of their newly remodeled bathroom, and this place was practically a palace.
And the room was even nicer in real life than in my imagination. It was much more chic than the Pride and Prejudice–era room I had pictured. And there were people milling around, standing near the floor-to-ceiling windows and luxurious curtains. I found an empty cream-colored chaise lounge and collapsed onto it, too distressed to even worry about getting it dirty.
I could be remembering wrong. I hoped I was remembering wrong. But the last time I could recall being on my period had been that final week in Peter Pan. It's why I forgot about the pill pack because we weren't exactly in danger of getting pregnant then. And that was . . . what? Six weeks ago? Maybe five? Either way, it was more than a month. But sometimes people were late without being pregnant. That happened . . . right?
I could totally be jumping to conclusions.
Or there could be something growing inside of me.
God, that sounded so sci-fi movie.
What did I know about being a mom? What did I know about anything? I was a total mess. I couldn't even do my own taxes, or survive an engagement party, or turn on a fucking light without breaking something. And I was supposed to grow and raise another human being?
My child would be so socially inept that it wouldn't even be able to walk upright or speak in complete sentences or be around other people.
I would give birth to a hermit child.
Breathe. Breathe.
Damn it. That reminded me too much of Lamaze, and I felt sick again.
What if it turned out like Hamlet the devil cat and it hated me?
Shit. Shit.
I really just wanted to shout that word at the top of my lungs, but probably not the time and place.
"Is she okay?"
I opened my eyes to see a tall blonde, whose legs put mine to shame. She wore a short, black sheath dress with kick-ass turquoise heels, and there was basically a model standing over me as I panted and tried not to lose the remaining contents of my stomach.
Thanks, world. I appreciate it so much.
"Now is not a good time, Kayleigh," Graham said.
"Did something happen? They didn't break up, did they?"
Why did she sound hopeful?
Rowland spoke before I could, "No, she's just not feeling well. We'll find you later, Kayleigh."
"Oh, okay. Well, feel better."
I hated when people said that. Like I could just magically make that happen. Or like I didn't already want that desperately. But gee, thanks for the recommendation.
When she was gone, I looked at Rowland. "Who was that?"
He looked at Graham, and maybe some of Mrs. Taylor's perceptiveness rubbed off on me because I just had a feeling. "Is she an ex?"
"Ehh . . . umm . . . uhhh . . ."
This day could stop getting worse at any time. Any time now. Really.
"Why would his parents invite an ex to this?"
"Well, Kayleigh is a friend of the family. But we're guessing that Eileen, Garrick's mum, was keen on causing some problems because . . . well, Kayleigh's not the only one."
"Seriously? How many?"
Rowland looked at Graham again, and I was on the verge of strangling him. If I was pregnant, I could just blame it on the hormones. Call it temporary insanity.
"How many, Rowland?"
He scratched at his head. "Well, it's not like I've counted."
"Guess."
"Man, did Eileen give you some of her super powers?"
"Rowland," I snapped.
"I don't know, ten."
"Ten?"
Garrick had ten ex-girlfriends here.
Garrick had ten ex-girlfriends before he'd even gone to college?
And that was just the ones who'd showed up here. No telling how many more there were.
Hey, Universe? Think you could take a break on the whole raining-down-shit-on-Bliss thing? I'd appreciate it.
I stood to go back to the bathroom when Garrick stepped into the room. "There you are. I was a little worried my mother had killed you and was hiding the body."
I didn't laugh.
"Are you okay?" he asked.
I started to nod when Graham answered, "She's feeling sick. And she might have just met Kayleigh. And Rowland has a big mouth."
"Jesus."
He reached a tentative hand out to touch my shoulder.
"On a scale of one to ten, how angry are you?"
I pressed a hand to my temple, where a dull throb was beginning to form, and said, "Tired."
Rowland said, "Oh, well that's good."
I heard a thwack that I guessed was Graham smacking him upside the head.
Garrick laced our fingers together, and kissed the back of my hand. "Come on. We can go ahead and go to bed for the night. It's a bit early, but we can blame the jet lag. No one will miss us."
Only the ten ex-girlfriends here to get him back. Yeah, I was totally good with going to bed early.
I said good-bye to Rowland and Graham, and wished Rowland luck at landing one of the exes. Then I let Garrick lead me out of the sitting room, and toward the staircase that wound up from the dining room.
His mother intercepted us just before we got to the stairs. "Where are you two going?"
"Bliss isn't feeling well. And we're both still adjusting to the schedule. We're going to retire early. I think we've seen the majority of the people you care about us seeing."
I didn't look her in the eye, scared she would be able to read my mind with her freaky Slytherin stare.
"Oh, that's too bad. I have the guest room all set up for her."
Garrick tightened his grip on our luggage, and maneuvered around his mother and onto the first couple steps.
"That's not going to happen, Mum. Her luggage is already upstairs, and we're not accustomed to sleeping apart." I blanched. If he said that to my parents, he would be staring down a shotgun. "We'll be in my room."
I let myself glance at his mother. She took a deep breath, and then her eyes met mine. Despite feeling miserable, I squared my shoulders and raised my eyebrows in a look that I hoped said, I told you so.
As long as it didn't say, I totally lied to you and might actually be pregnant after all.
I followed Garrick up the stairs, still trying to wrap my head around this evening. Should I tell him? What if I was just remembering wrong? I didn't want to freak him out over nothing.
I should just wait. I'd keep thinking back. Maybe I'd forgotten something or was remembering the days wrong. Or I could go buy a test.
Yes. That's what I should do . . . to be certain.
I was so eager to brush my teeth that I didn't even say anything to Garrick before I retreated into the adjoining bathroom. And maybe I would just check one more time to make sure I hadn't started in the last ten minutes.
Garrick knocked on the door a few minutes later, and who would have ever thought I'd be willing my period to start?
His voice was soft, tentative. "Are you okay, love?"
"Yeah. I'm okay. I'll be out in just a second."
I took a deep breath.
There was no reason to panic yet. I'd told Eileen that I was an adult, and it felt good to stand up to her. To say that and actually mean it. It was especially important that I act like one now. Because if I was . . . if we were pregnant, there was a lot more at stake than a visit to meet the parents and a stupid broken vase.
So tomorrow I would get a pregnancy test. People did that all the time. And it came back negative all the time. Tonight I just needed to put it out of my mind and get some rest. I would only make myself sick again worrying about it.
The bathroom door squeaked as it opened, and Garrick turned from where he was changing clothes. He was just sliding a pair of pajama pants up over his hips, and if that wasn't the perfect way to clear my thoughts, I didn't know what was.
Garrick
BLISS STOOD FRAMED in the bathroom door, and I was at a loss for how to act. I had no idea how things had gone with my mum or afterward. All I knew was that she was quiet. Too quiet. And as much as I didn't want her to be feeling ill, I hoped that that's all it was about.
"How are you feeling?"
She crossed her arms over her stomach and said, "Okay. I think it was just . . . a long day. And it got to me. I'm fine now."
"And my mother?"
"Should be a Disney villain."
I exhaled a laugh. Even sick and stressed she was . . . remarkable.
"But that was okay, too?"
After a torturous moment, she nodded. "I think so. We came to an understanding." That sounded ominous. "She invited me to lunch the day after tomorrow."
My eyebrows shot up.
"That means it went more than okay. It went well."
A small smile blossomed across her face. What was that science theory? Every action has an equal and opposite reaction? Seeing her smile lightened me. She anchored my thoughts, recentered my focus, balanced my life. And I needed that . . . desperately. Being back here . . . it was strange. I was struggling to walk that line between being polite and friendly, and falling back into my old ways.
"Now about these exes . . ."
Speaking of old ways.
"Exes?"
"Oh yes. Rowland estimated there were about ten in attendance."
Goddamn it, Rowland.
I closed my eyes to resist the urge to go downstairs and mangle him.
"I'm sure he was exaggerating."
The arms crossed over her stomach raised to cross over her chest, and she looked so deliciously bossy. Couldn't we just skip this part and get on to what we'd planned earlier?
"Do you have that many exes here in London?"
I wracked my brain for a way that this conversation wouldn't be disastrous.
"I don't know that exes is the right word."
"So they weren't all relationships? What . . . just sex?"
I grimaced. Guess we were cutting to the chase then. I didn't so much like this bold side of her when it was directed at me.
"Bliss . . . I was a right prick when I lived here. You would have hated me. My parents were not so good at the parenting aspect of life. They gave me money and a long leash, and like a stupid teenage boy, I took advantage of it. Often. Things are so beyond different now that that feels like a different life. A different person. And it was, really. When I left London, it was a rude awakening to live life outside this bubble of money and influence and tradition. But it was good for me. I grew up. I found something I really love, which led to finding someone I really love. If there were girls from my past here tonight, I didn't notice them. They don't matter. Nothing about this place matters at all in comparison to you."
She chewed on her bottom lip for a moment, surveying me. There was just a hint of a tear shining in the corner of her eyes, then she closed her eyes and shook her head. "It's impossible to be mad at you. This is setting a dangerous precedent for our relationship."
That was a good sign.
I stepped forward and settled my hands on her hips. "I like that precedent."
Her hands came up to my chest. "I know where you get it from. Your charm. Your father joins you and James Bond as a smooth-talking Englishman. He was really nice about the vase thing."
I groaned. "He is a smooth talker, yes. But don't let him fool you. He's not nearly as nice as he pretends to be."
She traced her fingers along my jaw and pulled my face down toward her. "What does that mean?"
I shook my head. "Nothing you need to worry about. We just have different priorities is all. Business and money and class always come first to him." I laced my fingers at the back of her neck and grazed her jaw with my thumbs. "I may have inherited some things from him, but not that. You will always come first. Our family will always be my primary concern."
Her eyes were wide and glassy, and I didn't know if that look was because of something I said, or just the long day getting to her again.
She said, "It's funny how children end up being so different from their parents."
"It's funny how we managed to grow into reasonable people despite our crazy parents."
She swallowed and laughed once. "Right. How does that happen?"
I pulled her into my arms, laying my cheek against her head. Her hair smelled sweet and calming, like lavender.
"Let's go out tomorrow. I'll show you around the city. I just need a break from this house."
"Sure. That sounds great. I need to run to the store anyway. I forgot a few things."
I kissed her forehead. "Like what? We might have whatever it is."
She pulled back. "Oh, it's nothing important. Just some little things."
She went to her suitcase on the floor and bent to gather her pajamas.
I stepped up behind her. "You sure you're not feeling sick anymore?"
"No, I'm fine," she called over her shoulder. "I just had a moment, that's all."
"Good." I swept an arm under her legs and pulled her up into my arms. "Because I'm pretty awake. But I've got an idea of how to tire myself out."
She dropped the clothes she'd picked up to clutch my shoulders, and her pretty little mouth formed a circle. That was all it took. No matter that there were hundreds of people downstairs, and we were in my parents' house. I wanted her as badly as I ever had.
I walked her toward the bed and she said, "Garrick! The people downstairs."
"Won't hear a thing unless you plan on screaming my name. In which case, it might be worth it."
She swatted my shoulder, and I deposited her on the bed.
"What if your mother comes upstairs?"
I knelt at the foot of the bed and slipped off her shoes.
"Then we'll have another awkward occurrence to add to our repertoire."
"That's not even remotely funny, Garrick."
I kissed the inside of her knee and said, "Do you see me laughing?"
She swallowed, and her eyes followed my hands as I reached for her. Her cotton dress was stretchy, and I slipped the straps down over her shoulders easily. It fell around her waist, revealing more skin to me. She wore a lacy blue bra that looked sweet and innocent, and damn if that kind of thing didn't always do me in.
"Do you have any idea how hot it is to think of having you here in my old room?" She shook her head, but her tongue darted out to wet her lips, and I think she knew exactly what I meant. "It reminds me of last year." How much it had fucked with my brain to think of her as a student, and how very little it did to deter my feelings for her. If anything, I wanted her more. "Every class I was so tempted to ask you to stay after everyone left. Even though your friends were outside and anyone could have walked in, all I wanted to do was touch you. Taste you."
Her eyes were large and dark, and her breath hitched. I kissed the side of her knee again and ran my hands up her thighs to the hem of her dress.
She asked, "Why didn't you?"
"Because that wouldn't have been fair of me. So I had to settle for my imagination."
Thank God I didn't have to do that anymore.
"And what did you imagine?"
I leaned over her and laid her back against the bed. Her arms stretched out across the mattress, and she looked up at me with wide, apprehensive eyes. It reminded me so much of the night we met, and all my blood rushed south so quickly that black spots dotted my vision.
I slipped my hands under her dress and said, "I imagined a lot of things. I thought about having you against the wall back behind the curtains." She closed her eyes and fisted the blankets in her hands. "I saw you in that skirt you wore the first day of school with your legs around my waist."
I hooked my fingers around her underwear and slid them down her gorgeous legs. "I wanted you in every seat in the audience." She made a low noise and tried to sit up, but I braced a hand on her stomach to hold her in place. "I wanted you in every seat so that you wouldn't be able to sit anywhere in that theatre without thinking about me."
"That was already true."
I smiled. "Good to know."
She laid both of her hands over mine on her stomach, and held my hand tighter against her for a second. She said, her voice small and quiet, "I love you so much."
I stood and leaned over her so that I could see her face. She blinked a few times, and I couldn't read her expression. It was sad and happy and confusing, and she had never had this kind of response in bed before.
I didn't know what was going on, but I could feel the panic rising under my skin, at the back of my throat, in the lining of my lungs.
"Are you sure you're okay?"
She shook her head until her expression cleared, and then smiled. "Yeah . . . just thinking about the future."
My heart jerked in my chest, and I tried to explain away the sadness and the fear I saw in her eyes. They didn't have to mean she was having doubts. They could mean a thousand other things. But for the life of me, I couldn't conjure one more possibility.
I dropped a kiss on her lips and said, "I did promise you forever. That's a lot of future."
She nodded, and then after a too long moment she smiled. "I'm sorry. But do you think we can . . . just go to sleep? I'm sorry. I know I said I was fine, but I'm feeling a little off after all."
I took a deep breath and tried not to read too much into this. She'd been sick. It didn't have to mean anything else. But damn it, now I couldn't think about anything else.
As calmly as I could I brushed her hair back and kissed her forehead. "Of course. Can I get you something? Water? Medicine?"
She swallowed and shook her head. "I think . . . I think I just need some sleep."
I nodded. "Of course."
I folded down the blankets, and she slid between the sheets, still only half covered by her dress. I took another deep breath that did absolutely nothing to relieve the pressure in my jeans or the pressure in my head.
I kissed her cheek one more time.
"I love you," I said, slowly, deliberately. I needed her to hear that through whatever noise might be happening in her head. "Get some sleep. I'm just going to go take a quick shower."
"I'm sorry," she called again as I walked away.
"No need to be sorry, love."
Unless she was saying sorry for something else, something she hadn't said.
"I'll make it up to you," she said.
"Also not necessary, though I do like the sound of that."
She pulled the blankets up to her neck, settling back on the pillow. I switched off the lights and said, "Good night, Bliss."
Then I ended our roller coaster of a day with an ice-cold shower and too many worries to count.
"WAIT, WAIT! JUST one more!"
"Bliss, there are children waiting."
And they probably hated us, but I was just so glad to see her smiling that I didn't care.
"Yeah, well, they all just jumped on the bandwagon. Most of them weren't alive when I read Harry Potter for the first time."
I turned to the Canadian family behind me and said, "I'm so sorry. This is the last one, I promise." Then I took one more picture of Bliss pretending to push the luggage cart through the wall at the Platform 9¾ monument at King's Cross Station.
A little boy stuck his tongue out at Bliss as we left. I pulled her away before she could follow suit.
"That kid better watch it. I'm totally a Slytherin."
I shook my head, smiling.
"Love, I'm going to need you to pull back on the crazy a bit."
"You're right. Realistically, I'm a Ravenclaw."
I laughed. Even when I didn't quite get her, I loved her. Probably because I didn't get her. She knew who she was, and she didn't ever compromise that. Not even for me.
I chuckled.
"What's so funny?"
"I'm just imagining you with kids someday. You'll probably end up fighting them to play with the toys."
I didn't notice that she'd stopped walking until I went to round the corner, and she wasn't beside me. I turned and she was still standing a few feet back.
"I was joking, love."
She crossed her arms over her middle and shrugged. "I know that."
"Then why do you look so freaked out?"
"I just didn't realize you thought about stuff like that."
Oh God. The last thing I needed on this already stressful trip was to scare her off with talk of kids, not when she seemed mostly back to normal today. I could be really thick sometimes.
I laid my arm across her shoulders and said, "Whatever thoughts are unspooling in your mind, stop them. I've still got a lot to show you, and I was only having a laugh."
"Right, where to next?"
"Well, we've seen the Globe."
I felt her relax beside me as we walked, and she said, "You mean the replica of the Globe."
"Close enough. We've done Big Ben, the Parliament, the Tower. What about the Eye?" I asked.
"Is that the giant Ferris wheel thing?" I nodded. "Yes, let's do that!"
Just spending the day with Bliss and introducing her to my old city was enough to erase some of the messiness of last night, to erase some of my worries. She really must have just needed sleep because this morning, she was as perfect as ever.
"Can we stop by a store first?" she asked. "A pharmacy? I just wanted to get something in case I start feeling sick again."
"Of course," I kissed her temple, and we headed for the tube that would take us to the other side of the city.
Bliss
WE STOPPED AT a small store that was just a little bigger than a convenience store. It had food and toiletries and a random assortment of items, but the pharmacy in back was my concern.
"Would you mind grabbing me a drink?" I asked. "I'm going to run to the bathroom, grab that medicine, and I'll meet you back up here."
I didn't wait for Garrick to agree before I turned to walk away. I headed for the pharmacy at a stroll, glancing behind me to see when he was no longer looking. When he turned, I picked up the pace and began scouring the shelves for pregnancy tests. It took me three tries to find the right aisle, and then all I could do was just stare at the display.
Why did there have to be so many?
There were brand names and off brands, digital and sticks and cups, one lines and two lines and plus signs and the signs of the apocalypse.
And oh God, why was this so terrifying?
Maybe I should just get one of each.
Then I looked at the price.
Eh . . . probably just one would do for now.
I grabbed the stick one with the plus sign, and bolted for the pharmacy counter at the back. An Indian guy in glasses was typing away at the computer.
"Excuse me?" He looked up. "Can I check out here?"
"No ma'am. Cashier is up front."
Fabulous.
I grabbed a couple other things. Ibuprofen and sunscreen and a box of tampons (wishful thinking). I gathered all the items in my arms, hiding the pregnancy test behind them all. Then I went to the front to meet Garrick.
He stood holding a bottle of Coke, smiling and perfect, and God, I wanted to tell him. But his comment about kids earlier had my head all twisted. I'd thought about telling him then, but then he'd been so insistent that it was a joke that I started to worry that he would freak out. I mean, why wouldn't he? We'd only been together a year. We were just about to get married. There were probably prison cells roomier than our apartment.
I waited until it was our turn to check out and then I turned to him and said, "Oh honey, I'm sorry. Would you mind switching that out for a water instead? Or maybe juice? I just think that would be better for my stomach."
As soon as he was gone, I dumped all of my things on the counter and thrust the pregnancy test at the cashier.
"Can you ring this up first?"
The girl on the register was blond, couldn't be much older than sixteen, and she laughed at me. Actually laughed at me.
"Look, I realize this is crazy. But please. Just do it quick."
She shrugged and said, "He's going to notice sooner or later."
I so did not need attitude right now.
She scanned the test, and I shoved it in my purse just as Garrick came around the corner. He set the water on the counter, and then scanned my things.
"I thought you were getting medicine?"
Excuse me, sassy checkout girl, could I borrow your register for a moment to smash against my face?
I picked up the bottle of ibuprofen and shook it.
"I've been having headaches, and I think that's what caused the nausea."
The girl snickered when I said nausea. It probably didn't bode well for my future as a mother that I really wanted to punch this teenager.
Garrick took the bag from her as I paid and carried it outside for me. On the sidewalk, he said, "You could have told me. I'm not that naive."
I choked on the sip of water I had just taken and said, "What?"
He held up the bag, and I could see the box of tampons through the semi-transparent plastic. "This? The painkillers? You could have just said you were having your monthly."
Only I could suffer the humiliation of discussing a nonexistent period with my boyfriend.
"Oh, I'm not. No, these are just . . ." I totally blanked. "It was on sale."
He raised an eyebrow. "So you decided to buy it now?"
I was going to look into a career as a mime. Because that appeared to be the only way I was going to stop saying stupid things.
I took the shopping bag back and stuffed it in my giant purse. "How close are we to this Eye thing?" I asked.
We turned a corner, and he pointed up ahead to a giant white Ferris wheel. "Very close."
Glad for the change in subject, I listened to him explain that the Eye had been built while he was in school, and that on New Year's they actually fired off fireworks from the Eye itself. He explained that we'd board one of the pods while the structure was still moving, albeit very slowly.
We had to wait in line for a little while, but since it was a weekday it wasn't too bad. With our fingers laced together, we stepped to the front of the line, the first people to board the next pod.
Another ten to fifteen people boarded with us, and we found a spot at the window that would give us a good vantage point as the wheel continued its slow rotation upward. Garrick said one revolution was about thirty minutes, so I held on to the bar and he wrapped his arms around my waist. He placed his cheek against mine, and together we watched the city become smaller and smaller as we were pulled up into the sky.
The Thames twisted along beside us, steeples and skyscrapers punctured the clear blue day, and little dots of people moved below us in the distance. Up here they looked remarkably small, and there were so many. Some were in line for the Eye, others hustled along the busy streets. I could imagine each one of them wrapped up in their thoughts, contemplating their dreams, falling in love, getting news that changed their entire world.
In life, it's so easy to get tunnel vision, to imagine this world is a movie set and your story—what you see through your eyes and think with your brain and feel with your heart—is the only thing that matters. But the world was so much bigger than that. Life was so much bigger than that. Sometimes, I couldn't understand how it could hold all of us, all of the hope and hurt of humanity.
It was just as remarkable to think about the fact that at this very second, a new life could be forming inside of me. I didn't understand how I could hold that, either, how I could have another person who would be entirely dependent on me. The camera of my life was very focused. There was Garrick, of course, but both of us were concentrated on our careers, on establishing ourselves. But if we had a baby that would change everything for both of us. Our lens would have to refocus, adjust. It couldn't just be about us anymore.
I could feel the warmth of Garrick's hand against my belly through my thin shirt, and thought . . . the responsibility wouldn't be entirely on me. Yes, Garrick was a guy, and yes, most of them were terrified of commitment and babies and all those kinds of things. But he was different. This was a man that would hold my bag of tampons without any complaint, a man that didn't get angry when I stopped him right before sex, and a man that loved me and cherished me despite all my oddities and issues.
He interrupted my thoughts to point out the window. "Over there, that's where we were this morning. That's the church we walked by. And that way is my parents' place. You can also see the primary school I attended there. Graham and I were in trouble almost every day. Our mums threatened to send us both to boarding school."
It was the worst transition in the history of the world, but I looked over my shoulder at him and blurted out, "I bought a pregnancy test."
"What?" He didn't say it like he was shocked or horrified. More like when someone just didn't quite hear what you said.
So I continued, "At the pharmacy. I was being weird and sending you off to get drinks because I was buying a pregnancy test, and I was scared to tell you."
That time I got a reaction.
His hands dropped from their spot on my stomach, and he moved to lean on the bar beside me. His eyes searched my face, and I thought the silence would kill me, tie my windpipe into a pretty little bow, and suffocate my brain.
"Say something."
He opened his mouth, but nothing came out for several long seconds until, "You're pregnant?"
Okay. Correction. Say something that actually gives me a clue as to how you're going to react.
"I don't know. I'm late. I think. It could be nothing. "
"Or it could be something."
Damn it, why couldn't I read his inflection?
"It could be. Because . . . well . . . I forgot to refill my prescription. For the Pill. Things got busy, and it slipped my mind. It's still so new to me, and I—"
"Why didn't you tell me?"
I was going to go crazy if he didn't say something more definitive soon. I sighed and looked out at the city. We'd just reached the peak of the wheel, and the pod gave a panorama view of the city. I gripped the bar that kept people back from the glass and said, "I was scared. The thought of having a kid is scary. I still feel like a kid myself sometimes. And we both work so much, our apartment is tiny, we live in this huge, sometimes dangerous city that we can barely afford already, and we've not really talked about having kids. When they do get mentioned it's this vague, far-off thing in the future, and I didn't know how you would feel. So I was going to wait until I knew for sure. Or until I could get home to look at my calendar."
"But?"
My breathing was too loud in my ears, almost deafening. "But I didn't want to be scared alone."
His hands cradled my face, and he touched his forehead to mine. My breath hitched. He said, "You don't ever have to be."
I let out a small sob and held tight to him. He lowered one hand to my waist, his thumb brushing over my belly.
"Do you think . . . Do you feel like you are?"
I shrugged my shoulders. "I can't tell. I'm exhausted, but that could just be jet lag. I'm emotional, but that could be because I'm a social cripple who breaks expensive vases as a first impression. And I did get sick yesterday, but only once, so that could have just been the fatigue and shock."
He nodded, this time slipping his hand beneath my shirt to touch my stomach.
"If I am . . ."
"Then everything will be okay. All of those things you said are true, but we'll be okay. You will be an extraordinary mother, and we'll do whatever it takes to take care of our child." He smiled and shook his head, "Our child. Wow. That's what's was bothering you yesterday?"
I nodded, and he exhaled in relief. That was a good thing, right?
"Does that mean you're okay with this?" My heart was skipping.
"It means I love you and want to marry you and call you the mother of my child. It doesn't matter to me what order it happens in."
I leaned my head down against his chest, and suddenly the weight of my body felt like too much. His hand slid around to my back, and he pulled me in until my stomach pressed against his. I let him support more of my weight and said, "We do have a tendency to do things out of order."
"The world has given us plenty of surprises, but each one has turned out better than the last. I have no doubt that this will be the same."
He lifted my head up and caught my lips in a kiss.
We spent the rest of the ride ignoring the skyline for each other, and by the time the pod let us off back on solid earth, a really small part of me was actually beginning to hope for that plus sign.
Garrick
"THANK YOU FOR squeezing me in today, Mr. Woods. I really appreciate your time." He stood from behind his massive black desk, and came around to meet me.
"Nonsense. Anything for the Taylors. I'm just glad you decided to reconsider. You'll call me after you've talked to your fiancée?"
"Yes sir. I'll talk to her tonight."
"Fantastic. I think this could be a really good match, Garrick."
"Thank you, sir. I'll give you a call tomorrow."
A knot sat heavy in my stomach as I entered the elevator, and rode down the thirty-seven floors back down to the lobby. It had started yesterday when I'd called to set up the interview, and now it felt like it took up my entire midsection. Maybe it had actually started on the Eye. Or when Bliss took that first test, which had been negative. I'd almost canceled the appointment, but the instructions on the pregnancy test box suggested taking multiple tests, so I'd gone out to get another one.
That one had been positive.
Bliss took two more this morning, both negative, and we eventually decided that we were just testing too early. She wasn't sure exactly how many days she was late, but she guessed just a few, and everything we saw on the Internet suggested testing after a week.
So we decided to wait.
That seemed to be a staple in our relationship.
But whether she was pregnant or not, that didn't change the facts.
She was about to be my wife. We didn't have the money for a child any more than we had the money for a big wedding or a honeymoon. Neither of us had health insurance.
I loved acting, but how was I any different from my father if I chose to do that over providing for my family?
When Bliss had met me out on that empty stage after that performance of Pride and Prejudice and I'd gotten down on one knee, everything had changed. She had to be my priority. My job was to take care of her, and if that meant taking a job in London that made more money, then I would do it. Sure it was a job in my father's world, a world I had never wanted to be a part of, but I knew taking this job would make me different from my father, regardless of whether we appeared the same on the outside.
London had an even better theatre scene than Philadelphia, so Bliss could continue working here, and I'd make enough that she wouldn't have to work another job, she could just audition. And I . . . I would see her on stage, and that would have to be enough. I'd discovered my talent for theatre because pretending came so naturally to me. It was my way of life growing up. But I'd fallen in love with theatre when I found that it was the only kind of pretending that could also tell a truth. It would hurt to leave that behind, that feeling that I was a part of something bigger, something greater.
I would just have to learn how to find that same feeling in the audience.
Besides . . . marrying Bliss, starting a family, that was my something bigger.
The company would cover our move and health insurance. Baby or not . . . this made sense. It was the right thing to do. The smart thing.
I kept replaying all my reasons as the tube rocked back and forth on the tracks on my way back to Kensington. Bliss was out at her lunch with Mum, but we should be getting home around the same time. I needed to have all my thoughts laid out when I told her.
I wasn't sure how she'd react to the idea of leaving the States. She'd seemed really excited about coming to London, but visiting and living here were two very different things. But besides a slow start, she'd really held her own here. It was an almost seamless transition, actually. Even better than I'd hoped.
It would be okay. This would make everything okay. And Bliss could stop worrying about the pregnancy because this job would take care of everything. And after a couple years in this job, I could probably find a comparable one back in the States if she wanted to go back.
I arrived back at my parents before Mum and Bliss, and surprisingly met my father on the way in the door.
"Oh Garrick, I'm glad I caught you. I swung by to pick up some things on my lunch. How did the interview go?"
Of course he would know. I hadn't told anyone, but he must have heard it from Mr. Woods.
"It went well. I'm going to talk to Bliss about it tonight."
He nodded, pulling his BlackBerry out of his pocket after it buzzed.
"Good." He started tapping away at a message, and with his head down said, "You're making the right decision, Garrick. The smart one."
The knot in my stomach soured as he literally took the words right out of my head.
I wasn't like my father. We were different. This was different.
He left with one more proclamation that this was the right thing, and I had the massive, empty house alone to fill up with thoughts.
I'd taken a turn of pacing and sitting and stressing in nearly every room in the house by the time Bliss arrived home. It was hours after I expected them, and I was in the dining room, drumming my fingers against the long table, when the front door opened, and I heard laughter.
"Did you see her face? I haven't laughed so hard in . . . well, decades probably."
"I thought she was going to murder me, right there in the shop."
"I thought I was going to lose a lung laughing. You don't know how much I can't stand that woman."
I crossed into the foyer, and Bliss and my mother were smiling like the oldest of friends.
"What have you two been up to all day?" I asked.
Mum waved a hand. "Just causing a bit of mischief. It comes quite naturally to your future wife."
Of that, I was very well aware.
"And where have you been all this time?"
"Oh, here and there. Don't worry. I took good care of her. And I was nice, as you put it. To her anyway."
Bliss laughed, and whatever I was missing, it must have been one hell of a story. And I wanted to hear it . . . later. Right now I had about a thousand things to get off my chest, and I had everything I wanted to say arranged in my mind. I needed to say it before it all came tumbling down like a house of cards.
"I'm glad you two had fun, but can I steal her away for a while?"
"By all means," Mum said. "Steal away."
I held Bliss's hand as we climbed the stairs up to my room. I shook my head, chuckling. "Unbelievable. How do you do it?"
Deadpan, Bliss said, "I knocked down five racks of clothing at some upscale boutique she took me to. Seriously, it was horrifying. The most expensive domino line in the history of the world."
I burst out laughing.
She said, "That's about how your mother reacted, too. She was civil before that, but then it was like some kind of flip had switched. We had a blast."
This was a good sign. A great sign. Maybe she would want to be in London.
"My mother is all work. Today was probably the most fun she's had in ages."
"It was good for me, too," she said. "Listen, I—"
"I need to talk to you about something," I said.
"Oh." She frowned. "Of course. Go ahead."
I sat her on the edge of the bed, and out of habit my eyes went to her midsection. I think I'd looked at her stomach more in two days than in the entirety of our relationship before now.
"I did something today. Something a little crazy."
"Okay," she said tentatively, her fists clenched on top of her knees.
I blew out a breath.
"I interviewed for a job."
"You what?"
"I know, I know." I paced the length of the carpet in front of her. "I know it's out of nowhere, but an old boss talked to me about it at the party the other night. I didn't think anything of it until yesterday, but it solves all of our problems. The money is great, and they'll pay for us to relocate. We'll have health insurance to cover the birth. We'll be able to afford to live in a very safe part of the city with good schools. You can audition here, and you won't have to worry about working any other jobs."
"You interviewed for a job here in London without telling me?"
"I haven't accepted it."
"You sure as hell better not have accepted it."
I was mucking this up completely. I forced myself to stop pacing and kneel in front of her on the bed.
"I know this is a lot. I'm only asking you to think about it, to think of all the problems it could solve."
"What about all the problems it creates? I'm already booked for a show in the fall."
"You'd have to give that show up if you're pregnant anyway. You'd be showing by then."
She stood, and then it was she who started pacing.
"We don't even know if we're pregnant yet. You want to uproot our entire life on a possibility?"
I took hold of her elbows and said, "No. No, of course not. We can wait to answer until next week, until we know for sure. But even if you're not pregnant, Bliss, you might be someday. This job is a rare opportunity. Most people have to work their way up for years to get this kind of job."
"And what kind of job is it?"
"What do you mean?"
She gripped my shoulders like she wanted to shake me. "What will you be doing? You love theatre. You said it made you grow up. It led you to me. You're going to leave that for what? A job behind a desk?"
"I love you, more than I've ever loved acting."
She pulled her elbows out of my grasp and threw up her arms.
"What does that have to do with any of this?"
"Bliss, I'm doing this for you. For us."
"Well, stop."
I shook my head. "What?"
"You heard me. Stop. I didn't ask you to do any of this."
"You don't have to ask." I dragged a thumb across her jaw. "I just think it's time for a bit of realism. It would be stupid not to take this job."
"I'm hearing a lot of stupid things at the moment."
Okay. So she wasn't excited about the idea of living in London.
"Damn it, Bliss. We need this. I'm trying to grow up, to get a real job, and be an adult about all this."
"Being an adult doesn't mean you change everything about yourself. You were an adult already without this fancy job and the money."
"But now I can be an adult that can provide for you."
"You already provide all I need. You said we needed a dose of realism?"
"Yes. We do."
I could see that now.
"You said almost the same thing to me on the first night we met, on the night we kissed. We were talking about theatre, about Shakespeare."
"Bliss—"
"I never would have even stopped at that table if you hadn't been reading those plays. We would have met for the first time as teacher and student, and nothing would have happened between us. We might not have fallen in love if you hadn't been the assistant director for Phaedra. You proposed to me on stage, Garrick. Our whole life is theatre. The love we have is because of theatre. I associate all of our greatest moments with a play. If we'd thought about what was safe or smart when we met, we wouldn't be together today. And you'll always be the man that encouraged me to follow through on my dreams, the man that taught me how to make the bold choices and go after what I wanted. You said you weren't like your father. He's supposed to be the one whose primary concern is money."
"The money is just a means to an end. You and the baby are my priority."
"If you really want to do something for me, you'll turn down this job."
"Bliss, just think about it."
"I am thinking about it. I'm thinking about how I fell in love with a man who told a classroom full of seniors that the hardest thing about this life isn't landing roles or having enough money. It's keeping up your spirit and remembering why we chose theatre in the first place. So take your own advice, Garrick. You could have had this life all those years ago, but you didn't want it. You wanted something different. Something better. And either you still want that other life, that life with me. Or you don't. But I would leave before I'd let you ruin your own dream."
The silence detonated in my ears. My heart was raging in my chest, and I felt like my ribs were going to crack if it beat any harder. I couldn't lose her. I wanted her more than I wanted anything else. She eclipsed every dream, every desire, every doubt.
"Bliss—"
"I mean it, Garrick. I appreciate what you're doing, and I get it. I love you for being willing to do this, but it's not worth it. Not if you stop being you."
She took my hand and pressed it to her stomach. "If we did have a child, and he came to you with something like this, would you tell him to take the money, to take the job that didn't mean anything? Why am I even asking, I know what you'd say. You'd tell him to do the thing he loved, the thing that made him feel more alive. Life's too short to waste time living it any other way."
She was right.
Damn it. She was right.
The knot in my stomach loosened, and I released a heavy breath.
"How is it that you know me even better than I know myself?"
"Because I love you."
My heart sprinted, and the force of each beat drew me closer to her. Every time she said those words . . . every time it felt like the first time. I wrapped my arms around her and pulled until I had her feet dangling off the floor. I kissed the corner of her jaw and returned the words.
"But if we're pregnant . . . there are so many things we'll have to overcome. It's going to be hard with our lifestyles."
She threaded her fingers through my hair and said, "Your mother took me to see a friend of hers who's a doctor."
I met her gaze, and set her feet back on the floor. "You told my mother?"
She shrugged. "That woman has a way of prying out my secrets."
"And?"
"And I'm not pregnant."
I swallowed, my stomach twisting with a combination of emotions, too vast for me to really identify.
"You're not?"
She shook her head. "The doctor said she thinks it's probably just stress that's thrown off my cycle. Probably the combination of all the work and thinking about meeting your family."
My heartbeat was slow, but loud in my ears.
"So . . . so we don't have to worry about any of those things."
"Not now, no."
For the life of me, I couldn't tell if I was disappointed or relieved. Not about the baby. The job though . . . that felt like I was a hundred times lighter.
"You okay?" she asked.
I kissed her forehead, then the tip of her nose, followed by her lips. I absorbed the calm from her warm skin, breathed in the balance from her closeness. I said, "Yes. I'm more than okay."
She nodded. Her expression was just as hard to read, and I got the feeling that she was just as confused about how she felt as I was.
"Garrick? One more question."
"Anything."
Her smile widened, brilliant and beautiful. All her confusion disappeared.
"Marry me?"
Half a dozen responses flitted through my mind, from simple to snarky. But there was one thing that would always be true about me. I preferred action to words.
So, I pulled her close and answered her as thoroughly as I could.
Continue reading for a sneak peek
at Bliss's best friend Kelsey's story in
_FINDING IT_
Coming in October 2013
from William Morrow
EVERYONE DESERVES ONE grand adventure.
We all need that one time in life that we always get to point back to and say, "Then . . . then I was really living."
Adventures don't happen when you're worried about the future or tied down by the past. They only exist in the now. And they always, always come at the most unexpected time in the least likely of packages.
An adventure is an open window, and an adventurer is the person willing to crawl out on the ledge and leap.
I told my parents I was going to Europe to see the world and grow as a person. (Not that Dad listened beyond the second or third word, which is when I slipped in that I was also going to spend his money and piss him off as much as possible. He didn't notice.) I told my professors that I was going to collect experiences to make me a better actor. I told my friends I was going to party.
In reality, it was a little of all of those things. Mostly, I was here because I refused to believe that my best years were behind me now that I'd graduated from college. I wanted to experience something extraordinary. And if adventures only existed in the now, that was the only place I wanted to exist, too.
After nearly two weeks backpacking around Eastern Europe, I was becoming an expert at just that.
I trekked down the old cobblestone street, my stiletto heels sticking in the stone grooves. I kept a tight hold on the two Hungarian men that I'd met earlier in the evening, and followed our two other companions down the street. . Technically, I guess it had been last night when we met since we were now into early hours of the morning.
I couldn't keep their names straight, and I wasn't even that drunk yet.
I kept calling Tamás, István. Or was that András? Oh well. All three were hot with dark hair and eyes, and they knew four words in English as far as I could tell.
American. Beautiful. Drink. And dance.
As far as I was concerned, those were the only words they needed to know. At least I remembered Katalin's name. I'd met her a few days ago, and we'd hung out almost every night since. It was a mutually beneficial arrangement. She showed me around Budapest, and I charged most of our fun on Daddy's credit card. Not like he would notice or care. And if he did, he'd always said that if money didn't buy happiness, then people were spending it wrong. So if he got mad, I'd just say I was finding my joy.
"Kelsey," Katalin said, her accent thick and exotic. "Welcome to the ruin bars."
I paused in ruffling István's hair (or the one I called István, anyway). The five of us stood on an empty street filled with dilapidated buildings. I knew the whole don't-judge-a-book-by-its-cover thing, but this place was straight out of a zombie apocalypse. I wondered how to say brains in Hungarian.
The old Jewish quarter—that's where Katalin said we were going.
Oy vey.
It sure as hell didn't look to me like there were any bars around here. I looked at the sketchy neighborhood, and thought at least I'd gotten laid last night. If I was going to get chopped into tiny pieces, at least I went out with a bang. Literally.
I laughed, and almost recounted my thoughts to my companions, but I was pretty sure it would get lost in translation. Especially because I was starting to question even Katalin's grip on the English language, if this was what bar meant to her.
I pointed to a crumbling stone building and said, "Drink?" Then mimed the action just to be safe.
One of the guys said, "Igen. Drink." The word sounded like ee-gan, and I'd picked up just enough to know it meant yes.
I was practically fluent already.
I cautiously followed Katalin toward one of the derelict buildings. She stepped into a darkened doorway that gave me the heebiest of jeebies. The taller of my Hungarian hotties slipped an arm around my shoulder. I took a guess and said, "Tamás?" His teeth were pearly white when he smiled. I would take that as a yes. Tamás equaled tall. And drop-dead sexy. Noted.
One of his hands came up and brushed back the blond hair from my face. I tilted my head back to look at him, and excitement sparked in my belly. What did language matter when dark eyes locked on mine, strong hands pressed into my skin, and heat filled the space between us?
Not a whole hell of a lot.
We followed the rest of the group into the building, and I felt the low thrum of techno music vibrating the floor beneath my feet.
Interesting.
We traveled deeper into the building and came out into a large room. Walls had been knocked down, and no one had bothered to move the pieces of concrete. Christmas lights and lanterns lighted the building. Mismatched furniture was scattered around the space. There was even an old car that had been repurposed into a dining booth. It was easily the weirdest, most confusing place I'd ever been in.
"You like?" Katalin asked.
I pressed myself closer to Tamás and said, "I love."
Tamás led me to the bar, where drinks were amazingly cheap. Maybe I should stay in Eastern Europe forever. I pulled out a two-thousand-forint note. For less than the equivalent of ten U.S. dollars I bought all five of us shots.
Amazing.
The downside to Europe? For some reason that made no sense to me they gave lemon slices with tequila instead of lime. The bartenders always looked at me like I'd just ordered elephant sweat in a glass.
They just didn't understand the magical properties of my favorite drink. If my accent didn't give me away as American, my drink of choice always did.
Next, Tamás bought me a gin bitter lemon, a drink I'd been introduced to a few weeks ago. It almost made the absence of margaritas in this part of the world bearable. I downed it like it was lemonade on a blistering Texas day. His eyes went wide, and I licked my lips. István bought me another, and the acidity and sweetness rolled across my tongue.
Tamás gestured for me to down it again, so I did, to a round of applause.
God, I love when people love me.
I took hold of Tamás's and István's arms and pulled them away from the bar. There was a room that had one wall knocked out in lieu of a door, and it overflowed with dancing bodies.
That was where I wanted to be.
I tugged my boys in that direction, and Katalin and András followed close behind. We had to step over a pile of concrete if we wanted to get into the room. I took one look at my turquoise heels, and knew there was no way in hell I was managing that with my sex appeal intact. I turned to István and Tamás—sizing them up. István was the beefier of the two, so I put an arm around his neck. We didn't need to speak the same language for him to understand what I wanted. He swept an arm underneath my legs, and pulled me up to his chest. It was a good thing I wore skinny jeans instead of a skirt.
"Köszönöm," I said, even though he probably should have been thanking me, based on the way he was openly ogling my chest.
Ah, well. I didn't mind ogling. I was still pleasantly warm from the alcohol, and the music drowned out the world. And my shitty parents and uncertain future were thousands of miles away across an ocean. My problems might as well have been drowning at the bottom of said ocean for how much they mattered to me in that moment.
The only expectations here were ones that I had encouraged and was all too willing to follow through on. So maybe my new "friends" only wanted me for money and sex. It was better than not being wanted at all.
István's arms flexed around me, and I melted into him. My father liked to talk, or yell, rather, about how I didn't appreciate anything. But the male body was one thing I had no issue appreciating. István was all hard muscles and angles beneath my hands, and those girls were definitely a-wandering.
By the time he'd set my feet on the dance floor, my hands had found those delicious muscles that angled down from his hips. I bit my lip and met his gaze from beneath lowered lashes. If his expression was any indication, I had found Boardwalk and had the all-clear to proceed to Go and collect my two hundred dollars.
Or forint. Whatever.
Tamás pressed his chest against my back, and I gave myself up to the alcohol and the music and the sensation of being stuck between two delicious specimens of man.
Time started to disappear between frenzied hands and drips of sweat. There were more drinks and more dances. Each song faded into the next. Colors danced behind my closed eyes. And it was almost enough.
For a while, I got to be blank. A brand-new canvas. Untouched snow.
I checked my baggage at the door, and just was.
There was no room for unhappiness when squeezed between two sets of washboard abs.
New life motto, right there.
I gave István a couple notes and sent him to get more drinks. In the meantime, I turned to face Tamás. He'd been pressed against my back for God knows how long, and I'd forgotten how tall he was. I leaned back to meet his gaze, and his hands smoothed down my back to my ass.
I smirked and said, "Someone is happy to have me all to himself."
He pulled my hips into his and said, "Beautiful American."
Right. No point expending energy on cheeky banter that he couldn't even understand. I had a pretty good idea how to better use my energy. I slipped my arms around his neck and tilted my head in the universal sign of kiss me.
Tamás didn't waste any time. Like really . . . no time. The dude went zero to sixty in seconds. His tongue was so far down my throat it was like being kissed by the lovechild of a lizard and Gene Simmons.
We were both pretty drunk. Maybe he didn't realize that he was in danger of engaging my gag reflex with his Guinness-record-worthy tongue. I eased back and his tongue assault ended, only for his teeth to clamp down on my bottom lip.
I was all for a little biting, but he pulled my lip out until I had one half of a fish mouth. And he stood there, sucking on my bottom lip for so long that I actually started counting to see how long it would last.
When I got to fifteen (fifteen!) seconds, my eyes settled on a guy across the bar, watching my dilemma with a huge grin. Was shit-eating grin in the dictionary? If not, I should snap a picture for Merriam-Webster.
I braced myself and pulled my poor, abused lip from Tamás's teeth. My mouth felt like it had been stuck in a vacuum cleaner. While I pressed my fingers to my numb lip, Tamás started placing sloppy kisses from the corner of my lips across my cheek to my jaw.
His tongue slithered over my skin like a snail, and all the blissful, alcohol-induced haze that I'd worked so hard for disappeared.
I was painfully aware that I was standing in an abandoned-building-turned-bar with a trail of drool across my cheek, and the guy across the room was now openly laughing at me.
And he was fucking gorgeous, which made it so much worse.
Sometimes . . . the now sucked.
If you've missed any of Cora Carmack's Losing It series,
read on for a look at where it all began . . .
_LOSING IT_
I TOOK A deep breath.
You are awesome. I didn't quite believe it, so I thought it again.
Awesome. You are so awesome. If my mother heard my thoughts, she'd tell me that I needed to be humble, but humility had gotten me nowhere.
Bliss Edwards, you are a freaking catch.
So then how did I end up twenty-two years old and the only person I knew who had never had sex? Somewhere between Saved by the Bell and Gossip Girl, it became unheard of for a girl to graduate college with her V-card still in hand. And now I was standing in my room, regretting that I'd gathered the courage to admit it to my friend Kelsey. She reacted like I'd just told her I was hiding a tail underneath my A-line skirt. And I knew before her jaw even finished dropping that this was a terrible idea.
"Seriously? Is it because of Jesus? Are you, like, saving yourself for him?" Sex seemed simpler for Kelsey. She had the body of a Barbie and the sexually charged brain of a teenage boy.
"No, Kelsey," I said. "It would be a little difficult to save myself for someone who died over two thousand years ago."
Kelsey whipped off her shirt and threw it on the floor. I must have made a face because she looked at me and laughed.
"Relax, Princess Purity, I'm just changing shirts." She stepped into my closet and started flipping through my clothes.
"Why?"
"Because, Bliss, we're going out to get you laid." She said the word "laid" with a curl of her tongue that reminded me of those late-night commercials for those adult phone lines.
"Jesus, Kelsey."
She pulled out a shirt that was snug on me and would be downright scandalous on her curvy frame.
"What? You said it wasn't about him."
I resisted the urge to slam my palm into my forehead.
"It's not, I don't think . . . I mean, I go to church and all, well, sometimes. I just . . . I don't know. I've never been that interested."
She paused with her new shirt halfway over her head.
"Never interested? In guys? Are you gay?"
I once overheard my mother, who can't understand why I'm about to graduate college without a ring on my finger, ask my father the same question.
"No, Kelsey, I'm not gay, so keep putting your shirt on. No need to fall on your sexual sword for me."
"If you're not gay and it's not about Jesus, then it's just a matter of finding the right guy, or should I say . . . the right sexual sword."
I rolled my eyes. "Gee? Is that all? Find the right guy? Why didn't someone tell me sooner?"
She pulled her blond hair back into a high ponytail, which somehow drew even more attention to her chest. "I don't mean the right guy to marry, honey. I mean the right guy to get your blood pumping. To make you turn off your analytical, judgmental, hyperactive brain and think with your body instead."
"Bodies can't think."
"See!" she said. "Analytical. Judgmental."
"Fine! Fine. Which bar tonight?"
"Stumble Inn, of course."
I groaned. "Classy."
"What?" Kelsey looked at me like I was missing the answer to a really obvious question. "It's a good bar. More importantly, it's a bar that guys like. And since we do like guys, it's a bar we like."
It could be worse. She could be taking me to a club.
"Fine. Let's go." I stood and headed for the curtain that separated my bedroom from the rest of my loft apartment.
"Whoa! Whoa." She grabbed my elbow and pulled me so hard that I fell back on my bed. "You can't go like that."
I looked down at my outfit—flowery A-line skirt and simple tank that showed a decent amount of cleavage. I looked cute. I could totally pick up a guy in this . . . maybe.
"I don't see the problem," I said.
She rolled her eyes, and I felt like a child. I hated feeling like a child, and I pretty much always did when talk turned to sex.
Kelsey said, "Honey, right now you look like someone's adorable little sister. No guy wants to screw his little sister. And if he does, you don't want to be near him."
Yep, definitely felt like a child. "Point taken."
"Hmm . . . sounds like you're practicing turning off that overactive brain of yours. Good job. Now stand there and let me work my magic."
And by magic, she meant torture.
After vetoing three shirts that made me feel like a prostitute, some pants that were more like leggings, and a skirt so short it threatened to show the world my hoo-hoo in the event of a mild breeze, we settled on some tight low-rise denim capris and a lacy black tank that stood out in contrast to my pale white skin.
"Legs shaved?"
I nodded.
"Other . . . things . . . shaved?"
"As much as they are ever going to be, yes, now move on." That was where I drew the line of this conversation.
She grinned, but didn't argue. "Fine. Fine. Condoms?"
"In my purse."
"Brain?"
"Turned off. Or well . . . dialed down anyway."
"Excellent. I think we're ready."
I wasn't ready. Not at all.
There was a reason I hadn't had sex yet, and now I knew it. I was a control freak. It was why I had done so well in school my entire life. It made me a great stage manager—no one could run a theater rehearsal like I could. And when I did get up the nerve to act, I was always more prepared than any other actor in class. But sex . . . that was the opposite of control. There were emotions, and attraction, and that pesky other person that just had to be involved. Not my idea of fun.
"You're thinking too much," Kelsey said.
"Better than not thinking enough."
"Not tonight it's not," she said.
I turned up the volume of Kelsey's iPod as soon as we got in the car so that I could think in peace.
I could do this. It was just a problem that needed to be solved, an item that needed to be checked off my to-do list.
It was that simple.
Simple.
Keep it simple.
We pulled up outside the bar several minutes later, and the night felt anything but simple. My pants felt too tight, my shirt too low-cut, and my brain too clouded. I wanted to throw up.
I didn't want to be a virgin. That much I knew. I didn't want to feel like the immature prude who knew nothing about sex. I hated not knowing things. The trouble was . . . as much as I didn't want to be a virgin, I also didn't want to have sex.
The conundrum of all conundrums. Why couldn't this be one of those square-is-a-rectangle-but-rectangle-is-not-always-a-square kind of things?
Kelsey was standing outside my door, her high-heeled shoes snapping in time with her fingers as she roused me out of the car. I squared my shoulders, tossed my hair (halfheartedly), and followed Kelsey into the bar.
I made a beeline straight to the bar, wiggled myself onto a stool, and waved down the bartender.
He was a possibility. Blond hair, average build, nice face. Nothing special, but certainly not out of the question. He could be good for simple.
"What can I get for y'all, ladies?"
Southern accent. Definitely a homegrown kind of boy.
Kelsey butted in, "We need two shots of tequila to start."
"Make it four," I croaked.
He whistled, and his eyes met mine. "That kinda night, huh?"
I wasn't ready to put into words what kind of night this was. So I just said, "I'm looking for some liquid courage."
"And I'd be glad to help." He winked at me, and he was barely out of earshot before Kelsey bounced in her seat, saying, "He's the one! He's the one!"
Her words made me feel like I was on a roller coaster, like the world had just dropped and all my organs were playing catch-up. I just needed more time to adjust. That's it. I grabbed Kelsey's shoulder and forced her to stay still. "Chill, Kels. You're like a freaking Chihuahua."
"What? He's a good choice. Cute. Nice. And I totally saw him glance at your cleavage . . . twice."
She wasn't wrong. But I still wasn't all that interested in sleeping with him, which I suppose didn't have to rule him out, but this sure would be a hell of a lot easier if I was actually interested in the guy. I said, "I'm not sure . . . there's just no spark." I could see an eye roll coming, so I tagged on a quick "Yet!"
When Bartender Boy returned with our drinks, Kelsey paid and I took my two shots before she even handed over her card. He stayed for a moment, smiling at me, before moving on to another customer. I stole one of Kelsey's remaining shots.
"You're lucky this is a big night for you, Bliss. Normally, nobody gets between me and my tequila."
I held my hand out and said, "Well, nobody will get between these legs unless I'm good and drunk, so hand me the last one."
Kelsey shook her head, but she was smiling. After a few seconds, she gave in, and with four shots of tequila in my system the prospect of sex seemed a little less scary.
Another bartender came by, this one a girl, and I ordered a Jack and Coke to sip on while I puzzled through this whole mess.
There was Bartender Boy, but he wouldn't get off until well after 2:00 A.M. I was a nervous wreck already, so if this dragged on till the wee hours of the morning, I'd be completely psychotic. I could just imagine it . . . straitjacketed due to sex.
There was a guy standing next to me who seemed to move several inches closer with every drink I took, but he had to be at least forty. No thank you.
I gulped down more of my drink, thankful the bartender had gone heavy on the Jack, and scanned the bar.
"What about him?" Kelsey asked, pointing to a guy at a nearby table.
"Too preppy."
"Him?"
"Too hipster."
"Over there?"
"Ew. Too hairy."
The list continued until I was pretty sure this night was a bust. Kelsey suggested we hit another bar, which was the last thing I wanted to do. I told her I had to go to the bathroom, hoping someone would catch her eye while I was gone so that I could slip away with no drama. The bathroom was at the back, past the pool and darts area, behind a section with some small round tables.
That was when I noticed him.
Well, technically, I noticed the book first.
And I just couldn't keep my mouth closed. "If that's supposed to be a way to pick up girls, I would suggest moving to an area with a little more traffic."
He looked up from his reading, and suddenly I found it hard to swallow. He was easily the most attractive guy I'd seen tonight—blond hair falling into crystal blue eyes, just enough scruff on his jaw to give him a masculine look without making him too hairy, and a face that could have made angels sing. It wasn't making me sing. It was making me gawk. Why did I stop? Why did I always have to make an idiot of myself?
"Excuse me?"
My mind was still processing his perfect hair and bright blue eyes, so it took me a second to say, "Shakespeare. No one reads Shakespeare in a bar unless it's a ploy to pick up girls. All I'm saying is, you might have better luck up front."
He didn't say anything for a long beat, but then his mouth split in a grin revealing, what do you know, perfect teeth!
"It's not a ploy, but if it were, it seems to me that I'm having great luck right here."
An accent. He has a British accent. Dear God, I'm dying.
Breathe. I needed to breathe.
Don't lose it, Bliss.
He put his book down, but not before marking his place. My God, he was really reading Shakespeare in a bar.
"You're not trying to pick up a girl?"
"I wasn't."
My analytical brain did not miss his use of the past tense. As in . . . he hadn't been trying to seduce anyone before, but perhaps he was now.
I took another look at him. He was grinning now—white teeth, jaw stubble that made him look downright delectable. Yep, I was definitely seducible. And that thought alone was enough to send me into shock.
"What's your name, love?"
Love? Love! Still dying here.
"Bliss."
"Is that a line?"
I blushed crimson. "No, it's my name."
"Lovely name for a lovely girl." The timbre of his voice went into that low register that made my insides curl in on themselves—it was like my uterus was tapping out a happy dance on the rest of my organs. God, I was dying the longest, most torturous, most arousing death in the history of the world. Was this what it always felt like to be turned on? No wonder sex made people do crazy things.
"Well, Bliss, I'm new in town, and I've already locked myself out of my apartment. I'm waiting on a locksmith actually, and I figured I'd put this spare time to good use."
"By brushing up on your Shakespeare?"
"Trying to anyway. Honestly, I've never liked the bloke all that much, but let's keep that a secret between us, yeah?"
I'm pretty sure my cheeks were still stained red, if the heat coming off of them was any indication. In fact, my whole body felt like it was on fire. I'm not sure whether it was mortification or his accent that had me about to spontaneously combust in front of him.
"You look disappointed, Bliss. Are you a Shakespeare fan?"
I nodded, because my throat might have been closing up.
He wrinkled his nose in response, and my hands itched to follow the line of his nose down to his lips.
I was going crazy. Actually, certifiably insane.
"Don't tell me you're a Romeo and Juliet fan?"
Now this. This was something I could discuss.
"Othello actually. That's my favorite."
"Ah. Fair Desdemona. Loyal and pure."
My heart stuttered at the word "pure."
"I, um . . ." I struggled to piece together my thoughts. "I like the juxtaposition of reason and passion."
"I'm a fan of passion myself." His eyes dipped down then and ran the length of my form. My spine tingled until it felt like it might burst out of my skin.
"You haven't asked me my name," he said.
I cleared my throat. This couldn't be attractive. I was about as sociable as a caveman. I asked, "What's your name?"
He tilted his head, and his hair almost covered his eyes.
"Join me, and I'll tell you."
I didn't think about anything other than the fact that my legs were like Jell-O and sitting down would prevent me from doing something embarrassing, like passing out from the influx of hormones that were quite clearly having a free-for-all in my brain. I sank into the chair, but instead of feeling relieved, the tension ratcheted up another notch.
He spoke, and my eyes snagged on his lips. "My name is Garrick."
Who knew names could be hot too?
"It's nice to meet you, Garrick."
He leaned forward on his elbows, and I noticed his broad shoulders and the way his muscles moved beneath the fabric of his shirt. Then our eyes connected, and the bar around us went from dim to dark, while I was ensnared by those baby blues.
"I'm going to buy you a drink." It wasn't meant to be a question. In fact, when he looked at me, there was nothing questioning in him at all, only confidence. "Then we can chat some more about reason and . . . passion."
_FAKING IT_
Cade
YOU WOULD THINK I'd be used to it by now. That it wouldn't feel like a rusty eggbeater to the heart every time I saw them together.
You would think I would stop subjecting myself to the torture of seeing the girl I loved with another guy.
You would be wrong on all counts.
A nor'easter had just blown through, so the Philadelphia air was crisp. Day-old snow still crunched beneath my boots. The sound seemed unusually loud, like I walked toward the gallows instead of coffee with friends.
Friends.
I gave one of those funny-it's-not-actually-funny laughs, and my breath came out like smoke. I could see them standing on the corner up ahead. Bliss's arms were wound around Garrick's neck, and the two of them stood wrapped together on the sidewalk. Bundled in coats and scarves, they could have been a magazine ad or one of those perfect pictures that come in the frame when you buy it.
I hated those pictures.
I tried not to be jealous. I was getting over it.
I was.
I wanted Bliss to be happy, and as she slipped her hands in Garrick's coat pockets and their breath fogged between them, she definitely looked happy. But that was part of the problem. Even if I managed to let go of my feelings for Bliss completely, it was their happiness that inspired my jealousy.
Because I was fucking miserable. I tried to keep myself busy, made some friends, and settled into life all right here, but it just wasn't the same.
Starting over sucked.
On a scale of one to ghetto, my apartment was a solid eight. Things were still awkward with my best friend. I had student loans piling so high I might asphyxiate beneath them at any time. I thought by pursuing my master's degree, I would get at least one part of my life right . . . WRONG.
I was the youngest one in the program, and everyone else had years of working in the real world under his or her belt. They all had their lives together, and my life was about as clean and well kept as the community bathrooms had been in my freshman dorm. I'd been here nearly three months, and the only acting I'd done had been a cameo appearance as a homeless person in a Good Samaritan commercial.
Yeah, I was living the good life.
I knew the minute Bliss caught sight of me because she pulled her hands out of Garrick's pockets, and placed them safely at her sides. She stepped out of his arms and called, "Cade!"
I smiled. Maybe I was doing some acting after all.
I met them on the sidewalk, and Bliss gave me a hug. Short. Obligatory. Garrick shook my hand. As much as it irked me, I still really liked the guy. He'd never tried to keep Bliss from seeing me, and he'd apparently given me a pretty stellar reference when I applied to Temple. He didn't go around marking his territory or telling me to back off. He shook my hand and smiled, and sounded genuine when he said, "It's good to see you, Cade."
"Good to see you guys, too."
There was a moment of awkward silence, and then Bliss gave an exaggerated shiver. "I don't know about you guys, but I'm freezing. Let's head inside."
Together we filed through the door. Mugshots was a coffee place during the day and served alcohol at night. I'd not been there yet, as it was kind of a long trek from my apartment up by the Temple campus and because I didn't drink coffee, but I'd heard good things. Bliss loved coffee, and I still loved making Bliss happy, so I agreed to meet there when she called. I thought of asking if they'd serve me alcohol now, even though it was morning. Instead I settled on a smoothie and found us a table big enough that we'd have plenty of personal space.
Bliss sat first while Garrick waited for their drinks. Her cheeks were pink from the cold, but the winter weather agreed with her. The blue scarf knotted around her neck brought out her eyes, and her curls were scattered across her shoulders, windswept and wonderful.
Damn it. I had to stop doing this.
She pulled off her gloves, and rubbed her hands together. "How are you?" she asked.
I balled my fists under the table and lied. "I'm great. Classes are good. I'm loving Temple. And the city is great. I'm great."
"You are?" I could tell by the look on her face that she knew I was lying. She was my best friend, which made her pretty hard to fool. She'd always been good at reading me . . . except for when it came to how I felt about her. She could pick up on just about all my other fears and insecurities, but never that. Sometimes I wondered if it was wishful thinking. Maybe she never picked up on my feelings because she hadn't wanted to.
"I am," I assured her. She still didn't believe me, but she knew me well enough to know that I needed to hold on to my lie. I couldn't vent to her about my problems, not right now. We didn't have that kind of relationship anymore.
Garrick sat down. He'd brought all three of our drinks. I didn't even hear them call out my order.
"Thanks," I said.
"No problem. What are we talking about?"
Here we go again.
I took a long slurp of my smoothie so that I didn't have to answer immediately.
Bliss said, "Cade just finished telling me all about his classes. He's kicking higher education's ass." At least some things hadn't changed. She still knew me well enough to know when I needed an out.
Garrick nudged Bliss's drink toward her and smiled when she took a long, grateful drink. He turned to me and said, "That's good to hear, Cade. I'm glad it's going well. I'm still on good terms with the professors at Temple, so if you ever need anything, you know you just have to ask."
God, why couldn't he have been an asshole? If he were, one good punch would have gone a long way to easing the tightness in my chest. And it would be much cheaper than punching out a wall in my apartment.
I said, "Thanks. I'll keep that in mind."
We chattered about unimportant things. Bliss talked about their production of Pride and Prejudice, and I realized that Garrick really had been good for her. I never would have guessed that out of all of us, she'd be the one doing theatre professionally so quickly after we graduated. It's not that she wasn't talented, but she was never confident. I thought she would have gone the safer route and been a stage manager. I liked to think I could have brought that out of her, too, but I wasn't so sure.
She talked about their apartment on the edge of the Gayborhood. So far, I'd managed to wriggle out of all her invitations to visit, but sooner or later I was going to run out of excuses and would have to see the place they lived. Together.
Apparently their neighborhood was a pretty big party area. They lived right across from a really popular bar. Garrick said, "Bliss is such a light sleeper that it has become a regular event to wake up and listen to the drama that inevitably occurs outside our window at closing time."
She was a light sleeper? I hated that he knew that and I didn't. I hated feeling this way. They started relaying a story of one of those nighttime events, but they were barely looking at me. They stared at each other, laughing, reliving the memory. I was a spectator to their perfect harmony, and it was a show I was tired of watching.
I made a promise to myself then that I wouldn't do this again. Not until I had figured all my shit out. This had to be the last time. I smiled and nodded through the rest of the story, and was relieved when Bliss's phone rang.
She looked at the screen, and didn't even explain before she accepted the call and pressed the phone to her ear. "Kelsey? Oh my God! I haven't heard from you in weeks!"
Kelsey had done exactly what she said she would. At the end of the summer, everyone was moving to new cities or new universities, and Kelsey went overseas for the trip of a lifetime. Every time I looked at Facebook, she had added a new country to her list.
Bliss held up a finger and mouthed, "Be right back." She stood and said into the phone, "Kelsey, hold on one sec. I can barely hear you. I'm going to go outside."
I watched her go, remembering when her face used to light up like that talking to me. It was depressing the way life branched off in different directions. Trees only grew up and out. There was no going back to the roots, to the way things had been. I'd spent four years with my college friends, and they felt like family. But now we were scattered across the country and would probably never be all together again.
Garrick said, "Cade, there's something I'd like to talk to you about while Bliss is gone."
This was going to suck. I could tell. Last time we'd had a chat alone, he'd told me that I had to get over Bliss, that I couldn't live my life based on my feelings for her. Damn it if he wasn't still right.
"I'm all ears," I said.
"I don't really know the best way to say—"
"Just say it." That was the worst part of all of this. I'd gotten my heart broken by my best friend, and now everyone tiptoed around me like I was on the verge of meltdown, like a girl with PMS. Apparently having emotions equated to having a vagina.
Garrick took a deep breath. He looked unsure, but in the moments before he spoke, a smile pulled at his face, like he just couldn't help himself.
"I'm proposing to Bliss," he said.
The world went silent, and I heard the tick-tick of the clock on the wall beside us. It sounded like the ticking of a bomb, which was ironic, considering all the pieces of me that I had been holding together by sheer force of will had just been blown to bits.
I schooled my features as best as I could even though I felt like I might suffocate at any moment. I took a beat, which is just a fancy acting word for a pause, but it felt easier if I approached this like a scene, like fiction. Beats are reserved for those moments when something in the scene or your character shifts. They are moments of change.
Man, was this one hell of a beat.
"Cade—"
Before Garrick could say something nice or consoling, I pushed my character, pushed myself back into action. I smiled and made a face that I hoped look congratulatory.
"That's great, man! She couldn't have found a better guy."
It really was just like acting, bad acting anyway. Like when the words didn't feel natural in my mouth and my mind stayed separate from what I was saying no matter how hard I tried to stay in character. My thoughts raced ahead, trying to judge whether or not my audience was buying my performance, whether Garrick was buying it.
"So, you're okay with this?"
It was imperative that I didn't allow myself to pause before I answered, "Of course! Bliss is my best friend, and I've never seen her so happy, which means I couldn't be happier for her. The past is the past."
He reached across the table and patted me on the shoulder, like I was his son or little brother or his dog.
"You're a good man, Cade."
That was me . . . the perpetual good guy, which meant I perpetually came in second. My smoothie tasted bitter on my tongue.
"You had auditions last week, right?" Garrick asked. "How did they turn out?"
Oh please no. I just had to hear about his proposal plans. If I had to follow that up by relaying my complete and utter failure as a grad student, I'd impale myself on a stirring straw.
Luckily I was saved by Bliss's return. She was tucking her phone back into her pocket, and had a wide smile on her face. She stood behind Garrick's chair and placed a hand on his shoulder. I was struck suddenly by the thought that she was going to say yes.
Somewhere deep in my gut, I could feel the certainty of it. And it killed me.
Beat.
Beat.
Beat.
I should say something, anything, but I was stalled. Because this wasn't fiction. This wasn't a play, and we weren't characters. This was my life, and change had a way of creeping up and stabbing me in the back.
Oblivious, Bliss turned to Garrick and said, "We have to go, babe. We have call across town in like thirty minutes." She turned to me, "I'm sorry, Cade. I meant for us to have more time to chat, but Kelsey's been MIA for weeks. I couldn't not answer, and we've got a matinee for a group of students today. I swear I'll make it up to you. Are you going to be able to make it to our Orphan Thanksgiving tomorrow?"
I'd been dodging that invitation for weeks. I was fairly certain that it had been the entire purpose of this coffee meeting. I'd been on the verge of giving in, but now I couldn't. I didn't know when Garrick planned to propose, but I couldn't be around when it happened or after it happened. I needed a break from them, from Bliss, from being a secondary character in their story.
"Actually, I forgot to tell you. I'm going to go home for Thanksgiving after all." I hated lying to her, but I just couldn't do it anymore. "Grams hasn't been feeling well, so I thought it was a good idea to go."
Her face pulled into an expression of concern, and her hand reached out toward my arm. I pretended like I didn't see it and stepped away to throw my empty smoothie cup in the trash. "Is she okay?" Bliss asked.
"Oh yeah, I think so. Just a bug probably, but at her age, you never know."
I just used my seventy-year-old grandma, the woman who'd raised me, as an excuse. Talk about a douche move.
"Oh, well, tell her I said hi and that I hope she feels better. And you have a safe flight." Bliss leaned in to hug me, and I didn't move away. In fact, I hugged her back. Because I didn't plan on seeing her again for a while, not until I could say (without lying) that I was over her. And based on the way my whole body seemed to sing at her touch, it might take a while.
The two of them packed up to leave, and I sat back down, saying I was going to stay and work on homework for a while. I pulled out a play to read, but in reality, I just wasn't ready for the walk home. I couldn't spend any more alone time locked in my thoughts. The coffee shop was just busy enough that my mind was filled with the buzzing of other people's lives and conversations. Bliss waved through the glass as they left, and I waved back, wondering if she could feel the finality of this good-bye.
Max
MACE'S HAND SLID into my back pocket at the same time the phone in my front pocket buzzed. I let him have the three seconds it took for me to grab my phone, then I elbowed him, and he removed his hand.
I'd had to elbow him three times on the way to the coffee shop. He was like that cartoon fish with memory problems.
I looked at the screen, and it showed a picture of my mom that I'd snapped while she wasn't looking. She had been chopping vegetables and looked like a knife-wielding maniac, which she pretty much was all the time, minus the knife.
I jogged the last few steps to Mugshots and slipped inside before answering.
"Hello, Mom."
There was Christmas music on in the background. We hadn't even got Thanksgiving over with, and she was playing Christmas music.
Maniac.
"Hi, sweetie!" She stretched out the end of sweetie so long I thought she was a robot who had just malfunctioned. Then finally she continued, "What are you up to?"
"Nothing, Mom. I just popped into Mugshots for a coffee. You remember, it was that place I took you when you and Dad helped me move here."
"I do remember! It was a cute place, pity they serve alcohol."
And there was my mom in a nutshell.
Mace chose that moment (an unfortunately silent moment) to say, "Max, babe, you want your usual?"
I waved him off, and stepped a few feet away.
Mom must have had me on speakerphone because my dad cut in, "And who is that, Mackenzie?"
Mackenzie.
I shuddered. I hated my parents' absolute refusal to call me Max. And if they didn't approve of Max for their baby girl, they sure wouldn't like that I was dating a guy named Mace.
My dad would have an aneurysm.
"Just a guy," I said.
Mace nudged me and rubbed his thumb and fingers together. That's right. He'd been fired from his job. I handed him my purse to pay.
"Is this a guy you're dating?" Mom asked.
I sighed. There wasn't any harm in giving her this, as long as I fudged some of the details. Or you know, all of them.
"Yes, Mom. We've been dating for a few weeks." Try three months, but whatever.
"Is that so? How come we don't know anything about this guy then?" Dad, again.
"Because it's still new. But he's a really nice guy, smart." I don't think Mace actually finished high school, but he was gorgeous and a killer drum player. I wasn't cut out for the type of guy my mother wanted for me. My brain would melt from boredom in a week. That was if I didn't send him running before that.
"Where did you meet?" Mom asked.
Oh, you know, he hit on me at the go-go bar where I dance, that extra job that you have no idea I work.
Instead, I said, "The library."
Mace at the library. That was laughable. The tattoo curving across his collarbone would have been spelled villian instead of villain if I hadn't been there to stop him.
"Really?" Mom sounded skeptical. I didn't blame her. Meeting nice guys at the library wasn't really my thing. Every meet-the-parents thing I'd ever gone through had ended disastrously, with my parents certain their daughter had been brainwashed by a godless individual and my boyfriend kicking me to the curb because I had too much baggage.
My baggage was named Betty and Mick and came wearing polka dots and sweater vests on the way home from bridge club. Sometimes it was hard to believe that I came from them. The first time I dyed my hair bright pink, my mom burst into tears, like I told her I was sixteen and pregnant. And that was only temporary dye.
It was easier these days just to humor them, especially since they were still helping me out financially so I could spend more time working on my music. And it wasn't that I didn't love them . . . I did. I just didn't love the person they wanted me to be.
So, I made small sacrifices. I didn't introduce them to my boyfriends. I dyed my hair a relatively normal color before any trips home. I took out or covered my piercings and wore long-sleeved, high-neck shirts to cover my tattoos. I told them I worked the front desk at an accounting firm instead of a tattoo parlor, and never mentioned my other job working in a bar.
When I went home, I played at normal for a few days, and then got the hell outta Dodge before my parents could try to set me up with a crusty accountant.
"Yes, Mom. The library."
When I went home for Christmas, I'd just tell her it didn't work out with the library boy. Or that he was a serial killer. Use that as my excuse to never date nice guys.
"Well, that sounds lovely. We'd love to meet him."
Mace returned to me then with my purse and our coffees. He snuck a flask out of his pocket and added a little something special to his drink. I waved him off when he offered it to me. The caffeine was enough. Funny how he couldn't afford coffee, but he could afford alcohol.
"Sure, Mom." Mace snuck a hand into my coat and wrapped it around my waist. His hand was large and warm, and his touch through my thin tee made me shiver. "I think you would actually really like him." I finished the sentence on a breathy sigh as Mace's lips found the skin of my neck, and my eyes rolled back in bliss. I'd never met an accountant who could do that. "He's very, ah, talented."
"I guess we'll see for ourselves soon." Dad's reply was gruff.
Hah. If they thought there was any chance I was bringing a guy home for Christmas, they were delusional.
"Sure, Dad."
Mace's lips were making a pretty great case for skipping this morning's band practice, but it was our last time to practice all together before our gig next week.
"Great," Dad said. "We'll be at that coffee place in about five minutes."
My coffee hit the floor before I even got a chance to taste it.
"You WHAT? You're not at home in Oklahoma?"
Mace jumped back when the coffee splattered all over our feet. "Jesus, Max!" I didn't have time to worry about him. I had much bigger issues.
"Don't be mad, honey," Mom said. "We were so sad when you said you couldn't come home for Thanksgiving, then Michael and Bethany decided to visit her family for the holiday, too. So we decided to come visit you. I even special ordered a turkey! Oh, you should invite your new boyfriend. The one from the library."
SHIT. SHIT. ALL OF THE SHITS.
"Sorry, Mom. But I'm pretty sure my boyfriend is busy on Thanksgiving."
Mace said, "No, I'm not." And I don't know if it was all the years of being in a band and the loud music damaging his hearing, or too many lost brain cells, but the guy could just not master a freaking whisper!
"Oh, great! We'll be there in a few minutes, sweetie. Love you, boo boo bear."
If she called me boo boo bear in front of Mace, my brain would liquefy from mortification. "Wait, Mom—"
The line went dead.
I kind of wanted to follow its lead.
Think fast, Max. Parentals in T-minus two minutes. Time for damage control.
Mace had maneuvered us around the spilled coffee while I was talking, and he was moving to put his arms back around my waist. I pushed him back.
I took a good look at him—his black, shaggy hair, gorgeous dark eyes, the gauges that stretched his earlobes, and the mechanical skull tattooed on the side of his neck. I loved the way he wore his personality on his skin.
My parents would hate it.
My parents hated anything that couldn't be organized and labeled and penned safely into a cage. They weren't always that way. They used to listen and judge people on the things that mattered, but that time was long gone, and they'd be here any minute.
"You have to leave," I said.
"What?" He hooked his fingers into my belt loops and tugged me forward until our hips met. "We just got here."
A small part of me thought maybe Mace could handle my parents. He'd charmed me, and for most people that was akin to charming a python. He may not have been smart or put together or any of those things, but he was passionate about music and about life. And he was passionate about me. There was fire between us. Fire I didn't want extinguished because my parents were still living in the past, and couldn't get over how things had happened with Alex.
"I'm sorry, babe. My parents have made an impromptu visit, and they're going to be here any minute. So, I need you to leave or pretend like you don't know me or something."
I was going to apologize, say that I wasn't ashamed of him, that I just wasn't ready for that. I didn't get a chance before he held his hands up and backed away. "Fuck. No argument here. I'm out." He turned for the door. "Call me when you lose the folks."
Then he bailed. No questions asked. No valiant offer to brave meeting the parents. He walked out the door, lit up a cigarette, and took off. For a second, I thought about following him. Whether to flee or kick his ass, I wasn't sure.
But I couldn't.
Now, I just had to figure out what to tell my parents about my suddenly absent library-going-nice-guy-boyfriend. I'd just have to tell them he had to work or go to class or heal the sick or something. I scanned the room for an open table. They'd probably see right through the lie and know there was no nice guy, but there was no way around it.
Damn. The coffee shop was packed, and there weren't any open tables.
There was a four-top with only one guy sitting at it, and it looked like he was almost done. He had short, brown curls that had been tamed into something neat and clean. He was gorgeous, in that all-American model kind of way. He wore a sweater and a scarf and had a book sitting on his table. Newsflash! This was the kind of guy libraries should use in advertising if they wanted more people to read.
Normally I wouldn't have looked twice at him because guys like that don't go for girls like me. But he was looking back at me. Staring, actually. He had the same dark, penetrating eyes as Mace, but they were softer somehow. Kinder.
And it was like the universe was giving me a gift. All that was missing was a flashing neon sign above his head that said ANSWER TO ALL YOUR PROBLEMS.
ABOUT THE AUTHOR
**CORA CARMACK** is a twenty-something writer who likes to write about twenty-something characters. She's done a multitude of things in her life—retail, theatre, teaching, and writing. She loves theatre, travel, and anything that makes her laugh. She enjoys placing her characters in the most awkward situations possible, and then trying to help them get a boyfriend out of it. Awkward people need love, too.
Visit www.AuthorTracker.com for exclusive information on your favorite HarperCollins authors.
Books by Cora Carmack
_All Lined Up_
_All Broke Down_
_All Played Out_
_Losing It_
_Faking It_
_Keeping Her (Novella)_
_Finding It_
_Seeking Her (Novella)_
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This is a work of fiction. Names, characters, places, and incidents are products of the author's imagination or are used fictitiously and are not to be construed as real. Any resemblance to actual events, locales, organizations, or persons, living or dead, is entirely coincidental.
Excerpt from Finding It copyright © 2013 by Cora Carmack.
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Half-title page: Close-up of the embrasure for the 57mm chase gun in the Swedish armoured train _Boden_ , which gives an idea of the thickness of the armour.
( _Photo: Sveriges Järnvägs Museum_ )
Title page: Armoured Train PP 53 _Śmiały_ dressed overall for Polish Army Day, on 15 August 1921. ( _Photo: Adam Jońca Collection_ )
Copyright © Paul Malmassari 1989 & 2016
First published in French as _Les Trains Blindés 1826–1989_ in 1989 by Editions Heimdall
This revised and expanded edition first published in
Great Britain in 2016 by
Seaforth Publishing,
An imprint of Pen & Sword Books Ltd,
47 Church Street,
Barnsley
South Yorkshire S70 2AS
www.seaforthpublishing.com
Email: info@seaforthpublishing.com
_British Library Cataloguing in Publication Data_
A catalogue record for this book is available from the British Library
ISBN 978 1 84832 262 2
All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without either prior permission in writing from the publisher or a licence permitting restricted copying. The right of Paul Malmassari to be identified as the author of this work has been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.
Designed by typeset by Mousemat Design Ltd
Printed and bound in China by Imago
## CONTENTS
_Introduction_
Angola
Argentina
Armenia
Austria
Austria-Hungary
Belgium
Bosnia and Herzegovina
Brazil
Bulgaria
Burma-Myanmar
Cambodia
Canada
Chile
China
Colombia
Confederate States of America
Congo-Léopoldville
Croatia (Independent State)
Croatia (Republic)
Cuba
Czechoslovakia
Egypt
Estonia
Finland
France
Georgia
Germany
Great Britain
Greece
Guatemala
Honduras
Hungary
India
Indonesia
Iraq
Irish Free State
Italy
Japan
Latvia
Lithuania
Malawi
Malaysia
Mauritania
Mexico
Morocco
Mozambique
The Netherlands
New Zealand
Nicaragua
North Korea
Norway
Ottoman Empire
Paraguay
Peru
Poland
Portugal
Rhodesia & Zimbabwe
Romania
Russia, USSR & Russian Federation
Slovak Republic
South Africa
South Korea
South Sudan
Spain
Sweden
Switzerland
Thailand
Tunisia
Ukraine
United States of America
Vietnam
Yugoslavia
_Appendix 1_
_Appendix 2_
_Acknowledgements_
## INTRODUCTION
In my native France, for many of us of the generation born before the Internet and the fall of the Berlin Wall, our first meeting with armoured trains was the screening of René Clement's classic film _La Bataille du Rail_ (1946). The famous German armoured train depicted in the film, which has come down to us through the magic of the cinema, would have become the icon of the armoured train, had it not been cut up by the breakers' torches.
Two decades later, we witnessed the destruction of another German armoured train, in the Burt Lancaster film _The Train_ (1964), but it was the dramatic arrival of Strelnikov's armoured train in _Dr Zhivago_ (1965) which imprinted itself on countless imaginations as it punched across our screens, with the scream of its whistle in a forest of red flags, much more than a military machine, in fact a projection of pure power.
The armoured train – which we will use here in the general sense, only referring to 'rail trolleys', 'railcars' and so on in specific cases – is neither an armoured vehicle like the others, nor a train like the others. Neither fish nor fowl, and difficult to classify in the range of military technology, the fall from favour of this weapon probably results from this paradox. The armoured train has usually been denigrated by railway enthusiasts, who have been more inclined (in a Saint-Simonian fashion) to emphasise the social advantages of the railways. Even the famous French author Stendhal expressed the pious hope that 'The railway will render war impossible'. For their part military historians have paid the armoured train scant attention up until recent times: traditionally they dismissed it as the poor relation of the tank, unable to manoeuvre freely, unsuited to offensive missions, and only suitable for policing duties. In sum, in Western culture the armoured train seems to be unworthy of inclusion in any line-up of major weapon systems.
However, even a brief review of the regions, the different historical periods and the conflicts in which armoured trains served will show that they were present almost everywhere, from a single, unique light armoured rail trolley, to heavy trains operating in groups, and even in 'fleets'. Obviously, the approach to their use differs according to the nations involved and the chronological period under consideration. Despite their widespread use, especially since the end of the nineteenth century, the first concise work, written by an Italian, dates only from 1974, followed by an English publication in 1981. In 1989, we in our turn published a detailed study of the subject, opening it up to all countries on all continents. Since then, having taken the measure of the scope of the subject – from a geographical as well as a chronological standpoint – we decided to undertake this new study of the employment of armoured trains across the whole world, from the birth of the railways up until the most recent conflicts, and in as much detail as the existing sources permit.
The bibliographical references, which we have quoted in the Sources for each country's chapter, show that many studies of the armoured trains of individual countries have been published in recent years. However, few of their authors have attempted to set them in the overall context of armoured trains or to make comparisons with other units and their employment. There are many omissions in the links between different chronological periods on the one hand, and on the other, the different means of employment according to geographical area. Historical technical material in museums and archives is widely dispersed, is not referenced on a standard basis, or is often extremely rare. In this encyclopaedia we have therefore decided to follow a logical progression for each separate country, rather than attempt to write exhaustive national histories, which only a historian fluent in the language of the country concerned will be qualified to undertake. Again, where a national work exists, we will not attempt to duplicate the text, but will restrict ourselves to the pictorial aspects.
### Why Study the History of Armoured Trains?
There are three principal reasons.
Firstly, the contemporary use of these units (as in recent years in the former Yugoslavia, in Colombia, in the Caucasus and in Chechnya...) awakens our curiosity and leads us to want to link these events with historical precedents.
Secondly, armoured trains are the victims of a paradox which can be summed up as follows: in light of the common perception that, in order to defeat an armoured train, it simply suffices to cut the tracks, why is it that the armoured train has continued to be widely employed without interruption, and with varying degrees of success, ever since railways were invented? There is obviously a multitude of answers, depending on the mentality and the geography of each user nation, and on their perception of each of the threats the armoured train was intended to counter.
Thirdly, the armoured train is an inseparable part of the railway and military heritage of the nation concerned. Again, a train can be armoured for other than specific military uses, for example as official transport or for transfer of cash and specie. Various numbers of units were built, differing in quality according to the period and the armament mounted. On the other hand, the very design of the units was a reflection of the industrial capacity of the nation concerned and the doctrine for their use: the latter varied depending on the geographical area of influence, later the colonial experience, the various alliances entered into, and an evaluation of the capacities of likely opponents.
### An Overview of the Use of Armoured Trains
Before examining armoured trains on a country-by-country basis, it is sensible to present a general panorama of how armoured trains evolved. Obviously, this panorama will allow us to link technical advancement to the innovations applied to armoured trains, and in particular to attempt to identify trends caused by the observation of equivalent enemy units, their battlefield recovery and repair, and finally by an analysis of the enemy's capabilities. Three major periods can be discerned, each one subject to varying availability of source material:
**1825–1917: APPEARANCE OF THE RAILWAY AND ITS ADAPTATION TO MILITARY REQUIREMENTS**
The appearance of the railway is a Western and European phenomenon. The introduction of the steam engine and its use in industry had already generated many projects (that of Cugnot among others), but the perfection of the iron rail allowed the creation of a homogenous artificial roadway, finally guaranteeing easy transportation. A brief study of the pre-1825 period is thus justified.
**_1765–1825: Pre-history of the motorised vehicle: steam creates the automobile era_**
The steam engine was invented by James Watt in 1765, then in 1769 Cugnot built and tested the first steam-powered automobile. Apart from his artillery tractor, this period was hardly propitious to military automobile applications. Nonetheless, surviving sources indicate a growing intellectual interest in the notion of a 'tank' or 'armoured vehicle' in the true sense of these terms.
**_1825–1871: First adaptations of the railway to military use, appearance of the armoured train_**
Many projects conceived during this period show the influence of the American Civil War, as much by the proposed methods of employment as in the actual construction details. The first appearance of armoured trains in Europe dates from the Franco-Prussian War, and their perceived effectiveness depends on which side prepared the evaluation. Several contemporary projects proposed in France and Great Britain were intended for coastal defence.
**_1871–1917: Colonial use and methodical studies for future armoured trains_**
An analysis of the Franco-Prussian War led to the creation of armoured trains or wagons around the turn of the century by the major Powers. This period also saw the expansion of colonial empires, and armoured trains would be employed in the colonies to maintain internal security, then ultimately to conquer the German colonies in southern Africa in 1914. Great Britain was in the lead, experimenting with and using armoured trains on a large scale, notably during the Second Boer War. On the other hand, it is difficult today to evaluate the significant thought given to developments in Germany. 1917 seems to be a propitious date to end the first period of the history of armoured trains, as the Russian Civil War was about to break out, and 1917 was also the year when the first tanks entered service.
**1917–1945: THE 'GOLDEN AGE', WITH ARMOURED TRAINS IN ACTION ON MULTIPLE FRONTS**
The Russian Civil War would be the first time that relatively modern armies would confront each other on such vast continuous open spaces (from Germany and Poland to the ends of Siberia), which were beyond the capabilities of contemporary armoured vehicles, mainly designed for use on roads. In addition, the Bolshevik Revolution, and the Chinese Revolution which followed, both created a new need for mobile artillery.
During this period, new nations were born from the dismemberment of the Austro-Hungarian Empire on the one hand, and on the other the independence of provinces which had previously been part of Russia. The centre of gravity of the users of armoured trains moved to the East. Thus the Baltic States and Poland based their artillery firepower principally around armoured trains, while Czechoslovakia, Austria, Hungary and Yugoslavia shared the former Austro-Hungarian units. And finally the Revolutionaries inspired by the October Revolution all began to build new armoured trains.
**_1917–1922: Standardisation of the role of armoured trains in combat_**
The young states continued to develop their trains, with national characteristics which became more and more marked, notably in the Baltic States. The employment of the armoured train as the principal weapon system became the norm in the battles which followed the victory of the Entente Powers in 1918, from all the operations in the Russian Civil War, to the Russo-Polish War, the German Revolution and the Baltic Freikorps, the uprisings in Silesia, Hungary, and the Ukraine, and the Civil War in China.
**_1922–1941: Equipping the armies and modernising the armoured trains_**
These efforts begun in the early 1920s were put into effect in the countries of central and eastern Europe. In Germany, after the destruction of the armoured trains ordered by the Inter-Allied Armistice Commission, a new generation was created with the object of maintaining internal security. In Asia, the Sino-Japanese incidents all took place around strategic rail lines, requiring the use of armoured trains by the opposing sides. The Spanish Civil War saw their use by the Republicans, and the Second World War in Europe began at 02.00 in the morning of 1 September 1939 with co-ordinated attacks by armoured trains and trolleys on either side of the Danzig Corridor.
**_1941–1945: The peak of technical and doctrinal development facing widespread partisan warfare_**
With the Wehrmacht's attack on the USSR, for the next four years armoured trains took on an importance which has never been equalled. On the one hand Soviet technical know-how influenced German designs, and on the other, the widespread partisan warfare which broke out behind Axis lines in Russia, the Balkans, France and Poland led to a sense of insecurity which only armoured trains could alleviate. For one side the armoured train had become a 'progressive' political weapon and for the other a symbol of fascist oppression.
**1945–2016: DECLINE AND REGULAR REAPPEARANCES**
1945 marked the end of the fundamental importance of the railway networks. The ALVF disappeared from the military inventory to be replaced by missiles, and while armoured trains lived on as major weapons in certain Communist countries, they mainly continued in an anti-guerrilla role, this time in the overseas possessions of the Western countries. They came to the fore in certain conflicts, but never regained their former primary role despite excellent propaganda successes.
**_1945–1962: Armoured trains during revolutionary struggles_**
Despite the arrival of air superiority and missiles partly replacing conventional artillery, armoured trains did not disappear completely. They remained in use in Russia up until the 1970s and probably also in China. But it was in the front line of the endless crises, conflicts and civil and decolonisation wars that they would play their last and most brilliant card: in the Korean War, the Malaysian Emergency, Cuba, Indochina, Algeria, Netherlands East Indies and the Vietnam War, all of the railway networks virtually without exception made use of them. In the case of France, which had never truly believed in their effectiveness, the armoured trains of Indochina (all erroneously called 'Rafales') would become legendary, while those in Algeria ensured the security of the rail network up to the very end.
**_1962–2016: Railway networks proof against nuclear warfare and frequent reappearances for political ends_**
The immediate effects of nuclear warfare are impressive. On the other hand, the harmful effect of the radiation is the very real enemy of the troops who have to exploit the breakthrough facilitated by the initial strike. To counter the physical effects, attempts to adapt armoured vehicles were undertaken but without any real success. The crossing of contaminated zones by vehicles remained virtually impossible, so in about 1970 in the USSR, special armoured trains were developed, three of which later saw service in the Caucasus. A journey of the North Korean leader to Russia, and the conveyance of Euro banknotes have been the subject of intense media coverage and have helped to keep the armoured train in public awareness, to say nothing of the intense speculations about the supposed discovery of a Nazi armoured train loaded with gold hidden 'somewhere in Poland', and which remains to be proved.
Finally, complete coverage of our subject requires that we consider the perception of the armoured train in the minds of the public, and that we show several examples of their impact on popular culture by way of novels, poems, comic books, films and song.
### Armoured Train Design and Construction Techniques
All the functions united in the crewing of an armoured train give it an all-arms character, bringing together all the various armed services of the nation concerned. And this feature was present from its very beginnings: the ability to manufacture and assemble large armour plates, the use of turrets, and finally the selection of crewmen trained in the use of heavy artillery, pointed to the use of sailors to serve in these land battleships. So it was during the Siege of Paris in 1871, during the British intervention in Egypt in 1882, in the Cameroons and before Antwerp in 1914, in the Russian arsenals... Coast-defence armoured trains, which were the subject of several proposals, would have been the responsibility of the Navy. However, the significant use of armoured trains in operations on the battlefield turned them into an essential arm of land warfare, since in many conflicts they supplanted tanks and other armoured vehicles.
From the moment that aircraft were employed for military purposes, an 'air' component became essential, either in the form of specialised armoured or unarmoured anti-aircraft trains, or by permanently mounting anti-aircraft guns in existing armoured trains. Just as in the case of anti-aircraft ground artillery units, on the trains these pieces were manned in most cases by air force personnel (for example in German armoured trains up until 1942, and British armoured trains from 1940 to 1944). There was also the special case of an improvised armoured train built and manned by the Royal Air Force during the Mau Mau Uprising in Kenya.
The varied appearance of armoured trains remains one of their main characteristics, even if several countries attempted to rationalise the overall design features of these units, which were often assembled in a haphazard manner. The variations could be found at two levels: that of the whole train and that of individual wagons. In the first case, the original configuration would vary following the destruction of wagons on the one hand, and their replacement – or not – by repaired or improved wagons, or by wagons originating in other trains, enemy or friendly, on the other. As for the individual wagons, the availability of the weaponry was more important than the availability of a particular platform to be armoured. The case of Soviet armoured trains (as much for those of the Civil War as for the Second World War) shows that the design of the wagons, despite constants which were obviously imposed under official programmes, varied from one workshop to another, and it is often impossible to ascribe them to any standard regulation type of train. In a similar way, the design features of 'BP 42' and 'BP 44' German armoured trains were applied in the same manner to the trains produced by LHW as to those built in workshops close to the front lines, their silhouettes differing even if the armament was standardised.
### The Role, Missions and Classification of Armoured Trains
Orinally, the mounting of armament on railway wagons arose from the basic need to provide this armament with mobility, which would otherwise be impossible to achieve on the ground due to lack of adequate motive power. As it was necessary to protect the gun crews, the units were armoured. The first armoured trains can therefore be classed in the same category as railway guns.
When each side began to damage railway lines to prevent their use by the opposition, the primary role of the trains became that of protecting the network. This defence was assured by providing a random presence at any point on the line, as well as by bringing down heavy and light firepower while allowing troops and vehicles carried on board to disembark and extend the combat capabilities of the trains. With the increasing intensity of ground firefights, especially towards the end of the Second World War, the armoured and anti-aircraft trains saw their armour protection augmented to the point where they were able to take part in close-range combat, similar to tanks. To this end, their tactics evolved continually since the American Civil War, and specialist units were conceived, tested and developed by all the countries concerned.
Globally, and depending on the specific period, the following missions can be defined, which are not mutually exclusive, as each armoured train was required to be autonomous:
– breakout train (especially in the case of towns or fortresses).
– reconnaissance train.
– artillery train (field and anti-aircraft artillery, light or heavy).
– internal security train/riot control train.
– command train.
– supply train (living quarters, logistics)
– train/railcar for carrying out repairs
– troop training duties.
In order to carry out these missions, each train should be autonomous and thus carry on board, or in close proximity, specialised equipment and crews:
– command element.
– driving element.
– communications element.
– field artillery/mortars (indirect fire).
– anti-tank guns (direct fire).
– anti-aircraft armament.
– flamethrowers.
– assault group (infantry), also for close-in defence.
– possibility of a mobile armoured unit (tank or armoured vehicle carried onboard).
– technical repair unit (engineers).
– scouting element (rail trolley or troops on foot).
– reconnaissance unit (trolley).
- support element (accommodation, galley, medical etc).
**CLASSIFICATION OF ARMOURED TRAINS**
In the absence of an international standard we need to propose a method of classifying armoured rail units to be able to use a common base to describe them. An armoured train is a combination comprising:
– the intended use.
– the offensive and defensive armament carried.
– the makeup of the train (the order of each successive wagon and motor unit).
– the characteristics of the wagons (specialised type, level of protection etc).
– the means of propulsion (steam, diesel-electric, electric, exceptionally, animal power).
According to their intended missions, their zone of deployment and the tactics of each country, the trains can be classed as light, medium, heavy and special. In general, trains carrying a heavy armament, intended for long-range fire are less-heavily protected than trains armed with field guns or anti-tank guns, which bring their armament to bear at close range, which are therefore more exposed, and thus carry thicker armour. The weight, and the power, of the guns to be carried will often decide the choice of the rolling stock to be used as the base for armoured wagons:
– flat wagons, bogie platform wagons = safety wagon, command wagon, anti-aircraft platforms.
– high-sided bogie wagons = wagons armed with tank turrets.
– covered bogie vans = idem, plus machine-gun wagons, assault group transports, galley, infirmary, command...
– four-wheel vans, brake vans = used for their short length, often to separate two major units, or to carry light armament.
– coach = for transporting officers or officials, or when a long armoured unit is required.
This non-exhaustive and particularly unsystematic division of types does not apply to those units built in factories or in well-equipped workshops. On the other hand, for its newer trains (BP 42 and BP 44) the Wehrmacht decided to only use four- or six-wheel rolling stock, wartime experience having revealed that the bogie types were too difficult to lift and put back on the tracks once derailed.
### The Rail War
Before describing the armoured trains and trolleys of each individual country, we will review certain general aspects common to rail warfare, beginning with the raison d'être of armoured trains, namely sabotage on the line.
Mines could be detonated by simple pressure, or by a rack and pinion delay device, which would be set to operate after the pressure of the passage of a certain number of axles, for example to let a safety wagon pass over them but then explode under the engine.
The actual physical destruction of the tracks is not desirable when one intends to use them for one's own trains, notably during the phase of an advance into enemy territory, which of course is not the case for guerrilla forces who do not operate trains. In the 1930s the Russian Army perfected a type of rail torpedo capable of destroying, or at least derailing, an enemy train. Hence the value of safety wagons at the front of trains.
An example in Russia of rails unbolted and left in place, which can appear safe from a distance, but which will twist under the weight of a passing train, or even rails refastened with a slight offset, undetectable by the naked eye but sufficient to drop the wheels of the train onto the sleepers.
_(Photo: Paul Malmassari Collection)_
Removing a mine placed under a length of track, seen here in Russia. The unhappy sapper appears to be a Russian PoW.
_(Photo: Paul Malmassari Collection)_
Sabotage of a set of points, much more difficult to replace than a simple length of rail, again in Russia.
_(Photo: Paul Malmassari Collection)_
Use of small explosive charges in the centre of a length of rail, sufficient to cut it, but easy to repair, in Russia.
_(Photo: Paul Malmassari Collection)_
Sabotage carried out by the guerrillas under Lawrence of Arabia on the Hejaz Railway: the characteristic 'tulip' shape of the rail bent under the force of a very small explosive charge.
_(Photo: N V Salt)_
Placing of an obstacle (here a wheel rim) after unbolting and refastening the fishplate, in Russia.
_(Photo: Paul Malmassari Collection)_
A similar type of sabotage, this time in Algeria in 1957, which targeted the armoured train commanded by Sub-Lieutenant Loiseau.
_(Photo: Dominique Loiseau)_
In Indochina, the Viet Minh used the cattle from nearby villages to pull a section of rail to one side, the inertia effect of which would cause hundreds of metres of track to overturn, or else to drag entire sections off to disappear in the jungle. Here in the distance is the train which has reversed and is ready to use its firepower to protect the repair gang.
_(Photo: BORDAS)_
Reversing the process reset the sections of rail, but it was the troops and often the passengers who had to do the hard work.
_(Photo: BORDAS)_
A Soviet ZhDT-3 rail torpedo, designed in the Podolsk factory in 1938. This simple, cheap 'fire and forget' device could cause considerable damage with its 100kg (220lb) explosive charge, launched at 50km/h (30mph) with a range of some 10km (6 miles). Although five examples of this device were issued to each armoured train in 1941, it is not known whether any were actually used in action. Its principal tactical drawback would have been that in 'Barbarossa', the Germans attacked using tanks, whereas the rail torpedo was most useful against enemy railway traffic, armoured or not, using the Russian broad gauge.
_(Photo: Maxim Kolomiets Collection)_
The primary means of detecting, or better still preventing, a sabotage attempt, is to patrol the line in a random manner. Since the armoured trains were too heavy, only the rail trolleys could carry out this work of scouting and reconnaissance. The panoply of these machines included a myriad of different types, from original railway inspection trolleys to road vehicles converted for rail use. A noteworthy development dating from the First World War period was the specific pairing of a reconnaissance railcar with an armoured train: the armoured train of Captain Schober in Austria and Armoured Train _Orlik_ of the Czech Legion in Siberia, would lead to the NKVD trains coupled to railcars in 1941.
The following list of this type of rolling stock covers the main classifications. The difference between the various types, as well as between heavy, medium and light vehicles, depends on the dimensions of the machines and national predilections, and finally the civil designation of the machine from which the military version is derived.
– reconnaissance trolley (unarmoured, ultimately armed).
– light armoured trolley (with or without turret).
– heavy armoured trolley (with or without turret).
– armoured railcar (without turret).
– multi-turreted railcar (one, two or three turrets, or even four in a Soviet project).
– chase railcar (anti-tank turrets).
– motorised wagon or van.
– armoured car on rails (combined road/rail machines, with integral rail conversion system or with a wheel change, with or without provision for carrying troops for ground combat).
– rail tank.
– design for amphibious road/rail machine.
– expendable remote-controlled vehicle.
The complete Czech armoured train _Orlik_ , with two artillery wagons behind the engine, and the railcar (ex-Russian _Zaamurietz_ ) at the front, capable of patrolling on its own, and itself preceded by a safety flat wagon.
_(Photo: Paul Malmassari Collection)_
Unarmoured reconnaissance trolleys in Finland during the First World War, adequate for use in low-intensity combat zones.
_(Photo: Paul Malmassari Collection)_
Posed propaganda shot, but useful in showing the use envisaged for these trolleys, more to cover working parties than for offensive reconnaissance.
_(Photo: Paul Malmassari Collection)_
A good example of an integral rail conversion system for a road/rail vehicle, on condition that the vehicle's track on the road was the same as the rail gauge. This was the case with this unique SdKfz 231 (6-rad) attached to PZ 3.
_(Photo: Paul Malmassari Collection)_
A completely different approach, these Ford motorcars of the King's Own Royal Regiment converted by the British in Palestine in 1938, were intended only for rail use. This scene also illustrates the fate of numerous trolley crews, sacrificed in order to ensure the safe passage of the trains.
_(Photo: Paul Malmassari Collection)_
Diesel-electric locomotive 060 DY of the _Chemins de fer d'Algérie_ (CFA) which cab has been fitted with armoured shields. Note the vertical sliding door fitted to the side windows.
_(Photo: Paul Malmassari Collection)_
Here in Krapina (25 miles north of Zagreb), the Panzerzug (s.Sp.) 202 is an illustration of the tactical trend which countries confronted with railway warfare were gradually developing, namely self-propelled units capable of employment either in full armoured trains or detached as individual combat units.
_(Photo: Paul Malmassari Collection)_
First introduced by the Soviets with their NKVD railcars, then more widely by the Wehrmacht from 1944 with the PZ le.Sp and PZ s.Sp, reconnaissance units composed of trolleys capable of independent action, coupled together in a small group or in a complete train, seem to have become the norm at the end of the Second World War.
**SECURITY: ANTICIPATION, DISCRETION, ARMOUR, ADAPTABILITY**
Armour, as with all armoured fighting vehicles, is not the sole guarantee of survivability. It is always combined with other functions and capabilities. For the sake of simplicity, we can consider that the rolling stock is either protected, or armoured, or armoured and also armed. The following examples will illustrate several solutions adopted.
The use of wooden sleepers to protect the crew of this 2cm FlaK 38 AA gun at the head of a convoy, covered by a PzKpfw III tank. The protection has been left deliberately low to permit fire against ground targets.
_(Photo: Paul Malmassari Collection)_
Coupled in a German train in Russia, two high-sided wagons have been crudely armoured by fastening steel plates on the inside, rising 50cm above the planking and pierced with loopholes.
_(Photo: Paul Malmassari Collection)_
Based on their previous combat experience, the Poles crewing British armoured trains in 1940 insisted on having a means of entry/egress through the floors of the wagons.
_(Photo: IWM)_
An example of simple necessity: the armouring of only the driving cab of 4-6-2 engine No 231 501, seen at Phnom Pen on 1 December 2001. The track in Vietnam and Cambodia has never been sufficiently robust to allow the complete armouring of engines and locomotives.
_(Photo: Gérard Pouille)_
Armoured driving cab on this diesel locomotive No BB 1005 in a depot in Cambodia. Note the space left between the armour plate and the cab, which increases the protection through causing the projectile to fragment.
_(Photo: Florian Grupp)_
**_The importance of camouflage_**
Camouflage is intended to deceive the eye of the enemy observer, either by disrupting the shape or by making the object disappear. It should be noted that maximum efficiency requires static non-moving machines, emitting neither smoke nor light. The moment a tank or a train begins to move, no camouflage can hide it, and all that can be hoped for is that land-based observers have difficulty in determining its precise position and its nationality. On the other hand, one must consider the psychological aspects: one cannot leave a military train unpainted (metal will rust, wood will rot), and since it is essential to paint it, one can profit from the use of paint intended for other military vehicles. And its crew will always feel less visible in camouflage paint than without it.
In a Russian forest, two lines cross at right angles: a railway line, on which a train is burning, and a forest track. It is useless to try to hide an armoured train. But at least one can delay the moment when it will be clearly identifiable.
_(Photo: Paul Malmassari Collection)_
The plume of black smoke from the steam engine will give away the exact position of this armoured train (PZ 26 to 31) running on the Russian gauge during Operation 'Barbarossa'. Note the armour protection formed from rail lengths fitted to the front of the safety wagon, transforming it into an observation platform.
_(Photo: Paul Malmassari Collection)_
Smoke deflector apparatus on the ex-Austro-Hungarian steam engine of the Polish PP _Smialy_. This unarmoured fitting has suffered from shell or bomb fragments or machine-gun rounds.
_(Photo: Wawrzyniec Markowski Collection)_
Thousands of miles away, but the same principle: this smoke deflector equips a Chinese armoured train of the Fengtian Army in the 1930s. The smoke could be diverted under the engine or along the side of the train.
_(Photo: All Rights Reserved)_
First used in Spain, and lastly up until the end of the war in Indochina, the painting of false rails and sleepers on the vehicles seems to us to be a way of boosting the morale of the crews, rather than an effective camouflage technique.
_(Photo: Paul Malmassari Collection)_
An impression of rails and sleepers painted on the roofs of these Finnish armoured wagons, apparently in two different colours.
_(Photo: SA-Kuva)_
An interesting camouflage scheme on Soviet Armoured Train No 47 of the 12th Armoured Train Battalion.
_(Photo: Paul Malmassari Collection)_
Towards the end of the Second World War, Allied air superiority obliged the Germans to heavily camouflage their trains. Here it is difficult to make out a train composed of s.Sp heavy trolleys at the moment of its surrender to the Americans in 1945.
_(Photo: Paul Malmassari Collection)_
Perfect camouflage for an armoured train in a static position. Seen here in 1914, one can just make out to the left of the gunner one of the wheels of this French train armed with a 95mm gun.
_(Photo: Paul Malmassari Collection)_
The front section of SSZ _Blücher_ in June 1943 reutilising a static PzKpfw I (armed with two 7.92mm MG 13s, in the more distant wagon) and a PzKpfw II (armed with a 2cm KwK 30 or 38) encased in outer armour protection, for anti-partisan duties.
_(Photo: Paul Malmassari Collection)_
Partial camouflage on a Russian armoured train captured near Kiev in 1941. Camouflage based on foliage is difficult to keep attached to moving vehicles, and moreover deteriorates badly, dying leaves being easily spotted in the middle of nearby growing vegetation.
_(Photo: Paul Malmassari Collection)_
**_Offensive capability_**
Ever since the birth of armament carried on the railways, the object was to be able to transport artillery pieces. The evolution of the armoured train having given it an offensive role, it combined all or parts of the three following types of artillery: anti-aircraft, indirect fire (light guns, heavy guns, howitzers, mortars, rockets) and direct fire (notably anti-tank guns). These combinations are found on wagons dedicated to a single type, or on specialised wagons, with in every case close-in defensive armament, distributed along the whole length of the train. The armament is carried either in a casemate firing ahead or to the rear of the train, or in a turret. In the latter case, either the turret alone is mounted, or the turret is mounted on the complete hull of a tank. The type with the complete tank can be in a static version, with only the turret remaining operational, or in a mobile version, in which the tank can fight on board or disembarked, greatly extending the combat radius of the train. Here are several examples, again only a small part of the multiple variations.
Here a BT-7 tank with its engine removed adds to the protection of the wagon and provides the firepower of its 45mm M32 gun and its 7.62mm anti-aircraft machine gun.
_(Photo: Paul Malmassari Collection)_
One of the more advanced design concepts: the Polish Trolley R (for Renault) which fulfilled the dual mission of rail reconnaissance while preserving its ability to disembark without docking facilities in the open countryside to fight at some distance from a train. Following their capture, it appears that these machines influenced the tank transporter wagons of PZ BP 42/44.
_(Photo: Jońca Collection)_
PZ BP 42 and 44 were equipped with two PzKpfw 38(t) tanks. Here we see one mounting aboard the Panzerträgerwagen facing forwards, whereas normally they are seen facing the ramp, ready for rapid deployment. In addition to supplying firepower, the tank served as a command post and forward look-out post. Note the Soviet PPSh sub-machine gun carried by the pipe-smoking crewman.
_(Photo: Paul Malmassari Collection)_
Obsolete tanks were also used by the French Army in Algeria. Here, following an FLN ambush, the tank wagon has remained upright by some miracle, while the rest of the train has been overturned.
_(Photo: Guy Chabot)_
One of the first stages in introducing anti-tank armament: a 7.5cm L/41 gun replacing the limited traverse casemate on PZ 3.
_(Photo: Paul Malmassari Collection)_
The ultimate stage in anti-tank armament on armoured trains: a PzKpfw IV turret armed with the 7.5cm KwK40 L/43 or L/45 (here seen attached to PZ 3 between July and October 1944). A previous stage involved using turrets from T-34s in a similar fashion, by both the Germans and the Soviets.
_(Photo: Paul Malmassari Collection)_
**_Anti-aircraft defence_**
The ability of an armoured train (and in general of all military trains) to survive in modern warfare relies also on the manner in which its anti-aircraft defence is organised. In many armoured trains (Polish, Baltic States, Spanish) the defence of the train itself was provided by machine guns installed either on wagons or on the engine tenders. On several Soviet armoured trains, specialised anti-aircraft wagons were added to the rake. On the other hand, the Wehrmacht, the Soviets from 1943 onward then later in the 1970s, and the Canadians with their Armoured Train No 1, armed certain wagons with anti-aircraft guns, capable also of firing against ground targets.
Twin Maxim SPM 7.62mm machine guns, or in rarer cases a quadruple set, were carried on turrets mounted on the tenders of Soviet steam engines and on railcars. Here is a captured train made up of NKVD D-2 railcars. Note the complete lack of protection for the AA machine gunners, who even lack any form of safety rail to prevent them from firing on each other or into their own train.
_(Photo: Paul Malmassari Collection)_
A twin mounting with 7.62mm ItKk 31 VKT MGs on a Finnish anti-aircraft wagon which allows freedom of movement for the gunners.
_(Photo: Paul Malmassari Collection)_
The anti-aircraft position of PZ 32 (the German armoured train used in the 1946 film _La Bataille du Rail_ ) with a 3.7cm FlaK 36. A quad 2cm Flakvierling 38 was standard equipment on PZ BP 42 and BP 44.
_(Photo: Paul Malmassari Collection)_
At the southern edge of Europe, during the Spanish Civil War, the installation of this anti-aircraft machine gun mounting on either diesel armoured train No 7 or No 8 is very different, favouring the protection of the gunners more than their ability to spot and follow a target. The militiaman is fixing a protective cover over the muzzle of the 70mm Schneider Model 1908 gun.
_(Photo: BN from Rojo y Azul, via Jacinto M. Arévalo Molina)_
The original anti-aircraft trains had been designed to provide strong defences around strategic points such as towns, railway centres, refineries, industrial complexes etc, with no or light armour protection. Over time, they had evolved as the anti-aircraft units drew closer to the front lines, or as the partisans had become bolder and had begun to sabotage the lines used by these trains. Further research is required into whether these developments resulted from specific programmes on the part of the Russians and the Germans.
Russian anti-aircraft train, with only the sides protected against bomb and shell fragments. These captured wagons have been rearmed with 88mm guns.
_(Photo: Paul Malmassari Collection)_
An integral feature of the artillery wagons was the rangefinder in the foreground. Note the rustic nature of the wagon interior.
_(Photo: Paul Malmassari Collection)_
This captured Soviet train was armed with 85mm ZP obr.1939g guns, one of the most efficient Russian anti-aircraft guns.
_(Photo: Paul Malmassari Collection)_
The barrel stuck in the recoil position would indicate that the crew had rendered the gun inoperable prior to abandoning the train.
_(Photo: Paul Malmassari Collection)_
One can make out the origins of this German anti-aircraft wagon: the folding sides of the Russian bogie wagon used as the base have been increased in height by a double skin of planks. The gun is a 7.62cm FlaK M31 or a 7.62/8.8cm FlaK M31(r).
_(Photo: DGEG-Malmassari Collection)_
One of the more developed versions is this wagon with an 8.8cm FlaK 36. In travelling mode, the side nacelles have been lifted and the wagon will now conform to the loading gauge.
_(Photo: DGEG-Malmassari Collection)_
Seen here in firing position, at the base of the mounting the wagon is now twice the width.
_(Photo: DGEG-Malmassari Collection)_
The wagon seen in the previous shot, here in the final stages of construction. The 50-tonne capacity bogie flat wagon used as the basis of this unit is of Russian origin, as per the following drawing.
_(Photo: DGEG-Malmassari Collection)_
The Russian 50-tonne bogie wagon used as the base for many armoured wagons, including the above.
_(Drawing: Die Güterwagen der Regelbauart, Übersichtszeichnungen, Reichsbahn-Zentralamt Berlin, 1945)_
Close-up of one end of the wagon under construction, showing its similarity with the wagons of PZ BP 42 and BP 44.
_(Photo: DGEG-Malmassari Collection)_
A common feature which runs through all the pages of this encyclopaedia is the durability and the capacity of railway rolling stock – and in particular the armoured trains – to be re-used. Observing and following certain wagons and railcars through the various conflicts adds a new dimension compared to that of other armoured vehicles. Thus we can follow the itinerary of many armoured wagons, Austro-Hungarian from 1914 to 1945, Polish and Czech from 1938 to 1945, Russian from 1916 to the Chinese Civil War and then from the 1970s to the present day, French from 1950 to 1975 in Indochina.
This continual regeneration owes much to the solidity of the base platforms, but also to the relative lack of hits on the vital parts of the trains, and finally to the inventiveness of the front-line workshops. The psychological dimension, and by extension the political dimension, form part of the attractiveness of the armoured train.
As a combat platform, the armoured wagon has carried, and still carries, practically all types of existing armament. One can therefore refer to general works for details of the specific armament of a particular period. Again, few wagons or railcars were built for the purpose of being armoured, the vast majority of armoured units being created by fastening a framework covered with armour plates to a standard item of rolling stock. Further details can be sought by reference to the motive power units and the rolling stock of the different countries involved.
### Conclusion
It is not our intention in compiling this encyclopaedia to trace a linear history of the evolution of the armoured train. Nor is it our intention to describe each and every engagement involving armoured trains or the specific confrontations which gave rise to their invention. Our aim is to examine how each individual country invented, experimented with, utilised and, in some cases, abandoned this military weapon system, while not ignoring the effects on states outside the countries of origin. If, as we believe, military progress consists of destroying the adversary by engaging him at longer and longer ranges while remaining better and better protected, then the armoured train has a significant place in the history of military technology and in the genesis of the tank in particular.
Armoured trains (and the armoured railcars and trolleys derived from them) are at the same time a common arm and an atypical arm. The longevity of their success was first and foremost due to their ability to supplant the tanks and armoured vehicles that many nations lacked the means to design or acquire; then to their ability to neutralise or at least minimise the threats to the railway networks on which the logistics of the armies of the Second World War and the wars of decolonisation relied; finally to their capacity for regeneration through repairs, innovation and reuse of captured units. To demonstrate and study armoured trains, over the swathe of the battlefields on which they participated, illustrates the industrial history and the economic, social, cultural and political makeup of a nation.
To conclude, we feel that interest in armoured trains remains strong, whether in order to lift the veil on fascinating and still mysterious military machines, or to encourage the continued design and construction of armoured units, the use of which has never ceased – and will never cease while railway networks continue to be an efficient modern means of transport, and therefore a tempting target of attempts at destruction and obstruction. If as Plato said, necessity is the mother of invention, the story of the armoured train is one of the best proofs that he was right.
An extremely rare shot of an armoured Flak wagon, with a profile which appears to allow the gun to fire at low elevation to either side of the cabin.
_(Photo: DGEG-Malmassari Collection)_
Despite continuing research and analysis, the subject of armoured trains still has many mysteries to be solved: many machines are still unexamined, either because their existence is documented but no photos or drawings have come to light, or the converse such as this photo of an unidentified trolley, which is almost certainly Russian.
_(Photo: Paul Malmassari Collection)_
**SOURCES:**
**Books**
Caiti, Pierangelo, _Atlante mondiale delle artiglierie: artiglierie ferroviarie e treni blindati_ (Parma: Ermanno Albertelli Editore, 1974).
Dupuy, R Ernest, and Dupuy, N Trevor, _The Harper Encyclopaedia of Military History_ (New York: HarperCollins Publishers, 1993).
Heigl, Fritz, _Taschenbuch der Tanks_ , 4 vols (Munich: J F Lehmanns Verlag, 1935 [re-edited in 1970]).
Malmassari, Paul, _Les Trains blindés 1826-1989_ (Bayeux: Editions Heimdal, 1989).
Westwood, John, _Railways at War_ (San Diego: Howell-North Books, 1980).
Zaloga, Steven J, _Armored Trains_ (Oxford, Osprey Publishing Ltd, 2008).
**Journal articles**
Aiby, Lieutenant André, 'L'emploi des trains blindés', _La Revue d'Infanterie_ Vol 83 (November 1933).
'Du XIXe au XXe siècle l'histoire des trains blindés', _Champs de Bataille thématique_ No 43 (November 2015).
Ferrenz, Tirell J, 'Armored Trains and Their Field of Use', _The Military Engineer_ Vol XXIV, No 137 (Sept–Oct 1932).
Gallacher, Ian, 'Armoured Trains', _Military Illustrated_ No 191 (July 2004).
'Les Trains blindés', _La Nature_ No 2150 (12th December 1914).
M., Capitaine, 'Les Trains blindés', _La France militaire_ No 11795 (23 May 1924).
Malmassari, Lieutenant-Colonel Paul, '1914: Quand la voie ferrée annonce le char', _14-18, le magazine de la Grande Guerre_ No 20 (2004), pp 22–7.
Mayer, Major Franz, 'Introduction à l'histoire des trains blindés', _Militär-Wissenschaft und technische Mitteillungen_ (Nov–Dec 1929). Purdon, Charles J, 'Fortress on steel wheels', _Trains_ Vol 41, No 11 (September 1988), pp 30–1.
Urbański, Hauptmann August, 'Über die Verwendung von Panzerzügen im Feldkriege', _Mitteilungen über Gegenstände des Artillerie- und Genie-Wesens_ (1900), pp 402–12.
Van Volxum, Major, 'Le rôle des trains blindés dans les opérations de guerre', _La Science et la Vie_ No 25, (March 1916), pp 305–12.
**University Studies**
Malmassari, Paul, _Etude comparée des trains blindés européens (1826-2000)_ , DEA en Histoire militaire, défense et sécurité, Université Paul Valéry, Montpellier III, under the guidance of Professor Jean-Charles Jauffret, 2004.
**Conferences**
Malmassari, Lieutenant-Colonel Paul, _Les Trains blindés et la fortification au XIX° siècle_ , communication au colloque de l'artillerie, Draguignan, 9 April 2005.
**NOTES ON THE SOURCES AND REFERENCES**
No author can hope to master all the publications in a multitude of foreign languages. Therefore many of the quoted sources are French, but we have listed at the end of each country's chapter all the pertinent references we know of, a certain number of which have been made accessible through translations often supplied by our correspondents. Here we warmly thank them for their efforts. We have made a particular effort to include the maximum number of previously unpublished photographs or those from private collections. Even when making use of archival documents or those kept by museums we have given priority to less-well-known photographs. We must emphasise the aid provided by the Internet, on a worldwide basis, through the ease of correspondence, and the use of online auction sites to acquire items, or the use of search engines to identify documents.
The level of support we have received for this project has been extremely widespread: we have been able to study the majority of the countries thanks to the documents supplied by the archival centres (and which the author has patiently collected over more than thirty years), or by enthusiastic correspondents, historians, eyewitnesses and enlightened amateurs. Sometimes, lacking original documentation on certain units, we have resorted to using unedited photographic evidence furnished by their military opponents of the period, which has left us with serious historical lacuna due to the lack of reliable references.
Again, the level of detail which we can provide varies according to the country under review. For example it is not possible in one volume to name all the commanding officers of the various trains, except for a very few, nor to list each and every single armoured train, railcar and trolley for the major user countries we have covered. We therefore assume full responsibility for the selections we have made, just as we accept any errors that readers may find in this study. They are the responsibility of the Author and not of those who have helped him.
We would therefore like to seize this opportunity to welcome any positive criticism which will allow us to make further progress in our research.
**NOTES ON THE PLANS**
Except where indicated to the contrary, the plans are here reproduced to 1/87th (HO) scale, which is the most popular scale in worldwide railway modelling. Certain plans were previously published in 1989 in our encyclopaedia of _Les Trains Blindés 1826-1989_. We have decided to not reproduce those which suffer from too many inaccuracies, which we discovered as the result of research in the interim, but we have added new plans drawn since then. M. Frédéric Carbon kindly agreed to prepare several plans of vehicles from newly discovered documents. M. Francisco Cruzado Albert kindly authorised us to publish several plans of Spanish armoured trains. Finally, wherever possible we have preferred to reproduce original technical drawings, accepting some minor loss of definition.
. ' _The Battle of the Railways_ '.
. The idiom continues in the modern Russian film _The Last Armoured Train_ , where the true hero is the armoured train itself, which comes through to win at the very end.
. In _Mémoires d'un touriste_ , published in 1837. It would be several decades before the ability of the rail network to facilitate rapid mobilisation and the concentration of forces would dash his hopes.
. Pierangelo Caiti, _Atlante mondiale delle artiglierie: artiglierie ferroviairie e treni blindati_ (Parma: Ermanno Albertelli Editore, 1974). Two previous volumes by D Bishop and K Davis, _Railways and War_ (London: Blandford Press Ltd, 1972 and 1974) had included some armoured trains.
. George Balfour, _The Armoured Train, its development and usage_ (London: B T Batsford Ltd, 1981).
. Paul Malmassari, _Les Trains Blindés 1826–1989_ (Bayeux: Editions Heimdal, 1989).
. The majority of the German archives were destroyed during the bombing of Potsdam in 1945, along with the destruction of Breslau where PZ BP42 and BP44 had been built.
. ALVF: _Artillerie Lourde sur Voie Ferrée_ = Heavy Railway Guns.
. Such as the Russian 'Object 279' prototype tank, with its quadruple track system and armoured hull specially contoured to resist being overturned by a nuclear shockwave.
. The same reasons led the British to ascribe a 'naval' connotation to the first tank developments: the project was the responsibility of the Admiralty, the first tanks were described as 'land battleships', their tactical employment was initially copied from naval rules of engagement, etc
. George Balfour, _The Armoured Train, its Development and Usage_ , (London: B T Batsford Ltd, 1981).
. ItKk, or _Kaksoisilmatorjuntakonekivääri_ = Twin anti-aircraft machine gun. KKT or _Valtion Kivääritehdas_ = State rifle manufacturing factory.
## ANGOLA
### ARMOURED TROLLEYS
The end of the war of independence saw the beginning of the civil war which lasted up until 1991. Several ex-Portuguese Wickham Type 42 armoured trolleys (see the chapter on Portugal) continued in service, notably on the southern rail network, the C.F.B. ( _Caminho de Ferro de Benguela_ ). Here their role was to counter possible incursions by the South African armed forces supporting UNITA.
A Wickham Type 42 armoured trolley photographed outside the Huambo railway workshop in January 1987.
_(Photo: DuSewrer)_
**SOURCES:**
_Defensa_ No 33.
. Independence from Portugal was declared on 11 November 1975.
. _União Nacional para a Independência Total de Angola_.
## ARGENTINA
### AUTOVIA PAGADOR PE-1 ARMOURED RAILCAR
In 1941 the _Ferrocarril del Sud_ put an armoured railcar into service. Built by Buxton Ltd in Buenos Aires on the chassis of an Austin truck, it was designed to transport cash on the railway network at a maximum speed of 50km/h (30mph), and weighed 7.52 tonnes. Light weapons could be fired through slits, and security was enhanced by automatic doors, which were quite rare at the time. It was used to convey cash collected at the railway stations. This vehicle was restored by the Ferroclub Argentino between September 2001 and September 2007.
Front view of the PE-1 Railcar. It has a wheelbase of 4m (13ft 1½in), was 6.78m (22ft 3in) long overall, and 1.88m (6ft 2in) wide.
Despite appearing almost symmetrical, the PE-1 has only one driving position (here on the left), and has to be turned by means of a turntable seen here resting on top of a wooden block.
_(Photos: Ferroclub Argentino)_
## ARMENIA
### First Democratic Republic of Armenia – Armoured Trains (1918–1920)
Towards the end of the First World War, the collapse of the Russian Empire and its forces in the Caucasus left the Armenians exposed to Ottoman attack. Following the break-up of the short-lived Transcaucasian Federation, the First Democratic Republic of Armenia was proclaimed on 28 May 1918. The Treaty of Versailles did not resolve the question of the frontiers of the new Armenian state, which was in conflict with its neighbours in a tangle of ethnic and religious issues.
In the course of these conflicts, during the Turkish-Armenian War of September to November 1920 and the subsequent invasion and takeover of Armenia by Bolshevik forces, several armoured trains – no doubt having their origins in the Russian Civil War – were employed. The lack of reliable independent sources does not allow us to construct an accurate historical record of these trains and the actions in which they were engaged.
### _Soviet Armenia_
During the Second World War, an armoured train bearing the name _Soviet Armenia_ recalled the status of this nominally autonomous Republic (1936–91).
Two photos of the Type OB-3 armoured train _Soviet Armenia_.
_(Photo: Paul Malmassari Collection)_
The turrets are armed with 76.2mm Model 27/32 guns, identical to those mounted in T-35 tanks, plus a quadruple 7.62mm machine-gun mounting.
_(Photo: Paul Malmassari Collection)_
## AUSTRIA
Before considering the history of Austrian armoured trains, it is first necessary to detail the successive states that succeeded the Empire, then the separate countries which arose from it. The armoured trains of the latter will be found in the corresponding country's chapter.
The Austrian Empire lasted up until 1867. In that year Emperor Franz Josef I was crowned King of Hungary, and the new Empire (the Dual Monarchy) thus created lasted until 1918. It united the Imperial Crown of Austria (Austria, Bohemia and Galicia) with the Royal Crown of Hungary (Hungary and Croatia-Slavonia), and in 1908 Bosnia-Herzegovina officially joined the Dual Monarchy. After 1918 the Austro-Hungarian Empire, dismantled by the Treaty of St Germain, fractured into five separate nation-states: Austria, Hungary, Czechoslovakia, Poland and the Kingdom of Serbia (which included the territories of the Croats and the Slovenes). Parts of former Imperial territory were also annexed by Romania and Italy. The Treaties of St Germain (10 September 1919) and Trianon (4 June 1920) established the new frontiers of Austria and Hungary. The First Austrian Republic existed until 12 March 1938 when it was absorbed into the German Reich.
Concerning the first armoured trains of the Austrian Empire, an article in a French military journal published in 1851 stated that in Austria 'for several years now wagons [have been built] so arranged as to allow infantry platoons to bring into play their weapons as necessary'. This probably refers to trains built to counter the revolution of 1848.
After November 1918, the First Austrian Republic was affected by problems caused in large part by the Empire's defeat, and then by the Wall Street Crash of 1929. Demonstrations in 1918–19 led to the construction of an armoured train in January 1919 in the state railway workshops in Villach. The train, designated PZ XIII (following on from the numerical series of the Austro-Hungarian armoured trains), went into action in Carinthia and lost its locomotive (one of the Class 29 C-n2 series). Wagons Nos 1 and 2 were converted from Types G and O respectively, with improvised ballast protection and armed with heavy machine guns. After derailing on 31 May 1919, Wagon No 2 was rebuilt, this time with improved armour protection and an observation cupola. In addition, it could now deploy a 37mm Italian M 15 gun. The train was disarmed following the cessation of hostilities between Austria and Yugoslavia on 6 June 1919.
PZ XIII in its original form in January 1919. Note the wooden protection on the cab of the engine. The thickness of the ballast protection can be gauged from the openings for the 8mm Schwarzlose machine guns.
_(Photo: All Rights Reserved)_
Civil war broke out in February 1934, setting government supporters against the socialists and revolutionaries. At that time trains were armoured to ensure the security of the lines of communication.
On 27 January 1938 Panzerzüg M 39, a modern armoured train with electric propulsion, was designed by _Abteilung PV_ which produced the sketch above. At that stage the armour protection had not been finalised, in contrast to the optical equipment and the armament.
The 1938 sketch shows the overall layout of the projected train. The central railcar would have mounted 40mm M 36 anti-aircraft guns (licence-built Bofors) and four M7/12 heavy machine guns. Each artillery wagon was to have been armed with a turret-mounted 100mm M 14 or M 38 howitzer and two heavy machine guns. Finally, thirteen men were to form the crew of the railcar and an assault group would be divided between the two wagons. Work on the project was brought to a halt by the _Anschluss_.
**SOURCES:**
'Des Chemins de Fer considérés au point de vue militaire', _Le Spectateur Militaire_ Vol 50 (June 1851), p 306.
One of the six Panzerzüg Types M 33 ordered by the Bundesheer, photographed on 13 February 1934 in Vienna-East Station. In front and rear of the 2-6-2 Class 73 kkStB engine (with armour protecting the upper part of the cab door) are two Type O wagons, with internal armour protection. Trench shields protect the riflemen, while in the centre of the wagon is a Schwarzlose M1907/12 machine gun behind its characteristic shield.
_(Photo: Paul Malmassari Collection)_
. _Pionier und Verkehrstechnik_ , Engineers and Transport Technical Section.
## AUSTRIA-HUNGARY
### ARMOURED TRAINS AND RAILCARS
Austria-Hungary formally came into existence on 29 May 1867 and was dissolved on 31 October 1918. When the Empire went to war on two fronts in 1914, the Army possessed no armoured trains. During the first months of the war, the Austro-Hungarian Army was forced to pull back in the face of Russian forces which outnumbered them three-to-one, and they were unable to transfer sufficient men from their second front due to initial Serbian Army successes. In view of the serious situation, local commanders organised improvised armoured trains, such as the one formed by Captain Schober, commander of the 15th Railway Company. These improvised trains served as the basis of experiments leading to the production series which was built during the Winter of 1914–15.
These eight standardised armoured trains were built by MÁV in the Budapest-North workshops. In his study published in 1992, Professor Dr Wolfgang Sadowny showed that no official classification had in fact existed. The author had previously accepted an incorrect classification commonly used in the 1980s. To rectify the situation, we can now use Dr Sadowny's classification system, as follows, to describe the makeup of the three types of armoured train (from front to rear):
– Infantry wagon/engine/infantry wagon = Type A, of which the prototype was PZ II.
– Wagon with turret-mounted gun/engine/infantry wagon/second engine/wagon with turret-mounted gun = Type B.
– Artillery wagon/infantry wagon/engine/infantry wagon = Type Ae or Ae* according to the type of artillery wagon.
The ten standard armoured engines were all of the MÁV Class 377 (overall length of 8.105m [26ft 7in]), while Dr Sadowny classifies the infantry wagons into three types:
– Type 1: using Type 140 wagons, with handbrakes, lockers for equipment mounted beneath the body, and an observation cupola (six examples built).
– Type 2: using wagons Types 148 to 150, without handbrakes, water tank carried centrally, locker for additional coal supply (seven examples built).
– Type 3: using Type 150 wagons, with a water tank at the end nearest the leading engine, and machine-gun positions at the ends (two examples were built, and were used only with PZ VII and VIII).
The first five armoured trains (Type A) were divided between the _Eisenbahn-Linienkommando Debreczen_ (three units) and the _Feldtranportleitung_ at Miskolcz (the remaining two units), to carry out reconnaissance missions and cover troop withdrawals. The first two trains reached the Front on 10 November 1914, and the three others, apparently with a sixth train added, followed at intervals up until 20 November. The Type B trains, PZ VII and VIII, entered service in March 1915. These two armoured trains included armoured wagons with a turret (approx 270 degrees horizontal field of fire) mounting a 7cm L/30 gun (the actual calibre of these guns, designed for use on torpedo boats, was 66mm). Five such wagons were built, one going to reinforce PZ V, while PZ I and II each received an artillery wagon built in 1915 on tender chassis.
Following Italy's entry into the war on 23 May 1915, two armoured trains were built in the workshops at Villach, in Carinthia. Initially numbered I and II, to avoid confusion they were subsequently renumbered as PZ IX and X in late October 1915.
The first armoured train designed by Captain Schober, commander of the 15th Railway Company, seen here in Galicia in 1914. The intention is obviously to provide the train commander in the armoured engine with an elevated position compared to the low profile of the infantry wagons (with their less comfortable firing positions), for him to be able to see over both ends of the train.
_(Photo: Paul Malmassari Collection)_
In the Spring of 1915, the workshops at Neu-Sandec began construction of the second armoured train designed by Captain Schober. Initially it was composed of a Class 59 engine and two six-wheel wagons. On 1 May 1915 the train was ready, and after several tests, the Class 59 engine was replaced by fully-armoured engine No 97.247 coupled to tender No 76.177. A new motorised six-wheel wagon was also included, armed with a turret mounting a 7cm L/30 QF gun. This wagon was powered by a petrol-electric engine driving the central axle, and when detached on reconnaissance it could run at up to 40km/h (25mph). The complete train was crewed by sixty-five officers and men, and in addition to the main gun it was armed with eight machine guns. After modifications, it returned to service in July 1915, initially under the name of its designer, as _Panzerzüg Schober_ , then in the Spring of 1916 it was redesignated PZ XI.
The numerical series contained another train, PZ XII, of which no trace remains in the official archives. Powered by a Class 229 engine, it appears to have comprised two armoured wagons built on Series O originals, to a design closely resembling that of Captain Schober's first armoured train.
Aside from the standard armoured train designs, several experiments were carried out, such as adding a high-sided bogie wagon protected with lengths of rail and armed with an 8cm gun to PZ VII; or again mounting a 10cm naval gun on a wagon attached to PZ V. In addition, improvised armoured trains were also built to meet local needs: in the Spring of 1915, an armoured train was built at Cracow using armoured engine No 229.85 and two wagons armed with machine guns. When Romania entered the war on 28 August 1916, the Railway Command at Bucovina ordered the construction of a train to protect the Jakobeny-Dorna Völgy line. Lastly, at least one narrow-gauge armoured train was put into service on the metre-gauge network in Bosnia.
The Class 59 engine of Captain Schober's first armoured train, with hastily-added armour which covers only the most vital parts.
_(Photo: Paul Malmassari Collection)_
This photo shows the prototype train PZ II just out of the shop, without its artillery wagon which would not be built until 1915, and also lacking its observation cupola. Note that the machine-gun embrasures in leading wagon No 140.914 are inset at the top at an angle, whereas later photos of PZ II show that they were modified to sit flush with the armoured sides.
_(Photo: Paul Malmassari Collection)_
Tactically, the armoured trains were operated in pairs for mutual support, as proposed by Captain Kossowicz, commander of the 5th Railway Company. The same deployment would be adopted by the Red Army.
Following the relative stabilisation of the various fronts, the need for armoured trains lessened, and in September 1917 it was decided to demobilise six trains: thus PZ I, III, VI, X, XI and XII were laid up, and only PZ II, IV, V, VII and VIII remained in service (PZ IX having been destroyed during the previous month). The remaining trains were organised in a new manner, with the artillery wagon leading, then the engine, followed by an infantry wagon. A second infantry wagon would be held in reserve in the support train. The existing rolling stock was redistributed, making the later trains difficult to identify in photographs. In the Spring of 1918, a number of armoured trains were built to the Russian broad gauge for operations in Russia, but at the time of writing no trace of their deployment and fate has come to light.
At the end of the war, the surviving trains (PZ I to VII and PZ XI) were shared out between the following countries (refer to the corresponding country chapters for their subsequent use):
– PZ IV, VII (1917 numbering), XI (less its engine) and parts of PZ I, VI and VIII to Hungary.
– PZ III and part of PZ VIII to Poland.
– PZ II and parts of PZ VI and VII to Czechoslovakia.
– PZ V and part of PZ I to Yugoslavia.
The excellence of their basic design, their capacity for further development and their underlying durability are proved by their continual employment up until 1945, often in adverse conditions.
Drawing of MÁV Class 377 engine.
_(Paul Malmassari)_
The rear wagon (No S 150.003) of PZ II before modification of the machine-gun embrasures. Note the arrangement for the machine-gun fitting in the door facing away from the engine, and also the coupling rail, doubtless attached to a safety wagon. There were no cowcatchers/stone guards fitted to the infantry wagons of PZ I, II and III.
_(Photo: Paul Malmassari Collection)_
PZ I entered service with only two wagons and the engine, but in 1915 this artillery wagon was added. Note the safety flat wagons in front.
_(Photo: Paul Malmassari Collection)_
A rare interior view of an infantry wagon, with the shield for the lateral machine gun. The external armour was 12mm thick, fitted over a 40mm layer of wood, plus an internal layer of armour.
_(Photo: Paul Malmassari Collection)_
Here is PZ I apparently leading a part of a different armoured train.
_(Photo: Paul Malmassari Collection)_
PZ II has here received its header wagon built on a tender chassis and armed with a 7cm L/30 chase gun.
_(Photo: Paul Malmassari Collection)_
Here the side machine-gun positions of the infantry wagons are clearly vertical and flush with the armour sides. The header wagon is armed with a 4.7cm gun on each side, and these, plus the 7cm chase gun, gave it formidable firepower.
_(Photo: Paul Malmassari Collection)_
Two views of PZ II (with the number painted on the engine) being inspected by Archduke Karl, who would become Emperor on 21 November 1916 as Karl 1. Note that the cab window is not yet protected by armour.
_(Photos: Paul Malmassari Collection)_
At the rear of PZ II can be seen a high-sided bogie wagon which appears to be carrying a field gun. Behind engine MÁV 377.116 is wagon No S 150.003 and in front, No 140.914.
_(Photo: Paul Malmassari Collection)_
A superb photo of one of the side-mounted 4.7cm l.F.K. guns in the header wagon of PZ II.
_(Photo: Paul Malmassari Collection)_
PZ II photographed on 5 August 1915, festooned with traditional decorations for a public celebration. The Austrian flag flies proudly in front of the left-hand wagon, on which the column on the rear facing the engine denotes the handbrake. Note also the rectangular armour plate covering the engine cab.
_(Photo: Paul Malmassari Collection)_
Probably a view of wagon No S 148.105 of PZ V in camouflage, fitted with the cowcatchers used on PZ IV, V and VI.
_(Photo: Paul Malmassari Collection)_
An overall view of a Type B PZ. Four hooks seen on the armour skirt around the turret were used to clamp the turret in place when travelling.
_(Photo: Paul Malmassari Collection)_
A fine attempt at camouflage on PZ VII, easily recognisable by the circular ventilator cowls on the turret.
_(Photo: Paul Malmassari Collection)_
The artillery wagon with its 70mm turret was characteristic of Type B armoured trains. On this wagon, which is carrying sleepers and lengths of rail, is painted the name 'Oberleutnant Becker', perhaps the commander of the train.
_(Photo: Paul Malmassari Collection)_
This overhead view is interesting because it allows us to see the horizontal armour on the top of the engine. Detailed differences sometimes allow us to tell one MÁV Class 377 engine from the others. The lighter tone of certain armour plates tell of more recent additions. This is PZ VII, and the artillery wagon in the foreground is No 141.172, fitted with angular ventilator cowls on its turret.
_(Photo: Paul Malmassari Collection)_
This armoured wagon mounting a 10cm L/50 naval gun, seen here at the exit from the Montfalcone tunnel in the Summer of 1916, was temporarily attached to PZ V.
_(Photo: Paul Malmassari Collection)_
This view of PZ VII allows us to see the shape of the rear face of the artillery turret of wagon No 141.963 which precedes one of the engines, either MÁV 377.455 or 377.118. Between the two engines is wagon No S 150.271.
_(Photo: Paul Malmassari Collection)_
PZ VII was immediately recognisable by the round shape of the armoured ventilator cowls on wagon No. 140.963, while the wagon at the other end of the train had angular ones.
_(Photo: Paul Malmassari Collection)_
Some time in 1915 this high-sided bogie wagon MÁV No Ikn 169.011 armoured with a double row of rails was coupled to PZ VII. The chase gun was an 8cm Feldkanone M 05. The wagon was dismantled in December 1915 as it blocked the field of fire of the wagon behind it.
_(Photo: Paul Malmassari Collection)_
A fine photo of life on the Italian or Russian Front, with a Škoda 30.5cm Model 1911 howitzer and the pensive crew of a Type B armoured train observing the piece. No doubt some are wondering how they could carry off the howitzer for some additional firepower.
_(Photo: Paul Malmassari Collection)_
Red Cross postcard representing an attack on the Russians, specifically the Cossacks, with a certain amount of artistic licence.
_(Postcard: Paul Malmassari Collection)_
The Carinthian PZ I which would become PZ IX, seen here on 1 October 1915, with its original number 'I' painted on its sides. The embrasures allowed the crew to bring to bear two Russian machine guns and thirty personal weapons. The engine is probably a Class 97.
_(Photo: Paul Malmassari Collection)_
Several months later, an 'X' has been added beside the 'I' to form the number 9 in Roman numerals. The crew complement of each of these Carinthian PZ was two officers and thirty-three men. PZ IX would be destroyed by Romanian artillery fire on 29 August 1916.
_(Photo: Paul Malmassari Collection)_
The second of the Carinthian armoured trains, with its engine No 63.07, was given the designation PZ X in the revised numbering system. The armoured wagons are Ke 65.370 (on the right) and K 802.163 (on the left). Here it is seen at Tarvis.
_(Photo: HGM)_
The engine of the improvised armoured train built by the 19th Railway Company in the Summer of 1916, probably a Class 94 of the Bucovina Railway.
_(Photo: Paul Malmassari Collection)_
This improvised armoured train was employed in 1916–17 in the Jacobeny region of Bucovina, before being destroyed in May 1917.
_(Photo: Paul Malmassari Collection)_
An overall view of the train.
_(Photo: Paul Malmassari Collection)_
The header wagon bearing the inscription '19 E.K.' after the 19th Railway Company which built it.
_(Photo: Paul Malmassari Collection)_
The initial configuration of PZ _Schober_ , with a Class 59 armoured engine, identical to the one which powered the original armoured train designed by Captain Schober. The two wagons are numbered 314.706 and 334.457.
_(Photo: Paul Malmassari Collection)_
The improved version of PZ _Schober_ was built in the Spring of 1915 and was renumbered PZ XI in 1916. The new engine (its lower armour protection not yet in place) was No 97.247 coupled to tender No 76.177. Here the train has not yet been fitted with the antennae on the wagon roofs.
_(Photo: Paul Malmassari Collection)_
This view of the entire train allows us to compare the two sides of the motorised armoured wagon, and to note the presence of the radio masts, as shown in the drawings below, and which would ultimately be removed. Also, in this configuration the motorised wagon is coupled to the rear of the train.
_(Photo: Paul Malmassari Collection)_
The front end of the wagon is differentiated by having only three firing embrasures, compared to five at the rear end, plus the radiator grill. Here the searchlight can be clearly seen, together with its power cable which feeds it at all angles of training of either its housing or the turret.
_(Photo: Paul Malmassari Collection)_
Rear view of motorised wagon No 303.343 (in German a _Motorkanonenwagen_ ). It weighed 45 tonnes and was 9.86m (32ft 4in) long overall. The cylinder on top of the turret contains a trainable searchlight.
_(Photo: Fortepan)_
In this photo dated March 1916 note the machine guns mounted in the firing embrasures, the stone guard fitted in front of each end wheel, and the Austro-Hungarian flag proudly flown. On each of the three wagons in the train, access was by hatches in the roof, reached by means of the handrails and steps at each corner.
_(Photo: Paul Malmassari Collection)_
An inspection by Archduke Friedrich, Duke of Teschen, on the Carpathian Front in February 1917. Commander-in-Chief of the Austro-Hungarian Army, he would be dismissed from his post by the Emperor just a few days later.
_(Photo: Paul Malmassari Collection)_
In this previously unpublished photo, from a glass-plate negative, note the flat face of the low-profile infantry wagon facing the tender. On each of the two infantry wagons, this end had a machine-gun port in the centre. In the diagram reproduced below the lead wagon is shown running with this flat face forward, so this position would then become the chase gun.
_(Photo: Paul Malmassari Collection)_
Probably the only photo showing the wreck of PZ XI, perhaps as the result of an artillery bombardment to judge by the churned-up earth. PZ XI was withdrawn from service in September 1917.
_(Glass-plate negative, date and place unknown: Paul Malmassari Collection)_
Engine No 97.247 of PZ XI with its fully-armoured tender seen at Roveretto. Under the canvas sheeting is railcar No 303.343.
_(Photo: HGM)_
The theoretical layout of PZ _Schober_. It appears that the normal position for the motorised wagon was at the rear of the train, perhaps to enable it to manoeuvre independently in case the train was immobilised.
_(Plan: Private Collection)_
Drawing of the motorised wagon. A close inspection of the observation slits in the turret shows that they are neither symmetrical nor regularly spaced.
_(Plan: Private Collection)_
Drawing of one of the two identical infantry wagons, clearly illustrating the armour protection formed from lengths of rail.
_(Plan: Private Collection)_
Drawing of engine No 97.247 with its tender No 76.177.
_(Plan: Private Collection)_
In 1916 the train which would later be numbered PZ XII was attached to XXV Army Corps, powered by a Class 229 2-6-2 tank engine, coupled to an auxiliary armoured tender. The appearance of the armoured wagons is very similar to those of Captain Schober's first train, illustrated at the beginning of the chapter.
_(Photo: Hungarian Historical Service)_
PZ IV (new numbers in 1917) was put together with units from PZ VII. Here we can clearly see one of the hooks which held the turret in the travelling position.
_(Photo: Paul Malmassari Collection)_
An unidentified armoured train, which we believe to be an Austro-Hungarian unit in Galicia, perhaps dating from after the Russian retreat in May 1915. Close inspection of the original photo reveals an inscription in Cyrillic letters on the door of the building visible between the chimney and steam dome of the engine.
_(Photo: Paul Malmassari Collection)_
An unofficial badge issued to commemorate 'Christmas at the Front' in 1916.
_(Badge: Paul Malmassari Collection)_
An unofficial badge produced for the Hungarian crews of armoured trains in 1914–16.
_(Badge: Paul Malmassari Collection)_
Two Type B armoured trains were built. But in this photo we are looking at either a reorganisation, or rolling stock brought together at the end of the war. Note the smoke deflector on the left-hand engine.
_(Photo: Paul Malmassari Collection)_
In 2003 the Austrians commemorated their armoured trains by issuing this postage stamp, showing the artillery wagon which was perhaps the most iconic image of these trains.
_(Photo: Paul Malmassari Collection)_
An armoured train assembled by the Czechs: the engine is probably No 377.362 from PZ VI (recognisable by the cupola on the cab roof), coupled between the wagons of PZ II which was captured in Prague. The nearest wagon is No 140.914, and the one behind the engine is No 150.003. The Czech soldiers are wearing Italian uniforms.
_(Photo: Paul Malmassari Collection)_
**SOURCES** :
**Books:**
Hauptner, R, and Jung, P, _Stahl und Eisen im Feuer_ (Vienna: Verlagsbuchshandlung Stöhr, 2003).
Scopani, Paolo, _L'Ultima guerra dell'impero austro-ungarico, Storia fotografica delle operazioni militari sul fronte russo, serbo-albanese ed italiano 1914-1918_ (Novale-Valdagno: Gino Rossato Editore, 2002).
**Journal articles:**
Lankovits, J., 'Panzerzüge in Österreich und Ungarn', _Eisenbahn_ (Austria) (1986), No 8, pp 142–6; No 9, pp 164–7; No 10 pp. 184–6.
Sawodny, Wolfgang, 'Die Panzerzüge Österreich-Ungarn und ihre Verbleib', _Eisenbahn_ (Austria) (1992), No 2, pp 26–8; No 3, pp 44–6; No 4, pp 64–6; No 6, pp 105–8.
**Website:**
<http://www.heeresgeschichten.at/>
. The Austrian and Hungarian armoured trains after this date are covered in their individual chapters.
. Sawodny,'Die Panzerzüge Österreich-Ungarn und ihre Verblieb', p 26.
. Debreczen Line Railway Command and Campaign Transport Directorate.
. Probably in commemoration of the battle of Petrovaradin in 1716, a victory over the Ottoman Empire.
. The actual calibre was 76.5mm.
## BELGIUM
### ARMOURED TRAINS 1914–1915
A small country sandwiched between the two main belligerent powers of the First World War, in 1835 Belgium had embarked on the construction of an extensive railway network, just five years after the country had won its independence. By 1914 the network included some 4400km (2700 miles) of main line, backed up by around 4000km (2500 miles) of branch lines. Its sovereign territory was invaded on 4 August 1914, and the armoured trains (constructed primarily for the defence of Antwerp) would play a significant role in the conflict, as much from a psychological viewpoint as from their military impact. And this especially when one compares their numbers and their actions with the size of Belgium. The railway troops were formed in 1913, as an integral part of the Corps of Army Engineers, but the notion of 'armed trains' had been considered as far back as 1871, and the concept had been the subject of courses at the Belgian War College.
The railway war was considered to be first and foremost defensive in nature, involving the destruction or blocking of numerous tunnels, and the cutting of bridges in the provinces directly menaced by an enemy attack, while at the same time seeking to avoid obstructing the movement of one's own troops. 'Phantom' (or 'ram') trains would be sent to crash into enemy trains or crucial elements of infrastructure such as turntables, in order to block the free circulation of enemy traffic.
### The Siege of Antwerp
In September 1914, the decision was taken to link together the different forts around Antwerp by a single track circular rail line. The construction of the line took from 7 September to 1 October. In particular it would allow the movement of armoured trains during the final days of the siege.
Four Light Armoured Trains, for patrol and protection duties, were ordered by the Army High Command, and were constructed out of metal sheets meant for ship construction in the Antwerp North workshops with the aid of the Engineers' Railway Company (CFG). They were to be followed by three Heavy Armoured Trains, to be armed with naval guns provided by the British, to act as mobile artillery in advance of the line of forts.
The first Light Armoured Train was completed in ten days, the second in eight days and the third in just six days. The fourth train, however, was captured incomplete when Antwerp fell to the German Army.
The first train (No 1, Light, commanded by Lieutenant Michel then, when he was wounded, by Sub-Lieutenant Goutière) became operational on 5 September and was in action continuously right up to 8 October, in particular on 25 and 26 September 1914 when it supported the operation to block the Brussels-Tournoi line, by means of 'phantom trains' launched in the direction of Enghien and Hal. This operation was repeated on 7 and 8 October, when the target was Duffel. In addition to their normal ammunition load of 12,000 rifle cartridges, 240 shrapnel shells and 120 57mm HE rounds, the armoured trains also carried 25kg (55lbs) of explosives for blowing up key installations.
The only known plan of the Light Armoured Trains. Although schematic, it gives a good idea of the overall dimensions on the one hand, and of the layout of the armament (a 57mm chase gun firing straight ahead and three machine guns, including one firing to the rear). We have never seen a photo of the four-wheel van.
_(Drawing: Bulletin belge des sciences militaires, July 1932)_
Class 16 armoured engine. These 4-4-2 tank engines were among the most modern of their day.
_(Photo: Paul Malmassari Collection)_
The other type of engine used with the Belgian armoured trains, the Class 32 Etat, an 0-6-0 tender engine also used on French railways.
_(Photo: Paul Malmassari Collection)_
Armoured wagon of a Belgian Light Armoured Train. The chase gun is a 57mm QF model on a casemate mounting with a severely restricted field of fire, its embrasure closed by sliding shutters. Of the three machine guns on the train, one fired to the rear from the van at the tail of the train. Each wagon carried six rails 6m (19ft 8in) long, ten pairs of fishplates and repair gear.
_(Photo: Paul Malmassari Collection)_
Armoured Train No 2 (commanded by Lieutenant Deleval) went into action for the first time between 11 and 14 September, along with Armoured Train No 1. It participated in the destruction of the bridges at Denderleeuw and Alost on the River Dendre. It then operated on several occasions at Alost, Renaix and Audenaerde, at Eine and Zingem, at Tielt, and at Deurle. On 8 October, the crew launched phantom trains from Mortsel in the direction of Lierre.
Despite these actions, the German advance forced the Belgian Army to retreat. It entrenched itself in the fortified stronghold of Antwerp, from which the armoured trains also stationed there took part in sorties, in particular that of 9 to 13 September towards Vilvorde, Louvain and Aarschot. On 7 and 8 October, a violent bombardment struck the fortress, but it held firm, allowing the evacuation of an enormous quantity of stores and virtually all the troops. On 9 October, the last Belgian and British troops pulled out, heading west. On that date, the unfinished Armoured Train No 4 was abandoned in Antwerp and captured. The demolition of the railway bridge at Boom cut off the retreat of Light Armoured Train No 1, which was sabotaged by its crew who were evacuated on Armoured Train No 2. They reached Ostend on the evening of the 9th, and formed the crew of Armoured Train No 3 which had been evacuated to Ostend the day before. The two surviving armoured trains were sent to Dunkirk on 13 October 1914. Then on the 19th, Armoured Train No 2 returned to Dixmude. Its crew were then employed in repairing the lines, notably on 21 and 22 October, in order to re-establish the rail link on the Caeskerke-Nieuport line.
Close-up of the armoured bogie wagon of Armoured Train No 1 after its capture by the Germans. Note the armour protection for the bogies and the buffer beam, which now has no buffers. It is uncertain whether this modification was carried out by the Belgians or the Germans. In addition, although the armament is not in evidence, the horizontal sliding armoured shutters have been removed, giving way to a much larger embrasure opening.
_(Photo: Paul Malmassari Collection)_
One of the results of a 'phantom train' launched against German rail transport. The CFG driver and fireman of the ram engine jumped to safety before the collision and were only slightly injured. They were both later decorated by King Albert.
_(Photo: All Rights Reserved)_
A Belgian Light Armoured Train following its capture by the Germans near Boom. It was subsequently used by them for some time, as shown by the postcard below.
_(Photo: Paul Malmassari Collection)_
This postcard is in fact German, showing PZ No 1. The armoured van on the left is the one seen in the background in the two photos above, indicating that the Germans rearranged the order of the train units, as the engine now brings up the rear.
_(Postcard: Paul Malmassari Collection)_
Here on the left one can just make out the rear of the artillery wagon with its larger embrasure.
_(Photo: Paul Malmassari Collection)_
Class 32 engine captured at Antwerp.
_(Photo: Paul Malmassari Collection)_
Another captured Class 32 engine. Note the armour plating which extends much lower than is seen on other engines in service, together with the inspection hatches.
_(Photo: Paul Malmassari Collection)_
The role of the Belgian Light Armoured Trains came to an end in late October 1914. The two trains were sent back to Calais where their armour protection was removed, apart from the armour on one Class 32 engine used to haul a British heavy railway gun, and on two armoured engines allocated to the French 200mm artillery battery 'Pérou'. There was also a special train armed with a 21cm mortar originally mounted in the Blauwgaren Redoubt, double-headed by two armoured engines, which was in action during the battle of the Yser.
### The Heavy Armoured Trains
From 8 September 1914 the construction of these three trains in Antwerp was entrusted to Lieutenant-Commander A. Scott Littlejohns, who was acting as attaché to General Deguise, the Military Governor of Antwerp. This co-operation resulted in the trains often being referred to as 'Anglo-Belgian Armoured Trains', notably in the newspapers of the day. Some days earlier, it had been agreed to cede to the Belgian Army several British naval guns, which were the only ones capable of counter-battery fire against the German artillery.
Of the three trains planned, two were constructed in the Hoboken workshops (by the British Engineering Company) and the third in the North Antwerp workshop. The first two were armed with three 4.7in (120mm) naval guns and armoured from the outset. Each train was composed of three Class 32 or 32S Etat Belgian engines (of which one could be detached for track reconnaissance), three 40-tonne artillery platform wagons 18m (59ft) long, and three Bika Type vans. The mixed nationality crews comprised one Royal Navy officer and six senior gunnery ratings, seventy NCOs and gunners from the Belgian fortresses, and finally railway personnel of the CFG. The armament of the third train was to comprise two heavier 6in (152mm) naval guns without shields, which at first were simply bolted onto unarmoured platform wagons (one with girder chassis underpinnings and the other with bar-type chassis underpinnings).
The first armoured wagon was completed on 15 September and its firing trials were successfully carried out the same day. The next ten days were spent fixing the armour protection in place, training the crews and reconnoitring the railway lines and the Belgian positions. On the 23rd, the first train with one armoured wagon left Antwerp at 11.00, carrying Lieutenant-Commander Littlejohns who was the overall commander of the Heavy Armoured Trains, Captain Servais, French and Belgian officers, and the British Military Attaché. An observation aircraft was to correct the fall of shot on the German batteries which were thought to be in Epperghem. In spite of the mist which interfered with observation, based on the interrogation of prisoners and refugees the shoot actually took place.
From their base in Antwerp, the first two trains went into action at Malines between 24 and 27 September, co-operating with spotting aircraft and balloons. One of the trains was even able to approach within 1800m of the German lines. On the 28th and 29th, they were in action in front of Forts Waelhem and Wavre-Sainte-Catherine (Sint-Katelijne-Waver), as the guns of the forts were unable to reach the German batteries. At one point, a German 42cm shell only just missed one of the trains, whose movements were followed by German Drachen balloons. In spite of the trains taking shrapnel fire which fortunately burst too high, the Allied fire was effective, and forced the Germans to pull back.
On 4 October, the trains were fired on by German artillery, and one balloon was shot down by a 4.7in gun, served by Gunner's Mate T. Potter. On their withdrawal, still under fire, the trains were visited by Winston Churchill, then First Lord of the Admiralty, accompanied by Admirals Horace Hood and H F Oliver. On 5 and 6 October, they went into action around Kleine-Miel, supported by two French armoured trains. But on the evening of the 6th, near Buchout, the artillery wagon at the head of one of the trains derailed on a section of line which had been cut by artillery fire. The derailed wagon was detached from the train and left there until the rails could be repaired, which took several hours. In the meantime the remaining five guns of the two trains engaged the German positions and silenced three batteries. On the 7th, the trains were successfully evacuated with reduced crews towards Saint Nicolas, before the lines were cut.
A direct hit on the shield of a 4.7in gun of a Heavy Armoured Train, possibly that on 21 October when Lt Robinson's train was hit.
_(Photo: Le Miroir, 1 November 1914)_
One of the 6in guns mounted on a Belgian platform wagon, seen here in Ostend on 9 October 1914.
_(Photo: IWM)_
A rare postcard, showing the armouring of a wagon of a Heavy Armoured Train. The vertical armour was 15mm thick compared to 10mm for the horizontal plates. Note however the chassis reinforcement system, which is different from that on the other Heavy and Light wagons. This is one of the two British 6in guns.
_(Photo: Paul Malmassari Collection)_
At Ostend from 12 October the armoured trains covered the withdrawal of troops from Gand. Then on the 15th, one leading and the other as rearguard, they protected the British troops marching on either side of the tracks between Roulers and Ypres. On entering the latter town, the lookouts posted on the engine fired on a scouting party of six German cavalrymen, killing an officer and a trooper. From 19 and 31 October, the trains were made available to General Rawlinson. Armoured Train No 3 (Lieutenant Robinson) went into action in the attack on Menin on the 19th and in the direction of Passchendale on the 20th. On the 21st, the train went into action on the Ypres-Roulers line, where it was fired on by German artillery, which failed to pierce its armour, but which prevented it from advancing further. From the 26th to the 31st, the trains were in action at various locations in support of the Belgian 3rd and 4th Divisions, fighting to the east of Dixmude and to the west of the bend of the Yser.
A photo dated with certainty to 13 November 1914, the square bearing the number '23' is not painted on the train but is a kilometre marker.
_(Photo: From J'ai Vu, 13 December 1914)_
The 6in guns which had been mounted on bogie platform wagons in Antwerp, were evacuated to Ostende on 7 October, and received their full armour protection in late October. They were formed into a new train which, under the command of Lieutenant-Commander Ridler RN, rejoined the two other trains in the Ypres sector. From 1 to 7 November, the trains went into action against the German lines, and notably against an observation balloon on the 3rd. German prisoners even indicated that the 6in shells from the trains had killed eighty-seven soldiers in a trench on the 6th. Then HMAT _Deguise_ left for Boulogne to be repaired. When it reached Oostkerke on the 11th, it was targeted by two salvoes which fell just 15m short of the train, forcing it to retreat 500m behind the station. But on the 13th, while the train was stationed at Km 23 on the Caeskerke line, a shell hit the second engine, killing the driver. From the 15th, HMAT _Jellicoe_ came under the orders of I Corps, and went into action each day to the east of Ypres. It was also the target of German artillery on the 17th, and one man was wounded. The heavy rail traffic evacuating casualties had prevented the train from quickly manoeuvring out of range. On the 18th, a German shell damaged an engine and one of the 6in guns. The train pulled back towards Ypres Station but the German artillery succeeded in following it and ended up also firing on the station itself. The German bombardment was renewed on the 19th, but the tracks were undamaged.
For its part, HMAT _Churchill_ went into action in December in the area around Oostkerke against German batteries to the south of Dixmude. On 18 December, a shell wounded Commander Littlejohn's second-in-command. Between the end of December and March 1915, the three armoured trains were continuously in action, sometimes in support of an assault ( _Jellicoe_ at la Bassée on 10 January), but in particular in counter-battery or bombardment missions and in actions to neutralise trench lines ( _Jellicoe_ at Beuvry between 20 and 24 January, _Churchill_ at Oosterkerke on 28 and 29 January, and against an observation post at Ennetières on 11 February, _Déguise_ at Beuvry firing on a rail junction on the 15th, among other targets, _Churchill_ against a battery at Fleur d'Ecosse on 3rd March). The guns of the trains were extremely effective, notably against troop concentrations: on 18 February, HMAT _Deguise_ fired seven shells at German troops to the South-West of la Bassée. These actions brought the trains within range of the German artillery. The Germans scored hits, but the armour protection and swift manoeuvring of the trains normally protected the crews, except on 25 January when _Jellicoe_ was hit, with two men wounded and the Belgian engine driver killed. Between 10 and 13 March the three trains supported the action at Neuve Chapelle. On that occasion, Field Marshal Sir John French paid a surprise visit to HMAT _Churchill_ , which was the command train for Commander Littlejohns.
The extreme length (18m/59ft) of the bogie platform wagons used in the trains is evident in this side view of a 6in gun wagon. Note the name 'Leman' painted on the side armour.
_(Photo: Paul Malmassari Collection)_
A well-known shot of a Heavy Armoured Train. The length of the protruding rifle barrels adds to the offensive look of the train, even against troops on the ground.
_(Photo: Paul Malmassari Collection)_
A popular postcard, showing the 6in gun wagon with girder underpinning, where it appears that one of the side doors is missing.
_(Postcard: Paul Malmassari Collection)_
Another postcard which shows the armoured van between the engine and the gun wagon, beyond which is the second train engine.
_(Postcard: Paul Malmassari Collection)_
A fine view of the open breech of the 4.7in gun on one of the Heavy Armoured Trains.
_(Photo: La Guerre de 1914–1918)_
This view, again from _La Guerre de 1914-1918_ , is interesting as it shows the relative lack of comfort for the crews of the gun wagons, even if they are glad of the protection given by the armour!
Here we can see the girders joined in an 'X' which support the gun mounting.
_(Photo: La Guerre de 1914-1918)_
We lack information on the armoured trains after March 1915. Nevertheless, a well-illustrated article was published by the magazine _Sur le Front_ No 18 on 8 May 1915. The photos used in the article show the Light Armoured Trains, which leads us to think that the Heavy Armoured Trains were no longer in use at that time (otherwise they would have been shown), and this was probably because the front lines had become fixed. Finally, the armoured trains were formally taken out of service in September 1915.
In the section of Commander Littlejohns' report dealing with the radio sets installed in the trains, he mentions the names of three armoured trains: H.M.A.T. _Sinclair_ , which entered service at Boulogne on 26 December 1914, and which, after the succesful trials conducted up to 7 January 1915, led Commander Littlejohns to introduce H.M.A.T. _Singer_ on 15 January, followed by H.M.A.T. _Sueter_ on 23 January. In addition to their radio sets, they were equipped with a radio mast 8m (26ft 3in) high which could be erected in three minutes, plus 15m (49ft) of aerial cable. This installation gave radio reception over a range of 50km (30 miles) by day and 70km (40 miles) by night. The defence of these trains was provided by a machine gun installed on the roof. We must conclude that the designation 'HMAT' was used for convenience in the report but did not correspond with actual armoured trains.
The observation ladder used by the armoured trains in conjunction with observation from balloons and vantage points such as factory chimneys and belfries, which had become priority targets for the gunners of both sides.
_(Photo: All Rights Reserved)_
An anti-aircraft gun obviously mounted in the position formerly occupied by a shielded 4.7in gun. There is no documentary evidence to show when this conversion was carried out.
_(Photo: All Rights Reserved)_
An illustration from a German publication, based on the principle known since the times of Julius Caesar, namely to emphasise the courage of one's own side by demonstrating the threat or the power of the enemy.
_(Illustration: Paul Malmassari Collection)_
This postcard seems to have inspired many variations and derivatives, as much by the Belgians and the other Allies as by their enemies.
_(Postcard: Paul Malmassari Collection)_
Virtually the same view, in an American postcard which places the action at Antwerp.
_(Postcard: Paul Malmassari Collection)_
This German postcard correctly attributes the train as belonging to the Belgian Army, but sites the scene as being in front of Dixmude; another, this time attributing the train to the German Army, can be seen in the colour section, page 499.
_(Postcard: Paul Malmassari Collection)_
The engine at the head of a Belgian Armoured Train was not usual. However, certain sources do indicate that each armoured train had one engine which could be used for reconnaissance.
_(Postcard: Paul Malmassari Collection)_
**SOURCES:**
**Archives:**
SHD, carton 9 N 464 SUP
**Books:**
Littlejohns, Commander A Scott, RN, _Royal Naval Air Service: Armoured Trains, Report on Operations Sept. 1914 to March 1915_ , Air Department, June 1915 (MRA B.1.178.4).
Ministère des Chemins de Fer, Marine, Postes et Télégraphes: _Compte-rendu des opérations 04/08/1914 - 04/08/1917_.
Scarniet, Vincent, _D'Anvers à l'Yser. La Compagnie de Chemin de fer du génie et les trains blindés_ (Jambes: ASBL Musée du Génie, 2014). Wauwermans Major H., _Fortification et travaux du Génie aux armées_ (Brussels : Merzbach & Falk, 1875).
**Journal articles:**
Harlepin, J., 'Les Trains Blindés', _Newsletter of the Centre liégeois d'histoire et d'archéologie militaires_ Volume IV, No 7 (July– September 1990), pp 45–66.
_________, 'Les Trains Blindés', _Militaria Belgica_ (1998), pp 69–88.
'Trains blindés et "trains fantômes" pendant l'investissement d'Anvers', _Belgian Bulletin of Military Sciences_ Volume II, No 1 (July 1932), pp 1–14.
**Website:**
<http://pages14-18.mesdiscussions.net/pages1418/forum-pages-histoire/autre/trains-blindes-sujet_12036_1.htm>
. Wauermans, Major H, _Fortification et travaux du Génie aux armées_ (Brussels: Merzbach & Falk, 1875).
. CFG = Compagnie de Chemins de Fer du Génie.
. On 5 September 1914, the region of Boom and Tisselt; on the 7th, the region of Puurs; the 8th, at Beveren-Waes and Lockeren; the 9th, at Zele and Termonde; from the 11th to the 14th (with Armoured Train No 2), destruction of the bridges at Denderleeuw and Alost on the River Dendre; from the 25th to the 26th, the region of Gand, Grammont, Lessines; the 27th, launching of phantom trains from Muizen towards Louvain; 2 and 3 October, protection of the engineers demolishing the Duffel railway bridge.
. No 17 MT (0-6-0) of the Compagnie Malines-Terneuzen, and No 3479, a Belgian Class 32 Etat.
. The equivalent of a Major in the Army ( _Commandant_ in French).
. From 9 November they were allocated the following names: HMAT (His Majesty's Armoured Train) _Deguise_ (after the Lieutenant-General who was the Military Governor of the Fortress of Antwerp, commanded by the Belgian Captain Servais; HMAT _Jellicoe_ commanded by Lieutenant Lionel Robinson RN, and finally HMAT _Churchill_ , commanded by Lieutenant Ridler RN. The train names were also painted on the wagons. Note that the Belgians serving on these trains wore British uniforms.
. The first two armoured trains were completed by 25 September.
. Evidently fired from an M-Gerät 'Big Bertha'.
. Churchill was in Antwerp from the afternoon of 3 October to the evening of the 6th.
## BOSNIA AND HERZEGOVINA
When civil war broke out in Yugoslavia in 1991, the tensions which had been building up over a long period caused the breakup of the country. On the territory of the new Bosnia and Herzegovina (Herzeg-Bosnia), each of the three ethnic groups – Serbs, Bosnians and Croats – attempted to create their own zone of influence with the ultimate aim of becoming autonomous. Along with other improvised armoured vehicles, armoured trains played an important role.
### REPUBLICA SRPSKA
At Gradačac, an important railway junction 45km (28 miles) to the south-east of Slavonski-Brod and the River Sava (which serves as the frontier), and 30km (18.6 miles) to the west of Brčko, one can see the Bosno-Serbian armoured train which was used as a 'Trojan Horse' in an attempt to capture the town in October 1992. The attack failed when the train was stopped by the Muslim defenders, who have since preserved it as a monument to the fighting.
Note in the third photo the camouflage pattern on the left which positively identifies the wagon as the same in the two previous photos. Here the side armour protection is intact, which would suggest that the explosion of the charges which caused the impressive damage visible on the museum train occurred at a later date – either to prevent the risk of the train being put back into service by its previous owners, or for propaganda purposes.
Our research has unearthed another armoured train, probably Serb, at Brčko in 1995.
The camouflage scheme is irregular patches of red-brown and dark grey on pale-green.
_(Photo: Michael Hansson)_
Brčko lay between the two Serb regions of Bosnia during the civil war, and was an entry point from Croatia via the Republic of Krajina. The Serbs therefore seized the town in May 1992 after six days of fighting, and it is likely the armoured train photographed there had been used to protect supply lines between the various Serb enclaves.
The train at Brčko. The camouflage pattern of sky blue on a mid-blue background was apparently created by rolls pasted on like wallpaper, continually repeating the motifs.
_(Photo: All Rights Reserved)_
The train at Gradcačac on the day it was captured.
_(Photo: All Rights Reserved, via Yves Debay)_
The train at Brčko 1995. A view of the armoured diesel locomotive with the Serbian flag visible at the front end.
_(Photo: All Rights Reserved)_
A view of one of the armoured wagons at Gradcačac, showing the armour plating deformed by explosions.
_(Photo: Michael Hansson)_
A view of the front and right-hand side of the Muslim-Croat Federation trolley, which well illustrates the asymmetrical protection, when one considers that the coupling is fitted on the centre line. The initials HVO stand for ' _Hrvatsko Vijeće Obrane_ ' or Croat Defence Council, formally dissolved in November 1995.
_(Photo: ECPA–D)_
The left-hand side of the trolley, with the added protection of sheets of rubber and tyres, fitted on the side facing the enemy, who here would be Muslims.
_(Photo: ECPA–D)_
French and Croatian soldiers inside the trolley. The internal lining of sheets of plywood can be seen, and at the far end, one of the driver's cabs which is identical to that of the Konćar trolley described elsewhere. To the right, there appears to be a hatch in the roof, maybe for observation?
_(Photo: ECPA–D)_
### Moslem-Croat Federation
We have discovered no details of this armoured trolley, apart from the fact that it was used during 1996 in Mostar, on the BosnianCroat side of the lines. At that time, French troops of the 3rd Engineer Regiment (Charleville-Mézières) used it for movements in high-risk zones.
**SOURCE:**
<https://www.youtube.com/watch?v=TY3ODhgFtMc>
. A self-proclaimed enclave, covering half of Bosnia and Herzegovina, and whose autonomy within the Republic was recognised by the Dayton Accords in 1995
## BRAZIL
### Armoured trains of the Constitutionalist Revolution, 1932
In the fallout from the financial crash of 1929 which triggered an economic recession in Brazil, in October 1930 President Vargas deposed his discredited predecessor and established a provisional government. But his increasingly dictatorial style alienated him from the people, and in particular the inhabitants of the State of São Paulo, who called for autonomy from the federal government. The 'Unique Front' ( _Frente Única_ ) which contained several senior army officers began an armed revolt against the federal forces. Alongside the Air Force and the Navy, improvised armoured vehicles and armoured trains were built, principally for the 'Paulist' forces, by both the railway workshops and the Technical College. The latter institution supervised the construction of six armoured trains. In principle, each train would comprise an armoured wagon in front of and behind the locomotive, plus a safety pilot truck at the head of the unit, the crew of which would include fifteen men in each of the two wagons. There is no information on where trains Nos 1 and 6 were first employed; Nos 2 and 3 served in the Sorocaba region to the west of São Paulo, and Nos 4 and 5 served around Mogiana in the north of the state.
Armoured Train No 3 wagon with its 7mm machine gun in a square turret. The camouflage was inspired by contemporary French schemes using olive green/dark green/grey/chestnut brown.
_(Photo: Periodical Section of UFDF/Defesa)_
Armoured Train No 3, showing the cowcatcher on the leading safety wagon.
_(Photo: Reginaldo Bacchi)_
Armoured Train No 1 of the Sorocabana sector, which became Armoured Train No 3 after modifications, and was christened _Phantom of the South_. The engine is a 2-8-2 Mikado, No 216.
_(Photo: Periodical Section of UFDF/Defesa)_
Another view of a wagon from Armoured Train No 3.
_(Photo: Periodical Section of UFDF/Defesa)_
Baldwin 2-8-0 No 730 armoured locomotive of Armoured Train No 4, built in the workshops of the Companhia Paulista de Estradas de Ferro in Campinas, Sáo Paulo State. It was operated by the Mogiana railway company, and was considered to be the best of the armoured train designs.
_(Photo: Periodical Section of UFDF/Defesa)_
Armoured Train No 4 showing the symmetrical layout typical of these armoured trains, with an armoured machine-gun wagon in front and behind the locomotive, and a pilot wagon at the head of the unit. The turret at the rear of the left-hand wagon is square.
_(Photos: Reginaldo Bacchi)_
Baldwin 2-8-0 locomotive from one of Armoured Trains Nos 3 to 5, seen from the left-hand side.
_(Photo: Reginaldo Bacchi)_
A photo which despite its below-average quality is still a fine shot of a machine-gun wagon from one of Armoured Trains Nos 3 to 5, armed with two 7mm Hotchkiss in square turrets.
_(Photo: Reginaldo Bacchi)_
Armoured Train No 5 of the Companhia Mogyana, with Baldwin 2-8-0 No 732.
_(Photo: Periodical Section of UFDF/Defesa)_
Armoured Train No 6 _Phantom of Death_ , built in the Central do Brasil Company's workshops in Pindamonhagaba. Two notable features are the roof sloping down towards each end of the armoured wagons, and the leading wagon armed with an unidentified gun firing forward.
_(Photo: Police Military Museum of Sáo Paulo via UFJF/Defesa)_
Armoured locomotive of Armoured Train No 6, showing the overall armour protection on the tender, leaving a firing loophole in the side. This type of train was designed by Clément de Baujaneau, a French engineer living in Brazil.
_(Photo: Reginaldo Bacchi)_
The same train seen from the opposite side, revealing that the design was symmetrical. The sloping roof armoured wagon is based on a bogie wagon. In the following photo, the forward 75mm Krupp gun is clearly visible.
_(Photo: Reginaldo Bacchi)_
Close-up of the 75mm Krupp gun of Armoured Train No 6. The cowcatcher carries its lamp in an unusually low position, indicating that the two-plank safety wagon seen in the previous photo was not always attached – unless this view shows the rear of the train.
_(Photo: Periodical Section of UFDF/Defesa)_
**SOURCES:**
Bastos, Expedito Carlos Stephani, _Blindados no Brasil – Um Longo e Árduo Aprendizado, 1921/2011_ , Vol I (Bauru e Juiz de For a: Taller Editoria e UFJF/Defesa, 2011).
Duarte, Paulo, _Palmares pelo avêsso_ (Sao Paulo: Instituto Progresso Editorial, S.A., 1947).
Walsh, Paul V, _The 1932 Paulista War : An Example of Conventional Warfare in Latin America during the Inter-War Period_ , lecture presented in 2001 at the annual conference of the Society for Military History of the University of Calgary.
**Website:**
<http://netleland.net/hsampa/epopeia1932/blindados1932.html>
. Also known as the Autonomist Revolution or the Paulist Revolution (from the name of the State involved).
## BULGARIA
### ARMOURED TRAIN PROJECT
It would appear that Bulgaria began a project for at least one armoured train. In 1936 the General Staff ordered a train from the Varna workshops, to comprise six wagons, armed with a total of four 75mm guns and eight anti-aircraft machine guns. Interestingly, the armour protection was to be reinforced concrete.
Delivery was planned for 1937, but no information has come to light as to whether it was actually built.
**SOURCES:**
SHD, 7 N 2751.
## BURMA-MYANMAR
Annexed by the British Empire after three wars between 1824 and 1886, Burma became a Crown Colony in 1937. Five years later, Burma was invaded by the Japanese, who were driven out in July 1945. On 4 January 1948 Burma regained its independence, but the security situation remained highly unstable due to continuing ethnic and religious conflicts. In 1962, a _coup d'état_ brought General Ne Win to power.
Two of the Wickham armoured trolleys probably supplied by Malaysia, photographed here in February 1995.
_(Photos: Olaf Güttler and Florian Grupp)_
As late as 1994, the security situation on the railway network required that trains be preceded by a safety wagon, here seen with a cowcatcher. The locomotives are Alsthom DF diesels.
_(Photos: Olaf Güttler)_
1. The name Myanmar was adopted in 1989 by the Burmese government and recognised by the UN, with the exception of the United States and the United Kingdom. Myanmar is a local variant of the ancient name Burmah.
. D = Diesel, F = six axles, delivered in 1987.
## CAMBODIA
### ARMOURED TRAINS
Under the French protectorate, the railway network was defended by armoured trains and trolleys (see the chapter on France). It is likely that similar measures were used during the Khmer Rouge uprising btween 1967 at 1975. Following the intervention of Vietnamese forces and the overthrow of the Pol Pot regime, in 1979 the Khmer Rouge carried out a systematic destruction of the country's infrastructure, including harassing attacks on the rail network. Armoured wagons were hastily built and added to each civilian train.
The Paris Peace Accord signed on 23 October 1991 allowed for the despatch of a UN contingent (MIPRENUC then UNAMIC), which promised a return to normality despite the millions of mines which had been laid and the continuing presence of pockets of resistance. Nevertheless, trains continued to be the target of attacks, and improvised armour was added to the locomotives, including the veteran Pacifics left over from the French period.
A scene from everyday life on the railway, with passengers piled onto the leading flat wagon, intended as a safety wagon to detonate explosive devices. Rather than indicating a return to more peaceful times, the passengers seemed to be motivated by the fact that travel on these wagons was free of charge, despite the continuing danger.
_(Photo: Olaf Güttler)_
Pacific No 231-501 with its armoured cab, practically identical to the types used during the war in Indochina.
_(Photo: Olaf Güttler)_
In 1966, the railway received thirteen BB diesel-electric mainline locomotives and eight shunting/branch-line locomotives from Alsthom. On the mainline locos only the front and side faces of the cabs at each end were armoured, and the observation slits show several variations.
_(Photo: Olaf Güttler)_
In 2013 BB No 1055, photographed here in 1991, was being rebuilt in the Phnom Penh workshops.
_(Photo: Olaf Güttler)_
On the right is armoured BB No 1055 seen at a junction north of Phnom Penh. The BB shunter No 1005 on the left has only an armoured cab.
_(Photo: Olaf Güttler)_
Close-up of an armoured wagon taken in July 1991 near Phnom Penh, showing the internal armour plating clearly.
_(Photo: Olaf Güttler)_
**SOURCES:**
Chlastacz, Michel, 'Les 50 ans de malheur du rail cambodgien' ('50 troubled years of the Cambodian railways'), _La vie du rail_ No 2237 (22–28 March 1990), pp 16–17.
Roussel, Daniel, 'Cambodge, les trains de la guerre' ('Cambodia, the trains at war'), _La vie du rail_ No 2237 (22–28 March 1990), pp 11–15.
. Built in Mulhouse by SACM and in Haine-Saint-Pierre in Belgium.
## CANADA
The first project for a Canadian armoured train dates back to 18 April 1867, when the Great Western Railroad Company proposed the construction of an armoured wagon, equipped with a turret 2.5m (8ft 4in) high at the front end, and at the rear an armoured casemate with firing loopholes for the crew. The project was intended to counter the incursions of the Fenians, an Irish republican organisation based in the United States, which had carried out several raids on Canadian territory, which at the time consisted of a collection of colonies before amalgamation into a British Dominion on 1 July 1867. However, this armoured wagon never got beyond the planning stage.
Canadian troops were among the crews of British armoured trains during the Second Boer War, but their participation was purely incidental. Less than twenty years later, Canadian units were sent to Russia to fight the Bolsheviks, in the north near Murmansk and Arkhangelsk and in the east in Siberia. In the north, the Canadians manned an armoured train armed with an 18pdr field gun and two naval guns in the region of the important rail junction of Vologda.
The cowcatcher wagon which was mirrored at the other end of the train. Note the total absence of armour protection (apart from the minimal gunshield) around the mount. The weapon is the American 75mm Model 17 (derived from the British 18pdr field gun, rechambered for the French 75mm round) on Mounting Mk I.
_(Photo: Public Archives of Canada – PAC)_
### Canadian Armoured Train No 1
The impetus for construction of the first Canadian armoured train during the Second World War was the fear of a Japanese landing on the Pacific Coast (guided or aided by the Japanese fishermen who had traditionally trawled as far as the Skeena Estuary). The initial project was for two infantry companies patrolling in light trolleys, but in late March 1942 it was agreed to construct an armoured train, and the Canadian National Railway was charged with its design and construction. The work was carried out by the Transcona workshops near Winnipeg.
The train was designed symmetrically around the central locomotive unit, and consisted of four bogie artillery wagons (two with field guns, two with anti-aircraft guns) and two carriages for infantry, with the addition of a mess carriage. After numerous delays due to the difficulty of supplying armour plating, the availability of guns and their mountings, the locomotive to be used, etc., the train conducted its first patrol on 29 July 1942, some four months after it had been ordered, but the service carriage with its radio installation did not join until 7 August. On 31 July 1944, the train was withdrawn from service and its individual components were returned to the CNR.
The crew of this armoured train (three officers and twenty-six men) were from the 68th Field Battery of the 16th Artillery Brigade, and formed the railway detachment in the region of Vologda (170km [107 miles] to the south of Archangelsk). What at first sight appears to be a machine gun on a tripod just placed on the roof next to the armoured cupola is more likely a portable rangefinder.
_(Photo: Paul Malmassari Collection)_
The four 40mm Bofors were of Canadian manufacture. In this photo of the brand-new train, they are seen mounted directly onto the planking of the wagons, but between September and November 1942 their mountings were fixed higher up, allowing them to engage ground targets.
_(Photo: PAC)_
The kitchen/mess section of the service carriage. At the other end was the radio compartment, the train commander's office and a first-aid post.
_(Photo: PAC)_
Bogie wagon, 15m (49ft 2½in) long by 2.85m (9ft 4¼in) wide, with sides 1.05m (3ft 5¼in) high. The armour protection for the bogies on all the wagons was 8mm thick.
_(Photo: PAC)_
Stripped of their civilian fittings, the carriages were armoured on the inside faces up to a height of 0.95m (3ft 1½in) under the window openings and 2m (6ft 6¾in) between them. The bench seats would be reinstalled prior to November 1942.
_(Photo: PAC)_
Two general views, showing both ends, but without either the locomotive or the service carriage. The whole train (inside and out) was painted matt khaki-green overall.
_(Photos: PAC)_
On the end wagon, the second in this shot, is one of the train's two 90cm (3ft) Mk III searchlights, powered by a Leyland Westinghouse petrol generator, which in November 1942 would be replaced by 1.20m (4ft) diameter searchlights.
_(Photo: PAC)_
The anti-aircraft wagon at the other end of the train. No higher armour protection was planned, and the tubes are safety rails limiting the firing angles of the Bofors.
_(Photo: PAC)_
The anti-aircraft positions on the roofs of the infantry carriages (Mounting Seat AA .303 MG Mk II), intended for a Bren Gun with a 100-round drum magazine.
_(Photo: PAC)_
Armoured diesel-electric loco CN-9000, initially intended for the Santa Fe Railroad, which was not completed until August 1943 and never saw service with the train. In April 1943, it was fitted with a new motor as well as the armour protection, and pending discussions re the future of the train, it was stored at the Transcona workshops.
_(Photos: PAC)_
The typical central automatic coupling found on trains in North America, protected by articulated armour plates.
_(Photo: PAC)_
**SOURCES:**
**Books:**
Lucy, Roger V, _The Armoured Train in Canadian Service_ (Ottawa: Service Publications, 2005).
Stevens, G R, _History of the Canadian National Railways_ (New York: The Macmillan Company, and London: Collier-Macmillan Co.,1973).
**Journal articles** :
Anonymous note (untitled), _Canadian Rail_ No 291 (April 1976), pp 126–7.
Anonymous, 'Canada's Armoured Train', _Canadian Rail_ No 297 (October 1976), pp 300–4.
Grimshaw, Major Louis E, 'No.1 Armoured Train', _Canadian Defence Quarterly_ Vol 21, No 2 (October 1991), pp 40–4.
Purdon, Charles J, 'Fortress on steel wheels', _Trains_ Vol 48, No 11 (September 1988), pp 30–1.
______________, 'Canada's Armoured Train No.1', _Canadian Journal of Arms Collecting_ Vol XVII, No 1 (1979), pp 14–18.
**Website:**
<http://laughton.ca/documents/ww1/pub7.pdf>
. Public Archives of Canada, Public Archives Canada (Ottawa), RG9, IC8, Vol 18.
. The first Canadian contingent left Victoria on 11 October 1918, and arrived at Vladivostok on the 26th. The last Canadian soldier left Russia on 5 June 1919.
. CNREF = Canadian North Russian Expeditionary Force.
. CSEF = Canadian Siberian Expeditionary Force.
. With 4-6-0 steam engine CN 1426.
. Built by Otis-Fensom in Hamilton from 1942 onwards.
. The first diesel-electric locomotive built in Canada along with No 9001 in 1928, by the Canadian Locomotive Company of Kingston, it had been laid up since October 1939.
## CHILE
### 1891 ARMOURED TRAINS
In January 1891 a revolutionary struggle broke out between the 'Constitutionalists' or 'Congressists' (the revolutionaries, who were in fact the supporters of the Parliament) and the 'Balmaceditas' (the loyalists, named for President Manuel Balmaceda, who favoured a strong executive). The principal Congressist combatants were naval units, but on the presidential side the railway network was widely used in the movements of troops on land. On 15 February, locomotives sent to break through Congressist lines were used by presidential troops to concentrate at Huara, where Colonel Robles was victorious.
In the struggle for the northern ports, the Congressists used an armed locomotive and an armoured train with two machine guns. It carried out reconnaissance missions leading up to the battle of Pozo Almonte on 7 March, then took part in the battle itself, which saw the rout of the Presidential troops under Colonel Robles and the death of the latter. The civil war ended on 28 August 1891 with the victory of the insurgents.
It should be noted that an armoured wagon for the transport of explosives is currently kept at Copiapó Museum in Atacama Province, but there is no indication that this wagon was involved in the civil war.
## CHINA
### ARMOURED TRAINS 1920–1951
The very first Chinese armoured trains had appeared at the start of the 1920s during the Zhili-Anhui War. Writing in March 1930 an American military attaché described an armoured train he had seen at that time on the Beijing-Hankow line: ordinary flat wagons protected by two thicknesses of mild steel plates. The rapid development of Chinese armoured trains would have to await the arrival of the White Russian mercenaries, notably on the side of the warlord Zhang Zongchang.
### White Russian Armoured Trains
In October 1922, the Red Army laid waste to Vladivostok and a large number of White Russian soldiers fled to China with their weapons (it is thought that the famous _Zaamurietz_ / _Orlik_ crossed into China during this period), and took up service as mercenaries in the army of Marshal Zhang Zuolin (Chang Tso-Lin) and one of his subordinates Zhang Zongchang. On 15 September 1922 the latter had been sent to Vladivostok to buy arms. One of his contacts was a certain Nikolai Merkulov, who moved to China and became the first commander of the White Russian armoured trains.
The very early White Russian armoured trains were improvised for the most part from bogie wagons reinforced with sandbags. Near the end of the Second Zhili-Fengtian War, in October 1924, the forces of Zhang Zongchang (which were part of the Fengtian Army) carried out a surprise attack on the part of the Zhili forces commanded by Dong Zhengguo, and seized the important railway junction of Luangzhou. By blocking the bridge over the Luan River, they surrounded a huge number of men and large amounts equipment. The absorption of these troops increased the size of Zhang Zongchang's army to 60,000 men in only a few days. The captured railway rolling stock was immediately recovered by Russian engineers, who improvised their first armoured trains (which would be immortalised on film by White Russian cameramen).
A _coup d'état_ in Beijing had temporarily put Duan Qirui in power. The latter, in order to strengthen the position of his ally Lu Yongxiang in south-east China, and at the same time to crush Qi Xieyuan (the warlord of the Zhili clique), sent Zhang Zongchang to attack towards the south. On 14 November 1924, his troops arrived at Pukou. In the absence of any ferryboat link on the Yangtze between Pukou and Nanjing, his soldiers fitted railway tracks aboard barges, and thus ferried their armoured train across the river at night. The resistance they encountered at Jiangsu was weak, and with the armoured train in support the troops of Zhang Zongchang arrived in Shanghai on 28 January 1925. As there were many White Russian émigrés in the town, the Russian soldiers on the train were the subject of a great deal of attention, and it was then that the famous Russian artist Sapajou sketched the armoured train for the North China Daily News.
Note the rustic nature of this armoured wagon, obviously reinforced by armour plates and sandbags, and armed with a French 75mm APX field gun.
_(Sketch by Sapajou, in_ North China Daily News _, 30 January 1925)_
One example of the rolling stock transferred to China at the end of the Russian Civil War: this machine-gun wagon is of White Russian origin. Note the sliding armoured door which was less common than the hinged type.
_(Photo: Paul Malmassari Collection)_
### The Battle of Guzhen (in the North-West of the Province of Anhui)
After Zhang Zongchang had become Tuchun of Shandong in early 1925, he discussed with Merkulov the possibility of building classic armoured trains in the Tianjin-Pukou Railway workshops at Jinan, the capital of the Province of Shandong.
One of the most notable actions in which the White Russian armoured trains took part, and in which they suffered badly, occurred during this period. In September 1925 the provisional head of state Duan Qirui decided that two officers of the Fengtian clique, named Yang Yuting and Jiang Dengxuan, should take over as heads of the Provinces of Jiangsu and Anhui. Their appointments infuriated the warlord Sun Chuanfang who was in _de facto_ control of these two provinces, and he immediately sent them away. Zhang Zongchang sent Shi, his highest-ranking officer, to launch a counter-offensive using his White Russian mercenaries, but they were defeated at Bengbu. Shi did not accept this defeat, and with his general staff boarded Armoured Train _Chang Jiang_ (the Yangtse river), and headed for Guzhen to the north of Bengbu to continue the fight. The bloody battle fought there was described as follows by a former regimental commander in the forces of Sun Chuanfang:
After Shi retreated North from Bengbu, he did not admit defeat but continued to command from his armoured train. He was unaware that a regiment of Sun's forces had marched to the North of the Guzhen railway bridge, thus cutting off his intended escape route, while a second regiment launched a major attack from the South. When he became aware of the southern force, Shi ordered his armoured train to attempt to cut a way through to the North. When he approached the bridge, he saw it was completely blocked by his own troops who were desperately trying to escape to the North. Not wishing to run them down, he decided to change direction and ordered the train to return to the South. He quickly came into contact with the forces of the army of Sun, in overwhelming numbers, and he had to once more reverse course towards the North. Although the railway bridge was still blocked by the throng of his escaping troops, the powerful attacks of his opponents finally convinced Shi that he should ignore the fate of his men and force the crossing of the bridge to save his own skin. Over a thousand men trying to cross were either crushed by the train or thrown into the river. The terrible scene beggared description...
Shell damage to a White Russian armoured train of the army of Zhang Zongchang during the fighting in 1926 between the latter and Feng Yuxiang.
_(Photo: Yichuan Chen Collection)_
Despite this ruthless action, the armoured train carrying Shi did not escape its fate. Sources differ as to the manner in which the forces of Sun managed to destroy the train, but one suggests that Sun Chuanfang's artillery played a major role: the White Russian armoured train was hit by shells which caused its ammunition to explode. Most of the White Russians fought to the death, but others chose to surrender along with Shi himself. Very few of the mercenaries escaped. To show his fury at the way the fighting had developed, Sun Chuanfang immediately ordered that Shi be beheaded, and all the prisoners executed. One officer of his army who inspected the battlefield wrote that: 'The wreck of the armoured train of Zhang Zongchang was lying on its side, blocking the track. The White Russian soldiers, apart from a few who had escaped, had been burnt alive inside the armoured train. Their remains resembled piles of coal, and they were completely unrecognisable.'
### The Composition of the White Russian Armoured Trains
In early 1926, a number of completely redesigned armoured trains were built at Jinan. According to a Chinese source these trains (the _Tai Shan_ , the _Shan Dong_ , the _Yun Gui_ and the _He Nan_) were converted from 40-tonne bogie flat wagons, passenger coaches and steam engines, armoured with steel plates 20mm thick. Following the lesson of the Battle of Guzhen, all these trains included flat wagons carrying searchlights and materials for track repairs.
The armoured trains were composed of eight wagons:
1. Safety flat wagon carrying rails and sleepers.
2. Artillery wagon converted from a 40-tonne flat wagon.
3. Machine-gun wagon.
4. Armoured engine.
5. Mess and living quarters wagon for the officers, converted from a First Class coach.
6. Machine-gun wagon.
7. Artillery wagon converted from a 40-tonne flat wagon.
8. Safety flat wagon carrying rails and sleepers.
7.7cm FK 96 (German) or 75mm Type 38 (its Japanese version), crewed by White Russians.
_(Photo: Philip Jowett Collection)_
Note the mixed Russian and Chinese crew of this armoured train.
_(Photo: Paul Malmassari Collection)_
It was possible to pass between wagons (2) to (7) via armoured gangways. Finally, a wagon carrying two sections of Chinese infantry for close-in protection brought up the rear of the train.
In theory, their armament was to consist of seven 75mm Japanese Type 38 field guns and twenty-four Maxim heavy machine guns, but evidence from photographs shows that in fact there were major divergences from this. The floors of the artillery wagons of _Tai Shan_ were protected by a layer of reinforced concrete poured onto a steel plate fastened to the metal floor of the wagon. Also the vertical side walls were formed from two metal plates with the intervening space filled with concrete. To carry the increased weight, additional springs had to be fitted to the bogies. These trains were finished in a three-colour camouflage scheme. Two other armoured trains were also built in the workshops of the Beijing-Hankow Railway at Chang Xin Dian, to an identical design to the trains of the Province of Shandong, by order of Chu Yupu, the main ally of Zhang Zongchang and Governor of the Province of Chili during this period.
The safety wagon carrying a hand trolley, at the head of a White Russian armoured train, captured at Chin Wang Tao, seen here in 1928.
_(Photo: Paul Malmassari Collection)_
One of the artillery wagons from the same train. The turrets here are both armed with Russian 76.2mm Putilov guns. On the original photo it is just possible to make out the former Russian roundel in the centre of the side armour, under the new coat of camouflage paint.
_(Photo: Paul Malmassari Collection)_
The next wagon in line is perhaps the command wagon, coupled directly in front of the engine.
_(Photo: Paul Malmassari Collection)_
The train's engine, on which the simple form of the armour is intended to enable it to blend in with the wagons.
_(Photo: Philip Jowett Collection)_
This artillery wagon has two different turrets, both apparently armed with 75mm Type 38s.
_(Photo: Paul Malmassari Collection)_
In early 1927, a White Russian armoured train, the _Chihli_ , was placed in service at Tienstin by the forces of the Fengtian. Composed of six wagons arranged symmetrically on either side of the engine, it was armed with 75mm guns (in the lower turrets of artillery wagons Nos 2 and 6, with a horizontal field of fire of 270 degrees) and 47mm guns (in the upper turrets, with a 360-degree field of fire). Wagon No 3 carried a Stokes mortar in a circular tub mounted centrally on the wagon. According to certain other contemporary sources, it carried a different armament: as with other White Russian trains it carried eight to twelve heavy machine guns, and the artillery was 76.2mm Putilov models with between 200 and 300 shells per gun. As for the engine, its armour was designed to give it a similar outline to the machine-gun wagons.
### The Armoured Trains of Wu Peifu
Wu Peifu and Zhang Zuolin were the two most important warlords who used armoured trains other than those of the White Russians. Their crews were primarily Chinese. Wu Peifu began to use armoured trains in the mid-1920s, after he had rebuilt his forces following the defeat he had suffered during the Second Zhili-Fengtian War in 1924. They were probably inspired by the White trains of Zhang Zonchang and of Chu Yupu, but it appears, however, that their technical characteristics and operational doctrines were inferior to those of the Whites. The only information we have is that they were built at Hankow by the Mechanical Workshops of the Yang Tze, specialists in ship construction, including the gunboats of the Chinese Navy. The financial investment in the trains was so heavy that it brought about the bankruptcy of the Workshops in 1926.
In 1925, the principal adversary of Wu Peifu was the Kuominchun, whose Second Army commanded by Yue Weijun occupied Xinyang in the Province of Henan. Kou Yingjie, one of Wu Peifu's commanders, had used armoured trains during the siege of that town in the Winter of 1925. According to the memoirs of an officer, Kou had planned to embark a large number of shock troops in an armoured train. The train was to have been used as a battering ram, supporting the main assault on the city by disem-barking its troops to overwhelm the defences constructed along the line of the railway. Despite the advice of one of his subordinates that the enemy's dispositions could be intended as a trap for any such action, the order was given to attack. Barely had it begun to penetrate the enemy lines, when the train plunged into a large ditch prepared by the defenders. Although the sides of the train were armoured with iron plates, the wooden roof offered scant protection, and the troops inside were wiped out by the enemy firing from the high ground on either side of the ditch.
### The Armoured Trains of Zhang Zuolin and the First Battle between Armoured Trains
Paradoxically, the first battle between armoured trains did not involve the modern trains such as those of the White Russians, but rather the trains of Wu Peifu and Zhang Zuolin. Very little information survives on the trains of the latter. According to the memoirs of Marshall Zhang Xueliang, these improvised trains were built on the Central East Railway by the troops of Zhang Zongchang, when his army was in Manchuria in the early 1920s. Sleepers and lengths of rail had been used as armour by pouring cement between them, and their armament consisted of artillery and machine guns. The crews were Chinese.
Although Wu Peifu allied himself with Zhang Zuolin and the letter's subordinates Zhang Zongchang and Chu Yupu in their common struggle against the forces of the Kuominchun, the year 1926 had seen the rout of Wu Peifu's main forces faced with the rapid advance of the Nationalist 'Expedition of the North'.
It was now, with Wu at a disadvantage, that once again Zhang Zuolin looked on the troops of Wu as standing in the way of his ambitious plan to conquer the whole of China. He therefore declared war in February 1927, sending his elite troops into Henan Province to attack those of Jin Yun-é who was loyal to Wu. This would be the last great battle between the 'historic' Warlords of the North. For his part, Jin Yun-é launched his own counter-offensive against the city of Zhengzhou, led by his most loyal commander, Gao Rutong. At least one armoured train was used by his main force along the Beijing-Hankow railway line, guarded on each flank by the infantry. The official report of the Fengtian Army, preserved in the archives, describes the battle as follows:
On the morning of 24th March, the enemy commander Gao Rutong, accompanied by his bodyguard and his shock troops, took personal control of an armoured train, and led a major attack. After advancing towards Wu-shi-li Pu along the Beijing-Hankow railway, the enemy was surrounded and their armoured train destroyed by our artillery. Gao and his head of staff Shen Qichang, his brigade commander Song Jiaxian and 40 other officers were killed inside the armoured train. The enemy forces thereafter retreated towards Xinzheng. After the battle, over 1,000 men were taken prisoner, and their armament, including one armoured train, eight artillery pieces and a large quantity of small arms, were captured. The bodies of General Gao and the other officers were sent to Zhengzhou and buried with all due honours.
A fascinating view of an armoured train built of cardboard on 1 September 1926, in honour of the dead of the Fengtian and Chili-Shantung Armies during the war against the Kuominchun. Interestingly, modern-day Chinese still leave presents such as televisions and microwaves made of card and paper as symbolic offerings on the graves of their ancestors.
_(Photo: Yichuan Chen Collection)_
The above official report does not mention the role played by the Fengtian armoured train. But several descriptions prove that it was involved in a rather curious train-versus-train combat. In the 1960s, Xu Xiangchen, a close subordinate of Jin, wrote on the subject of this battle:
A major obstacle to the advance of the troops of Jin was a Fengtian armoured train positioned to the South of Zhengzhou. Goa had planned to use the coupling hook of his own armoured train to harpoon that of the Fengtian Army's train in order to capture it. Gao's train was able to make its approach to the Fengtian train and managed to couple to it. However, he possessed only one engine as against the enemy's two (although individually of less power). After stalling for a moment, the coupling on the engine of Gao's armoured train let go, and the whole of his train was pulled towards the Fengtian lines, with Gao still on board. The latter ordered his on-board artillery to fire on the enemy train. The gunners on the Fengtian train replied, and the whole of Gao's train was destroyed, Gao being killed during the fight.
Marshal Zhang Xueliang, fighting on the other side, recounted this episode in his memoirs:
Cao Yaozhang, commander of the squadron of armoured trains, gave me the following report of the fighting. When in action our armoured train was always accompanied by the infantry, and in fact two companies of infantry had supported the train on the previous day. Following hard fighting, the infantry retreated, abandoning the train which had no engine attached. The troops on the train reported this to their commanding officer, who told them not to panic as he believed the engine would return to find them the next morning. In the morning, the train in fact began to roll, but the crew quickly noticed that they were going in the wrong direction. After checking on the situation, they concluded they were being towed by an enemy train – the mobile command post of Gao Rutong. At one end of our train was a Russian cannon, originally installed by the men under Zhang Zongchang. A section head in charge of the cannon fired desperately on the enemy train. The shock effect on the closed-up wagons killed many of the soldiers in the enemy train.
This remarkable photo of Gao Rutong's armoured train allows us a view of the cement backing to the vertical steel armour plating. One or more shells have evidently penetrated and exploded inside, with devastating effect.
_(Photo:_ History Illustrated _, [June 1927], Yichuan Chen Collection)_
Although the reports differ in the details, the accounts from both sides agree on the main features of the incident. A photo of Gao Rutong's wagon damaged by artillery fire appeared in various Chinese and Japanese publications.
### The Birth of the Nationalist Armoured Trains
The first armoured trains of the Nationalist Government in Canton, including the famous 'armoured train squadron of the Grand Marshal' (in other words, Sun Yat-sen, who was proclaimed Grand Marshal of the Army and the Navy by the government run by the Communists), were all of improvised construction. A Soviet adviser described one of the trains on which he had travelled in 1925: 'The equipment of these trains was very rudimentary, consisting of goods wagons armoured with iron plates, and they even lack flat wagons.' Perhaps these were trains put in service to counter the bandits who had roamed around Canton since the beginning of the twentieth century. They remained extremely active, and the railway was their target of choice. In 1925 the managers of the Canton Railway had sent four recommendations to the Nationalist Government for the protection of the railway, and the first one concerned the establishment of armoured trains to protect the passenger trains.
An armoured train photographed between 20 and 27 February 1927 in Beijing by a British married couple. Note the artillery wagons inserted between the armoured machine-gun wagons.
_(Photo: Paul Malmassari Collection)_
The commanders of the National Revolutionary Army responded rapidly, and by 1926 the protection of all the commercial trains on the main lines around Canton was assured by armoured wagons. According to the newspapers of the period, these 'armoured trains' comprised a single armoured wagon, manned by soldiers, and hauled by a small steam engine.
One armoured train, probably of the same improvised type (with protection consisting of sleepers and sandbags) was put into service by the volunteer workers of the Canton-Hankow Railway during the difficult siege of the town of Wuchang, controlled by the forces of Wu Peifu, by the Fourth Army of the National Revolutionary Army (ANR). In order to defeat the ramparts, the sappers carried out a mining operation under the protection of the armoured train. But during an enemy sortie, the forces of Wu Peifu surrounded and temporarily captured the armoured train. After the town fell, General Chiang Kai-shek ordered the Hanyang Arsenal to build armoured trains after consulting with Soviet advisers.
### The Battle of Shanghai (March 1927)
The armoured trains of the ANC employed during the attack on Shanghai were still of the improvised type. In his memoires, General Bai-Chongxi tells that an armoured train armed with Russian 76.2mm guns had been used at Songjiang near Shanghai, to cover the assault sappers tasked with clearing the barbed wire entanglements which were blocking a railway bridge, and at the same time to destroy enemy machine-gun nests.
According to the photographic record, the improvised trains of the ANR were simply reinforced vans, with loopholes for firing rifles and machine guns cut in the side walls. 82mm trench mortars were mounted on revolving platforms protected by iron plates, probably inspired by the heavy 150mm mortars on the White Russian armoured trains.
After the fall of Shanghai, several White Russian armoured trains were captured by the ANR. According to the memoires of Zhang Pei, a staff officer of the ANR, hundreds of White Russian soldiers were captured at Songjiang along with their armoured trains, on which 'the wagons used by the officers were richly decorated, and contained expensive cigarettes and perfumes'. A Soviet adviser demanded that all the White Russians be decapitated, which was then carried out.
The captured White Russian armoured trains were all reused by the ANR against their former owners and were often renamed _Zhong Shan_ in honour of Sun Yat-sen, differing only by a following number. One source indicates that during the Expedition of the North, twenty armoured trains bearing this name were created from captured wagons.
One of the very early improvised Nationalist armoured trains, photographed at Canton.
_(Photo: Yichuan Chen Collection)_
Seen near Shanghai in 1927, this tub shelters a 150mm mortar served by the White Russian crew of the _Chang Chen_ ('Great Wall').
_(Photo: Paul Malmassari Collection)_
_Chang Chen_ seen at Shanghai in April 1927, preparing to repulse the attack by Communist troops. The gun is a 7.5cm/L14G 'Shanghai-Krupp' mountain gun.
_(Photo: Yichuan Chen Collection)_
One of the 82mm mortars on the _Zhong Shan_ No 1 photographed in July 1927.
_(Photo: Yichuan Chen Collection)_
The Nationalist armoured train _Zhong Shan_ , photographed in August 1927 after being captured from the Northern forces.
_(Photo: Paul Malmassari Collection)_
### The Golden Age of the Chinese Armoured Trains (Part I): Hand-to-hand Fighting against Armoured Trains in 1927
After having captured the cities of Shanghai and Nanking in April 1927, the Nationalist Government of Chiang Kai-shek broke with the rival Government of Wuhan and began eliminating the Communists. At the same time the Nationalist forces continued their progression against the forces of Zhang Zongchan and the other Warlords, in what was known as the 'Continuation of the Expedition of the North'.
Their primary objectives were the minor towns around Nanking to the north of the Yangtze. The Northern forces had placed their best units, including the 65th Division consisting of White Russian soldiers and armoured trains, near the railway junctions of Hua Qi Ying and Dong Ge. Despite their dispositions, they found themselves unable to check the advance of the numerically superior Nationalist forces, who continued to advance northwards. The two sides clashed again in the town of Linhuai, where according to reports, an armoured train named _Hubei_ was captured.
These actions formed only a minor part of the great advance across the northern province of Jiangsu and the Province of Anhui to the north-east. Although the Northern forces were superior technically, employing armoured trains, White Russian cavalry units and aircraft in their defensive actions, the town of Xuzhou finally fell on 2 July 1927. According to the report by General Bai Chongxi, three Northern armoured trains were destroyed in the course of the fighting. The Nationalists were finally stopped when they entered Shandong, when the troops of General Wang Tianpei found themselves held up to the south of the Grand Canal. The latter wrote in his memoirs that 'the enemy was bolstered by his barbaric armoured trains and bombarded us night and day, our efforts to cross the Canal being countered at every turn by overwhelming firepower'.
An overall view of _Hubei_ (from the name of the Province, Hopei) captured by the Southern Army, seen here at Tientsin in 1927.
_(Photo: Paul Malmassari Collection)_
Chiang Kai-shek and Feng Yuxiang (known as 'the Christian General') concluded an alliance at Xuzhou. However, the rear of the forces of the Nanking Government were threatened by their opponents in the Government of Wuhan, which also possessed powerful armies. Accordingly, Xuzhou was abandoned on 7 August and the Nationalist troops rapidly withdrew to Nanking. Seizing their opportunity, the Northern troops returned from Jinan, supported by armoured trains, and very soon after reached Pukou, leaving the Yangtze River as the only obstacle before the capital of the Nanking Government. It appeared that at this moment the course of history was about to change.
According to contemporary reports, the armoured trains in Pukou Station were used by the joint forces of Sun Chuanfang and Zhang Zongchang as mobile artillery batteries, supporting the amphibious attack attempted against Nanking. But the guns of the trains could not neutralise the heavy naval guns positioned along the bank of the Yangtze to the north of the city. The coastal batteries repulsed not only the armoured trains, destroying one of their steam engines, but also the infantry attempting a landing. Finally the forces of Sun Chuanfang crossed the river and landed beside the town Longtan, out of range of the coastal defence batteries. But just as Nanking seemed on the point of falling, the Nationalist forces launched a desperate counter-attack, encircling the forces of Sun Chuanfang. Nanking had been saved.
The command wagon of _Hubei_ bearing the inscription 'Armoured Trains General Staff ' on its side.
_(Photo: Paul Malmassari Collection)_
An anti-aircraft gun on the forward flat wagon of _Hubei_ , devoid of armour protection apart from the low side plates here seen in the raised position.
_(Photo: Paul Malmassari Collection)_
Close-up of one of the artillery wagons of _Hubei_ , armed with a 75mm Model 38.
_(Photo: Paul Malmassari Collection)_
Needless to say, the fighting continued, bloodier than ever. The most serious combat involving the White Russian armoured trains took place in Linhuai and Fengyang. These two towns fell to the Nationalists on 11 and 12 November 1927 respectively, but the crucial strategic site of Ma An Shan changed hands several times. It was finally held by the Northern forces, and blocked the Nationalists' advance towards Bengbu. Four troop trains protected by two armoured trains had been sent to reinforce the Northern forces.
A Nationalist trolley converted locally from a Japanese road-rail truck, captured in Jinan Station in August 1927. Note the road wheels on the hull and the searchlight on top of the dome-shaped turret.
_(Photo: Yichuan Chen Collection)_
The armoured trains terrified the Nationalist soldiers: Nationalist General Xu Tingyao even declared that the White Russian crews were cannibals who killed captured soldiers in order to eat them. On their own side, the Nationalists had no artillery capable of inflicting any serious damage to the armoured trains. The General wrote:
On the third day we were at Linhuai, the number of enemy armoured trains increased to four. The White Russian crews, after having drunk wine, fired on us furiously and when our offensive had been stopped, they arrived to repair the tracks and advanced. Two of the armoured trains advanced up to 4 km behind our lines and fired on us from behind. On the fourth day, seven enemy divisions completely surrounded us, and the situation was only improved on the fifth day thanks to the arrival of nine of our divisions.
On 16 November 1927, the Nationalists broke through into Bengbu, while the White Russian armoured trains continued to support the Northern troops during the street fighting. All combat finally ended at 16.00 on the same day.
The Nationalists' next objective was Xuzhou. Although no descriptions of the actions involving the White Russian armoured trains have come to light, several Nationalist reports, and various publications, referred to the power of the enemy trains in their accounts of the fighting during the second battle for Xuzhou. The armoured trains, together with the air element and the trench mortars, were the three most formidable arms deployed by the Northern troops. But this time, the battle lasted only four days and ended with the Nationalists seizing Xuzhou, in the process capturing at least one armoured train.
### The Golden Age of the Chinese armoured trains (Part II): Train versus Train Combat and the End of the White Russian Armoured Trains
The war rapidly spread in the south of the Province of Shandong and as usual, the Northerners made effective use of their armoured trains. According to Nationalist documents, two tanks and four armoured trains were used by the forces of Zhang Zongchang. However, at this point we should pause to consider the use of artillery and armoured trains by the Nationalists. On the night of 17/18 April 1928, the Nationalist armoured train _Shandong_ (perhaps an ex-White Russian armoured train, from its name) and artillerymen with six Krupp guns (also captured from the Northerners) were ordered to advance to protect the line near Tengxian (today a city in south Shandong), and to destroy enemy armoured trains. However, they arrived too late to engage the latter, as the following report describes:
During the attack on Tengxian on 17th April, the Engineer Corps of the 9th Army had destroyed a length of track to the south of Tengxian, and had succeeded in surrounding an enemy armoured train. At this juncture, our artillery had not arrived, and our armoured train could not advance due to the damaged track. If our artillery had arrived in time, or if the track had been repaired more quickly, we would certainly have captured the enemy armoured train.
In the days which followed, the Nationalist armoured trains were primarily used for counter-battery fire, particularly against the enemy armoured trains. In the battle around Tai'an, two Nationalist armoured trains, _Zhong Shan No 4_ and _Ping Deng_ ('Equality'), engaged three White Russian armoured trains. At the same time, armoured trains were employed by the Kuominchun under Feng Yuxiang in their fight against the Northern Warlords, as the former advanced across the province of Hebei towards Tianjin (Tientsin) and Beijing.
Armoured Train _Beijing_.
_(Photo: Philip Jowett Collection)_
An artillery wagon of Armoured Train _Chang Jiang_ ('Yangtse River') at Tianjin (Tientsin) in around 1928. Note the two French soldiers, probably from the _Corps d'occupation de Chine_ (COC = China Occupation Force) which in 1929 became the _Troupes françaises en Chine_ (French Troops in China).
_(Photo: Paul Malmassari Collection)_
Another artillery wagon of the _Chang Jiang_ , with the hull armour extended upwards probably to offer increased protection to the gunners serving the gun in its open-backed shield.
_(Photo: Paul Malmassari Collection)_
Armoured train at Mukden (the modern Shenyang) in 1928. The second wagon in line has an armoured tub on the roof, perhaps for a mortar. The flat wagon in the foreground is loaded with sleepers.
_(Photo: Paul Malmassari Collection)_
Nationalist armoured trolley employed in September 1928 at Tang Shang. Standing front left is General Bai, whose son wrote a book containing his father's memoirs.
_(Photo: All Rights Reserved)_
Tientsin and Beijing fell to the Nationalist forces in June. On 4 July 1928, Marshal Zhang Zuolin who was the major supporter of the Northern forces (by this time consisting principally of the troops of Zhang Zongchang and Chu Yupu) was assassinated by the Japanese. Almost immediately, Zhang Zongchang and Chu Yupu fell out with the 'Young Marshal' Zhang Xueliang, who allied himself with the Nationalists and ordered the Northern warlords to cross the River Luan to reorganise their forces as part of the Fengtian Army. Zhang Zongchang made his last address to his troops, who still numbered some 70,000 men, in his brutal bandit chief style, asking them to attack their former allies, the Fengtian Army. The attack by Nationalist forces supported by the armoured trains _Honan_ and _Min Sheng_ put a stop to his plans.
According to a Nationalist report, the Northern forces still possessed at least three armoured trains. Heavy fighting took place between Nationalist and Northern armoured trains. On 12 August 1928, the remaining Northern forces crossed the River Luan, only to be defeated by a combination of the Northern Warlords and the Fengtian Armies. Surviving documents of the latter indicate that the three remaining armoured trains of the Northern troops, with their White Russian crews, changed sides and joined the Fengtian Army, in passing wiping out the last Northern troops who had not surrendered. Thus a page of history was closed, the adventure of the armoured trains of Zhang Zongchang coming to an end there where it had begun four years earlier.
### The Last War between the Dragons: the 1930 War of the Central Plains
An obscure chapter in the history of the Chinese armoured trains was written in Northern China between 1925 and 1928. It involved the struggle between the White Russian armoured trains of Zhang Zongchang and their lesser-known adversaries, the Soviet-designed armoured trains of the Kuominchun under General Feng Yuxiang. According to Russian sources, five armoured trains designed by Soviet advisers working with the Kuominchun were built in the Kalgan workshops (the modern Chang-chia-k'ou) in May 1925. The existence of the trains and the advisers is confirmed in the journal of General Feng Yuxiang, but information on and photos of these trains and their operations are extremely rare.
Like the Nationalists in the south, in 1927 and 1928 the forces of the Kuominchun made rapid advances against the Northern warlords, and several White Russian armoured trains were captured. With these trains and others built locally, the Kuominchun rapidly consolidated an armoured train force which equalled the Nationalist trains of Chiang Kai-shek. In May 1929, Fen Yuxiang formally declared war on Chiang, and in March 1930 Yan Xishan from Shanxi allied himself with Feng. China was once more plunged into civil war.
A rear wagon of the _Ho Nan_ , with the now classic layout of two artillery turrets.
_(Photo: Philip Jowett Collection)_
Chinese crew members of the _Ho Nan_ , of the army of General Feng Yuxiang.
_(Photo: Philip Jowett Collection)_
This armoured train was the escort for the special train which transferred the remains of Sun Yat-sen when his ashes were repatriated from Beijing to Nanking in June 1929.
_(Photo: Paul Malmassari Collection)_
During the war between Chiang Kai-shek, Feng Yuxiang and Yan Xishan, known as the 'War of the Central Plains', many battles between armoured trains took place. According to contemporary documents, the two principal objectives of the armoured trains were to silence or destroy enemy trains and to act in support of the infantry, missions which closely followed the classic role of the armoured train. On 24 May 1930 a typical battle took place, as described by General Xu Tingyao of Chiang Kai-shek's forces:
During the fighting on the Longhai railway line, I was second-in-command of the 1st Division, and I was responsible for the leading echelon of the attack. An enemy armoured train, the _Zhongshan_ , was positioned on the line and completely blocked our advance, which caused me a great deal of anxiety. Later I recovered two trains, the _Yun Gui_ [the Provinces of Yunnan and Guizou] and the _Chan Cheng_ [Great Wall]. These armoured trains could not match the enemy train in terms of firepower, but had more powerful engines. Thus I conceived the plan to combine our two trains – making a total of four engines – then to ram the enemy train with two engines, to couple it up and drag it back to our lines. I climbed aboard the leading train and personally supervised the operation. The enemy crew spotted our trains and fired on us without hitting us. Our own fire was also unsuccessful. However, when our trains came within 400m [almost 400 yards] of the enemy train, two shells struck our leading train, causing many casualties and appearing to knock it out of the fight. I therefore dis-embarked to lead the troops on the ground. The enemy train continued to fire and I was severely wounded by the explosion of a shell beside me.
### Epilogue: the Chinese armoured trains 1931 to 1951
While the different factions were fighting each other in Central China, the Fengtian forces (the future Army of the North-East) had put together a formidable force of armoured trains in north-east China. As with the trains of the Kuominchun, details are hard to come by. Nevertheless, by the beginning of the 1930s, the Fengtian trains demonstrated remarkable features. Their main characteristic was the semi-cylindrical form of the artillery and infantry wagons, which provided superior protection compared with previous Chinese armoured trains. In addition, the ex-White Russian armoured trains were also used by the Army of the North-East. The armoured trains were in the vanguard when the Army of the North-East conquered Peiping and Tientsin under the command of Marshal Zhang Xueliang, thus putting an end to the war of the Central Plains.
The characteristic form of the Fengtian trains is well in evidence here, with their semi-cylindrical shape topped by turrets or an observation tower.
_(Photo: Paul Malmassari Collection)_
They also fought the Japanese during the Manchurian incident in 1931, and showed themselves to be as effective as contemporary Japanese trains. Later, several were obliged to withdraw to the south to the areas still held by Chinese troops, such as Peiping and Tientsin.
_(Photo: All Rights Reserved)_
An armoured train photographed near Shanghai in 1932. Note the unusual profile of the artillery wagon, which allows a wide field of vision for the armoured observation cupola on the following wagon.
_(Photo: Paul Malmassari Collection)_
Armoured Train _Chang Jiang_ , with a wagon the hull of which is identical to that in the previous photo, but with a single gun protected by a shield which appears to be open at the rear. Note the hand trolley carried on the flat wagon.
_(Photo: Paul Malmassari Collection)_
37mm Type 94 gun mounted aboard a Chinese armoured train captured by the Japanese.
_(Photo: Paul Malmassari Collection)_
Communist armoured train on the Hunan-Guangxi line in 1949. The Japanese wagons have been modified to carry turrets from Type 97 Chi Ha tanks, but armed with 57mm Type 97s in place of the 47mm gun normally mounted. It appears that a cylindrical nacelle has been fitted to the left-hand wagon.
_(Photo: Yichuan Chen Collection)_
On the Nationalist side, from 1930 onwards there was virtually no renovation of the fleet of armoured trains, and their importance declined. The Chinese armoured trains, once a formidable force, had ceased to be the principal arbiter of the battlefield. They played a minor role during the war against the Japanese between 1937 and 1945. From the photographic record, the Chinese trains of that period were either the former trains of the Army of the North-East or ex-White Russian trains.
When the civil war between Nationalists and Communists began in 1946, Chinese armoured trains seem to have undergone a renaissance. As the Communists' principal tactic against the Japanese had been the destruction of the railway lines, they continued this against their new adversary, while the Nationalists inherited the tactics and the techniques of defence of the railway network from the Japanese, and even several Japanese armoured trains. From late 1947, the Communists began their counter-offensive with attacks against the cities held by the Nationalists. At that time the Nationalist armoured trains, rather than patrolling the railway network, were frequently used as a mobile force within the defensive systems of the cities. One of the first confrontations between the Communist besiegers and an armoured train took place in November 1947 during the battle for Shijiazhuang. The Nationalist force was composed of between four and six trains, including one of Japanese origin. The remainder were improvised from goods wagons and flat wagons reinforced with concrete and steel plates, often considered as being better protected than the Japanese trains, and carrying tanks. To fight them, the Communists employed captured weapons which were new to them, such as bazookas and anti-tank guns. Similar fighting occurred during the sieges of Jinan, Tianjin (Tientsin) and Taiyuan.
The last chapter in the history of armoured trains in China was written by the Chinese Communists. In the late 1940s and early 1950s, a few armoured trains were retained in service to guarantee the security of the rail network against bandits. In July 1951 all the armoured trains from the different regions of China were recalled and stocked at Shenyang. Their crews were distributed among infantry units and sent to Korea. Thus ended the thirty-year history of armoured trains in China.
Communist armoured train in north-east China, also converted from former Japanese wagons, on which armoured cupolas have been installed. These hemispherical cupolas were originally from bunkers, some of which are today on public display in the Museum of the Battery of the West at Yingkou (Liaoning Province).
_(Photo: Yichuan Chen Collection)_
Nationalist armoured train derailed during the battle for Taiyuan in 1949. The turret is armed with a 75mm mountain gun.
_(Photo: Yichuan Chen Collection)_
A Nationalist armoured train captured during the battle for Taiyuan. Originally a Japanese safety flat wagon, the wagon shown in the centre has been converted by adding wooden walls pierced by loopholes.
_(Photo: Yichuan Chen Collection)_
This scene purporting to show an armoured train captured by the Communists in the Shanxi has perhaps been posed for propaganda purposes, but it illustrates the method of attack in those zones where it was possible to dominate the trains from high ground.
_(Photo: Yichuan Chen Collection)_
This Nationalist armoured train was captured during the Zheng-Tai campaign in 1949 on the Zhengding-Taiyuan line. Note the familiar form of the ex-Japanese safety wagon with its armoured lookout cabin.
_(Photo: Yichuan Chen Collection)_
**SOURCES**
**Books:**
Jowett, Philip, _The Armies of Warlord China 1911-1928_ (Altglen, PA: Schiffer Publishing, 2014).
___________, _China's Wars: Rousing the Dragon 1894-1949_ (Oxford: Osprey Publishing, 2013).
Krarup-Nielsen, Aage, _The Dragon Awakes_ (London: J. Lane, 1928).
Malraux, André, _La Condition humaine_ (Paris: Gallimard, 1933).
**Journal Articles:**
'Chine: Trains blindés', _Revue d'Artillerie_ Vol 99 (January–June 1927), pp 694–5.
Girves, Captain, 'La Guerre civile en Chine', _Revue militaire française_ Vol 1 (1927), p 190.
'Manchurian Armored Train', _Coast Artillery Journal_ (USA) Vol 66, No 5 (May 1927), pp 481–2.
Rouquerol, General J, 'Chine: Les trains blindés en Asie Orientale', _Revue d'Artillerie_ (July–December 1927), pp 605–9.
Zaloga, Steven, 'Armour in China', _Military Modelling Manual_ (1983), pp 4–9.
**Website :**
http://www.chinaheritagequarterly.org/features.php?searchterm=sapajou_page12.inc&issue=022
**Film:**
Russian-made film of the advance of the forces of Marshal Chang Tso-Lin, Warlord of Mukden, South towards Nanking, 1924-1925. (1925), IWM 172.
An interesting view of a Communist armoured train used for track repairs, with the red star surrounded by the slogan 'Our work takes us where the frontiers lie'.
_(Photo: Yichuan Chen Collection)_
This photo is not what it seems. Here is film star George Sanders with a 'Chinese armoured train' from the 1938 Hollywood film _International Settlement_ , set in Shanghai. The ideograms on the side of the wagon read 'Government Property Do Not Touch'. Sadly, the scene with the armoured train seems to have ended on the cutting-room floor, so this is the only surviving record.
_(Photo: Paul Malmassari Collection)_
. This war which lasted one week in July 1920, between the two rival factions named for the respective provinces of their leaders (today in the region of Hebei), was fought to control the Chinese government in Beijing: the Zhili faction came out the winner.
. Nicolai Merkulov was a merchant who, along with his brother Spiridon Dionisovich, headed the short-lived Government of Pryamure (from May 1921 to October 1922), the last White enclave in Siberia.
. A conflict which was started by the _coup d'etat_ of General Feng Yuxiang in Beijing.
. Refer to the Sources at the end of this Chapter, for the film which was produced on that occasion, preserved in the Imperial War Museum. In it one can see that the artillery component was a 75mm Japanese Type 41 mountain gun or a Type 6 (the special version built for China).
. The first ferryboat was not imported from England until 1933.
. Provincial Governor.
. Respectively: Mount Tai, Shantung, the regions of the Provinces Yunnan and Guizhou, Ho Nan. It is difficult to know whether the armoured trains of the same name photographed several years later were the same ones, modernised, or completely different trains.
. The White Russian armoured trains were commanded by a certain Tchekov.
. Described in 'Manchurian Armored Train', _Coast Artillery Journal_ (USA), Vol 66, No 5 (May 1927).
. A Nationalist Army created in 1924 and commanded by Feng Yuxiang.
. This campaign carried out between 1926 and 1928 by the Kuomintang, commanded by Generalissimo Chiang Kai-shek, had as its objective the reunification of China, which was completed by October 1928, with Nanking as capital.
. Certain sources believe that Jin Yun-é was secretly preparing to negotiate with the Nationalists.
. Depending on which historical period is under consideration, the term 'Nationalist' could also be applied to the Communist forces, since their objectives and those of the Kuomintang included opposition to the Warlords. Chiang's rupture with the Communists and his war against them began in April 1927.
. Soviet advisers had been sent by the Comintern as early as 1923.
. Recorded in the archives preserved in Taiwan.
. The central element of André Malraux's novel _La Condition Humaine_.
. 'Zhong Shan' was the most famous surname of Sun Yat-sen, given to him by the Japanese philosopher Töten Miyazaki, one of Sun's supporters during the Revolution.
. Today in the District of Pukou, Nanking.
. Today in the County of Fengyang, in the town of Chuzhou.
. Which linked Beijing to Hangzhou, built between AD 605 and 609.
. To the south-west of Nanking. The name literally means 'horse saddle mountain'.
. More likely vodka.
. 12 November 1866 – 12 March 1925, he was one of the founders of the Kuomintang, and in 1912 had become the first President of the Republic of China. In June 1929 his ashes were buried in the mausoleum specially built to receive them.
. Known as Gongchen in China.
## COLOMBIA
It appears that the only use of armoured locomotives in Colombia is the recent protection of coal trains in the region of the El Cerrejón opencast mine in the north of the country. The company of the same name was created in the 1970s and a railway line was built to transport the coal 150km (93 miles) to Puerto Bolivar. The original eight locomotives were General Electric type GE B36-7. Additionally five Type AC4400CW locomotives have been employed to work alongside the original units. In 2009 the guerrillas of the FARC and also certain elements of the Wayuu Tribe began to attack the trains, causing several derailments. The fitting of armour to the locomotives, which is still in place at the time of writing, was carried out by two Bogotá-based companies, ISBI Armoring and Armor International.
Two diesel locos of the Cerrejón Company with armoured cabs, on the left a GE B36-7, and on the right a GE AC4400CW.
_(Photo: Armor International)_
The team of fitters in front of a GE AC4400CW in the process of being armoured.
_(Photo: Armor International)_
A superb frontal view of a GE AC4400CW, showing how the armour protection blends in well with the overall silhouette of the loco.
_(Photo: Armor International)_
Fitting the armoured windscreen on a GE AC4400CW by the company ISBI. The original glass has been replaced by 50mm-thick armoured glass panes.
_(Photo: ISBI Armoring)_
One of the 50mm-thick windscreens ready for fitting.
_(Photo: ISBI Armoring)_
. _Fuerzas armadas revolucionarias de Colombia – Ejército del Pueblo_ , A communist guerrilla movement.
## CONFEDERATE STATES OF AMERICA
### ARMOURED RAILWAY GUN AND COTTONCLAD SHARPSHOOTER CARS (1862)
### The Dry Land _Merrimac_
In June 1862 the Union Army of the Potomac advanced on the Confederate capital of Richmond. General Robert E Lee looked for a means of countering the enemy's preponderance in heavy siege artillery, which they would be transporting into position by rail. On 5 June he asked Colonel Josiah Gorgas, the Chief of Ordnance, if it would be possible to mount a heavy gun on a railway car. The challenge was taken up by the Navy, who already had experience of armouring the famous _Virginia_ (ex- _Merrimac_ ), which had taken on the Union blockaders and fought the first ironclad battle with USS _Monitor_.
On 26 June, Captain M Minor reported to Lee: 'The railroad-iron plated battery designed by Lieutenant John M. Brooke, C.S. Navy, has been completed. The gun, a rifled and banded 32-pounder of 57 cwt, has been mounted and equipped by Lieutenant R.D. Minor, C.S. Navy, and with 200 rounds of ammunition, including 15-inch solid bolt shot, is now ready to be transferred to the Army.' The railway gun was manned by Lt James Barry CSN, Sergeant Daniel Knowles and thirteen gunners of the Norfolk United Artillery Battery, many of whom had previously served on the _Virginia_.
The Battle of Savage's Station, fought on 29 June 1862, was a Union defeat, watched by Confederate Major General Magruder from the rail overbridge. The railway gun was propelled towards the Union lines along the track of the Richmond & York Railroad by an unarmoured steam engine, with obstacles being removed or pushed aside by the gun itself. Firing explosive shells as it advanced, it forced the Union troops to abandon their lines across the track and take up flanking positions beside it, which the gunners could not counter as they had no means of training the gun to one side. Eventually, the gun had progressed so far in front of the Confederate lines that it risked being lost due to the Union flanking fire, and Lieutenant Barry ordered it to pull back.
Note that no means of propelling the railway gun, other than manpower, has been depicted in this illustration. The design is based on the memories of Charles S. Gates.
Fifty-nine years after the event, the Confederate veteran Charles S. Gates described from memory the famous 'Dry Land _Merrimac_ ', as the railway gun was called by Richmond newspapers in 1862. Later descriptions, and reconstructions in model form, have been based on his recollections, including the painting above.
Fortunately we also have an eyewitness to the action, who fixed the scene in a watercolour. Private Robert Knox Sneden of the Union Army was a topographical engineer, who produced maps for the Army of the Potomac. Among his almost 1000 watercolours, sketches and maps was a painting of the Battle of Savage's Station, with the railgun as the centrepiece. While answering many questions, his depiction poses others.
Private Sneden may have painted this scene from memory afterwards, as the Army of the Potomac was forced to withdraw from in front of Richmond in some disorder. He certainly stretches the platform wagon to a unbelievable length, which would be too weak to support the weight of the gun, never mind withstand the recoil. As he obviously observed the event from a considerable distance away, his rendering of the moving flatcar may not be all that accurate. Nevertheless, what his illustration does reveal is the ' _Virginia_ -like' armoured casemate surrounding the cannon and its gunners, with armour on the sides as well as the front. He has correctly depicted the Union force being obliged to take up position flanking the railway track, which would ultimately oblige Lieutenant Minor and his men to pull back, for fear of being fired upon from the rear.
There has been some confusion in the minds of railway enthusiasts between this gun and the Union railway gun used at the siege of Petersburg, mounted on a fourteen-wheel wagon (see the United States of America chapter). The latter gun, however, is clearly protected by timber baulks alone, even if they do cover the sides as well as the front, and there is no covering of iron as mentioned in all the accounts of the Confederate piece.
Accounts differed as to its effects in action, and certainly the Union commanders did not make much of it in their reports. But then, mentioning the attack of an unstoppable railway weapon adding to the debacle of the battle would be like rubbing salt in one's own wounds. After the battle, presumably recognising its tactical drawbacks, the Confederate Navy retrieved their valuable gun and the platform would be returned to freight work.
### Cottonclad Sharpshooters Cars
Whatever its value or otherwise, the railway gun has completely overshadowed another Confederate innovation, the cottonclad armoured Sharpshooters Car, two of which can clearly be seen in Sneden's watercolour, coupled between the railway gun and the engine
Protection of these cars with cotton bales at first sight seems a strange choice. Certainly raw cotton was far more readily available to the Confederacy than iron. But how effective would it be against rifle fire? The British Army certainly recognised that bales of cotton waste could absorb the impact of .303 projectiles which would not penetrate a certain thickness. That would leave the risk of the bales being set on fire by exploding shells. Apart from the fact that tightly-packed cotton, like stacked paper, is extremely difficult to set on fire, if a Sharpshooters Car were to be struck by a shell, the risk of subsequent fire would be a minor consideration. These early experiments in using cotton as protection would continue in the form of bulletproof vests, resulting in modern textile body armour.
The height of the Battle of Savage's Station, painted by Private Robert Knox Sneden.
_(Painting: Diaries, Volume 3, 29 June –25 October 1862, Virginia Historical Society, Richmond, Va.)_
A representation of a Sharpshooters Car in HO scale in the livery of the Richmond & York River Railroad.
_(Model & Photo: Scott Cameron)_
**SOURCES**
**Archives:**
_Private Robert Knox Sneden Diaries_ , Volume 3, 1862 June 29– October 25, Virginia Historical Society, Richmond, Va.
_The War of the Rebellion: a Compilation of the Official Records of the Union and Confederate Armies_ (Official Records), Series I – Military Operations, Volume 11, Part III, Serial 14, Cornell University.
**Books:**
Alexander, Edwin P, _Civil War Railroads & Models_ (New York: Clarkson N Potter Inc., 1977).
Miller, Lt Col H W, _Railway Artillery, A Report on the Characteristics, Scope of Utility, Etc., of Railway Artillery_ , Volume I (Washington DC: Government Print Office, 1921), p 8.
**Websites:**
<http://scooters-stuff.blogspot.fr/p/a-sketch-of-csa-gun-car-followed-by.html>
<https://markerhunter.wordpress.com/2012/06/29/railway-arty-savage-station/>
<http://ebooks.library.cornell.edu/m/moawar/waro.html>
<http://www.civilwar-online.com/2011/06/civil-war-naval-artillery-part-one.html>
. Official Records, Series I, Volume 11, Part III, Serial 14, p 574.
. The US Navy had standardised all its guns as '32-pounders', being the weight of solid shot each one fired. Small, medium and large guns all of the same calibre (6.4in /16.256cm) were built, and only the powder charge and therefore the propulsive force varied between models. Each size was described by the weight of the gun barrel, expressed in cwt (hundredweight, or 112lbs/50.8 kg, of which twenty made up one Imperial ton). 57cwt = 2896kg.
. A curious choice of ammunition, only useful against armoured ships, the projectile being a cylinder rather than a ball. Against infantry the gun would fire an explosive shell weighing 26lbs (11.8kg).
. Official Records, Series I, Volume 11, Part III, Serial 14, p 615.
. Lt Col H W Miller, _Railway Artillery, A Report on the Characteristics, Scope of Utility, Etc., of Railway Artillery_ , Volume I (Washington DC: Government Print Office, 1921), p 8.
. Named after Union marksmen using Sharps breech-loading rifles, the original term was 'Sharps-shooters'.
. This type of protection was also used on Confederate river gunboats, the famous Cottonclads, to protect the boiler, engine, ammunition and other vulnerable areas.
. Towards the end of the Civil War the South was even forced to salvage and reuse obsolete inverted-U section rails.
. Described to the Translator by Major George Geear, Royal Artillery (retired), Chapel Bay Fort, Pembrokeshire, UK.
## CONGO-LEOPOLDVILLE
### ARMOURED TRAINS AND TROLLEYS (1960–1965)
On 30 June 1960 Congo-Léopoldville was declared independent. On 5 July the Force Publique, the former colonial gendarmerie, mutinied and civil unrest broke out, with white civilians coming under attack and many being forced to flee to neighbouring countries. There began a period of instability characterised by murder and rape, fuelled by anti-colonialist resentment and tribal rivalries. At the same time the integrity of the country was threatened by the breakaway of Katanga (11 July 1960 to January 1963), with the aid of mercenaries, and of South-Kasaï (20 August 1960 to 30 December 1961), and finally UN Forces intervened to aid Congolese forces in resisting the breakaway of these two provinces.
Maintaining freedom of traffic was vital for the provisional Katangese government, to be able to maintain the flow of copper exports, and for the supply needs of the UN contingents. The rail network (originally built to the metre gauge, but converted in 1955 to 1067mm [3ft 6in] gauge) came under attack, leading to the introduction of armour protection for rolling stock, at first by the railway staff and the remaining Belgian troops, then finally by all the belligerent parties. A Wickham armoured trolley (No 8453 built 1960) had also been acquired prior to independence.
In the station at Kongolo, two trolleys fitted locally with armour protection, using as a base Wickham Type 18 inspection trolleys, six of which had been delivered between 1956 and 1959. Under the shed roof is diesel locomotive Class 200 1-D DH with an armoured cab, leaving two observation slits. The gauge on the CFL network was 1.067m (3ft 6in).
_(Photo: Cegesoma-Bruxelles Collection Ref 280703)_
In the centre, a trolley armoured by the workshops of the BCK, on the line between Lubudi and Kamina in February 1961. A close examination of the photo suggests that the Wickham on the left is the same as the one in the previous photo.
_(Photo: CEDOMI)_
An armoured train used by the Katangan forces, employing an American M8 Greyhound armoured car.
_(Photo: Ltc Young, via Denis McCarthy)_
Unidentified armoured trolley, supporting Katangan or Belgian troops ensuring the BCK line is clear.
_(Photo: CEDOMI)_
Inspection trolley which formed the basis of the armoured versions, seen here in 1959 between Elisabethville and Kamina.
_(Photo: Paul Malmassari Collection)_
A photo taken some time in March or April 1961, showing an armoured train during Operation 'Conga' on the Kongolo-Kabalo axis.
_(Photos: CEDOMI)_
In February 1961, during Operation 'Banquise', the railway networks provided rapid deployment and needed protecting: here an armoured wagon is propelled by locomotive 2305 of the KDL, seen here in Luena Station. Following this operation, the BCK network which had profited from the heightened security, could henceforth operate without an escort.
_(Photo: CEDOMI)_
The same units seen from the locomotive end, with No 2305 of the KDL here operating on the BCK lines.
_(Photo: CEDOMI)_
Armoured wagon bringing up the rear of the train on the Benke to Kamina line (Operation 'Banquise').
_(Photo: CEDOMI)_
The United Nations intervened with contingents of troops from thirty-two nations. Here men of the Swedish contingent are fitting protection to open bogie wagons of the KDL. They were tasked with train protection in August 1960.
_(Photo: CEDOMI)_
_(Photo: CEDOMI)_
Three photos of the armoured train carrying the 1st Shock Unit (6th Foreign Commando Battalion), bearing the insignia of the 'Affreux' (a red devil's head on a white triangle), which supported Operation 'Ommegang' in November 1964.
_(Photo: CEDOMI)_
The 6th Battalion was formed of mercenaries commanded by the famous Bob Denard. The 0.615m (2ft) gauge line of the CVC appears hardly suitable to carry combat units. The operation was in support of a Belgian battalion, and a parallel movement by a motorised column opening up the road leading to Buta-Aketi, to clear the Simba rebels out of the Upper Congo.
_(Photo: CEDOMI)_
The makeshift protection of the locomotive can clearly be seen in this shot, which is reminiscent of the film _The Mercenaries_.
_(Photo: CEDOMI)_
**SOURCES:**
Blanchart, Charles, _Le rail du Congo belge 1945-1960_ , _Volume III_ (Brussels: Editions Blanchart & Co, 2008).
Malmassari, Paul, _Les Blindés de l'ONU_ (Guilherand Granges: La plume du temps, 2000).
Film _The Mercenaries_ , Director Jack Cardiff, 1968, running time 100 minutes.
. For descriptions of these dramatic events, see the 1965 novel _The Dark of the Sun_ by Wilbur A. Smith, the 1968 film _The Mercenaries_ , and _Chimères noires_ by Jean Lartéguy, published in 1963 by Presses de la Cité.
. DH = Diesel-Hydraulic. A locomotive built in Haine-St-Pierre in 1955.
. CFL = Chemin de Fer des grands Lacs (Great Lakes Railway).
. BCK = Companie du Bas Congo au Katanga.
. KDL = Compagnie du Katanga-Dilolo-Léopoldville.
. ONUC, the United Nations Operation in the Congo, deployed troops to support the Congolese Government from 14 July 1960 to 30 June 1964.
. In January 1964 the Simba ('Lion' in Swahili), rose in revolt, and carried out indescribable atrocities in all the territory they overran. The revolt was crushed in November by Operation 'Ommegang' conducted by the Belgian Para-Commando Regiment supported by two columns of mercenaries.
. CVC = Chemins de fer Vicinaux du Congo.
## INDEPENDENT STATE OF CROATIA
### ARMOURED TRAINS AND TROLLEYS 1941–1945
The Independent State of Croatia, initially a monarchy, later a republic, was created following the break-up of Yugoslavia in 1941.
Armoured trains ( _oklopni vlak_ ) were envisaged for anti-partisan operations from the very start. In September 1941 an improvised armoured train operated on the stretch of line between Maglaj and Doboj, and it remained in service up until December in the Tuzla region, assisting with the encirclement of the partisans in the Orzen Mountains.
The Slavonski Brod railway centre specialised in the repair and construction of armoured trains and trolleys, of which twenty were ordered in April 1942. At the same time, an 800-man Railway Battalion was formed. The armoured trains would not become an independent arm of service but were attached to and formed part of infantry regiments, each being designated a half-company to undertake this specialist role.
In November 1942 the Croatian trains came under the tactical control of the Wehrmacht, and records for 1943 indicate the existence of seven or eight armoured trains, grouped into five Armoured Train Companies ( _Satnija Oklopljenih Vlakova Nos 1-5_ ). Each train was composed of several armoured wagons and of one or two static Renault FT tanks (armed with a 37mm gun), carried on three-plank wagons. A mortar, two heavy and four light machine guns made up the rest of the armament. In all, 364 officers and men, a mixture of Croats and Germans, commanded and crewed the trains.
At the time of writing details of the exact makeup of each train, specifying the type of wagon, are not available. Equally it has not been possible to correlate the known numbering and naming of individual trains. Although we know that armoured trains were built for both standard gauge and narrow gauge, it is sometimes difficult to differentiate between them in photos. The sole indicator is that narrow-gauge armoured trains used central automatic couplings, whereas the standard-gauge units were fitted with buffers and screw link couplings.
A rough indication of the trains' geographical distribution is as follows:
– 1st Company: HQ at Doboj at the time it was formed in 1942; by September 1944 it was based at Slavonski Brod.
– 2nd Company: Created in 1942, by 1943 it operated to the north and east of Zagreb with Armoured Trains Nos 1 and 2.
– 3rd Company: Created in 1942, operating in the III Corps zone in Bosnia-Herzegovina with Armoured Trains _Ris_ , _Vuk_ and _Lisac_.
– 4th Company: No details at the time of writing.
– 5th Company: Formed in late 1943, operating in the Karlovac region with two armoured trains, then in 1944 on the Karlovac-Zagreb-Ozalj-Recica line.
Finally, two improvised armoured trains bearing the numbers 412 and 432 operated during 1941 in Bosnia-Herzogevina. Because of the through connections of the different railway networks, several of these trains also operated in Greece, and perhaps as far away as Italy, where Croatian-type armoured wagons were photographed.
Armoured trolleys built at Slavonski Brod on the chassis of Steyr 1500 trucks.
_(Photo: Wolfgang Sawodny)_
Narrow-gauge armoured train with a mixed German-Croat crew. The initials HDŽ stand for _Hrvatske Državne Želejnice_ or Croatian State Railways.
_(Photo: Paul Malmassari Collection)_
Protection improvised from sleepers on a pilot truck armed with an Italian 20mm Breda Model 35 cannon, seen in Katerini Station in Greece.
_(Photo: Paul Malmassari Collection)_
The same train on patrol in Greece, seen here in Tembi in 1943. The turret is an APX from a French tank, in original condition without the opening top hatches usually fitted by the Germans.
_(Photo: Paul Malmassari Collection)_
On the left, a standard-gauge armoured train, and on the right, a narrow-gauge track.
_(Photo: Paul Malmassari Collection)_
Running along the coast at Palatamon in Greece.
_(Photo: Paul Malmassari Collection)_
A fine view of a standard-gauge wagon, with an APX turret.
_(Photo: Paul Malmassari Collection)_
The same wagon photographed from the opposite side, showing the offset position of the lookout. The inscription 'O.V.T.102' may be the wagon's number.
_(Photo: Paul Malmassari Collection)_
German and Croatian soldiers pose for the camera in front of an armoured train.
_(Photo: Paul Malmassari Collection)_
Major-General Johann Fortner (1884–1947), commander of the 718th Infantry Division from May 1941 to March 1943, seen in front of an armoured wagon.
_(Photo: Paul Malmassari Collection)_
A more distant view of the same wagon, showing the arrangement of firing loopholes. In the centre of the train is the armoured engine.
_(Photo: Paul Malmassari Collection)_
An armoured wagon of an unidentified armoured train. The wagon's origins are obscure; is it an old Austro-Hungarian armoured wagon modified in the inter-war period, or a more recent model? The Croatian coat of arms can be seen on the right. The inscription 'O.V.A.12' may be its serial number.
_(Photo: Paul Malmassari Collection)_
The artillery element of the trains in the Balkans and in Italy was usually furnished by the 37mm guns of Renault FT tanks on three-plank wagons.
_(Photo: Paul Malmassari Collection)_
A different type of armoured wagon attached behind an FT Tank three-plank wagon, clearly showing the Croatian coat of arms.
_(Photo: Paul Malmassari Collection)_
Another view of the same train.
_(Photo: Bojan Dimitrijevic)_
Beside the road from Sarajevo to Vareš is a plaque commemorating the heroism of the partisans who appear to have attacked an armoured train in 1941.
_(Photo: Paul Malmassari Collection)_
Two interesting views of typical Croatian armoured trains, with their different types of wagon and the engine with only the driving cab being armoured.
_(Photos: Bundesarchiv – BA)_
Armoured train derailed by partisans on 4 August 1943.
_(Photo: Yugoslav Railway Museum)_
A narrow-gauge armoured engine as captured at the end of the war. Note the second engine which is only partially armoured.
_(Photo: Bojan Dimitrijevic)_
**SOURCES:**
Dimitrijevic, Bojan and Savic, Dragan, _German Panzers and Allied Armour in Yugoslavia in World War Two_ (Erlangen: Verlag Jochen Vollert – Tankograd Publishing, 2013).
Article by H.L. deZeng IV, on the website <http://www.axishistory.com>.
DGEG Archives/ W. Sawodny Collection. Author's archive.
Three photos of the narrow-gauge Croatian armoured wagon preserved in the Museum of the Revolution in Sarajevo, as seen in 2006.
_(Photos: Paul Malmassari Collection)_
. _Nezavisna Država Hrvatska_ or NDH (August 1941–May 1945).
. Thus we find several trains bearing the same number but serving under different commands, and the following designations, which are either the name of the station where the train was based, or the name of an animal: _Lisac_ (No 3), _Ris_ , _Gabela_ , _Lašva_ , _Neretva_ , _Travnik_ , _Vareš_ , _Vuk_ (No 2) and _Zenica_.
. It is possible that an attack on one of these trains is commemorated by the plaque beside the Sarajevo-Vareš road, since no report mentions the presence of a German armoured train during the period mentioned on the plaque.
## CROATIA
### CROATIAN WAR OF INDEPENDENCE (1991–1995)
On 25 June 1991, following several years of rising tensions between the constituent republics of Yugoslavia, Croatia declared its independence. In July, the Yugoslav Army, which by then was composed mainly of Serbs following desertions by the other nationalities, went into action to try to keep the country together. The civil war which broke out lasted until 12 November 1995.
### Croatian Armoured Trains
The young Croatian Republic put into service the following armoured trains, in chronological order: OV No 1 _Šišmiš_ ('Bat'); OV No 2 in Osijek; OV _Split I_ and an armoured trolley.
The first armoured train, _Šišmiš_ , was completed on 17 August 1991 and went into action in the Novska region, then in the Sisak-Sunja sector. To date no photos of it have come to light.
The second armoured train went into service on 30 September 1990 in the Osijek-Vrpolje zone. It was organised in four sections, two combat and two anti-aircraft, carrying a crew of some forty men. The anti-aircraft wagons were armed with triple 20mm PA 20/3 M55 mountings. The train was demobilised on 10 July 1992.
The third, _Split I_ , was built by the naval shipyard in Brodosplit and was shown to the authorities on 31 January 1992, but it was never called upon to go into action. It is now part of the collection of the Zagreb Railway Museum.
A view of the diesel locomotive of the Osijek armoured train, in a siding in 2013. The brick-red livery was the scheme carried during the war and not a subsequent repainting. Of note is the lower armoured skirt consisting of reinforced rubber sheets.
_(Photo: All Rights Reserved)_
Plans of the armoured locomotive.
_(Drawing: HŽ Museum, Zagreb)_
End view of 0ne of the armoured wagons of _Split 1_ , which is reminiscent of the wagons of the German BP 42 and 44. One must suppose that additional wagons were planned, since the train as it stands has no specific units to protect the ends.
_(Photo: All Rights Reserved)_
Left-hand side of diesel-electric locomotive HŽ 2062-045 seen from the rear.
_(Photo: HŽ Museum, Zagreb)_
The armoured locomotive viewed from the front right-hand side, showing the cab.
_(Photo: HŽ Museum, Zagreb)_
Close-up of the cab of the armoured locomotive.
_(Photo: HŽ Museum, Zagreb)_
The second armoured wagon of _Split I_ , armed with a 12.7mm machine gun. The armour protection is formed of two layers of armour plates, one of 6mm and the other of 8mm, with gravel ballast sandwiched between the two plates. The bogies are protected by 10mm plates. The wagons used as the base were 22.5-tonne Series G, one being 16.52m (54ft 0½in) long and the other 16.79m (55ft 1in).
_(Photo: HŽ Museum, Zagreb)_
The leading wagon of the _Krajina Express_ , with the Hellcat carried on the front platform.
_(Photo: Wide World Photos)_
A detailed close up showing the insignia of the _Krajina Ekspres_ : the four Cyrillic letters 'C' in the coat of arms of the Nemanjić dynasty stand for ' _Samo Sloga Srbina Spasava_ ' or 'Only Union Will Save the Serbs'.
_(Photo: Paul Malmassari Collection)_
### Armoured Train _Krajina Ekspres_ of the Serb Republic of Krajina (1 April 1991–August 1995)
The railway line linking Zagreb with the Dalmatian Coastline by way of Knin crossed Bosnian territory, passing through Bihać. The line's strategic importance led to the construction of an armoured train known as the _Krajina Ekspres_ ('Krajina Express'). Its name gave rise to a popular song, and even in late 1994, to widespread press coverage, somewhat surprising for a train which long ago dropped out of sight of the popular media
The train was built in Knin during the Summer of 1991 and was brought into service by the twenty men of the Railway Company of the 7th Motorised Brigade. From 27 November 1992, it was operated by the Railway Company of the 75th Motorised Brigade of the VII Corps (Dalmatia) of the SVK. In late 1994, it became Armoured Train No 7, reporting directly to VII Corps.
Initially it was made up of two wagons protected by sandbags, with 25mm armour plate added, propelled by diesel locomotive JZ 664-013. The first wagon carried a 20mm M38 cannon (ex-FlaK 38) and a 40mm Bofors M12. The second wagon carried two AT-3 rocket launchers and a second 40mm Bofors M12. In the Autumn of 1991 a third wagon was added, armed with a 20mm M55A4B1 triple mounting and a single 20mm M75 mounting. A 7.62mm Zastava M84 MG was mounted on each side. In early 1992 the 20mm cannon on the rear wagon was replaced by a 76.2mm ZiS-3 field gun, and two L-57-12 rocket launchers replaced the 40mm Bofors on the front wagon. In 1993 an American M-18 Hellcat Tank Destroyer from the stocks held by the JNA ( _Jugoslovenska Narodna Armija_ – the Yugoslav People's Army) replaced the 76.2mm ZiS-3, its turret-mounted 76mm having a much greater traverse. At the same time the original 25mm armour protection was reinforced with rubber sheets fixed at approximately 10mm from the plates, the space between being filled with ballast. Finally, a fourth wagon carrying two 120mm mortars was attached to the train. On the other hand, a project to build a wagon armed with an 88mm gun did not see the light of day. During the operations around Bihać, three safety pilot wagons were pushed ahead of the train.
In 1991 the train was employed near Gradačac, on the Knin-Drnis line, then at Lika. In 1992 it was in action near to Zemunik Airport at Zadar, at Maslenica and at Ravni Kotari where two crew members were killed. In early 1993, it operated notably at Škabrnja, where it was to be the delivery system for a wagon loaded with 3.5 tonnes of explosives and 5 tonnes of shrapnel, with the aim of blowing up an ammunition dump at Zadar: a landmine attached to one of the wagon buffers was meant to initiate the explosion of the load when the wagon was released to roll downhill from the village of Nadin towards its target. The train was in action near Bihać where it was hit by an anti-tank missile, and it was deployed on numerous occasions during the siege of the town up until December 1993.
Finally in 1995, the train was sent in the direction of Lika, but during Operation 'Oluja' (Tempest) which took place from 4 to 7 August, to avoid its being captured by the Croatian Army the crew sabotaged the train by running it off the rails into a ravine alongside the track, before they sought refuge in the _Republika Srpska_.
Two photos of below-average quality but nevertheless unique: this train was secretly photographed in 1992 near Benkovac. At the time not yet camouflaged, this is almost certainly the wagon armed with a 76.2mm field gun, added to the _Krajina Ekspres_ in early 1992.
_(Photos: Paul Malmassari Collection)_
The accommodation coach of the armoured train, with its name on it in Cyrillic letters, with the flag of the Serb Republic of Krajina in the centre (from top to bottom the colours are: red-blue-white).
_(Photo: Medija centar Odbrana)_
In this view looking back along the length of the train, the armoured wagons have not yet been fitted with the rubber panels which were to break up their silhouettes. Note the armour plates which protect all the lower parts of the locomotive apart from the bogies.
_(Photo: Medija centar Odbrana)_
Note the efficient construction of the train, which consisted of mounting precisely-measured armoured superstructures on standard bogie wagons.
_(Photo: Medija centar Odbrana)_
The badge of the _Krajina Ekspres_ , featuring, as would be expected, the arms of Serbia, the initials of the train, and the winged wheel, typical of the symbol used to represent armoured trains in many Eastern European countries.
_(Photo: Paul Malmassari Collection)_
A superb frontal view of locomotive No JŽ 664-013 of the _Krajina Ekspres_ (Type G-26C, of which fifty-eight units were delivered to Yugoslav Railways by the Diesel Division of General Motors of Canada Ltd in 1973). The camouflage paint has covered over the serial number of the locomotive and its civilian markings. The two plates behind the handrails provide partial protection to the crew when working on the machinery or when using the door on the left of the loco.
_(Photo: Medija centar Odbrana)_
The crew of the train celebrating Mass on 11 March 1994.
_(Photo: Paul Malmassari Collection)_
One of the train's 57mm rocket launcher pods photographed beneath its overturned wagon.
_(Photo: Paul Malmassari)_
The author standing inside one of the wagons of the _Krajina Ekspres_. The wagon platform was 2.51m (8ft 2¾in) wide.
_(Photo: Paul Malmassari)_
One of the wrecked wagons in the ravine. Some of the armour plates carry NVA ( _National Volksarmee_ = former East German Army) markings. The black shape on the left is one of the reinforced rubber sheets which covered the sides of the train, giving it a rounded profile.
_(Photo: Paul Malmassari)_
The curve where the crew of the _Krajina Ekspres_ derailed it into the ravine to avoid its being captured by the Croatian Army. The wreckage can be seen on the left-hand side of the embankment.
_(Photo: Paul Malmassari)_
**SOURCES:**
Radic, Alexandre, 'Historia – _Krajina Ekspres_ ', _Arsenal_ (Defence Ministry) No 14 (15 February 2008), pp 51–4 (in Serbian).
_National Railway Bulletin_ , Vol 60–1 (National Railway Historical Society, 1995).
Medija Centar Odbrana via Bojan Dimitrijevic.
Notes and photos by the author (March 1998)
Video: <https://youtu.be/qj6OSOAmYyM>
### ' _Domoljub 101_ ' Armoured Rail Trolley
Designed in a few hours by Mr Ivica Zigolić, one of the Directors of Rade Končar in Zagreb, and built in seven days, this armoured unit was based on a TMD 22-119 locotractor, normally used on private branch lines. The initial plan was to provide an armoured railcar capable of defending the factory grounds against snipers posted on the roofs of surrounding buildings during the opening weeks of the war. This plunging fire led to the adoption of armour protection which was inclined inwards at the base, compared to the classic layout where the armour is inclined inwards at the top.
' _Domoljub 101_ ' had a large armoured compartment capable of carrying fifteen men. It was driven from the original cab, reached by a door on the right-hand side, and has no provision for a rear-facing driving position. The locotractor, immediately requisitioned by the Defence Ministry, went to the front and was employed as far as Nova Gradiska, where the railway network had been seriously damaged. It was the very first armoured rail vehicle of the Homeland War.
**Technical Details:**
Length (over buffers): 8.1m (26ft 7in)
Armour: 10mm
Motor: Diesel TDM 22-119
Power: 148hp
Weight: 11 tonnes
Load capacity: 6 tonnes
Maximum speed: 60km/h (37mph)
A TMD 22-119 identical to the one used as the base for _Domoljub 101_.
_(Photo: Paul Malmassari)_
Three-quarters front view of _Domoljub 101_. The attached emblem was not used during its combat deployment, but a national flag was carried on a pole in the socket seen to the left of centre.
_(Photo: Paul Malmassari)_
Sketch plans drawn by the author from actual measurements taken by him.
_(Drawing: Paul Malmassari)_
Close-up of the buffers, almost completely covered by the armour. Also note the two stone catchers to clear the rails of minor obstacles, and the feed pipes of the sanding gear.
_(Photo: Paul Malmassari)_
Two views of the rear of the unit, with the personnel access door. The unusual disposition of the inclined armour can clearly be seen in these shots.
_(Photos: Paul Malmassari)_
The access door to the driving position. The central slot clearly has only a limited field of vision. This vehicle is preserved in the museum devoted to improvised armoured units of the Homeland War.
_(Photo: Paul Malmassari)_
Photocopy of the sketch drawn by Mr Ivica Zigolić which served as the basis for the construction by Konćar. Note that his original plan showed a locotractor with driving cab in the middle.
_(Document: Končar)_
The stark interior of the locotractor, showing the structure, the rudimentary benches and the firing loopholes closed by sliding shutters.
_(Photo: Paul Malmassari)_
**SOURCES**
Lajnert, Siniša, _Hrvatske Željeznice u Domovinskom Ratu_ (Zagreb: 2010).
The author's visit and discussion with Mr Ivica Zigolić, Director of the Končar factory, 1998.
. Official Croatian name: _Domovinski rat_ , the Homeland War.
. Slovenia declared itself independent on the same day but the fighting on its territory lasted only two months.
. In Croat: _oklopni vlak_ , or OV.
4. HŽ = _Hrvatske Zeleznice_ , Croatian Railways created in 1991 from parts of the ex-JŽ ( _Jugoslovenske Zeleznice_ ) network.
. _Republika Srpska Krajina_.
. Examples of press coverage are _Ouest-France_ edition of 19–20 November 1994, the _Washington Post_ of 26 November 1994, the _VSD_ of 3 August 1995 etc.
. _Cpпska Bojcka Kpajинe / Srpska Vojska Krajine (CBK/SVK)_ = Serbian Army of Krajina, formed on 19 March 1992.
. The author does not know the outcome of this operation.
. August 5th, the anniversary of the recapture of Knin, is now a national holiday in Croatia.
## CUBA
### SANTA CLARA 1958
During the Cuban Revolution (1956–9), the railways came under attack by the Castro revolutionaries, who aimed to cut the supply lines of the government troops. Accordingly, in 1958 the Ferrocarriles Occidentales Company built an armoured train. The attack on Santa Clara, defended by the 6th Regiment 'Leoncio Vidal', began on 20 December 1958, and on the 29th the armoured train, commanded by Colonel Florentino Rosell y Leyva was tasked with defending the north-eastern part of the town. Withdrawing in the face of an attack by Castro's forces, the train was derailed on a stretch where some 20m (65ft) of the rails had been torn up, and its crew were captured. Several armoured wagons from the train are among the main attractions in the Museum of the Revolution in Santa Clara.
The site of the derailment, at the level crossing on the Camajuani road. Centre left, behind the armoured wagon, is the rear end of the locomotive which is lying on its side.
_(Photo: Paul Malmassari Collection)_
The rear and underside of the armoured loco in the centre of the scene of devastation.
_(Photo: Paul Malmassari Collection)_
The nose of the overturned armoured loco seen behind the crossing barrier.
_(Photo: Paul Malmassari Collection)_
The armoured driving cab of the locomotive, a 1350hp GMC diesel.
_(Photo: Paul Malmassari Collection)_
**SOURCES:**
**Book:**
Batista y Zaldivar, Fulgencio, _Cuba Betrayed_ (New York: Vantage Press, 1962).
**Websites:**
Discussion of the armoured train battle, at: <http://trenblindado.com/Story.html>
Visit the Museum, at: <http://www.tripadvisor.fr/LocationPhotosg671534-d2718318-w2-Monumento_a_la_Toma_del_Tren_Blindado_Santa_Clara_Villa_Clara_Province_Cuba.html#63606290>
One of the armoured wagons from the train and below, the bulldozer said to be the one used to rip up the tracks and derail the train, on display at the 'Monumento a la Toma del Tren Blindado' at Santa Clara.
_(Photos: Cairns, 1997)_
## CZECHOSLOVAKIA
### ARMOURED TRAINS 1918–1950
Born from the geographical reordering of Europe at the end of the First World War, Czechoslovakia was formerly a part of the Austro-Hungarian Empire. The efforts to meet the national aspirations of the Czechs and Slovaks and to integrate them into the Allied camp had begun in 1916.
### The Birth of an Army and a Nation in Russia and France
The key to understanding how this army came into being, before the birth of its nation state, is the fact that the Czechs and the Slovaks had long been submerged in a multi-national empire, which paid scant attention to their individual aspirations, power being vested in the more populous constituent nations. Two famous individuals laboured to promote the interests of these two peoples: Thomàs G Masaryk, a philosophy professor, and Edouard Beneš, one of his pupils who himself became a philosophy professor. In the course of numerous negotiations, the Allies, who at that point included the Russian Empire, began to consider that the enmity the Czechs and Slovaks bore towards the Austrians could be turned to their advantage. As early as 18 October 1914, the Czechs and Slovaks in Russian prisoner-of-war camps began to be separated from other Austro-Hungarian prisoners. Then in February 1915, the 11th Austrian Regiment, composed of a majority of Slavs, refused to fight the Serbs, and the 36th Regiment mutinied against its officers.
The National Council of the Czech Peoples was created in Paris with the support of Aristide Briand. Also in Paris, the popular artist and illustrator Alphonse Mucha also laboured tirelessly to promote Czech nationhood. At the Front, the embryonic Czech Army, the _Česka Družina_ scored its first victories and took its first prisoners. In 1915, there were 4000 Czech prisoners of war in France, 50,000 in Russia and 10,000 in Italy. Their potential employment against the Austro-Hungarians would weigh heavily against the Central Powers. By 1916, there were 300,000 in Russia, and the decree recognising the existence of the Czech Army was signed. The Russian Revolution upset the existing situation, however, and an agreement between the Bolsheviks and the Czechs allowed for the latter to move to the Western Front. The Germans, however, stood in the way of this redeployment, and the Czechs began their long withdrawal to the East over the Trans-Siberian Railway, with the 1st Regiment acting as rearguard throughout.
### Czech Armoured Trains, 1918 to August 1920
Their route followed the railway, and their primary concern was the security of the rearguard, especially when the Reds began attacking them. To hold the critical junction at Bakhmach, Captain Cervinks, commanding the 6th Regiment, set in hand the construction of an armoured train in March 1918, comprising a steam engine, a van and three mineral wagons. Protection was provided by sandbags, and it was armed with machine guns and the crews' rifles. On 1 June the train gained a field gun in the chase position, greatly improving its firepower, and its patrol missions ensured the safe passage of the Czech troops. Thus the armoured trains were born out of the mission assigned to the Czechoslovaks by General Janin, head of the French Military Mission, which was to guard the railway lines. The territory they controlled extended for 10km (6¼ miles) on either side of the tracks, and by 1919 this so-called neutral band was the only territory not in the hands of the Reds. The protection of certain parts of the line was assured by the Polish Legion, which deployed three armoured trains.
Of the twelve regiments taking part in the withdrawal, it appears that only two, the 5th and 11th, did not possess armoured trains. Construction and entry into service of the armoured trains took place principally from May to September 1918, even though certain trains did not see the light of day until 1919, such as those of the 8th and 9th Regiments. Other trains were not incorporated into regiments, such as the anti-aircraft train built by Captain Kulikovski in late September 1918 at Chaytanka. The armoured train of the Attack Battalion was built between the 16 and 20 June 1918 at Kansk, and took part in the battles covering the retreat as far as Lake Baikal in July–August 1918.
The 1st Regiment possessed one train, built near Kinel in June 1918, armed with a 76.2mm Putilov gun in the leading wagon. Designated No 3, it was destroyed during the battle of Bouzoulouk on the 25th of the same month.
Of the four armoured trains of the 2nd Regiment, the two equipped and manned by the First Platoon were destroyed, one on the Volga on 23 October 1918, and the other on the River Ik. The train commanded by Lieutenant Netik had to its credit a Red armoured train knocked out on 26 June 1918.
The 3rd Regiment was the most prolific user of armoured trains, but the size and armament of each of its trains was relatively modest: in general one single wagon with a chase gun, and several bogie wagons protected by sleepers and sandbags. These trains were all built in June 1918, and instead of individual train names they were known by the name of their commander: Malek, Lt. Iijnsky, Lt. Sembatovic, Captain Nemcinov, Captain Urbanek (of which the command passed to Captain Troka on 6 July) and Nepras.
The 4th Regiment possessed the most famous armoured train of the Civil War period, _Orlik_ (see also the chapters on Russia and China). Bearing the name _Lenin_ , it was captured intact from the Reds at Simbirsk on 22 July 1918 and was renamed _Orlik_ two days later. It immediately went into action on the Simbirsk-Tchita line. In October 1918 it was split into _Orlik I_ and _Orlik II_ , which operated from Priytovo and Abdulino respectively. Once more combined into one train, it assured the security of the Trans-Siberian during the Summer of 1919, at a time when the line was suffering continual sabotage. When the train was based at Irkoutsk Station, General Janin noted that the area was calm and that 'Armoured Train _Orlik_... guaranteed order'. At Tchita on 8 April 1920, it was involved in an incident when the Japanese forced the crew of four officers and 100 men to hand over the train to them. Following diplomatic exchanges, the train was handed back to its crew on the 13th. After the last Czech troops departed on 20 May 1920, the train once more came into the possession of the Japanese, who were occupying the region, but the Americans insisted it be handed to the White Russians. The latter used it up until Autumn 1922, but when Vladivostok fell to the Reds, _Orlik_ joined the army of Zhang Zongchang in China.
The name of this train was popular with the Czechs, as the 4th Regiment possessed another _Orlik_ , built at Penza in May 1918. Commanded by Captain Sramek, it had a crew of sixty men, and carried an armament of nine machine guns and two armoured cars. In late May a flat wagon carrying an artillery piece was added, but the train was seriously damaged the very same day. In a single night, it was rebuilt using new wagons. Its crew was reinforced, to a total of six officers and 200 men. It took part in the battles of Abdulino and Tchichma on 3 July. On that date it assumed the name of _Orlik I_ to avoid confusion with the ex- _Lenin_ of the same name, and was in action continuously up until the battle of Simbirsk on 8th and 9th September, where its leading wagon was destroyed and its gunners killed or wounded, along with the train commander. Shortly after withdrawing to Kindiakovka it was taken out of service.
The 4th Regiment built an _Orlik II_ which was in action from July to November 1918. After the fighting before Bougoulma in early August, it was hit by fire from a Red train and was forced to retreat. It then covered the retreat from Bougoulma to Zlatoust, where its combat damage was repaired, then on 20 November it was decommissioned.
Armoured Train _Grozny_ , built at Penza in May 1918 and armed with an artillery piece and three machine guns, had a crew of 107 men. It was given the unenviable role of covering the rearguard of the 4th Regiment during the retreat, this regiment being now the rearguard of the entire Czech Legion. The most powerful part of its armament was the rear flat wagon, on which was mounted a Putilov-Garford armoured truck. It was reorganised twice: on the first occasion its crew was increased to 160 men and its armament to two guns and ten machine guns. Two armoured bogie wagons were added on 24 June. In August 1918 it was again transformed, being split into two: the part retaining the name _Grozny_ kept the armoured truck. Its crew were forced to sabotage it on 23 October 1918. The other part kept the second gun and the ten machine guns, under the designation 'Armoured Train No 29'. It too had to be sabotaged in September.
Little is known about Armoured Train _Sirotek_ , but a last train operated by the 4th Regiment was improvised by Captain Snajor to replace _Grozny_ and continue its mission of supporting the rearguard.
The 6th Regiment, in addition to its first train built in March 1918, equipped three armoured trains (two in early June and the third in August). One 'Train of the 6th Regiment' counted among its battle honours the destruction of a Red armoured train on 27 June.
The sole train operated by the 7th Regiment was built on 25 May at Mariinsk. During its first action it comprised just one bogie wagon armed with two machine guns. Its armament was then increased by the addition of an artillery piece. On 26 June, it was hit by fire from a Red train but was able to retreat to Lake Baikal, where it took part in the fighting at Koultouk on 18 July, before continuing to cover the withdrawal.
The 8th Regiment operated Armoured Trains _Mariinsk_ and _Těšín_ , and also a train formed on 1 July 1918 at Ougolnaya in Manchuria, at first armed just with machine guns, but later naval guns were added. Towards the end of the fighting, it operated in the Oussouri sector between Vladivostok and Khabarovsk.
Armoured Train _Údernik_ of the 9th Regiment saw service in May–June 1919.
The 10th Regiment lost its only armoured train, built at Nijne-Oudinsk in June 1918, when it was captured by the Reds on the 22nd of that month.
The 12th Regiment employed an armoured train about which little is known, apart from it taking part in the battle of the Ekaterinenbourg junction in October 1918.
Six trains were deployed in May–June 1919 to secure the central line of the Trans-Siberian to the west of Ienissei and assure the freedom of movement so vital to the Czechs. They were: the train of the Light Battery (not attached to a regiment), Armoured Train _Údernik_ of the 9th Regiment, and Armoured Trains _Těšín_ and _Mariinski_ of the 8th Regiment; the zone to be patrolled extended from Taiga/Tomsk to Atchinsk, a distance of some 300km (190 miles), and in the Summer of 1919 this became the responsibility of Armoured Trains _Tajšet_ and _Spasitel_ of the 1st Regiment.
In conclusion, during their withdrawal to Vladivostok via the Trans-Siberian Railway, which was their only chance of returning to Western Europe, the Czech Legion used thirty-two armoured trains, three of which were captured from the Reds. In all, in the course of the campaign, they captured twenty-five Bolshevik armoured trains, and destroyed two more.
Despite the apparent sense of security in the open countryside, the trains, armoured or otherwise, used by the Czech Legion in its long journey towards Vladivostok suffered continual attacks.
_(Photo: Paul Malmassari Collection)_
A well-known photograph taken at Oufa. It is interesting as it shows the considerable firepower provided by at least six machine guns mounted on each side of the wagon. On the left are 7.62mm Maxim Model 1905/1910s, and on the right the first machine gun is a Colt-Browning M1895 'Potato Digger', of which several thousand were ordered by Russia in 1914 in 7.62mm calibre.
_(Photo: Vojenský Ústřední Archív, Vojenský historický archiv – VÚA-VHA)_
One of the first improvised armoured trains, probably No 6, seen here at Tcheliabinsk in 1918. Note the limited protection, even on the engine which has only the cab protected, but sufficient at the start of the conflict to cut a path through the bands of marauding Bolsheviks.
_(Photo: Paul Malmassari Collection)_
Seen from this angle, the train appears unarmoured, but over and above those trains formally designated as 'armoured', all the Czech trains were fitted with a certain minimum level of protection.
_(Photo: Paul Malmassari Collection)_
A typical shot of one end of an armoured bogie wagon armed with a Russian 76.2mm gun. Note that only a small amount of training is possible. Obviously, the work to fit the internal armour has not yet been completed.
_(Photo: VÚA-VHA)_
Perhaps another shot of the same wagon. The 76.2mm Putilov Model 1902 gun, with a range of more than 8000m (5 miles), was the standard armament of the Czech trains.
_(Photo: VÚA-VHA)_
One of the various types of armour protection on the bogie wagons used by the Czech Legion. The sides have been raised, and the V-shaped armour prevents projectiles from remaining on the roof before exploding. In addition, loopholes have been pierced in the wagon sides. Unusually, the armament appears to be a German 7.58cm Minenwerfer (trench mortar) neuer Art.
_(Photo: VÚA-VHA)_
This wagon coupled behind the engine shows the typical features of the first armoured trains: increasing the height and roofing over of the sides, particularly to protect the crewmen against the extreme cold (note the stove chimney). Clearly visible are the diamond bogies which were particularly adapted to the often-irregular track found on the Trans-Siberian.
_(Photo: ECPA-D)_
A wagon from Armoured Train _Praha_ , proudly displaying the national flag. The armour is well-designed, again fitted on a standard Russian Railways wagon.
_(Photo: ECPA-D)_
A well-known postcard of the period showing a Czech armoured train assembled from Russian rolling stock. The protection on the engine, seen here from the front right, is relatively simple, and the armoured wagons have all been built on the base of standard high-sided bogie wagons. As time passed, the design of the armour protection would evolve significantly.
_(Photo: Paul Malmassari Collection)_
Another example of an armoured bogie wagon on the Trans-Siberian. This one is perhaps a captured Bolshevik wagon, with its 76.2mm gun in the chase position.
_(Photo: Paul Malmassari Collection)_
On the other hand, this wagon is instead devoted to close-in protection of the train, with loopholes for small arms, and perhaps also a machine gun, as suggested by the larger central embrasure.
_(Photo: Paul Malmassari Collection)_
This interesting view allows us to clearly see the roof protection provided by lengths of rail, and through the rear opening more rails arranged to form an internal partition, separated from the sides of the wagon by a layer of wood.
_(Photo: Paul Malmassari Collection)_
Seen in 1918, one of the revolving casemates of the armoured train of the Second Battery of the 1st Artillery Regiment. The van to the right bears the usual 'X' marking denoting explosives.
_(Photo: VÚA-VHA)_
It is difficult to tell whether this train is Czech or White Russian. Nonetheless, the revolving casemate is rudimentary but interesting. Note the the cowcatcher, and also that the van next in line has an upper firing position and an observation cupola.
_(Photo: Paul Malmassari Collection)_
The other casemate of this battery shows the construction technique used, with plates fastened over an internal framework.
_(Photo: Paul Malmassari Collection)_
This photo of the leading wagon of the same train, probably taken later in the campaign, show how it has evolved, notably in the profile of the casemate. Cowcatchers have by now become standard, and also double as snowploughs.
_(Photo: Paul Malmassari Collection)_
An interesting shot showing the final version of _Orlik_ , on 2 June 1918. The Austin armoured car was used as a machine-gun wagon. Note the open door of the van in which a field gun is installed.
_(Photo: VÚA-VHA)_
_Orlik_ as a complete train, with the railcar _Zaamurietz_ coupled immediately behind the engine. Note the Czech flag.
_(Photo: VÚA-VHA)_
One of several views of the self-propelled element which made up _Orlik I_ when operating independently of the rest of the train.
_(Photo: VÚA-VHA)_
Designed in 1915, later changes involving principally its armament, this railcar had a modern configuration, much more advanced than most later designs.
_(Photo: Paul Malmassari Collection)_
A shot showing the interior of an end compartment on _Orlik_ , with the two corner machine guns and the access hatch open.
_(Photo: VÚA-VHA)_
As the inscription in Czech confirms, this wagon belongs to the part of the train made up of the wagons and the engine (Vuz cis. 2 = Part No 2, Part No 1 comprising the railcar operating independently). The turret is armed with a Russian 76.2mm Model 02, which can train through approximately 270 degrees.
_(Photo: Paul Malmassari Collection)_
The machine-gun positions in the central section of the railcar. Note the essential element present in all the armoured trains and even the wagons on the Trans-Siberian, the stove.
_(Photo: VÚA-VHA)_
A view of the other end of the artillery wagon, here coupled to the railcar.
_(Photo: Paul Malmassari Collection)_
The other artillery wagon of _Orlik_. Despite the fact that the two wagons were built on the same base vehicle, the turret with all-round traverse installed in place of the original chase gun has a different armament, a 76.2mm Model 1904 mountain gun.
_(Photo: Paul Malmassari Collection)_
A fact never previously published: Armoured Train _Orlik_ received the French Croix de Guerre (top left of the pennant) from General Janin on 24th March 1920, for its service during the entire Trans-Siberian conflict. This pennant bearing _Orlik_ 's insignia no longer exists.
_(Photo: VÚA-VHA)_
Interestingly, a postal service was set up to convey the correspondence of the Czech Legion, but also that of the local Russians, whose postal service had collapsed because of the Revolution. It began to operate on 18 September 1918, over an initial distance of 4000km (2500 miles), and was then extended to 7000km (4375 miles), taking two weeks to travel the length of the line to Vladivostok. Among several different images used on the stamps was one featuring Armoured Train _Orlik_ , on a stamp of the second issue which appeared in 1919.
The yellow-gren 50-kopeck issue.
_(Stamp: Paul Malmassari Collection)_
A series of three stamps, printed in red, bistre and green, was also issued to commemorate the Czech soldiers who made the epic crossing of Siberia to build their nation, here featuring the bi-colour flag of the period flying from the armoured wagon at the head of the troop train.
_(Stamp: Paul Malmassari Collection)_
### The Czechoslovak Army during the Inter-War Period
While the _Družina_ was forging the national spirit of Czechoslovakia by fighting its way across Siberia, the new army was also being created in the homeland. Called to fight on the new national borders, it used armoured trains firstly of foreign origin then those produced at home. The Czech Army subsequently maintained a force of six standardised armoured trains up until 1938.
With the defeat of the Central Powers in 1918, PZ II (MÁV engine 377.116, wagons Nos 140.914 and S150.003) and several wagons and a steam engine from Austro-Hungarian PZ I and IV were captured in Prague. On 18 November 1918 the first Czech armoured train, numbered II, left for the Slovak Front and added a new infantry wagon (S150.271) from the ex-Austro-Hungarian PZ VII. It was then divided into two, one part forming the principal armoured train proper (PV II-a) and the other the support train (PV II-b). The first part remained in Slovakia from December 1917 to the following Spring, to secure the new borders. It next fought the Hungarians, and on 12 June in particular, it employed a technique unique to armoured trains, sending a safety wagon loaded with ballast to crash into a Hungarian armoured train parked in Hronská Breznice Station. The Hungarian train was certainly damaged, but having expended its safety wagon, the Czech train set off a mine the following day. Renumbered as No 1 on 21 July, it defended the border between Luèenec and Filakovo up until March 1920.
A composite of two ex-Austro-Hungarian armoured trains, as confirmed by the presence of a wagon on the left from a Type B (see the chapter on Austria-Hungary) and from a Type A on the right.
_(Photo: Paul Malmassari Collection)_
Armoured engine 310.440 (ex-MÁV 377.362). The name ' _Libuše'_ refers to a legendary prophetess, granddaughter of Cech, the mythical founder of the Czech people, who chose a husband to favour the national interest over her personal feelings. Note the observation cupola above the cab, as well as the pipe enabling the transfer of water between the engine and the wagons.
_(Photo: VÚA-VHA)_
PV II-b went into service on 15 December 1918 and left Prague for the Sudetenland border. In the region of Kosice, it was integrated into the 6th Division of the Italian Legion until May 1919. On 1 May it attacked the Hungarian station of Miœkolec and enabled the Czechs to recover engines and wagons captured by the Hungarians in the Slovak zone. It was renumbered as No 2 on 21 June 1919.
Engine 179.01 of Armoured Train _General Štefányk_ seen here in 1919.
_(Photo: All Rights Reserved)_
Armoured Train _Bratislava_ at Slovensky Meder Station.
_(Photo: VÚA-VHA)_
An unidentified armoured train, dating from the period when the Czechs were forced to intervene militarily against their new neighbours. Its construction is interesting: the body has symmetrical openings at both ends, probably mounting two 76.2mm Putilov guns, and two-thickness wooden protection visible. Either the van at the rear is badly overloaded at one end, or the springs at that end have seen better days.
_(Photo: All Rights Reserved)_
On the left, wagon Kn 141.172, on the right wagon 149.902, and in between engine 377.455 of PV No 3. Note that this postcard features the tricolour Czechoslovak flag and not the bicoloured (red and white) original version, which dates this photo to later than 30 March 1920.
_(Postcard: Paul Malmassari Collection)_
In late 1918 Armoured Train _Brno_ was built in three weeks in the state armament factory in the Moravian capital. It comprised an armoured engine and two wagons. The leading wagon was armed with two Maxim machine guns in the chase position, and a 75mm M15 Škoda mountain gun in a turret; the other wagon was armed with two Schwarzlose machine guns. After having seen action against the Poles, it remained in service up until December 1920 when it was demobilised and put in reserve. Profiting from the experience gained, it was decided to build two similar trains, No 3 _Bratislava_ and No 4 _General Štefányk_. Each train included a safety wagon, an artillery wagon and two infantry wagons.
_Bratislava_ went into action in Slovakia in July 1919 against the Hungarians. Seriously damaged at Nové Zámky, it was dismantled at the Škoda factory in August and its number transferred to the Hungarian train being repaired in the same workshops. _General Štefányk_ was completed too late to take part in the fighting against the Hungarians, but remained in service until 1925, with PV 1 first at Lučenec then at Milovicer.
In 1919, the railway workshops at Vrútky built a fourth armoured train following the pattern of the Austro-Hungarian trains (engine No 377.83, but flat wagons protected with concrete slabs), carrying the No 7. Then in January 1920 PV 3 went into service, being the units of the Hungarian train captured at Seèovce which had been repaired by Škoda.
Škoda built two complete armoured trains in 1919, _Pilzen_ (No 5) and _Praha_ (No 6), each one having two Class 99 armoured engines with protection 6mm thick, two safety wagons, two artillery wagons, two infantry wagons and an ammunition wagon, all the wagons being protected by 8mm of armour. Each train could also be divided up into two smaller units. Their crews numbered three officers and eighty-eight men.
The period 1919 to 1938 also saw the introduction of the Tatra-Škoda armoured trolley. During the 1920s the firm of Koprivnice built a reconnaissance trolley, which also interested the Poles, who purchased some twenty examples in 1926. It could be used coupled to a train (with the driving axle disconnected) or as an independent vehicle. The Armoured Trains Company received the only example purchased by the Czechoslovak Army in 1927.
**Tatra-Škoda Czech Armoured Trolley**
**Technical** specifications:
Overall length: | 3.68m (12ft 03/4in)
---|---
Width: | 1.75m (5ft 9in)
Overall height: | 2.14m (7ft 01/4in)
Ground clearance: | 0.14m (51/2in)
Armour thickness: | 6mm to 10mm
Weight empty: | 2.5 tonnes
Crew: | 3 to 5 men
Armament: | 2 x 7.92mm Hotchkiss machine guns
Motor: | 2-cylinder 4-stroke water cooled
Cylinder capacity: | 1.1 litre
Fuel capacity: | 80 litres (21 Imperial gallons)
Maximum speed: | 45km/h (28mph)
Range: | 700km (435 miles)
Opinions differ as to the existence of a reconnaissance road-rail vehicle. According to Major Heigl, Tatra was to have designed a 6x6 armoured vehicle of this type, with the following specifications, armament: two machine guns in diagonally-offset turrets; length: 7.6m (24ft 91/4in); width: 1.86m (6ft 11/4in); height: 3.1m (10ft 2in); speed: 60km/h (37mph) on roads, 80km/h (50mph) on rails. According to M. Caiti, this vehicle could have been created from the conversion of all the PA 1 and PA 5 armoured cars. To date we have found no evidence as to the existence of such a road/rail vehicle.
The Czech model Tatra, here armed with two Schwarzlose vz.7/24 machine guns.
_(Photo: VÚA-VHA)_
Armoured Train No 3 in Slovakia.
_(Photo: All Rights Reserved)_
A rare photo showing the Czech Tatra armoured trolley with a modified turret, mounted on a special flat wagon which perhaps could allow it to dismount without external support. Note that when it is so mounted, its armour descends to the level of the flat car (it is also possible that the hull has been mounted without its wheels). Of interest is the complex camouflage scheme carried by Czechoslovak armoured trains, which remained unchanged when they were taken over and reused by the Wehrmacht.
_(Photo: Paul Malmassari Collection)_
The artillery wagon of Armoured Train No 4, seen from the safety flat wagon. It possessed a powerful armament capable of end-on fire, comprising a 75mm gun and two machine guns.
_(Photo: Paul Malmassari Collection)_
The six armoured trains remained in southern Slovakia between 1919 and 1923. On 7 July 1922 they were formed into an armoured battallion based at Milovice. In order to reduce the cost of hiring rolling stock, the railway company reclaimed the unarmoured wagons in 1925, leaving just the armoured engines and wagons. Then the armour plating was dismounted from the Class 99 engines and put into store, on condition that it would be refitted on the engines after giving two days' notice to the railway authorities. Finally, in 1933 the unit became a regiment.
By 1934, the existing armoured trains were wearing out, and plans were made to build new units. The first option was the construction of armoured railcars weighing between 54 and 70 tonnes, with 32mm of armour and armed with 66mm and 80mm guns in turrets. ČKD and Škoda proposed designs, that of the latter firm was chosen, and and a model was built. The German occupation put a stop to these plans. The second option considered was to put improvised armoured trains into service to defend the frontiers, with rapidly-added protection, to be manned by reservists. Their armament was to be the classic 8cm vz.5/8 in the chase position plus several machine guns. A total of twelve such trains was envisaged.
This type of wagon was designed and built by Škoda. Here is PV No 4. The machine-gun armament initially came from four different countries, standardised on 7.92mm German Maxim Model 08s, replaced in 1925 by 8mm Hotchkiss, and ending in 1929 with Schwarzlose vz.7/24 models.
_(Photo: Paul Malmassari Collection)_
### The Munich Crisis of 1938
Long before the negotiations leading up to the Munich agreement, separatist agitation broke out in Slovakia and Ruthenia. But on 30 September, the day before the agreement was signed, Czechoslovakia mobilised and put on alert the twelve improvised armoured trains to contain the _Freikorps_ insurgents in the Sudetenland.
Overall view of a train with the second infantry wagon (also designated a machine-gun wagon) coupled at the rear, followed by a Class 377 engine, then the first infantry wagon and finally the artillery wagon. A safety wagon is only coupled at the front end of the train.
_(Photo: Paul Malmassari Collection)_
In this rare photo of an improvised armoured train at the time of mobilisation in 1938, note the hastily-applied camouflage on the wagon, and the ill-fitted armour plates on the engine. The gun is an 8cm Feldkanone M.5. The large number of crew members probably comprise the personnel of both the armoured train and the (unarmoured) support train. On the right in the front row is a railway employee of the CSD. In the centre of the front row is the train commander with the rank of captain (five-pointed star) and his sub-lieutenant assistant (three-pointed star). Finally, it appears that these reservists, assembled for the occasion, are wearing new uniforms.
_(Photo: Paul Malmassari Collection)_
Each train had a crew of two officers, one NCO and between eighty and ninety-one men (apart from Train No 3 which had only seventy-four men).
The Munich agreement did not put a stop to Hitler's ambitions, and his annexation of Bohemia and Moravia led to the collapse of Czechoslovakia on 15 March 1939. This led to the incorporation of the Czechoslovak trains in the list of German armoured trains, and at that period these units comprised the most modern elements of it. Their component wagons would continue to be divided up and regrouped until the end of the Second World War. The German trains composed of Czechoslovak elements would be PZ 23, PZ 24 and PZ 25. On the other hand, one of the improvised armoured trains of 1938, No 40, stationed at Zvolen, would join the newly-formed Slovak Army on 14 March 1939.
In March 1939, German soldiers photographed the depot at Milovice where all the armoured trains were gathered together (on the right, an artillery wagon of Train No 4, and on the left, the sole Tatra trolley mounted on its flat wagon).
_(Photo: Paul Malmassari Collection)_
Inside the depot, the artillery wagon (photo above) and the trolley (next photo) have aroused a great deal of interest. Several months later these units, still wearing their distinctive camouflage, would form new German armoured trains.
_(Photo: Paul Malmassari Collection)_
Note the device for moving from one track to the other, mounted on the bonnet of the trolley.
_(Photo: Paul Malmassari Collection)_
### The Slovak National Uprising, 29 August – 28 October 1944
This uprising which started in Slovakia had as its aim the restoration of the former Czechoslovakia created in 1918, as proved by the names given to the three armoured trains taking part.
In Slovakia, resistance to the pro-German puppet government had begun during the invasion of the Soviet Union, when Slovak tank commanders and maintenance units deliberately returned broken-down tanks to Slovakia for possible future use against the regime. The initial 'anti-fascist' units were formed in late 1943, in the mountain regions. Their development was accelerated under the impetus given by the approach of the Red Army, by way of Poland towards north-east Slovakia. Two divisions of the Slovak Army officially tasked with supporting the Wehrmacht in reality were part of the plans for the Uprising, and were to make contact with the advancing Russians. The centre of gravity of the whole operation was the Banská Bystricka–Brezno–Zvolen triangle. The uprising began on 27 August, the towns were seized, and railway traffic was halted. In addition to equipment recovered from the Slovak Army, three armoured trains were built to compensate for the lack of armoured vehicles, since the majority of the Slovak tanks belonged to the two divisions in the East, which were immediately disarmed by the Germans. On 1 October, the insurgents deemed themselves to be the First Czechoslovak Army in Slovakia, in order to mark their return to their former country. On 18 October, the Germans counter-attacked from Hungary, and Banská Bystricka, the epicentre of the uprising, had to be evacuated on the 27th. The end of the uprising was notified to the government-in-exile in London the following day. The conflict then devolved into a guerrilla campaign which ended on 3 November.
PZ 23 formed from ex-Czechoslovak units. The flat wagon which carried the Tatra trolley seen earlier is on the right of the photo, now used as the safety wagon.
_(Photo: Paul Malmassari Collection)_
The three improvised armoured trains (IPV = _Improvizovaný pancierový vlak_ ) bearing the names of famous national personalities, _Štefánik_ , _Hurban_ and _Mazaryk_ , were built in that order, in record time (five weeks in total) in the Zvolen workshops, under the direction of Colonel Štefan Čáni, with the technical assistance of Engineer Lieutenant Hugo Weinberger. Lacking recent experience, the technicians and workers turned to an old regulation laying down rules for the construction of improvised armoured trains. The faults shown up in the first train, in particular the insufficient armour protection, were corrected in _Hurban_ and _Masaryk_ , which were of superior construction. It is our opinion that the description of these trains as 'improvised' should by no means be considered pejorative, as they demonstrated practices found on contemporary production armoured trains.
Each armoured train was accompanied by a support train, with sleeping accommodation, sickbay, kitchen etc. The makeup of each train differed, but all were powered by a Class 320.2 steam engine, and included a leading gun wagon plus several artillery wagons mounting turrets from Czech LT-35 tanks.
Armoured Train _Štefánik_ was built between 4 and 18 September. Commanded first by Lieutenant Anton Tököly then Captain František Adam, its crew numbered seventy men. On 27 September it went into action on the line from Hronskà to Kremina, and on 4 October supported a counter-attack from Stará Kremnička. Its engine was hit, but following repairs it operated on the line from Zvolen to Kriváň up until the end of October. On the 25th, it left Zvolen in order to reach Ulmanka, where it found itself trapped. The crew destroyed the train's armament and joined the partisans.
Armoured Train _Hurban_ was begun on 25 September and completed in just eleven days. Under the command of Captain Martin Ďuriš Rubansky, it went into action on line from Hronská Dúbrava to Žiar nad Hronom up until 4 October, when it moved to the line from Banska Bystricá to Diviaky. On the same day, it fought German forces near Čremošné, where it suffered several casualties. At the end of October it had to be abandoned in Horný Harmanec Station.
Armoured Train _Masaryk_ was completed on 14 October. It was the most sophisticated of the three units, and its engine had complete armour protection. The high-quality armour plates came from the Podbrezová steelworks. Under its commander Captain Jan Kukliš it operated on the line from Brezna to Červená Skala where it was damaged on 21 October. On the 24th, the engine was destroyed by a direct hit, and the commander, driver and fireman were killed. Beyond repair, it was towed to the tunnel at Horný Harmanec Station, where its crew destroyed its armament and joined the crew of _Hurban_. Captured when that town fell, both trains were sent to Milowitz for repairs before being shared out between SSZ _Max_ and _Moritz_.
To celebrate the 300th anniversary of the Treaty of Utrecht (1713), Utrecht Museum organised an exhibition on trains in warfare. For the occasion, _Štefánik_ was restored and partly reconstructed. After having been one of the major attractions at the exhibition, it returned to Zvolen in September 2013.
One of the three armoured trains at the Zvolen workshops. The artillery wagons were built using as a base Type U coal wagons. The protection was formed from two sheets of wood each 5cm thick separated by 15cm of gravel ballast.
_(Múzeum Slovenského nároného povstania, SNP)_
The handing-over ceremony of _Štefánik_ at the Zvolen workshops on 18 September 1944. Engineer Lieutenant Hugo Weinberger (codename 'Velan') is second from the right. The civilian in the centre is Engineer Ivan Víest, Director of the Railways of Slovakia, with Colonel Štefan Čáni immediately to his left.
_(Photo: Múzeum SNP)_
At the head of IPV I _Štefánik_ is the 80mm vz 5/8 gun, seen during a halt at Viglas. The safety platform wagon is not coupled directly to the train, but is propelled by a timber beam.
_(Photo: Múzeum SNP)_
An overall view of IPV I _Štefánik_ seen from in front, with its safety platform wagon, the leading cannon wagon, the two turret wagons armed with 37mm guns and the tail wagon.
_(Photo: Múzeum SNP)_
_Štefánik_ seen from the rear.
_(Photo: Múzeum SNP)_
This shot of _Štefánik_ and the photo on the right clearly show the difference between the tail wagon (with an embrasure for a 37mm gun) and the leading wagon with its large opening for the 8cm FK.
_(Photo: Múzeum SNP)_
The Class 320.2 steam engine of _Štefánik_. The initial camouflage tones were white, green and red-brown. Subsequently, all the trains would be repainted an overall green shade.
_(Photo: Múzeum SNP)_
Interior view of the infantry wagon of IPV I _Štefánik_ , with one of the lateral 7/24 Schwarzlose machine guns.
_(Photo: Múzeum SNP)_
_Štefánik_ in its overall green paint scheme under foliage camouflage, far more discrete than the original three-colour scheme.
_(Photo: Múzeum SNP)_
The chase gun mounted on all three trains (here we see IPV II _Hurban_ ) was an ex-Austro-Hungarian 8cm FK M 05 or 05/08, also used by the Wehrmacht during the Second World War. Thanks probably to the successive improvements included in each of the trains, the embrasure of _Hurban_ is virtually closed by an armour plate which was not present on _Štefánik_.
_(Photo: Múzeum SNP)_
A fine view of the tail wagon of _Hurban_. The cupola does not appear to have observation slits, but it has a frame to mount a machine gun for close-in or anti-aircraft protection.
_(Photo: Múzeum SNP)_
An impressive view of _Hurban_ wearing camouflage, with its crew disembarked. After the uprising was crushed, they would be forced to join the partisans in the mountains.
_(Photo: Múzeum SNP)_
Leading safety wagon of IPV III _Masaryk_ in camouflage, which however fails to disguise the fact that the wagon sides are vertical.
_(Photo: Múzeum SNP)_
The main armament of the trains – seen here on _Hurban_ – was an LT-35 tank turret armed with a 37mm gun and a co-axial 7.92mm machine gun. In Wehrmacht service, this tank was designated the PzKpfw 35 (t). Note in this photo the roof of the hull of the tank, enveloped in the armour protection which leaves only the hatches visible.
_(Photo: Múzeum SNP)_
The armoured steam engine of _Masaryk_ seen in 1946, in one of the depots where all the equipment retrieved from the various wartime fronts was collected.
_(Photo: All Rights Reserved)_
_Hurban_ restored during the post-war period. Note the cupola of the infantry wagon to the right.
_(Photo: Múzeum SNP)_
A monument to the Slovak National Uprising, in the form of a reconstruction of IPV I _Štefánik_ at Zvolen with T-34/85 turrets altered to resemble those of PzKpfw 35(t)s.
_(Photo: Fréderic Guelton)_
In 1974 this medal was struck to commemorate the thirtieth anniversary of the uprising.
_(Private Collection)_
### The Czech Uprising (1945)
On 6 April 1945, the day after the liberation of Bratislava in Slovakia, a coalition government was established in Košice, and on 5 May Prague rose up and the Wehrmacht was driven out in the course of fighting which lasted until 11 May. A large quantity of German rolling stock was captured, including PZ 27, PZ 80 and PZ 81, the PZ (s.Sp trolleys) 205 and 206, including several heavy railcars, security train _Moritz_ , PT 36 ( _Littorina_ ) and several anti-aircraft trains. The latter units were put back into service and formed twelve improvised armoured trains. Two other armoured trains (ex-German vehicles) were activated in Prague and Milovice (Milowitz, the former Czechoslovak armoured train base). Lastly, Type BP 44 wagons were discovered at Česká Lipa during the reconquest of the Sudetenland at the end of the month. One complete ex-German armoured train, less certain elements, was put back into service and used up until 1948.
Armoured Train _Praha_ ('Prague') made up from assorted wagons, including this hull of a Panzerjäger IV placed on a four-wheel mineral wagon.
_(Photo: Tomáš Jakl Collection)_
A fine view of the 20mm Flugabwehr-MG 151/20 (Drilling) mounted on the anti-aircraft trains in concrete tubs.
_(Photo: Tomáš Jakl Collection)_
Complete view of an anti-aircraft wagon.
_(Photo: Tomáš Jakl Collection)_
Type 1 FlaK wagon, with the armour strengthened by the addition of a layer of wood.
_(Photo: Tomáš Jakl Collection)_
A completely improvised low-sided wagon, with earth piled up between a central compartment and the side planking. Notwithstanding, earth would be quite effective in stopping small-arms projectiles. Note the German helmets worn by the crew.
_(Photo: Tomáš Jakl Collection)_
Armoured Train _Uhřiněves_ composed of various flak wagons grouped together in 1945. The engine is unarmoured.
_(Photo: VÚA-VHA)_
### The Armoured Trains of the Second Czechoslovak Republic
The new Czechoslovak Army included an Armoured Train Company in its establishment, created on 1 October 1945, based at Nymburg (modern Nymburk), and placed under the command of the 11th Tank Brigade. This company had two platoons. One platoon was comprised of armoured trains, with each unit organised as follows: one artillery wagon, two infantry wagons, two tank transporter wagons, command wagon, engine and a trolley. The other platoon was composed of reconnaissance trolleys, made up into rakes comprising a command wagon, PT 36, two artillery wagons, and three infantry wagons. In addition, an armoured train and a trolley intended for training were activated. With the addition of new armoured rolling stock, the Company became a Battalion in September 1946, with a separate command structure, support units and three companies:
– 1st Company (steam engines): Armoured Trains _Benes_ , _Masaryk_ , _Štefánik_ and _Svoboda_.
– 2nd Company (petrol locotractors): Armoured Trains _Pavlik_ , _Stalin_ , _Hurban_ and one armoured trolley.
– Reserve and Training Company: Armoured Train _Orlik_.
These trains included five artillery wagons with a 2cm Flakvierling but with different main turrets: one with a 10.5cm le.Fh 18, two PzKpfw IIs and two PzKpfw IVs. The tank transporter wagons carried LT vz.38 tanks (ex-PzKpfw 38 (t)). The remaining units were infantry, mortar and command wagons.
The Battalion was reorganised in Autumn 1949: the 2nd Company was based at Sopot (100km/ 63 miles to the south-east of Prague) while the 1st remained in Nymburg, these two centres bringing together all the armoured trains, which on this occasion lost their names and were thereafter referred to by numbers. However, the armoured train units were dissolved in 1954–5 and the rolling stock was scrapped, except for several infantry wagons used in a stationary role, notably by the Air Force.
Reduced to a propaganda weapon, these trains had not been able to play a decisive role in the battles of liberation which stressed the actions of the partisans and paratroops.
The elements of two Panzerzüg (s.Sp) formed a train which comprised three turret-equipped trolleys, a command trolley (with frame aerial) and an infantry trolley. Note the Czechoslovak flag on the side of the leading unit.
_(Photo: VÚA-VHA)_
This view shows the tool set of an infantry trolley, with the jack which is identical to that carried by tanks.
_(Photo: VÚA-VHA)_
The opposite view of a turreted trolley, to be able to compare the two ends. Here is the motor end, identifiable by the semi-spherical armoured domes.
_(Photo: VÚA-VHA)_
The command trolley, with its frame aerial.
_(Photo: VÚA-VHA)_
Note the lack of a coupling hook on this unit. Regretably, none of these vehicles have been preserved in a museum.
_(Photo: VÚA-VHA)_
**SOURCES:**
**Archives:**
SHD, boxes 17 N 629.
Múzeum Slovenského nároného povstania, Banská Bystrica.
Vojenský Ústředni Archív, Prague.
Vojenský historický ústav, Bratislava.
**Books:**
Catchpole, Paul, _Steam and Rail in Slovakia_ (Chippenham: Locomotives International, 1998).
Hyot, Edwin P., _The Army without a Country_ (New York: MacMillan Company, 1967).
Jakl, Tomáš, Panuš, Bernard, and Tintěra, Jiří, _Czechoslovak Armored Cars in the First World War and Russian Civil War_ (Atglen, PA: Schiffer Publishing, 2015).
Janin, General, _Ma Mission en Sibérie 1918-1920_ (Paris : Payot, 1933).
Kliment, Charles K, and Francev, Vladimir, _Czechoslovak Armoured Fighting Vehicles 1918-1948_ (Atglen (PA): Schiffer Publishing, 1997).
Kmet, Ladislav, _Povstalecké Pancierové Vlaky_ (Zvolen, Slovakia: self-published, 1999).
Lášek, Pavel, and Vanĕk, Jan, _Obrn ná drezína TATRA T 18_ (Prague: Corona, 2002).
Richet, Roger, _Les émissions de la Légion Tchécoslovaque en Sibérie (1918-1920)_ (Bischwiller: L'échangiste universel, nd).
Rouquerol, Général J., _L'Aventure de l'amiral Koltchak_ (Paris: Payot, 1929).
Uhrin, Marian, _Pluk utocnej vozby v roke 1944_ (Zvolen, Slovakia: Múzeum Slovenského Národného Povstania, 2013).
**Journal articles:**
'Československé obrnĕné vlaky 1818 až 1939', _Železnice_ No 3/94 (1994), pp 23–6.
Chen, Edgar & Van Burskirk, Emily, 'The Czech Legion's Long Journey Home', _MHQ: The Quarterly Journal of Military History_ Vol 13, No 2 (Winter 2001), pp 42–53.
Kudlicka, Bohumir, ' _Orlik_ Armoured Train of the Czechoslovak Legion in Russia', _The Tankograd Gazette_ No 15 (2002), pp 27–30. _Militär-Wochenblatt_ , No 44 (1937), pp 2744–5.
'Povstalecky improvizovany pancierovy vlak _Stefanik'_ , _Modelar Extra_ No 20 (June 2013), pp 37–49.
In 1948, the Czechoslovak authorities published this postcard, which tended to overlook the exploits of the Czech Legion in favour of the Reds, using a fictional portrayal of an armoured train.
_(Postcard: Paul Malmassari Collection)_
. In Czech: _Pancéřový vlak_ , or PV. Alternatively in Slovak; _Obrnĕný vlak_.
. ' _Little Eagle_ ' in Czech, and also the name of a castle.
. The stamp issue, known as 'silhouettes', was printed at Irkoutsk by printers Makusin and Posochin: 35,520 examples of the 50-kopeck yellow-green stamp were printed. The third issue (for the Yugoslavs) and the fourth series (commemorative, which appeared between October 1920 and March 1921) show slight variations in the design.
. Heigl, Fritz, _Taschenbuch des Tanks_ , Vol II p 577.
. Caiti, Pierangelo, _Atlante mondiale delle artiglierie: artiglierie ferroviarie e treni blindati_ (Parma: Ermanno Albertelli Editore 1974), p 25.
. Milan Ratislav Štefánik (1880–1919), airman, Vice-President of the Czechoslovak National Council then War Minister, Slovak General.
. Jozef Miloslav Hurban (1817–86), one of the leaders of the Slovak Uprising of 1848, Member of the Slovak National Council.
. Tomáš Garrigue Mazaryk (1850–1937), President of the Czechoslovak National Council in Paris, then President of Czechoslovakia from 1920 to 1935.
. Several LT-35 tanks were stationed in the Slovak zone on the partition of Czechoslovakia.
. _Štefánik_ and _Hurban_ were popular subjects for photographers, and a comparison of the resulting images shows that often the captions were attributed in error, which means that it is not possible today to be absolutely certain of positively identifying either train.
## EGYPT
### AHMED ARABI'S ARMOURED TRAIN 1882
British troops began landing in Alexandria on 17 July 1882, and on 5 August they made a probing attack on the main Egyptian lines at Kafr-el-Dawwar which blocked the route to Cairo. Perhaps inspired by the British use of an armoured train, on 25 August the Egyptian forces of Colonel Ahmed Arabi assembled an armoured train of their own to support their position. Once the British under Sir Garnet Wolseley had moved the main thrust of their attack to Ismailia on the Suez Canal, the Kafr-el-Dawwar front became a side-show, and there is no mention of the Egyptian armoured train after 29 August.
**SOURCES:**
_Hawera & Normanby Star_ (NZ), Volume III, No 294 (30 August 1882), p 2.
. One also finds the name written as 'Kafradowar'.
## ESTONIA
### ARMOURED TRAINS 1918–1940
### The War of Independence (28 November 1918 – 2 February 1920)
Estonia declared its independence from Russia on 24 February 1918, but the capital Tallinn was occupied by German troops the following day. The Estonians had to wait for the Armistice of 11 November to gain their autonomy, and began to build up their own armed forces five days later. Profiting from the chaotic situation at the end of the Great War, on 28 November the Red Army attacked a German unit and troops of the Estonian National Guard, and the War of Independence began. In some areas the armoured trains were the most powerful armament available to the Estonians. The standard gauge was widespread apart from the narrow-gauge network which connected the southern part of Estonia with the northern part of Latvia.
The very first Estonian armoured train was in fact German, found abandoned at Tallinn in November 1918. It was made up of two artillery wagons (76mm guns) and two infantry wagons, with improvised protection which the Estonians upgraded. This train, allocated the number 1, arrived at the front on 30 November. It was made up of the following units: artillery wagon + two infantry wagons (one protected by sandbags, the other with iron plates) + unarmoured engine \+ the same units in reverse order. The crew was composed of 120 troops, made up of artillerymen, machine-gunners, and a strong infantry assault contingent.
The next five trains (on the standard gauge) went into action in the following order: on 15 and 23 December 1918, and then 21 January, 19 March and 12 August 1919. Armoured Trains Nos 5 and 6 included modern wagons (one artillery wagon + three machine-gun wagons + five infantry wagons). In August 1919, an Armoured Trains Division was created, which formed the strategic reserve of the Commander-in-Chief. By the end of 1919, the Armoured Trains force had fifty-five standard gauge wagons, and each of the artillery wagons was individually named.
Five armoured trains were built to operate on the narrow-gauge network. These were delivered on 1 January (SR No 1), 18 to 26 January, 21 February, 1 May (replacement SR No 4), and 2 July 1919 respectively. Several narrow-gauge trains were protected by trench shields, which gave them a distinctive appearance. In general these trains were made up of two artillery wagons, one or two machine-gun wagons and three or four infantry wagons. They carried a lighter armament than the standard-gauge units, with 47mm and 57mm guns, but included several 76.2mm Russian field guns.
After the Russian forces had been repulsed, the Estonians concentrated their military efforts against the _Landeswehr_ who were attempting to maintain German influence throughout the Baltic States. Peace with Russia was signed on 31 December 1919. By the ceasefire date, the Estonian armoured trains numbered eleven: six armoured trains on the standard gauge (numbered from 1 to 6, the first bearing the name _Kapten Irv_), and five trains for the narrow gauge (numbered 1 to 5). Between them these eleven trains carried twenty-seven artillery pieces and 118 heavy machine guns.
### The Peacetime Army (1920 – June 1940)
On 1 February 1921, several trains were demobilised and the Division was reformed as a Brigade, with the following units: (standard gauge) SR _Kapten Irv_ , SR No 2 and SR No 3, (narrow gauge) SR No 1 and SR No 2. In total the Brigade had three armoured engines, twelve artillery wagons, sixteen machine-gun wagons and twelve infantry wagons. In 1922, the narrow gauge SRs were demobilised and stored in depots, and then finally disbanded during the 1930s (certain units would resurface in modernised form in 1941 to face the Wehrmacht).
In addition to the formed armoured trains, there were certain individual wagons which could be attached to or detached from any existing train as need be. As these wagons each carried their own name, it is often difficult to identify a specific train solely from the name of the wagon seen in a photo.
On 1 February 1923, the Brigade was reorganised into two Regiments each comprised of two trains, then in December 1934 these two Regiments were merged into the Armoured Trains Regiment, comprising trains _Kapten Irv_ , SR No 2 and SR No 3, the long-range railway gun battery, two engineer companies and two machine-gun companies. In 1936 the railway gun battery comprised one gun truck ('Suur Tõll') armed with a 152mm Canet gun, and two ('Müristaja' and 'Tapper') each armed with a 4in (102mm) gun. The plan was to combine the armoured trains with the railway gun but the financial situation of the country slowed down progress, to the point where, when the Soviets invaded Estonia on 17 June 1940, three gun trucks were still under construction, a part of the armament of the trains had been dismounted, and the acquisition of certain wagons had been put on hold.
### Armoured Trains incorporated into the Red Army (September 1940 – August 1941)
The former Estonian Army became a corps of the Red Army and on 12 February 1941, the armoured trains were attached to the Baltic Sea Military District. Although their ultimate fate is unknown, it appears that several wagons were sent to the front around Leningrad. At the start of Operation 'Barbarossa', the Russian High Command ordered the construction of new armoured trains at Tallinn where the rail workshops had the necessary experience. Two narrow-gauge trains and a standard-gauge railway gun battery were built, and these units took part in the defence of Tallinn up until it fell on 28 August 1941.
Despite details given in the following sources, it is extremely difficult to identify a particular train from the names painted on the wagons, given the transfers between trains and successive modernisation schemes. The photo captions which follow are therefore indicative only.
### SR No 1
One of the wagons of the train captured from the _Landeswehr_. Note the assorted headgear: Russian caps, German Stalhelm and French Adrian helmets.
_(Photo: Paul Malmassari Collection)_
A telescopic observation platform extending up to 25m (82ft) high could be attached to an armoured train. Here the unit is shown lowered in the travelling position. The elements of the trains are heavily camouflaged with branches.
_(Photo: Paul Malmassari Collection)_
The pennant of SR _Kapten Irv_ on an unidentified wagon, probably part of SR No 5. In the left background is the telescopic observation tower in the raised position.
_(Photo: Paul Malmassari Collection)_
'Tommi', the leading wagon of _Kapten Irv_ , showing its 6pdr (57mm) gun.
_(Photo: Paul Malmassari Collection)_
The wagon 'Pisuhänd' of SR No 1 _Kapten Irv_. This photo shows the later configuration of the wagon fitted with a gun cupola.
_(Photo: Paul Malmassari Collection)_
Captain Irv, who gave his name to the armoured train he commanded.
_(Photo: Paul Malmassari Collection)_
An artillery wagon forming part of SR No 1. An armoured box encloses one end of a long-wheelbase outside-framed wooden wagon. The vulnerable axle boxes are protected by simple rectangular plates.
_(Photo: Paul Malmassari Collection)_
This view of 'Pisuhänd' appears to show its final configuration circa 1939.
_(Photo: Paul Malmassari Collection)_
_Kapten Irv_ in original condition.
_(Photo: Paul Malmassari Collection)_
### SR No 2
SR No 2 in 1919. Note the assorted collection of machine guns: From left to right, a Lewis, a Madsen (Russian calibre), a Russian Maxim on a wheeled carriage, and a Colt Browning 'Potato Digger'. A second Maxim is mounted inside the wagon. Note also the accordion held by the crewman on the right.
_(Photo: Paul Malmassari Collection)_
SR No 2 in winter camouflage. Note the smoke from the heating stove in the second wagon.
_(Photo: Paul Malmassari Collection)_
Vickers 130mm railway gun 'Kalewipoeg' attached to SR No 2.
_(Photo: Paul Malmassari Collection)_
The crew of SR No 2 in front of artillery wagon 'Uku', built on the chassis of a Russian wagon, probably in 1919. Their armband bearing the number of the train is a feature which appears in many photos. In addition to the fir trees attached as camouflage, 'Uku' carries a wreath for an official ceremony attended by August Rei (the civilian in the centre), Chairman of the Constituent Assembly 1919–20, and his wife. Note the letters 'Uku' painted in shadow to give the impression of relief.
_(Photo: Paul Malmassari Collection)_
One of several postcards dedicated to SR No 2, this one bearing the armoured train's pennant.
_(Postcard: Paul Malmassari Collection)_
### SR No 3
75mm gun on wagon 'Onu Tom' of SR No 3. The gun appears to be a British naval 3in HA, for anti-aircraft use. Later, this wagon would be rearmed with Vickers 152mm howitzers.
_(Photo: Paul Malmassari Collection)_
A view of 'Onu Tom' of SR No 3, on 15 April 1919, showing the naval 3-inch HA gun. It was also armed with a 76.2mm Russian field gun at the opposite end.
_(Photo: Paul Malmassari Collection)_
### SR No 5
Wagon 'Tasuja' of SR No 5, armed with British 18pdr (84mm) and 13pdr (76mm) field guns.
_(Photo: Paul Malmassari Collection)_
A view of the end of 'Tasuja' carrying the 18pdr in the lower position. Note that the wheels of the field gun are bolted to a plate on which it revolves.
_(Photo: Paul Malmassari Collection)_
A view of 'Tasuja' rearmed with a Russian 76.2mm field gun.
_(Photo: Paul Malmassari Collection)_
Close-in anti-aircraft defence of the armoured trains was provided by Russian Maxim heavy machine guns, here seen on SR No 5 with a five-man crew. The mount has been given the necessary elevation by the simple expedient of propping the front legs of the tripod on a pile of empty cartridge boxes, stacked on a two-plank wagon. This improvised solution would give only limited traverse to avoid the mount toppling over on its side. The planking and roof in the background belong to a goods wagon on the neighbouring track.
_(Photo: Paul Malmassari Collection)_
'Woitleja' in October1919, equipped with what may be a Canet 120mm Pattern 1892 gun in its end casemate. Note that the field piece has retained its wheeled mounting, which severely limited its horizontal field of fire.
_(Photo: Tiit Noormets Collection)_
An interesting photo of SR No 5, showing a Russian bogie wagon with the armour increased in height and pierced for four firing positions for machine guns and lookout hatches. This type of wagon would not be kept in service once the fighting had ended.
_(Photo: Tiit Noormets Collection)_
6in (152mm) railway gun 'Lembit', attached to SR No 5.
_(Photo: Paul Malmassari Collection)_
Closeup of the 'Lembit' gun. The combination of fixed round and screw breech indicate this is a Russian Canet 6in/45 built to a French design. Similar guns can still be seen on board the museum ship _Aurora_.
_(Photo: Paul Malmassari Collection)_
### SR No 6
SR No 6 in action in 1919. The artillery wagon in the foreground is 'Rummu Jüri', armed with a Russian 76.2mm field gun. The artillery wagon with the long gun is 'Leitnant Sabolotnõi'.
_(Photo: Paul Malmassari Collection)_
An overall view of the latter artillery wagon with its long-barrelled 4.7in (120mm) British gun. Several crew members wear armbands specific to the train. The wagon carries camouflage paint panels in addition to the standard pine tree.
_(Photo: Paul Malmassari Collection)_
### Narrow Gauge Armoured Trains SR (narrow gauge) No 1
SR No 1 (narrow gauge) in January 1919. Each infantry wagon appears to be equipped with one Lewis Gun. Note the medical orderly, and the wounded crew member in the centre of the group.
_(Photo: Paul Malmassari Collection)_
### SR (narrow gauge) No 2
Artillery wagon 'Suur Tõll' armed with a Russian 76.2mm field gun, part of SR No 2.
_(Photo: Paul Malmassari Collection)_
A closeup of the type of armour protection used on some narrow-gauge infantry wagons, comprising Russian trench shields. This type of wagon formed part of Armoured Trains Nos 2, 4 and 5. Note the riflemen have fixed bayonets. At first sight this seems incongruous, as they are fighting from behind armour and would not expect to use bayonets in close combat. But the Mosin-Nagant was never issued with a bayonet scabbard, so the bayonet is usually seen fixed.
_(Photo: Paul Malmassari Collection)_
### SR (narrow gauge) No 4
The crew of SR (narrow gauge) No 4 in front of the artillery wagon armed with a 76.2mm Russian field gun.
_(Photo: Paul Malmassari Collection)_
### SR (narrow gauge) No 5
An overall view of SR (narrow gauge) No 5.
_(Photo: Paul Malmassari Collection)_
SR (narrow gauge) No 5 wearing camouflage.
_(Photo: Paul Malmassari Collection)_
SR (narrow gauge) No 5 showing one of its 76.2mm Russian field guns.
_(Photo: Paul Malmassari Collection)_
### Modernised Armoured Trains of the 1930s
A bronze plaque on the wall of the station at Tapa, mounted on 9 June 1934 (restored to its position on 20 February 1993), bearing the insignia of the Armoured Trains Regiment.
_(Photo: Paul Malmassari Collection)_
Trolley No 145 of the 2nd Armoured Trains Regiment, used for the high-speed liaison role away from combat zones. The crew are lightly armed, with one rifle and pistols, probably Brownings. One occupant in the rear seat is talking on a field telephone, the cable reel for which is on the ground beside the track.
_(Photo: Paul Malmassari Collection)_
Armoured wagon No 212 in 1930. The two ends are symmetrical, with the machinegun embrasures diagonally opposed.
_(Photo: Paul Malmassari Collection)_
Steam engine Od-130, with only the driving cab armoured, used in armoured trains in the 1930s. Here it is propelling wagon No 212.
_(Photo: Paul Malmassari Collection)_
Gunners on artillery wagon 'Vanapagan' around their 76.2mm Russian field gun.
_(Photos: Paul Malmassari Collection)_
The leading wagon on this train photographed in 1925 is No 302 'Maru', here armed with a 76.2mm Russian field gun on the right, and a 3in(75mm) HA gun on the left. Note the Estonian flag.
_(Photo: Paul Malmassari Collection)_
Wagon 'Tommi' as modernised in 1929, with two 152mm M1910 Schneider howitzers.
_(Photo: Paul Malmassari Collection)_
Armoured wagon No 303 'Võitleja' armed with two 76.2mm field guns.
_(Photo: Paul Malmassari Collection)_
Armoured wagon No 102 'Wapper', built to the same design.
_(Photo: Paul Malmassari Collection)_
Artillery wagon No 2 'Hävitaja'.
_(Photo: Paul Malmassari Collection)_
During the modernisation of the armoured wagons in the 1930s, 'Onu Tom' and 'Lembit' were rearmed with two Vickers 6in (152mm) 26 cwt BL howitzers. Serving these pieces required that the extending side armour walls be jointed to provide continuous protection. Note the presence of a Latvian officer with his Estonian colleagues.
_(Photo: Tiit Noormets Collection)_
In this photo of the same wagon, note the observation cupola with its four semi-conical sections which hinge open at the top to expose the lookout slots, a design which it seems was unique to Estonia.
_(Photo: Tiit Noormets Collection)_
An experimental armoured shield for a 76.2mm gun, using Russian trench shields bolted together. These trench shields were also used to protect several narrow-gauge armoured trains.
_(Photo: Tiit Noormets Collection)_
**SOURCES:**
Helme, Mehis, _Eesti Kitsarööpmelised Raudteed 1896-1996_ (Tallinn: self-published, 1996).
Õun, Matti, Noormets, Tiit, and Pihlak, Jaak, _Eesti Soomusrongrid ja Soomusronglased 1918-1941_ (Tallinn: Sentinel, 2003).
. In Estonian: _Soomusrong_ , abbreviated to SR.
. Used with the tender leading.
. The original narrow-gauge SR No 4 was destroyed in action on 7 April 1919.
. Captain Irv, the first armoured train commander, in charge of SR No 1, was killed in action on 27 April 1919.
. Made up of an engine + two combat wagons with a 76.2mm field gun, a 45mm anti-tank gun and nine machine guns + munitions wagon. The railway gun battery had three 130mm coast-defence guns on unarmoured 50-tonne platform wagons.
## FINLAND
### ARMOURED TRAINS 1918–1945
The story of the Finnish armoured trains began with the War of Independence of 1918, which saw the birth of the state freed from its bonds with Russia. The Finnish railway network had not seen major growth, but at least it linked the different regions reasonably well, and had a good connection with Russia via the Viipuri-Petrograd line. The Finnish railway workers were easy prey for Communist ideology, and the Finnish High Command paid special attention to the security of the network from the very beginning. Armoured trains would thus come to play a major role in the three wars fought against Soviet Russia.
### The War of Independence of 1918
Finnish independence was initially viewed by the Bolshevik leaders as a good thing, in the name of the 'right of the people to self-determination'. Almost immediately, however, the evidence that the country was determined to reject Communism led the Bolsheviks to change their minds and to try to reassert their domination by means of a 'Fifth Column'.
Under the overall command of Kullerco Manner, the President of the People's Commissariat, the Red forces were composed of Red Finns, bolstered by Russian troops commanded by Colonel Svetchnikov. At the outset armoured trains were almost exclusively used by the Reds, apparently up to ten in number. It is thought that four of these were of Russian origin, well-designed and solidly built, and that the remainder were constructed locally. It seems the first trains entered Finland only after the start of hostilities manned by Russian crews, which were not replaced by Finns until later. Nevertheless, on all the trains the Russian volunteers continued to serve as gunners and machine gunners. The crews were all part of the elite of the Red Guards, which helped to boost their morale, and the support of armoured trains helped to win many a battle.
The Red trains of Finnish origin were improvisations converted from bogie wagons in the workshops at Pasila, Viipuri and Fredericksberg (Helsinki). The steel plates used in their construction, although reasonably thick, had not been intended to be used as armour, and their lack of resistance could have been a serious weakness. Apart from small arms, their armament comprised naval guns of 37mm, 47mm, 57mm and 76mm calibre, with the mounting bolted directly to the floor of the bogie or flat wagon. On some trains, the guns were fitted with shields, as in the photo centre right, but on several others they were not. Tactically, the armoured trains formed a sub-division in the Red Guards and were used exclusively for artillery fire support. Their ultimate commander-in-chief would be G Tamlander who was previously the commander of Armoured Train No 1. Certain trains were designated by number (for Nos 1 to 4), and two others by a typical revolutionary name, which indicates that the last two were of Russian origin. They were PSJ _Kerenski_ and _Partissani_. If the first four numbered trains had a name, these have not been passed down in the historical records. On the White side, apart from trains they captured, there was a train improvised to meet the Red offensive of 11 February 1918, named _Karjalan Pelastaja_ ('Saviour of Karelia').
Red armoured train, built in the Fredericksberg workshops in Helsinki, armed with 75mm Canet guns originally intended for warships or coastal defence.
_(Photo: Jean-Gabriel Jeudy Collection)_
Fitted with rudimentary armour, the Class G1 engine of _Karjalan Pelastaja_ is nevertheless equipped with a smoke deflector.
_(Photo: All Rights Reserved)_
A wagon from _Karjalan Pelastaja_ , its armour protection comprising two layers of planks with the interval between filled with bricks. Its armament is a 76.2mm Model 76 VK/04 mountain gun with a shield.
_(Photo: All Rights Reserved)_
Three Red attacks on Viipula led by Russian Colonel Svetchnikov were repulsed. On 7 February 1918 an armoured train was engaged in support of 1300 men with seven artillery pieces, but again the attack failed. During their renewed attempts on the 21st and 22nd, Armoured Train No 1 bombarded the White lines, but without visible results. On 13 March the Reds tried again to break through, with a train loaded with explosives in the forefront of the attack. After these repeated failures, the Reds planned to bring up a second armoured train, but the Whites had blown a railway bridge, preventing the capture of the town. In the Savo sector, the White-occupied station at Mäntyharju fell to a Red attack supported by a Latvian infantry company and an armoured train from the south. But the town was recaptured by the Whites on 14 February and remained in their hands thereafter.
In the Karelian Isthmus, _Karjalan Pelastaja_ successfully went into action between 2 and 12 February, while in the south the Red Guards from Helsinki used a train in support of an infantry attack aimed at eliminating the Whites stationed on the Helsinki-Karjaa line at the strategic junction of the lines to Turku, Tampere and Lahti.
On 15 March the Whites launched their counter-offensive to block the Reds from reaching northern Häme. The fighting took place around the railway lines, and on the 15th the Whites blew up the track at Orivesi, preventing the Red trains from coming up from the south. On the 18th, the Whites were on the point of capturing Orivesi Station, but the intervention of a Red train coming from Lyly forced them out. This train, soon supported by a second, held back the Whites' attempts to recapture the station for two days before it finally fell. On the 21st, Armoured Train No 1 and a company of infantry defended Siitama on the line to the east of Tampere, and were soon joined by Armoured Train No 3. Damaged by White artillery, the trains withdrew into Tampere where they would later be captured. On the 24th, the Whites advancing from Orivesi reached Lempäälä and circled round to the east of Tampere. With the line to Helsinki thus cut, the Reds attempted to re-establish the link by sending an armoured train, but in vain. The White encirclement continued by their capture of Ylöjärvi and Sivro Station, which blocked the arrival of Red reinforcements from the west. Several Red armoured trains were sent to break through, one of them coming directly from Helsinki and going into action between that city and Tampere. At the same time, it was decided to complete the trains being built in Helsinki which still lacked their armament.
During the final fighting, the Red train guarding the Tampere-Lampäälä line was engaged by White artillery on the 25th and destroyed, and two days later Armoured Train No 3 suffered several direct hits, its commander being killed. The line to the south having been cut on the 24th, two Red trains sent from Lampäälä went into action, without being able to reach Tampere. From that moment on, the encirclement was complete, and among the trains cut off, the one defending Näsinlinna was seriously damaged on 4 April then destroyed by a direct hit to its engine. On 5 April Armoured Train No 3 was sabotaged by its crew to avoid it falling intact into the hands of the Whites. On the fall of Tampere on the 6th, the Whites captured thirty artillery pieces and two armoured trains.
German intervention in the fighting began with a landing at Loviisa, 60km (38 miles) to the east of Helsinki. On 11 April the von Brandenstein Brigade advanced towards the Lahti-Kouvola railway line in order to cut it, with the help of 400 Civil Guards. The fate of Lahti was decided only on the 17th. The Reds fled to the west, guarding their rear with a train on the Lahti-Helsinki line. On 20 and 21 April, Armoured Trains _Kerenski_ and _Partissani_ , supported by infantry, tried to cut a way through to Helsinki by attacking from the east. They failed, and tried again on the following day, without succeeding in breaking through. One of the trains had to withdraw to Viipuri for repairs. On 2 May Lahti finally fell, and the two abandoned armoured trains were recovered intact by the Whites in Herrala Station.
The typical outline of the engine of a Red armoured train, with armour plates fitted directly to the running board. Note the lifting ring beside the cab.
_(Photo: All Rights Reserved)_
The general aim of the Whites in their offensive in the east of the country was the definitive elimination of the Reds by cutting their lines of communication with Petrograd, as the Viipuri-Petrograd line was the Reds' umbilical cord. Their advance to the south, which began on 19 April 1918, led to the capture of the stations of Raivola, Kellomäki and Kuokkala. The latter station was defended by an armoured train which was forced to withdraw after suffering hits, while the Red resistance crumbled. At Raivola, the withdrawal of another armoured train led to the infantry retreating, and by the 24th, 40km (25 miiles) of track were in White hands, thus cutting off the Communists from Russia.
At the same time, another White force advanced on Viipuri itself from the north and the east. At dawn on the 24th, near Tali, a Red attack supported by two armoured trains failed. It seems that two armoured trains were involved in the defence of Viipuri, one crewed mostly by Russians escaping to the north, and the second withdrawing into the town.
To the south an armoured train was sent to try to break through to Petrograd. After Saïniö a broken rail forced it to halt, then as a temporary repair did not hold, to retreat. In withdrawing, it derailed, and its crew abandoned it. Re-railed by the Whites, it was taken away by them but does not seem to have seen service in their ranks. On the 27th, the Reds made another attempt to break through, but a destroyed bridge at Tienhaara forced their armoured train to retreat. A last train continued to defend Viipuri to the west of the town, patrolling as far as Simpla. Viipuri finally fell on the morning of the 29th, leaving three armoured trains in the hands of the Whites, and ending all hope of aid coming from Russia.
One of the two wagons of the Russian armoured train, either _Voloi Kapitalism_ ('Down with Capitalism') or _Partisaani_ , which was captured at Säïniö on 24 April 1918. The wagons were initially used by German troops as in the photo. The wagon shown here had already been modified by the addition of a fixed observation cupola (see the chapter on Russia) but retained its 76.2mm K/02 gun up until the 1935–9 period. Each of these wagons would be attached to a Finnish armoured train when the Germans left Finland in late 1918, and this one would join PSJ 2.
_(Photo: Paul Malmassari Collection)_
Three more armoured trains were included in the spoils recovered by the Whites at the end of the Civil War: two were captured intact at Kotka on 5 May and one when Helsinki capitulated on 14 April. The latter train was used on 19 April by the Germans on the Helsinki-Riihimäki-Lahti line.
One of the long artillery wagons probably built by the Reds during the Civil War, seen here with a flat roof, and a front turret armed with a 37mm Maxim pompom. These wagons would undergo continual modifications, reaching their definitive form in 1944.
_(Photo: Kari Kuusela)_
An interesting shot of one of the two mountain-gun wagons built in 1919, originally armed with a German 75mm VK/L14 mountain gun and two machine guns, and intended as the chase wagons for each of the armoured trains. The German mountain gun has been removed, and the wagon is now obviously used for training. It is coupled at the tail end of PSJ 1, and the observers appear to be controlling the fire of the gun turret of the short artillery wagon, now rearmed with a 76.2mm VK/04 mountain gun. This would date the photo to between 1932 and 1939. Interestingly, these wagons would continue in use for some years, included with the service trains accompanying the armoured trains. Note the Adrian helmet worn by one of the soldiers. The national insignia (the 'Cross of Liberty', a yellow short-armed swastika over a blue Maltese Cross, designed by Askeli Gallen-Kallela in 1918) is painted on each of the wagons.
_(Photo: Paul Malmassari Collection)_
At some time between 1935 and 1939 the (short) artillery wagon of PSJ 2 (recognisable by its two-level observation cupola) was rearmed with a 76.2mm VK/04 mountain gun, while PSJ 1 had received this modification in 1932.
_(Photo: Paul Malmassari Collection)_
Closeup of the front (long) artillery wagon of PSJ 2 seen on 1 January 1940. The 37mm pom-pom has been replaced by a 76.2mm VK/04 mountain gun. Note the upper part of the shield which elevates with the barrel. The armament of this wagon also included twenty 7.62mm machine guns, one of which is visible protruding from the observation cupola on the roof. Two more could be mounted alongside the 76.2mm mountain gun, firing through the oval ports.
_(Photo: SA-Kuva)_
### Armoured trains during the Russo-Finnish Winter War (1939–1940) and the Continuation War (1941–1944)
During this period, the two Finnish armoured trains were controlled by the High Command at Mikkeli, and were directly subordinate to the Army Corps Artillery Command. Used offensively during the Winter War, they were afterwards relegated to the role of mobile anti-aircraft batteries, and their armament was modified accordingly. Even then, the impression of power possessed by these units brought encouragement to the ground troops. The trains also aided the troops directly by transporting them in security, and by warding off traps and attacks by partisans. They were used against the Russians in the east of Finland, in the region of Lake Ladoga. During the Continuation War, PSJ 1 was transferred to Kollaa and PSJ 2 to the Isthmus of Karelia, then to the north of Lake Ladoga, which was armoured train country, where their fields of fire extended out to 6km (over 6500 yards).
Class Sk3 steam engine of PSJ 2. Of these goods engines, only two remained armoured after the Civil War. Initially, the engine of PSJ 1 was not fitted with a smoke deflector, which allowed Soviet aircraft to easily find the train in its various hideouts during the Winter War. Their armour was 10mm thick.
_(Photo: Paul Malmassari Collection)_
In 1940, K5 Class engine No 884 (redesignated as Class Tk3 in 1942) was armoured to reinforce the trains. The 77 plates which formed the armoured carapace were from 16mm to 22mm thick (16mm on the tender). This engine was allocated to PSJ 1, but also served with PSJ 2.
_(Photo: Paul Malmassari Collection)_
### Armoured Train No 1 (Panssarijuna 1)
Armoured Train No 1 consisted of two separate components, an armoured train armed with artillery and machine guns, plus an unarmoured support train.
In 1939 the armoured unit comprised:
1) safety wagon
2) safety wagon
3) long artillery wagon armed with a 76.2mm VK/04 mountain gun with a horizontal field of fire of some 270 degrees for firing against ground and aerial targets, plus two 7.62mm machine guns mounted at the sides of the turret and capable of forward fire, and six 7.62mm machine guns mounted three each side of the hull
4) machine-gun wagon armed with eight to ten 7.62mm machine guns mounted at the sides and two 7.62mm anti-aircraft machine guns mounted in tubs on the roof
5) unarmed armoured steam engine
6) armoured wagon (ammunition and various stores) serving also as a first-aid post
7) short artillery wagon armed with a 76.2mm VK/04 mountain gun and several 7.62mm machine guns
8) safety wagon
9) safety wagon
The unarmoured support unit comprised three or four Types Gb and T Third Class coaches, a kitchen wagon and various wagons containing a sauna, mess, radio compartments etc. The overall crew of the combined train was around ninety men, and the complement of the armoured unit alone was three officers, twenty-five NCOs and fifty men.
On 1 November 1939 the train made contact with the 34th Infantry Regiment of the 12th Division, in order to provide fire support during the delaying action against the Russians, and on 2 December, it covered the withdrawal of the 1st Battalion of the 36th Infantry Regiment to Suvilahti, the train forming the rearguard. On the 3rd, a counter-attack was launched with the train supporting the 3rd Battalion of the 36th Infantry Regiment, which withdrew at around 17.00 under the cover of its guns. On the 4th, Russian tanks attacked in the direction of the railway, but despite local penetrations, by the end of the day their attack had failed. Armoured Train No1 next participated in the destruction of the Russian forces attacking the front lines of the 34th Infantry Regiment between 8 and 16 December, and on the latter date the train received orders to restrict its patrols. Air attacks followed the ground attacks, and Russian artillery prevented the armoured train from reaching the front line. Between 17 December 1939 and 13 March 1940 the train was the target of twenty-five daytime and fifteen night artillery bombardments, and twenty-five air attacks, one of which caused it to derail, the track having been destroyed in a dozen places.
Between the two wars, PSJ 1 remained in reserve, until on 28 July 1941 it left for the Karelian Isthmus, then provided security on the Leningrad-Viipuri line. Before the outbreak of the Continuation War, it received several modifications: a new targeting system allowed indirect fire by the artillery, and an intercom system enabled communication between the wagons and the engine. In view of the main threat faced by the armoured trains during the Winter War the two 76.2mm mountain guns were replaced by two 40mm Bofors anti-aircraft guns. The armour protection remained between 15mm and 20mm depending on the different wagons. Finally, a deflector directing the engine's smoke towards the ballast as on PSJ 2 was installed.
On 28 November 1942, PSJ 1 and PSJ 2 were modified and transformed into two rail-mounted anti-aircraft batteries ( _1. & 2. Rautatieilmatorjuntapattereri_). As the main threat posed by the Soviet air force came in the form of ground-attack aircraft, both trains maximised their close-range automatic firepower by replacing the Obukhov guns with 40mm Bofors. By 30 August 1943, the armoured component of PSJ 1 carried the following armament:
PSJ 1 seen after the Winter War. The short artillery wagon has been rearmed with a 40mm ItK/35-39 B Bofors, and an additional central axle has been added between the original two. Note the spare lengths of rail mounted on the sides of the wagon.
_(Photo: Paul Malmassari Collection)_
PSJ1 in July 1941. The roof of the long artillery wagon been modified by sloping the sides to increase the anti-aircraft firing angles of the Bofors. Note engine Tk3 at the tail end of the rake and the armoured axle boxes of the safety wagon.
_(Photo: SA-Kuva)_
The long artillery wagon of PSJ 1 seen from the front in 1942. The 76.2mm ItK/02/34 Obukhov anti-aircraft gun was installed in about September 1941, displacing the Bofors to the rear of the wagon where it was re-mounted directly on the wagon floor. The new larger gun tub for the Obukhov has opening panels allowing it to fire below the horizontal to each side of an elevated track.
_(Photo: Paul Malmassari Collection)_
The final development of the long artillery wagon: In 1944, the wagon formerly from PSJ 1 was modified to optimise its anti-aircraft capabilities as part of Anti-aircraft Battery No 1. The rear part of the roof was sloped to increase the field of fire of the second 40mm Bofors. Seen here from the rear, as partially restored externally (the gun tub for the front Bofors is missing), and lacking armament, it is now on display at the Parola Armoured Museum. Note the revised national emblem, comprising a short-armed swastika painted black on white, as adopted by the armoured forces on 21 June 1941.
_(Photo: Paul Malmassari Collection)_
– three 40mm ItK/39 Bofors, one on the short artillery wagon and two on the long wagon.
– two 20mm ItK/40 Madsens, mounted on two new unarmoured wagons (Type Git) modified in June 1943.
The Soviets attacked in force on 9 June 1943, and PSJ 1 was allocated first to the defence of the railway complex at Maaselkä, then that of Viipuri. For that specific mission, each wagon split from the others accompanied a goods train. An equivalent role was allocated to it between 28 March and 10 April 1944 when its individual wagons were used as stationary anti-aircraft artillery batteries, then from 28 May to 12 June in Lapland, where the units covered troop movements. The train next moved to Nurmi, then Simola, and finally Taavetti on 30 July, where its crew heard the news of the Armistice several days later. On 22 September, the train moved to Kouvola, and on 3 October a part of its crew was demo-bilised, the rest remaining with the train up until the following November. PSJ 1 was taken out of service on 17 November 1944.
The final version of the short artillery wagon (first two, then three axles) from PSJ 1 as exhibited at Parola. The set of wagons had been transferred to the Museum in 1984.
_(Photo: Paul Malmassari Collection)_
A fine view of the Class G 10 engine (the future Sk3) seen here with PSJ 2 during the Winter War. Note the armour extended to the rear of the machine-gun wagon on the left to protect the personnel entering or exiting by the rear door. These wagons were those originally built by the Reds in Helsinki and were subject to continual upgrading.
_(Photo: SA-Kuva)_
### Armoured Train No 2 ( _Pansarijuna_ 2)
Due to the loss of its war diary and its archive records during the retreat from Karelia in June-July 1944, it is difficult to retrace the operational history of this train.
In early April 1942, its armament consisted of:
– one 76.2mm ItK/02/34 Obukhov anti-aircraft gun (on the long artillery wagon)
– two 40mm ItK/38 Bofors (one on the long artillery wagon and one on the short wagon)
– seventeen 7.62mm kk 09 machine guns
– five 7.62mm kk 32 machine guns.
It was provided with a stereoscopic binocular rangefinder (as seen in the previous photo of the training wagon).
Transferred to Tohmajärvi from 1 July 1941 under the command of the VIIth Corps, it participated in the capture of Värtsilä in the company of the 2nd Heavy Railgun Battery. Then on the 28th, these two units joined the Army of Karelia where they came under the command of the 163rd Infantry Division of the Wehrmacht, to which they provided effective fire support. Ensuring the security of the logistical lines of the VIIth Corps, the train also provided the principal anti-aircraft defence of the towns of Vitska, Syväri and Karhumäki.
On 28 November 1942 the train was reformed as the 2nd Anti-Aircraft Battery. It then provided cover to the key points of the network, the bridge over the Uunista, the Station at Malu and the Mäki-Lisma branch line. Broken up into separate units, each element took on the designation of _1 o, 2o, 3o etc Rautatiekonekiväärikomppania_ (abbreviated to _1 o, 2o, 3o Raut. It. KKK_.) or Railway Anti-aircraft Machine-gun Company. As such it participated in the defence against the Soviet offensive in June directed against Karelia, and was then transferred to the Aunus Isthmus. It found itself trapped by the landing of the 70th Marine Brigade at Tuulos and the cutting of the rail line on 23rd June. To prevent it falling into enemy hands, the crew sabotaged the train on the same day near the station at Mäkriä.
Original drawing of an armoured SK3 locomotive.
_(Private collection)_
The (short) anti-aircraft artillery wagon of PSJ 2, armed with a 40mm ItK/39B Bofors and seven machine guns. Note the searchlight on the stepped observation cupola. The following wagon is a machine-gun/kitchen wagon, with its machine-gun tub covered by a tarpaulin.
_(Photo: Paul Malmassari Collection)_
On display at Parola is this example of a machine-gun wagon, which was common to both armoured trains, with minor differences over the life of the units. It is here preserved in its 1942 state, the final version of the wagons originally built for the Reds in Fredericksberg.
_(Photo: Paul Malmassari Collection)_
PSJ2 seen in March 1942 without its armoured engine. The second wagon from the right is the machine gun/kitchen wagon with two anti-aircraft machine gun tubs on its roof. The ex-Soviet PL-37 wagon has its turrets aligned fore and aft, but the anti-aircraft Obukhov and Bofors are elevated ready for action. The coach on the left is probably intended as a rest and recreation vehicle for the train crew.
_(Photo: Paul Malmassari Collection)_
The long artillery wagon of PSJ 2 photographed in October 1941 at Jessoila. The 76.2mm ItK/02/34 Obukhov anti-aircraft gun was installed on 23 September 1941, replacing the Bofors which has been re-positioned on the roof, in the tub which formerly held a 7.62mm anti-aircraft Maxim. The new gun tub for the Obukhov has opening panels allowing it to fire below the horizontal to each side of an elevated track. The next wagon in line is a machine-gun/kitchen wagon with two AA machine gun tubs on the roof.
_(Photo: Paul Malmassari Collection)_
The long artillery wagon of PSJ 2 photographed on 7 August 1941. It is heavily armed, with a 40mm Bofors, the barrel of which can be seen in the background, the three 7.62mm Maxim machine guns shown here, a fourth 7.62mm Maxim on an anti-aircraft mount in a tub at the rear of the roof, and several more firing from the wagon sides.
_(Photo: SA-Kuva)_
In September 1941, the Finns captured a Soviet armoured train at Äänislinna, and reused its PL-37 artillery wagon as part of PSJ 2. However, since its Russian armament did not possess sufficient elevation for anti-aircraft fire, it saw little action in Finnish hands. Note the barrel of the Obukhov AA gun at the far left.
_(Photo: Paul Malmassari Collection)_
The installation of an anti-aircraft 7.62mm Maxim M/32-33 inside one of the machine-gun/kitchen wagons. A twin 7.62mm ItKk/31 VKT mount was also used. It is possible this is a posed propaganda shot, as normally the AA machine gun would be mounted much higher, in the circular tub.
_(Photo: SA-Kuva)_
**SOURCES:**
**Archives:**
Finnish Photographic Archives (www.sa-kuva.fi).
Sotamuseo, Helsinki.
Rauttatiemuseo.
SHD, cartons 7 N 2788.
**Books:**
Hannula, General Josse Olavi, and Perret, Jean-Louis, _La guerre d'indépendance de Finlande, 1918_ (Paris: Payot, 1938).
Sillanmäki, Jouni, _Panssarijunia Suomessa – Suomalaisia Panssarijunissa_ (Jyväskyla: Gummerus Kirjapaino Oy, 2009).
**Journal Articles:**
Talvio, Paavo, 'Panssarijunat Talvi- Ja Jatkosodan Taiteluissa', _Sotahistoriallinen Aikakauskirja_ No 5/1986, pp 193–235.
'Panssarijuna 2 : N Tuominta ja tuho' _, Veturimies Magazine_ No 11– 12/1986, pp 474–82.
**Website:**
<http://www.jaegerplatoon.net/MAIN.html>
. In Finnish: _Panssarijuna_ (PSJ).
## FRANCE
### Armoured Trains 1825–1870
### The first armoured train project of 1825
Inspired by the British plans for a railway to run the 28 miles (45km) from Stockton to Darlington, in 1825 _Capitaine de Frégate_ (Commander) Montgéry launched the idea of 'a type of steam-powered defensive war wagon, or mobile casemates, which if employed on a large scale would be formidable fortifications, and would be capable of manoeuvring on railway lines more rapidly than the finest cavalry units. This machine would comprise three vehicles proof against cannon shot. One of these vehicles, placed centrally, would be equipped with a steam engine. Each of the two others would carry three howitzers... The all-up weight of a casemate thus equipped, with its small garrison, and the appropriate munitions, would be approximately 85,000 kg [almost 94 tons]... .' The inventor envisaged their deployment 'especially for the defence of defiles, of highways, of main roads in non-fortified strategic towns, the approaches to certain fortresses, and chosen beaches... '. Unfortunately, it appears that no plan of this armoured train has survived.
### The Mexican Campaign (1861–1867)
In November 1866 during the Mexican Campaign plans were drawn up for a defensive wagon to counter the attacks of irregulars, which caused severe problems right up until the evacuation of the French Expeditionary Corps. The bogie wagon, protected by wooden cladding 12cm thick, was to have had eleven firing embrasures per side and three at each end. From the support pillars shown in the drawings it is possible the armament would have included large-calibre rampart guns, as befitting a 'mobile fortress'.
### Proposals for armoured trains prior to the Franco-Prussian War
In 1841, M. Schwickardi proposed a 'cannon-wagon', proposed for the defence of fortresses, and also for the defence of Paris. The mixed road-rail 'armoured machine' of Zéphyr Toffin dates from March 1858: 4m (13ft 1½in) long by 2m (6ft 6¾in) wide, armoured including cones protecting the wheels, and to be armed with three _Mitrailleuses_. The design was presented by the inventor again in December 1870. In 1862 Captain Veillet proposed armoured 'wagon-batteries' 3.1m (10ft 2in) long by 2.1m (6ft 10½in) wide by 1.9m (6ft 3in) high, to be formed into convoys.
The plan of the armoured wagon proposed for the campaign in Mexico. It is not known whether it was actually constructed.
_(Plan by the Author based on the original in SHD Archives)_
Layout of the armoured wagon (35cm of wood covered by 18cm of metal) proposed by Michel Body
_(_ Plan _: Les Chemins de Fer dans leurs applications militaries_ , Plate IV _)_
On 10 November 1863, the Artillery Committee received from Thomas Wright, a British subject, his project for a battery on rails which 'apart from being suitable for the French coasts, is also proposed for Algeria, India and the French "colonies"'. These trains composed of three or four batteries, each armed with between ten and forty guns and mortars on pivoting mountings, would have formed a defensive barrier extending over a mile (1.5km). Then in 1868, Michel Body presented his ideas of an integrated defensive system, encompassing railway systems, fortresses and armoured railway stations. He specified the construction of 'cannons mounted on trains and special motors proof against enemy fire [providing] this artillery with incomparable mobility', as detailed in the plan above.
### The Franco-Prussian War and the Siege of Paris (1870–1871)
### The Meudon Armoured Train
The origins of this train go back to 1867, when Colonel Brent, an American, had outlined to Napoleon III his ideas for railway war machines. Marshal Niel and General Leboeuf had considered the project, and had confided it to Captain de Reffye, Director of the Meudon Workshop, to be built in the utmost secrecy. The Armistice went into effect before the train could be used against the Germans. It was seized by the Paris Commune on 9 February 1871 and used on the _Chemin de Fer de Ceinture_ (the peripheral railway line around the city centre). After the war, it was planned to keep the train for deployment at Douai, but weight and loading-gauge problems led to it being broken up by the _Chemin de fer du Nord_ on 20 June 1872.
Two wagons of the Meudon Armoured Train. 13mm _Mitrailleuses_ would have fired through the protected scuttles. The whole train weighed 85 tonnes.
_(Photo: Musée Carnavalet)_
### Armoured trains of the _Chemin de fer d'Orléans_ (Dupuy de Lôme Batteries)
Out of all the numerous projects and inventions presented to the authorities, the one by Messrs Solacroup and Delannoy, two engineers of the _Chemin de fer d'Orléans_ , caught the attention of the Paris Defence Committee. Their first design study consisted of one or two large-calibre guns mounted on a platform carried by two trucks placed side-by-side on the double track and pulled by horses. The second design study had a single platform carried on two parallel tracks, armoured on three sides with lengths of rail. Finally, their third design was a wagon fully armoured with rail lengths, roofed over by a curved plate. The front face was pierced by an embrasure allowing fire up to 30 degrees on either side of the central axis.
The Committee decided to build the fourth version proposed, being two four-axle wagons, armed with a 14cm gun firing _en barbette_ over the top of the armour, 30 degrees to either side of the central axis, immediately followed by two other wagons, each armed with a 16cm gun mounted in a pivoting casemate. The firing embrasure in the 16cm battery had been much reduced in size compared with the previous proposals, and the roof was armoured.
In action two gun wagons were to be disposed side-by-side on parallel tracks. Behind the gun wagon on the track on the side facing the enemy was a second gun wagon. In place of the proposed armoured engines, two tank engines could be used to move the batteries. A tank engine would run on the track facing away from the enemy, propelling a leading gun wagon. On the side facing the enemy the engine would be protected by the second gun wagon in line, which was connected to the engine by a system of chains. After use for the defence of Paris, then by the Commune, these trains were broken up in 1871.
The drawing of the 14cm _en barbette_ wagon. The gun had a maximum range of 3300m (3600 yards) and required a crew of eleven men. The allup weight was 40 tonnes.
_(Plan: Paul Malmassari)_
Drawing of the engine which was protected by 5cm of iron over a wooden framework. It weighed 35 tonnes, or considerably less than the wagons it was supposed to move. The curious chain drive (from vertical cylinders? – not shown) to the centre axle is perhaps necessitated by the fact that the engine is a well-tank, with its water supply positioned below the boiler where one would normally expect to find the cylinders and cranks.
_(Plan: Paul Malmassari)_
Drawing of the pivoting casemate battery armed with a 16cm gun, with a range of 3900m (4265 yards) served by a crew of 13 men. Total weight was 47 tonnes.
_(Plan: Paul Malmassari)_
### Armoured trains in the French Provinces
An armoured train was ordered from the _Compagnie du Midi_ at the end of 1870. At the time of writing, research had turned up no details of this train, which was constructed at Bordeaux. Again in 1870, the _Compagnie de l'Est_ constructed armoured units. The main action undertaken by the _Est_ armoured train was the capture of a goods train at Peltre, near Metz, on 27 September 1870. To the west, General Kératry, commanding the Army of Brittany, ordered the _Compagnie de l'Ouest_ at Le Mans to construct three armoured trains, each comprising eight vehicles.
At Périgueux, beginning in early September 1870, the _Compagnie d'Orléans_ had also built twenty-four wagons, identical to the Parisian models with pivoting casemates, which were intended to be used against the Prussians. But Paris capitulated before the train could intervene. Then on the morning of 11 April 1871, the Versailles Government ordered the train to make its way towards Paris to take part in the battle against the Commune. At the end of the morning, on hearing of this, the staff of the railway workshops deliberately overturned wagons on the tracks, delaying the departure of the train until 12 April, after which date it disappears from history.
The original drawing for the engines of the Army of Brittany.
_(Plan: SHD)_
Drawing of the wagons of the armoured trains of the Army of Brittany.
_(By the Author)_
### The Period 1871–1914
Based on the lessons of the War of 1870–1, the future role of armoured trains would not be limited to defence alone, but would also encompass active employment designed to help push back the front lines. Numerous propositions dealing with this have come to light, like the project shown in the illustration below: the two rails of the central track are used by replenishment trains carrying munitions and coal. The gun battery and its engine run on the two outside rails. They make use of the firing embrasures let into the parapet at intervals, and the gun also uses a disappearing mounting. The artist appears to have imagined the small munitions locomotive – a Crampton – being fitted with a folding chimney, enabling it to take cover inside a tunnel in the body of the gun battery.
### The armoured trains of the Armoured Wagons Commission
This Commission had been created on 11 June 1878, presided over by General Schnéegans. After having collated the existing documentation relating to the railway batteries during the Siege of Paris, the Committee decided to proceed with the construction of separate prototypes of wagon and engine, in order to evaluate the form and resistance of the armour protection, and the type of armament and the maximum traction effort to be adopted. Firing trials against the engine took place on 15 May 1879 in the sand quarry at Courbevoie, and led to armour protection designed by M. Mayer, Chief Engineer, Rolling Stock and Traction, of the _Compagnie de l'Ouest_. The wagons from the _Est_ rail network were armoured with plates 10mm thick weighing a total of 4.5 tonnes. After three years of study, the decision was taken to create two types of train: reconnaissance trains (at first known as 'combat trains'), and trains intended for sorties from fortresses – but the latter type was quickly abandoned. The first train (which would remain the sole example), was assigned to Belfort in 1887.
An illustration from _Un bourgeois de Paris, Système de défense de Paris basé sur l'emploi des chemins de fer, des locomotives et des wagons blindés_
_(Saint-Nicolas-de-Port: E Lacroix, 1871)_.
The experimental armoured train assigned to Belfort, seen here during manœuvres. The engine and flat cars were placed in the centre of four wagons to front and rear. The main defect was the deafening noise caused by the armour plates, which were hung on the wagon sides but not fixed firmly in place.
_(Photo: La Vie du Rail)_
### The armoured railway batteries of Commandant Mougin
At the request of General Brialmont, in 1885 Commandant Mougin had conceived an armoured battery on rails, an immense device weighing 330 tonnes! It was described as follows: 'this project may be considered as a hollow girder construction, armoured on four of its sides, and capable of resisting substantial external shocks without deforming. This girder structure is fixed to a strong platform carried on nine sprung axles, allowing the whole battery to change positions. Two end panels and two internal frames separate the battery into three compartments, each enclosing a cannon. The armour on the side facing the enemy consists of two thicknesses of 45mm laminated iron plates...'. It was intended to deploy these batteries principally on the parapet of a continuous defensive line, and between two neighbouring forts, to cover the intervals in the case of an attack on the forts.
The armament was to have comprised three 155mm guns, each able to traverse through an arc of 70 degrees, with elevation from –5 degrees to +20 degrees. The maximum range was 7000m (7655 yards). The track gauge was to have been 3.15m (10ft 4in) at a time when the standard rail gauge in France (prior to standardisation) varied between 1.44m (4ft 8½in) and 1.5m (4ft 11in). Overall each battery would have measured 12.45m long x 3.5m wide (40ft 10in x 11ft 5¾in).
Armoured battery proposed by Commandant Mougin.
_(Illustration:_ La Nature _No 703 [20 November 1886], p 389)_
### Armoured train and armoured rail torpedo projects by Louis Gregori (1904)
Designed to run on rails and on roads, Gregori's 'armoured mobile battery' was intended to replace permanent and coastal fortifications, in Metropolitan France and also for defending the Colonies. The symmetrical layout was intended to protect the centrally-positioned engine, while the trucks at each end were used for observation and armament. In addition, the oval form of the vehicle's sides was supposed to offer superior protection compared with the usual vertical side walls. The secondary armament appears to be Hotchkiss revolver cannons, although Gatlings are also a possibility (they were being manufactured in France at that time for use in fortresses).
In the same year, this inventor proposed a 'land torpedo', inspired by naval torpedoes, propelled by a motor preferably powered by compressed air, and protected from rifle fire by a metal casing. The armament consisted of four 'warheads', which from the patent illustration appear to be large-calibre artillery shells with nose-mounted impact fuzes, covering four planes and intended to inflict all-round damage: to track, stations, platforms, enemy trains etc. The first shell exploding when its nose fuze struck a target – most likely the front one but one of the others could be activated if the enemy derailed the device – would then set off the remaining shells.
Detail from Patent No 350.168 submitted on 24 May 1904, granted on 13 September 1905.
Detail from Patent No 350.169, submitted on 28 May 1904, granted on 13 September 1904.
### The rebellion in the Côte d'Ivoire (1906–1910)
The river system and the railway network were the two methods of transport in this colony. During the uprising, the rebels began attacks on the railway in January 1910. An armoured train service was put into service which helped suppress the revolt.
Basic protection but sufficient against the arms used by the tribes in the Côte d'Ivoire: note the timber cladding on the engine.
_(Postcard: Paul Malmassari Collection)_
### The First World War (1914–1918)
### Armoured trains in the Colonies
The conquest of the German colonies in Africa involved the use of armoured trains of which no photos have so far come to light. While the Germans used armoured trains in Togo and Cameroon, the French deployed them only in Cameroon.
A naval gun was mounted on a wagon, probably armoured, for the advance on Medéa. Several wagons were fitted with armour protection for train escort duties and to fend off German harassing attacks, during which tracks and bridges were blown up. An armoured lorry was also built between 12 and 30 September 1915 and was used on the So-Dibanga–Eseka line.
### The armoured trains armed with 95mm guns (1914–1916)
Ordered on the declaration of war and designed very rapidly by Engineer General Gosselin in September 1914, with the initial aim of bolstering the ring of defences around Paris, three 95mm-armed armoured trains were built by the Batignolles Company using armour plates from the Commission in Gâvres. Each of the three trains comprised four wagons armed with a 95mm Model 1888 gun, plus corresponding ammunition wagons. A fourth train was assembled with two longer wagons each armed with two 95mm guns. They were delivered between the end of 1914 and the beginning of 1915, and remained in service until March 1916.
The lack of armour protection to the lower front end of this PLM engine shows that these trains were not intended for offensive operations. Of note is the miniature aircraft model mounted like a weather vane, but which we believe may be a visual indicator to the engine crew of the direction the turret is facing.
_(Photo: Paul Malmassari Collection)_
One of three armoured PLM Type B 111-400 4-4-0 engines requisitioned between 15 and 27 November 1914. The armour protection was designed by the Batignolles Company but installed by the PLM workshops. The front turret armed with a machine gun is a rare feature in the history of armoured trains, and must have made cleaning ash out of the smokebox a difficult task.
_(Photo: Paul Malmassari Collection)_
The following plans by the Batignolles Company show the 95mm armoured train. This is the first time these technical drawings, held by the SHD Archives, have been published.
General arrangement drawing showing a complete 95mm armoured train. The leading van has an extending observation ladder, and the tail van is armed with a Hotchkiss machine gun in a turret.
_(Plan: SHD Archives)_
The PLM Type B111 4-4-0 A engine.
_(Plan: SHD Archives)_
One of the 95mm gun wagons, with fixed side panels. Note the three jacks on each side for lifting the wagon wheels clear of the rails to relieve the stress on the springs when firing, and the clamps and spreader bars to fasten the wagon to the rails. Also the delivery chute from the ammunition van.
_(Plan: SHD Archives)_
It took only two minutes to prepare each wagon for firing, by jacking it up on stabilisers, and by clamping it securely to the rails. The 95mm cannon had a maximum rate of fire of eight rounds per minute. Each gun wagon carried 104 complete rounds. Note the number of the individual wagon painted above the builder's plate.
_(Photo: SHD)_
Batignolles built the armoured wagons in November 1914 on Nord 20-tonne flat wagon chassis.
_(Photo: Guy François)_
The armour protection of these wagons consisted of two 5mm steel plates spaced 5cm apart, with the gap filled with ballast gravel. Here the plates are partially dismantled, showing internal details.
_(Photo: Guy François)_
Wagons from a train with the Tenth Army in Artois. Each train had a crew of around forty men, including three officers. The armoured shields were fitted to the guns as early as 1893.
_(Photo: Guy François)_
An overall view of a train, compared with the plan. Note there are two tail vans with turrets, and in particular the exposed position of the artillery observers. Each ammunition van carried 1120 rounds.
_(Photo: SHD)_
On the right is a camouflaged gun wagon, and central a Bika van transferred from a Belgian armoured train. Next in line is a tail van followed by four ammunition vans specific to the 95mm armoured trains.
_(Photo: Private Collection)_
Armoured Train No 4 was built in Dunkirk, and entered service in February 1915. It was composed of two bogie wagons each armed with a pair of 95mm guns.
_(Photo: Private collection)_
The gun crew were from the 39th Battery of the 1er RAP (1st Fortress Artillery Regiment), and the engine crew were from the 5ème Génie (5th Engineering Regiment). Armoured Train No 4 was sent to the Third Army, where it carried out many fire missions, notably against a long-range 15cm K.i.S.L. gun, and was itself hit twice.
_(Photo: Private collection)_
This view shows the 8mm Saint-Étienne Model 1907 machine gun in place. As on the Belgian trains, firing slots pierce the sides of the wagons, allowing us to see the thickness of the armour.
_(Photo: Private collection)_
This photo shows the sliding armoured door giving access to the ammunition compartment. Armoured Train No 4 was decommissioned on 2 December 1918.
_(Photo: Private collection)_
A pair of 0-6-0 'Cuckoo' tank engines, identical to the ones which formed the motive power for Armoured Train No 4 from May 1915.
_(Photo: Paul Malmassari Collection)_
### The 194mm TAZ railway guns 1915–1940
Although related to the ALGP and the ALVF, this weapon, of which twenty-three examples were built, belongs in our study because it was completely armoured. The Schneider Works received four separate orders spread out between October 1914 and February 1915, aimed at an entry into service from April 1915 onwards. The gun was a 19cm Model 1870-93 coast-defence gun on coastal mounting Model 1886 PC, in a turret and placed on a 40-tonne chassis of the _Est_ Railway Company. The wagon had an all-up weight of 65 tonnes and could be brought into action in 15 minutes, at any point on the tracks. Range varied from 11.8km out to 18.3km (12,900 to 20,000 yards) depending on the type of ammunition used.
Rail Gun No 1017 _La Revanche_ ('Revenge') at Etrun (5km [3 miles] to the west of Arras) in October 1915. Overhead views are rare, and this one in particular shows the armoured shell replenishment corridor and the upper shutters on the revolving casemate. The firing stabilisers are in their lowered position.
_(Photo: Paul Malmassari Collection)_
This view is interesting as it shows the configuration of a train with each individual gun battery and its ammunition van separated from the rest of the train for safety reasons. Photo taken at Somme-Suippes on 29 September 1915.
_(Photo: Paul Malmassari Collection)_
194mm TAZ Rail Gun No 1018 seen in the 1930s. These artillery pieces remained in service up until 1940, when certain units were captured and put back into use, notably twelve examples by the Italians. The openings in the revolving casemate are clearly seen here: on the left for the gun crew, in the centre for the ammunition.
_(Photo: Paul Malmassari Collection)_
1940: Rail Gun No 1003, one of the twenty-four put back into service, captured by the Wehrmacht and designated as '19.4cm Kanone (E) 486 (f)'. The outer stabiliser pads are here seen removed and stowed in the travelling position.
_(Photo: Paul Malmassari Collection)_
An unidentified armoured engine. The cutaway profile of the front armour is unusual, but the shape of the sliding shutter on the cab side suggests Belgian origins.
_(Photo: Paul Malmassari Collection)_
A mystery photo: The Renault FT light tank, on a flat wagon propelled by the Prussian G8 0-8-0, and which is clearly the centre of attention of the French soldiers, is not in transport configuration. On the back of the photo is written 'Kutina', which is in Croatia, at the time part of the new Yugoslavia. Perhaps this is a photo taken in the period 1919–20 when Communists, including mutinous regiments, rose up against the government. These revolts were suppressed by Serb troops supported by French units from Salonika.
_(Photo: Paul Malmassari Collection)_
### French project to supply armoured trains to Latvia and Romania
See the relevant countries' chapters.
### Armoured trains in the Levant (Syria – Cilicia)
At the end of October 1919, France took over Syria from Great Britain. The Hauran rose in revolt on 20 August 1920. French retaliation was supported by troops carried by trains protected by an armoured train. On 1 October 1920 there were three armoured trains: 'B', commanded by Captain Baumann (who was also in overall command of all the armoured trains), 'S' and 'D' (from the initials of their commanding officers?), which were joined by Train 'A' in December. After such a lapse of time it is difficult to identify them, therefore this list may be incomplete. On 13 March 1921, the London Accords put an end to the fighting, but the revolt of the Djebel Druze in 1925 required once more the presence of three armoured trains on the lines leading to Damascus.
Damascus, 10 September 1926. A 65mm Schneider-Ducrest Model 1906 Mountain Gun, barrel in the rearward position (' _lancé_ '), is in the turret. The two timber shelters also serve as accommodation. Note the shrapnel shell resting on its base, officially forbidden for obvious safety reasons!
_(Photo: Paul Malmassari Collection)_
The artillery wagon (65mm mountain gun) of Armoured Train H'. _La Terreur des Druzes_ ('The Terror of the Druzes') is perhaps the name of the train, while the turret is named _Chouquette_ ('Cutie') a hangover from the 1914–18 War.
_(Photo: Paul Malmassari Collection)_
Armoured Train 'H' at Rayack, 17 May 1927. On the left is an unarmoured rail trolley. Note the makeshift nature of the protection on the wagons.
_(Photo: Paul Malmassari Collection)_
As part of this train photographed at Ezraa in September 1925 we see two armoured wagons assembled by mounting the hulls of captured Ottoman trolleys on bogie flat wagons (see the chapter on The Ottoman Empire).
_(Photo: Paul Malmassari Collection)_
Laffly armoured cars converted into armoured trolleys.
_(Photo: Pascal Danjou)_
An interesting shot taken in September 1925 which shows the smaller diameter of the rail wheels compared with the original road wheels, which often led to transmission and braking problems, and above all meant the speedometer reading was wrong.
_(Photo: Delhalle)_
Finally, several traditional rail trolleys were constructed using the Laffly hull as a base, mounted on a flat wagon, complete with all-round armour plates.
_(Photo: Paul Malmassari Collection)_
For reconnaissance missions, several machine-gun armoured cars were converted into armoured trolleys, firstly by replacing their road wheels, then by surrounding them with armour plates.
After the end of the revolt, these trains were repaired, continually updated and kept in reserve. They would reappear in 1941 during the fratricidal fighting between troops loyal to Marshal Pétain and Gaullist troops.
A view of the other side of Rail Motor No TF2 using a Laffly hull, on the Saïd Naïl-Yeferifa line on 22 March 1931.
_(Photo: François Vauvillier Collection)_
### The Inter-War Period
This period is rich in armoured rail vehicles, but poor in surviving photographic evidence, particularly from 1924 to 1939.
### The armoured reconnaissance trolleys
In the early 1920s it was decided to employ reconnaissance trolleys. A light unarmoured type was ordered in 1924 and an armoured trolley for the standard gauge in 1927. Billard and Renault both proposed design studies for the latter unit, and the Billard proposal was accepted.
**Technical specifications (Billard** Archives)
Height: | 2.6m (8ft 6in)
---|---
Length: | 4.25m (13ft 11in)
Width: | 1.90m (6ft 23/4in)
Wheelbase: | 2m (6ft 63/4in)
Wheel diameter: | 0.6m (1ft 111/2in)
All-up weight: | 5 tonnes14
Motor: | Ballot 4-cylinder petrol; bore/stroke 75mm x 130mm; power 13hp at 1000rpm and 24hp at 2000rpm
Starting: | Crank handle or electric starter motor
Mobility: | The trolley could move equally in both directions, using three gear ratios giving 13, 26 and 40km/h (8, 16 and 25mph) respectively
Autonomy: | Sufficient petrol for a range of 200–300km (124–186 miles) depending on the gradients
Armour: | 7mm
Turret: | Manual rotation
Armament: | Turret-mounted 8mm Hotchkiss machine gun, also adaptable on external pintle for anti-aircraft use
Trials were carried out with the prototype in late 1930, but it seems to have been abandoned in the third quarter of 1932, and disappeared without trace.
The prototype at the Billard Works in Toul, fitted with a dummy machine gun. Note the re-railing equipment carried on the lower hull.
_(Photo: Paul Malmassari Collection)_
One of the photos taken during anti-aircraft firing trials at Bourges, with an 8mm Hotchkiss machine gun installed.
_(Photo: SHD)_
Cutaway profile of the rival Renault trolley proposed for the competitive trials of 1927 and not proceeded with. The weapon is an 8mm Hotchkiss machine gun. The presence of two steering wheels appears strange in a rail-only vehicle, but from the drawing they seem to be connected to the braking system.
_(Document: Renault Foundation)_
General arrangement drawing of the Renault design.
_(Tracing: Paul Malmassari)_
Cutaway profile of the Billard armoured trolley prototype proposed for the design competition in 1927. The handwritten notes suggest the turret was originally to be the type used on the Renault FT tank, whereas a new welded design, with a much lower ventilator cowl, was actually fitted. The machine gun is not shown, and a draughtsman has added a sketch of a possible 37mm TR Model 16 gun as fitted to many FT tanks.
_(Drawing: Billard & Company calculations, undated Plan No 1751, Paul Malmassari archives)_
### Armoured train in China
An armoured wagon was put into service in 1929 in the Shanghai Concession, probably to act as escort for the International Train. Identification of this wagon is difficult (apart from a French source which indicates there were two wagons, but at Canton), and it is probable it was ultimately incorporated in one or other of the Chinese trains.
Sketch of the armoured wagons used in China by the French garrison, to a classic design typical of the period.
_(Sketch: Militärische Wissenschaft und Technische Mitteilungen)_
### Armoured trains in Ethiopia and in the Côte Française des Somalis
During the period 1935 to 1937, the French had watched with concern the incidents involving Italians and Ethiopians which had begun in the Spring of 1935, followed by the Italian invasion of Ethiopia in April and May 1936, and the subsequent revolts and incidents of looting. They were obliged to plan for the protection of the railway by means of armoured trains and escorts, which was put into effect in 1938. With the addition of armoured trolleys the protection of the railway at Djibouti continued up until 1944. However, in the absence of surviving photos, we can only record these basic facts without being able to furnish specific details.
### The Moroccan armoured train
During the Spanish Civil War, the French authorities feared incursions from Spanish Morocco. In August 1938 the project of an armoured train was mooted. General Charles Noguès estimated 'that the creation of such an armoured train in times of peace would have a certain usefulness in the case of operations in Spanish Morocco', and on 23 September, a decision was taken to proceed. This train was to be made up of an armoured 0-6-0 engine (then later a 4-6-0), two Type NN bogie platform wagons, one armed with a 75mm gun (later a 37mm) and the other with a pair of 81mm mortars; two Type UU steel-sided bogie wagons for the engineer element and track repair equipment, plus the command post for the train. Reconnaissance in advance of the train would be carried out by a motorcycle on rails.
Two possible configurations of the armoured train, prepared by Lieutenant Mainguenaud, commanding officer of the _Formation spéciale de chemin de fer_ , in June 1940. To the best of our knowledge this is the only surviving illustration of this train.
_(Drawing: SHD)_
The train, built with the help of the Tangier-Fez Railway Company's workshops, was completed in March 1939, and given the designation _Formation spéciale de chemin de fer_. It was such a well-kept secret that apparently no photograph of the train was ever taken. Following the military collapse in Metropolitan France, the _Formation spéciale_ was decommissioned on 3 July 1940.
### The Second World War (1939–1945)
Several armoured trains of various origins can be identified, in French overseas possessions as well as in Metropolitan France and during the fighting in Germany. They are listed here in chronological order.
### Morocco
As part of the plan for the defence of Morocco, a train armed by the French Navy with two 75mm guns was stationed on the line to the north of Oued Sebou, and took part in the fighting on 8 November 1942 against the Allied landings, in the Green Beach zone.
### Indochina
In this colony 12,000km (7500 miles) from France, the use of 'armoured trucks' had already been envisaged back in 1905. Re the armoured trains used from 1940 to 1945, it is difficult to be specific as to their exact number. It appears that in total there were three armoured trains built: one in Tonkin, which took part in the fighting at Lang Son in September 1940 and was destroyed there during the Japanese _coup de force_ in March 1945; a second train in Cochinchina; a third in Cambodia (Phnom Penh) which was deployed during the hostilities between France and Thailand in the period October 1940 and January 1941.
75mm gun wagon of the Tonkin Armoured Train in February 1942.
_(Photo: Paul Malmassari Collection)_
Photographed by the Americans near Casbah Mehdia to the west of Port Lyautey on 17th May 1943, these two guns were the only ones mounted on railway wagons in Morocco.
_(Photo: NARA)_
In order to provide as wide a field of fire as possible for the 75mm gun seen in the background, a system of hinged platforms and vertical plates has been installed, forming a large firing platform for the gunners while retaining vertical armour protection.
_(Photo: Paul Malmassari Collection)_
The same train on gunnery exercises at P.K. 210 (Marker Km 210) on 28 March 1942. The railway line runs alongside the Red River. The hinged vertical plates for the sides of the firing platform can clearly be seen.
_(Photo: Paul Malmassari Collection)_
The armament of these three trains was identical: one 75mm gun, four heavy machine guns, five light machine guns and one 7-tonne tank, probably a Renault FT from the Tonkin Motorised Detachment and the 9th Colonial Infantry Regiment.
### Captured armoured train used by the 5th Armoured Division
During their entry into Austria in 1945, at Bludenz Station the 5th Armoured Division captured intact a German anti-aircraft train with concrete tubs. Reinforced by a Sherman tank on the leading flat wagon, it was used in reconnaissance sorties on 4, 5 and 6 May.
The anti-aircraft wagons with a central concrete tub are instantly recognisable. Aside from the 75mm gun of the Sherman tank on the leading wagon, the armament consisted of 20mm Flak 38 and 20mm _Flakvierling_ 38.
_(Photo: Commandant Paqueteau)_
### The War in Indochina (1945–1954)
As concerned the railway network, the war in Indochina commenced in 1945/46 by reconnaissance runs to assess the tracks (badly worn), the infrastructure (destroyed by American bombing and sabotage by Vietnamese rebels), and the rolling stock (only 40 per cent of the engines remained in a usable state), following which railway traffic was gradually restarted. The Cambodian network was in the best condition. Essentially the railway network was the only viable means of transport in the colony, and its function was a gauge of economic recovery. To ensure success, the running of railway transport was delegated to the military, working in collaboration with tcivilian railway personnel.
Beginning in February 1946, armoured trolleys were sent out in front of the trains. For their part, the Viet-Minh set to work to destroy the network by laying mines, by tearing up the track, by demolishing the bridges and by simply removing the fishplates from sections of rails. To limit the damage, a system of static defence was established, with watchtowers, blockhouses and fortified stations in particular, to complement the active defences of the trains.
Track disrupted by overturning a complete section: to accomplish this it was necessary only to overturn a part of the track by pulling it with buffaloes or by requisitioning local villagers, and inertia would do the rest. Here the track has been tipped down a slope.
_(Photo: Paul Malmassari Collection)_
The result of a derailment. Clearly the rims of several driving wheels have been damaged, probably by the explosion of a mine.
_(Photo: Michel Protat)_
The Baika Viaduct (central Vietnam) was destroyed on 22 June 1953. At top right one can see an armoured wagon, and in the foreground the roof of the engine cab.
_(Photo: Le Bris, Paul Malmassari Collection)_
This is definitely one of the four Belgian trolleys, seen here at QuangTri.
_(Photo: Major Gricka)_
The first step was to deploy armoured trolleys. Initially (February 1946), Japanese trucks (often armoured) and civilian trolleys were recovered. Then road-rail Jeeps (specially adapted to the metric gauge) were used despite their fragile construction and their light armament. The difference in diameter between their 50cm (1ft 7¾in) rail wheels and the 70cm (2ft 3½in) road wheels caused the motors to over-rev.
In view of the deficiencies evident in the existing vehicles, the French Army studied a project for an armoured trolley or rail tractor, with the following modern features: duo-directional, traction capability and turret-mounted guns, but this project would not be built. Equally a study of a Dodge 4x4 on rails was not followed up. In late 1949, four trolleys of Belgian manufacture were received by the CFL and entered service after they had been fitted with armour and armament.
One of the rare surviving photos showing a trolley opening up a route in 1946 or 1947. It is not possible to identify its type.
_(Photo: ECPA-D)_
Jeep trolley in the region of the Col des Nuages, Lien-Chien Station in 1947. These machines remained in service up until late 1953. The 1990 book by Patrick Meney, _La Rafale_ , includes a love scene which takes place in a Jeep running blind – a completely hair-brained notion which brings discredit to the book which is elsewhere quite vague.
_(Photo: Jean-Gabriel Jeudy Collection_ 22 _)_
### Billard Trolleys
The Billard Works delivered at least three Type D 50 D 5 Trolleys for the metric gauge and six others designated D 50 D 5 V. Compared with the standard production trolleys, they had a reinforced chassis, a petrol tank capacity increased to 100 litres (26.5 gallons), a floor armoured with 8mm plate, and a more powerful Panhard motor.
### The introduction of the 'Rafale' to ensure the safety of train journeys
The ' _Rafale'_ was a traffic procedure involving the grouping together of two to five passenger and goods trains to run one after the other at 20km/h (12.5mph) or 25km/h (15mph) when preceded by an armoured trolley. A ' _Rafale_ ' would be composed of a 'pilot' or 'main' train, then trains ' _bis_ ', ' _ter_ ' and ' _quater_ ', so named for the firing of successive rounds from an automatic weapon in a ' _rafale'_ (volley or burst of fire). The pilot train would be the most heavily armed (Bofors wagon, armoured car wagon etc).
Type D 50 D 5 V trolley at Quang-Tri, fitted with anti-grenade wire mesh.
_(Photo: Major Gricka)_
The final version delivered to Indochina, which sports a camouflage scheme, an option rarely used in this theatre and all the more surprising because it features a representation of a railway track, as on certain Soviet or Spanish armoured trains.
_(Photo: ECPA-D)_
On 24 January 1949, this safety flat wagon, fitted with a cabin armoured with steel rail sleepers, was derailed between Hué and Tourane. On the right is the front end of a Jeep trolley.
_(Photo: Paul Malmassari Collection)_
An original drawing of the French Billard armoured trolley for Indochina.
_(Builders' drawing: Paul Malmassari Collection)_
But a ' _Rafale_ ' was not capable of repulsing a major attack on its own, and it was therefore necessary to also deploy patrolling armoured trains. The first of these was built in Saigon and entered service on 16 December 1947. It had an engine and just two wagons. In 1948, the second armoured train was built with the help of the Foreign Legion, and the workshops of the C.F.I., under the command of Captain Raphanaud (who was not a member of the Legion).
### The different armoured wagons: gun wagons, mortar wagons, command wagons etc.
The initial protection schemes added from mid-1947 were minimal (even using timber), but were followed by more solid and more efficient armouring. The safety wagon at the head of the train and, if possible, at the rear, had an armoured shelter which allowed the detection of track damage and mines.
Heavy firepower was provided by the gun wagons, armed with tank turrets, Coventry armoured car turrets, mortars and AA guns, and the following photos show several examples, demonstrating the inventiveness of troops confronted by two adversaries: the Vietnamese enemy and the scarce resources allocated by the home country in the process of reconstruction following the Second World War.
Type D wagon serving as control wagon for the pilot train of the _Rafale_. These platform wagons began to enter service in January 1947.
_(Photo: Le Bris, Paul Malmassari Collection)_
Type MM Wagon armed with a 40mm Bofors, put into service on 5 April 1947 on the line to Nha Trang. It was placed at the tail of the train and the flat wagon which followed normally ran unloaded.
_(Photo: Le Bris, Paul Malmassari Collection)_
Another version of the Bofors wagon which bears more than a passing resemblance to the Flak wagons with their central concrete tub.
_(Photo: Michel Protat)_
A third version of the Bofors wagon, here built up inside a high-sided Type HHff No 15415 bogie wagon.
_(Photo: Yves Bernard)_
Type HH wagon with the turret of a Coventry armoured car, in the armoured train of the 4th Regiment, who had the habit of christening this 'rail tank' with the name of a memorable battle.
_(Photo: Yves Bernard)_
The use of turrets from tanks or armoured cars had two advantages: on the one hand they were protected by armour 14mm thick, superior to the available armour plates, and secondly they allowed all-round traverse of the arms carried. On the Cambodian rail network, ex-Japanese Type HA-GO tanks were also used (see the chapter on Japan). For indirect fire, 60mm then later 81mm mortars were used, which allowed the gunners to hit the enemy firing from trenches or behind cover. In the case of trains following one closely behind the other, in the ' _Rafale_ ' configuration, they were also able to lob mortar rounds over the preceding train(s).
Type HHyf wagon built around a Coventry armoured car, with reinforced sides. The curved bands serve to deflect the cables stretched between trees to decapi-tate the unwary.
_(Photo: Yves Bernard)_
Recoving the wreckage of a Coventry wagon which has been blown up by a mine. Note that while the turret is standard (less its 2pdr gun), the armoured car hull has been lightened as much as possible.
_(Photo: Yves Bernard)_
One of the four Type H wagons built in June–July 1949 with APX turrets from H 39 tanks (37mm Model SA38 gun), seen here on the Mandarin Road between the Col des Nuages and Tourane. The H 39 tanks had been captured in 1940 then re-used by the Germans who had modified the commander's cupola.
_(Date unknown, photo: Paul Malmassari Collection)_
A fine shot of a mortar wagon (here a 60mm mortar, with a .303in Bren LMG), showing also the ammunition and equipment storage. As the mortars were mounted in elevated casemates, the remainder of the wagon could be put to other uses, and it is therefore difficult to distinguish between the different types of armoured wagons by appearance alone.
_(Photo: Michel Protat)_
In this view of an armoured train in central Annam, the intermediate flat wagon carries a shelter surrounded by aerials. To the right, a Type HH wagon is armed with a Coventry turret and on the left is perhaps a control van.
_(Photo: Michel Protat)_
GGc van of the first type to be built, in armoured train _Sud_ of the 2nd REI (2nd Foreign Legion Infantry Regiment). The wooden exterior is doubled by an internal metal skin.
_(Photo: Le Bris, Paul Malmassari Collection)_
Communications, whether to command posts, air support and stations or to other trains in the ' _Rafale'_ and to the sections of the same train, were from the command wagons. In Indochina, several types of bogie wagon and van were used, all with a built-up casemate, and which from the outside were difficult to distinguish from the mortar wagons.
HH 15306 bogie wagon in Cochinchina with a central casemate for a mortar pierced by loopholes for firing fore and aft along the line. On the second wagon is a MAC 31 machine gun.
_(Photo: Promotion Victoire via General Nicola-Vullierme)_
This shot gives a good idea of the dangers faced by the train crews, with dense vegetation which allowed the Viet-Minh to approach to within a few yards of the trains and then quickly vanish.
_(Photo: Promotion Victoire via General Nicola-Vullierme)_
An armoured van, well-supplied with firing loopholes which were always found at the corners, and which could be closed from the inside. On the casemate roof one can see opening vents, probably sheltering a mortar.
_(Photo: Yves Bernard)_
Despite the increased difficulty of re-railing these bogie vans and wagons after a derailment, their much longer hull sides allowed for increased firepower.
_(Photo: Yves Bernard)_
A typical view of a _Rafale_ , with the armoured wagons inserted in a random manner in the middle of the train. The escort coach on the left is Type GGy No 12803.
_(Photo: Institut du monde du travail)_
The armoured train of the 4th Dragoon Regiment in 1951–2, showing a classic wagon layout (which could be quickly varied). The engine is out of sight to the left, in front of the tank wagon, and from a distance the armoured train presents an appearance quite similar to that of a civilian rake.
_(Photo: Yves Bernard)_
### The Madagascar Campaign
On 29 March 1947 an insurrection began, which included the railway network among its targets. The main railway stations were fortified and 'protected trains' carried out patrols on the TCE and the MLA. Although lacking the firepower and protection of contemporary European armoured trains, they ensured the free circulation of traffic up until the end of the insurrection in 1948.
Quite adequate for fighting the Madagascan rebels, these patrol trains were far removed from the combat potential of the Russian and German types of the recent Second World War. The machine gun on the leading wagon is a Browning .50 Cal (12.7mm).
_(Photo: Private collection)_
### The War in Algeria
The French railways in Algeria were permanently threatened by rebels, and the seriousness of such threats varied from year to year. The Press regularly alluded to the need for armoured trains, for example the edition of 5 July 1896 of _Le Monde du travail de l'Afrique Française_ , in which a certain Francis Laure considered the use of armoured trains to be the only method of overcoming the Touaregs.
The war in Algeria began on 1 November 1954. At first the insurgents concentrated their attacks on individuals, and for the first year of conflict the communication infrastructure was left unaffected. Then the attacks against the railways began in earnest, in the manner typical of pure terrorism. As Algeria was a French Department, the authorities could not let the insurgents gain the upper hand over the circulation of passenger and goods traffic. There were over 4500km (2800 miles) of track in use, with regular timetables and published operating procedures, which allowed the terrorists to plan their attacks, but at the same time the economic prosperity of Algeria depended on its railways.
Derailment of a passenger train by a mine on 22 September 1957 at Km Post 135 + 200 on the Oran-Oujda line.
_(Report of the Police Aux Frontières at Tlemcen)_
An example of the armoured window openings applied to a derailed de Dietrich diesel-electric 060 YDA railcar of the S.N.C.F.A. (Algerian National Railway company).
_(Photo: Nepveux)_
Diesel locomotive 060DC-3 seen at Blida in September 1957, with all-round armour protection for the driving cabs.
_(Photo: Gérard Pouillé)_
Algerian Railways Alsthom diesel-electric locomotive BBB 060 YBD bearing the company's crest. The cab is armoured, and the holes in the buffer beam indicate that the locomotive was originally fitted with buffers for use on the main line, before being modified with central coupling knuckles.
_(Photo: Private collection)_
A rare shot of a steam engine on the metre gauge, a 2-8-2 named _MacArthur_.
_(Photo: Paul Malmassari Collection)_
An escort van partially-armoured with 7mm plates, lying beside a de Dietrich railcar after a successful ambush.
_(Photo: ECPA-D)_
The use of vehicles repatriated from Indochina was considered for the narrow-gauge lines. Several narrow-gauge armoured trolleys had been recovered and in early 1956 they were undergoing overhaul. They would serve as sweepers preceding trains. The driving cabs of the locomotives and railcars were also fitted with armour protection, commencing with the region around Constantine. In addition, a certain number of wagons and vans included in the rakes of trains operating in danger zones, or attached at the tail end of mineral trains, were also armoured.
In November 1955 the defence of the railway network was set in motion in earnest, with the creation of a battalion-sized specialist unit, supported by military specialists from the Algerian Railway Company. This move allowed the creation of an escort unit of Scout Cars (six pairs of coupled Scout Cars and six groups of trolleys of the C.F.A.), and three train escort units (or twelve sections, in specialised wagons of the C.F.A.). In summary, the fight against saboteurs was the role of the Army (surveillance and intervention by armoured train), and sweeping the track in advance of trains fell to the C.F.A. using the Billard Trolleys, the Dodge 4x4s on rails and the Scout Cars on rails.
By way of an example, the 587th Train Battalion was charged with three missions. The first was to ensure the regular running and the protection of the transport system. The second was to employ mobile means of sweeping, surveillance and intervention. The third and final mission consisted of supplying escort groups of up to a dozen men led by an NCO, initially in wagons protected by sandbags or anti-mine carpets then, from February 1956, in armoured wagons.
What means were available to these units? In chronological order, the first seven Billard Trolleys were put into service at the end of 1955. The initial experience gained with these was used to improve subsequent vehicles.
Two views of the first Billard trolleys, with armour protection which followed the form of the basic vehicle. The armoured grille featured at the front end of all these trolleys. The opening to the upper left of the grille allowed a wider field of vision to the driver. Whether military or civilian, all these armoured trolleys carried a C.F.A. serial number.
_(Photos: Paul Malmassari Collection)_
### Scout Car trolleys
Next, M3A1 Scout Car trolleys were introduced. They had been converted by the workshops of the C.F.A. to run on rails. Well armed but slow and lightly armoured, their main drawback was that they had only one reverse gear. The solution was therefore to couple two Scout Cars back-to-back, or to pair one with a Billard Trolley.
To make up for the lack of a turntable, this coupled unit of Scout Car and Billard trolley nicknamed the ' _Escargot'_ or 'Snail' (by analogy with the train called ' _Tortue'_ or 'Tortoise') functioned with the Scout Car at the front driving forward, and with the gearbox in neutral when towed in reverse.
_(Photo: Tallabardon)_
The front wheels of this Scout Car trolley have been fitted with additional armour. The shield is that of the 587th Transportation Battalion.
_(Photo: Paul Malmassari Collection)_
The unditching rollers appear to have been removed during the final years of the war in Algeria. Note the .50 Cal (12.7mm) machine gun which is the main armament. The secondary armament of the Scout Car was either one or two .30 Cal (7.62mm) US machine guns.
_(Photo: Paul Malmassari Collection)_
The sad fate of a Scout Car, its wreckage recovered in a bogie wagon.
_(Photo: Guy Chabot, 3rd Zouaves Association)_
### Dodge trolleys
The Dodge Weapons Carrier WC51 converted to a railway trolley was used from February 1956 up until the end of the war. The rail conversion had been carried out for the C.F.A. and for the armed forces by two firms: VERARO from 1951 and Desquesnes & Giral.
An early version of the Dodge Rail Trolley, with no side door.
_(Photo: Paul Malmassari Collection)_
Dodge trolleys of the Oran Army Corps, here seen coupled in pairs back-to-back to allow for travel in both directions without using a turntable, followed by a Scout Car.
_(Photo: All Rights Reserved)_
### Jeep trolleys
Eleven Jeeps were converted for the metric gauge between May and November 1959, and they were sent to the zone to the south of Oran to form a surveillance screen against terrorist incursions. Although far from perfect, all the converted vehicles continued in service right up until the end, as there were never enough Billard trolleys to meet all operational requirements.
Armoured Jeep trolley of the 2nd Company, 3rd Zouaves Regiment. Conversion for the standard gauge was not practicable, as it would have entailed fitting extensions to the brake drums which would have weakened the axles. Note the much larger diameter rail wheels compared with the Jeeps used in Indochina.
_(Photo: ECPA)_
### Later Billard trolleys
In addition to the machines of the C.F.A. mentioned earlier, the first additional trolleys were the metric gauge Type D 50 D 5 V machines repatriated from Indochina, which were received in poor condition.
Six basic types of Billard Trolleys were used:
– D 50 D 5 V (initially for Indochina, then Algeria).
– D 50 D 5 (Algerian version).
– D 50 D 4 B (built as an armoured version only, for the standard and metric gauges).
– D 50 D 4 (armour protection added).
– D 50 D 6 B (armour protection added).
The complete vehicle park of twenty units was shared out between the C.F.A. and the Army.
Armoured Billard Type D 50 D 5 trolley (standard gauge).
_(Photo: Paul Malmassari Collection)_
Front view, which shows that the armour protection was quite simple and followed the form of the original civilian bodywork. This is a Type D 50 D 5 trolley of the 587th Transportation Battalion.
_(Photo: Paul Schneider)_
The trolleys continued to evolve during the course of the conflict, but it is difficult to know whether this evolution resulted from the requirements of the Army High Command or from the availability of civilian chassis at the Billard factory. The final armoured versions were the Type D 50 D 6 B, built for both the standard and metric gauges, and which profited from the experience gained with the Type D 50 D 4. In the final models the 7mm armour plates were simply fastened to the body in such a way that the trolleys could easily be converted to civilian configuration.
A builders' drawing of the D 50 D4 B for the standard gauge.
_(Drawing: Paul Malmassari Collection)_
Armoured Billard Type D 50 D 4 B trolley (metric gauge). The roof cupola armed with a .30 Cal (7.62mm) Browning machine gun is typical. The Type D 50 D 4 B Trolleys were designed as armoured versions from the outset.
_(Photo: Alain Laffargue)_
Armoured Billard Type D 50 D 4 B trolley for the metric gauge.
_(Photo: Paul Malmassari Collection)_
This Type D 50 D 6 B had a buffer beam which differed slightly from older models such as the trolley seen in the previous photo.
_(Photos: Paul Malmassari Collection)_
Armoured Billard Type D 50 D 6 B, seen from the rear. The windows are in 6mm plexiglass and the floor is formed from long bags filled with sand to provide a minimum of protection against mines. Note the searchlight attached to the machine gun.
_(Photo: Paul Malmassari Collection)_
This trolley was the victim of an attack on the Oued Tebarit bridge, and has fallen 20m (65ft).
_(Photo: Tallabardon, 3rd Zouaves)_
### Radio-controlled trolleys
In a letter dated 12 April 1958, the Director General of the Algerian Railways admitted to being 'shocked by the degree of damage caused to the sweeper vehicles when they run over a live mine', and he expressed a wish that studies be undertaken into the production of a vehicle rolling with no-one on board, in other words a remote-controlled machine. In actual fact, the previous year the Billard Company had drawn up such a design to comply with an SNCF study of the use of shunters in marshalling yards. Two basic considerations for military use were, firstly to minimise the vehicle's profile so as to not overly obscure the view of the track when its controlling trolley followed close behind, and secondly to provide armour protection for all vulnerable parts so the controlling trolley could fire on the whole forward zone, which could involve rounds striking the radio-controlled trolley. It was planned to carry ten tonnes of ballast (worn-out rails) over each axle to ensure the detonation of mines. After several trials, ten trolleys were ordered, and the first was delivered on 10 April 1959. However, the results were far from satisfactory, and it appears that only two of these trolleys were used successfully.
The initial design proposed by Billard. The superstructure would be modified, but the overall dimensions of the chassis would be retained in the production version.
_(Builder's drawing: Paul Malmassari Collection)_
Billard Radio-controlled trolley (initial configuration). The armoured flap of the receiver unit has been left open.
_(Photo: ECPA-D)_
In the course of the entire war in Algeria, between 190 and 201 armoured trolleys of various types had been employed, which was the greatest number of such vehicles of all the countries engaged in anti-guerrilla struggles.
The production vehicle as delivered to the French army. The plan view is missing from the archives.
_(Builder's drawing: Paul Malmassari Collection)_
Billard Radio-controlled trolley equipped with an armoured cab. The obvious drawback of this configuration was that the cab obscured the view of the track from the following trolley or train.
_(Photo: ECPA-D)_
### Armoured trains in Algeria
The first armoured train was built in Algeria in October 1956. Traction was provided by a 400hp shunter, enabling it to run at 35–40km/h (22–25mph). In 1957 the Army Engineers in Algeria began construction of an armoured train (ultimately nicknamed ' _Tortue'_ or 'Tortoise') for the 587th Transportation Battalion. The four drawings below by the author show elements of the 'Tortoise'. In total six or seven armoured trains would be built.
Algeria would be the last theatre of war in which France used armoured trains and trolleys of indigenous design. But other countries or regions in conflict have profited from the French experience: Mauritania, Portugal, the Bosno-Croat Federation etc, which we describe in the relevant chapters.
Command van during a mission to escort a goods train (1st Company, 3rd Zouaves Regiment). The vehicle on the far right could be a Billard trolley, but the structure on its roof remains a mystery.
_(Photo: Tallabardon)_
Two infantry firepower wagons of an armoured train of the 587th Transportation Battalion, in an atypical configuration.
_(Photo: Dominique Loiseau)_
Here the armoured train has been split up and wagon TTuw 25483 has been included as the escort of a goods train. Note that the cab of diesel-electric locomotive 040-DC-13 has been armoured.
_(Photo: Dominique Loiseau)_
An escort van crushed between its train and the locomotive.
_(Photo: Guy Chabot, 3rd Zouaves Association)_
M3A3 Stuart light tank mounted on a two-plank wagon. A photo of this combination in use in Algeria appears in the Introduction.
_(Drawing: The Author)_
**SOURCES:**
**Archives:**
Guy François.
Paul Malmassari.
Cercle généalogiste de la SNCF (album Emile Moret et Eugène Hallard)
Carton SHD 16 N 755.
**Books:**
Chabot, Guy, _Le Plus sale boulot – Guerre d'Algérie 1956-1962_ (Coulommiers: Dualpha Editions, 2006).
François, Guy, _Les canons de la victoire, tome 2 : L'Artillerie lourde à grande puissance_ (Paris: Histoire et collections, 2008).
_Histoire militaire de l'Indochine française des débuts à nos jours (juillet 1930)_ (Hanoi-Haiphong, 1931), Vol 2, p 292.
Jeudy, Jean-Gabriel, and Tararine, Marc, _La Jeep, un défi au temps_ (Paris: Editions Presse Audiovisuel (E.P.A.), 1981).
Malmassari, Paul, _Les Trains blindés français 1826-1962, étude technique et tactique compare_ (Saint-Cloud: éditions SOTECA, 2010).
**Conferences:**
Malmassari, Lieutenant-Colonel Paul, ' _La Défense dynamique des voies ferrées contre le terrorisme: l'exemple français'_ , actes du symposium Armée et technologie, Pully (Switzerland) 16 to 20 March 2004, pp 535–54.
**Films:**
<http://www.britishpathe.com/video/french-gun-battery-onrailway/query/armoured+train>
_'Les trains vus par le cinéma des armées'_ , ECPA-D, 2012, 61 min. Kowal, Georges, ' _Avec la Rafale'_ , 1952, ref. SCA No 0050.
**Journal articles:**
Aiby, Lieutenant André, 'L'emploi des trains blindés', _La Revue d'Infanterie_ Vol 83 (November 1933), pp 775–95.
Dufour, Pierre, '1948 Rafale contre Viet-Minh', _Hommes de guerre_ (January 1989), pp 27–32.
Dupont, Michel C, 'Trains blindés sur voie métrique en Indochine', _Le Rail_ No 7/8 (December 1988), pp 72–5.
François, General Guy, 'Les Trains blindés français de 1914', _Ligne de Front_ No 54 (March-April 2015), pp 20–9.
Le Bris, Pierre, 'Les Chemins de fer du Viet-Nam de 1945 à 1954', _VAUBAN, bulletin de liaison du genie_ No 96 (3rd Quarter 1990), pp 6–11.
M., Captain, 'Les Trains blindés', _La France militaire_ No 11795 (23rd May 1924), p 1.
Medard, Frédéric, 'Le soutien de l'armée française pendant la guerre d'Algérie', _Revue Historique des armées_ No 4 (2002), pp 25–36.
Montgéry, M. de, _'_ Observations de M. Paixhans, avec les répliques de M. de Montgéry, au sujet de deux ouvrages intitulés: Nouvelle Force Maritime', _Bulletin des sciences militaires_ Vol 3 (1826), pp 218—19.
Neviaski, Captain Alexis, 'L'audace du rail: les trains blindés du Sud-Annam', _Revue Historique des armées_ No 234 (2004), pp 25–36.
**Novels:**
Meney, Patrick, _La Rafale_ (Paris: Denoël, 1990).
Tauriac, Michel, _La Vallée des Dieux_ (Paris: Flammarion, 1989).
**Website:**
<http://www.forum-auto.com/automobiles-mythiques-exception/voitures-anciennes/sujet388213.htm>
Two photos showing the opposite ends of armoured train ' _Tortoise'_ of the 587th Transportation Battalion. Although the wagons are of the same type, there are slight differences in the markings and also the position of the electric lamp sockets.
_(Photos: Dominique Loiseau)_
. In addition there were the projects of Baron Rystany (1864), M. Bukaly (1867), and M. Evrard (1868).
. For further details of this project, see the chapter on Great Britain.
. Michel Body, _Les Chemins de Fer dans leurs applications militaries_ (Paris: Eugène Lacroix, 1868), pp 21–2.
. Meudon was the workshop created by Napoleon III in 1860 to carry out secret research projects.
. Previously, in 1877 Mougin had proposed 155mm guns on disappearing mountings on rail platforms.
. Also described in ' _Panzerzug', Polytechnische Schau_ , 1916, Band 331, Heft 19, p 299.
. To complete the story of the overseas armoured trains, we must mention the armoured wagons built in Abyssinia in 1916, of which we have unfortunately found no photos.
. TAZ = _Tous AZimuts_ (all-round fire).
. ALGP = A _rtillery Lourde à Grande Puissance_ (High-Powered Heavy Artillery).
. ALVF = _Artillerie Lourde sur Voie Ferrée_ (Heavy Railway Artillery).
. Train 'F' at Damascus (Baranké Station), Train 'G' at Rayack, plus Train 'C'.
. Concerning projects, in October 1924 a certain M. Mescherinoff proposed an armoured road-rail tractor unit. As it lacked workable technical details, the Army High Command did not follow up his proposal (SHD W 872).
14. Report No 6, meeting of 1 December 1931, dealing with firing trials with a machine gun on an armoured trolley (C.A.A. file not found).
. Noguès commanded the XXIX Army Corps in Algeria in 1933 then from 1936 to 1940, he was resident general in Morocco.
. Service Note No 464/MC, of 3 July 1940, 3 H 1264/5 (SHD).
. In October 1942 the British intelligence service at the post of Bathurst in the Gambia reported the presence of an armoured train, armed with twelve machine guns, on the Dakar-Thiès line.
. During the Liberation fighting, in order to attack the German garrison at Ussel, plans were made to armour the 'Tacot' (the name for the Transcorrézian train), but this was never carried out.
. Three landing beaches were designated by the colours Blue (South), Red (North) and Green (Centre).
. Order of battle of the French troops in Indochina, 23 November 1943; Order of battle of the troops of the Indochina Group, May 1944 (10 h 80/D1, SHD).
. Paul Malmassari, _Les Trains Blindés 1826–1989_ (Bayeux: Editions Heimdal, 1989), p 199.
22. From Jean-Gabriel Jeudy and Marc Tararine, _La Jeep, un défi au temps_ (Paris: Editions Presse Audiovisuel (E.P.A.), 1981), p 182.
. 'V' for 'Vietnam'. Three were delivered on 7 February 1953 (Nos 89, 90, 91), and the following three on 18 April 1953 (Nos 94, 95, 96). Notes taken by the Author at the SOCOFER Works in 1983.
. A personal perspective has come down to us in the novel _La Vallée des Dieux_ by Michel Tauriac. He travelled several times on ' _Rafales_ ', and his eye-witness testimony worked into the narrative of his novel brings to life the dry facts reported in the Archives.
. These Type MM or D bogie flat wagons were also called 'control platforms', 'shock wagons' or 'protection chassis'.
. Range of the Bofors at high elevation was 9830m (10,750 yards) but British ammunition normally self-destructed at 3200m (3500 yards); max AP range of the Ordnance 2pdr (40mm) QF in the Coventry turret was 1370m (1500 yards) but no HE shell was ever mass produced, the turret relying on its coaxial 7.92mm Besa MG.
. The Type HH wagons, wood or steel high-sided bogie wagons 10.1m (33ft 1½in) long, were principally used for wagons with a central armoured casemate such as for armoured cars, mortars or command posts.
. The high-sided wagons Type H, 5.5m (18ft) long were specially used as gun wagons with turrets from armoured vehicles, and are not to be confused with the letter 'H' of the tank which corresponded to 'Hotchkiss'.
. TCE = _Chemin de fer Tananarive-Côte Est_ ; MLA = _Chemin de fer Moramanga -Lac Alastre_.
. In December 1956 it was noted that '... the rebels are beginning to attack rail traffic' (Note from the military transport HQ in French North Africa to the Colonel who was Transport Director of the 10th Military Region, 1 H 2177/D1, SHD)
. 2227km (1384 miles) as against 2113km (1313 miles) of standard-gauge track.
. Letter from the Director of the C.F.A. to the Governor General of Algeria, No IA8/67-15 dated 17 November 1955 (1 H 2177, sleeve 'Notes CGA 1955-1956', SHD).
. Their armament consisted of a semi-automatic pistol, an LMG, five rifles and a rifle-grenade launcher.
. The special pneumatic tyres on flanged wheels were produced by Michelin (as used on their _Micheline_ railcars).
. VEhicule RAil-ROute (Road-rail vehicles), the former Sibille company.
. 'V' for 'Vietnam'.
. One of these trolleys is still in existence at the time of writing.
. This scenario was far from uncommon in anti-guerrilla actions: in Indochina, tanks and even armoured railway wagons had been obliged to fire on their fellow units to sweep them clear of attackers who had scrambled on top of them.
## GEORGIA
### THE FIRST REPUBLIC: ARMOURED TRAINS (1918–1921)
Created following the break-up of the Russian Empire, Georgia declared independence on 26 May 1918, supported by several countries which opened embassies and consulates. Already in January 1918, the nascent republic had put into service eight armoured trains under the command of a certain Valodia Goguadze, a Social Democratic Party activist. From January to March 1918 they intervened in support of the troops falling back before the Ottomans, then in March–April during the battles against the Turkish Army at Adjara, Guria and Borchalo Mazra. Their final actions were against the Bolsheviks in 1920–1 when a total of some fifteen armoured trains were mobilised. The first Georgian Republic came to an end when, without having surrendered, it was incorporated as an autonomous republic within the Soviet Union.
**SOURCES:**
<https://icres.wordpress.com/2014/03/20/exhibition-soviet-occupation/>
One of the Georgian armoured trains. An identical train, christened _Republican_ , was commanded by Valodia Goguadze.
_(Photo: Paul Malmassari Collection)_
. The government in exile was based in France up until 1934.
## GERMANY
### ARMOURED TRAINS, RAILCARS AND TROLLEYS 1900–1945
At the beginning of the twentieth century, the German Army was no stranger to the armoured train, having had the chance to observe the French versions during the War of 1870–1, but despite the widespread reports of armoured trains during the Boer War, it took some time for the Germans to recognise the advantages this weapon could bring to them. Their country being sited at the heart of Europe, in time of war they would need to have the ability to rapidly move their forces between the various fronts. The only means of doing this was by the railway network, and therefore means had to be put in hand for its protection. A glance at a map showing the length of the front lines extending from the north to the south of Poland then on into the Ukraine, and the extent of the railway network inside Germany proper, would justify the deployment of armoured trains, the only force capable of intervening rapidly over the long distances involved, at a time when motor transport was neither fully developed nor highly regarded in military circles. Then during the Second World War, the armoured trains were the only effective means of countering the depredations of roaming bands of partisans. The German Army, with the bit between its teeth, wholeheartedly pursued the armoured train adventure, in the process continually perfecting or planning improvements up until the final defeat of the Third Reich.
### The First German Armoured Trains
Following the Boxer Rebellion, the foreign Legations in China drew up a co-ordinated defence plan, and at Tsingtao the Germans commissioned a small artillery train with two wagons mounting naval guns.
Postcard showing the German armoured train in China in 1900, with its two 8.8cm F.K. guns.
_(Postcard: Paul Malmassari Collection)_
In 1904, the revolt of the Herero tribe in German South-West Africa led to the construction of a narrow-gauge armoured train. Under the command of a Lieutenant Bülow, the train was armoured at Waldau Station with corrugated iron sheets and sacks filled with earth; its armament comprised a 37mm revolver cannon from the landing detachment of the gunboat _Habicht_ , plus the personal arms of the troops carried on board.
PZ III, one of the 1910-Type armoured trains seen at Lille in December 1914. The armoured wagons were converted from 40-tonne Type Omk(u) mineral wagons. One wagon was always equipped with an armoured command and observation tower, for the train commander.
_(Photo: Paul Malmassari Collection)_
Armoured Class D XII engine built by Krauss at the turn of the century. It is not known whether this prototype was included in the 1910 Programme, but it had a relatively modern outline, even if the vertical arrangement of its armour plates betray its era.
_(Photo: Krauss-Maffei)_
Apart from these local improvisations, in 1910 official German documents foresaw the necessity of building armoured trains in the case of hostilities. Based on the observations of Count von Schlieffen who had studied the Boer War, the Army High Command placed orders for thirty-two armoured trains. However, the financial situation that year obliged them to reduce the order to just fourteen. By the outbreak of war, manoeuvres carried out with the first trains had given some idea of their value. The standard composition of each train was:
– an armoured engine positioned centrally, in general a Class T 9.3 but also Prussian Class G 7.1, or a Class T.3 (as allocated to PZ IX), etc.
– twelve wagons protected against small-arms fire.
– an observation tower fitted on one of the wagons.
The trains required twenty-four hours' notice to prepare them for operations, crewed by railwaymen and soldiers from the regular army, up to a company in strength with four machine guns.
### The First World War
In Belgium several improvised trains were built and used by the right wing of the invading armies. In September 1914 an 'intervention section' was created, its mission being to fight franc-tireurs, cyclist troops and Allied cavalry. One armoured train, built by the Engineers, participated in these actions, one of which involved foiling a Belgian 'phantom train'. If the employment of these armoured trains in Belgium could be qualified as satisfactory, on the other hand they were criticised for their thin armour and weak armament. The crews asked for internal telephones and searchlights. Beginning in November 1914 these defects were remedied, and in 1915 the number of trains reached the fourteen planned five years earlier. In that year, the front stabilised in the West, and the war of movement continued in the East. Out of the fourteen trains, seven were demobilised in 1916, and the seven others retained only their engineering crew members.
In 1916, Panzerzug I and II, which had been sent to Romania, received a new wagon armed with a 76.2mm Putilov 02 in an armoured casemate pivoting on a set of rollers.
_(Photo: Paul Malmassari-DGEG Collection)_
Between 1916 and 1918 a certain number of armoured trains were built to carry out different missions depending on the front where they were engaged. Some wagons now carried Gruson 53mm portable fortress turrets and others were roofed over.
_(Photo: Paul Malmassari-DGEG Collection)_
The Prussian Class T 9.3 was a tank engine, and the two additional unarmoured tenders were attached to increase its range. The practical speed of a Panzerzug in fighting configuration was in the range of 25–30km/h (15–18mph), whereas on the main lines, with the engine at the front, they could reach 60km/h (38mph).
_(Photo: Paul Malmassari Collection)_
Photographed in Hamburg in January 1918, this Class T 9.3 engine is armoured overall, which distinguished it from the other standard engines. It was attached to either PZ II, V or VII.
_(Photo: Paul Malmassari Collection)_
The leading wagon of PZ III, converted from a 20-tonne mineral wagon. This train would be renumbered as PZ 54 in March 1919. Note the 37mm revolver cannon with a 180-degree field of fire. It is fitted with a front armour plate and muzzle cover with retaining chain, just as on the smaller Maxim 08. Also note the lateral machine gun in the upper casemate. The anti-aircraft machine gun is a 7.62mm Maxim which was not part of the original armament of this train.
_(Photo: Paul Malmassari Collection)_
Patrol train on which elements of armour can be seen, such as on the engine cab, and the wagon sides, photographed on 19 June 1918 at Potiflis.
_(Photo: Paul Malmassari-DGEG Collection)_
The German advance into the Ukraine involved building four trains for the Russian broad gauge, of differing design and with variable armour disposition, and also with the addition of captured wagons. Their armament was either German, using the 7.7cm field gun, or Russian with the 76.2mm.
On other fronts, armoured trains served in the German colonies: in the fighting in Cameroon against the French troops under General Dobell, a wagon was converted and used notably to defend the bridge over the Dibamda with its single machine gun. To the best of our knowledge, no photo of it was ever taken. In Palestine in 1918, German personnel of the _Asien-Korps_ formed part of the crews of Turkish armoured trolleys (see the chapter on the Ottoman Empire). During the Finnish War of Independence, the Germans used only one train, captured from the Reds probably at Helsinki on or around 13 April 1918, armed with two Russian guns and four machine guns.
Armoured wagon captured during the advance into Russia and reused by German troops to the east of Gomel.
_(Photo: Paul MalmassariDGEG Collection)_
A rare vehicle during the First World War, this armoured trolley captured by the Russians is an armoured Daimler lorry converted for use on rails. Note the firing ports in the rear side plating.
_(Photo: Wolfgang Sawodny Collection)_
### Post-War Conflicts
### The German Revolution and the Civil War
Humiliated by the terms of the Treaty of Versailles, undermined by their defeat and declining social conditions at home, Germany was easily destabilised by the export of the Bolshevik Revolution in Russia. Strikes, troubles and acts of sabotage multiplied, and led to the reactivation of the old armoured trains and the improvisation of many others. In late 1918, all the armoured trains, irrespective of the front where they were situated, were renumbered, beginning with 20 and ending in 55, plus several Roman numerals. The deployment of the trains became general in March 1919, when they operated principally in Halle, Magdeburg, Braunschweig, Leipzig and Munich. On the 'Red' side, in Leuna, where the factories were completely surrounded on 28 March 1919, a rudimentary armoured train was built by the revolutionaries, but it was captured intact.
The armoured train of the 'Leuna Arbeiter', converted from hopper wagons during the uprising inspired by Max Hoelz in Saxony between 23 and 29 March 1919. The industrial complex was recaptured by troops led by Colonel Bernhardt Graf von Paninski.
_(Photo: Wolfgang Sawodny Collection)_
The legend of Leuna was perpetuated by means of souvenirs such as a metal model train, and these plaques dated 1921, not 1919.
_(Items: Paul Malmassari Collection)_
The front part of PZ 45, seen in 1920. This train was built in March 1919 for the Lin. Kommando X (Stettin). From left to right: the machine-gun wagon (Type OmK) Breslau 55292; the artillery wagon (OmK) Essen 126 585, with its turret armed with a Krupp 8.8cm L/30 U-Boat gun on a C/16 mounting; a safety wagon; finally the machine-gun wagon (OmK) Cologne 62 455, with its armoured brakesman's cabin. The trooper sixth from the left in the front rank has an MP 18 sub-machine gun, and to his left is a soldier with a holstered Artillery Luger.
_(Photo: Paul Malmassari Collection)_
In February 1919, PZ VII (the ex-PZ XII of 1914) added two wagons from PZ II and operated in Lithuania. When the German troops withdrew in November 1919, the Lithuanians took over the train and renamed it _Gediminas_. Note the searchlight in its armoured tower on the left.
_(Photo: Paul Malmassari Collection)_
The Kapp Putsch in March 1920 involved six armoured trains in Berlin, numbered 30, 40, 46, 47, 55 and IV (seen here). The Gruson portable turrets were commonly used on armoured trains, but more usually inside a mineral wagon, and not mounted on a flat wagon as here.
_(Photo: Paul Malmassari Collection)_
PZ 48 (built in Dresden) was broken up at the end of 1920 after having intervened at Chemnitz among other places. Its 5.7cm Maxim-Nordenfelt L/36.3 gun seems to have been lifted complete from an A7V tank.
_(Photo: Paul Malmassari Collection)_
The rear half of PZ 45. On the right, armoured Class T.9.3, Stettin 7308; then the assault troop wagon, Cassel 14680; mortar wagon (OmK) Berlin 28630 with its characteristic inclined armour protection; finally machine-gun wagon (OmK) Cologne 64303. Note the two MP 18s, and the portable MG 08/15 beside the soldier sixth from the right.
_(Photo: Paul Malmassari Collection)_
An example of the armoured trains used during the Silesian uprising of 1921: this is the train of the Rossbach Free Korps. Behind the Type Om wagon is an armoured wagon fitted with an observation tower. Note the black-white-red flag of the German Empire, still used by the _Reichswehr_ even when the black-red-gold flag was the official version.
_(Photo: Paul Malmassari Collection)_
### The War of the Frontiers
These interventions were aimed at securing as much German territory as possible before the frontiers were definitively fixed. German troops were in action in the Baltic States, in Western Prussia and in Upper Silesia. Facing the three Polish uprisings, armoured trains were only deployed on the German side in the last two areas. In the Baltic States, a certain number of trains were also in action, including Panzerzug V in support of the Iron Division deployed in Riga in May 1919, and which was captured at Mittau.
For two years, Germany noted that armoured trains were not mentioned in the text of the Treaty of Versailles and demanded the right to keep some to maintain internal order and put down strikes. But on 5 May 1921, an ultimatum sent from London forced the German Government to accept 'without reservation' by letter of 20 May 1921 the handing over of all the trains. On 30 May 1925, the Inter-Allied Military Control Commission recorded having carried out the destruction of thirty-one armoured trains.
### The Inter-War Period and the Rearmament Programme
The period 1921 to 1939 saw the renaissance of the German armoured trains. Even if the _Reichswehr_ (which existed from March 1919 to March 1935) had no armoured trains, the _Reichsbahn_ possessed twenty-two track security trains, which would form the backbone of the future Panzerzug. However, according to the Railway Department (Section 5) of the Army High Command, these trains were in poor shape, and only by amalgamating their individual rakes could they constitute 'two trains which could actually be used'. Hauled by unarmoured Class BR57 or BR93 engines, the wagons were simple units reinforced with sleepers, or with concrete poured between two layers of wood. The first military armoured trains (Panzerzug 1 to 4, 6 and 7) were created from these units, under the rearmament programmes launched in 1935, but Section 5 did not accord them a high priority. In fact, the High Command thought these trains could be used to cover a withdrawal and that they would be expendable. For wartime operations they preferred armoured railcars armed with artillery and machine guns. Thus it was that during this intermediate period five Type VT railcars (Nos 807 to 811) were armoured, and at least one road-rail vehicle was the subject of a study based on the Schupo-Sonderwagen 21 from Daimler.
Wuppertal's armoured railcar No VT 809. The increase in weight required the installation of an extra central axle. Note the observation cupolas at each end of the roof and the wire of the radio antenna.
_(Photo: BA)_
Security train based in Munich, the future PZ 3, with its Type G vans armoured internally, and its radio masts deployed. Only the engine has overall armour. Note the observation cupola on the first van.
_(Photo: Paul Malmassari Collection)_
### Armoured Trains of the Second World War, their Evolution and Construction Programmes
As military operations became imminent, on 23 July 1938 the seven _Bahnschtzzug_ (security trains) were reactivated. However, only four of them (Nos 3, 4, 6 and 7) were selected for combat operations on the basis of their offensive and defensive qualities and equipped accordingly, the others (Nos 1, 2 and 5) being reserved for railway security duties behind the front lines.
### Panzerzug 41
This project begun on 13 December 1940 envisaged an armoured train comprising an armoured railcar capable of being used singly or coupled to other units, able to fight on road or rail, with the conversion even under fire taking only a few seconds. In addition, the armoured tank-transporter wagons would be self-propelled. In view of the complexity of the project, it was envisaged that production of the various units would extend over a period of time: as an urgent measure firstly the Type Omm flat wagons for carrying tanks, then the armouring of the locomotive, next the special wagons (auxiliary units, assault troop carrier, kitchen, infirmary), finally the conversion of all the wagons to self-propelled units. In actual fact only the Type Omm wagons would be built in 1941, and which were added to PZ 26-31.
### Panzerzug SP 42
Also launched on 13 December 1940, this project included seven armoured wagons powered by a 1260hp diesel locomotive, which was capable of moving 600 tonnes at up to 50km/h (31mph) on the level. The train was to comprise: a command wagon, an assault section wagon, three tank-transporter wagons and two safety wagons, the whole being capable of running on standard and Russian broad gauge; the command wagon and/or any of the other armoured wagons was to be capable of independent operation. The tank-transporter wagons should be capable of unloading their tank in ten minutes and of re-embarking it in fifteen. The armament was to comprise 7.5cm guns in turrets, 2cm Flakvierling and machine guns. The diesel locomotive was to have been built by L-H-W and the rest by Berliner Maschinen Bau A.G. The design study was to have been finalised by September 1942 with the first train available by the Summer of 1943. The project was never started, and the designs were probably absorbed into those of Panzerzug BP 42/44 and PT 16.
### Panzerzug BP 42 and BP 44
As the Panzerzug 1941 and SP 42 were not begun, in January 1942 the firm of Linke-Hofmann in Breslau was commissioned to build new armoured trains under the designation 'BP 42' ( _Behelfmässischer Panzerzug_ or 'makeshift armoured train', which suggests that this was to be a temporary solution), while Krupp was to fit the armour to the Class BR57 engines. The technical specifications were laid down in document K.St.N./K.A.N. 1169x dated 17 August 1942. This document standardised the composition of the armoured trains along with their armament. Thus, in addition to those trains built in 1942, the previous trains would be brought up to the same standard at each major reconstruction.
The armament planned for these units was to be a 76.2mm F.K.-295/1(r) and a 2cm Flakvierling for the artillery wagons (AWagen), a 10.5cm le.F.H.14/19(p) for the gun wagon (G-Wagen), and machine guns. The PzKpfw 38(t) tanks to be carried should be capable of combat off the train. The armour protection was to be 30mm thick. Despite shortcomings in the armour thickness, for lack of suitable materials, the remainder of the armoured train corresponded to the standard laid down.
Combat experience quickly showed that the four 76.2mm or 10.5cm calibre guns were incapable of successfully engaging Russian tanks, and an expedient resorted to at the front was the mounting of the hull of a tank (PzKpfw IV or T-34) in order to use its turret armament. In parallel, a design study initiated by L-H-W resulted in the construction of a 'Panzerjägerwagen' (tank destroyer wagon) in 1944, equipped with the turret of a PzKpfw IV armed with a 7.5cm L/48 gun. On 6 September 1944 the Army High Command ordered the construction of 12 PZ of a new type to be designated BP 44, which complied with these latest standards. In parallel with the coupling of two Panzerjägerwagen at each end of the train, the 10.5cm guns were replaced with 15cm le FH 18 howitzers.
In use, the BP 42 and BP 44, which represented the high point of the art, proved themselves highly efficient at maintaining the morale of troops fighting bands of partisans, but suffered from the weaknesses due to their conservative design: steam power, their extreme length, lack of flexibility and limited armour protection. As a result, in August 1944 a front-line officer proposed an armoured train comprising a diesel locomotive coupled in the centre of two heavily-armoured wagons and six Panzerjägerwagen.
10.5cm guns on the G-Wagen (top) and the A-Wagen (bottom) of the BP 44-type trains.
_(Drawings: Official German Military Archives)_
### Track security trains
The trains in this category were not expected to comply with any existing standards apart from those required by combat in their particular locality. They were the improvised trains (' _Behelfmässiger Panzerzug_ ') which would be used particularly in Yugoslavia, in Italy and in Eastern Europe. Under the order dated 12 July 1943 they took on the designation of ' _Streckenschützzug_ ' (SSZ or track protection train).
### Railway reconnaissance units
The official German classification system laid down the following list:
– Gleiskraftträder = unarmoured self-propelled rail vehicle.
– Eisenbahnpanzerzug (leichter Spähwagen) = light reconnaissance vehicle.
– Eisenbahnpanzerzug (schwerer Spähwagen) = heavy reconnaissance vehicle.
– Eisenbahnpanzerzug-Triebwagen = armoured railcar.
– Panzerjäger-Triebwagen = tank destroyer railcar.
### Trains comprising heavy and light self-propelled units
Trains were made up of a rake of these trolleys as follows: two sets of five trolleys (le.SP built by Steyr) or eleven trolleys (s.Sp also built by Steyr), alternating armed trolleys, command trolleys with radio antenna and trolleys with a tank turret. The train thus arranged was completed at each end by a Panzerjägerwagen slightly different to those used with the BP 42 and BP 44 type trains.
The organisation of the Eisb.Panz.Zg (le.Sp) was laid down in K.St.N. 1170P dated 1 October 1943, that of the Eisb.Panz.Zg (s.Sp) in K.St.N. 1170x dated 1 August 1944, that of the Pz. Triebwagen _Littorina_ by K.St.N. 1170i dated 10 April 1944, and finally that for the Pz. Triebwagen 'a' and the Panzerjäger Triebwagen by K.St.N. 1170a dated 1 January 1945.
### Road-rail armoured vehicles
Near the end of the war a road-rail vehicle project was studied, but the Nazi defeat put an end to it before any production vehicles resulted.
### Organisation and command structure
Initially the armoured trains were under the control of the Railway Troops, up until 9 August 1941. On that date, with the attachment of Rapid Deployment Troops, it proved necessary to concentrate technical and tactical information in a single command centre, to permit their rapid deployment under a technician with intimate knowledge of armoured trains: the Armoured Trains Commanding Officer attached to the Army High Command, a function which remained in force up until March 1945. On 1 April 1942, the armoured train force, which by then counted some 2000 men drawn from different units, was grouped together administratively under the control of a new centre created at Warschau-Rembertow (the Ersatz-Abteilung für Eisenbahn-Panzerzug-WarschauRembertow, or WK I). A further reorganisation came into effect on 1 April 1943, the armoured trains henceforth becoming an integral part of the 'Panzerwaffe' instead of the Rapid Deployment Troops. In late 1944, the Armoured Trains Centre at Warsaw-Rembertow was transferred to Millowitz in the Protectorate of Bohemia.
### Trains and railcars from 1938 to 1945
**PZ 1** was created on 26 August 1939. It did not take part in the Polish Campaign and in 1940 was in the region of Düsseldorf on guard duty facing the West. It advanced into Holland on 10 May 1940 in the direction of Gennep, then Mill, where it was knocked out by a mine. It was repaired in Darmstadt, where it received wagons from the demobilised PZ 5. In 1941, it participated in the invasion of the Northern USSR, with the 4th Panzergruppe in the direction of Leningrad, then operated on the Central Front around Vitbesk and Smolensk. After suffering major damage on 28 November 1943, it was completely rebuilt in Königsberg to the new standards. Up until early 1944 it remained with Army Group Centre, notably carrying out security missions as part of the 221st Sicherung-Division based at Minsk. It was destroyed by its crew on 27 June 1944 during the Soviet summer offensive.
PZ 1 derailed at Mill on 10 May 1940. The armour on the engine has been deformed by the impact with the leading wagons. Note that all but one of the armoured wagons are converted from passenger coaches.
_(Photo: Paul Malmassari Collection)_
Even if the engine is still the same, most of the wagons have been replaced by captured Soviet wagons. By comparison with the BP 42 production versions, the number of field artillery and anti-aircraft pieces remains the same, but distributed differently. The command wagon with its armoured casemate is the original GWagen which has been modified.
_(Photo: Paul Malmassari Collection)_
Close-up of the 2cm Flakvierling 38 mounting. All the trains brought up to the BP 42 standard had the same overall outline.
_(Photo: Paul Malmassari Collection)_
PZ 1 (on the right) inherited a Polish Tatra T-18 trolley as proved by the camouflage scheme (see the chapters on Poland and Czechoslovakia).
_(Photo: Paul Malmassari Collection)_
BR93 058 was the engine attached to PZ 2 ever since it was formed as the security train for Stettin. In 1945, the engine was the motive power for PZ 78.
_(Photo: Paul Malmassari Collection)_
PZ 2 seen from the rear. The original 75mm gun is still in place in the ex-Czech wagon but the turret behind it has been rearmed with a 2cm Flak.
_(Photo: Paul Malmassari Collection)_
The casemate destroyed at Könitz, with the 7.5cm F.K. M16 in the revolving turret.
_(Photo: Paul Malmassari Collection)_
Shortly after it was activated in July 1938 **PZ 2** participated in the occupation of the Sudetenland. It was next in action during the invasion of Russia. Between the Winter of 1941/42 and June 1944 it was under the orders of Army Group Centre in the region of Smolensk, then to the north-west of Kovel where it carried out anti-partisan security missions and troop transportation. It was updated to BP 42/44 standard, then was withdrawn from service in November 1944.
**PZ 3** is one of the rare examples where it is possible to illustrate each phase of its career, which began prior to 1938 and ended in October 1944. PZ 2 (the former BSZ _München_ ) was reactivated on 23 July 1938 and placed under the orders of the General Kommando, VII.Armee-Korps in Munich. An SdKfz 231 railway reconnaissance vehicle was attached to it. After 15 March 1939, when Germany invaded what was left of Czechoslovakia, PZ 3 returned to Brno passing through Austria. PZ 3 along with PZ 4 and 7 were in at the very start of the Second World War, going into action on 1 September 1939. A direct hit from a Polish anti-tank gun destroyed the command turret, killing Lieutenant Euen, the train commander, and his second-in-command Lieutenant Zetter immediately took over. Withdrawing under fire, the train was stopped by a demolished bridge, whereupon Polish shells caused serious damage, destroying the leading wagon, setting fire to the wagons behind it, and knocking the train out of action. During subsequent repairs, the interior armour protection was enhanced and the destroyed turret replaced by a fixed casemate with an embrasure allowing a degree of training for the gun.
Following repairs, PZ 3 was sent to Lublin. On 10 May 1940 it crossed the Dutch frontier. But it could not fulfil its mission to seize the bridges over the Ijssel as the Dutch had sufficient time to blow them up. It then passed through the Halberstadt workshops where the wagons at each end were fitted with a turret from the abandoned BN10H programme for an anti-tank halftrack, mounting a 7.5cm L/40.8 gun, an elevated command/observation casemate and an anti-aircraft position (2cm Flak in a tub, replaced in March 1941 by a 2cm Flakvierling). To compensate for the subsequent increase in weight, a third axle was added centrally. PZ 3 thus became one of the better armed and protected of the first-generation trains.
The leading artillery wagon of PZ 3 after leaving the repair shops in Danzig. Note the new command casemate and the replacement 7.7cm F.K. 96 gun in its fixed casemate. The painted death's-head is temporary.
_(Photo: Paul Malmassari Collection)_
SdKfz 231 armed with a 2cm cannon knocked out by anti-tank shells in front of the Ijssel bridges. This was the trolley attached to PZ 3, but the registration plate is a mystery, denoting a Bavarian Police unit.
_(Photo: Paul Malmassari-Regenberg Collection)_
PZ 3 at Veliki Luki in December 1942. The quadruple Flak mounting is clearly visible.
_(Photo: Paul Malmassari Collection)_
For Operation 'Barbarossa', PZ 3 crossed the River Bug on the night of 22 June 1941 heading for Grajevo. In late October 1941, it returned to Königsberg for repairs. On 1 April 1942, it was blown up by a mine, and in the fighting which followed eight partisans were killed. On the 22nd, a remote-controlled mine destroyed an artillery wagon and derailed the two following wagons, leaving seven dead and nine wounded among the crew.
Following serious battle damage in May, PZ 3 was sent for repair, then between 11 September 1943 and 12 July 1944 it was unavailable, being modernised to BP 42 standards in the Königshütte workshops in Upper Silesia (K.st.n./K.A.N. 1169x). The day after it left the workshops, the Russians launched an offensive towards the Baltic in the Dünaburg-Rositten zone, and on 24 July PZ 3 and PZ 21 counter-attacked at Kowno. On 1 August, a few kilometres after starting a mission, PZ 3 was derailed, and had to return for repairs.
A rare photo: the forward gun wagon was literally cut in two by a mine at Newel on 22 April 1942 and was recovered later, in this unusual configuration.
_(Photo: Paul Malmassari Collection)_
One of the few photos of PZ 3 in its final configuration, conforming to K.st.n./K.A.N. 1169x. From right to left, the G-Wagen armed with a 10cm le.F.H. 19(p), then the K-Wagen, and finally the A-Wagen with its 2cm Flakvierling 38.
_(Photo: Paul Malmassari Collection)_
One of the non-motorised Panzerjägerwagen of PZ 3. They were not equipped with _Schürzen_ nor hull up-armouring. On the left is the tank-transporter wagon. This arrangement of these two wagons back-to-back is very unusual.
_(Photo: Paul Malmassari Collection)_
The ambush at Kowno in July 1944, where PZ 3 was derailed. Note the original form of the G-Wagen, and one can just make out the Flakvierling wagon in the background. It would seem that this view and the previous one are the last-known photos of PZ 3.
_(Photo: Paul Malmassari Collection)_
An impressive view of the engine from PZ 4, with its virtually integral armour, notably in the smokebox area which has streamlined armour protection.
_(Photo: Paul Malmassari Collection)_
This wagon, which is characteristic of PZ 4, is armed with a 3.7cm in the front turret (later replaced by a 4.7cm Pak) and a 7.5cm infantry gun in the rear turret, followed by an armoured rangefinder position. The semi-circular centre section is an ammunition shelter.
_(Photo: Paul Malmassari Collection)_
On 5 October 1944 the Russians attacked the front of the Third Panzer Army and cut the German forces in two when they reached the Baltic. On 10 October 1944, the train was cut off by Russian tanks and had to be sabotaged by its crew.
**PZ 4** was put into service on 11 August 1939. During the Winter of 1941/42, PZ 4 was in the south of Russia in the region of Dniepropetrovsk. Between April and June 1944 it was under repair, then in December 1944 it no longer appeared in the active list, its units being broken up. Its number was passed to a new train.
Entering service at the same time as the other trains operated by the _Reichsbahn_ , **PZ 5** crossed into Poland on 15 September 1939, then from the 20th carried out security patrols around Lvov during the discussions on the demarcation line between the Russians and the Germans. It was readied for the campaign against the Dutch in which it was to support commandos disguised as Dutch soldiers. On 10 May it was halted by the destruction of the bridge over the Ijssel and was severely damaged by Dutch anti-tank guns. It was broken up in June 1940 and its wagons were transferred to PZ 1.
**PZ 6** was formed on 10 July 1939, and although incomplete, contributed to the capture of the town of Grajewo in Poland. Between 3 and 18 October 1939, it was in the Königsberg workshops being completed. It participated in the invasion of Holland but was blocked by a swing bridge being left open, and it then returned to Germany. During the Winter of 1941/42, it took part in 'Barbarossa' in Latvia then in Estonia, and finally in the region around Novgorod. Repaired after suffering serious damage, it was sent to Croatia. It was never brought up to BP 42 standards, and was destroyed in Serbia on 1 October 1944.
A rare view from above of the artillery position in the Type O wagon added after the Polish campaign, with the swastika added for aerial recognition. The gun appears to be a 7.5cm naval gun. Note the firing embrasures on the next wagon which seem to be useless in this configuration but which would have been used if the wagon was at the head or tail of the rake.
_(Photo: Paul Malmassari Collection)_
An overall view of the complete train, which shows its rough-and-ready external appearance, even though the armour was effective against small-arms. But the absence of heavy guns and howitzers soon brought about improvised solutions by adding wagons. At the rear of the train is just visible one of the ex-Soviet MBV-2 railcars used as artillery wagons since the Autumn of 1942.
_(Photo: Paul Malmassari Collection)_
**PZ 7** was created on 1 August 1939. It participated in the Polish campaign, then was used for security duties around Warsaw. On 8 March 1941 it was reinforced by 2cm Flak 38 mountings. In November, it participated in the invasion of the USSR (but on standard-gauge lines), then it returned to Germany for repairs. It returned to Russia and fought as part of Heeres-Gruppe Süd in the Kovel region. In June 1944, it was at the Warschau-Rembertow centre for modernisation, and was withdrawn from service in late 1944.
One half of PZ 7 probably being used as an artillery battery, profiting from the height of the line. The field gun is a 76.2mm F.K.295/1(r). One must suppose that the other half of the train is not far away.
_(Photo: Paul Malmassari Collection)_
Created on 26 November 1941, **PZ 10** was divided into two combat trains, Kampfzug I (one howitzer, two flak mountings, one anti-tank gun, two 10cm field guns and nineteen machine guns, from PP 53 _Śmiały_ ) and II (one flak mounting, one anti-tank gun, four 7.5cm and 10cm field guns and nineteen machine guns, from PP 51 _Marszalek_ ). The wagons were ex-Polish, adapted for the broad gauge. After entering the USSR, it moved to the Kiev region and became part of Army Group South up until early 1944. During this period it covered the retreat of the German forces after the defeat at Stalingrad. During operations near Sarny-Kovel, PZ 10a participated in the breakout from the Russian encirclement of that town, was heavily damaged but escaped. Intended to be repaired at Rembertow, it underwent an artillery bombardment in the second half of April. Its crew was therefore transferred to the ground troops and PZ 10 was abandoned.
PZ 10 as it appeared between June 1942 and March 1944. The infantry wagon came from PZ 29. Between the ex-Polish wagon from _Śmiały_ and the engine is an ex-Soviet wagon Type PL 35 or 37. On the far side of the engine is the infantry wagon from _Bartosz Głowacki_.
_(Photo: Paul Malmassari Collection)_
The ex-Soviet DTR trolley, used by PZ 10 as an armoured wagon. It had previously been used as a self-propelled reconnaissance vehicle.
_(Photo: Paul Malmassari Collection)_
When PZ 10 was separated into PZ 10a and PZ 10b on 1 April 1943, the latter was used on security operations on the Tarnapol (broad gauge) line, and received the number **PZ 11**. Between the middle of March and July 1944 it was taken out of service to be brought up to BP 42/44 standard. Railcars PT16 and PT18 were attached to it between the Summer of 1944 until January 1945. It was destroyed on 13 January 1945 near Chęciny to the south of Kielce, blocked along with PZ 25 by a destroyed bridge over the Nida.
Created on 10 June 1940 from ex-Polish rolling stock, **PZ 21** moved to the Eastern frontier where it was based in the 'Germano-Russian zone of interest' from 22 July 1940. It remained in Poland, under the orders of the 5th Panzer Division, up until April 1941 when it moved to France. There it came successively under the control of the 94th Infantry Division then the 337th Infantry Division up until July 1942. On 17 July it left for the Eastern Front and the Rshev sector, where it carried out anti-partisan missions for the 286th and 78th Security Regiments up until 6 February 1943. From 6 February 1943 up until the end, it remained in central Russia and in July, it went into action to the south of the Kursk Salient during that battle. In early 1944, it operated against partisans in the Pripet region to the east of Brest-Litovsk. PZ 21 was captured by the Russians on 30 October in Lithuania.
From June 1942, Class BR57 No 1064 from the series BR5710-35 (armoured at Kharkov), was attached to PZ 11 as replacement for the ex-Polish Class Ti3 engine.
_(Photo: Paul Malmassari Collection)_
An interesting view showing, in front of the artillery wagon, a Russian-type safety wagon, with armoured sides fitted with firing loopholes similar to those of the BP 44 trains.
_(Photo: Paul Malmassari Collection)_
In its initial configuration, from front to rear PZ 21 was made up of: the artillery wagon from PP 54 _Groźny_ (100mm howitzer and 75mm gun), then the assault group wagon from PP 11 _Danuta_ (without its antenna frame), Class Ti3-13 engine No 54 654, the assault group wagon from PP 54 _Groźny_ (with its antenna), and finally the artillery wagon from PP 52 _Piłsudczyk_.
_(Photo: Paul Malmassari Collection)_
The two Polish training wagons would join PZ 21. Here is the one without lower armour protection.
_(Photo: Paul Malmassari Collection)_
Two anti-aircraft flat wagons mounting 2cm Flakvierling were added in the Spring of 1941. The gun seen on the artillery wagon, on which the original armour has been reinforced by plates with loopholes, is a 100mm howitzer.
_(Photo: Paul Malmassari Collection)_
**PZ 22** was created on 10 July 1940, using captured Polish rolling stock. It remained in Poland up until the end of March 1941, and on 10 April 1941 it arrived in France, where it was based at Tours. On 6 September, it was transferred to Niort, then moved to the Mediterranean coast. It remained there up until the middle of 1944 and only just escaped capture during the landings in Provence. It was then sent to Poland, where it was destroyed on 11 February near Sprottau.
Created on 1 March 1940 from captured Czechoslovak rolling stock, **PZ 23** took part in the invasion of Denmark then was stood down on 2 October 1940. Reactivated on 19 June 1941, on the 27th it officially received the number 23. It moved to the Balkans where it reinforced the three Croat armoured trains already there. It remained in Croatia up to the end of the war, notably operating in the Belgrade region.
PZ 22 at Lesparre (50km/30 miles north of Bordeaux) in 1942. Behind the safety wagons is the artillery wagon from PP 54 _Groźny_ armed with two 75mm guns.
_(Photo: Paul Malmassari Collection)_
This 2-8-0 Class 140C armoured engine (from the Paris Depot, number unknown) powered PZ 22 from the Spring of 1944, replacing Polish Class Ti3-4 engine No 54651. The photo probably dates from June 1944, at Lons-le-Saunier.
_(Photo: Paul Malmassari Collection)_
An exceptional document: a sketch made by the Resistance for the Allies, describing quite precisely the composition of the train, notably the Flak wagons and the ex-Polish training wagon.
_(Drawing: Paul Malmassari Collection)_
The initial version of PZ 23, with only the death's-head insignia differentiating it from its Czechoslovak version. The leading flat wagon is the one which carried the Tatra T-18 trolley (see the chapter on Czechoslovakia).
_(Photo: Paul Malmassari Collection)_
A photo which illustrates the dramatic situation in Yugoslavia: the Royalist Chetniks finished up allied with the Germans in their common fight against the Communist partisans. By now PZ 23 had received Class BR93 engine No 220 which remained with the train up until late 1943.
_(Photo: Paul Malmassari Collection)_
Put into service on 1 March 1940, the early career of **PZ 24** , also composed of ex-Czechoslovak rolling stock, was identical to that of PZ 23. Reactivated on 19 June 1941, it took its number 24 on the 26th of that month. Up until 1943 it was in Serbia, then it moved to Italy. In early 1944 it was recalled to the rear for repairs. It moved to France where it was based from mid-1944 up until the landings in Provence on 15 August 1944. Recalled to the Eastern Front in the Winter of 1944/45, it was destroyed by its crew in Poland on 16 April 1945.
During the Winter of 1942/43, PZ 23 was rebuilt to BP 42 standards, including a Class BR57 engine. Here it is seen in Sisak (Croatia).
_(Photo: Paul Malmassari Collection)_
The rear of PZ 24. In front of the Czechoslovak artillery wagon is S Wagon 150.271 (ex-Austro-Hungarian PZ VII, afterwards Czechoslovak Armoured Train No 2), wagon 140.914 (PZ II, Czechoslovak Armoured Train No 1) and MÁV engine No 377.482.
_(Photo: Paul Malmassari Collection)_
Class BR57 engine No 2043 was attached to PZ 24 after December 1941. Note the Czechoslovak infantry wagon added in June, on which a 2cm anti-aircraft cannon position has been fitted.
_(Photo: Paul Malmassari Collection)_
A photo probably taken in August or September 1943, when PZ 25 had been transferred to Italy where it carried out coast-defence missions. The PzKpfw 38(t) tanks have replaced the Somuas.
_(Photo: Paul Malmassari Collection)_
Created on 1 March 1940 as No 9 from ex-Czechoslovak rolling stock, **PZ 25** was stood down, then reactivated on 10 December 1941 under the number 25. At that point, Eisb.-Panzer.-Triebwagen 15 was attached to it. The train was sent directly to France, at the moment when PZ 21 was sent from France to the Eastern Front. The main armament of PZ 25 consisted of two 7.5cm guns and two Somua S35 tanks, replaced later by PzKpfw 38(t) tanks. From late 1943 up until 1 March 1944, it patrolled between Albenga and Nice, then from south-west of Nîmes to Montpellier. Following the landings in Provence, PZ 25 went to the Eastern Front where it was destroyed on 13 January 1945 in the region of Kielce.
### Armoured trains for the broad gauge
As the start date for 'Barbarossa' approached, the Panzerzug 41 programme had not yet begun, and only the tank-transporter wagons had been designed. It was decided to use fifteen captured Somua tanks to create six armoured trains for the Russian broad gauge, to be numbered from 26 to 31. A lack of appreciation of the partisan menace (to say nothing of the weather, which was even more surprising) led the designers to provide open wagons, while only the cab of the Class BR57 engines was armoured.
**PZ 26** was activated on 26 May 1941. It comprised a Class G 10 armoured engine, three Type Omm wagons (wheelbase 6m /19ft 8in; length over the buffers either 10.1m /33ft 1½in or 10.8m/ 5ft 5in) each carrying a Somua, and two safety wagons. In December 1941 it was in the Leningrad area. During the Summer of 1942, certain wagons and the engine were replaced by Soviet units. Shortly afterwards, it was modified to run on the standard-gauge lines that the German engineers were laying down as and when the front advanced, replacing the Russian tracks. Between March 1943 and April 1944 it was in Germany to be modified, then it returned to the Eastern Front where it was deployed in the region of Idritza and Polozk. During the Winter of 1944/45, it saw action in Courland as part of the H. Gr.-Nord. It was captured on 8 May 1945 at Libau in Latvia.
The front of PZ 26, with two Somua tanks leading, a configuration used only on the first three trains. The tank was able to descend from the Type Omm wagon, but the procedure was not straightforward and hazardous when under fire: the safety wagon in front carried the ramp, and it was necessary to uncouple this wagon in order to lower the ramp for the tank.
_(Photo: Paul Malmassari Collection)_
In early 1942 a Soviet wagon of the 'Krasnoye Sormovo' type was added, and by modifying one of the two turrets it was possible to provide the train with an anti-aircraft defence position.
_(Photo: Paul Malmassari Collection)_
After the train was rebuilt in 1943, the 2cm Flakvierling was installed on a wagon converted from one of the old infantry wagons (with side armour protection extending below the level of the floor). The overall construction of the train was similar to that of PZ 1 and PZ 23.
_(Photo: Paul Malmassari Collection)_
During the Winter of 1941/42, **PZ 27** operated in the region of Briansk and Kursk and was then reconverted to standard gauge. On 30 May 1942 it was stood down and was not put back in service until 13 July using Soviet rolling stock, then in November 1942 it was converted to BP 42 standard. It was then engaged in the Pripet Marshes region and in March-April 1944 in the region of Brest-Litovsk to the north-west of Kovel. During the breakthrough at the 'Cauldron', it was immobilised by a direct hit to its engine, and several wagons were then destroyed. The remaining vehicles, together with those from PZ 66 took part in a counter-attack. Withdrawn to Warschau-Rembertow for repairs, it was abandoned there.
PZ 27 at Roslavl, in its initial configuration. Here we see one of the reasons for the limited height of the vertical armour protection beside the Somua: while it protected the tracks it also needed to allow access via the side hatch. Note the rail which allowed alignment of the tank on its platform. Also, the Somua tank turret marked with the number of the train has not had its cupola replaced by a hatch.
_(Photo: Paul Malmassari Collection)_
The assault group wagon from PP _Pierwszy Marszałek_ has been converted to an anti-aircraft wagon in late 1942. The original Class BR57 engine No 2300 is now completely armoured.
_(Photo: Paul Malmassari Collection)_
Commissioned on 1 June 1941 at the Police Barracks in Teschen-West, **PZ 28** entered Russia as part of Army Group Centre and operated with PZ 27 in the region of Terespol. During the Winter of 1941-42, it was in the zone Briansk-Orel-Kursk. In late March 1942, the Type Om infantry wagons were replaced with Soviet armoured wagons with 76.2mm guns. The engine was also ex-Soviet, an armoured Class Ob or Oa. Transferred to Army Group South in early 1944, it was at Nikolaiev for repairs then returned to the Warschau-Rembertow centre. It was destroyed in June 1944, during operations in the Carpathians.
Two captured Soviet wagons, the one on the right with the 2cm Flakvierling 38, and on the left, a 2cm Flak 36.
_(Photo: Paul Malmassari Collection)_
Faced with the threat of Russian tanks, before the anti-tank wagons were built, guns were placed on the leading flat cars: 7.5cm Pak, 3.7cm Pak etc. Here is a 76.2mm Soviet ZIS-3 installed in the Spring of 1944 at the head of PZ 28 in the place of a Somua tank.
_(Photo: Paul Malmassari Collection)_
**PZ 29** was activated on 1 June 1941 and placed under the orders of Army Group Centre in the region of Platorow. It was partially destroyed on 21 December 1941 when it lost three wagons in a ditch dug by partisans. Various demolitions (track, bridges) prevented the recovery of the wagons, and finally the train was broken up, the engine returned to the depot and its remaining wagons were shared between PZ 27 and 28.
A rare view of the WR 360C diesel locomotive with its frame antenna.
_(Photo: Paul Malmassari Collection)_
**PZ 30** entered Russia with Army Group North and operated in the Eydtkau region with Panzerzug 26. In December 1942, it left the front to be brought up to BP 42 standards, but using captured Soviet wagons. In early 1944 it was in southern Ukraine, then it was forced to retreat to the west of the Nicolaiev-Odessa line. Its engine was replaced by a Soviet Class S engine. In late April 1945, it returned to the Warschau-Rembertow centre for repairs, then participated in the defence of Danzig against the Russians. It was destroyed on 21 March 1945 near Gross-Katz.
Engine BR57 1504 on which the armoured cab is clearly visible.
_(Photo: Paul Malmassari Collection)_
PZ 30 in its final configuration. The Soviet wagon at the front has received an observation cab, and the Soviet origin of the infantry/command wagon, with its 2cm Flakvierling covered with a tarpaulin, is also evident. The armoured passages between wagons have been added at the same time as the protection for the couplings.
_(Photo: Paul Malmassari Collection)_
Very few photos of PZ 29 are known. Note that the flanks of the Somua lack protection, but that the infantry wagons have received protection from the weather. Note also the diesel locomotive fourth in line. In the background are a Soviet BP 35 wagon and engine.
_(Photo: Paul Malmassari Collection)_
**PZ 31** , the last of the trains specifically built for 'Barbarossa', was activated on 19 May 1941. Initially it was attached to the Sondertruppen, then as with the other trains, it came under the Heerestruppen. It entered Russia in 1941 in support of Army Group South and operated in the region of Zuravicav then Poltava. In early Summer 1942, it was equipped with Soviet vehicles, and soon afterwards was converted to run on the standard gauge. It was destroyed in December 1943 in Russia, but its crew escaped and were transferred to France, where they manned PZ 32.
Profile shot of PZ 31 with its BR57 engine between Soviet vehicles, in which the degree of comfort compared with the open Type Om wagons was certainly appreciated by the crew.
_(Photo: Paul Malmassari Collection)_
This photo is interesting as shows the conversion of one of the Soviet gun-armed turrets to an anti-aircraft position with a 2cm Flakvierling, the barrels of which have not yet been installed. From later photos it appears the 76.2mm gun was also retained on the mounting. Just visible on the left is one end of the (Russian) infantry wagon.
_(Photo: Paul Malmassari Collection)_
**PZ 32** is probably the most famous of all the German armoured trains. It was immortalised by René Clément in his film _La Bataille du Rail_ in which it – quite involuntarily – had the starring role. Its K-, G- and A-Wagen (the latter with 10cm 14/19 guns) were built in the Somua workshops at Lyon Vénissieux, the 0-10-0 engine (050A 33) was armoured in the Schneider workshops in Le Creusot, and the two tank-transporter wagons arrived complete from the Linke-Hofmann factory in Breslau. But as the Pz 38(t) tanks were delayed, they were replaced by two 122mm howitzers on GwLrs (Lorraine Schlepper). Its crew came from PZ 31. PZ 32 had an extremely short career in German hands: at 08.45 on 7 September 1944, as it entered Berain-surDheune Station, the train came into contact with French tank destroyers from the 3rd Squadron of the 9th RCA. At around 11.00 a shell from a tank destroyer shattered one of the coupling rods of the engine, which was repairable, but at 13.50, a shell hit to the boiler finally immobilised the train. The crew escaped, but did not have time to destroy the train. With the end of the war, PZ 32 embarked on a cinema career which was mysteriously ended by the torches of the scrap merchants.
0-10-0 engine 050A 33 of PZ 32 was armoured at Le Creusot. Its overall form followed the style of the engines of the BP 42/44 trains. Note that it was attached to the depot of Alès (Gard).
_(Photo: Paul Malmassari Collection)_
The A-Wagen of PZ 32 was in fact a Type BP42 G-Wagen, equipped with a 37mm Flak 36 anti-aircraft mounting. This modification reinforced the anti-aircraft defences of the train at a time when the Allies dominated the skies.
_(Photo: Paul Malmassari Collection)_
The K-Wagen. Note the shortened antenna, probably for the purpose of filming _La Bataille du Rail_.
_(Photo: Paul Malmassari Collection)_
In January 1942, **PZ 51** was formed using Soviet rolling stock under the name of SSZ _Stettin_. It then became PZ 'A' on 10 May 1942, and finally PZ 51 on 16 June 1942. It operated within Army Group North, where it remained for the whole of the war. In early 1944 it was between Dno and Tchichatchevo, then in the region of Novgorod. In March it conducted operations against the partisans of the Idritza-Polozk region. It was destroyed in combat on 28 August 1944 in the region of Walk in Estonia.
PZ 52 was created in June 1944 by reinforcing the Streckenschützzug _Blücher_ (seen here at Idriza). After fighting in Russia, it was destroyed near Danzig during the defence of that town in March-April 1945.
_(Photo: Paul Malmassari Collection)_
**PZ 60** (PZ R) was the training unit for the Rembertow Battalion. It was a Type BP 42 but does not appear in the official listing under that definition. In February 1944, it was in combat in the Lemburg region under the designation 'R'. Then it was engaged in security operations to the west of Tarnopol. Seriously damaged in March 1944 it returned to Warschau-Rembertow for repairs, which were never carried out.
These two views (above and below} show PZ 60, which had all the features of the new Type BP 42 trains. It served as the training unit and was then sent into combat.
_(Photos: Paul Malmassari Collection)_
The three specialised wagons (A-Wagen, K-Wagen and G-Wagen) were built on Type Omm wagons with 6m (19ft 8¼in) wheelbase, 10.1m (33ft 1½in) long overall, coupled symmetrically in rakes on the BP 42 trains and asymmetrically on the BP 44s.
_(Photo: Paul Malmassari Collection)_
The armament of PZ 51 was made up of four 4.5cm KwK(r) guns in turrets from BT-7 tanks complete with coaxial machine guns, plus the turret guns of the PzKpfw 38(t) tanks carried on flat wagons after April 1944. In front of the engine is a Type OO wagon converted into a command wagon, and equipped with a Flak mounting.
_(Photo: Paul Malmassari Collection)_
Created on 1 September 1942, **PZ 61** was the first of the initial series (Nos 61 to 66) of the new Panzerzug BP 42-type trains. It joined its operational area during the counter-offensive towards Velikiye-Liki in late December 1942, and remained in the Velisch-Dorogobouch zone, then in that of Vitebsk, up until the end of 1943. On 22 February 1944 it had to undergo repair, then rejoined the fighting in the Polok-Molodetchno-Wilna zone. On 27 June 1944 it was destroyed in the region of Bobruisk during the Soviet summer offensive.
PZ 61 probably undergoing maintenance, with its tanks not present, the Flak mounting with its side armour panels folded down, and the muzzle-cover on the gun. Note the reinforcement under the sides of the tank-transporter wagon.
_(Photo: Paul Malmassari Collection)_
**PZ 62** was created on 15 August 1942, and it received its official number on 1 September. Sent to the Eastern Front, it joined Army Group South, where it still was in 1944 on the ChristinovkaTalnovie line. It next carried out security operations and joined in the counter-attacks launched to the South-East of Stanislav. During the Winter of 1944/45, it joined Army Group 'A' in Poland, where it was destroyed in January 1945.
This type of wagon was a modification of the Type R wagon, which allowed the tank to reverse into a protected well which sheltered its running gear. Extra protection was provided by four plates each side, folded outwards during the entry and exit of the tank. The permanently-fixed ramp required the adoption of mixed coupling types, a classic type at the rear and a Scharfenberg at the front. This arrangement allowed for a safety wagon to be coupled in front of the Panzerträgerwagen.
_(Photo: Paul Malmassari Collection)_
This photo of PZ 62 allows us to see a normally concealed feature, namely the raised central section of the floor which served to guide the tank into the well, and certainly increased the rigidity of the chassis.
_(Photo: Paul Malmassari Collection)_
As the tank itself was armoured, the armour of the tank-transporter wagon was very thin (only 10mm as against 30mm for the other wagons), as a crew member demonstrates here, following the impact of a Soviet anti-tank round.
_(Photo: Paul Malmassari Collection)_
A fine shot of one anti-tank wagon followed by a second, made up of the complete hull of a PzKpfw IV placed on the safety wagon, thus providing a second 7.5cm gun capable of firing over the top of the wagon in front. Note that the casemate of the anti-tank wagon is fitted with additional vertical armour.
_(Photo: Paul Malmassari Collection)_
**PZ 63** was attached to Army Group North immediately on being commissioned, where it stayed until 1944, operating against the partisans on the Pleskau-Luga line. In early 1944 it transferred to the reserve of Army Group South and in April went into action around Lemberg. It was destroyed on 17 July 1944 to the East of Krasne. It was one of the trains most often photographed for propaganda reasons.
The A-Wagen of PZ 63, with its special camouflage scheme. The 2cm Flakvierling mounting is placed quite high, and by folding down the side armour it could engage ground targets.
_(Photo: Paul Malmassari Collection)_
The armoured tender was provided with hatches over the top of the coal supply. Nevertheless the demand was always greater than the standard quantity carried, as this extra pile of coal shows. On certain trains, the carrying capacity was increased with vertical planking. An identical tender was coupled to the front of the engine.
_(Photo: Paul Malmassari Collection)_
PZ 64 in Croatia in July 1943, probably at lunchtime judging by the crowd gathered next to the G-Wagen.
_(Photo: Paul Malmassari Collection)_
**PZ 64** was created on 1 October 1942. It became operational on 18 June 1943 and was sent to the southern zone of the Eastern Front. In early 1944 it was required in the Balkans where it fought the partisans in Croatia, and in late 1944 it was sent to Hungary. During the Winter of 1944/45, it was reinforced by the attachment of Panzertriebwagen 19. During fighting in February 1945 one of its PzKpfw 38(t) tanks was destroyed. The train was captured 30km (18 miles) to the north of Graz on 9 May 1945.
Created on 1 November 1942, **PZ 65** immediately went to Croatia where it was placed under the orders of the Security Troops High Command. It ultimately withdrew into Germany where it was captured by the Americans at Hotlthusen.
**PZ 66** was the last train of the first order for the Type 42. Sent to the East, it operated on the Minsk-Orscha line, then to the south of Mogilev. In April 1944 it participated in the counterattack to the North of Kovel, and patrolled in the zone Brest-Barano-Vitchi. During the retreat in the Summer of 1944, it was destroyed near Warsaw on 30 July.
The first train of the second order for BP 42 types, **PZ 67** became operational on 15 March 1943 and was sent to the East. In early 1944 it was in the region of Polozk where it operated as part of the 281st Security Division. On 28 August 1944 it was damaged near Mitau in Courland and the crew sabotaged it. **PZ 68** was formed on 1 August 1943, and by early 1944 it was in the Pripet region where it operated against the partisans. It was destroyed in April 1945 during the battle for Danzig. On 22 March 1944, **PZ 69** was heavily damaged and was finally destroyed by its crew near Tarnopol. **PZ 70** operated from March 1944 in the region of Slobodka-Birsula (Army Group South). On 4 April 1944 its crew found themselves blocked by the destruction of the track in Radelsnaya Station, and they destroyed the train during the Soviet breakthrough. **PZ 71** was created on 16 September 1943 then operated in the region of Tarnopol in January-February 1944. In late April 1944 it was at Lublin for maintenance work, and it was sabotaged at Slanic (Romania) on 31 August 1944.
The case of **PZ 72** was different: created on 23 November 1943, in the Spring of 1944 it was converted into two armoured command trains, Befehls Panzerzug 72a and 72b. The former became part of Army Group Vistula from 2 February 1945 and participated in the defence of East Prussia. It was destroyed during the fighting for Kolberg on 16 March 1945. Befehls Panzerzug 72b was sent to the Warsaw region where it only just escaped being surrounded, only to be destroyed on 28 March 1945 near Danzig.
This command train carried an unusual form of antenna on its K-Wagen.
_(Photo: Frédéric Carbon Collection)_
A sectional view (no scale) of an A-Wagen of a Type BP 44 PZ, in a special version where the quadruple Flak mounting was protected by a turret similar to that of the Wirbelwind (Whirlwind) anti-aircraft tank.
_(Drawing: Marcel Verhaaf)_
The Panzerjägerwagen is the surest way to identify a Panzerzug BP 44 (and earlier trains brought up to that standard). Designed by the LHW Company, this wagon had a 5m (16ft 4¾in) wheelbase. Sloping armour protected the sides and the axle boxes, while a stoneguard in the shape of a snowplough was fixed to the front end. This wagon could propel itself independently at modest speed thanks to four rollers placed in front of the rail wheels. The coupling system was mixed: standard at the front and Scharfenberg at the rear.
_(Photo: Frédéric Carbon Collection)_
The turret from a PzKpfw IV AusF H, armed with a 7.5cm KwK40 L/48 was mounted on a well-shaped casemate, provided with firing and observation ports; in general the turret and casemate would have had additional external armour plates fitted.
_(Photo: MHI)_
Here we see PZ 75 being emptied of its equipment and ammunition, which is being piled on the passage between wagons. The camouflage foliage appears reasonably fresh. One can only regret that practically no elements of any of these captured trains has survived, and that no technical reports – which must have been prepared at the time – have come to light.
_(Photo: MHI)_
**PZ 73** was created on 19 November 1943, then operated in Italy up until mid-1944, where it was captured intact at the end of the war. Powered by a Class BR93 engine with a different armour arrangement to the rest of the series, it had served as the prototype for the Panzerzug Type BP 44.
The first Type BP 44 train, **PZ 74** went into action on 25 July 1944 while it was still at Rembertow in an unfinished state, and on the 29th it was destroyed in an attack by T-34 tanks.
As with PZ 74, **PZ 75** went into action in an unfinished state, near Warsaw on 15 July 1944 then with Army Group Vistula, as Instructional Train No 5. In this capacity it transferred to the base at Millowitz in October 1944. It returned to operations on 31 December, and was captured intact by American troops at Hagenow.
**PZ 76** was created in April 1944 and sent to Poland to join Army Group Centre, where it covered the retreat of the German troops to the north of Warsaw. It was destroyed on 14 April 1945 near Königsberg in Sambie.
Despite the camouflage, the shape of the 10.5cm turret is clearly visible. Note the two tubular structures which may be limiters to prevent the turret from firing into the tender. This photo seems to have been taken at Millowitz when PZ 76 was being demonstrated.
_(Photo: Paul Malmassari Collection)_
Created in May 1944, **PZ 77** was attached to Army Group Vistula and was at Millowitz from February 1945. It was destroyed on 26 February in Pomerania.
**PZ 78** was created in late May 1944 and attached to Army Group South. In February 1945 it moved to Hungary where it remained for the most part. On 9 May, after the news of the German surrender, the train made its way to Thalheim where it was abandoned. Its crew succeeded in escaping to the American Zone.
PZ 77 was destroyed in combat on 26 February 1945 at Bubitz. Note the creation of a storage space out of sleepers, on the rear of the anti-tank wagon in the foreground.
_(Photo: Paul Malmassari Collection)_
PZ 78 captured intact at Thalheim on 9 May 1945. One special feature of this train was the A-Wagen with a turret similar to that on the Wirbelwind AA tanks.
_(Photo: RAC-Tank Museum)_
Armoured engine BR52 1965 K (Condenser) in Czechoslovakia post-1945. It is not known whether the armour was fitted by the Germans or the Czechoslovaks, and for which of three possible trains.
_(Photo: Glöckner Collection)_
BR52 K 2021 with partial armour protection. This engine was part of PZ 80. Here it is seen after the war, in the American Occupation Zone, in use by the 740th Railway Operating Battalion.
_(Photo: Paul Malmassari Collection)_
Railway modellers will know that the firm of Mikrometalkit used the same serial number for their BR52 K armoured engine.
_(Photo: Paul Malmassari Collection)_
PZ 81 seen after its surrender in Czechoslovakia, at Pisak in 1945. It was powered by BR52 7305. PZ 82 was completed just before the end of the war and included BR52 1965.
_(Photo: Tomáš Jakl Collection)_
Evidently taken in the Summer of 1945 (it is in the process of being dismantled: note the missing buffers) in this photo of a PzJgWn with an American soldier we see a forward observation position, which precludes the 7.5cm gun from depressing below the horizontal. This could be from PZ 73.
_(Photo: Paul Malmassari Collection)_
Here this PZ has shared the fate of so many armoured trains on the Eastern Front. Evidently several days have passed since it was destroyed, judging by the fact that the armament has been removed and there is a deal of rust on the overturned K-Wagen.
_(Photo: Frédéric Carbon Collection)_
### Improvised armoured trains
Following the 1940 invasions, then the occupation, of various European countries, 'protected' trains were put into service as for example in Norway with trains _Norwegen_ , _Bergen_ etc...
The Russian Front saw the use of numerous makeshift armoured trains such as the security trains (Streckenschützzug) _Polko_ , _Michael_ , _Max_ etc, and it is difficult to appreciate why they were not considered as 'regulation' armoured trains. Certain ones were later transformed into armoured trains and given a number, as with _Blücher_ which became PZ 52, and others which were listed as Panzerzug.
In early 1945, security train '350' operated with Army Group Vistula and in February 1945 was in the Krupp-Drückenmüller workshops for upgrading.
In the final days of the war in Europe, armoured trains were being put together using a variety of materials, such as the trains under construction in the Linke-Hofmann factory in Breslau.
In Greece, security trains Nos 204 to 214 were put into service, but the actions they took part in are poorly documented.
One of the security trains in Norway, with an interesting method of mounting the gun, allowing it to fire at an angle forward, and small openings used as observation/firing slots, also on the following wagon.
_(Photo: Paul Malmassari Collection)_
A Norwegian 4-6-0 engine, probably a Class 18, hastily armoured. On later photos this engine was also named _Sandhase_ ('Sand-hare', German slang for an infantryman).
_(Photo: Paul Malmassari Collection)_
_Bergen_ , showing its unusually low silhouette compared with other contemporary armoured trains. Note that the two wagons in front of and behind the FlaK wagon are open-topped, despite the climate.
_(Photo: Paul Malmassari Collection)_
One of the wagons of _Blücher_ , converted from a Russian bogie wagon on which a PzKpfw II was encased in wooden protection, no doubt doubled internally with steel plates.
_(Photo: Paul Malmassari Collection)_
SSZ _Polko_ , formed out of captured Soviet rolling stock, including an artillery wagon from BP 1, the engine, a flat wagon equipped with an anti-aircraft mounting and safety wagons.
_(Photo: Paul Malmassari Collection)_
The front of S.S.Z.350, with its infantry wagon, a Flak wagon (in fact a wagon with sides protected by concrete, leaving firing slots, with a Flakvierling mounting), then a leading wagon carrying the hull of a PzKpfw IV.
_(Photo: Wolfgang Sawodny Collection)_
Security train _Leutnant Marx_ made up by the 221st Sicherungs Division, which operated in the area of Orel and Livno. In 1942, this train was transferred to the 707th Infantry Division stationed at Rembertow.
_(Photo: Paul Malmassari Collection)_
On entering Germany, at Ohringen American troops found wagons probably intended for the anti-aircraft defence of train rakes, provided with a concrete tub protecting the gunners. Note the rungs to climb up into the fighting position.
_(Photo: All Rights Reserved)_
Security train in Greece, with its concrete blockhouse and a Renault FT tank, here armed with a 37mm gun. The engine is a Class Zd, obtained by Greece following the First World War. Another such train was powered by a Class La engine.
_(Photo: Paul Malmassari Collection)_
This wagon (ex-command wagon of PP _Pierwszy Marszałek_ , No 3930.88) was the sole armoured element on this train.
_(Photo: Paul Malmassari Collection)_
Security train in Latvia, formed of several four-wheel wagons with the hulls of BT-5 tanks.
_(Photo: Paul Malmassari Collection)_
### Steyr armoured trolleys
The light armoured reconnaissance trains Panzerzug (le.Sp) 301 to 304 created on 16 September 1943 were sent to the Balkans. No 301 operated in March and April in Serbia in the Ujse-Raska region and was destroyed at the end of the year. No 303 would be captured at the end of the war and No 304 was destroyed. To the best of our knowledge only one of these trolleys survives, in Trieste, being the one used by the British in their zone (see the chapter on Great Britain).
Steyr built the trolleys which would form the heavy reconnaissance armoured trains Eisenbahn-Panzerzug (s.Sp) Nos 201 to 210 on the mechanical base (chassis and motor) of the le.Sp. Train PZ (s.Sp) 201 was created on 5 January 1944 then was sent to the Balkans, where it would be captured at the end of the war. Nos 202, 203 and 204 became operational on 10 January 1944, 21 February 1944 and 23 March 1944 respectively, and were also sent to the Balkans. Nos 205 to 208 were built between April and June 1944. The last two in the series were not completed, at least one of them being captured at Millowitz in April 1945 (see the chapters on Czechoslovakia and Yugoslavia).
These machines are popular with enthusiasts who are passionate about armoured trains, probably because they resemble tanks on rails. In 2013 one was reconstructed by mounting a hull and turret built of plywood on a flat wagon. The turret revolved and could even fire blanks. It was planned to dismantle it in late 2015 to recover the original flat wagon for the railway preservation society collection.
PZ (le.Sp) 304 at Amorion in Greece on 30 August 1944, following its capture by partisans led by V Kassapis, seen here perched on the side of the vehicle.
_(Photo: V Kassapis via Georges Handrinos)_
A train formed of heavy trolleys being inspected by American soldiers at Dachau in 1945. Note that the coupling hooks have been removed. Although Steyr was responsible for building the hulls, the PzKpfw III turrets were fitted by Kraus Maffei in Munich.
_(Photo: Paul Malmassari Collection)_
Two original drawings of the le.Sp Steyr trolley. The number 'K/2670' often found in literature is in fact the number of the plan drawing. Note that the form of the armoured air intakes corresponds to the final production model. The same chassis was used as the base for the heavy trolleys, and the difficulty of adapting it to carry the increased weight slightly delayed the production of the s.Sp.
_(Drawings: Steyr-Daimler-Puch Archives)_
A rare shot from above showing a train of heavy trolleys captured by the Americans in South Germany. Why none of these units has been preserved and that no technical report has come to light (if one was established, which is unsure) remains a mystery.
_(Photo: Stuart Jefferson Collection)_
The reproduction s.Sp trolley named _Thor_ built by the Levisham Historical Re-enactment Group (North Yorkshire) seen on 11 October 2013.
_(Photo: Mark Sissons)_
### 'Eisenbahnpanzertriebwagen' armoured railcars
**Eisb.-Pz.-Triebwagen 15** , the only railcar put back into service after having been used by the _Reichsbahn_ , was sent to France in 1942, then in 1944 to the Larissa region in Greece.
TR 15 seen in Greece.
_(Photo: Wolfgang Sawodny Collection)_
**Eisb.-Pz.-Triebwagen 16** , activated on 27 January 1944, was the most powerful railcar built for the Wehrmacht, by Schwarzkopf at Berlin-Wildau, on the base of diesel locomotive WR 550 D 14. The armour protection was fitted by Berliner Maschinenbau AG in Wildau. In the Summer of 1944, it was associated with PZ 11 (along with PT 18) and operated in the Ukraine. In July, the train and its two PTs broke out of a Soviet encirclement in the Rawa-Russka region then participated in the defence of Lublin. It retreated towards the River San on 27 and 28 July. On 12 January 1945, it was surrounded during the Soviet offensive, but succeeded in breaking out of the encirclement by a remarkable action on the part of its crew, who constructed a track on which to escape. Today PT 16 is preserved in the State Railway Museum in Warsaw (see the chapter on Poland).
In its original form, PT 16 had no turrets, just two antiaircraft positions each with a 2cm Flakvierling mount but no shields. Hitler having found it to be under-armed for its size (200 tonnes, with two layers of side armour each 100mm thick!), the order was given to equip it with artillery turrets armed with 7.62cm F.K. 295/1(r) cannons.
_(Photo: Paul Malmassari Collection)_
An outstanding photograph taken in August 1944, showing probably for the first time PT 16 in its final form with one tank destroyer unit at each end, built around T-34 tank hulls secured on flat wagons. They are armed with one T-34/76 E Model 43 to the right, and T-34/76 Model 42 to the left. Note that the wagon side armour is low above the tracks, while the armour was only protecting the axles some months before. Here PT 16 is seen from the rear left, and the commander's cupola is open above the front compartment.
_(Photo: Paul Malmassari collection)_
**Eisb.-Pz.-Triebwagen 17 to 20** were formed of ex-Soviet MBV D-2 railcars repaired, re-armed and re-engined. PT 17 was activated in April 1943. Remaining on the Eastern Front, it was destroyed in August 1944 near Warsaw. PT 18, 19 and 20 were activated on 20 November 1943 and were sent respectively to Poland, to Army Group Centre, and to the camp at Lissa on the Elbe. All were armed with 7.62cm F.K. 295/1(r) guns. PT 20 was attached to PZ 11 from the Summer of 1944, and was destroyed on 16 January 1945 at Kielce.
After PZ 29 was broken up, its diesel locomotive was used for other tasks, as here hauling ex-Soviet MBV D-2 railcars intended to be put back into service.
_(Photo: Paul Malmassari Collection)_
Railcar from the PT 17 to 23 series. Note the frame antenna, the position of the exhaust silencers, and the additional armour added around the base of the turrets. The machine measured 10.30m (33ft 9½in) long on a wheelbase of only 3.90m (12ft 9½in).
_(Photo: Paul Malmassari Collection)_
In this photograph taken in August 1944, PT 18 is shown in its final version, namely with an additional armour covering the front half of each turret. Note the unusual camouflage scheme. PT 18 remained in service along with PT 16 until the 1945 fighting in Poland. It received several hits on 13 January 1945 and had to be abandoned in Kielce.
_(Photo: Paul Malmassari collection)_
**Eisb.-Pz.-Triebwagen 30 to 38** were the Italian LiBli Type Aln-56 railcars, one of which had been seized at the Italian Armistice in 1943. Eight of the anti-aircraft version were ordered new from the Italian constructors, making a total of nine LiBli operated by the Wehrmacht. The first three units, TR 30 to 32, were activated on 12 May 1944.
**Panzerjägertriebwagen 51, 52 and 53**. Built in late 1944, but never put into service, these tank-destroyer railcars were armed with turrets from PzKpfw IV Ausf H or J. One of them was captured and put into storage in an American depot in Augsburg, and the other two were damaged by bombing in the Linke-Hofmann factory in Breslau.
One of the three railcars Nos 30 to 32, probably photographed at Millowitz.
_(Photo: Paul Malmassari Collection)_
Either PT 30 or 31 in Serbia after extensive modification: apart from the installation of a 2cm Flakvierling in place of the roof armament of the Italian version, note the 2cm cannon in the turret and a new arrangement of the buffers.
_(Photo: Aleksandar Smiljanic Collection)_
Photographed in Augsburg at the end of the war in Europe were several rail vehicles, including the only complete example (in service?) of the tank destroyer railcar No 51. Note the unprotected buffers and couplings, perhaps intended to be armoured later, as well as the protected left headlight. As was done on all captured pieces of equipment, a white 'ALLIED FORCES' is painted on the side.
_(Photo: Paul Malmassari Collection)_
This exceptional close-up allows us to note that the two sides were not the same, this side having only one door and the antenna base.
_(Photo: Stuart Jefferson Collection)_
### Panhard Panzerspähwagen Trolley P204(f)
Forty of the 190 Panhard 178 armoured cars captured during the Battle of France were converted to trolleys and attached in pairs to each Type BP armoured train. The rail wheels were made by two firms: Gothaer Waggonfabrik and Bergische Stahlindustrie (Remscheid). Certain examples were fitted with buffers.
_(Photo: Paul Malmassari Collection)_
### PzKpfw III SK 1 (1943)
Trials and demonstrations took place in the grounds at Arys in October 1943, with two or three PzKpfw III Ausf L/N of the final series, armed with the 7.5cm KwK L/24. The machine was given the designation of 'SK 1' meaning ' _Schienenkampfwagen 1_ ' (Rail Tank No 1). The transmission, motor and cooling system were identical to those of the original tank, the last three torsion bars of the suspension needed modifying. With the added parts under the tank the ground clearance decreased from 48cm (1ft 7in) to 34.2cm (1ft 1½in). The drive on the rails was transmitted via the forward axle, the other being free-rotating. No matter how well the system performed, and the speed and haulage capacities were impressive, by 1943 the PzKpfw III was completely outclassed as a fighting vehicle.
SK 1 Technical specifications:
Length (buffers folded): | 5.62m (18ft 51/4in)
---|---
Length (buffers extended): | 6.00m (19ft 61/4in)
Width: | 2.94m (9ft 73/4in)
Height (on road): | 2.435m (8ft)
Height (on rails): | 2.825m (9ft 31/4in)
Weight: 25 tonnes Motor type: | 12-cylinder Maybach HL 120 TRM
Horsepower: | 320hp at 3000rpm
Transmission: | Fichtel & Sachs six-speed gearbox
Speed on rails (maximum): | 100km/h (62mph)
Speed on rails (normal): | 60km/h (37mph)
Wheelbase on rails: | 2.94m (9ft 73/4in)
Gauge (European standard): | 1435mm (4ft 81/2in)
Gauge (Russian): | 1524mm (5ft)
Fuel capacity: | 350 litres (921/2 Imperial gallons)
Drawing of the SK 1 tank.
_(Saurer Archives)_
### 'Zepellin' trolley
This machine was built in Finland from Russian components: the doors came from Komsomoletz artillery tractors, the turret from a BA-10, and so on. It was used on the Kemijärvi-Salla-Alakurtti branch, which straddled the frontier with Russia.
The trolley in Salla Station (Finland) which allows a good view of the camouflage scheme and allows an extrapolation onto the horizontal panels. The serial number marked on the hull side is 'WH-E.P. 1' which could indicate it was intended as the first of a series of such builds.
_(Photo: Paul Malmassari Collection)_
The SK1 could act as a locomotive hauling four loaded wagons. Conceived as a 'rail security vehicle' ('Bahnsicherungsfahrzeug'), its rail power train pivoted on axles fixed in the interior face of the hull sides. Lowering and lifting were hydraulically operated, controlled from a lever beside the driver's seat, either operation taking only a few seconds.
_(Photo: PKB)_
An interesting view showing the trolley being unloaded onto the track from an Sd. AH. 115 road trailer. Note the open access hatches for the crew.
_(Photo: Paul Malmassari Collection)_
A VT 137 railcar in Western Europe on an unknown date, with the glass panels of the cab replaced with armour plates. Note also the armoured window at the side rear. The fact that this particular train is composed of two railcars may indicate a railway gun battery.
_(Photo: Paul Malmassari Collection)_
The partisan threat: a German 'strike' trolley, unarmoured, captured by Resistance fighters, seen here at Bannalec Station, Brittany, on 7 August 1944.
_(Photo: Bannalec City Hall Archives)_
Probably a unique example, this SdKfz 223 reconnaissance armoured car has been converted for running on rails. We have no information concerning the date, place or usage. Note the serial number A-22225 (for Anhalt?) and the name _Bärbel_.
_(Photo: Paul Malmassari Collection)_
**SOURCES:**
**Books:**
Anonymous, _50 e Anniversaire de la Libération_, 4 September 1994, brochure published by the town of Saint-Bérain sur Dheune (Panzerzug 32).
Dimitrijevic, Bojan, _German Panzers and Allied Armour in Yugoslavia in World War Two_ (Erlangen: Verlag Jochen Vollert – Tankograd Publishing, 2013).
Gawrych, Wojciech J, _Panzertriebwagen Nr.16_ (Warsaw: PROGRES Publishing House, 2003).
Gottwaldt, Alfred B, _Deutsche Kriegslokomotiven 1939-1945 (Die Eisenbahn im Zweiten Weltkrieg-2)_ (Stuttgart: Franckh'sche Verlagshandlung, 1974).
Lauscher, Stefan, _Die Diesellokomotiven der Wehrmacht_ (Freiburg: EK-Verlag GmbH, 1999).
Malmassari, Paul, _Les Trains blindés 1826-1989_ (Bayeux: Editions Heimdal, 1989).
Porte, Lieutenant-Colonel Rémy, _La Conquête des colonies allemandes_ (Paris: 14-18 Editions, 2006).
Regenberg, Werner, _Panzerfahrzeuge und Panzereinheiten der Ordnungspolizei 1936-1945_ (Wölfersheim-Berstadt: Podzun-Pallas-Verlag, 1999).
Roques, Paul, _Le Contrôle Interallié en Allemagne Septembre 1919 -Janvier 1927_ (Paris: Berger-Levrault, 1927).
Sawodny, Wolfgang, _Deutsche Panzerzüge im Zweiten Weltkrieg_ (Friedberg: Podzun-Pallas-Verlag GmbH, 1983).
________________, _Panzerzüge im Einsatz auf deutscher Seite 1939-1945_ (Friedberg: Podzun-Pallas-Verlag GmbH, 1989).
________________, _Panzerzüge an der Ostfront 1941-1944_ (Wölfersheim-Berstadt (RFA): Podzun-Pallas-Verlag, 2000).
________________, _German Armored trains on the Russian Front_ (Atglen, PA: Schiffer Publishing Ltd, 2003).
________________, _Die Panzerzüge des Deutschen Reiches 1904-1945_ (Freiburg: EK-Verlag GmbH, 2006).
________________, _German Armored Trains 1904-1945_ (Atglen, PA: Schiffer Publishing Ltd, 2010).
________________, _Deutsche Panzerzüge_ (Eggolsheim (RFA), s.d., Dörfler Zeitgeschichte, nd).
Trojca, Halina and Waldemar, _Panzerzüge Teil 1, (Pociagi pancerne cz.1)_ (Warsaw: Militaria, 1995).
Trojca, Waldemar, _Panzerzüge Teil 2_ (Zweibrücken: VDM, 2002).
**Journal Articles:**
Blümner, Oberst a. D., 'Panzerzüge', _Heerestechnik_ 1st and 2nd Instalments (1916), pp 18–21.
__________, 'Panzerzüge in und nach dem Weltkriege', _Heerestechnik_ (January & February 1925), pp 21–4 and 49–52.
Bolster, Hauptmann, 'Panzerzug und Panzerkraftwagen', _Militär-Wochenblatt_ No 143 (1917), pp 3471–5.
'"Deutschland", Panzerzüge', _Schweizerische Zeitschrift für Artillerie und Genie_ No 6 (1900), p 224.
'Eisenbahn in Krieg', _Bahn Extra_ No2/2002, Special Number.
'Eisenbahnwaggons, gepanzerte', _Leipziger Illustrierte Zeitung_ 154 Band (January-June 1920), p 296.
'German Armored Trains of WWII', _Ground Power_ No 5 (1999), pp 102–47 (in Japanese).
Kopenhagen, Oberstleutnant Dipl. Journalist Wilfried, 'Panzerzüge-Schienen-Dinosaurien oder moderne Militärtechnik?', _Eisenbahn Jahrbuch_ (1977), pp 155–65.
Malmassari, Paul, 'Panzerzug 3 1938-1944', _Batailles et blindés_ No 48 (April-May 2012).
_____________, 'Draisine SdKfz 231', _TnT_ No 14 (July-August 2009).
_____________, 'Panzer sur rails', _TnT_ No 22 (November-December 2010).
_____________, 'Panzerdraisine "Zeppelin"', _TnT_ No 40 (November-December 2013).
_____________, 'Panzerkampfwagen III SK 1', _World War Two Railway Study Group Bulletin_ Vol 16 No 5 (2006), pp 16.131–16.133.
Pesendorfer, F, 'Im Panzerzug in die Sowjetunion', _Die Wehrmacht 5_ , No 14 (1941).
Peters, Dr. Jan-Henrik, 'From Kassel via Schöneweide to the Eastern Front – The Class 52 Condensing Locos'(translated by Walter Rothschild), _World War Two Railway Study Group Bulletin_ No 16/2 (March/April 2006), pp 16.48–16.58.
Sawodny, Wolfgang, 'Les Dinosaures de la guerre', _La Vie du rail_ No 2314 (1991), pp 27–30.
Surlemont, Raymond, and Pied, Robert, 'Forteresses sur rails: les trains blindés allemands de la seconde guerre mondiale', _VMI_ (Belgium) No 10 (1986), pp 36–9.
Wagner, Hauptmann a.D. Hans, 'Panzerzüge', _Militär-Wissenschaft und technische Mittellungen_ (1929), pp 30–40.
_________________________, 'Gefechtwagen für neuzeitlische Panzerzüge', _Wehr und Waffen_ (1933), pp 299–306, 349–51.
'Zukunftsentwicklung des Panzerzuges, _Militär-Wochenblatt_ No 38 (1934), pp 1266–7.
**Official Documents:**
_Dienstanweisung für Panzerzüge_ , 1910 (War Ministry).
Bulletin de Renseignements No 23, _Trains blindés allemands_ , état-major de l'armée, 2e bureau, March 1945.
_Note au sujet de l'emploi des trains blindés par l'Armée Allemande_ , s.d. (circa 1941, writer and addressees unknown).
**University Studies:**
Malmassari, Lieutenant-colonel Paul, _Etude comparée des trains blindés européens (1826-2000)_ , DEA in Military History, Defence and Security, Université Paul Valéry, Montpellier III, under the academic guidance of Professor Jean-Charles Jauffret, 2004.
. In German: _Panzerzug and Panzerdraisine_. From 21 October 1944, the official designation changed from the original _Eisenbahnpanzerzug_ to _Panzer Zu_ g, and for all the designations concerning armoured trains, the prefix ' _Eisb_.' disappeared. For the sake of simplicity, here we will use the generic term 'Panzerzug' or 'PZ'.
. For the record they were Frankfurt/Oder: PZ 1; Stettin: PZ 2; Munich: PZ 3; Breslau: PZ 4; Nuremburg: PZ 5; Königsberg: PZ 6 and 7 (the latter with railcar PT 15)
. K.st.n/K.A.N. = _Kriegs-Stärke-Nachweisung/Kriegs-Ausrüstung-Nachweisung_. These two documents listed the men and equipment allocated to a specific unit.
. The insignia colour therefore changed from black to pink and the 'E' for Eisenbahn was retained on the shoulder patch.
. This remained in use up until late 1940-early 1941.
. This was the episode which inspired Pierre Thomas' comment 'The Second World War began in the middle of the railway lines' in Septembre 1939 mai 1940, des trains contre les Panzers, 1999, _La Voix du Nord_ (1999), p 5. This may have been the first _combat_ between the two opposing forces, but in fact the first shells of the Second World War were fired at 04.47 on 1 September 1939 by the battleship Schleswig Holstein against the Polish fortifications at Westerplatte.
. Flak = _Flieger Abwehr Kanone_ = anti-aircraft gun.
. Flak Vierling = quadruple Flak cannon, also written as Flakvierling. This new mounting was fitted at the same time on PZ 1 to 4, 6, 7, 21 and 22.
. The derailed wagons were not able to be recovered until a month later, when a crane was finally available.
. The Class La and Zd were former Prussian P8 engines.
. Modern Orzysz in Poland.
. To the east of this part of the frontier, the tracks torn up by the retreating Germans have never been replaced.
. Construction of the 316 machines in the VT 137 series began in 1932 by several firms. On the outbreak of war, they were shared out between the different arms of service. In France, for example, fourteen VT 137 railcars were in use. After the war the surviving examples remained in service in many countries.
## GREAT BRITAIN
### ARMOURED TRAINS AND ARMOURED TROLLEYS 1859–1957
Britain has systematically deployed armoured trains in virtually all the regions where the interests of the country have been threatened, in the British Isles themselves and in its overseas possessions. Even if the British were not the pioneers of armoured trains, it is they who without doubt have made the most widespread use of them.
### William Bridge Adams' Artillery Train
In August 1859 a certain William Bridge Adams, a civil engineer by profession, proposed the construction of a double ring of railway lines around London, 150 miles (240km) in circumference, on which heavy artillery pieces would circulate to defend the capital. To allow this circuit to be usable in times of peace, he planned for the rails to be let into the tarmac of a road surface, after the fashion of a tramway. The lower parts of the artillery wagons were to be protected, where practicable, by a parapet running around the outside of the lines. His plan was not taken up, but thirty years later a line of thirteen defensible positions was built along a stretch of the North Downs, the high ground to the south-east of London, to act as infantry concentration centres and as stores for mobile field guns.
### Lieutenant Walker's Armoured Train
After introducing the subject in a letter to _The Times_ on 16 July 1860, which he wrote under a pseudonym, in 1865 Lieutenant A Walker took up his idea once more in an article entitled 'Coast Railways and Railway Artillery'. He pointed out that, if an enemy landed on certain parts of the coast devoid of railway lines, they would meet no opposition for up to two days, the time it would take for British troops to march to the area. (He obviously thought little of the capabilities of the cavalry, although it was they who had thwarted the last invasion of the British Isles, in Pembrokeshire.) His proposal was to form a defensive train comprising armoured artillery turrets with two guns each, protected from enemy fire by thick armour on the upper parts and by an earth embankment shielding the lower parts. It seems the turrets were fixed, meaning that the guns would have very limited traverse. It also meant that they would always have to be positioned to fire seawards. Spades lowered on the landward side would absorb recoil. In summary, according to the writer, this type of rampart was advantageous since the trains 'would form a continuous fortress along the coast'.
This moving fortress hauled at 30km/h (19mph) by an armoured 0-4-0 steam engine weighing 18 tons, carried on board ammunition for the guns and food for the crew.
### Mr T Wright's Armoured Train
In August 1864, another civil engineer, Mr T Wright, proposed building trains with three or four artillery batteries, each containing between ten and forty guns and mortars, the whole forming a 'wall' of a large number of artillery pieces extending over a mile (1.5km). Each wagon would be built entirely of iron, containing one or more guns or mortars on a revolving base plate. The drawing clearly shows the method the inventor proposed to prevent the wagons from being overturned by the impact of enemy projectiles as well as to brake the recoil of firing, limiting the sideways displacement of the wagons with an inverted L-shaped guard rail running alongside the track on both sides. In addition, the mortar wagon in Fig. 2, subject to downward-acting forces from its armament, was to be supported by lowering wooden buffer plates onto the guard rail. The mortar would not be fired in the vertical position shown, and it is probably depicted thus to emphasise the downward recoil to be buffered. The running gear was to be protected by vertical plates of sheet iron. From the proportions of the drawings, it is obvious the inventor was thinking of using broad gauge (7ft 0¼in) lines such as introduced by Brunel on the Great Western Railway rather than the much narrower standard gauge (4ft 8½in). Although having a greater load carrying capacity and being far more stable, the use of the broad gauge would have meant the trains would be unable to connect with the majority of the existing railway network.
Thomas Wright's armoured train and railway battery (1864), showing a cross-section of the longitudinal guard rail.
### John Smith's Armoured Battery
In 1871, a certain John Smith proposed and patented an armoured battery with the armour covering a wooden framework. The completely enclosed casemate pivoted on its axis by means of rollers running on a circular rail. The armament was to consist of either an artillery piece or a machine gun, or a mixture of both, and loopholes were to be arranged for rifle fire. As the casemate overhung the rear of its wagon, the design would be limited to a battery in front and possibly a second behind the engine. Mr Smith appears to have made no provision for handling the recoil when firing at 90 degrees to the track. The engine appears to be completely unarmoured. The revolving casemate could either be hauled by the engine, or be articulated to it by a common bogie – a curious arrangement, simple to draw but difficult to build, with perhaps the sole advantage of adding the weight of the front of the engine to stabilise the gun wagon when firing.
The basic problem with all these early coast-defence proposals, and presumably one reason why none were taken up, was the small calibre of gun which could be carried by the railways of the period, and the relatively light armour protection which could be fitted, compared with the increasingly heavy firepower of contemporary warships. Despite building extensive fortifications around sensitive points, the British of course relied principally on their all-powerful fleet to deter a landing, or isolate a beachhead.
Note that no means of closing the gum embrasure is shown in the drawing, but a device would have had to be included to protect the crew when reloading. The engine depicted in the upper drawing is an early Adams 4-4-0, commonly known as the Metropolitan Tank.
_(Plan attached to Patent No 1138)_
### Armoured Trains in Egypt, 1882
In 1882 Egypt's failure to honour its international debt obligations led the British to intervene in the country, and gave rise to the use of two armoured trains, one at Alexandria and the other on the line from Ismailia to Tel-el-Kebir.
The train at Alexandria, crewed by men from the torpedo boat carrier HMS _Hecla_ , in its usual form was made up of the following elements:
– Safety flat wagons.
– Six-wheel gun wagon _Hecla_ , armed with a 5in 40pdr Armstrong breech-loader (the stern gun dismounted from HMS _Hecla_ ), fastened to a wooden platform 4in (10cm) thick. The wagon was protected at the front end only by metal plates 120mm thick, backed by 3ft (1m) of wood and sandbags. The sides and rear of the platform were left exposed.
– Steam engine protected by rails covering the boiler and by a rectangular plate 2ft x 4ft (60cm x 120cm) covering the steam cylinders and the reversing gear. The cab was also protected by armour plates.
– Infantry wagon, to carry fifty men. The protection was provided by removable wooden planks 2in (5cm) thick backed by 3/8in (1cm) of metal plus sandbags.
– Artillery wagon, protected as for the infantry wagon, armed with a Gatling gun at the front with 5000 rounds, and a Nordenfelt cannon at the rear, with 120 rounds.
– Transport wagon, protected as for the two previous wagons, carrying two 9pdr guns intended to be unloaded and used on the ground.
In addition, an observation platform could be raised on a system of ladders to a height of 18ft (6m) above ground level. A second unarmoured train followed a short distance behind in support of the first train.
In its first sortie on 27 July 1882, the train consisted of simply the gun wagon, the engine and the artillery wagon, but wagons continued to be added on each successive sortie, until finally by 5 August it totalled nine armoured wagons. At this point, it was divided into two parts, the armoured train proper retaining only two transport wagons in its rake, and the back-up train bringing along all the support wagons. On operations, the latter train was left behind at Gabarri.
Another armoured train was built by the crew of the armoured corvette HMS _Penelope_. It was first employed on 26 August, when sixteen horses towed it from Ismailia to Nefiche. After minor repairs, it was sent under power to Kassassine on 1 September, where it was unable to fire on the Egyptians for fear of hitting the British troops. It was itself hit several times, and its commander was killed, but after withdrawing a considerable distance the train was able to take part in repulsing the enemy. The train was manned by Royal Marines and comprised a flat wagon armoured along the sides with ½in (1.2cm) thick plates 3ft (90cm) high and 6ft (1.80m) long. The armament was a 5in 40pdr firing _en barbette_ over the top of the armour. A second wagon, protected by sandbags packed tightly behind wooden sides, carried 230 rounds of ammunition. Its overhead protection consisted of 3/8in (1cm) plates covered by sandbags. When in action, this wagon stayed about 150ft (50m) behind the gun wagon, and its crew brought up the ammunition by hand.
The engine which propelled _Hecla_ was armoured with lengths of rail and iron plates, adequate in view of the limited capabilities of the enemy. The wagon name has been changed to 'HMS INVINCIBLE', apparently written on the photo when the crew was provided from this ship.
_(Photo: Paul Malmassari Collection)_
These trains made a big impression and the newspapers of many countries reproduced images of them, often with surprising accuracy. Here the artist has added 'HMS' to the name ' _Hecla'_.
_(Engraving: Paul Malmassari Collection)_
### Armoured Train on the Suakin-Berber Railway (1885)
Planned in 1883 as part of the campaign against the Mahdi, in March 1885 the Suakin Berber Railway Corps, commanded by Captain Llewellyn Edge, was formed under the control of the 17th Squadron of the 22nd Engineer Regiment of the British Army, with the aim of building a railway from the Red Sea to Berber on the Nile, in anticipation of continuing efforts to avenge the death of General Charles Gordon, murdered two months earlier in Khartoum, and to reconquer the Sudan. The troops sent to save Gordon had been fatally delayed ascending the Nile Cataracts, and the railway appeared an attractive alternative way to penetrate deep into the Sudan. To defend the tracks against the marauding local tribesmen, an armoured train was formed, armed with a 3.75in 20pdr BL chase gun. During the short life of the railway, the train patrolled the track and guarded the construction and repair parties. Intended to run for 300 miles (480km), the tracks had only reached Otoa, just 15 miles (24km) from the port of Suakin, when the British Government decided to pull out of the Sudan, and the project was cancelled on 22 May 1885. After eleven months spent in Suakin, the final British troops of the garrison were withdrawn, but the railway was not forgotten: Rudyard Kipling mentioned the project in his novel _The Light That Failed_ , written in 1890.
### Early Armoured Trains in India
In 1885 and 1886 a prototype train with an armoured engine and nine wagons was the subject of experiments at the Exercise Camp, conducted by Captain W F G Moberley, on the metric gauge Rajputana-Malwa line. A 40pdr Armstrong gun weighing 1.7 tons, with a muzzle velocity of 1180ft/sec (360m/sec), was selected for trials, mounted on 13ft (4m) long four-wheel and 25ft (7.6m) long eight-wheel wagons. The results led to the conclusion that it was necessary to adapt a well-wagon to carry the gun, and to employ a system of stabilisers to absorb the recoil.
The complete train with its artillery wagon in the foreground. Trials showed that it would even be possible to mount a 6in gun with a muzzle velocity of 1770ft/se (540m/sec) on an Indian wide gauge (5ft 6in /1676mm) wagon.
British and Anglo-Indian employees of the railways were required to join a militia force known as the 'Railway Volunteers', from which native Indians were deliberately excluded. The Volunteers attended annual camps where they were given basic military training to prepare them for security duties on the network. They were also called upon to crew the first armoured trains, which carried regular troops of the Indian Army.
Rudyard Kipling observed the firing trials of one of the first armoured trains built in the workshops in Lahore in December 1887. In 1890 he mentioned this train in his novel _The Courting of Dinah Shadd_ , when during manoeuvres 'mounted infantry skirmished up to the wheels of an armoured train which carried nothing more deadly than a 25pdr Armstrong, two Nordenfelts, and a few score Volunteers, all cased in three-eighth inch boilerplate'. By the end of the century the Armstrong guns would be replaced by 12pdr QF guns, the Nordenfelts by .455/.570 Martini-Henry calibre Gardiner machine guns, and finally by .303 Maxims. Some trains also included a second artillery wagon armed with a 6pdr QF gun.
Metre-gauge (3ft 33/8in) armoured train preserved in the National Railway Museum in New Delhi. The initials 2ND BN. B. B. & C.I. RY. VOLS. along the side stand for the 2nd Battalion, Bombay & Baroda Central India Railway Volunteers.
_(Photo: Prakash Tendulkar)_
The preserved train, which is identical in layout to the standard type of train used on the Indian Broad Gauge, was built at Ajmer, in the workshops of the Bombay, Baroda and Central India Railway. No engine is coupled to it, but as displayed the train comprises:
– Low-sided bogie wagon (safety wagon) No 8952 of 1886, with cowcatcher, which would carry lengths of rail and tools.
– Bogie van No 9908 of 1890, armed with two Maxim machine guns, plus an armoured searchlight on the roof.
– Four-wheel van for the electricity generator set and its petrol tank.
– Bogie well-wagon for a 12pdr gun.
– Bogie van No 9919 of 1890, identical to No 9908, with two Maxims and a searchlight.
– Low-sided bogie wagon No 8956, identical to wagon No 8952.
The armour was formed of a 3in (76mm) layer of felt (for insulation) sandwiched between two steel plates ½in (12.7mm) and ¾in (20mm) thick.
In addition, the trains would also comprise an infantry wagon carrying ammunition, food and other supplies, with loopholes for rifles. Communication between the parts of the train was by telephone, and flags were used for co-ordinating movements with supporting infantry units. The train commander could remain in contact with the railway divisional headquarters, assuming the trackside telegraph wires had not been cut, by making a connection to the line with the aid of a long pole. The armoured trains were limited to a speed of 15mph (24km/h), the maximum allowed when an engine was propelling rolling stock.
The trains normally mustered one or two unarmoured civilian coaches to carry the troops, offering more comfort and especially a cooler environment than the confines of the armoured wagons. When action was imminent, these coaches would be parked in a siding at a nearby station. Mirroring the good practice introduced in other armies, which were beginning to operate armoured trains in pairs, when going into action the artillery wagon and wagons behind it could be detached and left some distance from the combat zone, with the engine propelling the machine-gun and infantry wagons forward, leaving the 12pdr gun to give fire support.
During annual exercises, and even when in action, the armoured trains provided an essential support function. They would include in the rake a dining car, specifically to provide tiffin to the officers. At lunchtime, having ensured that the troops were well-provided with sandwiches and curry puffs, the officers would converge on the dining car.
In British India armoured trains continued in widespread use, both for internal security and to guard the volatile North-West Frontier with Afghanistan, where the threat of Russian incursion occupied the Raj for many years. The North-Western Railway Volunteer Rifles, which later became the North-Western Railway Regiment, was responsible for protecting some 7000 miles (11,200km) of track. Its 1st Battalion kept an armoured train at Lahore, and the 2nd Battalion one at Karachi. An artillery practice range was built at Moghalpura for sub-calibre firing training, using .22 calibre rifles clamped to the 12pdr gun barrels on a 25-yard (23m) range.
### William Smith's Armoured Battery (1887)
Having proposed a design of wagon chassis for the transport of heavy loads, including large artillery pieces, in 1887 William Smith proposed an imposing armoured wagon which was one and a half times wider than contemporary rolling stock. This huge wagon carried a naval gun in the centre and a fixed turret at each end armed with QF guns.
Jumping ahead several years to 1906 we once more find an armoured train used in exercises on Whale Island, the oldest coastal training ground for the Royal Navy.
The plan attached to the patent shows the central turret supplied with ammunition on small wagons running inside the chassis. The presence of hydraulic jacks to stabilise the vehicle brings this design close to that of heavy railway guns.
_(Drawing: Patent No 11,207)_
Armoured trains became a standard part of the British military establishment. Here, the engraving shows a simulated attack by an armoured train during the Royal Tournament of 1887, a major military tattoo and pageant which had taken place each year since 1881 in the Royal Agricultural Hall in London. The Tournament was used to show off the military capabilities of the British Army to the general public.
_(Engraving: Illustrated London News)_
An exercise involving sailors dismounted from a (dummy) armoured train to repel an enemy landing party.
_(Photo: Paul Malmassari Collection)_
### Richard Richardson Hutchinson's Armoured Train (1888)
This train was to have been formed of 'forts' with roofs shaped like the shell of a tortoise, armed with light guns and surmounted by observation turrets or revolving searchlights. Electricity for the latter was to be provided by dynamos, and a compressed-air system-would provide ventilation. One major innovation introduced by this project was that the motive power would not come from coal, but by burning petroleum or 'hydro-carbon', with the fuel divided up between the various wagons and conveyed to the locomotive by means of armoured piping forming part of the coupling system.
Plan attached to Patent No 6520.
### The Brighton Casemate Wagon (1890–1900)
In 1891, at the instigation of Captain F G Stone of the 1st Sussex Artillery Volunteers, an armoured train was built for the defence of the Sussex coast, armed with a 40pdr Armstrong gun. The design of the cannon wagon, conceived by a Mr Billinton, closely resembled the 16cm cannon wagons of Dupuy de Lôme's armoured train, the gun being fixed to an armoured revolving platform (see the chapter on France). A pair of inclined chocks up which the wheels of the gun ran absorbed part of the recoil, the rest being damped by a centrally-mounted recoil cylinder as fitted on the fortress mountings used with this gun. A system of screw jacks stabilised the wagon during firing.
The gun crew travelled in one of the two armoured coaches, the other being reserved for the harness which would allow the gun to be moved when dismounted from the train. An armoured roof protected the troops, who were provided with low loopholes for firing their artillery carbines from the prone position. The carriage walls were reinforced internally. The designer intended that a number of such mobile coast-defence batteries could continually be on the move to evade return fire.
This plan attached to Patent No 2982 granted on 2 February 1895 differs only very slightly from the wagon as actually constructed, shown in the following photo.
Put into service on 19 May 1894 after a short trial period, this train was normally made up of a 0-6-0 or 0-4-4 engine, followed by the artillery wagon and two armoured coaches. Note that no loopholes were installed in the armoured sides of the artillery wagon.
_(Photo: Illustrated London News, No 2877, 9 June 1894, p 723)_
The armoured train took part in many public demonstrations and accompanied the Volunteers on manœuvres. It was even mobilised for action in July 1898, during a French invasion scare at the time of the Fashoda Incident. It was dismantled in 1900, its armament being quite outmoded by that time. The good results obtained with the train would certainly have had an influence on subsequent developments of the same type.
### Mr Billinton's Project (1894)
The designer of the successful Brighton prototype proposed two schemes for much heavier artillery vehicles, with two turrets mounted either on the same wagon, or on two wagons running on parallel tracks. Neither scheme progressed beyond the granting of the patent.
Plan attached to Patent No 2982. The inventor does not seem to have taken into account the destabilising effect of having the 6in guns recoil backwards and upwards on the Vavasseur mountings, when fired to one side. Compared with his earlier workable gun wagon, here the stabiliser pads rest on the rails, and the wagon is rigidly clamped to the same. The recoil from firing such large guns would have quickly destroyed the track. Again, presumably for added strength, the wagons are shown as rigid-wheelbase eight-wheelers, a definite anachronism by that time.
_(Photo:_ Illustrated London News _, No 2877, 9 June 1894, p 723)_
### The Simms Armoured Trolley (1899)
This machine was designed by Mr F R Simms for Vickers and Sons and Maxim Ltd. in 1899. Intended for reconnaissance and as an auxiliary to armoured trains, the employment of twenty-five such trolleys on a stretch of track would cover a zone of action of some 20 miles (over 30km). The inventor considered that just 100 crewmen could do the work of the two or three regiments normally considered necessary to control 500 miles (800km) of track. This economy in trained manpower was also one of the sales ploys of Hiram Maxim when promoting his machine gun to colonial powers. The hull was made of laminated steel, mounted on spiral springs. The steel axles ran in ball bearings instead of the usual plain railway bearings. The 7hp Simms motor was water-cooled, and equipped with a Simms-Bosch magneto which was used to boost maximum speed in each gear. The Panhard gearbox had three speeds in forward and reverse, and final drive was by chain. One man alone was required to drive the machine, and a double system of foot and hand brakes could bring it to a halt in just 10ft (3m). In trails the maximum speed obtained in the gears at 1200 revolutions was 1st: 8mph (13km/h); 2nd: 15½mph (25km/h); 3rd: 23½mph (38km/h), with a short sprint up to 30mph (48km/h) in top gear using the magneto to boost the motor to 2000 revs. The trolley could normally carry sufficient fuel for 200 miles (320km). Three out of the crew of four men could find space to sleep in the vehicle, protected by a removable canvas roof. It seems that at least one trolley was sent to Nairobi in 1900 for operational employment.
The armament of the Simms Trolley was to consist of a .303 calibre Maxim machine gun, with 40,000 rounds. The weapon being demonstrated by Mr Simms is an air-cooled Light Maxim, and not the standard water-cooled version in contemporary use. A 1pdr Maxim pom-pom and a searchlight could also be mounted, although neither appears in any photo. The lower armour plates protecting the drive components were fixed by bolts passing through rubber blocks, to reduce vibration and noise levels. Weighing 1.422 tonnes, the trolley measured 6ft 8in (2.03m) long by 5ft 6in (1.68m) wide and 4ft (1.22m) high. The machinery was mounted at least 2ft (60cm) from ground level and was protected by a solid metal belt which greatly reduced the machine's vulnerability.
_(Photo:_ The Autocar _)_
### The Boer War (1899–1902)
The incident when Winston Churchill, as a war correspondent, was involved in the ambush of an armoured train did a great disservice to the reputation of this weapon system in many countries. It was during the Boer War, however, that a formal doctrine for the use of armoured trains was first laid down, despite the fact that most military minds of the period remained wedded to the idea of the railway as a simple aid to mobility rather than as a weapon. South Africa was comparable to Russia in view of the great distances to be covered in a country lacking roads and tracks, and with a total dependence on rail transport. For his part the Boer was an intrepid horseman capable of long journeys, who in the darkest hours of that war would sabotage the tracks and find refuge in the bush, or blow up the trains and pillage them for his essentials. Although built to a standard 3ft 6in (1067mm) gauge, the railway network in South Africa was far from continuous: a gap of some 500 miles (750km) existed between the Cape and Natal Province, blocking the movement of troops by rail, who had perforce to travel by road.
Thirteen armoured trains were in service before the war: five in Natal, five in Cape Province and three in Rhodesia. In Natal, the initial composition of each train was three armoured wagons with a steam engine (apart from one train which had only two wagons). The wagons were protected by plates 6ft (1.83m) high, giving a total height above the rail level of 8ft 10¼in (2.7m), completely encasing a platform wagon 38ft 4½in (11.7m) long, and pierced by two rows of loopholes allowing for firing standing and kneeling. The wagons had inter-communicating doors. Each of the two trains in Durban were armed with a 3pdr QF gun, while for all the others, the armament consisted of the individual arms of the crew.
An interesting view showing a detail often hidden by the camera angle: the communicating door at the end of the wagon. Note also the overhead protection from hastily-added roof plates held on with cables. These wagons were simple containers lacking any comfort, difficult of access and especially of egress.
_(Photo: HGM)_
The famous 'Hairy Mary' being fitted by sailors with her additional rope protection over the existing armour plates.
_(Photo:_ The King _, 17 February 1900)_
Haulage of the Natal armoured trains was provided by 4-8-2 engines with complete armour protection of 10mm thick plates, and they possessed an adequate reserve of power. One famous engine was No 48, christened 'Hairy Mary' which operated over the northern Natal railway network. Built in August 1888, 'she' was covered by a layer of ships' ropes providing a certain degree of resistance to Boer fire. Despite the ropes appearing flexible, this was deceptive, as on at least one occasion the excessive tension of the cables led to the tender derailing on a curve.
In Cape Province, four of the five trains dated from 1899. They were composed of an engine and two armoured wagons pierced by loopholes for individual arms, and each wagon carried three Maxim machine guns firing end-on and to the flanks. The poor disposition of the Maxims meant that unfortunately some 75 per cent of the ground surrounding the train was not covered.
Four trains were deployed as follows: two at Kimberley, one supporting the advance of Lieutenant-General Methuen towards that town, and one at Stromberg under the orders of Lieutenant-General Gatacre. One of the trains at Kimberley was destroyed by the Boers on the very first night of the war, and from the start the remaining trains were fully employed, within the limits of their inadequate capacity to engage the Boer artillery, as no artillery was mounted in the wagons. The trains were therefore reduced to the defensive role of mobile fortresses. The fifth train was put together at Mafeking to take part in the siege, and the gun it carried caused heavy Boer casualties.
One of the many armoured wagons built for inclusion in armoured trains, here with H. M. A. T. _Wasp_.
_(Photo: Paul Malmassari Collection)_
After the capture of a train between Vryburg and Mafeking, their employment was temporarily suspended. Their return to combat was due to Lord Methuen's requirement that they control the railway to the north of Kimberley while he carried out the conquest of the south bank of the Vaal at Fourteen Stream. The trains were then engaged once more to counter the tactics of the Boer General De Wet, who aimed at systematically destroying the tracks in the region of Kroonstadt followed by those of the whole network. The trains were given the secondary role of covering the construction trains despatched to repair sections of destroyed track. A construction train would be based at every one station in three. Armoured Train No 1 undertook over sixty missions of this nature.
The first attempts to arm the trains with effective artillery only began a year after the start of the war. In September 1900 the naval authorities of Simonstown mounted four 12pdr QF guns on two wagons. These were stationed at Pretoria, and then were attached to Armoured Train No 1. Just a few days later, the two hard-fought engagements against De Wet's troops on the Wolwehook-Heilbron line proved the worth of these artillery wagons. According to availability, the armoured trains then all received either a QF gun or a Maxim pom-pom.
### Organisation of the armoured trains
In 1900, the number of trains reached their maximum of twenty, and Lord Kitchener, the new C-in-C, set in hand a reorganisation, leading to a more centralised command structure but with greater flexibility in the way they were employed. One of his staff officers was appointed to supervise the armament and equipment of the trains, and the recruitment of their crews. Through his rapid appreciation of reports from the field he could, on his own initiative, organise the despatch and movements of the trains. On the other hand, the sheer size of the Cape rail network required the appointment of two deputies, one for the southern part (Captain F G Fuller) and the other for the north (Lieutenant H O Mance), the Orange River forming the boundary between the two zones. Both came under the command of Captain H C Nanton, responsible for the armoured trains, and of Major Girouard, Railway Director. In addition, Captain R S Walker was responsible for the operation of the searchlight equipment. Three engine supervisors were also designated to supervise the maintenance and the general state of the locomotive stock.
The armoured trains were numbered from 1 to 20, and some bore names, although it is not always possible to correctly make the connection between a specific name and a train number. All carried the prefix 'H.M.A.T.' which derived from naval parlance, and signified 'Her Majesty's (and after the death of Queen Victoria in January 1901, 'His Majesty's') Armoured Train'.
The crews were made up of artillery detachments, engineers (one NCO, six railway sappers, three signallers, two firemen and two engine drivers), and infantry (each train always carried men drawn from one regiment). Each train was controlled by two officers: the train commander in the leading wagon and his deputy in the artillery wagon.
### The rolling stock
**E NGINES**
Class 03 4-4-0 types at the beginning of the war, the Cape Railway engines were later replaced by Cape Government Railways 4-6-0 engines and Dutch Railways 0-6-4 engines, both types being much more powerful and capable of carrying and hauling additional armour protection. At first the armour only protected the cab, but as the war progressed and casualties mounted, the whole engine finished by being protected. On tender engines the gap between the cab and tender was protected by a curved overhead plate, and many engines on normal trains received armour protection which reached halfway up the cab sides and helped protect the crews. A code based on a series of whistle blasts signalled the need to brake in an emergency.
The well-known H.M.A.T. _Sweet Seventeen_ ('Her Royal Majesty's Train' No 17), hauled by a Dutch South African Railways Class B 0-6-4 engine.
_(Photo: Paul Malmassari Collection)_
**I NFANTRY WAGONS**
Often referred to as 'Maxim Wagons' because of their main armament, they were always positioned at the ends of the train, the leading vehicle being the command wagon. In general the space between the roof and the side armour was seldom used for firing, for fear of being hit by friendly fire from the unengaged side of the train. The preferred stance was firing from a kneeling position through loopholes 3ft (1m) above floor level, spaced every 2ft (60cm) at the ends and every 5ft (1.5m) in the centre of the sides. Corner firing slits were provided for the Maxim machine guns, which were fitted with a shield. The machine gun compartment was separated from the infantry compartment by a wall pierced by a door 16in (40cm) wide.
Armoured Train No 13, with its 'Maxim Wagon' carrying two roof-mounted searchlights, followed by the artillery wagon.
_(Photo: Paul Malmassari Collection)_
Six special wagons were built under the direction of Captain Fuller. Their roof was formed of 10mm plates inclined at an angle. From his individual compartment, the train commander could operate the braking system without leaving the protection of his additional armour plating. Lastly, sliding doors were installed at each end, enabling easy circulation between wagons. For his part, Lieutenant Mance built wagons with armour protection using lengths of rail. These were placed one above the other on the wagon sides, reaching up 5ft (1.5m) above floor level and held in position by vertical strakes. At 4ft (1.2m) from the floor a rail was left out, to allow observation and firing. The wagon ends were built up with wooden sleepers on which rail lengths were fastened. These wagons were employed in the armoured trains and also as escort wagons in civilian rakes.
The header wagon of H.M.A.T No 18 _Coldstreamer_ , with its upper armour protection formed of rails welded together.
_(Photo:_ Army & Navy Illustrated _, 6 September 1902)_
Drawing corresponding to the wagon in the previous photo.
_(Drawing: Royal Engineers' Report)_
The armour removed from the Fowler road trains is clearly visible on this wagon of H. M. A. T. No 2 _Disturber_.
_(Photo: RAC Tank Museum)_
The internal protection of these wagons was composed of a space filled with crushed stones. Note the armband worn on the left sleeve, signifying that the wearer is in mourning.
_(Photo: Paul Malmassari Collection)_
An overall view of an armoured train built at Kimberley. Note its symmetrical composition.
_(Photo: Paul Malmassari Collection)_
We must also mention the armour obtained by dismantling the Fowler road trains. These had been sent to South Africa following apparently satisfactory trials on the road between Leeds and Pontefract in England. Deemed too heavy for their intended role, their armour protection was removed and mounted on bogie wagons, finishing their armoured train career on rails, notably with Armoured Train No 2.
An examination of photos reveals a final form of armoured wagon, quite modern in appearance but dating from the early stages of the war, as the type was used at the siege of Kimberley. The overall armour protection covering the wagon is in fact pierced by loopholes closed by sliding shutters. A long gap just below roof level allows for firing and particularly all-round observation.
**A RTILLERY WAGONS**
12pdr, 6pdr and 3pdr QF guns were the armament used most often. In the course of the war 6in and 9.2in (152mm and 230mm) guns were added according to operational requirements. Although properly speaking not 'armoured wagons', these latter guns were attached to the armoured trains, mounted on lengthened tender chassis or on specially-designed platform wagons. Stability when firing was guaranteed by extending support arms fitted with screw jacks. One of the 6in guns was attached to Armoured Train No 2 and in action its experienced gunners vindicated the theories put forward by Captain Girouard.
Fifteen 12pdr guns were mounted on armoured wagons during the war. The first four were mounted diagonally on two bogie wagons, bolted down onto 6ft (1.8m) square steel plates to spread the shock of firing. Built at Simonstown, this type of wagon was certainly comfortable and was theoretically very efficient. However, the disposition of the armament did not allow both guns to be fired at the same time, as during an ambush the Boers logically took up position all on the same side of the track (so as not to fire into one another). Thus this armament arrangement was abandoned in favour of a central mounting for the remaining eleven guns. The revised arrangement consisted of positioning the 12pdr on a naval or land Mark II mounting in the centre of a bogie platform wagon, surrounded by armour plates 3ft (90cm) high in the centre sloping down to 2ft (60cm) high at the wagon ends. The gun itself had a shield, the top of which was 9ft (2.75m) from the wagon floor. Each ammunition locker contained 100 rounds. In this revised version, the crew consisted of one officer and five gunners.
Artillery wagon named 'Bobs' (probably after Lord Roberts), armed with a 6in gun mounted on a lengthened tender chassis.
_(Photo: Paul Malmassari Collection)_
The left-hand side of a 12pdr gun wagon, showing the four steel doors fitted only on this side, which give access to the ammunition lockers. The gunners are carrying out maintenance, and the lockers with wooden doors at each end of the wagon contain tools, oil and grease and cleaning materials.
_(Photo: Paul Malmassari Collection)_
H. M. A. T. No 3 _Cock O' The North_ shows another form of armoured gun wagon, with a pom-pom in the central position.
_(Photo: IWM)_
**S PECIALISED ROLLING STOCK**
A certain number of armoured escort wagons were also built to accompany civilian trains. The Pretoria workshops built one prototype which was followed by a series of eighty-four wagons, on which the armour protection consisted of two thicknesses of steel plate pierced by firing loopholes. This type of wagon was used in the Transvaal in particular. North of the Orange River, the wagons were instead armoured with lengths of rail. Lastly, the Imperial Railways workshops in Pretoria built passenger carriages on which the upper section of armour plating could be inclined at a 45-degree angle to protect against overhead fire (when, for example, passing through a ravine or a cutting), and they were pierced by loopholes allowing the crew to fire back at up to 45 degrees elevation. The brake vans were also armoured, in view of their essential security function.
Drawing of a brake van included in the Royal Engineers' report on armoured trains in South Africa.
This huge 9.2in gun from the coast defences of the Cape was mounted on a railway truck in August 1900 in order to participate in the fighting at Belfast (to the north-east of Johannesburg). However, as the battle was over by 27 August, the gun never saw action.
_(Photo: S.A.R.)_
A training ground was created on Fox Hills in Aldershot Camp in England specifically to prepare the troops for deployment to South Africa. One feature involved firing practice at moving targets fixed to an 'armoured train' running on a narrow-gauge track.
_(_ Revue Universelle _, No 66, 15 July 1902, in the Paul Malmassari Collection)_
### Representations and illustrations of armoured trains of the Boer War
The conflict aroused a wide range of international sympathy for the 'underdog' Boers: brand-new Krag rifles were smuggled to them from a consignment ordered by the Norwegian Army, and a host of international volunteers flocked to fight on the Boer side from many countries in Europe and the Americas. The armoured train in particular became an iconic symbol of this struggle.
The Boer War remains the first conflict in which armoured trains were systematically employed, despite early setbacks. British engineers and military men would draw inspiration from this war in order to conceive the First World War armoured trains _Norma_ and _Alice_.
The characteristic shape of the 4-4-0 engines, and especially the curved armour over the top of the cab, used in the siege of Kimberley in 1899 made a lasting impression.
_(Photo: Paul Malmassari Collection)_
A magnificent Epinal image representing the first British armoured trains in South Africa. In the original colour print the officer wears the typical scarlet jacket, long since replaced by the more discreet khaki. The shape of the engine would inspire many later illustrations, even down to the post-Second World War period. On the other hand, the armoured roof and the chase gun were developments which would appear later in the Boer War. It has to be said that the engine bears more than a passing resemblance to the Märklin version shown opposite.
_(Image: Pellerin & Co, in the Paul Malmassari Collection)_
A typical scene favoured by the French press, showing the destruction of a British armoured train. Here the wagons are simplified – even the engine seems to be copied from a British tramway engine – and the armour protection has been emphasised to glorify the (very real) courage of the Boers.
_(Illustration:_ Le Pélerin _No 1289, 1901, in the Paul Malmassari Collection)_
This engraving was made in a similar vein, and accentuates the sinister aspect of the wagons. Sadly, Boer women and children were the unintended victims of the first concentration camps, instituted by the British to starve the Boer commandos of their popular support in the countryside.
_(Engraving: Paul Malmassari Collection)_
Caricature does not spare its own camp: a drawing by Harry Furniss evokes the difficult ordeal of Question Time in Parliament, where the Government passes through the House of Commons inside the wagons of an armoured train!
_(Illustration:_ The King _, 17 February 1900, in the Paul Malmassari Collection)_
The toy industry often reflects the preoccupations or the key references of a particular epoch. Here is the engine of the famous O-Gauge armoured train produced by Märklin under reference No K 1020 in 1900.
_(Model: Private Collection)_
More basic but still immediately recognisable is the pull-along toy armoured train produced by Pinard in 1915, with its typical cab profile.
_(Toy: Paul Malmassari Collection)_
### Armoured Trains in Uganda (1905)
In 1905, the decade-long resistance of the Nandi tribe in Kenya led to attacks on Europeans. At the same time they intensified their raids on the railway. The Ugandan Railways put in hand the construction of two armoured trains for internal security, and to protect their vital connection to the coast. However, before the trains could come into service, the death of the Nandi leader Arap Samoei at the hands of Colonel Richard Meinertzhagen on 19 October 1905 brought the revolt to an end.
### The Armoured Garratt (1911)
In August 1911 the famous engineer Herbert William Garratt registered a patent for an armoured steam engine. Well-known for his articulated engines which operated throughout the world, he proposed a machine fully protected by armour, and carrying armament at both ends, where space was available thanks to the siting of the boiler in the centre. The inventor also suggested that additional armour could be fitted as and when required. The military version of his design did require certain modifications, such as the provision of a water tank under the central part of the engine, due to the armament taking up part of the space normally used for feed water. Although his proposal would have resulted in an extremely powerful armoured railcar, it was an expensive solution and wasteful of the haulage potential of the engine. In any case, the engine of an armoured train was too valuable to risk at the head of a train.
The diagram included in Patent No 19.338, showing the pom-pom at one end and two Vickers machine guns at the other. The firing platforms could be lowered to the horizontal to facilitate the gunners' training through wider angles of fire. If the armour plates were hinged downwards they could provide protection for the wheels, cylinders and motion gear.
### The First World War in Europe, 1914–1918
The initial use of armoured trains by the British Army in the First World War was in Europe, and in fact the trains were Anglo-Belgian, as much from the composition of their crews as by the arrangement of their artillery wagons (see the chapter on Belgium). Their zone of operations, between Liège and Antwerp, was particularly vital for the Allies who relied on resupply by sea. The primary role of the Light and Heavy Armoured Trains was the protection of the railway network.
The name on this train leaves little doubt as to its nationality, even though one of the soldiers sitting on the gun barrel appears to be French or Belgian.
_(Photo: Paul Malmassari Collection)_
The British troops sent by Winston Churchill, then First Lord of the Admiralty, mounted available naval 4.7in and 6in guns on bogie wagons, protected by 3ft 3in (1m) high armour plates surrounding the centrally-mounted gun, although at least one gun was used initially without armour. Despite their designation as 'armoured trains', in actual fact the two trains in use prior to the evacuation of Antwerp were essentially used as mobile artillery.
Three armoured engines took part in the battle of Loos in 1916, as it was noticed that the glow from the firebox of unarmoured engines prevented any discreet approach near to the front lines. The armour plates around the cabs hid the glow from the firebox, even if the armoured cab was less comfortable for the crew. Immediately after the battle, the armour was removed and all three engines returned to normal use on the Hazebrook-Ypres line.
A Manning Wardle Armoured Petrol Mechanical Tractor in France. Some ten examples were built, initially to haul railguns into position.
_(Photo: Paul Malmassari Collection)_
More discreet than the steam engines, which allowed them to serve immediately behind the front line, the Simplex Tractors which the Motor Rail and Tram Company Ltd began to produce in 1916 were based on the original Simplex weighing 6 tons: a 'protected' version for the 60cm gauge tracks, an 'armoured' version and a 'protected' version for the Standard Gauge, weighing 8 tons. Several other makes of tractor were also used, in armoured or protected versions.
### Armoured Trains _Norma_ and _Alice_
Studies undertaken prior to the First World War, and based on experience in the Boer War, enabled the British Army and the railway companies to rapidly produce armoured trains for defending the British coastline. Their designs benefited from the fact that the British track gauge of 4ft 8½in permitted the carriage of a greater load than the South African 3ft 6in gauge.
Armoured Train No 1:
– artillery wagon.
– infantry wagon (No 53996).
– armoured engine (No 1587).
– infantry wagon (No 53986).
– artillery wagon.
Armoured Train No 2:
– artillery wagon.
– infantry wagon (No 53994).
– armoured engine (No 1590).
– auxiliary tender.
– infantry wagon (No 53981).
– artillery wagon.
The artillery wagons were 30-ton bogie wagons with a 12pdr gun mounted at one end immediately above the end bogie pivot. The gun shield, open at the rear, bore a striking resemblance to those used on the Belgian armoured trains. Armour protected the entire wagon, and there were four entrances, one behind the gun mounting, one on each side, and a fourth giving access to the infantry wagon. A number of loopholes placed at a height of 3ft 3in (1m) allowed for small-arms fire. Lastly, the ammunition compartment was placed in the centre of the wagon.
The two engines used were Class N1 0-6-2 tank engines, built in 1912 and therefore quite modern. Compared with their civilian configuration, their coal capacity was reduced to permit an increase in their water capacity to 1850 gallons (7m3) compared to 3 tons of coal. In addition, a stock of one ton of coal was carried in one of the infantry wagons and four 200-gallon water tanks were slung beneath its frame. 15mm armour protected the whole engine including the moving parts.
On the train itself, the armour protection extended down to cover the wheels and chassis plus the couplings. The transmission of orders between the wagons was effected by speaking tubes as on board ship. One of their special features was the ability for the train to be driven from either end, for greater safety in traffic and when approaching signals. The driver at the front of the train could communicate with the fireman in the cab via a telephone link, and he could remotely control the engine via an intermediate regulator valve fixed on the smokebox, and operated through a link and lever.
The LNWR was given the task of assembling and armouring the trains at its Crewe workshops. They were not built at the same time: the first one (the future _Norma_ ) was completed in December 1914 and posted to North Walsham. The second train ( _Alice_ ), completed in April 1915, was sent to Scotland, based in Edinburgh. Although they carried out many patrols, they obviously never engaged in combat, and both were dismantled in 1919. The armour was removed from the engines only in 1923, and both were retired from service in 1956.
Armoured Train No 1 _Norma_. The infantry wagons were converted from GWR 40-ton coal wagons.
_(Photo: Paul Malmassari Collection)_
Armoured Train No 2 _Alice_ sporting the characteristic cowcatchers fitted only to this train, in 1916. The artillery wagons were converted from 30-ton Caledonian Railway boiler trucks. The 12pdr QF guns of these trains were the same as those which armed the trains of the Boer War. Note the armour plates surrounding the gunshield, which could be folded down to allow the gun to train. They had firing loopholes for when they were secured in the upright position during reconnaissance missions.
_(Photo: NRM)_
Two views of one of the infantry wagons from _Alice_ , showing (above) the firing loopholes open, and (top right), the loopholes closed. On the wagons of this train, No 2, the exterior reinforcing T-section strapping did not extend beyond mid-height on the wagon sides, while on _Norma_ they continued to the roofline between the rows of loopholes.
_(Photo: NRM)_
The two rows of loopholes were intended for simultaneous firing by troops in the standing and kneeling positions, which is why they are staggered horizontally. Note the modern appearance of the plates protecting the couplings. A horizontal plate allowed for communication between wagons. The interiors of both wagons were fitted out with folding tables, ammunition lockers, rifle racks, tanks for drinking water and a coal-fired stove for the troops.
_(Photo: NRM)_
GNR Class N1 tank engine No 1587, seen here at Doncaster in December 1914. This 0-6-2 engine weighed 72 tons and was designed for hauling passenger trains.
_(Photo: NRM)_
### Conquest and Occupation of the German Colonies (1914–1916)
Two improvised armoured trains were employed against the German colonies in Africa. One train was used by the British on the line heading west from Dar es Salaam to Tabora and Oudjidji to take over German East Africa.
On the other side of the African continent, when the British invaded German South-West Africa (the future Namibia) in April 1916, the Royal Navy supplied 4.7in (120mm) and 6in (152mm) guns mounted on wagons. The two sides competed with novel ideas: when the British added a safety wagon, the Germans laid delayed-action mines; when the former sprayed whitewash on the ballast to spot areas where the track had been disturbed, the latter brought their own white paint with them. In the course of this guerrilla conflict there were more than fifty attacks which derailed trains or destroyed bridges. The armoured trains remained in use to the very end of the Great War.
Engraving from a contemporary German magazine at the time of the operations in German East Africa, showing the train built by Ugandan Railways operating out of Dar es Salaam.
_(Illustration: Paul Malmassari Collection)_
H. M. A. T. _Simba_ , composed of an armoured engine, an armoured wagon at each end and a passenger coach which appears not to be armoured, was built in the Nairobi workshops in just ten days.
_(Photo:_ The Sphere _, 16 January 1915)_
The rear wagon, showing the thickness of the armour protection.
_(Photo:_ The Sphere _, 16 January 1915)_
### The Sudan
After the defeat of the Khalifa at the battle of Omdurman, the agreement of 19 January 1899 established shared sovereignty by Egypt and Great Britain over the Sudan. Order was restored but several expeditions were necessary to pacify the whole region. In 1914, Sultan Ali Dinar declared his allegiance to the Ottoman Empire and declared war on the British. A small force of 2000 men was despatched in 1915 and Ali Dinar met his death in March 1916 in the Darfour region. Armoured trains were utilised to defend the communication and resupply routes.
British armoured train in the Sudan. Note the elaborate camouflage scheme on the engine which does not seem to extend to the armoured wagons, which are protected by lengths of rail, recalling their predecessors in the Boer War.
_(Photo: IWM)_
### British Armoured Trains in Ireland (1916–1919)
Fearing uprisings and attacks, the British Government deployed a self-propelled armoured wagon in Haulbowline Docks, and ordered two armoured trains from the GNR(I). These trains comprised an engine and two wagons, with wooden sides doubled on the outside with steel plates. Two rows of loopholes were arranged for small-arms fire, and a safety platform was coupled at front and rear. Two additional armoured engines were built in 1918 by the GNR of Ireland, and they remained active until 1919.
### Upper Silesia
In Upper Silesia, as part of the Allied forces supervising the Plebiscite, the British Army put together an armoured train in Oppeln Station in June 1921, to secure the railway network and support the British, French and Italian troops involved. Made up of an armoured engine and two armoured wagons, its armament comprised a Vickers HMG and two Lewis LMGs in each wagon, plus the personal arms of the crew of one officer and twenty men. This train, with sufficient supplies of food and water to undertake a mission lasting up to three days, was on two hour standby to intervene on the orders of the RTO (Railway Transport Officer).
The engine was a Prussian Class T-14. The Type Om armoured wagons perhaps came from German trains.
_(Photo: Krysztof Margarinski Collection)_
Another view of the BSF (British Silesia Force, also known as the Upper Silesia Force) train seen at Oppeln in 1919 following modifications. Note the wagon on the left on which the armoured side has been increased in height and the plates on the engine have been altered.
_(Photo: Krysztof Margarinski Collection)_
### Latvia (1918)
In November 1918, a British detachment helped crew a Latvian armoured train during the fighting against the Germans and the Reds (see the chapter on Latvia).
### British Intervention in Russia
Following the Revolution, the British sent forces to North Russia to secure the two main ports of Archangelsk and Murmansk, the termini respectively of the narrow-gauge and broad-gauge networks. In line with local tactics they improvised armoured trains which compared favourably with those of their Russian opponents: a 4.5in howitzer mounted on a circular platform, a Simplex Tractor cannibalised for use as a turret mounting a French 75, a casemate improvised out of steel plates and beams protecting a 6pdr naval gun, etc. The Allied intervention on behalf of the Whites ending in total defeat, their armoured trains ending up with the other Red war trophies.
The wagon preceding the one in the last photo, showing a well-executed piece of improvisation at the Front. The hull of an armoured Simplex Tractor, with an opening cut for a 75mm APX gun, has been converted into a revolving turret.
_(Photo: IWM)_
A 6pdr naval gun mounted as a chase piece.
_(Photo: IWM)_
Between August 1918 and April 1919, an independent force of 500 men under the command of General Wilfrid Malleson was sent from India to support the Transcaspian forces in what is modern day Turkmenistan. Two armoured trains were used by the Anglo-Transcaspians against three Bolshevik armoured trains.
British 4.5in Howitzer Mk II installed on a cut-down bogie van. The side plates forming the armour protection could be lowered to the horizontal to form a platform for the gunners when firing to one side. This piece was extremely effective against opponents in trenches or bunkers.
_(Photo: IWM)_
### The Middle East
When the First World War began, the Ottoman Empire extended from Turkey proper, to take in the Lebanon, Palestine, Syria, Mesopotamia (modern-day Iraq), as far as the Persian Gulf and down a coastal strip to the end of the Red Sea. Medina and Mecca were included. Turkey mobilised in the Levant on 15 August 1914, but entered the war on the side of Germany only on 29 October. The fighting took place in five zones: Palestine and Sinai, Mesopotamia, Persia, the Caucasus and Gallipoli. British armoured trains faced the Turks in the first three of these zones. For their part, the Turks defended the Hejaz Railway (see the chapter on the Ottoman Empire) and Palestine. In Egypt (to defend the Suez Canal), in Mesopotamia and then in Persia, it was the British who employed armoured trains. Following the end of the First World War, occupation forces and mandates were set up in the former provinces of the Ottoman Empire, which necessitated maintaining the security of the railway networks.
### Mesopotamia (1918–1921)
The British Army entered Bagdad on 11 March 1917 but Mesopotamia was placed under British mandate only following the Armistice of 31 October 1918 and the surrender of the Turkish Sixth Army at Mosul. In this region dominated by tribal traditions, an undercurrent of continuous insurrection existed, with raids by armed bands, who were highly mobile and motivated by Turkish and Syrian agitators to fight for the establishment of an Arab government. The revolt grew in intensity, and the tribes had some successes in surrounding and even eliminating isolated British detachments. The railway network, vital for the movement of troops and their resupply, was constantly under attack, which led to the deployment of armoured trains and trolleys. Several armoured cars, notably Leylands and Austins, were converted for rail use by the simple expedient of changing their wheels. Often employed in pairs coupled back-to-back, they made up the 16th and 17th Railway Defence Batteries, which would come together to form the 1st Railway Armoured Motor Battery. The revolt was finally crushed in February 1921.
A fine view of one of the four Leylands converted for rail use. The device for turning the trolley can be seen beneath the chassis. Note the complete lack of the original vehicle fittings: mudguards, headlamps, trench-crossing rails etc. The vertical device made of sleepers seen behind the trolley does not appear to be part of it, except perhaps as a bulldozer blade to clear obstacles.
_(Photo: All Rights Reserved)_
A patrol with two Leylands. Four machines were built in 1915 and were initially sent to East Africa, where it was found they were too heavy. They were therefore transferred to the Middle East and used to protect the rail network.
_(Photo: RAC Tank Museum)_
Two Austin trolleys coupled back-to-back. Note the protection for the couplings and the names of the machines: H. M. A. C. _Warspite_ and _Valiant_ , the initials standing for 'His Majesty's Armoured Car'.
_(Photo: Sepia Images Collection)_
A FIAT armoured car converted to an armoured trolley. The name H. M. A. C. _Malaya_ continued the tradition of naming armoured vehicles in the manner of warships: as with HM Ships _Warspite_ and _Valiant_ , _Malaya_ was one of the _Queen Elizabeth_ class super-dreadnoughts.
_(Photo: RAC Tank Museum)_
Another view of a Fiat trolley, here seen manned by Australian troops.
_(Photo: Australian War Museum)_
Possibly one of the ugliest rail trolleys ever built! Six machines were ordered for use in Mesopotamia from the Drewry Car Company Ltd., with twin turrets each armed with a Lewis Gun plus a searchlight. The armour was 6mm thick. Note the armour panels protecting the running gear, seen raised in the photo. There is no information on their use in Mesopotamia.
_(Photo: The Industrial Railway Society via Lichfield Record Office)_
The front of the machine, with the armoured hatch for the driver, the small aperture enabling him to see when driving closed down. At the bottom, the two radiator shutters are also openable, in order to increase the flow of air. The surface texture reveals a covering of asbestos, to help with heat insulation. The two photos were taken in January 1922 at the Baguley workshops in Shobnall Road, Burton upon Trent.
_(Photo: The Industrial Railway Society via Lichfield Record Office)_
Armoured wagon _Julius_ of an armoured train on the Bagdad Railway, with a mixed crew of Scottish and English troops. It is armed with a 3in gun from HMS _Marlborough_ , and a second similar wagon bore the name of the ship. _Julius_ perhaps refers to the British naval base in Istanbul.
_(Photo: Paul Malmassari Collection)_
View of an armoured train on the Mesopotamia Railway (note the letters 'MR' on the leading wagon), armed with a 13pdr 6cwt anti-aircraft gun, of which four examples were recorded as being in Mesopotamia at the end of the First World War.
_(Photo: Sepia Images)_
A different armoured train with a 12pdr naval gun in a well wagon. The lack of tunnels and overbridges allowed the construction of unusually high observation towers.
_(Photo: Private Collection)_
British armoured train derailed on 5 September 1920 at Samawah on the Bagdad line.
_(Photo: Illustration No 46 in_ The Insurrection in Mesopotamia 1920 _, by Sir Aylmer L Haldane)_
### Egypt and Sinai
The British troops in Egypt were there to defend the Suez Canal, a vital supply artery for the forces of the Empire, against the Turks based in Palestine. In the Autumn of 1915 the first lines of a defensive network of 2ft (61cm) and 3ft (91cm) gauge track were laid in the Canal Zone between Port Said and Mohamedieh on the Egyptian bank of the Canal. After the Egyptian Expeditionary Force (EEF) won the battle of Romani on 4 and 5 August 1916, the network was extended as far as Rafah (reached in March 1917). But the Turkish withdrawal reduced the importance of the network, and its components were sent to Gallipoli. However, a 3ft-gauge line 15 miles (23km) long was built to support the advance into Palestine as an extension of the standard-gauge line which ended at Deir-El-Balah. In November 1917, Gaza was finally captured, Jerusalem fell to the British on 9 December and Jaffa on the 22nd. The Armistice put an end to the fighting on 31 October 1918.
Two armoured trains were built by the Royal Engineers. The design of those in Egypt was fairly basic. Here is No 2 at Zagazig with no engine attached. Note the uniforms drying on the armour plate!
_(Photo: Paul Malmassari Collection)_
The safety wagons were fitted with cowcatchers and protected by sandbags.
_(Photo: Paul Malmassari Collection)_
A rare interior view of a chase artillery wagon. The small 2.95in QF Mountain Gun can train to fire through each of the three apertures. Note the telephone and notepad on the right.
_(Photo: IWM)_
### Armoured Trains in British India (1919–1930)
In addition to the standardised purpose-built armoured trains, improvised armoured trains were also built during periods of crisis. Lacking overhead protection, they were much more vulnerable than the standard types, as shown during the Afghan War of 1920, when troops of a Sikh regiment were trapped in a cutting on the Peshawar to Jamrud line, and suffered heavy casualties.
After the First World War, the trains' armament was supplemented by the addition of 3in Stokes mortars carried in high-sided armoured wagons, such as the one in the photo below. They had a range of 800 yards (730m) and a rate of fire of up to thirty-two rounds a minute. The infantry were supplied with the .303 Lewis light machine gun which greatly augmented their firepower. The 12pdr guns remained in use up until 1939, when with the risk of invasion from Russia long since past, they were removed for mounting on merchant ships.
On 18 March 1919 the introduction of a new law, the Anarchical and Revolutionary Crimes Act, known also by the name of its author as the Rowlatt Act, caused revolts which although localised, were sufficiently unsettling as to give rise to severe repression, culminating on 13 April 1919 in the incident which became known as the Amritsar Massacre. In the backlash after this tragic event, the troubles and countermeasures multiplied in Punjab Province. An armoured train based at Lahore had to intervene to ensure the repair of the line at Amritsar while other troops arrived from Jullundur. As always in such circumstances, the protection of the railway network had to be increased.
A machine-gun 'barbette' wagon of the Punjab Rifles (IDF) Armoured Train Section, at Moghalpura in 1919. Note the basic similarities between the armoured wagon and those used during the Boer War. The rifles are .303 calibre P14s manufactured by Winchester and Remington during the First World War.
_(Photo: Hal Walters Collection)_
A pair of Commer trolleys seen in 1919.The broad-gauge examples above are mounted on four wheels, whereas on the narrow-gauge pair in the next photo the front axles have been replaced by a four-wheel bogie. This arrangement would reappear later, for example on Japanese SO-MO trolleys (see the chapter on Japan). Apart from the superior ride on uneven track, the bogies were easier to repair when damaged by mines.
_(Photo: RAC Tank Museum)_
Coupling these trolleys back-to-back was the classic arrangement in the absence of a rear driving position and suitable gearing, whereas to attempt to turn one vehicle under fire would be suicidal.
_(Photo: RAC Tank Museum)_.
### The UK General Strike of 1926
In 1926 in England, the derailment of a train in Northumberland led to the building of an armoured train, composed of a Type 4-4-4 engine and four wagons reinforced with steel plates. Intended to safeguard against possible sabotage, the two brake vans and two cattle wagons were provided with firing loopholes. The strike ended without the train having been used, and it was dismantled.
### China
The British Army was charged with defending the possessions of Hong King and Kowloon (three battalions of which one was Indian), as well as the concessions at Shanghai (two battalions) and Tientsin (one battalion). The permanent state of insecurity in China between the wars obliged the Great Powers to look to their own security and that of their supply routes, plus access to the sea. The British placed in service an armoured train. According to documents we have discovered, in 1928 this train was manned by the 1st Battalion the Bedfordshire & Hertfordshire Regiment. Part of the International Defence Force at Shanghai since February 1927, in May 1928 they moved to Kuyeh, where they were assigned to protect the mining facility there – where the following photos were taken. The unrest in the area had settled down by November, after which the battalion moved to Hong Kong.
An overall view of the armoured train, with its two armoured engines back to back, separated by a central wagon. The security flat wagon was only coupled at one end.
_(Photo: Paul Malmassari Collection)_
Two views of one of the two Ordnance 3pdr QF Hotchkiss (47mm/L40) naval guns on the train, on a naval Model 1915 mounting. Note the Royal Navy gunners, and the internal armour in the wagon.
_(Photos: Paul Malmassari Collection)_
One of the two 4-6-0 engines.
_(Photo: Paul Malmassari Collection)_
Since the role of this train was as much political as military, the crew had not skimped on depictions of the flag.
_(Photo: Paul Malmassari Collection)_
One of the armoured trains in India during the 1930s, with its classic silhouette and notably a 12pdr naval gun on a bogie wagon. The rail gauge was the Indian broad gauge of 5ft 6in (1.676m).
_(Photo: Military vehicles Museum)_
### Armoured Trains in India (1930s)
During the 1930s India was a hotbed of disaffection and revolt against the British, and the railway security units were always more numerous compared to the other regular regiments. Two armoured trains were permanently stationed in Lahore, up until 1939 when the Royal Navy reclaimed their guns for fitting to merchant ships. The troubles of 1930 on the North-West Frontier once more called for the presence of armoured trains. At least one of them was employed on the Peshawar line, crewed by the 4th Bengal Engineers Company.
A similar artillery wagon in 1930 at Peshawar, with a crew probably furnished by the North Western Railway Regiment, which was responsible for 1750 miles (2800km) of track. The 1st Battalion covered the North-West Frontier and the 2nd Battalion covered Baluchistan.
_(Photo: Paul Malmassari Collection)_
### British Mandate in Palestine and Sinai (1923–1939)
With the breakup of the Ottoman Empire, carved up between the victors under the Sykes-Picot Agreement, Palestine was to be ruled by the League of Nations under an International Mandate. However, secret discussions between Clemenceau and Lloyd George which had begun in 1918 led to Britain obtaining control of Mosul and Palestine. The British Mandate over Palestine came into effect on 23 September 1923. Disturbances had already taken place in 1922, but it was during the Arab revolt of 1936–9 that the railway network was seriously threatened. On 26 September 1937 the British High Commissioner for Galilee was assassinated, and in 1938 alone, 340 attacks on the railway network were recorded, the aim of the Arabs being to cut communications between Egypt and Iraq. The British sent 20,000 men to maintain order, and in order to ensure the security of the railway network, they put armoured wagons and trolleys into service.
Model T Fords converted into rail trolleys, with minimum protection, to patrol the tracks. In September 1938 the 2nd Battalion the King's Own Royal Regiment was made responsible for protecting the Jerusalem-Jaffa line.
_(Photo: Library of Congress)_
Before bomb attacks and gunfire targeting the crews became the norm, civilian vehicles were adapted for rail use, propelling a ballasted chariot, and with a machine gun on a pivot in the back of the pickup.
_(Photo: Paul Malmassari Collection)_
One of the methods successfully used to put a stop to mines placed on the tracks was to sit local Arab leaders on the ballasted chariot. After the first two hostages were killed in October 1938, no more mines were laid.
_(Photo: Paul Malmassari Collection)_
Here the machine guns are Lewis Mk I in .303 (7.7mm) calibre, mounted in the back of Ford Model 1937 pickups.
_(Photo: Library of Congress)_
The fate of too many crews of reconnaissance machines was to be sacrificed to ensure that the trains, and especially those carrying civilians, would not be derailed.
_(Photo: Paul Malmassari Collection)_
This train was used on the Samaria narrow-gauge line. Note the anti-grenade netting and the letters 'H.R.' standing for 'Hedjaz Railways'.
_(Photo: Hans Kohit via Chen Melling)_
One of the great advantages of the train: the water tanks on the wagon which also served as the safety vehicle.
_(Photo: Hans Kohit via Chen Melling)_
Three trolleys (official designation: Lightly Armoured Patrol Vehicle) for the metre gauge were ordered from the Drewry Car Co. Ltd. on 28 January 1938 and built by Baguley Cars Ltd. Note the wire netting protection, and the installation of a Lewis Gun.
_(Photo: Lichfield Records Office)_
Two armoured escort wagons were built in Palestine. Here is the first one, _The Hillmen's Pride_ , a concrete blockhouse mounted on 30-ton platform wagon No 3708, 24ft 3in (7.39m) long and 7ft 6½in (2.30m) wide.
_(Photo: Library of Congress)_
A view of the other side of the flat wagon, showing the entry door. No glass or armour was provided for the openings. The concrete was 8¼in (21cm) thick.
_(Photo: Uzi Raviv)_
A second bogie flat wagon No 3702 was fitted with a steel bunker, and named _Noah's Ark_. Note the complete roof protection.
_(Photo: Uzi Raviv)_
### Armoured Trains in Great Britain during the Second World War
Reliving the old fear of a landing by enemy forces, the British decided in May 1940 to create a militia, which would become the Home Guard, and studied the possibility of building armoured trains to defend the coastline. A large number of proposals, proof of the British spirit of inventiveness, saw the light of day in the course of 1940, and on into 1941. Admiral Sir Frederic Dreyer wanted several trains to defend the north coast of Cornwall (which would in fact be defended by Trains A, D and F after July 1940) and the coastline of the Firth of Clyde south of Glasgow. In December 1940 Captain Kenneth Cantlie, of the Transport Bureau, proposed a train of modern construction, crystallising the various ideas on the subject discussed by the officers of the Armoured Train Groups in Scotland on 24 August. The project was not proceeded with, and neither was the idea of armouring a certain number of railcars. On the south bank of the Humber, the docks of Grimsby and Immingham proceeded with the construction of an armoured train so heavy that it was barred from using the normal tracks. In February 1941 a project by the Home Guard in the Peterborough area for an armoured train comprising a shunting engine and an armoured wagon armed with Bren LMGs was turned down, as was the equally basic train proposed by the Home Guard in Essex. Finally, in June 1941 a super-heavy armoured train was proposed, with twin 4in (105mm) AA turrets and lighter anti-aircraft armament. Again, this project was not pursued.
The armour covered only the upper parts of the engine and tender, an economical solution adapted with a view to protecting them from attacks by the Luftwaffe.
_(Photo: University of Glasgow)_
Here the crew composed of men of the Black Watch have removed the metal roof, certainly due to the stifling heat in the interior.
_(Photo: Library of Congress)_
In 1943 Austerity 2-8-0 engine No 7195 of the War Department was fitted with experimental armour protection with a view to future employment on the Continent. Built by the North British Loco Co. in Glasgow, the engine was armoured in the same workshops. In the event, the aerial threat had decreased by the time the engine was sent to the Continent, and it was deployed without the armour.
The machine breathes an aura of raw power, and in addition allows the crew to carry out regular maintenance without having to hinge upwards or otherwise dismantle armour plates.
_(Photo: University of Glasgow)_
### The standard armoured trains of the Second World War
The basic principle consisted of armouring a standard series of wagons by the addition of a layer of concrete in the interior. In fact, it was decided to pour the concrete inside a sandwich of two armour plates, to avoid the concrete spalling when the armour was struck. Depending on the planned use, the wagons would be cut away to allow the armament to be deployed.
The choice of base wagon fell on the 20-ton steel coal wagon of the LMS, which would have to be cut down at one end in order to allow the gun to train. The main armament was to be a 6pdr 6cwt Hotchkiss Mark II, as used in the side sponsons of the heavy tanks of the First World War. These had been in store ever since the tanks had been scrapped, and had the advantage that the original long barrel of the Hotchkiss naval gun used in the Mark I tanks, proving a distinct disadvantage in the confines of the trenches, had been reduced in length for the Mark IV and later tanks. In the armoured wagons, the guns could therefore be trained laterally without fouling the tight British loading gauge. At the suggestion of the Poles, the virtually cylindrical gun shields from the tank sponsons were cut down to a half-circle in section, and the two offcuts were welded back on, but reversed, thus extending the protection for the gunners.
At the rear of the gun compartment a door communicated with the infantry fighting compartment, which had sides extended upwards by armoured shields with sliding shutters. The rest of the train armament comprised three Bren LMGs and a Boys .55in (13.9mm) anti-tank rifle in each combat wagon, plus the personal arms of the crew. Later a Vickers machine gun would be added. No overhead protection was ever fitted throughout the life of the trains, as it was envisaged the machine guns would need to fulfil an anti-aircraft role. The later Vickers was admirably suitable for close-range AA actions, but trying to engage a fast-moving enemy aircraft with a Bren with a magazine containing only twenty-nine rounds was impractical.
In order to avoid encumbering the combat armoured wagons, lightweight intermediate wagons for ammunition, stores and the like were inserted between the armoured wagons and the engine, thus extending the length of each train and providing for virtual all-round observation from the combat units.
The engine was a 2-4-2 LNER tank engine, covered in armour except for the top of the boiler, the smokebox and the wheels. The crew was provided with vision ports closed by sliding shutters.
The normal composition of each train was as follows:
– gun wagon.
– lightweight wagon.
– armoured engine.
– lightweight wagon.
– gun wagon.
No safety wagon was included, as the threat of mines on the track was felt to be so slight as to not justify diverting goods rolling stock. One of the lightweight wagons, originally three-plank, was later replaced by a five-plank wagon, and there were minor differences in the armouring of the various engine whistles, pumps and valves.
It appears that construction of the trains was begun in May 1940 and proceeded at an extremely rapid pace, as the first seven engines were delivered from the Stratford workshops before the end of June, while the Derby workshops supplied the fourteen armoured combat wagons and an equal number of intermediate wagons before 27 June. The component units of the five other trains were delivered in July. During 1940, the protection was reinforced by adding wooden planking to the interior walls of the wagons, to avoid ricochets off the armour. At the same time, each train was fitted with fixed mountings for their Bren Guns, produced in local workshops, placed in the front part of the combat compartment.
In order to have spare engines to hand, apart from those which could be provided by local engine sheds in an emergency, an additional engine was attached to each Armoured Train Group between January and February 1941. In addition an armoured tender was added to each train in early 1941. Planned already in 1940, they provided an increase in water and coal capacity sufficient to increase the range of each train to over 106 miles (170km). The additional braking capacity of the tenders improved the overall stopping distances of the trains, with the aim of avoiding accidents such as the one involving Train F in September 1940, when the driver of a lorry was killed. In actual fact, only nine armoured tenders were delivered: five six-wheel tenders to Trains A, F, H, L and M, and four bogie tenders to Trains D, G and K.
As described in the relevant section of the chapter on Poland, when the trains were being operated by Polish crews, they began to receive armoured vehicles carried on flat cars, in order to train the Poles to operate armour.
**O RGANISATION**
Attached to the Royal Armoured Corps which supplied one officer, seven NCOs and twenty-nine men, each train also carried eight members of the Railway Engineers, responsible for the driving and other technical matters. Each crew was composed of active members and a reserve ready to take over as replacements as required. At least on paper, there was also supposed to be a flying reserve based at the command centre of each Group. A Group of armoured trains was composed of at least two trains which could each operate independently. The Group was commanded by a major of the Royal Armoured Corps assisted by an officer of the Transport Engineers.
Finally, on 21 September 1940, it was decided that all the crews would be Polish, a changeover which was completed in April 1941. When the Polish crews had accumulated sufficient experience with the armoured vehicles attached to their trains, the Poles were transferred to armoured units, and the trains were handed over to the Home Guard.
**O PERATIONS**
The trains were mobilised in two stages: the first batch of Trains A to G were mobilised on 30 June 1940, and the subsequent batch, Trains H to M, on 10 July.
According to operational requirements, and especially in view of the lack of defences in Scotland, the trains were divided between the following five regions: Scottish Command, Northern Command, Western Command, Eastern Command and Southern Command. It was even planned to build a further eight trains for the Scottish Command to protect the extremely long Scottish coastline, but the project was never begun.
**Armoured Train A:** Attached to Eastern Command on mobilisation, it joined Group No 1 (with Trains C, D and G) and carried out training missions in Norfolk in the vicinity of Norwich. It was then transferred to Southern Command on 25 July, where it joined the garrison at Newton Abbot, to the east of Plymouth. In July 1941 it moved to Cornwall to replace Train D which had been transferred to the east of England and took up garrison at Wadebridge. Its operational area took in practically the whole of Cornwall up until April 1943. On 20 April 1942 it moved to Hitchin, from where it patrolled on a 25-mile (40km) radius. It was dismantled in May 1943.
**Armoured Train B:** Designated as Armoured Train No 6, it was mobilised on 28 June 1940 and was part of Group 3 stationed in Scotland. It commenced patrols on 6 July on the north-east coast of Scotland, but on 28 July was transferred with Trains H and M to Northern Command. Its new area of operations extended from Newcastle to Berwick, with the various surrounding lines, where it remained for several months. In February-March 1941, the train was immobilised due to severe weather which was causing collisions and derailments in its area. It recommenced patrolling on 8 April, undertook a practice shoot on 23 August, and participated in a 'public relations exercise' on 1 February 1941. The remainder of the year passed without any particular incidents. On 8 November it suffered a bombing attack, which destroyed its base accommodation but only caused a few minor injuries among the crew. During the Winter of 1941/42, the armour on its engine was reinforced, but between 15 and 21 April 1942 it became the first of the armoured trains to be broken up, and its wagons were returned to civilian use.
**Armoured Train C:** Mobilised on 30 June 1940, it was part of Group 1 along with Trains A, D and G. On 3 July it began patrolling the east coast of Norfolk, and in late July 1940 it added to its area of operations that of Train D, which had been transferred to the west. In March 1941, it was transferred 19 miles (30km) further south to Westerfield, and shortly afterwards took on board its Polish crew. In August, its operational area was expanded further east and in April 1942 it received three armoured Bedford trucks, followed by a fourth in June. It was broken up in June 1943.
**Armoured Train D:** Mobilised on 30 June 1940, it was part of Group 1 along with Trains A, C and G, and began patrolling on 3 July along the coasts of Essex and Suffolk. On 25 July it was transferred to Southern Command to operate in Cornwall out of Wadebridge in the north of the county. After a year of patrols, it was once more transferred to the east, to Essex, and received an operational area which reached within 12 miles (20km) of London. In April 1942 it also acquired armoured Bedfords, and was broken up in September 1943.
**Armoured Train E:** Mobilised on 30 June and attached to Group 2 with Train F, it began patrolling on 1 July in Kent, on the rail network south of the Thames Estuary. At the end of July, it was sent to Tonbridge and was given the dangerous mission of patrolling the whole of the south-east coast, in other words the region most menaced by the threat of invasion. In March 1941 it moved to Ashford and shortly afterwards received its Polish crew. It patrolled within a radius of 25 miles (40km). In addition, it was designated as the experimental unit used to test modifications to be applied to the armoured trains. During the Winter of 1941/42, the armour protection on the engine was reinforced at Ashford, and at the same time the train received its first armoured vehicles in the shape of Bren Carriers, followed in early 1943 by four Valentine tanks transferred from Train H. Train E was dismantled in July 1943.
**Armoured Train F:** Mobilised on 30 June and attached to Group No 2 with Train E, it patrolled in Kent along the axis Ashford-Dungeness-Appledore-Hastings-Lewes, operating to a fixed timetable, and thus covered the whole south coast of Kent. On 25 July it was transferred to Barnstaple in Devon, coming under the control of Southern Command, and patrolled there until early 1942. In February 1942 it received several Covenanter tanks and on 20 April it began patrols on the lines to the north of the Thames, without going as far as London. It was broken up in April 1943.
**Armoured Train G:** Mobilised on 30 June, it was part of Group 1 along with Trains A, C and D, and began patrolling the north coast of Norfolk on 3 July. It was based in this area until September 1941, when it moved further south to Cambridge. In April, it began to take delivery of three Bedford armoured vehicles, the last one arriving in June. It was dismantled in June 1943.
**Armoured Train H:** Attached to Scottish Command, Group 4, from 6 July 1940 it patrolled in the region of Aberdeen, but from the 28th of that month it was transferred to Northern Command with Armoured Train M. In April 1940 it was in position near the Humber estuary, one of the most vulnerable points in the event of a German invasion. But overall, Armoured Train H seems to have been relatively inactive. On 14 December 1940 it was transferred to Canterbury, to the south-east of London. Then when the Polish crews began to take over railway duties, Armoured Train H undertook its first mixed patrol on 5 April 1941 between Canterbury, Faversham and Minster then returned to Canterbury. In early 1943, Valentine tanks arrived to supplement the Covenanter tanks attached as patrol vehicles. One of the tanks was, however, destroyed by a direct bomb hit on the night of 31 May/1 June 1943. Armoured Trains D and H were the last to be broken up in September 1943.
**Armoured Train J:** Attached to Scottish Command on mobil-isation, it was part of Group 4 and on 10 July it moved to the region around Stirling. Its area of operations extended from the Firth of Tay to the Firth of Forth. It remained there until late August. On 7 September, it was put on alert by mistake, which made the local population fear that German paratroops had landed in the area. It was one of the first three trains (with K and L) to receive Polish crews, following the decision of 21 September 1940. During 1941 it was the train which undertook the greatest number of operations. During the Winter of 1941/42, the armour protection of the engine was reinforced at Cowlairs, and in early 1942 the train was transferred to Thornton Junction. The order to dismantle it was issued on 5 November 1944.
**Armoured Train K:** Transferred to Scottish Command on mobilisation, it reached Edinburgh on 10 July with Group 4 and patrolled the south bank of the Firth of Forth. With Trains J and L, it was one of the first to receive its new Polish crew. Its operational area was extended in 1941 to take in stations 50 to 65 miles (80 to 90km) from its base. During the Winter of 1941/42, the armour protection of the engine was reinforced at Cowlairs. The train was then transferred to Saughton Junction in early 1942, where it was dismantled on 5 November 1944.
**Armoured Train L:** Attached to Scottish Command on mobilisation, it was part of Group 4, and on 10 July 1940 moved to the area around Glasgow. On the 18th, it moved to Dumbarton and carried out patrols in the direction of Stirling, then further north from the 21st. On 31 July it moved to Aberdeen to replace Train H which had been transferred further north, and it began patrolling from mid-August. Its operational area was the largest of any of the armoured trains. As with Trains J and K, it received its Polish crew and sent its engine to the Inverurie workshops, near Aberdeen, to have its armour protection enhanced. This would become its final base from 1942 until it was dismantled on 5 November 1944.
**Armoured Train M:** Attached to Scottish Command on mobilisation, it was initially designated Armoured Train 'I' before this was changed soon after to 'M'. On 12 July 1940 it moved to the town of Forfar to the north of Dundee, where it undertook patrols up until late July. On the 28th, it was transferred along with Trains B and H to Northern Command. On 30 July it reached Louth and began patrolling the east coast of Lincolnshire, undertaking various training activities such as firing its 6pdr guns on 27 October, and what we would today term 'public relations exercises'. In January 1941, the train was transferred further south, to Spalding, and shortly after received its Polish crew. At the end of the year, its area of operations was increased to include the Humber. As a result, it was transferred 15 miles (25km) further north, to Boston, but its stay there was brief. During the Winter of 1941/42 the armour on the engine was reinforced at Stratford, and in mid-April the train was dismantled, the rolling stock being sent to Catterick to be returned to civilian use. The engine itself was for a time under repair in Kent, but its armour was removed by 5 November.
**F INAL DISPOSITIONS**
When the majority of the armoured trains were demobilised and dismantled (apart from the engines), Scottish Command wanted to retain its own trains after the Polish crews left, in view of the huge length of coast which needed watching. Approval was given in April 1942, railwaymen from the LNER taking over the running of the trains, while the Home Guard would take over the military side. But to ensure that sufficient personnel would be available, without overstretching the crews, the trains had to be relocated in more important Home Guard bases. Thus between June and July 1942, Armoured Train J left Stirling and moved to Thornton Junction (Fife Sub-Area), Armoured Train K moved to Saughton Junction to the west of Edinburgh (10th City of Edinburgh – 3rd LNER – Battalion) and Armoured Train L set up base at Inverurie (8th North & South Highlands Area Battalion). On 5 November 1944, with the Allies just six months away from completing the downfall of the Reich, the decision was taken to withdraw the last three trains from active service.
### The Royal Navy armoured train project
This train was planned to act in support of the twelve armoured trains described above, especially in view of the meagre defences of the south coast of England, which was the area facing the greatest threat of German invasion. The Royal Navy Armoured Train, however, remained on the drawing board.
Armoured Train A, the first to come out of the workshops, seen here at Shoeburyness.
_(Photo: IWM)_
A fine view of a Vickers machine gun in a side mounting, manned by a sergeant of the Home Guard. The photo is obviously posed, as the ammunition belt contains no cartridges. The soldier behind him is armed with a P14 rifle. Note the internal wood cladding. The lack of overhead protection is glaringly obvious.
_(Photo: IWM)_
### The miniature armoured train
This 'thirteenth' train was built for use on the 40cm gauge line of the Romney, Hythe and Dymchurch Railway (RH&DR), once this line had been requisitioned by the army on 26 July 1940. Work had already begun on 16 July on converting the locomotive originally chosen, a diesel shunter, but it became immediately obvious that the additional weight to be carried could not be supported by the bogie and the two driven axles. A steam engine was therefore selected for conversion, the famous 4-8-2 _Hercules_ of the RH&DR. The work of fitting the armour took one month, and protected the whole engine except for the driving cab, which was left open at the rear. The two armoured wagons, former mineral wagons, were coupled in front of and behind the engine. Each wagon was armed with a Boys anti-tank rifle and a coaxial Lewis LMG mounted behind a shield on a ring at one end, with a second Lewis on an anti-aircraft mounting in the central compartment, but without a shield.
For all its reduced dimensions, with its four Lewis Guns the Miniature Armoured Train was credited with one victory, a Heinkel III, and one probable, a Messerschmitt Bf 109 on 7 October 1940.
_(Photo: IWM)_
Between 30 April and 30 June 1943 the line and the rolling stock were progressively returned to their previous use, and the armour plating was removed. But this famous train has been recreated, with a steam engine and a single wagon, clad in wood to represent armour.
_(Photo: RH &DR)_
### Armoured wagon 'HMS _Terror_ ', 1940–1944
During the Winter of 1940/41, the Home Guard unit at the Experimental Establishment at Shoeburyness built an armoured wagon armed with a naval 12pdr QF gun in the central position and a 2pdr pom-pom at each end. Originally built in 1916, the bogie well wagon was intended to mount an anti-aircraft gun, and entered service during the First World War. Then in 1940 at Swindon, it had previously been used for the trial mounting of a 6in gun. As armed in 1940–1, it was intended to be used for the anti-aircraft defence of the Shoeburyness polygon, at the mouth of the Thames, and therefore on the route taken by German bombers, and was hauled by an unarmoured diesel shunter. Although of imposing appearance, its organisation left much to be desired: the large mast defiantly flying the Royal Navy ensign was doubtless good for morale, but seriously reduced the fields of fire of the three guns. To be even moderately effective against modern aircraft it would have required some form of fire-control system, and in the photos it appears to lack even a basic rangefinder. The pom-pom was recognised by some in the Navy as an ineffectual AA weapon from the early 1920s (due to its low muzzle velocity and short range) but it could put up a useful barrage to deter strafing and hitand-run fighter-bombers. The well wagon survived the Second World War. It is now in the collection of the Railway Museum at Burnham-on-Crouch, but devoid of armament and armour.
Side views of the wagon taken in January 1941, the mast denoting an unequivocal naval origin. This gun battery falls halfway between an armoured train and an artillery battery.
_(Photos: PE &E)_
### Armoured trolleys in Ulster (1940–1944)
In Northern Ireland, the British Army needed to protect troop movements against sabotage by enemy agents or IRA sympathisers. Trials of an armoured trolley built on a commercial chassis failed because of the excessive weight. The choice therefore fell on a freight flat wagon, motorised via a belt drive to one axle, on which was mounted an armoured box allowing the firing of light weapons plus Lewis light machine guns. These were also to be used in an anti-aircraft role firing through a part of the roof which slid open. Each Lewis Gun was to be provided with 1000 rounds of .303. Nine units were ordered, but only six were built in Northern Ireland workshops: three were sent to the north-east area of Ulster centred on Antrim, and the three others went to Portadown to patrol further to the south-west. In 1944 they were dismantled, and no trace of them survives.
Converted from GNR(I) wagons, these trolleys were disguised as cement wagons operating from Whitehead and later Magherafelt. Note the right-hand sliding portion of the roof armour, to allow anti-aircraft fire. The initials stand for the 'London Midland and Scottish Railway – Northern Counties Committee' following the union of the two companies in the Grouping of 1923.
_(Photo: IWM)_
Exercise disem-barking to investigate a suspect location. The muzzles of the two Lewis Guns can be seen emerging from the front apertures. The soldier on the left has an SMLE, but the man on the right carries a P14.
_(Photo: IWM)_
### 'KROHCOL', Malaya, 8–11 December 1941
During Operation 'KROHCOL', an armoured train from Padang Besar manned by thirty men of the 2/16th Punjab Regiment entered Thailand in an attempt to destroy a bridge near Khlong Ngae, in order to delay the Japanese advance. The train was part of the third British attack column.
### East African Campaign, 1940–1941
Between June 1940 and November 1941, during the campaign conducted against the Italians (including a small German unit and colonial levies), launched from the neighbouring British colonies, an armoured train was used in the Sudan, about which no information has come to light.
### British Occupation Forces in Italy, 1944–1945
In their occupation zone, the British used a Steyr le.Sp as transport, more out of availability than necessity, as the fighting in the area had ceased.
_(Photo: Paul Malmassari Collection)_
The same machine in June 1946 at Cormans, an early model recognisable by the rectangular shape of the protective covers over its ventilation intakes. It was named _Atom_ by its users.
_(Photo: from the Collection of the late Andrew Gillitt, seen here in the observation cupola)_
### Winston Churchill's Armoured Train, 1944, and King George VI's Armoured Saloon
In the days leading up to the Normandy Landings, Churchill's special train (codename 'Rugged') was parked in the village of Droxford in Hants before returning to Waterloo Station. It was made up of eight coaches and was hauled by a 4-4-0 Drummond T9 engine. The LMS coaches were armoured on the exterior.
In comparison, the Royal Saloon built for King George VI on the basis of an LMS dining car was armoured on the interior and had bullet-proof glass windows, looking for all the world like a standard coach. George VI's armoured coach still survives, in the collection of the Severn Railway Society.
### General Eisenhower's Armoured Coach, 1945
In 1945 a special armoured coach was built in 1945 by the LNER for General Eisenhower, Supreme Commander, Allied Forces Europe. Converted from a wagon-lits, out of the ten original sleeping compartments, six were transformed into a large conference room and an office, with radio communication facilities. Sides and windows were armoured, and the total weight after conversion was 51 tonnes, or 7.5 tons more than the coach in its original state.
### Armoured Trolleys in Palestine up to the end of the British Mandate (1948)
After the end of the Second World War, during which the British Mandate in Palestine continued in force, the terrorist movement which was extremely active from 1945 to 1947 was Zionist. The Jewish revolt against British rule began in 1944 and continued through 1947, and was followed by the civil war in 1948. The converted armoured cars used as rail escort vehicles were supplemented by trolleys built on commercial chassis, and armoured wagons were coupled in the trains. The most murderous terrorist attack on the railways took place on 22 February 1948, when a mine exploded on the Cairo to Haifa line, causing the deaths of twenty-eight British soldiers and wounding another thirty-five.
Humber LRC (Light Reconnaissance Vehicle) Mk III converted into a rail trolley. Production of this 3.7-ton machine began in 1941. The mudguards have been removed so the headlights have had to be mounted on the bonnet.
_(Photo: RAC Tank Museum)_
A pair of Marmon-Herrington Mk IV armoured cars on rails, mounted back-to-back in the classic configuration. In between the two there is a cab for carrying troops.
_(Photo: All Rights Reserved)_
Daimler Mk III serial number F351115, seen here in 1948. Certain reference sources state that a prototype trolley conversion had been tested but not adopted. In this photo there is a second machine probably attached back-to-back with No F351115. The men from the 21st Lancers are posing with a .30 cal (7.62mm) Browning machine gun and signal flags; almost certainly the lower one is green and the upper, red.
_(Photo: Paul Malmassari Collection)_
The blockhouse from _The Hillmen's Pride_ seen dismounted and abandoned in the 1990s, on which the camouflage pattern can still be made out.
_(Photo: Paul Cotterell)_
_The Hillmen's Pride_ restored and on show today, on a modern bogie flat wagon, in the Israeli Railway Museum in the former station in Haifa. Note the bars fastened over the window openings, which were never fitted in its original state.
_(Photo: Israeli Railway Museum)_
### Land Rover Trolleys, Sudan (1952)
The Sudan became an Anglo-Egyptian condominium in 1899, after the country had been conquered by the British Expeditionary Force led by General Kitchener. Years of instability and revolt followed, until the accession of King Farouk who took the title of King of Egypt and the Sudan. Finally, in 1953 a treaty was signed between Great Britain and Egypt, recognising the right of the Sudanese to self-determination.
The railway network was now more important to the Sudan than the road system. It was therefore vital to ensure the security of the railway lines, and in about 1950 the British Army converted Land Rover 80s into trolleys for the metric gauge.
Two interesting views of the armoured Land Rovers converted for rail use. Note especially the folding side plates of the rear compartment and the doors, and the cage which was intended to offer protection against missiles thrown by a mob.
_(Photos: REME Museum)_
Drawing of the trolley prepared afterwards by the workshops of the East African EME at Nairobi.
_(Plan: REME Museum)_
Armour plating added to the cab of the engine.
_(Photo:_ Soldiers _Magazine)_
### Armoured Trains and Trolleys during the State of Emergency in Malaya (1948–1960)
The most widespread use of these units by the British Army was during the bloody conflict which began in Malaya in 1948 and which ended with the victory of the British over the Communist insurgents in 1960. Before standard production vehicles could be obtained, the urgency of the situation meant that many means were resorted to. Armoured Jeeps were used for the movement of individuals, armoured cars, driving along the ballast and skimming over the tracks (a procedure which required changing the tyres every evening after missions), were employed for track reconnaissance. As for the trains, apart from these same armoured cars carried on wagons at the head and tail of the rakes, the railway company mounted armoured cloches on flat wagons, permitting observation and the firing of individual firearms, and finally the engine driving cabs were armour-plated.
A fine view of one of the cloches placed on a bogie flat wagon with the planking removed. The casting may have originated in heavy industry such as a foundry.
_(Photo:_ Soldiers _Magazine)_
Humber Mk III armoured car photographed on 5 June 1950 in Kuala Lumpur Station. Note that the turret faces the rear.
_(Photo: Paul Malmassari Collection)_
A remarkable transformation of a Jeep for the Telecommunications Department. Note the added stoneguards, and also what appears to be a re-railing device carried beneath the vehicle.
_(Photo:_ Soldiers _Magazine)_
In 1950, the firm of Wickham supplied a dozen Type 40 Mk I chassis to the Malayan Railways. Once received, they were fitted with armoured hulls designed by the Royal Engineers. This was the first version of a much more sophisticated vehicle which would appear two years later. The design of this was begun after the receipt of an order on 29 July 1952, and was completed at the beginning of the following year. Between 2 March and 23 November 1953 the firm delivered forty-one units (Chassis Nos 6 538 to 6 679).
Technically, the vehicle was able to be re-railed with the aid of a second unit used as a tractor. In local use, the operators equipped it with a safety bogie, propelled in front to detonate mines. The motor was a Perkins P 6 diesel producing 60hp, which gave a maximum speed of 63mph (100km/h) in either direction. The crew comprised a commander, two drivers and one or two machine-gunners. The two drivers sat in tandem on the right-hand side, and each one was provided with a set of driving controls. The armour gave protection against small arms up to .30in (7.62mm) calibre. The main armament comprised a .30 cal (7.62mm) machine gun in the turret from a Ferret armoured car, mounted on the roof of the trolley. The searchlight was coupled to the machine gun by a mechanical linkage. On each side of the hull roof, sliding shutters allowed for ventilation and throwing grenades, while access was by two side hatches. Following independence, the trolleys were transferred to the Railway Police who used them for training. A certain number were also sold to South Vietnam and Thailand.
Wickham armoured trolley (Armoured Wickham No 6) of the first series, designed by the Royal Engineers. A new turret would be fitted before the 1953 trolleys arrived in the country.
_(Photo:_ Soldiers _Magazine)_
Drawing of the Wickham trolley, showing the coupling arrangement.
_(Plan: Wickham)_
### The Mau-Mau Revolt in Kenya
In 1953, the Royal Air Force was obliged to place in service two armoured mineral wagons protected by sandbags and armed with twin Browning machine guns on the line from Mombasa to Eldoret, an RAF base near to the frontier with Uganda.
### The Royal Family's Armoured Train
In 1985, plans were drawn up for the building of an armoured train for the Royal Family, following on from the armoured Royal Saloon built in 1941 by the LMS. Essentially defensive, its role would be to counter attacks by IRA or other terrorist groups, employing Chobham-type armour as used on modern main battle tanks. It would also have been equipped with a sensitive radar capable of detecting irregularities in the track or obstacles placed on the line. The cost threatened to be prohibitive, and criticism from certain Members of Parliament, notably those with republican sentiments, caused the project to be abandoned.
### Bullion Vans
In the days of the Gold Standard, bullion was physically transferred both ways across the Atlantic, and to and from Europe, so the UK railway companies owned specially reinforced Bullion Vans. For the USA traffic, the LNWR and successor company the LMS carried gold between London Euston and Liverpool; the LSWR and the GWR carried gold between London and Plymouth. The final special Bullion Vans were built in 1965, two years after the Great Train Robbery, when British Rail decided to convert five Mk I Brake Corridor Second Class coaches into Bullion Vans, installing internal protection, plating over most windows and fitting the remaining ones with armoured glass, and adding radio communications equipment. They were later painted Army Green and used for the high-security transfer of MoD ammunition.
Great Western Railway Bullion Van No 878 built in 1913 (in crimson lake livery) for the gold traffic between Britain and the USA, passing via Plymouth. These vans had doors only on one side for security reasons, and no other openings. A total of five GWR Bullion Vans were built between 1903 and 1913.
_(Diagram M.17 and Official Photo: British Rail)_
**SOURCES:**
**Books:**
Balfour, George, _The Armoured Train, its Development and Usage_ (London: B T Batsford Ltd, 1981).
Danes, Richard, _Cassell's History of the Boer War 1899-1901_ (London: Cassell and Company Ltd, 1903).
Fletcher, David, _War Cars: British Armoured Cars in the First World War_ (London: HMSO, 1987).
Forty, George, _A Photo History of Armoured Cars in Two World Wars_ (Poole: Blandford Press, 1984).
Girouard, Lieutenant-Colonel Sir E P C, _History of the Railways during the War in South Africa, 1899-1902_ (London: Harrison and Sons, 1903).
Goodrich, Lieutenant-Commander Caspar F, _Report of the British Naval and Military Operations in Egypt, 1882_ (Washington DC: Government Printing Office, 1883).
Hill, Tony, _Guns and Gunners at Shoeburyness_ (Buckingham: Baron Books Ltd, 1999).
Jervois, Major-General Sir W F D, _Defences of Great Britain and her Dependencies_ (Adelaide: E. Spiller, 1880).
Kearsey, A, _A Study of the Strategy and Tactics of the Mesopotamia Campaign 1914-1917_ (Aldershot: Gale & Polden Ltd, nd).
Pakenham, Thomas, _The Boer War_ (New York: Random House, 1979).
Pratt, Edwin A, _British Railways and the Great War, Vol 1_ (London: Selwyn and Blunt, 1921).
RE Institute, _Detailed History of the Railways in the South African War, 1899-1902_ (Chatham: 1904: new edition Arkose Press, 2015).
Sanders, Lt.-Col. E W C, _The Royal Engineers in Egypt and the Sudan_ (Chatham: The Royal Engineers Institution, 1937).
Tourret, R, _Hedjaz Railway_ (Abingdon: Tourret Publishing, 1989).
Townshend, Charles, _The British Campaign in Ireland 1919-1921_ (Oxford: Oxford Historical Monographs, nd).
**Journal Articles**
'17th/21st Lancers Armoured Rail Detachment' _, The White Lancer and the Vedette_ (History of the 17th /21st Lancers) Vol XXIX, No 2 (November 1947), pp 51–3.
Aitken, D W, 'Guerrilla Warfare, October 1900-May 1902: Boer Attacks on the Pretoria-Belagoa Bay Railway Line', _Military History Journal_ Vol 11 No 6 (December 2000), pp 226–35.
___________, 'The British Defence of the Pretoria-Delagoa Bay Railway', _Military History Journal_ Vol 11 No 3/4 (October 1999), pp 80–6.
'Armoured Trains in South Africa', _The Navy and Army Illustrated_ (6 September 1902), p 608.
'"B" Squadron letter', _The White Lancer and the Vedette_ (History of the 17th /21st Lancers) Vol XXX, No 1 (May 1948), p 20.
'Blockhouses', _The Royal Engineers Journal_ (2 November 1903), p 243.
Botha, Johannes, 'Armoured Trains of the Boer War', _Tank TV_ (NZ) No 22 (December 1999), pp 11–13.
___________, 'The Fowler Roadtrain and Mobile Blockhouses', _Tank TV_ (NZ) No 19 (June 1998), pp 10–11.
Conradie, Eric, 'The Firing of the First Shots in the Anglo-Boer War, 12 October 1899', _SA Rail_ (March/April 1993), pp 58–9.
Cooke, Peter, 'Armour in the Boer War', _Tank TV (NZ)_ No 2 (November 1992), pp 3–6.
Dillard, J B, 'Armoured Trains for Coast Defense', _The Engineer_ (14 February 1919), pp 150–2.
Fletcher, David, 'Les Véhicules militaires de F. R. Simms', _Tank Museum News_ (Belgium) No 13 (June 1986), pp 6–7.
Golyer, David G, 'The Miniature Armoured Train', _Bygone Kent_ Vol 12, No 7 (1991), pp 378–88.
Hill, R, and Hill, R H, 'The Suakin-Berber Railway, 1885', _Sudan Notes and Records_ Vol 20, No 1 (1937), pp 107–24.
Hussey, John, 'The Armoured Train Disaster, and Winston Churchill's Escape from Prison, South Africa, 1899', _British Army Review_ No 123 (nd), pp 84–103.
'In Loyal Natal', _The Navy and Army Illustrated_ (23 December 1899), p 369.
Lock, Ron, 'Churchill and the Armoured Train', _Military Illustrated_ No 133 (1999), pp 52–8.
McLean, C H, 'Havelock-Hairy Mary', _S.A.R. & H. War Services Union Newsletter_ (1975), pp 4–5.
Martin, Greg, 'LNER 2-4-2Ts on Armoured Trains', _World War Two Railway Study Group Bulletin_ Vol 14, No 1 (2004), pp 14.13–14.17.
Napier, Paul, and Cooke, Peter, 'Armour in Emergency', _Tank TV_ (NZ) No 4 (August 1993), pp 1–5.
Parsons, Major-General A E H, 'Railway Reconstruction by the Royal Engineers for the Military Railway Service, Allied Forces, Italy', _World War Two Railway Study Group Bulletin_ Vol 9, No 4 (1999), pp 9.111–9.116.
Phillip, S M, 'The Use of our Railways in the Event of Invasion or a European War', _Railway Magazine_ (May 1901).
Rue, John L, 'The Wickham Armoured Rail Car', _Army and Navy Modelworld_ (July 1984), pp 103–6.
'Science at the Front', _The Navy and Army Illustrated_ (15 December 1900), p 327.
'Tenders for Armoured Trains', _World War Two Railway Study Group Bulletin_ Vol 11, No 3 (2001), p 11.57.
'The Outlook in South Africa', _The Navy and Army Illustrated_ (7 December 1901), pp 273–4.
'The Siege of Ladysmith – Operations in Natal from 31st October to 19th November', _The Royal Engineers Journal_ (1 February 1900), p 23.
'The War in South Africa – North to South', _The Navy and Army Illustrated_ (20 October 1900), p 108.
'The Wide, Wide Veldt', _The Navy and Army Illustrated_ (17 May 1902), p 213.
'War Trains', _The Navy and Army Illustrated_ (9 December 1899), p 309.
Warner, Terry, 'Armoured Trains in Southern Africa', _Tank TV_ (NZ) No 6 (June 1994), p 1.
Weaver, Rodney, 'The Petrol Locomotives of McEwan Pratt', _Model Engineer_ (4 June 1971), pp 528–31, 554.
Zurnamer, Major B.A., 'The State of the Railways in South Africa during the Anglo-Boer War 1899-1902', _Militaria_ No 16/4 (1986), pp 26–33.
. R Hill and R H Hill, 'T _he Suakin Berber Railway_ '.
. 'Place of Peace'.
. _Schutzgebiet Deutsch-Ostafrika_ , subsequently divided between the British, the Belgians and the Portuguese.
. Fought on 2 September 1898.
. The rail gauge in the Sudan was 3ft 6in.
. The British withdrew their troops from Tientsin in December 1939 then from Shanghai in August 1940.
. The period from the Second World War to 1948 is covered later.
. See the chapter on France for the French zone of responsibility.
. The Austerity was a wartime version of the Stanier 8F of the LMS (London Midland and Scottish Railway), designed by engineer Robert Arthur Riddles, but using non-strategic materials. In all, 935 Austerities were built for the MoS (Ministry of Supply).
. Also known as 'XP' for Experimental Establishment.
. From Kroh, the starting point for the troops of the first, motorised, column (modern Pengkalan Huku) and 'Col' for Column. The second column was designated LAYCOL, Lay being the name of the commanding officer of the 6th Indian Infantry Brigade.
. Led by Sergeant Eddie Augustin of the Railway Operating Maintenance Company (ROMC) of the Federated Malay States Volunteer Force (FMSVF).
. A new name for the country decided upon in 1939 but not officially used before 1949, the former name Siam being used in parallel.
. 'Winston Churchill's Train – Codename "Rugged"', _World War Two Railway Study Group Bulletin_ Vol 24, No 3 (2014), pp 24.71–24.72.
. London Midland & Scottish Railway.
. London & North Eastern Railway.
. The British Mandate ended when the State of Israel was proclaimed on 14 May 1948.
. British forces had remained in Egypt after the formal occupation of the country ended in 1936.
. See H R J Davies, 'Les Chemins de fer et le développement de l'agriculture au Soudan', _Annales de géographie_ , Vol 70, No 380 (1961), pp 422–7.
. British units based in the Sudan in 1952 were: Sudan Signal Squadron; Eritrea Signal Squadron; 1st Btn South Wales Borderers; 1st Btn South Lancashire Regiment.
## GREECE
### ARMOURED TRAINS
After a long period of political instability, the Greek Civil War began in September 1946, sparked of by the refusal of the Communists to accept the return of King George II to the throne. At first the Communist forces, supported by Yugoslavia and Bulgaria, overran almost all of Greece, while the Government forces were supported by the British and later the Americans. Tito, who had broken away from Stalin, withdrew his support, and following a series of defeats the Communists agreed to a ceasefire in October 1949.
Humber Mk IV armoured car mounted on a railway flat wagon during the Greek Civil War. Note the check rail preventing the turret guns from firing straight ahead and thus hitting the wagon in front.
_(Photo: All Rights Reserved)_
Two views showing the methods of protecting trains during the Greek Civil War. It appears that the photo above left shows the interior of the casemate partly visible behind the armoured car in the previous shot. The armour seems to be concrete.
_(Both photos:_ L'Illustration _)_
**SOURCES:**
Metsovitis, Triantafyllos, '1945-1950', _NEA IMPS Hellas_ No 2 (1999), pp 36–40.
. In Greek: 'Tεθωρακισμέυο Tραίυο', pronounced 'Tethorakismeno Treno'.
. During the Second World War, EAM-ELAS, the armed wing of the Communist Party, had opposed EDES, the non-Communist resistance movement, and on the German withdrawal had risen in revolt, only to be crushed in February 1945 by an Allied force sent from the Italian Front.
## GUATEMALA
### ARMOURED WAGON
An attempted revolution against the rule of President Chacon broke out in January 1929 in western Guatemala. It failed, and the revolutionaries were dispersed, but they remained in control of certain towns. In February, in the course of their advance to regain control of the rebel towns, the government forces improvised an armoured wagon. It consisted of a field gun mounted on a platform wagon, protected by sleepers and sandbags.
**SOURCES:**
Ferrez, Major Turrel J, US Army, 'Armored Trains and Their Field of Use', _The Military Engineer_ Vol XXIV No 137 (Sep–Oct 1932), p 472.
A view of the leading wagon, with its field gun behind a wall of sleepers.
_(Photo: Philipp Jowett)_
## HONDURAS
### IMPROVISED ARMOURED TRAIN USED IN THE 1897 UPRISING
In 1897 the Honduran government was taken by surprise by an uprising, during which the rebels seized Puerto Cortez on 13 April, and then advanced towards San Pedro Sula. Along the way, at the Laguna Trestle they captured a train along with its driver, an American by the name of Lee Christmas, who was press-ganged into the service of the rebels, tasked with helping them enter the town. To that end, Christmas, turned mercenary somewhat against his will, organised the armouring of a flat wagon with walls of 20mm steel plates, reinforced by two layers of sandbags. A Hotchkiss gun was mounted at the front end.
The Federal army launched an attack on 14 April, but was driven off. The Federals were obliged to abandon San Pedro Sula and the train was able to enter the town. Lee Christmas was even promoted to the rank of Captain! His train was subsequently used to transport more rebel troops from Puerto Cortez, but the victory was short-lived: government troops, supported by Nicaragua, retook the port and the rebels, threatened from two sides, were forced to retreat precipitately towards Guatemala. The revolt fizzled out in May.
**SOURCES:**
Deutsch, Hermann B, _The Incredible Yanqui_ (London: Longmans Green & Co, 1931: reprinted by Pelican Publishing, 2012), pp 6–13.
. Originally from Louisiana, Lee Christmas was the local representative in Honduras for United Fruit. Six years earlier, he had lost his job as a train driver following an accident on the Memphis-New Orleans railroad. In Honduras his narrow-gauge train was being used to transport blocks of ice to the coast and return to the provincial capital with loads of bananas. After his service with the rebels, Christmas pursued a career as a mercenary in Latin America for many years.
. In 1895 Honduras, El Salvador and Nicaragua had agreed to form the Greater Republic of Central America.
## HUNGARY
### ARMOURED TRAINS 1918–1945
On 16 November 1918 the Kingdom of Hungary became the Democratic Republic of Hungary, and very quickly the new state lost border regions populated by non-Hungarian ethnic minorities. In April 1919 the government handed over power to Belá Kun who founded the short-lived Hungarian Soviet Republic, which was crushed on 3 August by the Czechs and Romanians. The country became a kingdom once more under the Regency of Admiral Horthy, who set about regaining the lost territories, a project which came to an end in 1945.
Austro-Hungarian armoured trains IV, VI, VII and IX were stationed on Hungarian territory in 1918. They were renumbered I, II, III and IV respectively. Four new trains, numbered V to VIII, were built between December 1918 and January 1919. Due to the continuing fighting on the new frontiers of the country, six additional trains to be numbered IX to XIV were ordered from MÁVAG, but the last two were never completed. The Communist regime intended to allocate these two trains, XIII and XIV, to the Red Railway Regiment, and a further five trains ordered in June 1919 were to be manned by the Hungarian Red Army. With the collapse of the regime, construction of these never even began.
On 12 June 1920 the new Hungarian Army reclassified the armoured trains as 'military surveillance trains', and distributed them across the country. In 1929, the four trains considered as worn out were broken up, and the four best trains, Nos I, II, III and V, were modernised. In 1938 smoke diverters were fitted on the engines, and turrets were mounted on the armoured wagons. Roman numbering was replaced by Arabic numerals. An armoured trolley, Type RÁBA Vp, was also put into service between 1932 and 1939. In the latter year, the trains were renumbered from 101 to 104, and came under the direct control of the Army High Command.
The four modernised trains went into action against Slovakia in March-April 1939, and took part in the reoccupation of Ruthenia in March. In 1940 they were used in the invasion of Transylvania and then in 1941 against Yugoslavia. They then took part in the invasion of the USSR, and finished the war on Hungarian territory. On the Eastern Front, anti-aircraft wagons with minimal protection were added to the trains.
Artillery wagon of the former Austro-Hungarian PZ IV or VI in use by the Hungarian Army in 1919.
_(Photo: All Rights Reserved)_
Armoured Train XII.
_(Photo: Magyar Műszaki és Közlekedési Múzeum)_
The engine of PV XII has only partial armour protection.
_(Photo: Magyar Műszaki és Közlekedési Múzeum)_
Interior shot of a Hungarian armoured wagon during the period of Communist rule. The armour protection extends down to the floor. Despite the spartan interior, note the communication system using voice tubes. The machine guns are Schwarzlose.
_(Photo: Magyar Műszaki és Közlekedési Múzeum)_
Armoured Train IX of the Red (Hungarian) Army in 1919, with its anti-aircraft flat wagon sandwiched between two armoured wagons. On this train, the machine guns fired through gunports in the wagons in front of and behind the engine, but the crew of the end wagon were limited to using rifles and pistols.
_(Photo: Magyar Műszaki és Közlekedési Múzeum)_
Austro-Hungarian PZ IX left in Hungary, seen in 1920 prior to being modernised. The two low-roof wagons would go to make up PV 102, and the powered railcar would go to PV 104.
_(Photo: Paul Malmassari Collection)_
8cm forward turret of the type originally mounted on the river patrol boat _Gyór_.
_(Photo:<http://militaryhistory.x10.mx>)_
PV 104 (ex-kkStB 303-343). In the 1930s, the turret was replaced by one taken from the Danube armoured river patrol boat _Gyór_ , when that vessel was rearmed with modern Bofors anti-aircraft weapons. Note the 'combat-type' coupling, which can be released from inside the hull.
_(Photo: Paul Malmassari Collection)_
Type RÁBA Vp armoured trolley, also designated a 'lightweight armoured train'. It does not appear to have been fitted with specific rail buffers or coupling gear.
_(Photo: Barta Zoltan)_
PV 102 seen in 1938, with engine MAV 377, and preceded by a lightweight trolley. Somewhat surprisingly, the national insignia is that used by the Hungarian Air Force between 1938 and 1941 (the colours being a green triangle then a white chevron and on the outside a red chevron), and in particular during the attack on Slovakia. Both 7cm guns taken from the _Gyór_ are now fitted to the reduced-height wagons of the former Austro-Hungarian PZ IX.
_(Photo: Magyar Műszaki és Közlekedési Múzeum)_
This photograph of either PV 101 or 103 shows the modifications to the shape of the roof on the artillery wagon. The lateral machine guns by this date would be the locally-manufactured 8mm Gebauer Type 34.AM.
_(Photo: Magyar Műszaki és Közlekedési Múzeum)_
Engine MAV 377 of PV 101 seen at Roznyo in 1938.
_(Photo: Magyar Műszaki és Közlekedési Múzeum)_
In the Autumn of 1941, during the occupation of the Bačka region which Hungary had claimed since 1918, PV 101 or 103 was halted by the demolition of the Ba ko Gradište Bridge by the retreating Yugoslav Army.
_(Photo: Muzej Vojvodine)_
Closeup of the gun in the leading wagon of either PV 101 or 103. Note the cutout in the armour mantle which allows the gunsight to follow the movement of the 7.5cm F.K. Model 08.
_(Photo: Muzej Vojvodine)_
The modernised wagons of PV 101 or PV 103. A turret armed with a 20mm Model 36 M has been installed on top of the roof, and a second 20mm Model 36 M is in a turret fitted at a lower level, the roof having been cut back. The smoke diverter was installed in 1938, and the Hungarian national insignia is now the white cross on a black square, which first appeared in late 1942.
_(Photo: Paul Malmassari Collection)_
A captured Soviet armoured wagon included in a Hungarian train.
_(Photo: FORTEPAN)_
Armoured train _Botund_ with its mixture of different types of wagon.
_(Photo: Hadtörténeti Intézey és Muzeum)_
The artillery wagon of _Botund_ on which is clearly visible the marking 'DR' denoting its previous inclusion in a Soviet armoured train, perhaps the _Leutnant Marx_ of the 221st Security Division.
_(Photo: Hadtörténeti Intézey és Muzeum)_
Artillery wagon from PV 103 abandoned in Budapest (note the damaged observation cupola) in front of the arched entrance to the Eastern Railway Station. Note also the markings in Cyrillic letters added by the Soviets who had taken the city on 13 February 1945.
_(Photo: All Rights Reserved)_
An anti-aircraft wagon seen in 1943, armed with a 40mm Bofors.
_(Photo: Paul Malmassari Collection)_
The final illustration shows a 40-florin stamp commemorating the armoured trains of the Bolshevik Revolution, dated 7 November 1917 in the Julian Calendar (25 October for the countries using the Gregorian Calendar).
_(Paul Malmassari Collection)_
**SOURCES:**
**Archive:**
SHD: Box 7 N 2893.
**Book:**
Bonhardt, Attila, A _Magyar Királyi Honvédség fegyverzete 1919-1939_ (Budapest: Zrínyi Katonai Könyvkiadó, 1992).
**Journal article:**
Villanyi, György, 'Magyar páncélvonatok', _Haditechnika_ 1994/1, pp 69–71; 1994/ 2, pp 48–52.
. In Hungarian: ' _Páncélvonat_ ', PV.
. MÁVAG = _Magyar Királyi Államvasutak Gépgyára_ , the Royal State Railway Manufacturers, Steelworks and Foundries.
. _Katonai Örvonot_.
. On that date, the crews of the ten armoured trains totalled 41 officers and 662 men.
. The eastern part of Czechoslovakia.
. The armoured river patrol boat _Györ_ was originally armed with two single turrets with 8cm guns (actual calibre 76.5mm).
## INDIA
The Republic of India inherited several British armoured trains, one of which has been restored, and is today preserved at the National Railway Museum in New Delhi (see the chapter on Great Britain). On 15 August 1947, the very day of the declaration of independence which was to see the majority of the states of former British India merged into the new Indian Union, the State of Hyderabad declared its independence from the rest of India. It was the largest of the princely states, situated in the very centre of the continent, and had a certain degree of administrative autonomy, having its own standing army and a militia, and running its own railway network. The new Indian Government refused to accept the situation, and after fruitless negotiations, on 13 September 1947 began Operation 'Polo' to annexe the state by force. Two main attacks were launched, from east and west, with a secondary attack from the south, the latter principally intended to secure the railway network, with three regiments of the Indian Army and two armoured trains. The whole operation benefitted from air cover, and Hyderabad was finally conquered on 17 September.
On 28 May 2010, the Jnaneswari Express derailed following sabotage of the track carried out by Maoist guerillas. More than 170 passengers were killed. Initial responses included only running trains by day, which caused severe passenger disruption. Faced with the guerilla threat in the region of Jangalmahal, the state of West Bengal was obliged to introduce armoured locomotives, plus a widespread system of surveillance cameras along the most vulnerable stretches of track. Currently the railway network is guarded by the Railway Protection Force, an armed militia which is also a major employer.
**SOURCES:**
Sharma, Gautam, _Valour and Sacrifice: Famous Regiments of the Indian Army_ (New Delhi: Allied Publishers, 1990).
. For its part, the state of Kashmir refused to integrate into the new Pakistan, and requested Indian military assistance when the Pakistanis invaded.
. No-one ever claimed responsibility for the attack, however. This guerilla movement which has affected virtually half of the states of the Indian Republic, began in 2005 after the formation of groups of Maoist insurgents, the 'Naxals', who preach revolt against the central government. Attacks against the trains began in 2006.
## INDONESIA
Although the country unilaterally declared its independence from the Netherlands on 17 August 1945, formal recognition was not granted until 27 December 1949. The defence of the railway network during these four years is covered in the chapter on the Netherlands.
Newly-independent Indonesia suffered from several years of separatist agitation, notably in the south of Sumatra in the years 1951 to 1953. Armoured wagons accompanied the trains, and it appears that Dutch trolleys were put back into service, which would explain why several examples are displayed in Indonesian museums.
**SOURCES:**
<http://www.overvalwagen.com>
<http://www.kaskus.co.id>
A train double-headed by two 2-10-2 Type D52 engines, propelling two flat wagons carrying the hulls of BRAAT armoured trolleys, on a line in the south of Sumatra in the years 1951–3.
_(Photo: All Rights Reserved)_
This Panser Rel V16 armoured trolley has an aggressive and elegant appearance. It was constructed by joining two BRAAT (second version) vehicles together back-to-back. Traces of the original camouflage survive under the patches of rust on this vehicle parked out of service in a station. A restored example (perhaps the same vehicle) is now on display in the Bandoeng Museum.
_(Photo: Tony Ford)_
The Panser Rel V16 (perhaps from the designation of the motor) on display at Bandoeng in a new paint scheme. This vehicle measures 5.20m (17ft 03/4in) long and weighs 7 tonnes.
_(Photo:<http://www.kaskus.co.id>)_
## IRAQ
Nominally an independent monarchy since 3 October 1932 but in practice under British control, the Kingdom of Iraq did not declare war on Germany in 1939 but did sever diplomatic relations. In 1941 British control of the Iraqi oilfields was threatened by proposed nationalisation and the formation of a national oil company run by representatives of the Axis powers. The British were determined to counter this threat to their vital oil supplies, and an infantry division was landed at Basra on 18 April 1941 to overthrow the Iraqi government. On 2 May 1941, an Iraqi armoured train, probably a veteran of the Mesopotamian uprising of 1920–2, was spotted on the metre-gauge line to the south of the town of Ur. Bombed by two Vickers Vincents. it was stopped outside Basra, and captured by the 3rd Sikhs. One report describes it as having been put back into service by the British.
**SOURCES:**
Northcote, H. Stafford, _Revolt in the Desert: Purnell's History of the Second World War_ , Vol 2 No 4 (London: Purnell, 1967), pp 346–8.
## IRISH FREE STATE
### ARMOURED TRAINS AND TROLLEYS (1922–1941)
The Irish Free State was created by the Anglo-Irish Treaty signed in London on 6 December 1921, following the bloody Easter Rising of 24 April 1916 and the ensuing Irish War of Independence (21 January 1919 to 11 July 1921). The Treaty was intended to come into effect on 6 December 1922, but following its ratification by the Irish Parliament on 7 January 1922, opponents of the Treaty (the Republicans) rose in revolt, and were opposed by the Irish National Army (INA). The latter inherited armoured cars from the British (Rolls-Royces, Peerless and Lancias), and began constructing armoured trains and trolleys to counter Republican attacks on the railways. In addition, the Railway Protection, Repair and Maintenance Corps (RPR&MC) was created in October 1922.
### The Irish Civil War
The first armoured train was based at Inchicore (Dublin) in July 1922, but it was destroyed by the Republicans. In August a second train was constructed in Limerick, using armour plates found in an abandoned British barracks, and other trains of variable effectiveness existed in Clonmel, Dundalk and Thurles. Following the creation of the RPR&MC, armoured trains were built in Cork and Dublin. The armoured train detachments organised by the RPR&MC and set up in Clonmel, Cork, Killarney, Limerick and Thurles had a total of nine trains, and in February 1923 they were stationed as follows: Clonmel: AT No 1; Thurles: AT No 2; Limerick: AT No 3; Cork: AT Nos 4, 5 and 6; Dublin: AT No 7; Dundalk: AT No 8; Mullingar: AT No 9.
The trains' main role was the protection of working parties repairing destroyed bridges and damaged track. In between the fixed bases, regular patrols were carried out by armoured trolleys. Of the various makes of Irish armoured cars, only the Lancia armoured personnel carriers were converted for use on rails. Out of a dozen set aside for conversion, only seven (AL Nos 22, 23, 31, 32, 33, 47 and 51) were in fact fitted in September 1922 with flanged wheels. Their configurations varied between individual cars, and at least two of those converted at Inchicore were fitted with a turret armed with a machine gun.
The Republicans in general preferred to avoid combat with the trains and trolleys, leading to less attacks on the railway which nevertheless continued to suffer. The fighting which did take place was often hotly contested. For example, on 15 October 1922, it took the Republicans some four hours of fighting to force the surrender of the famous Lancia known as the _Grey Ghost_ (from its camouflage scheme and its near-silent approach). After being disarmed, the crew were set free, and the Lancia partly destroyed by fire. On 27 February 1923 the Lancia trolleys were based as follows: Cork: Lancias Nos 1, 2 and 3; Limerick: No 4; Dundalk: No 5; Dublin: Nos 6 and 7. In addition, a further five Lancias had been set aside for quick conversion to trolleys. At the end of the Civil War, the Lancia trolleys were restored to road use and passed to the Armoured Car Corps.
### Up to the Second World War
In 1931, the Irish Government expressed interest in the project by the Swedish firm of Landsverk, described in the chapter on Sweden, but no orders resulted.
The Army High Command envisaged the construction of an armoured train in 1941, to be built around a diesel locomotive. However, the GSR turned down the idea, because of the impossibility of obtaining armour plate, and the lack of a sufficiently powerful locomotive to carry armour in the first place.
Armoured train built by the Great Southern Railway, and crewed by its employees under military supervision.
_(Photo: Irish Military Archives)_
Armoured train photographed at Mallow in 1923. The engine is a 4-4-2 tank of the GSWR.
_(Photo: Walter McGrath Collection)_
Armoured train photographed on 14 February 1922. The internal wooden supports holding the armour plates are clearly visible at the front of the engine. With internal Stephenson valve gear, these tank engines carried no protection below the footplate.
_(Photo: Paul Malmassari Collection)_
A view of the armoured train of the DSER, here in Grand Canal Street, Dublin in 1923.The engine is 2-4-2 No 64 _Earl of Bessborough_.
_(Photo: All Rights Reserved)_
Amusing play on words on 'the tank' engine of Armoured Train No 7. The discovery of the Pharaoh's tomb by Carter had taken place in 1923 and the news was all the rage at the time.
_(Photo: Irish Railway Record Society)_
Behind the repair train we can make out the armoured train from Cork, and behind the horizontal capstan is the famous Lancia, the _Grey Ghost_.
_(Photo: Irish Military Archives)_
The complete armoured train from Cork, powered by a Class 101 GSWR 0-6-0 engine. The imposing armoured wagon at the rear had been built by the workshops of the CB&SC. Note the carriage in front of the engine, armoured with plates over the windows, pierced by loopholes. On the other hand the engine crew are protected only by a simple plate at each side.
_(Photo: Irish Military Archives)_
Two Lancia armoured trolleys at Glanmire Road Station, Cork, in November 1922. The machine on the left is of the 'Hooded Terror' type, so-called from the nickname of the Lancia which had served as the prototype: the former open-topped crew compartment was now covered by an armoured roof. 'AL-23' on the rear of the body indicates 'Armoured Lancia' plus its original armoured car designation. It may in fact be Lancia Trolley No 1, and is ascribed to No 2 Company as marked on the left-hand cab door.
_(Photo: Walter McGrath Collection)_
A variant of the Lancia armoured trolley, photographed at Inchicore, with armour similar to that of the _Grey Ghost_.
_(Photo: Irish Military Archives)_
The second Lancia trolley fitted with a turret, seen in the Inchicore workshops. The generous Irish track gauge of 5ft 3in (1600mm) is particularly noticeable here: the mudguards are no longer aligned with the road wheels. To fit the latter required an extension to each axle.
_(Photo: All Rights Reserved)_
Yet another variant, with a different type of roof armour.
_(Photo: All Rights Reserved)_
The _Grey Ghost_ , the famous Lancia which resisted a Republican attack for some four hours, before the crew surrendered, and the trolley was set on fire.
_(Photo: Irish Military Archives)_
**SOURCES:**
**Archives:**
Irish Army Ref 2/69329.
**Books:**
Share, Bernard, _In Time of Civil War, The Conflict on the Irish Railways 1922-23_ (Cork: The Collins Press, 2006).
**Conference Notes:**
Walsh, Paul V, _The Role of Armoured Fighting Vehicles in the Irish Civil War, 1922-1923_. Lecture presented in September 1997 at the Cathal Brugha Barracks.
___________, _The Irish Civil War, 1922-1923: A Military Study of the Conventional Phase, 28 th June-11th August 1922_. Lecture presented 10 February 2001 during the 6th Annual Conference of the Barnes Club of Temple University.
**Journal articles:**
Bergin, Lieutenant-Colonel W J, 'Ambush on the _Grey Ghost_ ', _An Consantoir_ (May 1978), pp 135–6.
Leslie, Peter, 'Armoured Rail Cars in Ireland', _Military Modelling Annual_ (1974), pp 6–9.
McCarthy, Denis J, and Leslie, Peter, 'Armoured Fighting Vehicles of the Army No 3; The Lancia Armoured Personnel Carrier', _An Consantoir_ (May 1976), pp 136–8.
**Website:**
<http://railwayprotectionrepairandmainten.blogspot.fr/>
. The Lancia armoured personnel carriers were originally British vehicles built on either Lancia 1 Z or Lancia Triota chassis, 100 examples of which were in service with the Irish National Army. Crew: eight or nine men; speed: 45mph (72km/h) forward, 20mph (32km/h) in reverse; armour: 6mm; armament: .303in Lewis LMG.
. On the other hand, Peter Leslie states that several Lancia trolleys and an armoured train dating from the Civil War period were stored in a siding up until the 1950s.
. GSWR = Great Southern & Western Railway.
. DSER = Dublin & South Eastern Railway.
. CB&SC = Cork, Bandon & South Coast Railway.
## ITALY
### ARMOURED TRAINS AND TROLLEYS 1891–1945
The first Italian foray into the realm of armoured trains occurred in 1891, when an Italian officer, conscious of the difficulty of defending the long coastlines of his country, laid before Parliament a proposal to defend Sicily with armoured trains. Although the idea was not taken up at the time, the Italians, like the British, were well aware of the possibilities offered by using armoured trains for coastal defence.
### The Italians in Libya (1912)
The story of Italian armoured trains began after the Treaty of Lausanne was signed on 18 October 1912, recognising Italy's occupation of Libya. The conquest of Tripolitania and Cyrenaica had begun on 29 September 1911 with naval operations and landings. Benghazi was occupied on 20 October and Tripolitania was annexed on 5 November. There followed a year of fighting and an expansion of the revolt against the Ottoman Empire. The Treaty of Lausanne put an end to the war, but sporadic uprisings continued until 1931 when Sheikh Omar Al Mokhtar, the ally of the Senussi, was executed. Beginning in 1912, the Italians built a 95cm gauge network in Tripolitania and to guarantee security, put into service an armoured train comprising an engine and two armoured wagons based on a pair of flats used to transport long loads such as gun barrels.
The engine intended to haul the train, fitted with fairly comprehensive armour protection, including an armoured lookout on each side of the cab.
_(This photo and the two following: Nicola Pignato and Filippo Cappellano_ , Gli Autveicoli da combattimento dell'Esercito Italiano (Volumes 1 and 2) _, by kind permission of the Ufficio Storico dello Stato Maggiore dell'Esercito – USSME)_
Two external views of one of the armoured wagons, with personal weapons (Carcano carbines) ready to fire from a standing position. This type of wagon would be effective against the types of light armament possessed by its opponents at the time it was introduced.
Note the access door at the engine end. The five Maxim machine guns could train over a wide arc. The central part of the roof was left open. Photographed in the workshop with the wagon on a short length of temporary track.
### The Second World War
During the First and Second World Wars, the concern about coastal defence resulted in the ' _Treni Armati_ ' ('Armed Trains') which were operated by the _Regia Marina_ (Italian Navy). We will not study them in this work, as they are railway artillery rather than armoured trains in the true sense.
On the other hand, rail trolleys, not all armoured, were used in sensitive areas such as the Libyan-Egyptian frontier. In the absence of other photographic records we have to return to the works of Nicola Pignato and Filippo Cappellano for a poor-quality but nevertheless unique image.
Armoured trolley used on the frontier between Libya and Egypt.
_(Photo: Nicola Pignato & Filippo Cappellano_, Gli Autveicoli da combattimento dell'Esercito Italiano _, Volume 2)_
A type of escort wagon converted from a Type 1905 F van, with minimal armour protection and large loopholes.
_(Photo: Nicola Pignato & Filippo Cappellano_, Gli Autveicoli da combattimento dell'Esercito Italiano _, Volume 2)_
One of the first of the armoured trains, intended for coastal defence, with a Breda 20mm cannon and a 47mm Model 32 anti-tank gun.
_(Photo: Nicola Pignato & Filippo Cappellano_, Gli Autveicoli da combattimento dell'Esercito Italiano _, Volume 2)_
In the Balkans, the Italian zone of occupation included Slovenia, the Dalmatian coastline and the islands. Montenegro and Albania had already been included in the Italian Empire. At the time of the Italian invasion of Greece, Albanian resistance movements were disrupting communications routes, but when the Germans joined in the occupation of the Balkans, it was they who took over responsibility for the defence of the railway networks.
The _Compagnia Autonoma Autoblindo Ferroviairie_ (Independent Railway Armoured Car Company) was created in Yugoslavia on 15 May 1942. In order for it to carry out its mission, which was to control the railway lines, several improvised armoured trains were converted from bogie wagons. The Littorina Blindate ('Libli') railcars, Model 42 trolley and the rail version of the AB 40 will be considered later.
### The armoured trains
Separate from the escort wagons of the _Milizia Ferroviairia_ (Railway Militia) which were included in goods trains, ten armoured trains were built, beginning in 1941, to assure the security of the lines in the Italian occupation zone in Yugoslavia. They were of simple design, converted from goods wagons, with armoured sides, and were initially armed with infantry weapons. In each train, two wagons were equipped with a 47mm 47/32 Model 35 anti-tank gun, able to fire at 90 degrees to the track by opening doors which gave a horizontal field of fire of around 120 degrees. Each gun covered one side of the track. Another wagon was armed with 20mm Breda Model 37 cannon. With the partisan threat increasing in intensity, the trains later incorporated wagons (up to six) with improved armour protection, having a central covered compartment (of wood or steel) with firing loopholes, and at either end an open-topped firing position for an 8mm Fiat/Revelli Model 14/35 machine gun. The armament was completed by a 45mm Brixia Model 35 mortar.
A goods wagon base armed with a 47mm Model 37 gun fitted with a small shield. The canvas covers add a degree of comfort in a region where the winters are particularly harsh.
_(Photo: Nicola Pignato & Filippo Cappellano_, Gli Autveicoli da combattimento dell'Esercito Italiano _, Volume 2)_
A different form of protection on a Type L wagon, completely enclosed, the sides extended upwards and armoured, but once again armed with a 47mm gun with a very restricted field of fire.
_(Photo: Nicola Pignato & Filippo Cappellano_, Gli Autveicoli da combattimento dell'Esercito Italiano _, Volume 2)_
Machine-gun wagon converted from a goods wagon. Note the camouflage scheme.
_(Photo: Nicola Pignato & Filippo Cappellano_, Gli Autveicoli da combattimento dell'Esercito Italiano _, Volume 2)_
This photo shows an interesting combination: the armoured body of a narrow-gauge wagon has been mounted on a standard-gauge wagon, leaving a slight gap between the two. The result is an armoured wagon which is perhaps more resistant to mines.
_(Photo: Nicola Pignato & Filippo Cappellano_, Gli Autveicoli da combattimento dell'Esercito Italiano _, Volume 2)_
An overall view of Armoured Train No 3 at Novo Mesto, where it was stationed from August 1943. The muzzle of a 47mm Model 32 can just be seen protruding from the side of the third wagon.
_(Photo: Nicola Pignato & Filippo Cappellano_, Gli Autveicoli da combattimento dell'Esercito Italiano _, Volume 2)_
Goods trains were hauled by modern Class 06 engines, with extensive armour protection on the cab, including the door for the crew. The armoured trains were powered by Class FS 910 tank engines.
_(Photo: Nicola Pignato & Filippo Cappellano_, Gli Autveicoli da combattimento dell'Esercito Italiano _, Volume 2)_
Saloon coach S 294 fitted with armour, seen here in July 1942.
_(Photo: Archivo Ferrovie dello Stato Italiano)_
In Slovenia and Dalmatia, the Second Army used several Series Dpz and DI coaches, armoured against small-arms fire, to form a command train with 'passive' protection, with no heavy armament and organised like a troop transport train, with sleeping accommodation, kitchen and so on. The windows were replaced by several armoured blinds.
A view of the end of the coach. The armour plates have been riveted to the original bodywork.
_(Photo: Archivo Ferrovie dello Stato Italiano)_
A view of the former baggage van Dpz 1913 converted into an armoured coach, intended for the command train _SLODA_ (for SLOvenia-DAlmazia).
_(Photo: Archivo Ferrovie dello Stato Italiano)_
Although improvements to the protection and the armament of the wagons can be observed as the occupation continued, the Italian trains in the Balkans were not intended for an offensive role, which would be the province of the railcars and trolleys.
### The 'Libli' railcars
In 1942 it was decided to armour the ALn-556 railcars of the Ansaldo firm, for service in Yugoslavia. The Railway Engineers chose models produced from 1936 to 1938. They had to be shortened by 5.60m (18ft 4½in). The prototype was tested in the Ansaldo-Fossati workshops in Genoa, and was adopted on 5 September 1942, with several recommended changes, with the designation ' _Littorina blindata mod. 42 (Li.Bli 42)_ '. The first production model was rolled out on 20 September and joined the _1 o Compagnia Autonoma Littorine Blindate_. This company would receive eight railcars in total, and was made up of ten officers, twelve NCOs and 167 men. The 8.5mm armour protection was built in one piece, pierced only by access and maintenance hatches, and firing ports.
Armed with two tank turrets mounting 47mm guns, two versions were used at the same time. The first version had two openings in the roof to allow firing two 81mm Model 35 mortars, or flamethrowers through side apertures. The second had a circular tub with a pedestal-mounted 20mm Breda Model 35 cannon. The 8.5mm armour protection was built in one piece, pierced only by access and maintenance hatches, and firing ports.
When the Italian Armistice was signed, the 'Liblis' were based at Karlovac, Ogulin and Split (Croatia), Ljubljana and Novo Mesto (Slovenia) and Suse (in Italy, 30km/19 miles west of Turin). A series of machines was then ordered for the Wehrmacht in 1943 (see the chapter on Germany).
The Independent Railway Company saw hard service up until the Armistice of 1943, and suffered heavy losses. In particular two 'Libli' were destroyed, the first at Split in October 1942 and the second at Ogulin on 12 February 1943.
_(Photo: Paul Malmassari Collection)_
Technical specifications:
Length: | 13.50m (44ft 71/2in)
---|---
Width: | 2.42m (7ft 111/4in)
Height: | 3.57m (11ft 81/2in)
Weight: | 39.5 tonnes
Motor: | FIAT 355C, 80hp at 1700 rpm
Fuel: | Diesel
Maximum speed: | 80km/h (50mph)
Range: | 450km (280 miles)
Armour thickness: | 8.5mm
Armament: | 2 turrets similar to those fitted to the M13/40 tank, with 47mm/L32 gun with 195 rounds and 8mm Breda 38 machine gun
Either 2 x 81mm Mod. 35 mortars with 576 bombs Or 1 x 20mm Breda Mod. 35 anti-aircraft cannon
2 Mod. 40 flamethrowers
4 x 8mm Breda 38 machine guns in side ball mountings with 8,040 rounds
The personal arms of the crew and hand grenades
Crew: | 1 officer, 2 drivers, 2 gunners, 2 loaders, 6 machine gunners, 2 mortar specialists, 2 flamethrower engineers, 1 radio operator
Radio equipment: | Marelli RF2CA or RF3M set
Various: | Turret searchlights, track repair equipment.
### The AB 40 and AB 41 trolleys
To supplement the 'Libli' railcars, a request was made on 24 July 1942 for the conversion of twenty AB 40 and AB 41 armoured cars into road/rail vehicles, to be used equally on the road or on rails simply by changing the wheelsets. The modifications also included adding sanding boxes to the front and rear wings, and one swivelling headlight. The first version could be recognised by its low turret armed with two 8mm Breda Model 38 machine guns. The AB 41 received a higher turret, an automatic 20mm 20/65 cannon and one Breda machine gun. Lastly, the AB 43, of which only an experimental model existed in road/rail form, mounted a 47mm gun.
An AB 40 of the _2 o Raggrupamento genio ferrovieri_. The sanding boxes and delivery pipes are clearly visible. The armament comprised three 8mm Breda 38 machine guns, two in the turret and one in the hull rear. Stoneguards were fitted in front of each rail wheel to aid in pushing aside small obstacles.
_(Photo: Daniele Gugglielmi Collection)_
We are unable to say whether this camouflaged AB 41 is still in Italian hands or if it has been taken over by the Germans. The cannon is a 20mm Breda 35. This machine had a rear driving position, and therefore had no need for a turntable.
_(Photo: Paul Malmassari Collection)_
Technical specifications:
Length: | 5.20m (17ft)
---|---
Width: | 1.935m (6ft 4in)
Height: | 2.44m (8ft)
Ground clearance: | 35cm (133/4in)
Weight: | Between 6.9 tonnes and 7.7 tonnes
Motor: | FIAT-SPA ABM1, 6 cyl inline
Power: | AB 40: 88hp at 2700 rpm; AB 41: 108 hp at 2800 rpm
Fuel: | Petrol
Maximum speed (road): | 78km/h (49mph) AB 40; 81km/h (51 mph) AB 41
Range (road): | 400km (250 miles) AB 40: 350km (215 miles) AB 41
Armour thickness: | 8mm
Armament: | 3 x 8mm Breda 38 machine guns (AB 40); 1 x 20mm Breda 35 cannon and 2 machine guns (AB 41)
Crew: | 4
### Autocarretta Ferroviaria Blindata Mod. 42 trolley
Derived from the Autocarretta OM36, twenty examples were built for the Railway Engineers. After prototype testing in late 1942, the machines were put into production in early 1943 and entered service in May 1943 on the narrow gauge (76cm/2ft 6in) lines in Dalmatia and Slovenia. After 8 September 1943, they continued in use with the Wehrmacht.
Technical specifications:
Length: | 3.83m (12ft 63/4in)
---|---
Width: | 1.535m (5ft 01/2in)
Height: | 2m (6ft 63/4in)
Ground clearance: | 12.5cm (5in)
Weight: | 3.2 tonnes
Motor: | FIAT-SPA AM, 4 cyl inline, 20hp at 2400 rpm
Fuel: | Petrol
Maximum speed: | 15km/h (10mph)
Range: | 350km (215 miles)
Armour thickness: | 8mm
Armament: | 1 x 8mm Breda 38 machine gun
Crew: | 6
This three-quarter front view shows clearly the turning mechanism of the type normally used on asymmetrical trolleys, but which was extremely dangerous to operate under combat conditions. Note also that the only means of access is via the roof, making a turning manoeuvre even more perilous.
_(Three Photos: Daniele Guglielmi Collection)_
The front view shows the modest dimensions of the machine, which would have been relatively uncomfortable for its crew. The front plate, pierced by the emergency starting-handle, protects the radiator air intake.
In this rear view of the trolley, note the numerous firing and observation loopholes, plus the handrails which were the only means of climbing on the vehicle.
Two further projects were being studied in the Summer of 1943: the firm of Viberti had designed two trolleys (one for the narrow gauge and the other for the standard gauge) which did not go into production because of the Armistice. Extremely compact, they had probably benefitted from experience gained with the Autocarretta Mod. 42, despite the weakness of its armament and armour protection.
It would be simple to see in the defeat of the Axis Powers in the Balkans the failure of the means of defending the railway network. It is the case that the Italians were never able to prevent sabotage of the communications links, but the escort missions and the reconnaissance patrols carried out day after day by the Independent Company and the Railway Militia prevented the complete paralysis of the communications and supply lines in the Balkans. Lastly, the excellent qualities of the 'Liblis' are attested by the production orders and use by the Wehrmacht after 8 September 1943 in the zone which would now be known as the _OZAK_ ( _Operationszone Adriatisches Küstenland_ , Adriatic Coast Operations Zone).
At some time, probably in the early 1920s, Anslado proposed an armoured engine, and also an armoured railcar. Although the drawing for the railcar is annotated in French, no record of a specific request for this project has come to light in the French archives. The inclusion of Saint Etienne Model 1907 machine guns in the plan suggest it was intended for use in French North Africa, probably Morocco. Interestingly, the plan also depicted the Ansaldo version of the stroboscopic observation device on the turret, similar in concept to that fitted to the French FCM Char 2C.
**SOURCES:**
Benussi, Giulio, _Treni armati treni ospedale 1915-1945_ (Parma: Ermanno Albertelli Editore, 1983).
Guglielmi, Daniele, _Italian Armour in German Service 1943-1945_ (Fidenza: Roadrunner, 2005).
Luparelli Albion, Filippo Ettore, _La Sicilia nella probabilità di una invasione francese_ (Palermo: Michele Amenta, 1884).
Pignato, Nicola, _Atlante mondiale dei mezzi corazzati, i carri dell'Asse_ (Bologna: Ermanno Albertelli Editore, 1971, 1983).
____________, _Un secolo di autoblindate in Italia_ (Fidenza: Roadrunner, 2008).
____________, and Cappellano, Filippo, _Gli Autoveicoli da combattimento dell'Esercito Italiano (Volume 1)_ (Rome: Uffico Storico SME, 2002).
________________________________, _Gli Autoveicoli da combattimento dell'Esercito Italiano (Volume 2)_ (Rome: Uffico Storico SME, 2002).
Plan of the Viberti trolley for the narrow gauge (76cm).
Plan of the Viberti trolley for the standard gauge.
. The story of the Italian armoured trains in Libya ends in 1943, when Italy lost control of the country, renouncing all rights to Libya in 1947, the last Italian colonists being expelled in October 1970.
## JAPAN
### ARMOURED TRAINS 1918–1945
Beginning in 1894, in moves to establish footholds and expand territorial gains on the continent of Asia, the Japanese Empire became embroiled in several conflicts, firstly with the Chinese Empire, and then with the Republic of China. Amongst other territorial gains, the Sino-Japanese War of 1894–5 gave Japan Formosa and Port Arthur in Manchuria. Korea became a Japanese colony. Then Japan participated in the Allied intervention in Siberia from August 1918 to October 1922. In 1931 Japan conquered Manchuria and renamed it Manchukuo. Finally, the Second Sino-Japanese War which broke out in 1937 became part of the wider Second World War.
As for Japanese armoured trains, from 1918 they intervened in Siberia, in 1931 in the invasion of Manchuria, then in 1932 in the move against Shanghai, and finally across the whole of occupied Chinese territory. After the Japanese defeat in 1945, Japanese armoured trains were used by Chinese forces during the Chinese Civil War, and perhaps even in Korea.
### Intervention in Siberia (1918–1922)
Japan intervened in the Russian Civil War as part of an international force totalling 25,000 men. The Japanese first went into action in Siberia in July 1918 at the request of the American government, with the despatch of an initial contingent of 12,000 men under Japanese command.
Once the troops were in place, the security of the railway network was assured by armoured trains, most of which had been brought to the region by the withdrawing Czech Legion. The Japanese, however, refused to become involved to the west of Lake Baikal, and their priority was basically to support the White Generals Ataman Semyonov and General Kalymkov, who themselves were well-equipped with armoured trains, and then later General Baron von Ungern-Sternberg.
On 5 April 1920 the Japanese contingent, the sole non-Russian force remaining after the withdrawl of the American contingent, launched an offensive to disarm the local revolutionary forces, with the ultimate aim of protecting the Japanese Home Islands, as well as its colonies in Korea and Manchuria, against the threat of the anti-monarchist Bolsheviks. The Japanese crossed the Transbaikal, withdrew their support from Semyonov, and finally in October 1922, giving in to international and domestic pressure, withdrew their troops.
This gun crudely placed on an elevated platform, installed aboard a Russian bogie wagon and allowing for only head-on fire, appears primitive in comparison with other contemporary armoured trains with guns in turrets.
_(Photo: Paul Malmassari Collection)_
More in keeping with the standards of the day, this train which flies the Hinomaru, the Japanese flag, is built on the base of a classic Russian railways' bogie wagon.
_(Photo: Paul Malmassari Collection)_
This Japanese armoured wagon built on a Russian bogie wagon has rudimentary armour protection, but its armament is impressive.
_(Photo: Paul Malmassari Collection)_
A well-known photo of an interesting machine-gun wagon, with a mixed Czech and Japanese crew, typical of the forces defending certain sections of the Trans-Siberian Railway.
_(Photo: All Rights Reserved)_
A close-up of one end of the railcar of _Orlik_ , which still bears its Czech name, with the inscription 'VUZ CIS.1' meaning 'Wagon No 1'.
_(Photo: Paul Malmassari Collection)_
The artillery wagon of _Orlik_ , here in Japanese hands, as shown by the inscription painted on the sides. The gun is a 76.2mm Russian Model 1902 in a turret with a horizontal field of fire restricted to 270 degrees due to the armoured superstructure.
_(Photo: Paul Malmassari Collection)_
A fine view of the armoured railcar which operated with, or independently of, the armoured train _Orlik_. Note the Czech officer on the left, with a group of Japanese officers. Note also the latest modifications such as the searchlight mounted on the roof.
_(Photo: Paul Malmassari Collection)_
This photo shows the ultimate appearance of a Russian armoured wagon, formerly part of Kalmykov's forces but now taken over by the Japanese. Note the 'Japanese touch' of the additional armour, and in the overall arrangement of the train, which appears less haphazard than in its original version.
_(Photo: All Rights Reserved)_
A fine photo of a Japanese armoured trolley in service in Siberia. It is surrounded by Czech Legionnaires.
_(Photo: Vojenský ústředni archive-Vojenský historický archive)_
### Japanese Armoured Trains in Manchuria, China and Korea (1931–1945)
The civil war which began in 1911 had left China fragmented. In Manchuria, where Japanese influence had replaced that of the Russians since the war of 1905, on 18 September 1931 minor damage caused to a railway line passing close by a Chinese garrison, in what became known as the 'Mukden Incident', gave Japan the excuse to strengthen its hold by launching an invasion. By occupying Harbin on 5 February 1932, the Japanese completed their military conquest of Manchuria, one of the major Chinese provinces situated well to the north of the original Japanese zone of influence. Subsequently, on 18 February 1932 the Japanese created the puppet state of Manchukuo, ruled by Pu Yi, the last Emperor of China, which would never be recognised by the League of Nations.
In 1928, the Japanese had assembled six armoured trains in Manchuria, armed with 75mm Model 41 mountain guns. But following the Mukden Incident, the Railway Company of the Kwantung Army was created specifically to commission armoured trains and take over responsibility for their technical aspects. Alongside the growing number of armoured trains, 'guard trains' were brought into service, the latter composed of just one infantry wagon coupled to an artillery wagon. In addition, armoured wagons crewed by veterans of the Manchurian Railway Company were coupled in with scheduled trains. Thus by 1935, the Kwantung Army had a total of twenty-eight armoured trains and four guard trains.
A lack of detailed records prevents us describing all the actions in which armoured trains participated during the campaign, but several typical engagements were reported in the newspapers of the time. Although the Chinese Army in Manchuria had retreated in disorder, the railway lines were by no means secure. For example, on 15 November 1931, when the Japanese tried to outflank the Chinese lines near the bridge over the River Nonni, Chinese cavalry succeeded in cutting off the troop detachment which had disem-barked from their armoured train, and only a few of the Japanese succeeded in rejoining the train, under the covering fire of its guns.
The whole of Manchuria was nominally occupied by the Japanese, but they in fact controlled only the towns and the railway lines, along with a large part of the Chinese Eastern Railway. The Japanese presence obliged the Russians to maintain 150,000 men along the length of the frontier between Vladivostok and Manchuli (the station closest to the Manchurian frontier). The Japanese garrison, in addition to tanks and artillery, maintained some thirty armoured wagons.
In reprisal for a boycott of Japanese goods by the Chinese authorities in response to the invasion of Manchuria in early February 1932, the Japanese decided to take military action in Shanghai. The Chinese resisted the Japanese aggression and among other means, brought an armoured train into use on the Shanghai-Nankin line, operating principally by night, and added armoured wagons to their troop trains. It appears that their use ceased once the Japanese landed heavy artillery.
On 7 July 1937 the Marco Polo Bridge Incident between Chinese and Japanese troops led to the outbreak of the Second Sino-Japanese War on the 28th of the same month, in which the Japanese captured several Chinese cities. In March 1940 a Central Chinese Government was installed by the Japanese, but the war gradually developed into a series of guerrilla and counter-guerrilla actions. This conflict ended on 8 August 1945 with the Japanese surrender, the occupation of Korea by Soviet forces and the outbreak of a new civil war in China.
The lack of good roads in this immense territory meant that the railways were vitally important. The Japanese deployed large numbers of troops to protect the railways, and in turn these became a principal target for sabotage. The Imperial Army used several armoured trains and armoured trolleys. These units were obliged to operate over two different rail gauges depending on the area: 1520mm (5ft nominal) Russian gauge in the northern zone of Manchuria, and 1435mm (4ft 8½in) European gauge in the rest of the territory.
The first Japanese armoured trains, which according to Antoine Baseilhac 'represented the only highly mobile powerful elements across the vast Manchurian plains', were improvised from existing Manchurian rolling stock. They also used elements of captured Chinese armoured trains, which were often better constructed, many being former White Russian armoured trains brought to China when the Whites had fled Russia at the end of the Civil War. But to meet the need for modern equipment, two unique designs of armoured train were built for use in Manchuria: the Temporary Armoured Train in 1932, and the following year the Type 94 Armoured Train. At the same time, a large number of self-propelled units were put into service for use by rail reconnaissance patrols.
.
This type of armoured wagon is typical of the Korean or Manchurian railway network. Its construction is straightforward, with an armoured body attached to a standard bogie flat wagon which is the same as in preceding photos.
_(Photo: Konstantin Fedorov, Archivist, Collection)_
A view of the other end of the wagon.
_(Photo: Konstantin Fedorov, Archivist, Collection)_
This photo should be compared to that shown in the chapter on South Korea (1950–3). The arrangement of the opening flaps on the firing nacelle is interesting, as is the tripod fixture for a searchlight on the roof. In fact, this photograph viewed in conjunction with the preceding two proves that the nacelles were diagonally offset.
_(Photo: Paul Malmassari Collection)_
Similar construction features are evident on other armoured trains, here lacking lateral MG nacelles. Note the front observation position separated from the main armoured hull.
_(Photo: Paul Malmassari Collection)_
Another similar view – perhaps the other end of the same train, showing the various different types of protection, riveted plates, welded plates, sandbags, etc.
_(Photo: Paul Malmassari Collection)_
In these photos, we can see dark rectangles painted as a ' _trompe-l'œil_ ' to represent false firing ports.
_(Photo: Paul Malmassari Collection)_
In addition to armoured wagons intended to be included with normal trains, the Japanese put together armoured trains intended for offensive patrols. Here, the pilot/safety wagons have been uncoupled. The insignia on the side of the armoured wagon is that of the military railways.
_(Photo: All Rights Reserved)_
A different type of pilot/safety wagon, equipped with an armoured cabin for close observation of the track. The design of these cabins varied considerably, and there seems to be no standard pattern.
_(Photo: Paul Malmassari Collection)_
Two photographs of a typical armoured train on the Manchurian front. In this view, the train is lacking an artillery wagon which would normally be coupled to the wagon in the foreground.
_(Photo: Paul Malmassari Collection)_
Probably an earlier design of pilot/safety wagon, since the second wagon is a Russian high-sided bogie wagon of the type used during the Russian Civil War.
_(Photo: Heiwa Kinen Tenji Shiryokan)_
A view looking down on an artillery wagon, which would serve as the inspiration for a number of subsequent illustrations. For examples, see Appendix 1.
Here is the front part of the same train showing the partial protection on the engine, but with a fully-armoured cab fitted with a sliding blind. The gun appears to be a 75mm Type 41 (1908).
_(Photo: Paul Malmassari Collection)_
Another tactical feature of these trains is shown here: to provide sufficient water for the engine, a bogie tank wagon was inserted between the tender and the artillery wagon.
_(Photo: Paul Malmassari Collection)_
Here the horizontal board serves both as protection from the elements and as a recognition feature for Japanese aircraft. This photo was the inspiration for the postcard shown in Appendix 1.
_(Photo: Paul Malmassari Collection)_
The Japanese also put into service armoured trains on the narrow-gauge or metric lines within their occupied territory. These two views show two trains of this type, with a gun in a turret and with armour obviously tailored to the contours of the wagons. But it is just possible that these show a training unit (white armbands, irregular form of the armour etc)
_(Two Photos: Wawrzyniec Markowski Collection)_
Japanese protection wagon, converted from a van, seen as part of an unarmoured train photographed at Tientsin in August 1937. It is armed with a 6.5mm Type 11 light machine gun.
_(Photo: Paul Malmassari Collection)_
Another van roof fitting seen in Manchuria, this time armed with a 6.5mm Type 3 heavy machine gun. The lack of the special ring sight would suggest this is not meant for anti-aircraft protection.
_(Photo: All Rights Reserved)_
In the course of their offensive, several Chinese armoured trains were captured by the Japanese and were immediately put back into service, as we can see in this photo, where the side of the wagon to the right bears Japanese markings. For other views of these units, refer to the chapter on China.
_(Photo: Paul Malmassari Collection)_
An imaginative postcard issued by an anti-aircraft unit, their stamp bearing two AA guns, a searchlight beam and sound locators. In fact the Chinese air force put up little real opposition.
_(Postcard: Paul Malmassari Collection)_
### Temporary Armoured Trains (1933–1945)
'Temporary Armoured Train' was the official name given to this type of train, which was designed in 1932 as an experiment for service in Manchuria. In all, three of these trains were built, the first one being completed in July 1933. They were operated by the 3rd and 4th Railway Regiments. Each train was made up of the following elements:
– Pilot (track control) Wagon.
– Heavy Artillery Wagon.
– Light Artillery Wagon.
– Infantry Wagon.
– Command Wagon.
– Tender Engine.
– Auxiliary Tender.
– Technical Equipment Wagon.
– Infantry Wagon.
– Light Artillery Wagon.
– Howitzer Wagon.
– Pilot (track control) Wagon.
An overall view of the train, demonstrating the typical camouflage used on the Chinese front. Immediately obvious from this photo is the degree to which the plume of smoke from the engine, when it is not diverted to track level or otherwise dispersed, gives away the precise location of the train to enemy observers.
_(Photo: All Rights Reserved)_
Of note are the rails and sleepers attached to the sides of the wagon, and the well-executed camouflage scheme.
_(Photo: All Rights Reserved)_
One of the Pilot (track control) Wagons, built on a 30-tonne bogie platform wagon, with its turret for close-in defence, armed with a 6.5mm Type 11 LMG. The two armoured doors protect a 60cm diameter searchlight.
_(Photo: All Rights Reserved)_
The leading Artillery Wagon of the Heavy type, with its 100mm Type 14 anti-aircraft gun, in a turret with all-round traverse, and supplied with 500 shells. Its additional armament was composed of a heavy machine gun and ten rifles, served by a crew of one officer and fourteen men. Here the lower armour plates have been hinged upwards, allowing us a view of the means of stabilising the wagon when firing. Also visible are the seemingly excessive number of firing ports, closed by sliding shutters – although the total would allow for the full crew to bring their weapons to bear on one side.
_(Photo: All Rights Reserved)_
The same comments apply to the Light Artillery Wagon, whose crew of one officer and nineteen men served the two turrets, each mounting a 75mm Type 11 gun, supplied with a total of 500 rounds. The base for both units was the Type Ta-I 50-tonne coal wagon.
_(Photo: All Rights Reserved)_
A bogie platform wagon formed the base for the Infantry Wagon. Each turret was armed with a 13mm Type 92 HMG. The armament also included two 6.5mm Type 3 MGs (also known as the Taisho 14), two Type 38 rifles and a 30cm diameter searchlight. The crew consisted of one officer and eleven men.
_(Photo: All Rights Reserved)_
The Command Wagon had two levels, the lower for the radio compartment and the upper for the artillery command post – one can just see the binocular sight projecting from the roof. One of the observation nacelles is in the raised position, as is a radio aerial with its retractable mast passing through the roof. The light armament comprised two MGs and ten rifles.
_(Photo: All Rights Reserved)_
This view of the Command Wagon shows the two observation nacelles mounted on telescopic tubes. Note the plates protecting the sides of the open platform.
_(Photo: All Rights Reserved)_
There is no vertical armour over the boiler, but the steam dome is protected from horizontal fire.
_(Photo: All Rights Reserved)_
A passage ran behind the vertical armour plates on the Manchurian Railways 2-8-0 Type 'So-ri-i' tender engine, allowing crew members to pass from one end of the train to the other.
_(Photo: All Rights Reserved)_
The impressive Auxiliary Tender based on a 50-tonne coal wagon is fitted with two retracting turrets each armed with a 6.5mm Type 11 MG, which allowed observation and fire along the length of the train. Note the central access door.
_(Photo: All Rights Reserved)_
The Auxiliary Tender carried enough coal for 600km (375 miles) and enough water for 300km (188 miles).
_(Photo: All Rights Reserved)_
The Technical Equipment Wagon converted from a Type Ha-2 coach. The generator-powered radio equipment required the fitting of frame aerials mounted on insulator blocks.
_(Photo: All Rights Reserved)_
A fine view of the roof of the Technical Equipment Wagon.
_(Photo: All Rights Reserved)_
At the rear end of the train was the Howitzer Wagon, based on the same commercial wagons as the other artillery wagons, but with a turret armed with a modified 150mm Type 4 howitzer. The armament also included four Type 3 MGs and ten rifles, for a crew of two officers and twenty men.
_(Photo: All Rights Reserved)_
### Type 94 Armoured Train (1933–1945)
The Type 94 Armoured Train was conceived after feedback from operating the previous Temporary Armoured Train. Design began in October 1933 and in one year the train had been built. It would remain a unique example, as there was no follow-up. Although capable of running at up to 65km/h (40mph), it was essentially a coast defence/mobile artillery type of train rather than a track patrol unit. Compared to the other armoured trains used in China and Manchuria, its light armour protection of 6mm and 10mm plates shows that it was not designed for close-range combat.
Its eight elements were as follows, from head to tail:
– Pilot (track control) Wagon.
– Artillery Wagon No 1 (Kó).
– Artillery Wagon No 2 (Otsu).
– Artillery Wagon No 3 (Hei).
– Command Wagon.
– Engine.
– Tender.
– Electrical Generator Wagon.
The Pilot (track control) Wagon at the head of the train, equipped with a 30cm-diameter armoured searchlight. On can see the 7.7mm Type 92 MGs for close-in defence and the sliding shutters for the observation ports. The central coupling knuckle indicates that this wagon has been built on the base of a 30-tonne Type Ta-I mineral wagon.
_(Photo: All Rights Reserved)_
Turrets aligned fore and aft, here the train is photographed between Sakako and Furanten.
_(Photo: All Rights Reserved)_
A superb view of the complete train, which gives a feeling of invulnerability due to its homogenous design. It underwent running trials from 16 November to 16 December 1934, and in the interim its firing trials on 8 and 9 December.
_(Photo: All Rights Reserved)_
The interior of the Pilot Wagon, which appears to comprise a small command post. Its layout is similar to that of the Command Wagon of the Temporary Armoured Train, and it too carries rails and sleepers mounted on its sides.
_(Photo: All Rights Reserved)_
The Otsu Wagon was similar in design to the Kó Wagon, except that its super-structure was higher to enable it to fire over the latter. On this wagon all four MG turrets could be used against both ground and air targets. The same as used on board ship, the coincidence rangefinder and its crew are visible on the roof, with the binocular periscope to their left. In the camouflage pattern are yellow or ochre bands intended to break up the regular lines of the wagon.
_(Photo: All Rights Reserved)_
Interior view of the forward part of the Kó Wagon, with its armour plates backed with wood. In the background is the turret revolving basket, while on the left are some of the racks for the 200 shells the wagon carried.
_(Photo: All Rights Reserved)_
The interior of the Otsu Wagon. The ladder was needed for access to the rotating basket of the turret, set at a higher level than in the Kó version.
_(Photo: All Rights Reserved)_
The Kó Wagon is fitted with a single turret armed with a 100mm Type 14 anti-aircraft gun (here used solely against ground targets) with a 270-degree field of fire. Its maximum range was 15km (9.4 miles). The 7.7mm Type 92 MGs in the forward turrets are for use against ground targets, while those in the rear turrets are dual-purpose ground/AA.
_(Photo: All Rights Reserved)_
As with the other artillery wagons, the Hei Wagon was constructed on the base of a 60-tonne wagon Type Chi-i. The guns are 75mm Type 88 anti-aircraft guns, also capable of engaging ground targets, with a horizontal range of 14km (8.75 miles), provided with 300 rounds each.
_(Photo: All Rights Reserved)_
This interior view shows one of the turret baskets of Wagon Hei. At the very top of the photo the breech of the 75mm gun is just visible. Although it seems to be a relatively small weapon compared to the size of the wagon, each gun had a rate of fire of some twenty rounds per minute.
_(Photo: All Rights Reserved)_
The Command Wagon, constructed on the base of a 60-tonne coal wagon Type Ta-sa. Each turret is armed with a 7.7mm Type 92 MG. On can just make out one of the lateral searchlights in its armoured enclosure, plus various optical instruments.
_(Photo: All Rights Reserved)_
Two views of the interior of the Command Wagon. Above, the upper level with the base of the periscope and various fittings. Below, the lower level, clearly the office for the train command staff.
_(Photos: All Rights Reserved)_
The Mikado 2-8-2 tender engine has simple vertical armour protection, open at the top.
_(Photo: All Rights Reserved)_
The smokebox protection is completed by a plate fastened on the front. The cutout enables us to see the American-style smokebox door. The vertical cylinders are perhaps air pumps.
_(Photo: All Rights Reserved)_
Even the tender was armed: one can just make out the retracting turrets, centre-right and far-left. The water capacity (in the six tanks with circular hatches) and the coal carried sufficed for a range of only 150km (94 miles), showing that the train was never intended for long-distance patrols across the Manchurian plains.
_(Photo: All Rights Reserved)_
The left-hand side of the tender showing the retractable nacelle in the outboard position, topped by a small rotating turret armed with a 7.7mm Type 92 MG. One can just make out the door at the right-hand end.
_(Photo: All Rights Reserved)_
A view seldom seen, of the front end of the tender facing the engine, to which it is normally attached by the drawbar clearly visible here. In this photo the MG nacelle is in the retracted, inboard position.
_(Photo: All Rights Reserved)_
This side view of the Generator Wagon showing its roof-mounted aerial.
_(Photo: All Rights Reserved)_
End view of the Generator Wagon, bringing up the rear of the train, with its two 7.7mm Type 92 MGs for close-in defence and the armoured 30cm searchlight.
_(Photo: All Rights Reserved)_
The Kó Wagon having the wheelsets of its bogies changed.
_(Photo: All Rights Reserved)_
The shoe used to accurately level the artillery wagons for firing.
_(Photo: All Rights Reserved)_
Two views of a Japanese armoured wagon captured at the end of the Second World War. It is not possible to determine the location, but the presence of a central knuckle coupling plus buffers is indicative of the Russian network.
After the war, Japanese equipment was reused by the various combatants in China and in Korea. This is perhaps one of these armoured trains watched from afar by a group of children, while more adventurous adults scavenge in the wreckage of what appears to have been a head-on collision.
_(3 Photos: Paul Malmassari Collection)_.
### Japanese Armoured Trolleys
### SUMIDA RSW Armoured Trolley
It would appear that the Japanese Army authorised only the infantry and cavalry to use armoured vehicles armed with artillery, which would explain why armoured rail trolleys are only seen with machine guns in turrets.
The RSW trolley, based on an armoured truck, was designed in 1929 to carry out railway security missions in Manchuria. The armour was 6mm thick and covered the whole vehicle. Square ports were placed around the four sides of the hull for the personal arms of the crew. The armoured radiator slats could be fixed open to increase the flow of air. For it to run on rails, all that was needed was to remove the solid rubber tyres from the wheel rims. Three headlamps provided the lighting in front of the trolley.
Postcard showing an RSW trolley at the workshops in Paichengtzu in China.
_(Postcard: Paul Malmassari Collection)_
A view of an RSW Trolley with the crew disembarked. In this vehicle the driver sits on the right-hand side, which explains the larger hatch. The red sun (or 'Meatball' as the Americans called it) for air-recognition purposes is painted in the centre of the turret hatch.
_(Photo: Paul Malmassari Collection)_
### Type 91 SO-MO armoured trolley
This heavy trolley, with the official designation of ' _91-Shiki Koki Kenisha_ ' or 'Tractor for Wide Gauge, Type 91', was identified by Allied wartime intelligence as the Type 93 'Sumida' Armoured Car, an incorrect designation used ever since (and which the author has himself used in previous works).
Built from 1930 onward, this 6x4 vehicle had plain wheels which could be fitted alternatively with solid rubber tyres for the road or with flanged rims for running on rails. Derived from the Naval Type 90 Armoured Car, it weighed 7 tonnes and carried 16mm of armour over its vitals.
The road-rail conversion took around twenty minutes, and necessitated raising the vehicle by means of the four jacks fitted to the bumpers. In addition, the spacing of the wheels could be adjusted to suit the rail gauge. The trolley reached a maximum speed of 60km/h (38.5mph) on rails as against 40km/h (25mph) on roads. However, as the chassis was unidirectional and lacked a built-in turntable arrangement, it was necessary to couple two trolleys back-to-back to allow for rapid withdrawal under fire. It was armed with six 7.7mm Taisho Type 92 MGs, one of which was mounted in the turret.
Their principal zone of operations was the China and Manchurian theatres, but it seems that several examples were used in Indochina and Malaya. The stated production total of 100 examples could include the Naval Type 90 and the Army Type 91 versions.
The original Navy Type 90, which lacked the means of converting it for rail use. The inscriptions signify 'Vehicle No 1 offered by the town of Nagaoka'.
_(Photo: Matthew Ecker)_
The Army Type 91 on solid rubber tyres for the road, with rail rims and re-railing ramps clamped to the hull sides.
_(Photo: All Rights Reserved)_
A Type 91 SO-MO of the Tsudanuma Railway Regiment seen in 1939, lacking the brackets for the re-railing ramps.
_(Photo: Wawrzyniec Markowski Collection)_
A camouflaged version. The re-railing ramp is clearly seen, as is the built-in front railing jack.
_(Photo: Heiwa Kinen Tenji Shiryokan)_
Close-up of the front end detail in the previous view.
_(Photo: Heiwa Kinen Tenji Shiryokan)_
A well-known view of the front of a SO-MO, showing the central knuckle coupling which was adjustable for height. The four lifting jacks for raising the vehicle above the rails are protected by sacking.
_(Photo: Paul Malmassari Collection)_
A later configuration, with the front axle replaced by a bogie, easier to repair after hitting a mine, and also providing a better-quality ride over uneven track. The original front wheels are carried on top of the bogie, for reconversion to road use.
_(Photo: Wawrzyniec Markowski Collection)_
The protection against the cold helps break up the lines of the vehicle and aids in camouflaging it. Note the two boxes (a field modification?) on the cab roof in front of the turret.
_(Photo: Wawrzyniec Markowski Collection)_
A group photo of SO-MO units with their proud crews, in a summer setting with the armoured flaps of the radiators open. A second photographer is at work capturing the line of four SO-MOs in the background, with one or more wagons coupled in the rake, and behind him is a convoy headed by a road-rail ISUZU truck. This scene demonstrates the wide use the Japanese made of the SO-MO for patrol work. Note the uneven track in the depot, devoid of ballast, laid on closely-spaced wooden sleepers.
_(Photo: Heiwa Kinen Tenji Shiryokan)_
A fine view of the rear of a trolley, from which one can see that the two rear doors were not symmetrical. The two units are connected in tandem, and this time the armament is in place.
_(Photo: Paul Malmassari Collection)_
A paperweight in cast iron or white metal, made for the Manchurian Railway Company.
_(Private Collection)_
Problems on the track near Jehol on 3 September 1933. Troops scan the countryside for any sign of the Chinese who have removed sections of rail.
_(Photo: Paul Malmassari Collection)_
A train crossing a box-girder bridge with no side railings in March 1941. It is possible this is a construction train.
_(Photo: Heiwa Kinen Tenji Shiryokan)_
The rail-convertible ISUZU truck gave rise to an armoured prototype which closely followed the form of the SO-MO. One difference is that the wheels shod with pneumatic tyres can be replaced by complete flanged rail wheels, and not simply the flanged rims as on the SO-MO.
_(Photo: All Rights Reserved)_
The kind of souvenir photo that every soldier in every army wants, standing with his comrades beside his combat vehicle!
_(Photo: HeiwaKinenTenjiShiryokan)_
Length: | 6.57m (21ft 7in)
---|---
Width: | 1.9m (6ft 3in)
Height: | 2.95m (9ft 8in)
Speed: | 60km/h (37.5mph) on rails: 40km/h (25mph) on roads
Armour: | 6mm min; 16mm max
Armament: | 1 x 6.5mm Type 91 machine gun
Weight: | 7.7 tonnes
Range: | 240km (150 miles) on rails
Crew: | 6
### Japanese SO-KI Road-Rail Tank (1935)
In 1935 the Japanese designed the advanced SO-KI Type 95 Light Tank, of which sixty-five examples were built. A number were captured by the Chinese Nationalists, then taken over by the Communist forces, and one surviving example is now on display in the Beijing Military Museum. To the best of our knowledge this was the only tracked road-rail armoured vehicle to have seen operational use, in Manchuria and even perhaps in Burma.
The SO-KI Tank in its 'rail' configuration. Its compact dimensions can be gauged by comparison with its crew members beside it.
_(Photo: Wawrzyniec Markowski Collection)_
Two photos of the SO-KI on display in the Beijing Military Museum.
_(Photos: Yichuan Chen)_
A fine interior shot of the SO-KI. In the centre is the vehicle commander's seat, directly beneath the turret.
_(Photo: Wawrzyniec Markowski Collection)_
The SO-KI could be employed as a rail tractor, as proved by its fittings: hook and tow chains etc.
_(Photo: RAC Tank Museum)_
When in rail configuration, it was necessary to secure the central part of the track to avoid it rubbing on the sleepers, and to immobilise the outer rollers. The SO-KI could be employed as a rail tractor, as proved by its fittings: hook and tow chains etc.
_(Photo: All Rights Reserved)_
Length: | 4.53m (14ft 10¼in)
---|---
Width: | 2.50m (8ft 2½in)
Height: | 2.45m (8ft 0½in)
Speed: | 72km/h (45mph) on rails; 80km/h (50mph) on roads
Armour: | 6mm min, 8mm max
Weight: | 9 tonnes
Trench crossing: | 1.50m (4ft 11in)
Range: | 355km (222 miles) on rails; 123km (77 miles) on roads
Crew: | 6
### Various Japanese armoured trolleys
Alongside the armoured trains, a certain number of armoured trolleys of different types were also constructed, some of which we are unable to formally identify. Nevertheless, their interesting designs merit inclusion here. In Manchuria, several radio-controlled trolleys were put into service to act as pilot/safety trolleys in front of the trains. No technical details have come to light.
These unidentified armoured trolleys may be captured Chinese vehicles. The searchlight mounting is similar to the tripod seen in the previous photos of the armoured wagon in Manchuria.
_(Photo: Paul Malmassari Collection)_
Another unidentified armoured trolley, this time displaying more modern lines.
_(Photo: Paul Malmassari Collection)_
A well-known type of trolley, of which several examples were built by the Tokyo Gas and Electric Co., here in use as a scout vehicle for a train which is pushing a safety pilot wagon.
_(Photo: Wawrzyniec Markowski Collection)_
A pair of four-wheeled armoured trolleys, of which the design recalls aspects of the Temporary Armoured Train and the Type 94. The side extensions on the trolley do not have firing ports, only observation windows. The insignia on the officer's armband is that of the Combat Railways Command.
_(Photo: Wawrzyniec Markowski Collection)_
The same type of armoured trolley in Chinese service after the war.
_(Photo: Wawrzyniec Markowski Collection)_
**SOURCES:**
**Books:**
Baseilhac, Antoine, _Recherches sur l'armée de terre japonaise 1921-1931_ , Masters dissertation under the guidance of W Serman, Paris I Panthéon-Sorbonne, 1993–4.
Branfill-Cook, Roger, _Torpedo_ , _The Complete History of the World's Most Revolutionary Naval Weapon_ (Barnsley: Seaforth Publishing, 2014), pp 31–2.
Fujita, Masao, _Japanese Armoured Trains_ (Kojinsha Co., 2013) (in Japanese).
Surlemont, Raymond, _Japanese Armour_ (Brussels: A.S.B.L. Tank Museum V.Z.W., 2010).
**Journals and Journal Articles:**
Danjou, Pascal, 'L'automitrailleuse SUMIDA', _Minitracks_ No 4 (4th Quarter 2002), pp 49–52.
_Japanese Tanks up to 1945_ , _Tank Magazine_ Special Issue (Tokyo: Delta Publishing Co. Ltd., April 1992) (in Japanese).
_Lesser-Known Army Ordnance of the Rising Sun (Part 1)_ , _Ground Power_ Special 2005-01 (Cambridge: Galileo Publishing Co. Ltd., 2005) (in Japanese).
Malmassari, Paul, 'Le Char sur rails Type 95 SO-KI', _TnT_ No 24 (March 2011), pp 54–5.
Merriam, Ray, and Roland, Paul, 'Japanese Rail-Riding Vehicles', _Military Journal_ No 11, pp 12–13.
_Panzer_ No 6 (1996).
_Panzer_ No 9 (1996).
_Panzer_ No 7 (1997).
_Panzer_ Vol 13 No 9 (1990).
_Tank Magazine_ No 2 (1987).
_Tank Magazine_ No 4 (1987).
_Tank Magazine_ No 7 (1987).
_The Tank Magazine_ No 6 (1982).
_The Tank Magazine_ No 7 (1982).
_Panzer_ No 48 (June 1979).
_Panzer_ No 49 (July 1979).
The hull was constructed of plates 6mm and 8mm thick. Note the three headlights at each end to illuminate the track, and the masts holding the radio aerials to receive the control signals. The masts are remarkably similar to those used on the German radio-controlled _Fernlenkboot_ (exploding motorboats) built by Siemens-Schuckert in 1917, perhaps indicating German technical help.
_(Photo: Japanese Army Handbook)_
. The 12th Division was the first to land on 3 August 1918 and went into action alongside the Czechs in the region of the Amur and the Ussuri Rivers. At their peak, the Japanese contingent numbered 72,000 men commanded by General Otani, who in theory was nominal head of all the Allied troops. In fact the Russo-Japanese War was still fresh in local memory, and the Russians mistrusted the growing power of Japan.
. The AEFS, the American Expeditionary Force in Siberia, was withdrawn on 1 April 1920.
. The Japanese intervention had cost their forces 5,000 dead from combat and disease.
. Adopted in February 1870. The 'Hinomaru' differs from the better-known war ensign adopted in May 1870 which includes sixteen sun's rays.
. The Republic of China was created on 1 January 1912 by Sun Yat-sen.
. The rail network in that region belonged to the Japanese Railway Company of Southern Manchuria.
. The modern Shenyang.
. See also 'Armoured Trains in Comic Books' in Appendix 1.
. The island of Formosa had been Japanese since 1895, and only became Chinese again in 1945. We do not know if the defence of the island's railway network included armoured trains.
. In Japanese: _Soko Ressha_.
. Named after the River Sumida which flows through Tokyo. Originally, the name Sumida was that of the first truck built in 1929 by the Tokyo Ishikawajima Shipbuilding & Engineering Co. Ltd. The name of the workshops is often confused with the name of the SO-MO trolley (see below).
. The numbering system for Japanese armoured vehicles (and in fact, all weapons) related to the year the Empire was founded, i.e. 660 BC. The year 1931 therefore corresponded to the Japanese year 2091, of which the last two numbers were used, resulting in the designation '91'. For weapons introduced from 1941 onward, the 'zero' of '01' disappeared and the item became 'Type 1'.
. The year designations of four vehicles were close together, as were their characteristics: Types 90 (naval version), 91 (SO-MO Trolley), 92 (Chiyoda Motor Car Factory of the Tokyo Gasu Genki K. K., but also a light tank), which added to the confusion on the Allied side.
. 16mm on the turret sides and the front face of the hull; 11mm on the hull sides and rear; 6mm on the hull top and floor, and the turret roof.
. 'Hokoku-Koto' was the name of the organisation which offered the vehicles to the Navy, while the corresponding organisation providing vehicles to the Army was the 'Aikoku-Koto'.
. Some sources quote a total of 121.
. A photo was published in the 1 January 1950 edition of _El Mundo_.
. Paradoxically, the Japanese SO-KI Type 95 Light Tank ran slightly slower on rails than on roads, but on rails its range was much greater.
## LATVIA
### ARMOURED TRAINS
### The War of Independence (5 December 1919 – 11 August 1920)
The territory which would become the independent state of Latvia was occupied by German troops from March to November 1918. In the Russian Civil War, the majority of Latvian units fought on the Bolshevik side. In 1918, two 'governments' claimed hegemony, one being a coalition of democratic parties and the other the Bolsheviks. Both sides armed their troops for the conflict. Alongside them the German troops stationed in Courland together with Germans who had settled in Latvia formed the _Landeswehr_ under the command of General Rüdiger von den Goltz. Their aim was to fight the Reds with the aid of the White Russian forces commanded by Colonel Pavel Bermondt-Avalow, and then to march on Moscow. In October 1919 they began their offensive, but the German troops were halted by the combined efforts of the Allied fleet and two Estonian armoured trains (the Estonians at that time occupying the northern part of Latvia). In November, the 'Bermondtists' were beaten, and retreated to Prussia. In January 1920, the Latvian forces went on the offensive against the Bolsheviks, and the subsequent Treaty of Riga signed on 11 August 1920 formally recognised the independence of Latvia, no longer part of Russia.
As the military and political situation evolved, German and Estonian armoured trains were engaged in combat either alongside or against the Latvian forces. On 22 May 1919, a Bolshevik armoured train was captured by the _Landeswehr_ in Riga. It then fell into the hands of the Latvians at the battle of Cesis and was designated BV No 1. The future BV No 2 named _Komunistu iznicinātājs_ ('Destroyer of Communists') went into action on 9 July 1919. These units, forming an Armoured Train Battery created on 21 July 1919, were joined by BV No 3 in September 1919 and by BV No 4 (captured from the Bermondtist forces) in November 1919.
### The Inter-War Period
At the close of the War of Independence, Latvia possessed six trains, but by 1921 only two remained in service, and these lacked anti-aircraft armament. In October 1923 the Latvian Government made overtures to France for the construction of six engines, four or six armoured wagons and twenty wagons mounting turrets. However, following a political crisis in Latvia the project was shelved in January 1924.
Between 1925 and 1930, as part of a major modernisation and rearmament programme, four new trains entered service and made up the Armoured Train Battery based in Riga, which also included three 152mm Canet railway guns. The armoured trains were divided between the Russian gauge (1520mm/5ft nominal) and the standard gauge (1435mm/4ft 8½in) networks. The Latvian Guard ( _Aizsargs_ ) which came under the authority of the Minister of the Interior, appears also to have used armoured trains as part of its railway regiment.
On 1 July 1926, the Battery was reorganised as an Armoured Train Regiment, and in 1939 it was planned to build two additional units. The Regiment was eventually dissolved on 3 February 1940, because of a lack of ammunition which up until then had been supplied by Czechoslovakia and Germany. The two trains still in service were allocated to the Coast Artillery Regiment.
### Occupation by Soviet then German Forces
On 17 June 1940, Soviet forces occupied Latvia, and the armoured trains were incorporated in the Red Army. The following year, the Soviet armoured trains of obvious Latvian conception were cut off and captured by the Wehrmacht, who set about converting the Latvian railway network from Russian gauge to standard gauge. This task was virtually complete by the end of 1941, and the majority of Latvian armoured train units were thereafter reused by the Wehrmacht.
The badge of the Latvian Armoured Trains Regiment.
_(Photo: All Rights Reserved)_
PZ 5 of the _Landeswehr_.
_(Photo: Paul Malmassari Collection)_
In 1919, the Latvians captured a Bolshevik armoured train of the 'Krasnoye Sormovo' type, and put it into service with their own armed forces.
_(Photo: Latvijas Kara Musejs)_
Here is the same wagon, captured in turn by the Wehrmacht in 1941.
_(Photo: Paul Malmassari Collection)_
The platform wagon _Kalpas_ of BV No 5 in November 1919, with its crew of British sailors and Marines and their 3in HA gun.
_(Photo: Latvijas Kara Musejs)_
Unidentified Latvian armoured train, probably photographed in the 1920s.
_(Photo: Latvijas Kara Musejs)_
A similar armoured loco, seen here at Daugavpils in 1923.
_(Photo: Latvijas Kara Musejs)_
BV No 2 in 1919. Its armour protection consists of Russian trench shields, of which several thousand were available in the stores.
_(Photo: Latvijas Kara Musejs)_
The armoured locomotive from BV No 2, demonstrating that it too was armoured using Russian trench shields.
_(Photo: Latvijas Kara Musejs)_
A classic shot of one of the later Latvian armoured trains.
_(Photo: Paul Malmassari Collection)_
Probably BV No 1 near the Viksna bridge in the Summer of 1924.
_(Photo: Latvijas Kara Musejs)_
One of the two armoured wagons designed by engineer Oskars Dzervitis in 1925. Interestingly, the turret gun (which is probably a German 7.7cm 16 field gun) still retains its wheels and gunner seats, possibly allowing for it to be dismounted for use off the train. In the same year, the older locomotives were replaced by new engines, fitted with arrangements to vent the steam and smoke at rail level.
_(Photo: Latvijas Kara Musejs)_
Armoured train at gunnery practice in October 1931.
_(Photo: Latvijas Kara Musejs)_
One of the 152mm Canet railway guns, photographed in 1937.
_(Photo: Latvijas Kara Musejs)_
Photographed in Cietoknis Station, a modern train evidently made up of elements of shorter trains, including the old platform wagons from PZ 5 still in use, but now armed with British guns.
_(Photo: Latvijas Kara Musejs)_
One of the Canet guns seen here in travelling mode, attached in support of a complete armoured train.
_(Photo: Paul Malmassari Collection)_
An armoured train seen during the 1930s, armed with a 37mm Hotchkiss revolver cannon, a devastating close-range anti-personnel weapon despite its age.
_(Photo: Paul Malmassari Collection)_
**SOURCES:**
**Book:**
Lavenieks, J, _Bruņoto vilcienu pulks_ (New York: Izd. Vera Laveniece, 1971).
**Websites:**
<http://vesture.eu/index.php/Bru%C5%86oto_vilcienu_pulks>
<http://vesture.eu/index.php/Latvijas_armijas_Bru%C5%86oto_vilcienu_divizions>
<http://www.lacplesis.com/WWI_To_WWII/Pirmais_Pasaules_un_Brivibas_Kars/BRUNOTAIS_VILCIENS/index.htm>
. In Latvian: _Bruņoto' Vilcienu_ , abbreviated as BV.
. November 18th 1918 is recognised as Independence Day in Latvia.
. Territorial Defence Force.
. Included were two trains armed by the British who also provided training: _Kalpaks_ (the future BV No 5) and _Pikols_. Both were discarded in December 1919.
. BV No 3 was activated in 1928 and BV No 4 in 1930.
. The static defences had been reinforced in the late 1930s by two railway guns.
## LITHUANIA
### ARMOURED TRAINS
Lithuania waged three wars to gain its independence, beginning on 16 February 1918 and lasting for two years. The first was fought against the Bolsheviks, and ended in June 1919, the second against Russo-German forces invading Lithuania from neighbouring Latvia, and the third against the Polish Army which sought to seize Vilnius (Vilno) in defiance of the League of Nations' decision to cede that city to Lithuania. This third conflict ended in defeat for the Lithuanians. The latter used two armoured trains, incorporating parts of captured Russian armoured trains.
The ST _Gediminas_ was built in January 1920 in Kuanas (Kovno) and was despatched to Varena to confront the Poles. On the 19th of that month it was on the front line at Suvalkai, but was forced to withdraw to Vilnius, where it was captured intact by the Poles. It saw further service as part of the Polish armoured train PP 1 _Marzalek_.
In October 1920 a replacement armoured train bearing the name _Gediminas_ was built by the Lithuanians. On 21 November it was sent to Kedainai to confront the Polish forces, but the ceasefire took effect before it could go into action.
When the Lithunian army was formally established, it included a battalion with three armoured trains, all built at the Kaunas workshops: ST 1 _Gediminas_ , ST 2 _Kęstutis_ and ST 3 _Algirdas_. The layout of each train was standardised asd an engine, an artillery wagon with two guns, and two machine-gun wagons each armed with eight machine guns. In January 1924 the battalion became a regiment and was incorporated in the Armoured Group ' _Sarvuociu Rinkine_ '. However, ST 3 _Algirdas_ was broken up in early 1927. A directive dated 16 November 1927 fixed the establishment of the armoured trains as five officers, six NCOs and forty-one men. The armoured trains formation was finally dissolved on 14 August 1935. Certain sources give the name of the third armoured train as _Glezininku Vilkas_ , but at the date of writing we have been unable to confirm or refute this. Several wagons survived to be captured during the Soviet invasion, but they have not been identified as having been incorporated in later Russian armoured trains.
Artillery Wagon No 1 of ST _Gediminas_ , armed with a pair of ex-German 7.7cm _Feldkanone_ 16 field guns, retaining their original shields. The mixed armament reflects the tortuous frontier problems of this period of European upheaval.
_(Photo: Paul Malmassari Collection)_
Artillery Wagon No 3 of ST _Gediminas_ , armed with French 75mm Model 97 guns, again retaining their wheels but now fitted with large box gunshields.
_(Photo: Paul Malmassari Collection)_
In the foreground is Artillery Wagon No 2 of the ST _Gediminas_ , armed with ex-German Army 10.5cm _Leichte Feldhaubitze_ 98/09. The light howitzers, retaining their wheels, appear to be mounted on turntables. Each gun has been retrofitted with a large box shield providing good protection for the gunners. Artillery Wagon No 3 in the centre is armed with a pair of French 75mm Model 97 field guns with their wheels and original small shields.
_(Photo: Paul Malmassari Collection)_
. In Lithuanian: ' _sarvuotas traukinys_ ', abbreviated to 'ST'.
. Gediminas (c. 1297–1341), Grand Duke of Lithuania in 1316.
. Kęstutis (1297–1382), son of Gediminas, Duke of Trakai, co-ruler of Lithuania with his brother Algirdas.
. Algirdas (c. 1276–1377), brother of Kęstutis, Grand Duke of Lithuania 1345.
. 'Iron Wolf'.
## MALAWI
The various struggles for independence in Africa have left a legacy of extensive minefields. From 1981 Malawi Railways diesel locomotives were loaned to Mozambique to operate on the line to the port of Nacala, which allowed trains to avoid crossing Rhodesia following that country's unilateral declaration of independence from Britain. Since 1979 the other rail line leading to Beira had been put out of action by RENAMO. Because of the political instability and the constant threat of attacks during the decade 1980–90, four Malawi Railways locomotives – Numbers 401, 402, 407 and 408 – were fitted with armour plates around the cab and certain fittings. Shire Class locomotives were also armoured in a similar fashion, and improvised armoured wagons provided protection for the trains.
**SOURCES:**
Bagshawe, Peter, private archives
Warner, Terry, 'Armoured Trains in Southern Africa', _Tank TV_ (New Zealand) No 6 (June 1994, p 1.
One of the protection wagons on the Nacala line, fitted with the hull of a British Ferret armoured car.
_(Photo: Peter Cooke)_
On 22 November 1989, broken-down Zambesi Class Co-Co diesel-electric locomotive No 407 with its armour plating arrives at Blantyre towed by No 402. Diesel locomotives 401 and 408 were similarly armoured.
_(Photo: Peter Bagshawe)_
Shire Class Co-Co diesel-electric locomotive No 500 being armoured at the Limbe workshops in November 1989. The framework to support the armour plates has been fitted to the roof and hood, but it is not clear whether the intended all-round armour protection was ever mounted.
_(Photo: Peter Bagshawe)_
Another form of armour giving all-round protection to the cab of this Shire Class Co-Co diesel-electric locomotive No 501 seen at the Limbe workshops in 1989.
_(Photo: Peter Bagshawe)_
. The locomotives were 3ft 6in gauge units built by Metropolitan Cammell Carriage & Wagon Co Ltd of Birmingham/ Associated Electrical Industries (AEI), powered by a 1200hp Sulzer 6LDA28B motor.
. Resistência Nacional Moçambicana.
## MALAYSIA
The British began to intervene actively in the affairs of the Malay peninsula from the end of the eighteenth century, and it was made a Protectorate in 1910. After the Japanese occupation during the Second World War, the Malayan Union became a colony in 1946, and two years later was replaced by the Malaysian Federation. A Communist uprising which began on 16 June 1948, and ended in 1960, plunged the country into a hard-fought counterinsurgency war (the 'Malayan Emergency'). It was during this period, on 31 August 1957, that the Federation gained its independence from Britain.
Following use by the British armed forces, a number of Wickham armed trolleys remained in the country, while others were sold on to countries facing similar security threats and which, of necessity, used the same rail gauge. But the need for internal security continued even after the Communist guerrillas surrendered. Following the American withdrawal from Vietnam, the Malaysian authorities feared infiltration by guerrillas coming from Thailand. Therefore in 1978 they ordered a new design from Wickham, but in fact this was destined to remain on the drawing board. The machine was based on a development of the AT 105 armoured vehicle built by GKN Sankey, to be mounted on a Wickham chassis. Powered by a Perkins V8/540 water-cooled motor, via a Clark 13-H-R 28314 gearbox with three speeds in both forward and reverse, maximum speed was 95km/h (60mph). The 16mm armour would offer protection against 5.56mm and 7.62mm projectiles fired from as close as a dozen metres (13 yards), with a floor 6mm thick. The turret was to have been armed with either one or two 7.62mm L 37 A1 machine guns
Three trolleys are still preserved in museums: AWT Nos 56, 60 and 63. Here is AWT No 63 in front of the Royal Malayan Police Museum in Lake Garden.
_(Photo:<http://zureuel.blogspot.fr/2008/05/wickhamtrolley-legacy-of-malaysian.html>)_
An armoured brake van on display at Farlim. This type of armoured unit, of which several examples were probably constructed for use with goods trains, has never received as much attention as the offensive/patrol machines.
_(Photo: Jaafar Amil)_
**SOURCES:**
Wickham Archives.
Malayan Railways.
Wickham trolley No 57 in Kuala Lumpur in December 1968. It has probably since been scrapped.
_(Photo: Paul Middleton Collection)_
The original plan of the Wickham Project proposed to Malaysia in 1978.
_(Plan: Wickham)_
. Vietnam, Thailand and Burma. Certain sources also mention Cambodia.
. Ultimately named the Saxon, this vehicle went into production in 1976, and several examples equip the Malaysian Army.
## MAURITANIA
### ARMOURED LOCOMOTIVES & ESCORT WAGONS (1978)
Iron ore represents some 50 per cent of Mauritania's exports, and the iron mines of Zouérate, run by the Company MIFERMA (Iron Mines of Mauritania Ltd) are connected by an extremely long railway line to the Atlantic port of Nouadhibou. In the 1970s the operator, Mauritanian Railways, was owned by MIFERMA.
Following Mauritania's occupation of the southern part of former Spanish Western Sahara in 1976, this crucial link came under regular attack by the POLISARIO Front, who were fighting to establish an independent Sahrawi Democratic Arab Republic (SDAR) in the occupied territories. Exchanging their camels for armed Land Rovers, the POLISARIO fighters launched lightning raids against the railway, causing significant damage to rolling stock and installations.
In 1978 the Mauritanians decided to armour the driving cabs of the locomotives and, at irregular intervals in the 2,500m (over one and a half miles) long iron ore trains they inserted improvised escort wagons. These were very summarily protected, by welding lengths of rail around the mineral wagon roofs to form a precarious shelter for the lookouts and gunners. The armament consisted of ex-Soviet 23mm cannon behind rudimentary shields.
In 1979 an armoured command wagon was constructed, and coupled near the end of the train. It was in direct radio commication with the locomotive. The ex-freight container which was used as the body was not fixed rigidly to the wagon chassis, in order to try to minimise the shocks felt when the extremely long convoy accelerated or slowed down. With 200 to 210 mineral wagons each weighing 83 tonnes, even a small gap of a centimetre between wagons, plus the spring effect of the couplings, would mean a to-or-fro movement at the rear of the train of 2–3m! This could produce a shock effect powerful enough to make an occupant of the command wagon lose his footing, if he were not prepared. The attacks ended when on 5 August 1979 Mauritania's new government signed a peace treaty with the POLISARIO Front, recognised the right to independence of the SDAR, and withdrew its own forces.
MIFERMA Class CC 01-21 diesel locomotive, based on the SNCF CC 65000 Class (Alsthom) with two diesel engines as per the French locos but of higher power output.
_(Photo: Private Collection)_
The damage caused by a POLISARIO raid on the locomotive depot.
_(Photo: Private Collection)_
The weight of the loaded iron ore trains required the use of three or four coupled locomotives. Note the powerful track-illuminating searchlight mounted lower down on the header loco, and therefore less vulnerable than on the standard production models. The superstructure fitted to the loco roof contained and protected the engine's vital air-filtration system.
_(Photo: Private Collection)_
Armour plating of the driving cab, with the offset spacing of 3mm just visible, and the company's livery continued over the armour.
_(Photo: Private Collection)_
Each train was made up of at least 200 wagons, among which armoured wagons were inserted at intervals. They would be withdrawn from service in 1979. The guards in their exposed positions were far more likely to flee or seek shelter than to fight back against raiders...
_(Photo: Private Collection)_
In 1979, an armoured command wagon was inserted in the convoys. The mineral wagon next to it is only lightly armoured, and is armed with a shielded 23mm cannon.
_(Photo: Private Collection)_
## MEXICO
### ARMOURED TRAINS AND TROLLEYS
The use of various armoured trains by the governments of the day and by certain revolutionary factions make the railways of Mexico one of the lasting symbols of South American revolutions. It is generally held that there were two principal revolutions: that of 1910–12 followed by civil war, and that of 1935–8, and in between the two the War of the Christeros.
Under the dictatorship of General Porfirio Diaz, the development of the railways was a mark of real progress: by 1910 Mexico had 20,000km (c. 12,000 miles) of railway lines, divided basically between two North American Companies, the 'Ferrocarril Central Mexicano' and the 'Nacional Mexicano'. But then the political situation deteriorated and the revolution broke out in November 1910, with the Maderists rising up against the government, and the repression which followed. One of the future famous figures of the revolution, Francisco Villa, joined the insurgents at the end of November in Chihuahua (North Mexico). In February 1911 Emilio Zapata began his agrarian uprising in Morelos, 80km (50 miles) to the south of the capital. In May, President Diaz resigned and left the country. Madero was elected and crushed the revolutionaries under Zapata who had risen up against him. In February 1913 Madero was assassinated, and was replaced by General Huerta. This saw the beginning of a long troubled period (' _la decena tragica_ ').
Pancho Villa waged a guerrilla war against the large landowners in Chihuahua. At the head of the División del Norte he captured the major rail junction of Torreón in late September, together with a huge collection of rolling stock. In December 1913 he became Governor of the State of Chihuahua. For his part Zapata continued his guerrilla struggle in the States of Pueblo and Guerrero. In April 1914 the Americans intervened for the first time at Vera Cruz, following the arrest of US sailors and to prevent the landing of a cargo of arms bound for the Federales. To force General Huerta to leave office, the Constitutionalists of Carranza, the troops under Villa (first allies then opponents of Huerta), and those under Zapata converged on Mexico City in a race to see whose forces would enter first. Between April and July 1915, in the struggle between the factions which began after the entry of the Zapatists and the Villaists (on 24 and 28 November 1914 respectively), the railways and the various types of armoured trains played a major role. With some difficulty, the central government progressively regained control of the country. The railway system suffered heavily, with bridges demolished, lines torn up or dynamited, and rolling stock destroyed.
Two photos and a cutaway illustration of the armoured wagon specially camouflaged in a checkerboard pattern, so that at 30m (33 yards) range it was difficult to differentiate between real and dummy firing ports. The interior was sparsely equipped, but allowed the use of rifles at various firing positions. According to the magazine _Sciences et Voyages_ (No 50 12 August 1920, p 337), this wagon could have been built by rebel forces. But another magazine _La Nature_ (No 2053, 28 September 1912), described it as a government wagon, an identification confirmed on the cover of the _Illustrated London News_ of 29 April 1911. This divergence is the proof that one must always verify journalists' comments, as they may be led astray by their local correspondents.
Shown here in 1912 is one of the numerous convoys which attempted to protect the railway. In fact the armoured trains of this period were never used in an offensive role but solely as one component of a means of transport. The protection formed by a wooden wall in the interior of the wagon is clearly visible.
_(Photo: All Rights Reserved)_
A view of an armoured wagon here photographed during the defence of Chia in 1913. In reality, the field gun would not fire directly over the heads of the infantrymen manning the front casemate, as the muzzle blast would be too dangerous.
_(Photo: Philip Jowett Collection)_
The same wagon as above. The lowered side panels allowed for lateral fire, or they could be hinged upwards to protect the gun and crew.
_(Photo: Philip Jowett Collection)_
Federal armoured wagon with 80mm Mondragon field gun. That many of these scarce weapons are seen on armoured trains emphasizes their importance.
_(Photo: Paul Malmassari Collection)_
Built along similar lines to the one shown left, this armoured wagon lacks the firing ports in the front casemate. It appears the gun crew are removing the barrel rearwards, perhaps to change it.
_(Photo: Paul Malmassari Collection)_
An undated view of a Federal wagon with unique armour protection, armed with a centrally-mounted field gun and machine guns at the four firing ports. The protection appears to be made of wood, and the canopy protects the crew from the sun. The person on the right appears to be an American.
_(Photo: Philip Jowett Collection)_
Mack-Saurer trucks, known as 'Rikers' from the name of their designer Andrew Riker, were converted to unarmoured rail trolleys to supply the American Expeditionary Force on the Mexican Border in 1916. On the Mexican side, at least one Riker was converted to an armoured trolley for use by the Constitutionalist Army, and it appears the armour protection was installed by the North Western Railroad workshops in Juarez.
The Riker on its road wheels. The Constitutionalist Army was created on 4 March 1913 by Venustiano Carranza who established a rebel government in the State of Sonora. This army was divided into divisions, brigades and smaller units, each one bearing the name of a geographical area. Villa was the commander of the Division del Norte.
_(Photo: All Rights Reserved)_
The same machine again, this time on its rail wheels. The inscriptions in the previous shot are just visible on the hull sides, along with part of the decoration of one wheel. This photo was perhaps taken just prior to it receiving its complete disruptive checkerboard camouflage. Magnification of the photo revealed the name 'Mack' on the wheel hubs.
_(Photo: Paul Malmassari Collection)_
During the Christiade (1926–9) the Christeros rose in revolt in thirteen states of Central Mexico. Between March and May 1929, they conquered all of the west of the country (apart from the large towns), and attacked the communications networks. To assure free movement of its troops, the Government ordered the construction of armoured wagons. These units were clearly of much improved design compared with their earlier counterparts.
It only remains to cite the most recent mention of Mexican armoured trains. In the song _Adélita_ by Julien Clerc (1971) we hear the words:
The Mack-Saurer/Riker probably in its final configuration, with the lettering reapplied in a light colour over the (presumably black and white) checkerboard pattern. This is a form of disruptive camouflage – similar to the wagon shown earlier – intended to mask the actual firing points. On the other hand one must express astonishment at the wheel embellishments in the form of stars. Speed on the rails was estimated at 65–70km/h (40 to 45mph) and range as 350km (220 miles).
_(Photo: Albert Mroz)_
_« Elle s'appelait Adélita
C'était l'idole de l'armée de Villa
Pancho Villa_
_Des trains blindés portaient son nom
Pour son caprice sautaient des ponts
De toute la division du nord
Oui c'était elle le vrai trésor...»_
'She was called Adélita
The idol of the Army of Villa
Pancho Villa
Armoured trains bore her name
At a whim she blew the bridges
Of the whole Northern Division
Oh yes, she was a real treasure...'.
On the other hand the comic book _El Tren Blindado_ only shows an _armed_ train. But the title demonstrates how the image of the armoured train is indelibly stamped on the history of the Mexican Revolutions.
**SOURCES:**
Heigl, Fritz, _Taschenbuch der Tanks_ (Munich: J. P. Lehmanns Verlag, 1935), Vol II.
Meyer, Jean, _La Révolution méxicaine_ (Paris: Calmann-Lévy, 1973).
Mroz, Albert, _American Military Vehicles of World War I_ (Jefferson [NC] & London, 2009, McFarland & Company, 2009).
Segura, Antonio, _El Tren Blindado_ (Sueca: Aleta Ediciones, 2004).
Near the end of the revolution, the security of travellers was assured by protection wagons inserted in the passenger trains. An American railroad company with connections into Mexico had these armoured wagons built.
_(Photo: Le Miroir, No 326 [22 February 1920])_.
Taken from Heigl's famous _Taschenbuch der Tanks_ , this armoured wagon has been constructed on the base of the same type of bogie wagon as in the following shot, and is no doubt one of the wagons General Callès ordered to be inserted in all the trains in 1929.
_(Photo: Paul Malmassari Collection)_
This photo fits in completely with the notion of the 'rolling fortress' all too often applied to armoured trains. But the central structure with its firing ports is remarkable.
The influence of the Russian Revolution and the presence of Trotsky in Mexico inspired the title of this magazine created by Antonio Mella, of the Association of Proletarian Students. Here is Number 1 of September 1928.
. From the name of Francisco Madero, the founder of the anti re-election party.
. A well-known bandit, whose real name was José Doroteo Arango Arámbula. Better known by his popular nickname of 'Pancho Villa'.
. Zapata was killed on 10 April 1919, Villa laid down his arms in June 1920 and was assassinated in 1923.
. Ascribed by some sources to Pancho Villa.
. A rebellion by the Christian Mexicans, against the presidency of General Callès. The rebels opposed the suppression of the Catholic Church, the closure of churches and the arrest of priests.
## MOROCCO
### INSURRECTION 1952–1956
We have already examined the armoured train project conceived just before the Second World War (see the chapter on France). It appears that at last one armoured train from that period had been retained up until the events of 1952. The attacks in Morocco became more intense in July 1955, and measures were put in hand by the C.F.M. following the serious incidents at Oued-Zem, Khénifra and Kourigba. On certain routes trains no longer ran after dark, and security patrols commenced with two armoured trains which were reactivated in 1955.
These trains were made up of the following elements:
– a tank transporter wagon.
– an armoured diesel-electric locomotive.
– two bogie wagons with armour protection and internal equipment, transporting escort troops and a repair team.
– a second tank transporter wagon.
Trains of this type would be used during the Algerian War.
An armoured train of the type designed for Morocco, slightly modified after its transfer to Algeria, with an M3A3 light tank.
_(Photo: Dejoux)_
## MOZAMBIQUE
### ARMOURED TRAINS IN THE CIVIL WAR (1975–1992)
After Portugal granted independence to Mozambique on 25 June 1975, civil war broke out, which lasted up until 1992. The Limpopo railway line which ran between the port of Maputo and Zimbabwe, and also the line from Nacala in the north, were regularly subject to attacks, at least up until mid-1989. The locomotives were protected by steel plates, and the trains were preceded by ballasted flat wagons. The work of rebuilding the railway network began in 1990, with financial aid from several countries including France and India, under the protection of Zimbabwean troops.
Beginning in 1980, the company E C Lennings acquired several ex-Rhodesian armoured trolleys for use on the Beira corridor which linked Mutare to Beira. In 1992 the journalist Luca Poggiali published a study of the civil war in Mozambique, illustrated by a photo of an FPLM 'armoured train' captured by RENAMO. In addition, other means of protecting the rail traffic on this vital axis included reinforced bogie wagons armed with heavy machine guns.
**SOURCES:**
Lugan, Bernard, '1964-1992: Une Guerre de 30 Ans', _L'Afrique réelle_ No 56 (August 2014), pp 13–15.
Poggiali, Luca, 'La RENAMO, victoire au bout du fusil', _Raids_ (November 1992), pp 34–8.
_Afrique Defense_ : various numbers.
Part of the armoured train captured by RENAMO. It is likely that these two Wickham armoured hulls were Nos 191 and 192, built in 1969 and transferred to Angola via the Beira corridor.
_(Photo: All Rights Reserved)_
. The FPLM (Mozambique Popular Liberation Forces) were the armed branch of FRELIMO ( _Frente de Libertação de Moçambique_ ), Marxists.
. _Resistência Nacional Moçambicana_ , the anti-Marxists.
## THE NETHERLANDS
### ARMOURED TRAINS
### The Second World War
In Holland itself, from September 1944 Dutch Railways were forced to fit shelters for the crews of civilian steam engines to protect them against the RAF who were systematically attacking all trains running in occupied Europe. These concrete shelters constructed on the tenders offered limited protection, and none at all if the boiler exploded, so instead the train crews preferred to jump from their engine. True Dutch armoured trains were designed and built only in the Dutch East Indies.
### The armoured trains of the Dutch East Indies Railway Company (NIS)
In the Summer of 1941, two high-ranking officers of the Royal Dutch East Indies Army (KNIL) secretly made contact with the heads of the NIS in Semarang, in order to discuss the construction of two armoured trains to run on the Standard Gauge network (at that time the NIS operated two different gauges, metre gauge which was actually 1067mm or 3ft 6in, and standard gauge, 4ft 8½ins or 1435mm), to meet the possibility of a Japanese attack on Java. The mission of the first train would be to prevent troops disembarking from seaplanes arriving on the lakes to the south of the line from Toentang to Willem I. The other train was to operate on the Solo to Djokja main line. In the event, a start was made on armouring only the first train, but the work would never be fully completed.
For this train, the NIS set aside 0-6-0 Tank Engine No 106, together with two platform wagons for the gun armament and a tank wagon to supplement the water supply of the engine. The 7mm armour protection for the engine was conceived by M. Ir. J C Jonker, chief engineer of the NIS, and made up in the Djojka workshops. The armour for the platform wagons was designed by the KNIL, and was to be constructed by the firm of De Vries Robbé in Semarang. The completed train was sent to Semarang, where it was planned to reinforce the suspension springs of the engine, to refit a lower, less conspicuous funnel, and to complete the wagons with a steel floor and arm them.
_(Drawing: Bas Koster)_
Following Pearl Harbor the project was re-examined, but what gave it a degree of urgency was the Japanese occupation of the Dutch part of Borneo. Within the available timescale, the only work which could be carried out was the armouring of Tank Engine No 106, and the train's proposed artillery armament was replaced by machine guns, protected only by sandbags. In the event, the armouring of the engine was still unfinished when the Japanese attack on Java began on 1 March 1942. It was therefore an old unarmoured Beyer Peacock 2-4-0 engine which was used to haul the sandbagged wagons to the lakes, where in fact the anticipated landings from seaplanes never took place. On 5 March, the military crew abandoned the train and drew the fire in the firebox. They emplaced their machine guns in the mountains, and left the engine crew to return to their base on foot. As for No 106, after the surrender the Japanese removed its armour and returned the engine to normal use.
### The armoured trains of the State Railway (SS)
The KNIL commanding officers also wanted to operate two armoured trains on the metre-gauge network. The first would operate in the western region of Java, and the second in the central and eastern regions. The trains were to be built in the State Railway workshops in Madioen in eastern Java, and in Mangarrai to the south of Batavia in western Java. No information has come to light concerning the train constructed in Madioen, but the one built in Mangarrai is well-documented.
It was to be hauled by armoured 2-8-2 Tank Engine No 1406, one of a class of twenty-four engines built by Werkspoor in Amsterdam and by Hanomag in Hanover. Two reinforced flat wagons, armed with Madsen LMGs in revolving cupolas, two twoplank wagons protected by sandbags and armed with Breda machine guns for anti-aircraft defence, and an armoured command coach with most of the windows sealed off, formed the armoured train which became operational in November 1941. It was based at Tandjoeng Priok, the port of Batavia. On 22 February 1942 its crew of eighteen men (fourteen soldiers, two engineers and two train drivers) came under the orders of Infantry Sergeant W B Wisser, who was promoted to _Reserve Tweede luitenant_ (temporary Second Lieutenant), on the day he took command. Despite the Japanese bombing, the train was brought to a state of readiness between 24 November 1941 and 2 February 1942.
_(Drawing: Bas Koster)_
_(Drawing: Bas Koster)_
On 1 March, the Japanese began the invasion of Java, and on the 8th the Dutch garrison surrendered. During this week the Dutch carried out the destruction of elements of the rail infrastructure and the rolling stock was rendered unserviceable. At 02.00 on 1 March, the crew of the armoured train received orders to leave Batavia in order to reach Rangkasbetoeng, but it was halted at Paroengpandjang by the advance of Japanese forces. Returning the same day in the direction of Batavia, the train crew destroyed the bridges at Paroengpandjang and Serpong. Starting out on 5 March, the train offered protection to the transport by rail of the 11th Infantry Battalion between Tangerang and Soekaboemi, the armoured train following 5km behind the troop train. Near Tjitajam it was attacked by an enemy fighter, but the train rolling at 30 miles an hour (50km/h) took very few hits and in turn was unable to hit the aircraft. As the train accelerated to 40mph (65km/h) just before reaching Tjileboet, a bomb hit the track but without causing damage, and the armoured train was able to reach the station at Buitenzorg, where it laagered for the night.
On 6 March the train received orders to escort a long military train (two locomotives and sixty wagons) between Buitenzorg and Bandoeng. Lieutenant Wisser learned that the track was blocked by a derailment near the Lampegan tunnel, and he saw that the work of clearing the track was taking longer than anticipated. While waiting, in order to avoid being spotted by the Japanese, who were actively hunting for the train, he distributed his armoured wagons around the depot at Soekaboemi. This was fortuitous, as four fighters bombed the depot and strafed it with cannon fire at around 09.00. At 16.00 a message informed the train that the Japanese had reached Tjisaät, only thirty minutes' march from Soekaboemi. At that moment the decision was taken to sabotage the train with explosive charges, which was completed by around 17.00. Although the Japanese managed to repair engine No 1406 late in 1942, to this day no trace of the rest of the armoured train has come to light.
### The five armoured engines of the DSM
The private company DSM (Deli Spoorweg Maatschappi, based in the north of Sumatra, with its headquarters in Medan), operated a metre gauge network. In 1941 the decision was taken to armour the cabs of five 2-6-4 tank engines, to protect the crews against small-arms fire. The armour protection was left in place on these engines up to the end of 1953, as after the Japanese left, between 1947 and 1949 the region around Deli remained a hotbed of insurrection.
2-6-4 Tank Engine No 59 of the DSM (metre gauge) with partial armour protection, seen on Sumatra. These engines carried their armour plate from 1941 to 1953.
_(Photo: Jan de Bruin Collection)_
_(Drawing: Bas Koster)_
### Fighting during the decolonisation period
On 17 August 1945 Indonesian nationalists declared independence from Dutch colonial rule, and began many acts of sabotage and outright attacks, which the Dutch countered with 'peacekeeping' operations. Colonial institutions such as the rail network were especially singled out for attack. The conflict ended on 27 December 1949 when the Dutch recognised the independence of the Republic of Indonesia.
By July 1947 the majority of the 553km (344 miles) of the DSM Railway Company's routes on Sumatra were firmly in the hands of the Dutch authorities, but the free passage of trains was disrupted by frequent attacks. A number of flat wagons armed with machine guns, and with the gunners protected by sandbags and overhead netting, were placed at the front of trains as pilot/safety wagons.
Protected DSM train on Sumatra, 1946.
_(Photo: All Rights Reserved)_
Pilot wagon at the head of a DSM train (metre gauge) on Sumatra in 1947.
_(Photo: Jan de Bruin Collection)_
### DSM Armoured Jeep No P1 (Pantservoertuig nr 1)
On the most dangerous sections, a completely armoured Jeep preceded the trains. This unique machine complete with firing slits in a central armoured casemate was in fact based around a converted Jeep, and was designed and built in 1947 by the DSM workshops at Poelau Brayan, near Medan. It was fitted with a special gearbox and a more powerful motor than usual. Propulsion was by the four central rail wheels mounted on the Jeep's axles, while the forward and rear axles of the platform wagon helped spread the weight of the complete vehicle. No trace of this vehicle can be found after 1949.
_(Photos: Jan de Bruin Collection)_
### The situation on the Island of Java, August 1945–December 1949
After the Japanese surrender on 15 August 1945, the situation on Java became extremely complex: Sukarno declared independence on 17 August, and his supporters took over control of the transport infrastructure, notably the tramways and the railways. In September the British attempted to seize control, and they were soon joined by Dutch PoWs freed from Japanese prison camps. The private and state railways were combined under a single body: the Unified Railway Authority, abbreviated as 'VS', which worked in close cooperation with the Army. The reoccupation of Java took from December 1945 to December 1948, but railway traffic continued to be the target of continuing attacks, basically carried out using explosives seized from the Japanese. The principal method used by the nationalists was the traction bomb, activated by a wire stretched across the railway line. As on Sumatra, armed and protected flat wagons were propelled in front of the trains, and in the more dangerous zones, safety trucks were added in front of the flat wagons to protect the latter from mines.
Armoured train on Java, in the early days of the rebellion, January–August 1946.
_(Photo: All Rights Reserved)_
### The armoured trolleys on Java 1946–1949
Several Jeeps were armoured and converted to run on rails by the Dutch Army in workshops such as the one in Bandoeng, and armoured trolleys with two, or in the case of the heaviest, three axles were also built. Surprisingly, we do not know the total number converted, and the only proof of their existence which has come down to us are the photographs.
Jeep converted to run on rails (metre gauge) seen at Manggarai.
_(Photo: Jan de Bruin Collection)_
Trolley-Jeep seen in the process of being armoured in the Manggarai workshops in 1947. Note that in this version only the two front seats are protected.
_(Photo: Jan de Bruin Collection)_
Two Trolley-Jeeps attached back-to-back, in the classic configuration allowing for rapid withdrawal under fire. Note the style of armour protection on the first of these two Trolley-Jeeps. The rear vehicle has an unarmoured rear platform.
_(Photo: Jan de Bruin Collection)_
Trolley-Jeeps on patrol on Java, 1946–9.
_(Photo: Jan de Bruin Collection)_
A fully-armoured Jeep conversion with a third axle to carry the extra weight.
_(Photo: All Rights Reserved)_
To provide armour protection for flat wagons, one solution was to reuse the armoured hulls of Overvalwagen vehicles bolted onto the wagon deck.
_(Photo: Jan de Bruin Collection)_
An Overvalwagen hull protecting a train on the Tjibatoe-Garoet line, Java, 1949.
_(Photo: Jan de Bruin Collection)_
Two 1980s views of BRAAT armoured hulls bolted to flat wagons, built in the Manggari workshops. Ultimately, the armoured hulls of some of these vehicles were cut in half and the halves joined end-to-end to create armoured trolleys. See the chapter on Indonesia.
_(Photos: Tony Ford)_
**SOURCES:**
**Book:**
De Bruin, Jan, _Het Indische spoor in oorlogstijd_ (Rosmalen: Uitgeverij Uquiliar B.V., 2003).
**Website:**
<http://www.overvalwagen.com>
**Preserved vehicles:**
Jakarta Museum (BRAAT on a flat wagon)
Bandung Museum (Panser rel V16)
. _Nederlandsch-Indische Spoorwegmaatschappij_ , a private company.
. _Koninklijk Nederlands-Indisch Leger_.
. The first tracks were laid between 1864 and 1867 by a Dutch, German and British consortium, but the choice of standard gauge proved to be uneconomical. The narrower metre gauge was therefore used for the remainder of the network. Narrow gauge (70cm or 2ft 4in) was also used in the sugar-cane plantations on Java.
. Present-day Ambarawa.
. The present-day Soerakarta–Jogjakarta line.
. _Staatsspoorwegen_.
. Present-day Jakarta.
. Present-day Bogor.
. It is not known whether the decision to fit armour plating originated with the KNIL or with the DSM.
. Described as ' _Révolusi_ ' by the nationalists and as ' _Politionele Acties_ ' (Police Actions) by the Dutch.
. The result of co-operation between the Army which supplied the Jeep and paid for the modifications, and the DSM Company which built the vehicle.
. The ' _pemudas'_ or 'youths'.
. _Verenigd Spoorwegbedrijf_ (VS).
. Literal translation 'attack wagon' . These armoured vehicles were also known by the designation 'BRAAT', from the N.V. Machinenfabriek BRAAT, a company with workshops in Soerabaja (eastern Java). They resulted from a design by Engineer Captain Luyke Roskott and were based on a Chevrolet COE chassis. The KNIL used several different versions of the Overvalwagen.
## NEW ZEALAND
Already semi-autonomous since the end of the nineteenth century, New Zealand became an independent Dominion under the British Crown in 1907, and took part in both World Wars as part of the Commonwealth. During the Second World War, more than a quarter of the country's railway workers were in uniform, serving in the 16th and 17th Railway Operating Companies sent to the Middle East as part of the MEF (Middle East Forces). In 1941–2 the theatre received forty-two Stanier 8F steam engines. In October 1942 during the British offensive following the second battle of El Alamein, the first train to roll westwards was hauled by one of these engines, with armour protection against aerial attack. In addition, two anti-aircraft detachments were included in all trains, in wagons attached at the front and rear of the rake. They were armed either with rifle-calibre Browning machine guns, or 40mm Bofors or 20mm Breda cannon.
The armoured cab and front end of the tender. The following two tank wagons are being filled with additional water for the engine.
_(Photo: All Rights Reserved)_
Stanier 8F No 329 at El Alamein in November 1942, protected by concrete panels. The NZ Rly Op Coy (New Zealand Railway Company) were responsible for running this train and the railway system.
_(Photo: All Rights Reserved)_
Note the absence of armour protection over the top of the boiler unit, to avoid overheating problems.
_(Photos: All Rights Reserved)_
The 2-8-0 wheel arrangement is clearly seen in this side view.
_(Photo: All Rights Reserved)_
Ford trucks coupled back-to-back for patrol duties, with the central pillar mountings for machine guns.
_(Photo: All Rights Reserved)_
A wagon converted into an anti-aircraft battery in Egypt, showing one of its two quadruple .30 calibre Browning mountings. The machine guns probably came from US-built tanks. The Brownings have not yet been fitted to the mounting at the rear. There are no known photos showing wagons armed with either Bofors or Breda cannons.
_(Photo: All Rights Reserved)_
**SOURCES:**
Judd, Brendon, _The Desert Railway: The New Zealand Railway Group in North Africa and the Middle East during the Second World War_ (Auckland: Penguin Group New Zealand Limited, 2004).
. These units were disbanded in 1943.
## NICARAGUA
### ARMOURED TRAIN 1912
Under the terms of a treaty signed on 6 June 1911, the Nicaraguan railway network was run by an American company. In July 1912 a political rival of President Diaz stirred up a rebellion, and the latter asked for American help to suppress it. Some 3000 American troops, mostly Marines, were sent to Nicaragua to restore order. One of their missions involved reopening the Managua-Granada rail link passing next to Lake Nicaragua. A special train was therefore assembled in September 1912: eight flat wagons followed by the first engine, then eight vans, the second engine and four other wagons bringing up the rear. The crew included 400 Marines (basically there to help push the train on the gradients!). The vans were unarmoured, but the wagons were protected by sandbags. The train's armament comprised no less than sixteen machine guns, some mounted on the van roofs. The town of Granada was finally captured by the government forces, after a five-day journey to cover some 20km (13 miles) of railway line.
**SOURCES:**
Thomas, Lowell, _Old Gimlet Eye, The Adventures of Smedley D. Butler_ (New York: Farrar & Rinehart Inc, 1933).
Two poor-quality but nevertheless unique photos of the train in Nicaragua. This appears to show one end of the train, a bogie (?) wagon protected by a wall of sandbags. The machine gun is an American Vickers in .30/06 calibre, and centreleft is a US Marine (pointing towards the camera) wearing the traditional campaign hat. Given the preponderance of Nicaraguans it is probable this is the tail wagon. Interestingly the above photo is marked 'Rebel' armoured train.
_(Photos: above, David Spencer; below, Paul Malmassari Collection)_
## NORTH KOREA (DEMOCRATIC PEOPLE'S REPUBLIC OF KOREA)
From 1905 up to the end of the Second World War, Korea was under Japanese rule. After the Japanese surrender, the country was declared independent on 15 August 1945. However, the Korean peninsula to the North of the 38th Parallel was occupied by Soviet troops, and the remainder to the South by US troops. In the South, the Republic of Korea was declared on 17 July 1948, while the North self-proclaimed the establishment of the Democratic People's Republic on 9 September of the same year, under the direction of Kim Il-sung who had led the anti-Japanese resistance.
Because of the railway connections between Korea and Manchukuo, the Type 94 Japanese armoured train had been captured intact in the Soviet Zone, and in fact in December 1945 it was photographed by an Official US Army Photographer. During the Korean War, in the South, Japanese armoured wagons were put back into service to protect train convoys – see the relevant chapter on South Korea (1950–1953). The role of interdicting North Korean supply trains running along the east coast of the peninsula was carried out principally by the UN naval forces (among which the Canadian destroyer HMCS _Crusader_ marked up the highest train-busting score), with the support of aircraft from TF 77. On at least one occasion, a North Korean armoured train was reportedly engaged and destroyed.
In the original 1989 edition of this encyclopaedia, various sources were quoted as having indicated the existence of eight North Korean armoured trains, information which to date has remained unverified. Numerous reports by foreign tourists visiting North Korea mention seeing goods wagons on which soldiers manned anti-aircraft machine guns against possible air attack, unsurprising in view of the fact that the North and the South are still officially at war, since at the time of writing no peace treaty has ever been signed between the two states. Finally, the armoured train of the 'Dear Leader' Kim Jong-il was widely described in the media on the occasion of his visit to Moscow in August 2011.
**SOURCES:**
Directory of History and Heritage, Ministry of National Defence, _Le Canada et la guerre de Corée_ (Montreal: Art Global, 2002).
The Japanese Type 94 train photographed in the Soviet Zone in North Korea.
_(Photo: Don O'Brien)_
. Retired US Army Photographer Mr Don O'Brien at website <https://www.flickr.com/photos/dok1/3894782980>
. As a priority those coming down from the North, as they were carrying front-line supplies furnished by the Soviet Union.
. The UN Navies set up the 'Trainbusters Club', which by the end of the War had claimed twentyeight trains destroyed.
. Among other sources: <https://www.lebuzzcontinue.wordpress.com/2011/12/19/kim-jong-il-aquoi-ressemble-un-train-blinde-encoree-du-nord/>
## NORWAY
### ARMED TRAINS
This 75mm L/30 Schneider fortress gun was captured by the Wehrmacht and put back into service against Norwegian troops on 16 April 1940. Note the side plate which is perhaps not armour protection but probably a firing platform for the gun crew. We can also see the remains of an armoured shield.
_(Photo: Paul Malmassari Collection)_
A British 12pdr 12 cwt (3in) QF gun of the type fitted on British warships, and probably salvaged from one of the eleven A/S trawlers sunk or driven ashore by Luftwaffe aircraft, has been mounted on a short bogie wagon. It is coupled to an NSB Type E1 4 electric locomotive. It appears that both the gun and its locomotive have been sabotaged by their crews: the foreshortened barrel indicates it was first blocked and then a live round fired, and an explosive charge seems to have destroyed the centre section of the locomotive, followed by a fire.
_(Photo: Paul Malmassari Collection)_
It appears that the Norwegians never built classic armoured trains. On the other hand, from the time of the Great War, artillery pieces mounted on railway wagons and with minimal armour protection provided mobile defence on the Kiruna-Narvik (Ofotbanen) Line. In 1940, two such guns are recorded: a 75mm fortress gun and a British 3in.
**SOURCES:**
Website
http://forum.axishistory.com/viewtopic.php?t=114126&start=165 (also dealing with heavy railway guns)
. The Norwegians had also mounted a German 3.7cm S.K. C/30 AA gun salvaged from one of the sunken destroyers in Narvik fjord on a rail wagon.
. Built between 1925 and 1928, max. speed 60km/h (38mph), Type 1C+C1, overall length: 19.58m (64ft 3in).
## OTTOMAN EMPIRE
When Turkey allied with Germany during the First World War, the greatest threat to railway transport came from the Great Arab Revolt of 1916–18. The writings of Lawrence of Arabia detail attacks on Ottoman trains, but do not specifically mention armoured trains. However, it is certain that armoured trains were used by the Turks, despite the fact that apart from the possible exception of the armoured wagon preserved in Syria, no photos have come to light.
In late 1917, French forces identified three armoured trains at Medina, Boueir and Heddja. In addition, in almost all the stations, an armoured wagon (protected by iron plates or sandbags) was coupled to an engine with steam up, ready to intervene at any trouble spot.
In the same period armoured trolleys intended for the Middle East were built in Germany, although some were never delivered. At least two of these machines were captured by the Allies, one of which was in use hauling a train. The armoured bodies of two machines were converted by the French into armoured caissons mounted on flat wagons (see the chapter on France).
**SOURCES:**
**Archives:**
SHD: 4 H 27, Fonds Clémenceau, 6 N 191.
**Books:**
Strasheim, Rainer, _Panzer-Kraftwagen, Armoured Cars of the German Army and Freikorps_ , Tankograd-World War One No 1007 (Erlangen: Verlag Jochen Vollert, 2013), p 73.
_Das Ehrenbuch des Deutschen Pioniers_ (Berlin: Verlag Tradition Wilhelm Kolf, 1931).
Armoured wagon on display in the Al Qadam Museum in Damascus. The origins of the wagon and the reason why it was constructed are unknown.
_(Photo: All Rights Reserved)_
Ottoman armoured trolley, left-hand side, with its crew. Some photos show a German crew from the _Asien-Korps_ commanded by Colonel von Oppen.
_(Photo: Paul Malmassari Collection)_
Three views of armoured trolleys, the lower one showing one of these machines coupled as a train locomotive. This was perhaps the type of rake known as an 'armoured train' in contemporary reports.
_(Photos: Australian War Memorial)_
Right-hand front quarter of the armoured trolley, seen here between Rayack and Damascus.
_(Photo:_ Das Ehrenbuch des Deutschen Pioniers _)_
This example has been converted to a road vehicle (probably the only one of its type!) and used by the police in Weissefels near Leipzig, as well as in Zella-Mehlis near Suhl in 1919. It is likely that the rear of the armoured body has been reversed and has become the front end of this road version.
_(Photo: Jochen Vollert)_
. The Ottoman Empire was abolished on 1 November 1922.
. For example a coded message dated 10 November 1917 indicated a Turkish armoured train in combat on 12 and 13 October 1917 on the line from Antar to Boueit (Hedjaz). (SHD: 6 N 191)
. SHD: 4 H 27.
. Zone of activity of the _Freikorps_ of General Märkers, which later became the 16th Brigade of the _Reichswehr_.
## PARAGUAY
### THE ARMOURED TRAIN OF 1869, WAR OF THE TRIPLE ALLIANCE
This short-lived armoured train is believed to be the very first of its kind built in South America. Following territorial disputes, on 1 May 1865 war broke out between Paraguay, ruled by the dictator Francisco Solano Lopez, and the three countries of the Triple Alliance, Argentina, Brazil and Uruguay. The war began with a series of naval operations which resulted in the almost total destruction of the Paraguayan fleet on 22 March 1868, allowing the allies to take the Paraguayan forces in the rear and advance on the capital, which fell on 1 January 1869.
In the months which followed, the Paraguayans put together an improvised armoured train which went into action on 30 April 1869. It comprised two armoured wagons, each mounting a 3in gun, and in between the wagons an engine with an armoured cab, which had already seen distinguished military service: the _Piccadilly Pride_ , a large single-driver constructed in 1854 in Crewe, had seen service (unarmoured) as Engine No 11 on the Grand Crimean Central Railway, built during the Crimean War to haul supplies from Balaclava. The armoured train counted among its crew another veteran of the Crimea, Major Hadley Baines Tuttle, who was to command the sortie.
The armoured train left the station of Cerro Léon and advanced into the Valley of the Pirayu in the direction of the Brazilian advanced post at Aregua. After the sentries had been overcome, it crossed the bridge of the same name and opened fire on the camp, killing and wounding around a hundred men. But after 20 minutes' combat, the Brazilians rallied, and three men in the wagon at the head of the train were killed. Running in reverse, the armoured train retreated, and the crew blew the bridge to prevent the Brazilians from following. Unknown to them, however, more than 250 cavalrymen of the Rio Grande do Sul Regiment had crossed the river and set up an ambush for the train alongside the track. Galloping on either side they hotly engaged the thirty unwounded survivors of the train's crew with carbine and revolver fire, but as the engine gained speed and their mounts tired they were gradually left behind. Unfortunately for the daring Paraguayans, a small group of cavalrymen had ridden on ahead, and had blocked the rails with a pile of logs. Unable to stop in time, the speeding train ran into the obstacle and derailed. _Piccadilly Pride_ fell on her side, and her boiler, starved of water, exploded, killing two Brazilian ambushers as well as Major Tuttle.
**SOURCES:**
Capdevila, Luc, _Une guerre totale, Paraguay, 1864-1870. Essai d'histoire du temps présent_ (Rennes University Press, 2007), p 514.
Meister, Jürg, _Francisco Solano Lopez_ (Osnabrück : Biblio Verlag, 1987). 458 pages.
Uys, Errol Lincoln, _BRAZIL Book Five_ , _Sons of the Empire_ (Silver Spring, MD: Silver Spring Books, 2000).
## PERU
### ARMOURED TRAIN
From 1879 to 1883 Chile fought the War of the Pacific against Peru and Bolivia. The _casus belli_ was the imposition by Bolivia of taxes on the transport of saltpetre extracted by two Chilean companies. Peru relied heavily on its railway network, and when the Chileans advanced on Lima, the militia and civilians defending the capital built an armoured train equipped with machine guns as well as the rifles of the troops on board. On 15 January 1881 the heavily-armed armoured train, carrying fresh troops, left Lima and set off for Miraflores, which was in Chilean hands. The Chileans attacked the train and forced it to retreat. When they entered Lima on 17 January, they discovered an additional five armoured wagons which had apparently never been put into service.
**SOURCES:**
Arana, Diego Barros, _History of the War of the Pacific_ (Paris, J Dumaine: Vol I, 1881; Vol II, 1882).
## POLAND
### ARMOURED TRAINS AND TROLLEYS 1918-1950
Poland was reborn as an independent nation on 11 November 1918. Positioned in Central Europe, the country found itself hemmed in between Germany (including East Prussia) and Russia, and depending on the period, by its other neighbours Czechoslovakia, Hungary, Romania, the Ukraine, Belarus and Lithuania.
The Polish railway network reflected the various occupations of the country: the rail gauge in the region of Poznań (formerly Prussian Posen) and Galicia (formerly Austrian) was the standard 1435mm (4ft 8½in) whereas in Congress Poland (formerly Russian) it was the 1520mm (4ft 11¾in) broad gauge. Rail connections across Polish territory included five major junctions with the ex-German network but only two with the ex-Austrian lines. In 1915, the occupation of virtually all of what would become the new Poland by German troops led to the standardisation of the whole network on the European gauge, apart from the Ukrainian network which, after the Treaty of Brest-Litovsk, remained on the Russian broad gauge. The rolling stock accordingly originated from all the occupying or occupied countries: primarily German wagons in the region of Poznań and Prussia, plus Austrian, Hungarian, Russian and even Belgian rolling stock (the latter brought in from the Militär-Eisenbahn Direktion Brüssel). Even if the new Polish rail network offered few strategic advantages (compared to the German network which had been planned with mobilisation in mind), it remained the only sure means of transport in the absence of a good road system.
The employment of armoured trains, a weapon which was easily movable from one front to the other, was a reflection of the complicated and sometimes tragic story of this new country. They were therefore present from the very conception of the Polish Army of the Second Republic. In fact, the young Polish Army had to fight four wars almost simultaneously: the Polish-Ukrainian War of 1918–19, the Russo-Polish War from February 1919 to March 1921, the Silesian Uprisings from 15 August 1919 to 21 July 1921, and the Polish-Lithuanian War of August to 7 October 1920.
Then the Polish armoured trains settled down into the relative calm of the inter-war period, up until the German attack which started the Second World War. They were involved in the brief Polish campaign from 1 to 27 September 1939, then Poles in exile manned armoured trains in Britain between 12 October 1940 and November 1943. Finally they operated during the post-1945 internal security operations which were conducted by the Army and the Railway Guards up until the 1950s.
### Armoured trains of ex-Russian Army Polish units
Even before the declaration of independence, Polish troops (who were not yet officially designated as the Polish Army) were engaged in frontier conflicts with their neighbours. On those fronts where good roads were the exception, the railway was the only means of moving armies, and the only mobile weapons of any power during that period were the armoured trains. The very first armoured train, _Związek Broni-Szeroki_ ('United Arms') operated as part of Polish I Corps. Its protection was provided by sandbags and trench shields on a flat wagon, and its weapons comprised a 76.2mm Model 1902 field gun, plus several 7.62mm Maxim machine guns including two in the twin turrets of a broken-down Austin (1st Series) armoured car.
During the Russian Civil War, five Polish divisions designated 'Siberian' fought alongside the Czech Legion on the Trans-Siberian Railway where they operated three armoured trains, named _Warszawa_ ('Warsaw'), _Kraków_ (Craków) and _Poznań_. When the last of these was lost, they captured an armoured train from Kolchak's forces and renamed it _Poznań II_.
### The Polish Army of the Second Republic (November 1918 – September 1939)
In Poland proper, the new government set up an organisation tasked with creating and operating the growing fleet of armoured trains. In 1918, two Austro-Hungarian armoured trains, No III and No VIII (for their artillery wagons, see the chapter on Austria-Hungary), were in Polish hands. These formed the most modern units in service at the time, along with several former Russian wagons captured from the White forces. German armoured wagons (e.g. PZ 22) had also been abandoned in the Poznań region and in Prussia. A number of Russian, Ukrainian and Lithuanian wagons were also reused, plus civilian goods wagons and flat wagons seized by the Germans in Hungary, France and Belgium.
Armoured Train _Zwi_ ą _tek Broni-Szeroki_ , which had a brief existence between 10 February and 10 May 1918, when it was captured by German troops.
_(Photo: All Rights Reserved)_
The first national armoured trains were built in Lwów, then in Tarnow, Nowy Sacz, Warsaw, Poznań, Wilno and Slask. As the Poles lacked sufficient armour plate for entire trains, and which when it was available was used for the engines, the protection for the wagons initially consisted of concrete and sandbags, enclosing machine guns and field guns.
Between 1918 and 1920, the command of the armoured trains was in the hands of General Gawronski, Inspector of Army Railways, based in Warsaw. The Inspection Department then allocated them to the different military railway units: regiments, battalions, bridge guard detachments etc. Several trains were also made available to the Army High Command. In the course of the four wars which Poland fought, the armoured trains would pass from one Front to the other, would be broken up and distributed between other trains, or might be destroyed and ultimately pass on their name to a new train.
Before we begin to describe many of these trains, we need to detail the various conflicts which were all interlinked as part of the overall Russo-Polish struggle.
### The Polish-Ukrainian and Russo-Polish Wars
The Polish-Ukrainian War (November 1918 – July 1919) was fought between Poland and the Popular Republic of Western Ukraine who each claimed Galicia. Captured Ukrainian armoured trains were incorporated in the Polish Army.
The Russo-Polish War (February 1919 – March 1921) saw the young Polish Republic facing a Russia in the middle of civil war. Lenin in particular aimed at unleashing a worldwide revolution, and envisaged enrolling Germany by passing through Poland, which he regarded as 'White'. The first Russian offensive was halted and the victorious Poles advanced eastwards until May 1920. The Russians counter-attacked, and by July 1920 were close to capturing Warsaw. But the battle of Warsaw (13–25 August) was won by the Poles, thanks in part to supplies and aid provided by the Allied military missions. The Bolshevik retreat ended with the armistice of 12 October 1920. It is estimated that seventy armoured trains were employed by the Poles, plus some thirty others captured from the Bolsheviks. In the course of the war, the Polish Army had lost at least eight armoured trains. The decision was therefore taken to build fifteen new armoured trains at the Cegielski factory in Poznań, where on 1 August 1920 the KBPP, the military organisation responsible for armoured trains, was established, directed by Captain Stanisław Czerepiński. Many captured Russian armoured trains were recovered and parts of them or even entire trains were put into Polish service.
The first version of PP 1 _Piłsudczyk_ formed from elements of the Austro-Hungarian armoured trains of the 3rd Detachment captured in Craków on 1 November 1918. The artillery wagon remained in service with this train up until 1939.
_(Photo: Centralne Archiwum Wojskowe – CAW)_
PP 2 _miały_ was created after PP 1 was divided up into two separate parts on 26 October 1918. Note the Polish flag of the period and the wagon with turret at the rear of the train, probably inspired by a Russian vehicle.
_(Photo: CAW)_
Close-up of the artillery wagon of _miały_ (note the number '2' on the wagon side), lacking its gun which was probably being repaired. This train was demobilised in 1923 or 1924.
_(Photo: CAW)_
Following rebuilding, the new PP 1 _Piłsudczyk_ was powered by a Class 73 engine, and was armed with a Soviet 122mm howitzer. The artillery wagon was built in Lwów on the base of a German wagon in the Summer of 1920.
_(Photo: CAW)_
A fine profile view of the howitzer wagon of PP 1 _Piłsudczyk_ (built on the base of a German Type Ommku coal wagon at Lwów in September 1920).
_(Photo: CAW)_
Under the armour is an ex-Austrian engine: the kkStB Class 73 carried 15mm armour, fitted in the workshops of Nowy Sacz. They hauled PP 1 _Piłsudczyk_ (No 73.348) from August 1920 to 1921, in 1921 PP 18 _Huragan_ (No 73.419, completely armoured), PP 25 _Stefan Czarniecki_ in 1920, PP 7 _Smok_ ('Dragon'), PP 6 _Generał Iwaszkiewicz_ and PP 27 _Ochotnik_ ('Volunteer', hauled by No 73.235 armoured at Lwów).
_(Photo: CAW)_
The third armoured train originally numbered PP 3, then from late April 1919 named PP 3 _Lis-Kula_ , was built at Craków. The train was named in honour of Commandant (Major) Leopold Lis-Kula, a war hero who died of his wounds on 7 March 1919 at the age of twenty-two.
_(Photo: Artur Przeczek Collection)_
One of the artillery wagons of PP 3 at Lwów in May 1919. Note that the 76.2mm field gun is carried complete with its wheeled carriage.
_(Photo: CAW)_
After the wars had ended, the crews of several armoured trains arranged for commemorative badges to be struck. Here is the one for PP 3 which needs some explanation: 'Pe Pe Trójka' means 'Armoured Train No 3'.
_(Photo: Paul Malmassari Collection)_
The leading artillery wagon of PP 3, armed with an Austrian 8cm M 05/08 gun. The cylindrical turrets were inspired by Soviet models.
_(Photo: CAW)_
PP 3 camouflaged, seen during the 1920s.
_(Photo: Krysztof Margasiński)_
This Austro-Hungarian engine No 180.533 was the sole example of this class armoured by the Poles at Nowy Sacz in April 1919. It was then attached to PP 3 _Lis-Kula_.
_(Photo: CAW)_
The artillery wagon of PP 5 _Odsiecz I_. The layout of the main armament firing to the side indicates a defensive role, compared with the gun mounted in the chase wagon capable of firing along the track with the train advancing or withdrawing.
_(Photo: CAW)_
PP 8 _Rozwadowczyk_ (later renamed PP 8 _Wilk_ ) at Nowy Sacz in February 1919, which served during the Polish-Ukrainian and Russo-Polish wars. It was powered by a Class 229 engine, and its wagons were armoured internally with cement.
_(Photo: CAW)_
PP 9 _Danuta_ , built in Craków in January 1919. It took part in the defence of Warsaw against the Russians. It is headed by a Class 229 engine, followed by an ex-German armoured wagon (probably from PZ 22) and an armoured van.
_(Photo: CAW)_
Overall view of PP 10 _Pionier_ ('Engineer'), which was built in Lwów in February 1919. It served during the Polish-Ukrainian War and the Russo-Polish War. Note the virtual symmetry on either side of the engine, apart from one additional wagon.
_(Photo: CAW)_
The engine of PP 11 _Poznańczyk_ , originally a German Class G-52 with one of the first types of armour protection.
_(Photo: CAW)_
PP 10 _Pionier_ , seen here in May 1919, had two artillery wagons (8cm Austrian guns) built on the base of German mineral wagons.
_(Photo: CAW)_
Built in Warsaw in late 1919, PP 11 _Poznańczyk_ had a front turret armed with an Austro-Hungarian 8cm _Feldkanone_ M05. Note the armour covering the axle boxes.
_(Photo: CAW)_
One of the wagons of PP 13 _Zawiska Czarny_ armoured at Lwów in August 1920. The main weakness of these covered vans was the presence of ventilation slats, here seen covered by armour plates. The echeloned arrangement of the two sets of firing ports for riflemen was typical of Polish wagons.
_(Photo: CAW)_
Ex-Austro-Hungarian engine MÁV 377.402 originally with PP 1 _Piłsudczyk_ , later attached to PP 5 _Odsiecz I_ , seen here following Polish modifications such as the increased coal capacity. A second train was built under the name of _Odsiecz II_.
_(Photo: CAW)_
Class G3 engine of PP 14 _Zagończyk_ which was damaged in the Autumn of 1920. Simple armour protection of this type allowed the production of a large number of armoured trains.
_(Photo: CAW)_
PP 15 _Paderewski_ , built at Lwów in September 1919. It went into action on the Lithuanian frontier then took part in the battle of Warsaw against the Reds. It joined in the offensive against Wilno (Vilnius) in 1920 under the false name _General Żeligowski_.
_(Photo: CAW)_
One of the two Class 178 engines (this one is perhaps No 178.111) allocated to PP 15 _Paderewski_.
_(Photo: CAW)_
General view of PP 18 _Odsiecz II_ , with the artillery wagon leading.
_(Photo: CAW)_
One of the six Class 178 engines armoured at Lwów. Here is No 178.95 allocated to PP 15 _Paderewski_ , built in September 1919.
_(Photo: CAW)_
Artillery wagon of PP 15 _Paderewski_ , probably armed with an Austrian 8cm gun, protected by steel plates and with a horizontal field of fire of some 270 degrees.
_(Photo: CAW)_
This 0-6-0 tank engine of PP 17 _Saper_ was a kkStB Class 97. The train was built at Craków in March 1919. Here it is seen after having suffered collision damage in April 1919. It was repaired and put back into service. Note the smoke deflector (deactivated here, with the upper trap open) worked from inside the cab.
_(Photo: CAW)_
Engine 73.419 of PP 18 _Huragan_ which was built in August 1920 at Nowy Sacz.
_(Photo: CAW)_
Armoured van of PP 18 _Huragan_ , with its imposing roof casemate carrying an Austrian searchlight.
_(Photo: CAW)_
PP 19 _miały-Szeroki_ was built in April–May 1919 using Russian units captured at Lida (in modern Lithuania). Although its shape is disguised, the engine was a Class Ov. This train went into action on 28 September 1919 at Dyneburg, then it was broken up and distributed among other trains at the end of April 1920.
_(Photo: CAW)_
PP 20 _General Dowbor-Mu nicki-Szeroki_ was powered by a captured Russian Class Ov steam engine, of the type as used on the _Hunhuz_ type of armoured trains. _Dowbor_ was the former Ukrainian train _Sichovyi_ , captured on 24 May 1919.
_(Photo: CAW)_
The artillery wagon of PP 20 _General Dowbor_ was used unaltered from its Ukrainian configuration. The train was damaged in a fierce action against the Bolsheviks and was then captured on 23 June 1920.
_(Photo: CAW)_
Of quite modern appearance, PP 20 _Bartosz Głowacki_ was built in August 1920 at Craków. It had two artillery wagons armed with Russian 76.2mm guns, while the other wagons were covered vans of German origin, armoured internally with cement and sand. The two artillery wagons would later form the instruction school armoured train.
_(Photo: Wawrzyniec Markowski Collection)_
One of the artillery wagons of _Groźny-Szeroki_ in 1920 from the captured Bolshevik armoured train BP 56 _Kommunar_ and still armed with its Russian 76.2mm guns. After 1926 they were replaced with French 75mm.
_(Photo: All Rights Reserved)_
PP 23 _Sikorski-Szeroki_ was composed of high-sided bogie wagons from a Russian armoured train captured in March 1920. It was equipped with a 76.2mm field gun in the chase position, and a second 76.2mm in a fully-revolving turret. It was destroyed on 25 June 1920.
_(Photo: Artur Przeczek Collection)_
An impressive artillery wagon of PP 24 _Śmigły-Szeroki_ , the ex-Russian BP N 45, captured in August 1919. Note the trench shields reinforcing the turret armour. This train was dismantled in June 1921.
_(Photo: CAW)_
Not included in the classification of armoured trains, but fulfilling a similar role, the Craków Railway Batteries ( _Krakowska Bateria Kolejowa_ ) were armed with Austrian 8cm casemate guns.
_(Photo: All Rights Reserved)_
Photographed at Nowy Sacz in September 1920, the central wagon of PP 25 _Stefan Czarniecki_ , similar to that of PP 18 _Huragan_ , with an identical casemate but without lookout shutters (probably used on _Huragan_ to sight the searchlight when closed down).
_(Photo: CAW)_
The general layout of PP 25 _Stefan Czarniecki_ (seen here at Nowy Sacz) was quite modern, armoured vans alternating with turreted wagons, heavily influenced by captured and partially reused Russian vehicles.
_(Photo: CAW)_
On this artillery wagon of PP 25 _Stefan Czarniecki_ , note the casemates for machine guns. On these three photos, what might be mistaken for scratches on the negative at the bottom panels of the wagons are in fact foliage added for a ceremony.
_(Photo: CAW)_
### The Polish-Lithuanian War (1920)
The short Polish-Lithuanian War (August – 7 October 1920) was fought to decide who would have possession of Vilnius. The dispute had been building up ever since April of that year: the Poles had captured Vilnius in April 1919, but the Lithuanians wanted to recover the city, which they considered their historical capital. When the Red Army invaded Poland the Lithuanians changed sides and supported the Russians. Between 2 and 27 September 1920 the Lithuanian Army launched its own offensive, but was defeated. A ceasefire was agreed on 7 October. Despite the wishes of the League of Nations, Vilnius remained a Polish city.
During this conflict the Poles captured the Lithuanian armoured train No 1 _Gediminas_ , which was immediately renamed _Major Mond_ before taking on its official designation of PP 27 _Jan Kili ski_.
_(Photo: Krysztof Margasi ski Collection)_
### Third Silesian Uprising (May 1921)
The three Silesian Uprisings (15 August 1919 – 21 July 1921) were instigated by the Polish minority community to obtain the attachment of the rich mineral area of Upper Silesia to Poland. The Treaty of Versailles made provision for the holding of a plebiscite to determine the division of Upper Silesia between Germany and Poland. On the German side, the _Freikorps_ (Free Corps) exerted pressure on the non-German population, while Poland promised to give full rights to the indigenous Polish inhabitants. The First Uprising began with a general strike by the Polish miners on 16 August. The 60,000 men of the _Reichswehr_ crushed the revolt, which came to an end ten days later.
The Second Uprising broke out a year later. The plebiscite held under Allied (British, French and Italian) supervision on 21 March 1920 gave a large majority to the pro-German party. In August 1920, false rumours of the fall of Warsaw inflamed feelings on both sides. The Poles took control of administrative buildings in several towns without the Allied forces intervening. Following tense negotiations and a readjustment of the balance between Poles and German in the administration, the revolt began to calm down after 25 August, but the underground organisation created by the Poles remained.
This organisation was instrumental in starting the Third Uprising which began with the rumour that Upper Silesia was to remain German. In fact the French favoured the Poles while the British and Italians were co-operating with the Germans. What was at stake was possession of the rich industrial region in the Bytom-Gliwice-Katowice triangle. Against this background, the Uprising began on 3 May with the destruction of rail connections to block German intervention, notably by the _Grenzschutz_ (Border Guard East). The revolt ended on 21 July with a ceasefire, following which the greater part of the disputed territory was given to Poland. In all these wars, the Poles made extensive use of armoured trains, and a selection of these is illustrated in the following section.
PP 14 _Zygmunt Powstaniec_ during the Third Insurrection, on operations with the French, who are recognisable by their large berets and stripes on their sleeves, on the right. The armour of the engine was probably reinforced with trench shields. The wagons are of German origin, and the second one is armed with a gun in an open-topped turret.
_(Photo: Paul Malmassari Collection)_
PP _Kabicz_ , built at Gliwice, was the only narrow gauge (7.85cm/2ft 7in) Polish armoured train. Here in May 1921 in Silesia, the train and crew are being blessed by a priest.
_(Photo: Mariusz Zimny Collection)_
Side view of _Kabicz_ , with its ex-Prussian Class T37 engine.
_(Photo: Mariusz Zimny Collection)_
### The Armoured Trains of the Polish Army in the Inter-War Period
Following the victory over Russia, the Polish trains were demobilised, except for sixteen units which remained in service. During the Winter of 1923/24 these units were grouped together into two regiments, each with four battalions of two trains. In addition in October 1927 two trains were dedicated to the training role with the 1st Training Division ( _1 Dywizjon Pociagów Pancernych_ ) stationed at Jabłonna. In 1928 the six oldest trains were scrapped, and two armoured train divisions were formed (north of Warsaw and in Craków), which were integrated into the Armoured Force in 1930. Each armoured train formed the base unit, complemented by an instructional train, a support train and a reconnaissance company equipped with armoured trolleys. A modernisation programme was launched in 1931, intended to improve the trains' manoeuvring capabilities by reducing the numbers of wagons, while retaining two artillery wagons. A system of retractable lateral nacelles was introduced, permitting the machine guns to fire to front or rear along the sides of the train, the older artillery pieces were replaced with modern ones, and lastly the wagons themselves were replaced with more modern rolling stock.
Three classes of train were established:
Type I (Light).
Type II (Heavy).
Type III (Train composed of automotive units).
The Light Armoured Trains were composed of an infantry wagon and two artillery wagons, which kept the Austro-Hungarian and Russian artillery pieces, plus machine guns (from eight to sixteen on semicylindrical casemate mountings), and two anti-aircraft machine guns.
Their artillery wagons were of three types, inspired by the Soviet trains, classed Types I, II and III. Type I corresponded to the design of the _Sosnkowski_ with two cylindrical turrets. Type II corresponded to the wagons of PP _Danuta_ and _Poznańczyk_. Lastly the Type III corresponded to _Śmiały_ and _Piłsudczyk_.
The Heavy Armoured Trains were more powerfully armed, with 100mm guns, and their machine guns were mounted in turrets. They had more powerful steam engines such as the Class Ti3 (ex-Prussian G53). After the First World War, Germany had delivered sixteen Prussian G53 engines as war reparations, of which six were diverted to the Polish Army. Beginning in 1920, two engines were armoured using Soviet engines as a reference, in the workshops of Warsaw-Praga, and these served as examples for the remainder, work on which began in 1926. The allocation of these engines was ordered on 20 November of that year, and the work was completed by 1932. In addition, two trains, _Zagończyk_ and _Stefan Czarniecki_ , were used for training before being broken up in 1928.
Their armament was standardised as:
– 100mm Skoda wz.1914/19, placed in the lowest turrets.
– 76mm Putilov wz.1902, replaced in 1926 by 75mm Model 1902/1926.
– 7.92mm water-cooled Maxim Mle 08.
For each armoured train plus its support train, the crew was fixed at eight officers, fifty-nine NCOs and 124 men.
The trains were numbered and named as follows:
PP 11 _Danuta_
PP 12 _Poznańczyk_
PP 13 _General Sosnkowski_
PP 14 _Paderewski_
PP 15 _Śmierć_
PP 51 _Pierwszy Marszałek_
PP 52 _Piłsudczyk_
PP 53 _Śmiały_
PP 54 _Groźny_
PP 55 _Bartosz Głowacki_
PP 53 _Śmiały_ dressed overall for Polish Army Day, on 15 August 1921. Its camouflage scheme would still be in use in the 1930s. Note the presence of a cowcatcher under the coupling hook. These wagons were armed with two types of Russian guns: a 122mm Model 1909 howitzer and a 76.2mm Model 1902 gun. In 1939 these pieces would be replaced by Polish 100mm and 75mm guns.
_(Photo: Adam Jo ca Collection)_
_Śmiały_ in 1934: note the modernisation of the artillery wagons with the installation of observation cupolas on the roofs. The wagon for the assault infantry has not yet received its lower armour protection.
_(Photo: Mariusz Zimny Collection)_
This and the other photos in a series of five show the methods of mounting the Maxim machine guns in the ex-Austro-Hungarian armoured wagons, including the retracting lateral nacelles, which stressed the importance of bringing fire to bear from all available weapons towards the front of the train, reminding us that an armoured train can be used as a means of surprise attack. The same types of mounting were standardised in all the trains.
_(Photos: Mariusz Zimny Collection)_
PP 13 _General Sosnkowski_ , seen here with an engine borrowed from another train. The Type I artillery wagons built in Pozna in 1920 on the bases of Russian wagons are armed with two 75mm wz.26/02 field guns (rebarrelled Russian 76.2mm Model 02). The safety flat wagons of the three trains in these photos are Type Pdkz VIIIC four-wheel flat wagons 13m (42ft 7¾in) long.
_(Photo: CAW)_
PP 15 _Śmierc_.
_(Photo: CAW)_
PP 14 _Paderewski_ in a superb three-tone camouflage scheme: light green/olive green/red brown (the darker patches).
_(Photo: CAW)_
### Light Armoured Train Project (Petrol-electric Armoured Railcar wz.28)
In 1928, armoured train studies turned towards automotive units (the Type III armoured train), comprising two vehicles and two safety flat wagons. The first vehicle was to be armed with a turretmounted 75mm, and the second with a 37mm gun. Pddkz Type VIIc chassis, with two axles powered by tramway motors, were used for the prototype. The complete train was to be finished in August 1929. During the trials, its performance was far from impressive, one of the vehicles derailed, and the project was abandoned. The unit was not in fact dismantled, and was still on the roster of the armoured trains division in 1937, but it did not see service in September 1939.
Note that there are two hatches on the right hand side compared to just one on the left, and that the lower armour plating protects the whole vehicle.
_(Photo: CAW)_
Note the driver's vision slit front right. On this and the following three-quarters rear view, one can clearly see the two small lateral turrets intended for 7.92mm machine guns, and provided with virtually a 180-degree field of fire.
_(Photo: Grzegorz Pomorski Collection)_
To the left of the entry door the auxiliary braking system can be seen.
_(Photo: Artur Przeckek)_
Petrol-electric Armoured Railcar wz.28
---
**Technical specifications:**
Overall length: | 10.924m (35ft 10in)
Width: | 3.150m (10ft 4in)
Wheelbase: | 6.50m (21ft 4in)
Overall height: | 3.850m (12ft 7½in)
Height from rail to vehicle roof: | 2.93m (9ft 7¼in)
Armour thickness: | 6–12mm
Weight: | Approx 25.9 tonnes
Crew: | 1 officer and 12 men
Armament: | 1 x APX 75mm Mle 97; 3 x 7.92mm wz.25 MG
Maximum speed: | 32km/h (20mph)
Endurance: | Fuel for approx 10 hours
The second element of the Light Armoured Train project, armed with a 37mm gun in a turret. This vehicle seems to be much shorter. Note that it is coupled to an armoured wagon, perhaps from PP 53 _Śmiały_. It also appear to be much lower than the 75mm vehicle, probably to allow the heavier weapon to have a 360degree field of fire.
_(Photo: Adam Jo ca Collection)_
### Diesel-powered Armoured Train Project (1934)
In 1934, an article appeared in the military press mentioning a Polish project for a train without a locomotive, on which each wagon bogie would be powered by a diesel engine. This train was to have weighed 1000 tonnes and be 150m (495ft) long; it would have reached a top speed of 130km/h (80mph). In order to save weight, only the crew compartments of the wagons would be armoured, the upper hull parts along with the roof being of duralumin, with the aim of allowing HE shells to pass completely through without setting off their fuzes. At each end there would be safety/protection flat wagons with machine-gun positions, and three or four armoured wagons: an infantry wagon (twelve men) with turrets and firing slits, an artillery wagon with two turrets, and a command wagon with an observation turret. If the commander of the group of armoured trains was present, a second command wagon could be inserted for him and his staff. It is not known whether this proposal formed part of project wz.28.
### Armoured Trolleys and Rail Reconnaissance Units
In the early 1920s, the French company Crochat delivered ten light trolleys to the inspection department of the Polish Military Railways, in order to urgently make up for the lack of armoured trolleys. But the weight of the experimental armour fitted to one of the trolleys proved too much for the underpowered motor, so the machines were used as transport by the Engineers. We have no idea of what these machines looked like.
### Tatra T-18 Armoured Trolleys
In November 1926 Poland acquired six Tatra armoured trolleys from Czechoslavakia, and they were allocated to the armoured trains School Battalion at Jablonna. Despite trials which revealed that these machines were underpowered, nine additional trolley chassis were ordered, their armoured hulls being built and mounted by the firm CWS. It was planned to replace the original turrets with those from the wz.28 armoured car, armed with a 37mm Puteaux SA-18 gun and two 7.92mm wz.25 machine guns, one to be used in an anti-aircraft role. The conversion, however, was never carried out.
One of the Polish Tatra T-18 trolleys, unmistakable due to the heraldic eagle attached to the turret. Note the four enormous 'headlamps' which in fact are white and red lanterns to signal the presence of the vehicle, protected by armoured glass 65mm thick.
_(Photo: Adam Jońca Collection)_
The 7.92mm Hotchkiss wz.25 machine gun in its two possible positions in the turret: above, arranged for anti-aircraft fire; below, for direct fire.
_(2 Photos: Adam Jo ca Collection)_
In a rare photo, a Tatra trolley wearing a typical Polish camouflage scheme is seen coupled to a Type 'R' trolley, on which the FT tank turret has rounded-off corners. This may mean it is a Polish-built CWS 'iron tank' or perhaps even a rebuilt Renault TSF wireless tank. This could be a view of one of the platoons of PP 13.
_(Photo: Paul Malmassari Collection)_
Several Polish T-18s carried names, as here, _Žuk_ ('Scarab Beetle').The jack handle visible on the left operated the lifting system for moving the trolley from one track to another.
_(Photo: Janusz Magnuski Collection Via Mariusz Zimny)_
The equipment which allowed the Tatra trolley to move between parallel tracks. The turntable (item 40) and the rails (41) were carried on the sides of the hull, while the crank handle extension worked the jack.
_(Photo: Adam Jo ca Collection)_
A platoon of two Tatra trolleys was allocated to each of the armoured trains in the 1930s, but by 1939 these were only used with trains PP 13 and PP 15.
Tatra T-18 Armoured Trolley
---
**Technical specifications (from Polish records):**
Overall length: | 3.55m (11ft 73.4in)
Width: | 1.75m (5ft 9in)
Overall height: | 2.14m (7ft 01.4in)
Armour thickness: | 8mm sides; 5mm roof and floor
Weight empty: | 3.45 tonnes
Crew: | 3
Armament: | 2 x 7.92mm MGs, either Maxim wz.08 (water-cooled) or
Hotchkiss wz.25 (air-cooled)
Motor: | Tatra T-12, air-cooled
Maximum speed: | 45km/h (28mph)
Range: | 700km (435 miles
In view of the poor performance of the Tatra trolleys, a roadrail machine based on the Vickers 6-ton tank was studied. It would have been armoured to 12mm on a weight of 7.5 tonnes, and its turret-mounted armament, comprising a 37mm Puteaux SA-18, would have provided reasonable firepower. Estimated speed on the road was 36km/h (22mph) and on rails 65km/h (40mph).
This illustration of the Vickers-based road-rail tank shows the turret armed with a 7.92mm wz.25 anti-aircraft machine gun. The changeover from rail to road was effected by lowering the tracked suspension, not by raising the rail wheels.
_(Illustration: Tatra, via Marius Zimny)_
### Types 'R', 'TK' and 'TKS' Trolleys
At the same time, the innovative concept of tanks or tankettes with mixed road-rail propulsion was gaining in popularity. For example, as early as 1926 there were reports of various projects in Germany and France. This type of machine was the subject of patents taken out in 1933 by Colonel Tadeus Kossakowski, inventor of the system shown in the following patent drawing. The prototypes of two rail chassis for the Renault tank and for the TK/TKS tankettes were ordered at the same time.
Drawing showing the operating principles of the armoured platform Type 'R', which led to the prototype. The production model arrangements would differ considerably.
_(US Patent 2,014,769)_
Outline drawing of the production model.
_(Janusz Magnuski Collection via Mariusz Zimny)_
The first prototype, _drezyna pancerna torowo – terenowa_ , was built in 1932. It was not entirely satisfactory (even if it did move the lumbering Renault FT at 38km/h [23½mph]), principally because the platform was propelled by the revolving tracks of the tank turning rollers, transmitting the drive to the rail wheels through a system of chains and sprockets. This was a complex system, and had the disadvantage of wearing out the tank's tracks just as happened on the road. On the second prototype of 1933, the drive was transmitted from a connection on the gearbox via a hatch in the tank's floor (as shown on the original patent drawing), and speed rose to 45km/h (28mph) in either direction. After trials, the machine was accepted in 1938. More than thirty chassis were built in the Zieleniewski factory in Sanok and by Lilpop-Rau-Loewenstein in Warsaw. Two of these machines were allocated to each armoured train. Apart from the speed advantage compared with the previous Tatra trolleys (the platforms of the last batch reached 55km/h [34mph]), the idea was to be able to employ a railway reconnaisssance vehicle also capable of leaving the track to support assault troops disembarked from the trains. The unloading operation, as for that of loading, took less than three minutes.
The prototype of the Type 'R' trolley. Here the tank is a Renault FT CWS with small-link tracks. The chain final drive is clearly visible.
_(Photo: Artur Przeczek Collection)_
This arrangement of outside supports was seen only on the prototype. Note that the machine has a driving axle at the front and two carrying axles at the rear.
_(Photo: Artur Przeczek Collection)_
A Type 'R' trolley close to the definitive series production, with a Renault FT CWS tank. Note the reduced diameter of the wheels on the front axle.
_(Photo: Janusz Magnuski Collection via Mariusz Zimny)_
Type 'R' Trolley
---
**Technical specifications:**
Length: | 8.11m (26ft 7¼in)
Width: | 2.04m (6ft 8¼in)
Height with tank: | 2.83m (9ft 3½in)
Weight empty: | 3.4 tonnes
Weight with tank: | 10.5 tonnes
Crew: | 2
Armament: | 37mm L/21 Puteaux SA-18
Armour (FT tank only): | 16mm (hull vertical plates), 8mm (top deck), 22mm (cast turret), 16mm (rivetted turret)
Maximum speed: | 55km/h (34mph) in either direction
Rear view of the same machine, a much simpler arrangement than the prototype and at the same time more robust.
_(Photo: Janusz Magnuski Collection via Mariusz Zimny)_
Platoon of Type 'R' and 'TKS' trolleys allocated to PP 54 in Biadoliny Station. The conversions of the Renault tanks were carried out in the Lilpop-Rau-Lowenstein factory. This and the following view show to good effect the front of the platform, painted in the three-tone camouflage.
_(Photo: Paul Malmassari Collection)_
Close-up of the front suspension of the platform. It is just possible to make out the registration plate on the right, and there is an immobilising shoe on the track, suggesting that the platoon and PP 12 would be remaining stationary for some time.
_(Photo: Paul Malmassari Collection)_
The Wehrmacht captured virtually all the trolleys used in action by the Polish Army in 1939. However, they showed no interest in these machines and none were put back into service. Note on this FT from PP 12 the unusual form of the exhaust pipe where it leaves the silencer.
_(Photo: Paul Malmassari Collection)_
The two prototypes for the TK and TKS were completed in the Summer of 1932. The design was quite different to that for the Renault tank: instead of driving the rail wheels with the motor, the tracks remained in contact with the rails. The chassis built in this manner received the designation _prowadnica szynowa_ , which translates roughly as 'guide on rails for tracked vehicle'. A hydraulic system allowed the tankette to descend from its guide platform in just one minute. In parallel, a model was studied having the tankettes back-to-back. The testing was carried out over four years, with eleven pre-production models (Version III) built between 1934 and 1935. The definitive model (Version IV) was adopted in 1936 and thirty-eight chassis were ordered, as well as four models in tandem. One tankette in two was equipped with a short-range radio set, and all models were to have been modified to operate as trolleys, both independently and as part of an armoured train, with appropriate electrical and braking connections.
It is difficult now after so many years to know whether this pileup was the result of an accident or sabotage to prevent the two trolleys (Type 'R' with Type 'TK' upside down behind it) from falling into German hands intact. The latter explanation seems the more likely, as the gun on the FT is in the full recoil position, and the tank itself is positioned at the rear of its platform, whereas the shock of a collision would have been expected to push it further forward. The trolleys are perhaps from PP 54.
_(Photo: Paul Malmassari Collection)_
The three forms proposed for the guide platform for the TK tankette. The third solution was symmetrical to allow the tankette to dismount either forward or backward.
_(US Patent 1,933,811)_
Type 'TK' & 'TKS' Trolley
---
**Technical specifications:**
Length: | 6.30m (20ft 8in)
Width: | 2.15m (7ft 0½in)
Wheelbase (rail wheels): | 3.855m (12ft 7¾in)
Height with tankette: | 1.33m (4ft 4¼in)
Weight with tankette: | 4.15 tonnes (the tankettes weighed 2.6 tonnes)
Crew: | 2
Armament: | 1 x 7.92mm wz.25 machine gun in front casemate and 1 spare 7.92mm wz.28 Browning machine gun
Armour (TK/TKS only): | 8ߛ10mm (hull vertical plates), 6mm (top deck)
Maximum speed: | 46km/h (28.5mph). To travel in both directions, two TK or TKS trolleys would be coupled back-to-back.
A regulation platoon of armoured trolleys was made up of two half-platoons: each one with one 'R' Type trolley and one 'TK' or 'TKS' trolley. A fifth vehicle, a TK/TKS tankette, was held in reserve on the support train. In reality the Poles often made up combinations of 'TK-TK' without the Renault tank. Apart from the advantage of being able to travel in both directions, the tankettes would be carried with their tracks raised above rail level and could thus be disembarked very rapidly.
A 'TK' Type trolley.
_(Photo: Adam Jońca Collection)_
A 'TKS' Type trolley. There were three different versions of the TK-3 and TKS.
_(Photo: Adam Jońca Collection)_
In this photo of a captured trolley, note the extension which runs the length of the suspension beam, a sure way of identifying a TK belonging to an armoured train.
_(Photo: All Rights Reserved)_
The above and following photos show the prototype platform designed for the 7TP. Here, the trials are being conducted using a 6-tonne 7TP dw (a Polish development of the British Vickers Mark E). This model was armed with a 7.92mm Model 30 (Ckm wz.30) machine gun in each turret.
_(Photos: CAW)_
Note beneath the chassis the connection between the motor of the tank and the final drive to the rear axle.
### Trolley with 7TP Tank
This arrangement, similar to the platform for the C7P gun tractor was meant to supplant the Tatra T-18 and the TK-R-TK units. With its Bofors 37mm wz.37 gun this machine would have greatly increased the reconnaissance and raiding capabilities of the armoured trains. However, in light of the lack of 7TP tanks in the front line, the project was dropped.
As a final note, since 1935 the Model 34 half-track trucks used by engineer and supply units could be fitted with a set of rail rollers. They do not, however, belong in the story of the armoured train.
A fine rear view of the trial tank mounting on its platform. The lateral guides help correct small errors in the approach lineup, inevitable since the the manoeuvre could be carried out without any member of the crew having to leave the tank.
_(Photo: CAW)_
Shown here for comparison, the transporter platform for the C7P artillery tractor, which had the same tracked chassis as the 7TP tank. Note that this platform appears slightly longer than the one carrying the tank.
_(Photo: CAW)_
### Electric Armoured Trolley Project
This eight-wheeled trolley was to have been armed with a 37mm cannon in a turret. The diagram top right gives the only known information on this project.
Diesel-Electric Trolley Project
---
**Technical specifications:**
Length: | 7.92m (25ft 11¾in)
Width: | n/a
Height above rails: | 4.40m (14ft 5¼in)
Weight: | 32.5 tonnes
Main motors: | 2 x 110hp diesel (?) driving 2 x 300V 240 amp generators
Axle motors: | 4 x 550V 80 Amp
Crew: | 5
Armament: | 37mm Bofors wz.37 gun and 1 x 7.92mm wz.30 machine gun
Armour: | 10–20mm
Maximum speed: | 40km/h (25mph). The trolley was to have the capacity to haul armoured wagons of up to 110 tonnes.
Draft outline of the electric trolley.
_(Document: Adam Jo ca)_
### Unidentified Armoured Trolley
This machine, photographed in the early 1930s, was attached to the second armoured train unit. The turret is possibly one from a Samochód pancerny wz.28 half-track armoured car.
_(Photo: Adam Jo ca Collection)_
### Armoured Trains During the Polish Campaign
The ten armoured trains were mobilised between late August and the beginning of September 1939. Their numbering allocated during this period was a function of the division they were allocated to:
I _Dywizjon Pociągów Pancernych_ – Nos 11, 12, 13, 14, 15.
II _Dywizjon Pociągów Pancernych_ – Nos 51, 52, 53, 54, 55 (improvised armoured train used for training).
MDAL No 1, No 2 (Light Naval Artillery Armoured Rail Battery).
The improvised Armoured Rail Batteries for coastal defence were built in August and saw action in the Kartuzty region before being captured. The improvised training unit was assembled in September 1939 using rolling stock held in reserve. In action with German tanks at Jaroslaw, it was destroyed on 10 September. Another improvised train, _Smok Kaszubski_ ('Dragon of Kashub'), was built in the Gdynia port workshops in September, using steel plates intended for the destroyers _Orkan_ and _Uragan_ , which were still on the slips. It was allocated to coastal defence and took part in fighting for a week before being destroyed. Lastly in September two other improvised armoured trains were built to defend Warsaw, but surviving information is sparse. One of these trains was armed with four 75mm guns on two wagons.
_Smok Kaszubski_ parked in Kartuzy Station. It is possible there is a second armoured wagon armed also with a 75mm on the opposite side of the platform.
_(Photo: Mariusz Zimny Collection)_
The use of the names of the armoured trains was abandoned shortly before the start of the Second World War in favour of numbers. However, to assist the reader we will continue to quote the former name along with the train number.
The two armoured wagons which composed the instructional Light Armoured Train were nonetheless fully armed. They were captured together by the Germans, repaired and incorporated separately in two German armoured trains: the wagon in the foreground of the above photo, with armoured axleboxes, was used in PZ 21, while the fully-protected wagon in the photo below went to PZ 22.
_(2 Photos: Paul Malmassari Collection)_
These two wagons were the former artillery wagons of PP _Bartosz Głowacki_ dating from the Russo-Polish War, out of service until 1939. They had been built on the base of two Prussian Type Ommku mineral wagons.
Out of some ninety actions in which the armoured trains participated, each time they came up against tanks, the latter suffered heavy losses. Seven trains had to be sabotaged by their crews, only one was destroyed by Luftwaffe attack and two others in ground combat.
**PP 11** began the campaign in support of the 26th Infantry Division in the region of Chodziez-Szamocun and fought hard in support of the counter-offensive of 14–15 September towards the River Bzura. In the course of a bitter combat on 16 September near Jackowice, it was destroyed by the anti-tank guns of the 31st Infantry Regiment of the 24th Infantry Division.
PP 11 _Danuta_ during its last fight on 16 September. The engine has been hit by anti-tank rounds, and its crew killed, making further movement impossible.
_(Photo: Paul Malmassari Collection)_
The front section of PP 11 _Danuta_. Only this artillery wagon and the assault troop wagon seen on the right were salvageable, and they were incorporated in PZ 21. Note the handoperated trolley carried on the safety/protection flat wagon. The gun in the lower turret is a 100mm wz.14/19P howitzer.
_(Photo: Paul Malmassari Collection)_
Rear view of the artillery wagon of PP 11 _Danuta_ (identical to those of PP 12 _Poznańczyk_ ) prior to its inclusion in PZ 21. The upper turret is armed with a 75mm wz.02/26 gun (the Polish version of the 76.2mm Russian piece).
_(Photo: Paul Malmassari Collection)_
**PP 12** supported the Wielkopolska Cavalry Brigade in the region of Krotoszyn, Jarocina and Nowe-Miasto. It was employed during the offensive on the Szura then around 7 September in the Lowicz region. Damaged by artillery on the 9th, it was temporarily repaired at Błonie. On the 10th, the crew attempted to regain Warsaw, but Ołtarzew on their route had already been occupied by German forces. Its crew decided to sabotage the train and continued to fight the Germans on foot.
PP 12 _Poznańczyk_ which had been sabotaged by its crew, damaged beyond hope of repair, apart from its engine which appears to have been towed to a depot.
_(Photo: Paul Malmassari Collection)_
Steam engines of Class Ti3 had been the standard propulsion unit for the Polish armoured trains since 1927. They were former Prussian Class G5 (built between 1903 and 1906). They moved the armoured trains at up to 45km/h (28mph). Here is the engine from PP 12 _Poznańczyk_.
_(Photo: Paul Malmassari Collection)_
The assault troop transport wagon of _Poznańczyk_ moved to clear the track.
_(Photo: Paul Malmassari Collection)_
On 3 September **PP 13** took part in the defence of Giechanów then patrolled along the Narew and the Bug. On the 10th, it joined the 33rd Infantry Division retreating as far as Łochów Station. At around 14.00 the explosion of a bomb from a Stuka damaged the track and derailed the train, while other bombs set fire to the command/assault troop wagon. It was subsequently abandoned by its crew, who continued the fight on foot. It is certainly the most famous of all the armoured trains, as Hitler came to visit it on the 22nd, which generated hundreds of photos both official and private, reproduced in numerous publications.
PP 13 _Generał Sosnkowski_ derailed. On the left is the command/assault troop wagon with its characteristic wire antenna.
_(Photo: Paul Malmassari Collection)_
The rear artillery wagon of PP 13 _Generał Sosnkowski_. Its turrets each had a 270-degree horizontal field of fire.
_(Photo: Paul Malmassari Collection)_
The same wagon following repairs (note the buffers have been removed). Based on an engraving published in a German newspaper, it is rumoured that PP 13 took part in the invasion of Denmark, but no photographic proof exists.
_(Photo: Paul Malmassari Collection)_
**PP 14** was in action on 15 and 16 September at Łowicz. It began to withdraw, but near Jackowice its crew found themselves cut off from the rest of the retreating Polish elements. They abandoned the train between Jackowice and Rząśno.
Two photos of PP 14 destroyed between Jackowice and Rząśno.
_(2 Photos: Mariusz Zimny Collection)_
The last Polish armoured train remaining in action was PP 15 _Śmierć_. It was photographed in Modlin with an artillery wagon built in Lviv in 1920, then modernised, which had survived up until 1939. Its existence had long been ignored, for lack of previous photographic evidence. Its Class Ti3 engine has been set on fire.
_(Photo: Paul Malmassari Collection)_
The same artillery wagon seen from the opposite end. It is armed with a 100mm Skoda wz.14/19A howitzer. Note the state of the station roof with tiles blown off by artillery fire.
_(Photo: Paul Malmassari Collection)_
The rear artillery wagon of PP 15 _Śmierć_ , originally an Austro-Hungarian wagon used on Polish trains since 1918, rearmed with a 75mm wz.02/26 gun.
_(Photo: Paul Malmassari Collection)_
Initially held in reserve, **PP 15** went into action from 13 September in the defence of Modlin, where it was captured on the fall of the town.
Damaged by artillery fire near Wysoka on 2 September, **PP 51** _Pierwszy Marszałek_ managed to reach Oświęcim. From 12 to 14 September it defended a bridge on the River San and supported the resistance of Army Group Sandomierz. On the 27th, near Przeworsk Station, it was either destroyed by a bombardment or abandoned by its crew – accounts differ. Recovered by the Soviets, it served with the 77th Regiment of the 10th NKVD Division and operated in western Ukraine (former Polish territory). On 5 July 1941 it was captured by the Wehrmacht during Operation 'Barbarossa', who put it into service as PZ 10.
Close-up of one of the artillery wagons of PP 51.
_(Photo: Paul Malmassari Collection)_
PP 51 _Pierwszy Marszałek_ captured by the Soviets (who renamed it BEPO 77), then by the Germans who took this photograph.
_(Photo: Paul Malmassari Collection)_
A view of what is obviously a rake of Polish armoured wagons on the way to a depot to be reconditioned. Behind the two wagons from PP 51 are visible those from PP 53, which together would eventually make up PZ 10.
_(Photo: Paul Malmassari Collection)_
**PP 52** went into action on 1 September in the region of Mokre, in support of the 52nd and 53rd Infantry Regiments facing the 4th Panzer Division, where it was attacked by aircraft but escaped damage. It then took part in the fighting to prevent the Germans crossing the Warta, but it was forced to withdraw to the Laski-Łódź-Warsaw line. It was bombarded in the station at Laski, then when the tracks had been repaired it escorted the special train which evacuated the gold reserves from the Bank of Poznań. It next received orders to move to Siedlce because of the withdrawal of Polish forces, but the town had already fallen. Under the command of Colonel Więckowski, it formed the main element of an all-arms detachment which protected the pocket into which the Poles were withdrawing. Despite some successes (the destruction of reconnaissance vehicles and the capture of prisoners), its firepower was gradually worn down, until by 20 September only one turret with six shells and three machine guns remained operational. Too damaged to take part in a sortie, its crew sabotaged it with explosives.
Overall view of PP 52.
_(Photo: Mariusz Zimny Collection)_
**PP 53** supported the Wolhynie Cavalry Brigade on the morning of 1 September then took part in the battle of Mokra against the 4th Panzer Division. On the next day, it fought tanks of the 1st Panzer Division at Radomsko, then withdrew towards Lwów with PP 55. Arriving in the town on the 18th, the two trains were captured when Lwów fell to the Red Army.
In this view of the artillery wagon of PP 53, one can see the retractable nacelle system identical to that on the ex-Austro-Hungarian wagons.
_(Photo: Paul Malmassari Collection)_
PP 54 _Groz y_ seen at Craców in the Winter of 1939/40. The turret in the foreground is armed with a 100mm howitzer, and the other turret with a 75mm gun.
_(Photo: Paul Malmassari Collection)_
**PP 54** went into action in Silesia from 1 September in support of the 75th Infantry Company at Kobiór, where it was damaged and its commander was killed. It withdrew towards Tunel and engaged several armoured units. On 17 September it was abandoned at Biadolina, being unable to cross the River Dunajec as the railway bridge had been cut.
Bombarded in Koluszki Station on the first day of the war, **PP 55** remained in reserve and patrolled in the region of Brześć. At Żabinka, it destroyed several armoured vehicles then withdrew to Kowel and Lwów with PP 53, where it was captured by the Soviets after being hit by artillery.
### The Polish Armoured Train Battalions in Britain (12 October 1940 – November 1943
In 1940 the British built twelve trains to counter a threatened German invasion, by patrolling the coast from Cornwall in the West to the Moray Firth in Scotland. They were armoured at the Derby Carriage and Wagon Works of the LMS and at the Stratford Works of the LNER. Of the 17,000 Polish officers and men who were stationed in Britain, four battalions of the Polish Army of the West were assigned to the armoured trains from 1940 to 1942. They were organised as follows:
I _dywizjon_ : Armoured Trains C, G and E.
II _dywizjon_ : Armoured Trains A, D and F.
III _dywizjon_ : Armoured Trains B, M and H.
IV _dywizjon_ : Armoured Trains K, L and J.
In the early stages, to get round language problems, the Poles served their apprenticeship in armoured trains in Scotland, where there was the largest concentration of Polish units, liaising with the British crews of Armoured Trains Nos 10, 11 and 12. The Poles had completely replaced the British crews by April 1941, except for drivers and firemen transferred from the Royal Engineers, and for a few months longer, several radio operators.
From their long experience of armoured trains, the Poles rapidly suggested improvements to the rolling stock in their charge. Certainly the most active of the Polish officers was Colonel L Lodzia-Michalski, commander of the 1st Armoured Train Group. At countless meetings, he pressed for the augmentation of the trains' machine-gun and anti-aircraft armament; the amount of ammunition carried, including grenades and explosives for close combat, was greatly increased; and if it proved impossible to agree to his request for additional armour protection for the wagons, it was thanks to him that two basic improvements were put into effect: the enlarging of the gunshields on the 6pdr guns to improve crew protection, and the cutting of access hatches in the floors of the wagons to allow evacuation under fire.
Beginning in 1942, tracked and wheeled armoured vehicles were attached to the trains, to enable the trains to extend their zone of action, but also with a view to training the crews in armoured combat. This latter role gradually came to take precedence over the railway patrol function, and in 1942, the Polish train crews had absorbed sufficient training to be able to rejoin combat units. At that stage the armoured trains were transferred to British crews from the Home Guard.
A briefing for the crew of an armoured train, allowing us a view of their British kit with certain additions and badges from Polish uniforms.
_(Photo: IWM)_
In this view, the lack of a safety/protection flat wagon is not due to a request by the photographer, but a conscious decision on the part of the British General Staff. They considered the menace of mines so insignificant as not to warrant tying up much-needed transport wagons. The soldier climbing the ladder is carrying a .303in (7.7mm) calibre Bren LMG.
_(Photo: IWM)_
Bren gunners in firing position. Note the 'POLAND' shoulder flashes.
_(Photo: IWM)_
The gun shield has been fitted with the extensions demanded by the Polish crews, who were very experienced and therefore critical of many of the original details of the British armoured trains. The photo was taken after the trains had been handed over to the Home Guard.
_(Photo: IWM)_
A Universal Carrier from Armoured Train G, belonging to a reconnaissance unit and used by the Poles in an effort to extend their zone of operations further away from the railway. Covenanter and Valentine tanks were also allocated to various trains.
_(Photo: RAC Tank Museum)_
### Soviet Armoured Trains under Polish Command (1944–1945)
The part of the Polish Army which fell under Soviet control took on the designation of the Popular Polish Army ( _Ludowe Wojsko Polskie_ , LWP). Despite the fact that armoured trains were not officially part of its establishment, during the 1st Byelorussian Front's offensive on the Vistula in September and October 1944, the 31st Special (Gorki) Armoured Trains Division and the 59th Armoured Trains Division were temporarily put under the command of the First Polish Army.
The 31st Division comprised the BP _Cosma Minin_ and _Ilya Mouromietz_ , plus various support units and reconnaissance trolleys. The armoured trains of the 59th Division were of Type OB-3, Nos 668 and 675, and they operated in the Warsaw region from September 1944 to January 1945.
### The SOK Armoured Trains (1945–1947)
After the official cessation of hostilities in Europe, parts of the new frontiers of Poland, in particular those to the south-east, were threatened by units of the Ukrainian Revolutionary Army (UPA), who attacked the transport infrastructure, and principally the railway network. In the Autumn of 1945, the commander-in-chief of the SOK decided to set up his own armoured train units. A search for suitable rolling stock turned up several armoured wagons (primarily German but also Polish and Czech) scattered about the country (the German units still in good condition had been taken back to the USSR as war booty, and for study there). The remaining stock was identified, collected and repaired in the Ostrów workshops near Warsaw. The trains and their crews were brought together and formed in Warsaw and Craków, before being sent to the south-eastern regions.
The first SOK train (for the Russian broad gauge) was formed at Jaroslaw with a crew coming mostly from Szczecin, which gave the train its name _Szczecin_. It carried out patrols in the Medya-Lubaczow-Rawa Ruska region. In March 1946 its crew was replaced by personnel from Warsaw, then it returned to Ostrów for modification.
SOK Armoured Train No 2, later named _Grom_ ('Thunderbolt') was put together in Warsaw in October 1945. Sent to Sanok where it came under the orders of the 8th Infantry Division, it patrolled between Sanok and Łupków and between Sanok and Ustinov. It went into action on several occasions notably at Olszanica, Stefkowa, Komańcza and Oslanica.
The future _Huragan_ (Hurricane) which began as SOK Armoured Train No 3 was created in October 1946. In 1948 it was attached to the SOK training establishment at Toruń.
SOK Armoured Train No 4, the future _Błyskawica_ ('Lightning') was created at the DOKP near Kraków, using vehicles renovated in the Ostrów workshops. The former commander of Armoured Train No 1 took over control of SOK No 4, the train being allocated first to Zagora until June 1947, then to Zawada.
The existence of four armoured trains made it possible to create a SOK Division in early 1947, commanded by Captain M Jarosz, with its headquarters in the station at Zagórz, near Sanok. It was during this period that two newly-restored machines were allocated to it, one being a Steyr le.Sp trolley and the other, according to certain sources, being a Skoda trolley named _Baśka_ ('Barbara'). In April 1947 this new division came under the command of Major-General Stefan Mossor, commander-in-chief of Operation 'Wisla' ( _Ackja Wisła_ ) intended to eradicate the UPA. Two of the trains (probably Nos 1 and 2) were placed under the orders of the Fifth Army Group (Craków). We have no information concerning the fate of these trains after 1947.
Profile views of three trains reconstructed by Janus Magnuski, in which it is easy to recognise ex-German vehicles, both armoured trains and antiaircraft trains.
_(Illustration:_ Wozy Bojowe _, p 282)_
The K-Wagen of SOK Armoured Train No 3.
_(Photo: Janusz Magnuski Collection)_
This A-Wagen is one of the rare examples using a _Wirbelwind_ turret. Note that it is oriented in the opposite sense to the original use of these wagons, which placed the 10.5cm turret in front. The crew members are wearing the _rogatywka_ , the traditional Polish headgear.
_(Photo: Janusz Magnuski Collection)_
Train No 4 _Błyskawica_ with its crew posing in front of a K-Wagen.
_(Photo: Janusz Magnuski Collection)_
Note that the Steyr trolley used by the SOK units is one of the early versions with three rectangular plaques protecting the air intakes, as against the circular caps seen on the later series.
_(Photo: Janusz Magnuski Collection)_
### Lokomotor Armoured Railcar WP870027 (ex-PT 16) & Armoured Wagon WP 870028 in Closeup
This railcar is described in the chapter on Germany. After the Second World War, this machine was used by a unit of the Polish Army based at Przemyśl-Bakończyce. It took part in Operation 'Wisla' then remained in service up until the 1960s. In 1982 it joined the collection of the State Railway Museum in Warsaw. It has not been possible to identify the train from which the armoured wagon derived. It appears that it too had served for many years before finding its way into the collection of the Railway Museum.
The turrets on both units are identical, seen here armed with Russian 76.2mm Putilov guns. The oval-shaped opening in the casemate side was cut after PT16 entered service, in order to make up for the absence of firing ports for close-in defence.
_(Photo: Private Collection)_
The three small square blocks just below the turret ring, which exist only on this side, are without doubt smoke extractor vents, connected to internal pipework, used when firing. The gun seen here is not the original.
_(Photo: Private Collection)_
**SOURCES:**
**Archives:**
SHD: 6 N 249, 7 N 2999, 7 N 3009/2, 7 N 3017, 7 N 3018.
**Books:**
Jo ca, Adam, _Renault FT 17/NC 1/NC 2/TSF, Renault R 35/40, Hotchkiss H 35/39_ (Sandomierz: Stratus s.c., 2009).
__________, _Poci gi Pancerne Z Legionowa_ , Wrzesień 1939 Vol 24 (Warsaw: Edipresse Polska SA, 2013).
Jurczyk, Jozef, and Margasinski, Krzysztof, _Dziennik pociagu pancernego Hallercsyk_ (Cz stochowa: Towarzystwo Przyjacio ł Czechowic-Dziedzic, 2010).
Konstankiewicz, Andrzej, _Bro strzelecka i sprz t artyleryjski formacji polskich i Wojska Polskiego w latach 1914-1939_ (Lublin: Uniwersytetu Marii Curie-Skłodowskiej editions, 2003).
Krawczak T, and Odziemkowski, Jerzy, _Polskie pociagi pancerne w wojnie 1939_ (Warsaw: Biblioteka Pami ci Pokole, 1987).
Kraśnickca, Urszula, and Filipow, Krzysztof, _Poci gi Pancerne 1918-1943_ (Białystok: Ośrodek Bada Historii Wojskowej, 1999).
Kuntz, Captain Ch, _L'Offensive de l'Etoile Rouge contre la Pologne_ (Paris: Lavauzelle, 1922).
Ledwoch, Janusz, _Polskie poci gi pancerne 1939_ (Warsaw: Wydawnictwo « MILITARIA », 2015).
Magnuski, Janusz, _Poci g pancerny « ZYGMUNT POWSTANIEC »_ (Warsaw: Wydawnictwo Ministerstwa Obrony Narodowej, 1981).
_______________, _Poci g pancerny « DANUTA »_ (Warsaw: Wydawnictwo Ministerstwa Obrony Narodowej, 1972).
__________, _Poci g pancerny « MIAŁY »_ (Warsaw: PELTA, 1996).
_________, _Karaluchy Przeciw Panzerom_ (Warsaw: PELTA, 1995).
_________, _Wozy Bojowe LWP 1943-1983_ (Warsaw: Wydawnictwo Ministerstwa Obrony Narodowej, 1985).
Ostrówka, Adam Jacek, _Poci gi pancerne Wojska Polskiego 1918-1939_ (Toru : Adam Marszałek, 2013).
Porte, Rémy, _Haute-Silésie 1920-1922_ (Paris: Riveneuve Éditions, 2009). Sikorski, Major General L., _La Campagne polono-russe de 1920_ (Paris: Payot, 1928).
**Journal articles:**
Anon., 'Châssis sans moteur, pour le transport des chars d'assaut sur route et sur rails', _Le Génie civil_ (2 January 1927), p. 25.
Anon., 'Trains blindés', _Revue d'artillerie_ Vol 114 (July-December 1934), pp 93–4.
Anon., 'Panzerzüge in der polnischen Armee', _Militär-Wochenblatt_ No 45 (1932), pp 1582–4.
_Bulletin_ Vol 5 No 3 (1995), pp 5.31–5.32.
Jońca, Adam, 'The Polish Armoured Trolleys', _V.M.I_. (1989), No 3, pp 18–23; No 32, pp 18–19.
Magnuski, Janusz, 'Drezyna Pancerna SOK', _Militaria_ , Vol 1, No 1 (1991), pp 37–9.
Surlemont, Raymond, and Pied, Robert, 'The German Armoured Train in the Railway Museum in Warsaw', _V.M.I_. (15 February 1988), pp 29–31.
Szychowski, 'Armoured Trains', _Pryeglad Artyleryiski_ Volume IX, Fascicule 2 (1923), pp 162–80 (in Russian).
'The Polish Armoured Trains in the Campaign of 1939', _Lokotrans_ (9/2009), pp 27–33 (in Russian).
Zaloga, Steven, 'Polish Armored trains in 1939', _AFV News_ 12/3 (n.d.), pp 6–10.
____________, and Magnuski, Steven, 'Polish Armoured Vehicles of WW2', _Military Modelling_ (October 1983), pp 730–3.
____________, 'Polish Armoured Vehicles of WW2', _Military Modelling_ (November 1983), pp 843–5.
**Website:**
<http://derela.republika.pl/>
. In Polish _Pociag Pancerny_ , abbreviated as PP, followed by the number of the individual train.
. In Polish _Drezyna pancerna_.
. _Szeroki_ = broad gauge. Added to the names of all trains operating on the Russian railway network.
. Today modern Lviv in the Ukraine.
. The term 'Soviet' cannot be applied to this conflict as the Soviet Union was not officially established until 30 December 1922.
. KBPP = _woiskowe Kierownictwo Budowy Pociagów Pancernych_ (Organisation for the Construction of Armoured Trains).
. ' _Hunhuz_ ' is the transcription of the Chinese word signifying 'red beard', used to describe the bandits infesting the Russian Far East in the nineteenth and twentieth centuries.
. 'Adventurer'.
. Polish nobleman (1599–1665), one of their most famous generals, who notably defended Warsaw against the Swedes in 1655.
. A girl's name.
. 'Connected to the town of Poznań', or 'The Poznanian'.
. Kazimierz Sosnkowski (1885–1969), Polish nobleman, patriot, politician and general.
. Ignacy Paderewski (1860–1941), the celebrated pianist, one of the political founders of Poland.
. 'Death'.
. 'First Marshal', after the first Polish Marshal, Józef Piłsudski (1867–1935), one of the founding fathers of the Polish State, then Head of State in 1918–22 and again in 1926–35. Also found written as ' _I Marszałek_ '.
. 'Audacious'.
. 'Formidable'.
. Bartosz Głowacki (originally Wojciech Bartosz, circa 1758–94) was a peasant ennobled for an act of bravery against the Russian cannons during the Kosciuszko Uprising in 1794.
. Unofficial designation.
. Published in the _Red Star_ , Moscow, May 1934.
. In April–May 1927 Poland purchased two unarmoured Austro-Daimler trolleys. They were tested by the armoured trains training formation, but no further orders resulted.
. _Centralne Warsztaty Samochodowe_ = Central Car Workshops.
. An anonymous article 'Chassis sans moteur, pour le transport des chars d'assaut sur route et sur rails' which appeared on p 25 of _Le Génie civil_ of 2 January 1927 referred back to the _Zeitschrift des Vereines deutscher Ingenieure_ of 18 July 1926.
. The CWS tanks were the Polish version of the Renault FT, of which twentyseven examples were built in the CWS factory ( _Centralne Warsztaty Samochodowe_ = Central Car Workshops) in Warsaw. The small-link tracks designed in 1925 by Captain S. Kardaszewicz gave the tank a higher speed. But the steel used in the tanks' fabrication was not of armour quality, and these non-battleworthy machines were only allocated to training units.
. The TK tankette (known as the TK-3 when fitted with a Ford motor) went into production in 1931, followed by the TKS which was fitted with a Fiat 122 motor, an improved machine-gun mounting and new episcopes.
. An RKB/c set, its presence evidenced by the box installed on the front left wing.
. A crew of one officer, six NCOs and ten men, plus the crew of the reserve vehicle.
. Apart from PP 15 with two Tatra trolleys, and PP 13 with two Tatra trolleys and two TK/TKS.
. _Dwuwieżowy_ = double turret. An unofficial designation common today.
. Only 137 7TP tanks were available in total.
. Probably diesel-electric, given the contemporary use of 110hp diesel engines in the 7TP tank
. Known in Poland as the _Kampania wrze niowa or Wojna obronna 1939 roku_ , the Defensive War of 1939.
. _Wielkopolska Brygada Kawalerii_ , with its HQ in Poznań.
. _Wołyńska Brygada Kawalerii_ , with its HQ at Lódź.
. LMS = London, Midland and Scottish Railway; LNER = London and North Eastern Railway.
. Following their evacuation at the time of the Fall of France, along with many Polish airmen and seamen. The Government in Exile under General Sikorski had also left Paris for London.
. The designation 'Bren' is an amalgam of the names of the towns of Brno where the ZB26 was made for the Czechoslovak Army, and Enfield, where the British version was manufactured.
. _Polskie Siły Zbrojne na Wschodzie_. In the West, a Polish Army Corps commanded by General Anders, called the _Polskie Siły Zbrojne na Zachodzie_ , or Polish Army of the West, fought in Italy while other Polish units served at Tobruk.
. _Służba Ochrony Kolei_ , Railway Protection Service, reporting to the Interior Minister.
. Українська Побманська Армія, established in October 1942 in Volhynie to fight against all the occupying forces (successively, Germans, Poles and Russians) and obtain independence for the Ukraine.
. _Dyrekcja Okregowa Kolei Pa stwowych_ , State Railways Regional Management.
## PORTUGAL
### ARMOURED TRAINS AND TROLLEYS
Although they did not deploy armoured trains in Portugal proper, the Portuguese did use them in their colonies which were affected by anti-colonialist uprisings, which in chronological order were Goa, Angola and Mozambique.
### Goa, Portuguese Period
Goa was one of the three territories in the western part of India settled and exploited by the Portuguese since the sixteenth century. After Britain granted independence to India in August 1947, nationalist movements attempted to disrupt communications between the three territories and Portugal by attacking economic targets and the transport system. Goa itself was finally invaded and annexed by India between 17 and 19 December 1961.
Wickham armoured trolley supplied for use in Goa, with a different turret to the models built for Malaysia.
_(Photo: Wickham)_
### Angola, Portuguese Period
The first traffic on the Benguela Railway ran in 1905. The line was built following the discovery of copper in northern Rhodesia and Katanga in 1881. In the 1950s, the trains ran from Lobito to Elizabethville in the Belgian Congo. When the terrorist attacks began, armour plating was fitted to the cabs of the locomotives, and the inspection trolleys received complete armour protection. Additional trolley rolling chassis were ordered which were fitted with armour protection locally.
Behind armoured Wickham trolley No 193, Garratt Class 10 B No 323, followed by Garratt Class 10 D No 386 (4-8-2+2-8-4), both with armoured cabs, depart Luso en route to Munhango.
_(Photo: Peter Bagshawe)_
Close-up of the armoured cab on Garratt Class 10 E No 389.
_(Photo: Peter Bagshawe)_
The classic arrangement in zones liable to attack: an open bogie wagon in front of a Garratt on the Munhango–Luso line photographed on 27 August 1972.
_(Photo: Peter Bagshawe)_
In Texeira de Souza Station, Class 9 A 4-8-0 engine No 209 with armoured cab.
_(Photo: Peter Bagshawe)_
A line of armoured Wickhams parked in Luso Depot on the evening of 24 August 1972, when the train services stopped for the night for security reasons.
_(Photo: Peter Bagshawe)_
Armoured trolley No 172 in August 1972 at Munhango Depot, where a large number of these units were based.
_(Photo: Peter Bagshawe)_
A Wickham trolley leads 4-8-0 engine No 231 at the head of a Texeira–Lobito mail train, seen at Cangumbe Station.
_(Photo: Wickham)_
Wickham Type 42 Inspection Trolley (identical to the Wickham Type 40 Mk II), before the addition of armour protection.
_(Document: Wickham)_
Trolley No 83, delivered in November 1967. In around 1968 '100' was added to each serial number, which allows us to date this photo.
_(Photos: Wickham)_
### Mozambique, Portuguese Period
Two Wickham running chassis (Nos 191 and 192 built in 1969) were ordered and sent to Mozambique to be locally armoured.
In 1972 Portugal entered into secret negotiations with the French firm of SOCOFER with a view to supplying the Mozambique colony with armoured trolleys, in the belief that France had retained a stock of trolleys left over from the War in Algeria. SOCOFER, based in the former Billard Works in Tours, carried out a design study, but the units were never built, as no official order was forthcoming. One unusual feature for an armoured vehicle at this late date was an open-topped hull covered with an awning, for ventilation in the hot climate.
_Zorra_ was the name given to this armoured hull from an old Auto-Metralhadora-Daimler 4x4 Mod.F/64 (the Portuguese version of the British Dingo) mounted on a flat wagon. It offered scant protection against heavy weapons, but served as an excellent observation post for the five or six soldiers of its crew. Note the extra armour box added on top of the original hull.
_(Photo: All Rights Reserved)_
SOCOFER trolley design for Mozambique, which remained on the drawing board.
_(Drawing: SOCOFER Archives, in the collection of Paul Malmassari)_
**SOURCES:**
Harrison, Maurice A., 'Line across Angola', _The Railway Magazine_ (September 1973), pp 446–9.
Wickham archives
The files of Peter Bagshawe.
' _Zorra_ -The Railway Vixen', _Tank T_ V No 2 (1992).
. The fighting in Goa began in 1947, in Angola on 4 February 1961, and in Mozambique in September 1964. The last two wars ended with the Carnation Revolution of 1974.
. The Portuguese refused the annexation of its Indian territories on the grounds that when they had been established, India did not exist as a separate state, and therefore under international law India could not claim their return.
. Notably in July and August 1954, which led to the annexation of the two land-locked territories.
. Trolleys Nos 172 to 175, then Nos 181 to 190, with a question mark regarding trolleys Nos 171 and 186. Trolleys Nos 193 to 197 were ordered as bare rolling chassis to be armoured locally. (Information provided by Peter Bagshawe).
## RHODESIA & ZIMBABWE
### ARMOURED TRAINS AND ARMOURED TROLLEYS 1972–1979
In our opinion, the defence of the railway network during the 1972–9 bush war in Rhodesia by the security forces against the guerrillas of ZIPRA and ZANLA, who were armed respectively by the Russians and the Chinese, is the rail conflict which produced the most innovations in armoured rolling stock.
### The armoured trolleys
The first attacks on commercial trains began in January 1975 on the line between Thomson Junction and Victoria Falls. At first security patrols were carried out using unarmoured Wickham inspection trolleys (Types 3, 4, 5 and 6), nicknamed 'Green Beans'. Very quickly it was realised that armoured rail vehicles would be required. The concept initially chosen would remain the standard for all subsequent vehicles, namely an armoured 'capsule' with a V-shaped cross-section, mounted on an existing chassis. The first type of armoured capsule, called the 'Rhino', was adapted to fit on the Land Rover LWB chassis. The Rhino immediately attracted the interest of the railway operators, and late in 1976 three armoured capsules were delivered to the central railway maintenance workshops in Bulawayo for evaluation. During the war the MAP vehicles were continuously developed, increased protection and an improved drive train being added to the Rhino and later designs, culminating in the ultimate armoured trolley, the Cougar.
The original Rhino model, with the turntable carried at the side together with one of the rails which allowed the trolley to drive onto the turntable, and the rail wheels fixed directly onto the axles without any intermediate drive system, which would cause many problems because of the vibration. Bringing up the rear is a Wickham Type 18 Mk VI inspection trolley.
_(Photo: National Railways Museum, Bulawayo)_
The first Rhino model was mounted on a standard Land Rover chassis, modified for use on the rails. The initial problem to be surmounted was the fitting of special rail wheels, because the Land Rover's wheelbase was wider than the local rail gauge of 1067mm (3ft 6in).
A wheel had to be designed with its rolling surface inboard of the outer end of the vehicle's axle. In addition, the four-wheel drive function, the steering and the rear hydraulic brakes were all discarded. The Rhino trolley entered service in early 1977. Initial reports mentioned cracks developing in the chassis, due to the constant jarring caused by the rail joints, and the first remedy was to weld on reinforcing plates. The second recurring fault was the breakage of the half-shafts, which had never been designed with rail use in mind. A new chassis layout was therefore designed for the Rhino, and this would prove entirely satisfactory in service.
Before the introduction of the revised chassis, a new crew capsule was designed, with multi-angle armour protection. This resulted in an interim model known as the 'Kudu', which offered better protection, but still on the original type chassis with its limitations.
The following model, nicknamed the 'O-Jay', used the multi-angled armour body of the Kudu, but profited from a modified transmission system: a V-belt transmitted the power from the axle flange to a pulley driving the rail wheel, thus avoiding the transmission of shocks back to the drive axle. The front axle was changed to the Wickham type. The layout was well-adapted to rail use, and was repeated on all the subsequent designs. The first O-Jay entered service on 26 April 1977.
In service, growing numbers of Rhinos and O-Jays began to fall victim to mine explosions, sometimes with dramatic results. Remedies were sought for each part of the trolley affected. Armour plate 10mm thick in the form of a 'V' was fastened beneath the vehicle, effectively protecting it from the radiator to the rear axle. However, if a powerful explosive charge was used, one of the wheels could be torn off, resulting in a violent shock when the front of the vehicle fell onto the rail sleepers or the whole vehicle became derailed. To prevent this happening, an anti-derailment device was designed, consisting of a square-tube frame fastened at a height of a few inches above the rail surface. Each tube was as wide as the trolley, with plates welded to the ends of the tubes in such a way that they extended out beyond the rails at each side. Thus, in the event a wheel became detached, the trolley would slide along on top of the rails and would avoid becoming derailed thanks to the plates at each side of the tubular frame, which would keep it more or less in a straight line. Next, a cow-catcher was attached to avoid the trolleys striking obstacles (such as animals) and derailing.
The Kudu, with the armoured body of the O-Jay on the chassis of the Rhino, with the good protection offered by the newer crew compartment, but retaining the Rhino's shortcomings, especially in regard to its turning capabilities.
_(Photo: Boet Du Plessis)_
The explosion of the petrol tanks had resulted in some severe burns. The decision was taken to replace their rigid fixtures by sprung metal bands, held in place by 6mm 'veranda' rivets in such a way that, in the event of a violent shock, the tank would break free and be propelled some distance from the vehicle.
The question of how to turn the vehicle (since the Land Rover gearbox retained its four forward gears but only one reverse gear) was solved in the classic manner by the provision of a turntable. This was mechanically operated on the initial models and later hydraulically on certain subsequent models. On the Rhino, the turntable was carried on the side of the vehicle, which had to be driven up onto it and fastened in place before being turned. On the other models, the device was integral to the chassis, which saved a great deal of time and reduced the risk of accidents from the trolley being badly placed or even falling off.
The next model was the 'Tusker', which used the same chassis as the O-Jay, but with a revised crew capsule offering improved protection. Some Tuskers were used as transport by signals officers.
A Kudu parked up, seen from inside a trolley.
_(Photo: Horst Schobesberger)_
The last type of armoured trolley to be built was the 'Cougar', which incorporated all the previous improvements. In particular, it had a double braking system: hydraulic on the rear wheels and vacuum brakes on the front wheels. A radio-controlled trolley was also planned, remotely guided from a second trolley following some 500m behind, but it was not built.
Finally, the 'Jackal' was built in great secrecy. It was powered by a Leyland 680 diesel motor. Running 10 minutes in front of the postal train in the direction of Bulawayo, and then intended for use in the Beira Corridor, it did not prove to be a success, mainly because of its excessive weight. It could accommodate thirty-five fully-equipped troops, and was more akin to an armoured personnel carrier than a reconnaissance vehicle.
At midnight on 31 March 1980, all the armoured trolleys were withdrawn from service, with the exception of two Cougars made available to the engineers at Rutenga, and a third Cougar intended for the National Railways Museum, Bulawayo.
A photo of the O-Jay armoured trolley, showing the disk brakes fitted after it had entered service, and the deliberately flimsy fastening of the petrol tank. For scanning the track the central searchlight was preferred to the fixed front headlamps. The 'V' form of the lower armour is clearly visible.
_(Photo: National Railways Museum, Bulawayo)_
### Armoured locomotives and wagons
While the trolleys are well known, it should be remembered that the locomotives were also armoured, basically around the cabs and other vulnerable areas. To accompany goods trains, a certain number of platform wagons were fitted with heavy weapons and provided with an armoured shelter at each end and between the gun mountings. The wagon crews were drawn from the six specialist Railway Defence Companies of the Guard Force – the fourth element of the Rhodesian defence forces. They operated from Gwelo (Somabula) towards Rutenga and Beitbridge on the South-African border.
The twelve daily goods trains ran loaded in one direction during the night, and returned empty back south during the day. They followed each other at very short intervals to prevent the rebels from profiting from the five or six minutes necessary for planting explosives. This was the same procedure as used by the French 'Rafales' in Indochina. In addition, the armoured trolleys would run at an interval of about four minutes in front of each train. However, the system was not foolproof, as there were usually more trains than serviceable trolleys. The solution was to run patrols at random, to confine the goods trains to daytime runs, and use the trolleys to patrol during the nights.
Ever since Mozambique had obtained its independence in June 1975, the zone most at risk was the south-eastern section of the railway network carrying the trains vital for Rhodesia's survival. Therefore the majority of the armoured vehicles were concentrated on the Somabula-Beitbridge line, while the rest were divided between the Bulawayo-Plumtree line to the south and the Bulawayo-Victoria Falls line heading north, except for a few units on the east-bound line to Gwelo and Gatooma. All the armoured units were now linked by radio to the CTC (Centralised Traffic Control). In addition, by passing an electric current through the rails the CTC knew immediately if a section of rail had been cut, or if a trolley had been derailed, and they could despatch reinforcements to the point of attack. For this system to work, the trolleys were fitted with metal brushes on bars just behind the front wheels and just in front of the rear wheels, adjustable so that they would touch the rails and thus close the electric circuit. After independence was declared on 18 April 1980, the attacks by dissident elements led to the re-commissioning of certain units and their despatch in the direction of the Beira railway network.
In conclusion, it is clear that such a technical and tactical evolution of armoured rail units has rarely been achieved elsewhere, and in such a short time span. In the multiple attacks, not one single trolley crewmember was killed. Again, all of the damaged units were able to be repaired and returned to service thanks to their robust construction. One must also remember that these developments took place at a time when Rhodesia was suffering under international sanctions aimed at disrupting the supply of spare parts and technology transfer.
The armoured hull of the Tusker, carried on the standard-type chassis incorporating all the improvements found wanting in the original Rhino, was reputed to offer better protection to the crew, especially with the introduction of the netting to protect against the hollow-charge warhead of the RPG-7 with which the terrorists were well supplied. Of note is the rear door which was the sole means of access on all the armoured trolleys.
_(Photo: National Railways Museum, Bulawayo)_
A Tusker with a different design of motor compartment protection. These vehicles were painted in the contemporary British Army bronze green finish.
_(Photo: Horst Schobesberger)_
In this view of the Jackal (here with the rear wheels removed) of note are the access stairs which double as cowcatchers. The anti-derailment bars are here clearly visible, with the small plates welded on at each side, intended to keep the unit in a straight line in the case of one wheel being blown off.
_(Photo: National Railways Museum, Bulawayo)_
This photo of the opposite side of the Jackal on display in Bulawayo shows the different lower section.
_(Photo: Glöckner)_
The final type of trolley, the Cougar, incorporating all the modifications resulting from the experiences of the bush war.
_(Photo: National Railways Museum, Bulawayo)_
Another photo of a Cougar, parked in front of a fully-armoured Wickham trolley.
_(Photo: All Rights Reserved)_
The Cougar preserved in the Bulawayo Museum. Unfortunately, the interior of the vehicle is in poor condition.
_(Photo: Olivier Grognet)_
A closeup of the drive train, with a V-pulley which helped reduce the hammer blows caused by the rail joints and also to save the transmission from damage in the event of a derailment. Unfortunately the very first models had a tendancy to shed their belt.
_(Photo: Olivier Grognet)_
A photo taken in April 1980 showing one of the Garratts hired by the ZRR from South African Railways between August 1979 and September 1981. On these locomotives only the cab was armoured.
_(Photo: Peter Bagshawe)_
Two DE9A armoured locomotives, Nos 1959 and 1957, at Heany Junction in April 1980. The armour plating serving no further use was removed a few months after this photo was taken.
_(Photo: Peter Bagshawe)_
Two shots of the crew of a K Wagon.
_(Photos: Horst Schobesberger)_
Two diesel locomotives with armour protection (on the left an English Electric Class D.E.2 and on the right a Brush Class D.E.4) used on the Beira Corridor in July 1987.
_(Photo: John M. Batwell)_
Two K Wagons, each armed with a 20mm cannon and a 7.62mm MAG. One of these wagons is preserved in the Bulawayo Museum.
_(Photo: Horst Schobesberger)_
**SOURCES:**
**Books:**
Bryer, Tom, _Terror on the Tracks: a Rhodesian Story_ (Rothershorpe, Paragon Publishing, 2011).
Hamer, E D, _Locomotives of Zimbabwe & Botswana_ (Malmö: Frank Stenvalls Forlag, 2001).
**Website :**
<http://www.rhodesiansoldier.com/hist-bush-war-railwaysecurity.html>
. Rhodesian railways changed names twice following political changes. From Rhodesian Railways (RR) they became Zimbabwe Rhodesian Railways (ZRR) between 1 June 1979 and 30 April 1980, and then National Railways of Zimbabwe (NRZ).
. The country itself underwent several changes of name: from Southern Rhodesia (1923–64) to Rhodesia (from 1964), then Rhodesia-Zimbabwe (1979) and finally Zimbabwe (from 18 April 1980).
. The Zimbabwe African National Liberation Army (ZANLA) was the military arm of the Zimbabwe African National Union (ZANU), and the Zimbabwe People's Revolutionary Army (ZIPRA) was the military arm of the Zimbabwe African People's Union (ZAPU).
. The Rhodesians used the term 'security trolley'.
. Long Wheel Base.
. Mine and Ambush Protected.
. At one time it had been planned to install turntables at several predetermined points on the railway network, but the project was abandoned because of the excessive costs involved.
. For example, provision of a motorcycle helmet for the driver, the fitting of safety belts, and the inclusion of first-aid kits, etc.
. Known as 'K Wagons', ('K' for 'Kill').
. A line breakage would need on average 24 hours' work to repair.
. It is estimated that half of all the trolleys fell victim to an attack, except for the Cougars which entered service only a short time before the end of hostilities.
. Built in Spain by Babcock & Wilcox.
## ROMANIA
During the Russian Civil War, a Romanian Legion of some 3000 men was formed in Siberia from the elements of different units of the former Austro-Hungarian Army. It came under the orders of the Czech Legion. They protected the Trans-Siberian Railway between Taychet and Nizhneudinsk, and possessed at least one armoured train. The men were repatriated to Romania in May 1920.
At the end of the First World War, many of the former Austro-Hungarian armoured trains were in Romania, and they were retained in service. Little information is available as to their fate, other than the existence of a 'Group' composed of three armoured trains reported by the French Military Attaché in 1924.
In early 1919, a British officer, Captain Kyle, was tasked with studying whether the Jassy and Bender workshops were competent to produce armoured locomotives and rolling stock. He concluded that it would be possible to form two trains each composed of a locomotive and three or four wagons, and proposed that the execution of the work be carried out by a French officer. The armour plates to be used would be those originally intended for the protection of lorries in the Nicolina workshops. Despite the fact that the Minister of Public Works ordered the Romanian railways to carry out the work, we do not know if these new trains were actually constructed. The Romanian archives describe only one train, composed of an engine and two armoured wagons, based at Târgoviste in 1921, and attached to a tank regiment. This train was in a poor state of repair, missing parts of its armour protection, and lacking vital equipment such as lighting, automatic brakes, running lights and so on.
In 1926 records show that the Armoured Train Battalion contained four trains, two narrow gauge and two standard gauge. Each train was composed of ten armoured wagons (with two 76.2mm guns, six machine guns and two LMGs), and two engines. Their armament could be supplemented by attaching wagons with two 120mm naval guns, a 75mm gun and eight machine guns.
In a later (undated) development, the number of armoured trains increased to seven, each one being composed of two distinct parts: the combat unit with one locomotive and two wagons, and the support unit with accommodation and supplies. If no photographs have come to light, the Romanian archives hold details of their composition, summarised in the following table drawn up in 1934. The armoured wagons once more fell into disrepair, and in 1935 studies were begun with a view to overhauling them.
One of the Austro-Hungarian armoured wagons left behind in Romania, a standard component of the Romanian armoured trains during the inter-war period.
_(Photo: Paul Malmassari Collection)_
Studies were also conducted into eventually replacing the trains by armoured trolleys, or even by motorised platform wagons with removable armour protection, capable of carrying tanks armed with 57mm or 75mm guns. It is clear these plans showed Polish influence, as the Type TK, TKS and R trolleys were thought superior to the classic type.
**SOURCES:**
Romanian Military Archives (File references 3831/3330/15-17 and 3059/361/7-8; 100-105; 150-151). SHD: 7 N 3063.
. At the time two countries, France and Great Britain, were active in helping Romania.
. The support wagons provided sleeping accommodation, ammunition magazines, a galley, office, storeroom, eating area, baths and washbasins, and a flat transporter wagon.
## RUSSIA, THE USSR AND THE RUSSIAN FEDERATION
### ARMOURED TRAINS, RAILCARS AND TROLLEYS 1900–2016
For ease of historical reference, this chapter has been divided into three separate periods: the Tsarist period which lasted up until 25 October 1917, the Russian Civil War and the Second World War (1917–45) and from the Cold War until the present day. But these divisions are simply labels, behind which the development of armoured trains proceeded in leaps and bounds: for example the First World War saw the introduction of armoured trolleys and railcars, while the Civil War and the Great Patriotic War marked turning points in the strategic and tactical use of armoured trains, as well as in their technological development. Furthermore, the wide expanse of Russia gave rise to a great diversity in the design of the trains, and certain types can be identified as belonging to specific regions. Faced by the large number of armoured trains and motorised rail vehicles built in a variety of factories, or locally improvised using materials to hand, or captured from enemy forces, plus the huge variety of armoured wagons, we have been obliged to feature certain units while leaving others in the shade. The following chapter, while not comprehensive, will nevertheless form a visual guide complete enough to aid future researchers building on the work and publications of specialists such as Maxim Kolomiets.
### The Russian Railway System
The USSR was the country which made the most use of armoured trains, bringing improvements not only to their technical aspects but also their tactical deployment. They were used not only as short- and medium-range mobile artillery, but were also manoeuvred like the ships of a land-based fleet. Given the vast expanse of its territory, Russia was the country most likely to make maximum use of its railway system. From a late start compared with Western Europe, the Tsars created and expanded the network, but even so, when the Revolution began, the system was still underdeveloped in relation to the huge distances to be covered. Nonetheless, all the battles and campaigns of the Civil War would see the use of armoured trains, as much by the Reds as by the Whites. The larger towns and industrial areas were in fact linked by railway lines rather than by roads, which even where they existed were impassable in wet weather.
### The Armoured Trains of Tsarist Russia
The history of Russian armoured trains began well before the First World War, as a consequence of the Boxer Uprising of 1900 in China. The Russian contingent in Beijing, which was the largest of the Legation forces, was charged with the defence of the railway station which was on the other side of the river from the Legations. In order to secure communications with the coast, an armoured train was therefore improvised, which could transport 200 troops. Then during the Russo-Japanese War, to protect trains from the depredations of the Khunkhuz bandits, armoured wagons were inserted in the rakes, working in conjunction with the _radziesd_ , blockhouses armed with artillery and machine guns built along the line of the Trans-Siberian Railway. Then in 1907, the military press reported on the order by General Rennenkampf for armoured wagons to be armed with artillery and machine guns.
Armoured wagon of the type attached to rakes on the Trans-Siberian Railway, at least one of which was in service with the armoured train _Mstitiel_ during the Civil War. The armament is given as a revolver cannon which could fire from the front hatch (closed in the photo) or from the sides. Note the method of applying the brakes.
_(Photo: Enrique Rostagno, from_ Les Armées russes en Mandchourie _, p 34)_
The Russian Army built several improvised armoured trains on the outbreak of the First World War. After studying their performance, from June 1915 it built fifteen more. Seven of these were of a similar design to the Austro-Hungarian trains. Their makeup was straightforward: an artillery wagon/steam engine/artilley wagon. The first was christened _Khunkhuz_ after the bandits who had harassed the Trans-Siberian, and this train gave its name to the class.
The first improvised armoured train of the war: designed by the 9th Railway Battalion, it had two artillery wagons armed with captured 8cm Austrian field guns, as seen here, an infantry wagon, and at first an Austrian engine which was later changed to a Russian one.
_(Photo: Maxim Kolomiets Collection)_
The first train of the standard series, produced in 1915. Its artillery wagons had several firing embrasures along the sides of the casemate section. The revolving turret, which could train through some 270 degrees, did not extend to the roof level, on which was a small observation cupola.
_(Photo: Maxim Kolomiets Collection)_
These trains would be destroyed or captured during the first months of the Civil War. Train No 2 became the Red '2nd Siberian Armoured Train' after modifications at Tsaritsyn, which principally involved rearming its turrets with 76.2mm Model 02 guns and adding two flat wagons carrying 3in guns. Captured by the Whites, it was renamed _Officier_. Another example became the famous Czechoslovak train _Orlik_ , and a third, the Polish _General Dowbor_.
This improvised armoured train, first built by the Austro-Hungarians, was equipped with a Russian engine from a Khunkhuz-type train after being captured by the Bolsheviks, who named it Train No 56 ( _Red Peasant_ ). It was captured in turn by the Poles on 28 May 1920 and later served with the Ukrainian Army.
_(Photo: Paul Malmassari Collection)_
_General Dowbor_ in Polish service.
_(Photo: Maxim Kolomiets Collection)_
One of the two wagons built by the 4th Railway Battalion in November 1914, in the region of Łód . The Arbel-Fox bogie coal wagon is armoured with 7mm and 12mm plates, and carries a naval 37mm Hotchkiss gun and four machine guns. The next wagon in line is armed with an Austrian 8cm Feldkanone M.5.
_(Photo: Paul Malmassari Collection)_
View of the rear wagon of the armoured train of the 4th Siberian Railway Regiment, seen in the Summer of 1916. Designed by Engineer Balla, the train was armed with two 76.2mm Model 1902 guns. Built during the Summer of 1915 at Kiev, it later served with the Ukrainian Army. The armoured engine is a Class Ow, and the second wagon in line is a sixwheeler armed with nine machine guns, one of which is on an anti-aircraft mounting. Note the false embrasures painted black.
_(Photo: Maxim Kolomiets Collection)_
Armoured Train _General Annekov_ of the 8th Railway Battalion of the Russian Army. It was in action on the South-West Front where it was captured by the Bolsheviks. It was then sent to fight in Finland.
_(Photo: Maxim Kolomiets Collection)_
### The first armoured trolleys
The Russian Army rapidly recognised the need to deploy motorised combat vehicles on the railways, which did not emit the telltale smoke of steam engines. Several trolleys were built in the workshops in Vologda, Odessa and Kiev, but they were restricted to secondary duties on account of their weak armament. The Army's desire to deploy more powerful units led to the design of the _Zaamuriets_ railcar. At the same time, fifteen unarmoured trolley chassis were ordered from the British firm Drewery Car Co. Ltd., to be built by Baguley Cars Ltd (Burton-on-Trent), in 1917–18, and to be armoured on their arrival in Russia. With the outbreak of the Revolution, only chassis Nos 906 to 913 had been shipped from Liverpool, and the others remained in England. It is not known whether the armoured hulls were mounted on any of the chassis. Lastly, armoured trolleys were built according to local requirements and resources.
Armoured trolley of the Russian Army built in Kiev, bearing the insignia of the railway troops. It appears to be heavily armed, with four Colt Browning machine guns in turrets, and has a cupola in the centre between the turrets.
_(Photo: Maxim Kolomiets Collection)_
Two of the four trolleys designed by Captain Mescherinov from February 1915. They appear to be armed with Vickers machine guns. Trials took place using three Russo-Balt Type C armoured cars and one Renault. In June 1916 a platoon was formed which continued to carry out experiments but with some difficulty due to the extremely slow delivery of materials. In April 1917, the unit was to have been sent to the Romanian front, but with the stirrings of the Revolution it remained in action with the 2nd Railway Brigade during the following Summer. The ultimate fate of these trolleys is not known.
_(Photo: Paul Malmassari Collection)_
One of the two trolleys built in Odessa during the Revolution. Weighing 7 tonnes and armed with two machine guns in turrets, they had a maximum speed of 40km/h (25mph). This one is named _Strela_ ('Arrow').
_(Photo: Maxim Kolomiets Collection)_
The draft plan for the _Zaamuriets_ railcar. The semi-spherical turrets have not yet been raised. The overall form of this 'motorised wagon' – to use the contemporary description – is quite modern.
_(Drawing via Maxim Kolomiets)_
_Zaamuriets_ prior to its conversion by the Czechoslovaks. The 57mm guns are still in place. The Czechs would replace them with 76.2mm Putilovs (see the chapter on Czechoslovakia), but the heightening of the turrets was carried out in Odessa.
_(Photo: Paul Malmassari Collection)_
A plan of the final version of _Zaamuriets_ / _Orlik_.
_(Drawn by the Author)_
### From the Civil War to the Great Patriotic War (1917–1945)
### The Red armoured trains of the Civil War
At the beginning of 1917, Russia possessed 500,000 wagons and 20,000 steam engines. By 1919, there remained just 30,000 wagons and 2,000 engines in service, thanks to the failings of the new organisations which had been created, despite the fact that ironically the railway workers had been the group most heavily indoctrinated by the Bolsheviks in the years leading up to the Revolution. Despite the scarcity of rolling stock for the transport of essential goods, the first armoured trains of the Revolution had to be converted from existing wagons, on the orders of the Soviets. These trains were created in Petrograd in November 1917, under the direction of the VBK, the Provisional Armour Bureau. On 20 December 1917, the Executive Committee elected during the Second Pan-Russian Congress on Armoured Vehicles received the task of organising the armoured units. But systematic construction did not begin until the formation of the military technical organisation 'Centrobron', on 31 January 1918. By that date, twenty-three trains were already in service, with a large number under construction. The best-equipped factories were the naval construction yards and the railway workshops, such as those in Kharkov, Leningrad, Putilovak, Isorak, Balhjska and Skorochod.
An improvised Bolshevik armoured train (note the numerous red flags), converted from modified covered vans, probably at the start of the Revolution: they have thick internal armour as can be seen in the embrasure, and the roof has an opening for deploying a light artillery piece.
_(Photo: Paul Malmassari Collection)_
A basic division into two classes was introduced to try and standardise the anarchic proloferation of armoured wagons:
1st Class
Train No 1: safety wagon/ artillery wagon (75mm)/armoured engine/safety wagon, the armament also including twelve machine guns and two mortars.
Train No 2: safety wagon/partially-armoured artillery wagon (100mm or 150mm gun)/armoured engine/safety wagon.
2nd Class
Train No 3 in support with ammunition and supplies.
On 6 October 1919, a partial reform laid down the composition of the ' _Desantniy Otryad_ ' or Assault Detachment. With a strength of 160 infantrymen, plus forty-seven mounted men and a two-gun machine-gun section, this substantial reinforcement allowed a major increase in the radius of action of the train, extending its reconnaissance range and assuring close-in protection. To carry the men and horses, between twenty and thirty wagons were added to each train. For long-range observation, certain trains carried captive balloons of German (Parseval) or French (Kako) manufacture, linked to their train by telephone.
On 5 August 1920, the Revolutionary Council established three categories of train:
1) Heavy Assault Armoured Trains Type A1 (in wartime, crewed by 162 men) or Type A2 (with a reduced crew of eighty-six men), to comprise:
– safety wagon(s).
– artillery wagon (two 76.2mm Model 02 guns in turrets and five to eight machine guns).
– armoured engine.
– second artillery wagon armed similarly to the first.
– safety wagon(s).
The assault detachment of Type A1 Trains comprised 265 infantry and thirty-five cavalry; that of Type A2 Trains would comprise only infantry, totalling 234 men.
2) Light Armoured Trains Type B (subdivided into categories B1 to B6 according to the gun calibre, crewed by forty-three men), to comprise:
– safety wagon(s).
– artillery wagon (two turret-mounted guns with a calibre less than 152mm).
– armoured engine.
– safety wagon(s).
3) Light Armoured Trains Type V (subdivided into categories V1 to V6 according to the gun calibre), to comprise:
– safety wagon(s).
– artillery wagon (one turret-mounted gun with a calibre less than 152mm and one machine gun).
– armoured engine.
In these defined configurations, the trains would carry out only combat functions, logistics being catered for by accompanying trains which would be unarmoured, carrying the men's kit, the galley, the cells, sleeping accommodation and repair equipment. Accordingly, the Type A1 Trains would be accompanied by a support train of twenty-three wagons, and the Type A2 by a train of twelve wagons. Type B and Type V Trains would be supported by rakes of nine wagons.
Within the Red Army, each separate army formation (made up of five army corps) had an armoured train brigade under its command. In action, the basic formation was the section, in which Types B and V trains provided support to Type A trains. When necessary, they provided artillery support to disembarked assault groups. The reconnaissance function devolved to a squadron of aircraft which could act as necessary as fighters or bombers for attacks on enemy trains or stations and key lines.
When advancing, the section spread out as follows, using one or two tracks:
– armoured reconnaissance trolleys 1–2km in advance.
– light armoured train.
– heavy armoured train.
– support train.
– rearguard light armoured train.
Trains armed with artillery were divided into two broad categories:
– the 'Bepo' Trains (abbreviated to 'BP') which were armed and armoured trains, utilised for attacks and raids.
– the 'BB' Trains which were composed of railway guns. This second classification included Type M Trains defined under the 1920 rules as intended for coastal defence.
Red armoured train captured by the Czechoslovaks. The armoured wagon is a wooden variant of the metal-panelled mineral wagons.
_(Photo: Paul Malmassari Collection)_
A far superior design, issuing from an efficient technical/industrial base, the revolving casemate of this train is carried on a ten-wheel wagon. Note the two complete rounds of ammunition presented for the photographer.
_(Photo: Maxim Kolomiets Collection)_
The 'Sormovo' type wagons, named for the factory which built them, were typical of the high quality of the armoured trains of the young Red Army. A central observation tower would be added in 1931 when these wagons were modernised in Military Depot No 60. Note the profile of the armour on the engine. The guns are 76.2mm Model 1902s.
_(Photo: Maxim Kolomiets Collection)_
### The White armoured trains
The Red Army, which despite the best efforts of Trotsky was in a chaotic state of disorganisation, faced the Army of Volunteers, better known as the Whites. Formed mostly of officers who had escaped the Communists, the White Army attempted to overthrow the new regime by carrying out a pincer movement against Moscow from the south and the east. Their first armoured trains were war prizes, which were immediately turned against their former Red owners, then as they went from success to success, the recapture of stations and railway workshops allowed the Whites to improvise new trains of their own.
On the Siberian Front, the situation was different in that, by tentative agreement between the Allies, the role of guarding the railway network and in particular the Trans-Siberian Railway, was undertaken by the Czechoslovaks and the Japanese. It seems that the White army of Admiral Kolchak possessed no proper armoured trains, while another White leader, Ataman Semenov, had seven. There was no love lost between the trains of Semenov and the Allies, especially the French and the Americans. Their career ended badly: sent to crush the revolution in Irkutsk on 26 December 1919, they were blocked by the derailment of a goods engine sent to crash into them. Withdrawing to the East, they began fighting with American troops at Verkhne-Oudinsk and, according to one American source, were 'taken out with grenades'.
General arrangement drawing of the standard bogie wagon which would serve as the base for armoured trains built by the Russians, the Czechoslovaks, the Japanese etc, from the Russian Civil War to the Second World War.
_(Drawing by the Author)_
Denekin's army, operating on the Southern Front, had very few armoured trains, apart from those captured from the Reds. Under Wrangel, the Army of the South had eight armoured trains, including three commanded by Captain Wagner, a German officer fighting in the White ranks. The fiercest fighting they endured took place between 25 and 27 October 1920 on the Sivasch Dike, the last link between the Crimea and Northern Tauride.
One of the armoured trains controlled by Ataman Semonov. Note the effective protection for the bogies on the van, which has internal armour. On the other hand, the artillery piece on the leading flat wagon, at least at the time this photo was taken, has no protection at all, lacking even a gun shield.
_(Photo: Paul Malmassari Collection)_
A wagon from one of the Red trains captured by the Whites, probably No 96 _Red Hurricane_. The upside-down chevron insignia of the Whites became the emblem of the Armed Forces of Southern Russia (formed in April 1919), until it was replaced in April 1920 by the white, blue and red roundel. Recaptured by the Reds, this train was renamed _Béla Kun_ (after the Hungarian Communist leader in power from March to 1 August 1919, who later became a political commissar in the Red Army).
_(Photo: Pierre Touzin Collection)_
203mm naval gun of the 2nd Heavy Battery in 1917. It fought the Germans in February 1918 at Pskov then served during the Civil War.
_(Photo: Paul Malmassari Collection)_
The final Red offensive, launched with 85,000 men on 15 October 1920 in temperatures of -15º, pushed the White forces back and threatened to cut off their retreat to the Crimea. The famous cavalry under Budenny, 25,000 strong, was repulsed on the 17th, but renewed their attack on the 20th. Out of eight White trains, five had to be abandoned together with many guns and their ammunition. While Wrangel sought sufficient ships to evacuate his troops and civilians, the last armoured trains _Ivan Kalia_ , _Dimitri Donskoï_ and _Officier_ fought a delaying action on the dike. On the Red side, the troops were supported by eight armoured trains. At dawn on the 26th, the White trains enjoyed the support of the artillery batteries harassing the Reds. The latter, however, succeeded in landing 4km to the east of the railway line, which rendered the White positions untenable. At 10 o'clock on the 27th, the _Dimitri Donskoï_ was destroyed by artillery fire. The surviving two trains slowed down the Red advance up until 3 November 1920 which saw the end of the White presence in the Crimea.
### The campaigns of the Red Army
The civil war against the Whites ended in 1920, but the Bolshevik leaders, driven by their crusading zeal, decided to export their revolution, so the young republic attacked Poland, the Baltic States, the Ukraine and Finland, in the hope of creating a wave of Communist uprisings throughout Europe.
The Polish campaign began with a Polish raid which got as far as Kiev in April 1920. In response, two Red armies threatened Warsaw from the end of July up until 13 August. Commanded by Piłsudski, and aided by the French, the Polish Army regained the upper hand, turning the Russian withdrawal into a rout. During the two months of warfare, the railways played a key role. The Polish railway network was the result of construction by three companies which were formally Prussian, Austrian and Russian respectively. Of the three regions, the first was the densest and the best maintained, while the third was handicapped by the interaction of the standard gauge with the broad gauge, installed according to the whims of the occupying powers. This gauge difference in what was the principal combat zone would be a constant problem when deploying armoured trains. On the Russian side, a state of siege was declared in a zone reaching 50km on either side of the rail tracks, in order to discourage sabotage. As a result of the Polish victory, the captured Bolshevik armoured trains would be taken into Polish service and renamed.
This railway gun platform of the Russian Navy, cut down from a high-sided bogie wagon, is curiously armed with a British 60-pounder BL gun (127mm calibre). Note the white flags with the blue cross of Saint Andrew, used by the Russian Navy since 1712.
_(Photo: Paul Malmassari Collection)_
The Red armoured train (initially named _General Annenkov_ ) following its capture by the Finns. It was subsequently used by the Germans of the _Freikorps_ , before being incorporated into the Finnish Army which used it, regularly modernising its wagons, up until the Second World War. Note that in its initial form the roof had only one walkway with a single handrail. The gun is a Russian 76.2mm.
_(Photo: Paul Malmassari Collection)_
On the Finnish front, the war there also ended with the defeat of the Red forces. The armoured trains in this theatre were essentially the arm of the Reds. Russian intervention was restricted basically to technical support, the railway workshops which were now Finnish having been Russian up until the Revolution. On the other hand, the direct railway link between Petrograd and Viipuri allowed the Bolshevik trains to come to the aid of the Finnish Reds. It seems that the latter received three or four trains during the war. One of them was captured at Säiniö in 1918. Comprising an armoured engine and two modern armoured wagons each with two turrets armed with 76.2mm Model 02 guns, it was named _Kerenski_. It was employed in the attack on Lahti and had to cross the bridge over the Koria River in three sections due to its weight. It was finally captured intact on the afternoon of 23 March, after its crew had fled.
An example of the significance of the armoured train in Soviet revolutionary mythology: the play by Svevolod Ivanov, _Armoured Train 14-69_ , seen in the above photo being performed on 11 December 1934, and below is the commemorative stamp issue which was dedicated to the playwright in 1965. Despite the fact that the armoured wagon on the stamp appears to be of a later type, the play was set during the Revolution.
_(Photo and postage stamp: Paul Malmassari Collection)_
In 1975, the myth was revived by the publication of the novel _Our Armoured Train Nicolaï Grigoriev_. Note the resemblance between the leading wagon and the casemate wagon of the armoured train of the 4th Siberian Railway Regiment.
_(Illustrations: Paul Malmassari Collection)_
### The end of the Civil War and the Reforms of 1929
Despite the Bolshevik victory, even while the final Cossack and separatist revolts were coming to an end, fighting continued between the Red Army and various 'Green' peasant factions, and local bands of thieves and bandits. The improvised armoured wagons were returned to civilian use, while the better-designed trains were carefully preserved. It is thought that by the end of the conflict with the Whites, 103 armoured trains had been built and used. During the period 1921 to 1941, the best trains were retained, new wagons joined the fleet, and an ongoing attempt at standardisation was made in order to rationalise production. Thus, the construction of the engines was divided between three principal centres: Podolsk for the Class PB, Kolona for the Class KB and Kharkhov for the Class KhB. In 1923, the armoured trains came under the control of the Artillery Department.
The results obtained thus far encouraged the authorities to improve this arm. An operational study resulted in the Provisional Rules of June 1926, which were immediately put to the test in the Summer Manoeuvres. The definitive version was published in August 1929, in the same volume as that for Tanks and Armoured Cars. The new organisation was laid down as follows:
– light armoured train Type A.
– heavy campaign armoured train Type B,
– special armoured train Type ON.
Their composition was to be:
1) Light armoured train Type A (160 men) supported by a supply train of twenty-nine wagons (or eleven wagons depending on the size of the crew):
– safety wagon.
– safety wagon.
– artillery wagon (two 76.2mm Model 1902 guns and eight Maxim machine guns).
– armoured engine of Class PB, KB or KhB.
– artillery wagon identical to the first.
– safety wagon.
Between 1926 and 1939 new gun wagons were built in order to increase the anti-aircraft capabilities of the trains: armament was the heavy 12.7mm machine gun together with the 76.2mm ZP Obr. 1914g., or even two 37mm Zenitnaya Pushka Obr. 1939g. cannon.
2) Armoured train Type B (supported by a rake of twelve wagons):
– safety wagons.
– artillery wagon (106.7mm Pushka Obr. 1910/30g. gun or 121.9mm howitzer).
– armoured engine of Class CH or KB-2.
– artillery wagon (106.7mm and 76.2mm ZP Obr. 1914g. guns). or
– artillery wagon (122mm Gaubitza Obr. 1910/30 gun/howitzer, then an Obr. 1909/37g.)
– safety wagons (152mm howitzers could be mounted on these wagons).
3) Armoured train Type ON (the descendant of the Type 'M' trains, supported by a rake of twelve wagons):
– armoured or partially-armoured engine.
– two armoured wagons (106.7mm or 121.9mm gun).
– armoured wagon (76.2mm gun).
– three armoured ammunition wagons.
– two searchlight wagons.
Additional armament included a Maxim anti-aircraft machine gun.
A new tactical organisation was also introduced. The basic tactical unit would now be the battalion, composed of two light trains and one heavy train. In Europe, it was envisaged to use the armoured trains in support of the ground troops, while in Asia they would form the central part of forces committed to an attack. In combat, the five trolleys of the section, grouped together for administrative purposes, would be divided between the trains, primarily for reconnaissance, then to act as liaison and maintenance units.
At the time of the Reform, it was estimated that there were thirty Type A, twelve Type B and nine Type ON trains in service. Several series of manoeuvres enabled the new organisation to be tried out, notably those of September 1929, during which the stated objective was to test 'the co-operation with the infantry and the cavalry'. The principal problem noted was the lack of liaison between the infantry and the armoured trains group, whose commanders were not part of the decision-making process. The result was that during withdrawals, the trains tended to be left behind without covering units. Lastly, the capacity to transport cavalry during an advance was felt to be essential.
In 1931, the Red Army began research into special ultra-light wagons for armoured trains, and some were even built in Leningrad. Military Depot No 60 in Briansk was primarily responsible for studying the new equipment. Their research momentarily halted the reorganisation which was underway, and had an influence on the type of armament carried. In particular, the heavy armoured trains saw their artillery reduced to two heavy guns, four heavy machine guns and thirty-two anti-aircraft machine guns. It was estimated that in 1931 the Red Army could count on the use of forty trains, of which twenty-five were light, twelve heavy and from three to six Type ON, all under the Army Motorisation and Mechanisation Command. By 1932/33, there were sixty trains in service, and by 1934, ninety-two.
Although this Reform changed little in the ongoing rebuilding of the force, it did however define the assignments of the command structures of the battalions and regiments, at a time when interest in this arm of service was turning more towards the kind of usage envisaged by the Western Powers, namely anti-partisan action and keeping the railway network open. Finally, it introduced the Type W train, designed for combat roles requiring armament and armour protection similar to that of railway guns. Their composition was to be the following (plus a ten-wagon supply train):
– armoured engine.
– two armoured wagons carrying 152mm or 203.2mm artillery pieces.
– one armoured ammunition wagon.
– one armoured trolley.
Several wagons for the Type W trains were stored at Revall (Tallinn), which principally came from the Estonian arsenal. The armament appears to be 130mm Vickers naval guns.
_(Photo: Paul Malmassari Collection)_
Captured near Tallinn after it had been immobilised following the destruction of a bridge (or perhaps even following sabotage by the crew), this train corresponds to Type W.
_(Photo: Paul Malmassari Collection)_
Shortly after its capture, the engine seen here was put back into service by the Wehrmacht. But note that the lower armour panels have not been refitted, probably due to damage suffered during the derailment. One can read the class designation 'Oz' on the buffer beam.
_(Photo: Paul Malmassari Collection)_
Building of the Type BP-35 armoured trains began in 1933 in the 'Krasnoye Profintern' factories in Briansk. In all, forty-seven units were delivered to the Red Army. Production ended with the evacuation of the workshops in August 1941. Their successors are described below.
BP-35 type armoured train, with wagons from Military Depot No 60, recognisable by their cylindrical turrets, here seen armed with 76.2mm M. 1902/30 guns. From four to six machine guns were divided between the hull and the turrets. The engine in the middle is a Class PR-35 which carried either 10 tonnes of coal or 6 tonnes of fuel oil.
_(Photo: Paul Malmassari Collection)_
In its heavy version, the train comprised two wagons similar to these shown here, armed with a 107mm Model 1910/30 gun. An armoured train of this type weighed 400 tonnes and could cover a distance of 120km (75 miles) at a maximum speed of 45km/h (28 mph) between refuellings.
_(Photo: Paul Malmassari Collection)_
### The Finnish War and the Great Patriotic War
For the war with Finland, the Soviet Union deployed the 8th Special Armoured Trains Division in the Karelia Isthmus from January to March 1940, with the MBV-2 prototype and the sixteen (light) and twenty-one (heavy) armoured trains used for artillery support.
At the time the Soviets mobilised to face the German invasion in June 1941, there were nine armoured train battalions in existence (the 4th and 5th in the West, the 1st at Kiev, the 7th in the Caucasus, the 10th in Western Asia and the 9th in the Far East), with a training regiment at Briansk, one battalion of armoured trolleys, thirteen independent light armoured trains and two independent heavy trains. The Red Army and the NKVD each had their own armoured trains, but the NKVD was orientated towards internal security rather than front-line combat. The Army had nineteen heavy trains, thirty-four light trains, nine trolleys and a certain number of armoured railcars. For its part the NKVD had thirty-six railcars, twenty-five armoured engines and thirty-five wagons, as well as infantry and cavalry units.
A Soviet engine captured by the Finns at Karhumäki on 9 November 1941. The panels giving access to the wheels and rods appear to generate a great deal of interest.
_(Photo: Paul Malmassari Collection)_
Although we are in 1941 here, these wagons were directly derived from their counterparts in the Civil War. The small number of loopholes piercing the sides is surprising, especially as it is obvious that plates have been fixed over former openings. It appears that an access hatch has been fitted under the floorboards.
_(Photo: Paul Malmassari Collection)_
An NKVD armoured train complete with safety wagons, the unarmoured engine in the middle and two heavy trolleys. The second of these has suffered severe damage to the point where a part of the hull has collapsed.
_(Photo: Paul Malmassari Collection)_
Evidently after the launch of Operation 'Barbarossa' local authorities decided to create a number of new armoured trains in the factories capable of constructing them. A wide range of different designs resulted, in which one can recognise features from previous trains from the Civil War up to the BP-35s. The creation of a certain number of new trains was evidently decided upon following the German invasion, on the initiative of the local authorities and in those factories capable of building armoured trains. A great variety of different designs resulted, in which one can recognise several distinct features of previous trains from the time of the Civil War up to the BP-35. They all demonstrated a remarkable ability for adaptation, to the detriment of the quality of finish which took second place given the urgency of the situation. During the Great Patriotic War the armoured trains were employed in groups, and supplied fire-support for attacking troops, and if necessary they covered troops forced to break off contact, the trains pulling back after the main body had withdrawn. But apart from desperate situations, standard Soviet tactics forbade the trains from taking up static defensive positions or engaging in delaying actions, which would have risked their loss. One constant feature was that most wagons were equipped with two turrets, and in exceptional cases with three.
All the units which were available and capable of combat were thrown into the fray. The Germans encountered wagons which sometimes dated from the Civil War, such as these two shown here. This confirmed in the minds of the Germans that this type of arm was definitely obsolete, and led to them delaying the creation of their own modern armoured trains.
_(Photo: Paul Malmassari Collection)_
The gunlayer who aimed a HE shell at the cab window must have been a crack shot. But the solidity of the Russian armoured trains, and their resistance to the guns employed by the German Army in the early stages of the campaign, must have been a surprise similar to that of the first appearance of the T-34 tanks.
_(Photo: Paul Malmassari Collection)_
Unidentified armoured train captured at Nikolaïev in the Ukraine. The turrets which equip two of the four wagons are similar to those on the trains built in the Crimea. To our knowledge, no photo shows which engine would be attached.
_(Photo: Paul Malmassari Collection)_
This armoured train captured at Kiev in August–September 1941 is armed with a turret from a T-26 tank on the leading wagon, and three turrets from captured Polish 7TP tanks. The engine is apparently armoured only around the cab, which is probably the result of its urgent conversion.
_(Photo: Paul Malmassari Collection)_
The T-26 Model 1933 turret in the chase position with its 45mm gun (here destroyed by its crew) gives anti-tank capability, and the first compartment of the following wagon carries an unidentified gun, possibly a 57mm naval piece arranged for plunging fire.
_(Photo: Paul Malmassari Collection)_
This photo of the second wagon shows two interesting features. Firstly the curved armour protection, which is quite rare (see the chapter on China), and secondly the mounting of two turrets from Polish 7TP (twin-turretted) tanks. The right-hand turret on this wagon, and the turret on the wagon in front of the engine, both come from the 2nd prototype 7TP. This tank had served at No 1 training centre in 1939 before being captured by the Russians. Note the slot in the turret appliqué armour which allowed the fitting of a 13.2mm Hotchkiss heavy machine gun in Polish service.
_(Photo: Paul Malmassari Collection)_
Another type of train, this time built on the lines of the BP-35, with two turrets (here from two different T-26 tanks: on the right a T-26 Model 36, on the left a BT-5 or T-26 Model 35) and four machine guns in the hull.
_(Photo: Paul Malmassari Collection)_
An armoured train for the narrow gauge captured at Tallinn (Reval up to December 1918) in Estonia.
_(Photo: Paul Malmassari Collection)_
One of the turretted wagons of the narrow-gauge train. A trolley was also captured on the same day.
_(Photo: Paul Malmassari Collection)_
The only photo we know of this wagon of unusual dimensions, and also an end door with identical doors at the sides. It appears that the turret from a tank or an armoured car has been mounted in the centre of the roof.
_(Photo: Paul Malmassari Collection)_
Armoured Train No 1 of the 66th Battalion, famous for its turret from a KV-II tank. In the centre, the turret from a T-34/76 model 40, without its usual mantlet, and fitted instead with a 45mm gun for anti-tank use. In the front turret is a 76.2mm gun.
_(Photo: Paul Malmassari Collection)_
At the rear of this train is a wagon built on the lines of the BP-35, armed with a 76.2mm M1902/30 Divisional Gun, the modernised version of the First World War weapon. The polygonal turret is mounted on the engine tender, and just visible is a T-34 turret identical to that on the front wagon.
_(Photo: Paul Malmassari Collection)_
An armoured train captured incomplete in the ruins of a factory in Kerch. Note the imposing size of the command tower built on top of the tender, and the 76.2mm gun. The central turret is from a T-26 S.
_(Photo: Paul Malmassari Collection)_
An identical wagon which saw action in May 1942. Evidently the Germans felt they were of interest as shortly afterwards both wagons were to be found at Rembertow. Note that the gun is a 76.2mm M1902/30, production of which ended in 1937.
_(Photo: Paul Malmassari Collection)_
A mixed armament wagon with a 37mm anti-aircraft gun, of Armoured Train _Tambow Kholkhose_. The panels were folded downwards when the gun was used in a ground role. It appears that vertical armour plates protect the rear of the firing position.
_(Photo: Paul Malmassari Collection)_
Armoured Train _For Stalin_ was captured with its two anti-aircraft wagons. Its engine may have inspired the design of the Class BR57 engines of the future Panzerzug BP 42 and BP 44.
_(Photo: Paul Malmassari Collection)_
Armoured Train _Ordshonykydshoviek_ seen here in November 1941, built in the naval yards in the Crimea. Its naval origins are betrayed by the armament in gun shields and the cylindrical observation cupola. These dual-purpose guns were capable of firing against ground and air targets.
_(Photo: Paul Malmassari Collection)_
Armoured Train _Za Rodinu_ ('For the Motherland') carrying the same armament as in the previous photo, captured at Bataisk (south of Rostov-on-Don).
_(Photo: Paul Malmassari Collection)_
The armoured trains built in the Crimea had a particular design which gave them the appearance of belonging to a family of such units, despite differences in detail. The guns are naval 76.2mm 34-K anti-aircraft weapons, with a ceiling of 9500m (almost 31,200ft).
_(Photo: Paul Malmassari Collection)_
The gun shield is open at the rear, another naval feature of these trains. The top surface of the breech is seen here with the 76.2mm gun at its maximum elevation of 85 degrees.
_(Photo: Paul Malmassari Collection)_
This wagon from Armoured Train _Voykoviec_ is built to the same design but the casemate on the right is armed with either a 76mm M/14 Putilov anti-aircraft gun or a field gun on a wheeled carriage, hidden in this photograph.
_(Photo: Paul Malmassari Collection)_
Another type of wagon, armed with two 76.2mm/30 Lender (8-K). In 1943, at least six of these wagons would be converted by the Wehrmacht and included in PZ 21, 23 and 26.
_(Photo: Paul Malmassari Collection)_
An armoured train knocked out of action in the Crimea in 1941. The intact wagon would be put back into service with the engine seen in the following photo, to form a train used for security patrols (designation unknown).
_(Photo: Paul Malmassari Collection)_
The engine of one of the Crimean trains. Its design does not follow that of the 'continental' trains and its armour is much smoother. In particular note the lack of inspection hatches for the wheels and rods.
_(Photo: Paul Malmassari Collection)_
Armoured Train _Worker of Kolomna_ has a design which is totally different to that of its contemporaries (January 1942), even if the wagons still have two turrets, armed with 152mm Model 1916 howitzers. Built in Kolomna, it belonged to the 55th Independent Armoured Train Battalion.
_(Photo: Maxim Kolomiets Collection)_
In the direct line of descent from the armoured trains of the Civil War, certain trains were built in workshops with less sophisticated equipment, using materials at hand: a turret from a KV-1 tank, and 76.2mm/30 Model 1914/1915 Lender (87-K) anti-aircraft guns.
_(Photo: Maxim Kolomiets Collection)_
NKPS-42 Type armoured train in its standard configuration. Note the similarity with the older BP-35, of which they were a simplified, but better protected, version.
_(Photo: Paul Malmassari Collection)_
During the first months of the German invasion, the armoured trains of various types which we have examined in the previous pages played an important role in resisting the invaders, even if a large number were destroyed. The locomotive repair facility at Poltava designed a new armour layout based on that of the BP-35. Designated NKPS-42, it offered better protection, but the lack of good-quality armour plate meant that the appearance of the trains tended to vary.
On a PT-33 wagon, this 76.2mm Model 1939 Divisional Gun in an NKPS-42 turret is an unusual combination, due to the differing availability of artillery pieces in the particular region.
_(Photo: Paul Malmassari Collection)_
This view of a turret from Armoured Train _Marshall Budenny_ allows us to note the protection afforded to the gun in an NKPS-42 turret.
_(Photo: Paul Malmassari Collection)_
Coupled to an NKPS-42 type train, this engine seems to be equipped with a condensing tender. The USSR began to show interest in this technique in 1935, which had the dual advantage of reducing the plume of smoke, while tripling the range before stopping to take on water, due to the recycling system. Apart from this feature, the remainder of the engine is classic, with a command cupola on the cab roof and an anti-aircraft position on the tender.
_(Photo: Paul Malmassari Collection)_
Engine of a Type OB-3 armoured train painted with one of the many personal, geographic or patriotic slogans. Here we see the popular 'For Stalin', used on several trains.
_(Photo: Paul Malmassari Collection)_
The Type OB-3 trains were designed to overcome the problems experienced with the NBP-35 and NKPS-42 wagons due to their dimensions and their weight, and also the fact that bogie wagons were much more difficult to re-rail than four-wheelers. To meet the production target of sixty-two armoured trains (thirty-two battalions) to be ready by 1 January 1942, the State Defence Committee decided to standardise on the Type OB-3 train. The artillery wagons were shorter, armoured from 30–80mm, and armed with a single gun. The production of the Type OB-3 was undertaken in nine factories and forty-three rail depots, but by the planned date only two complete trains had been produced, with another twelve, seventeen and then twenty-six arriving in the next three months respectively.
A wagon typical of the Type OB-3 trains. The armament, served by twelve men, could vary to a surprising degree according to the local supply situation: 76.2mm Model 1902 guns, 76mm Model 1927, 76mm anti-aircraft Model 1914 and 76mm L/10 tank guns. As in this photo, even French or Polish 75mm Model 1897s from the Civil War were carried.
_(Photo: Paul Malmassari Collection)_
The engine normally used was a Class Ov or Ok, armoured to between 30mm and 80mm. Some twenty Type OB-3 trains would be destroyed or captured, mainly in 1942, like this train photographed in April 1942.
_(Photo: Paul Malmassari Collection)_
The Type BP-43 trains would be the final type built during the war on the Soviet side (twenty-one for the Red Army and a few for the NKVD). They represented a development of the OB-3: each wagon carried only one turret and three machine guns, and two coupled together provided the equivalent firepower of an old BP-35 wagon, but offering a smaller target. One of the more ingenious wagon designs, and one which offered the heaviest firepower, was incontestably the mixed armament wagons mounting sixteen M8 rocket-launcher racks, together with two 37mm Zenitnaya Pushka Pbr 1939g. anti-aircraft cannon. These wagons were produced for Trains No 659 _Kuzma Minin_ and No 702 _Ilya Mouromets_.
The PL-43 wagons which made up these trains were examples of the simplified solution which had been sought: the T-34 turret had an anti-tank capability, and it was mounted on a wagon offering a much reduced silhouette. The round opening in the side of the hull was a mount for a machine gun.
_(Photo: Maxim Kolomiets Collection)_
A PL-42 wagon from _For Stalin_ built at Kolomensa. The 76mm guns in T-34 turrets gave these trains powerful anti-tank firepower. Similar wagons were included in Armoured Trains _Kuzma Minin_ (in the next photo) and _Ilya Mouromets_. The central observation tower varied from wagon to wagon, as well as the lower armour skirt.
_(Photos: Paul MALMASSARI Collection)_
Seen here in the factory and below during a parade probably preceding departure on a mission, this type of wagon is derived from the hull of a T-34 tank, with the lines elongated to form an armoured wagon. In the photo below, on the right is a line of armoured wagons based on old T-28 tanks. Perhaps this is a changeover ceremony from the old wagons to the newer type.
_(Photos: Paul Malmassari Collection)_
A sketch showing the basic method of mounting the 'Stalin Organ' in a wagon, allowing 360-degree training. The same Soviet publication featured other mountings, for example on a river gunboat.
_(Illustration: All Rights Reserved)_
In late September 1941 the American illustrator Logan Reavis represented this tactical employment of Russian armoured trains. (For comparison he added a view of the last type of American Army armoured wagon, as used on the Mexican border.) With a certain degree of artisitic licence, the separate missions are reasonably well displayed, apart from the group of wagons spread out to repel an attack: such deployment was a favourite theme in illustrations intended for the public at large, but would have found little favour with armoured train commanders.
_(Illustration: Paul Malmassari Collection)_
### ARMOURED TRAIN ANTI-AIRCRAFT DEFENCE
Despite continuous growth in on-board anti-aircraft armament, the majority of Soviet armoured trains lost fell victim to air attack. In the battle for Smolensk alone, six were lost, all to Luftwaffe attacks. Although each armoured train carried its own anti-aircraft armament, special armoured wagons were built, which became more and more elaborate with greater and greater protection.
In addition, specialised anti-aircraft trains were introduced as a separate branch of the Soviet armoured train organisation, and some 200 such trains in all would be formed. The standard composition of each train was an engine and five wagons. Although the wagon chassis were unarmoured, the guns were provided with side armour protection generally 15mm thick, sheltering the gunners from bomb and shell fragments and small-arms fire. Their armament varied, and initially comprised 76.2mm guns, 37mm cannon and 12.7mm DShK heavy machine guns.
As a general rule, as each new armoured train battalion was formed it was allocated a PVO-4 AA defence wagon, for example initially armed with two 37mm cannon or two 12.7mm heavy machine guns. Each Type BP-43 train had two anti-aircraft wagons.
These two guns on anti-aircraft mountings are installed in a wagon at the rear of an unidentified armoured train (perhaps the train armed with a KV-II turret). Note the crude appearance of the gun tubs with their unfinished edges.
_(Photo: Paul Malmassari Collection)_
The anti-aircraft wagon coupled to _For Stalin_ with its 37mm Model 1939 cannon, followed by a second quite different wagon which was unique to this particular train.
_(Photo: Paul Malmassari Collection)_
A derailed PVO-4 wagon, allowing us a view of the internal arrangements, and the side panels in the lowered position. The 37mm cannon is mounted on a circular platform.
_(Photo: Paul Malmassari Collection)_
This wagon attached to Armoured Train No 339 photographed in 1942 carries a mixed anti-aircraft armament: a 37mm 61-K and a 12.7mm DShK Model 1938. It is probable that for the sake of standardisation, the base chassis was the same for both the OB-3 train wagons and the PVO-4 AA platforms.
_(Photo: Maxim Kolomiets Collection)_
The same armament is mounted on a different style of PVO-4 seen in 1942. An example of this design is on display in the Armed Forces Museum in Moscow.
_(Photo: Maxim Kolomiets Collection)_
The same type of wagon today in Moscow with two 37mm cannon. The other wagon on the left is a BP-43 type, modified with armoured compartments replacing the open end platforms.
_(Photo: All Rights Reserved)_
Narrow-gauge armoured train or anti-aircraft train at Tallinn in Estonia. The openbacked shield is of naval origin, with a 76.2mm (34-K) AA gun. An ex-tank or armoured car turret is mounted for local defence.
_(Photo: Paul Malmassari Collection)_
This anti-aircraft defence train is armed with 85mm M1939 guns. The unarmed wagons alternating with the gun wagons are equipped with rangefinders and other viewing devices, plus maintenance materials. Note that the base used for the conversions is the standard Russian Railways bogie flat wagon.
_(Photo: Paul Malmassari Collection)_
This wagon armed with two 37mm cannons has also three machine guns for close-in defence (one on each side and one in a turret). It is coupled in OB-3 type train No 664, and was built in the Kolomna factories. Note the similarity of its form with _Worker of Kolomna_ illustrated above.
_(Photo: Private Collection)_
### The armoured railcars and trolleys of the Red Army and the NKVD
As with other armies, the Red Army had noted that the vulnerabllity of armoured trains derived in part from their heavy weight and relative lack of flexibility. On the other hand, railcars (irrespective of their weight classification) had the speed needed for carrying out reconnaissance of the tracks. Contrary to the desire for standardisation, as far as possible armoured trolleys had used parts and equipment available in the areas where they were designed and built: motorised chassis, turrets and weapons, armour plates. In parallel, trolleys were developed from road-based armoured vehicles.
In 1938, the S.M. Kirov factory in Leningrad built several 'motorised armoured wagons' (MBV) which reached 80km/h (50 mph) and carried a dual-purpose armament for ground and antiaircraft use. The base vehicle used components and three turrets from T-28 tanks (which had been built in the same factory). The tank turrets were armed first with the 76.2mm PS-3 gun then the longer L-11 and F-34. The secondary armament comprised 7.62mm DT machine guns divided between the turrets, rear and sides, and anti-aircraft defence was provided by a quadruple Maxim mounting situated between No 2 turret and the command cupola. With a crew of just forty men, the railcar was practically the equal in firepower to an armoured train, being self-sufficient in ammunition with 365 shells, 10,962 rounds for the DTs and 22,000 for the Maxim machine guns carried on board, but was a great deal more versatile. The armour protection ranged from 16–20mm on the sides, the central command cupola and the turrets. The roof was armoured to 10mm. The whole machine weighed 80 tonnes and could reach 120km/h (75mph) on the 400h of its M17-T petrol engine. The prototype was tested during the Finnish War on the Viipuri-Viborg-Leningrad line in March 1940.
Viewed from the front, the MBV-2 was a battleship on rails. This version is the one equipped with T-28 turrets, and immediately noticeable are the false rails painted on the camouflage whitewash. Each electricallyoperated turret had a limited training arc, from front to rear respectively, of 280, 318 and 276 degrees. The twinaxle bogie was motorised whereas the three-axle bogie was simply a load carrier.
_(Photo: Maxim Kolomiets Collection)_
This machine was famous enough to feature on a Russian stamp issued in 2014 (part of the series on Glorious Towns, this one commemorated Tikhvin), along with a 203mm M1931 (B-4) howitzer and the Petlyakov Pe-8 bomber.
_(Stamp: Paul Malmassari Collection)_
Several models of armoured trolley were developed, using proven components, notably the turrets from T-26 or KV-1 tanks. One of the latter was mounted for example on the _Red Star_ railcar featured below. Other turrets were intended solely for use on special machines such as the D-2 railcars.
An unique example built in the Winter of 1942 and named _Krasnaya Zvezda_ ('Red Star'), with the designation KZ-1 painted on all four faces), this machine was equipped with a turret from a KV-1 tank, armed with a 76.2mm ZiS-5 gun. 11.72m (38ft 5½in) long by 2.48m (8ft 1½in) wide and 2.70m (8ft 10¼in) high, it weighed 60 tonnes in working order. Powered by two V-2K diesel motors it could reach a maximum speed of 43km/h (27 mph). One of its four 7.62mm calibre machine guns is visible here. It is not known whether it saw any action.
_(Photo: Maxim Kolomiets Collection)_
The D-2 railcars were produced in the factories in Lugansk and Orsk, which between them received orders for 200 units. They were armed with two 76.2mm guns and four machine guns. One successful innovation was the installation of a generator producing green smoke, which proved very successful in trials. There was no separate chassis, the running gear being bolted direct to the armoured hull as with the British Daimler Dingo. Used principally by the NKVD, many of these these railcars would be captured in 1941, and several were reused by the Wehrmacht (as PT 17 to 23).
_(Photo: Paul Malmassari Collection)_
This version is fitted with armour protection for the recoil cylinder, an arrangement rarely seen on armoured trains.
_(Photo: Paul Malmassari Collection)_
The BDT trolley was designed in 1935. It used the turret of a T-26 tank.
_(Photo: Maxim Kolomiets Collection)_
A BD-41 armoured trolley immobilised near the NKPS-42 armoured train to which it was assigned. This machine belonged to the 7th Independent Armoured Train Battalion. The turret comes from a T-26 Model 1931 tank, with a 37mm cannon and a 7.62mm DT machine gun. Around twenty BD-41 trolleys were built in Moscow in early 1942, and the last were still in service in 1944.
_(Photo: Paul Malmassari Collection)_
DTR armoured trolley. An example was included in PZ 10 (see the chapter on Germany).
_(Photo: Paul Malmassari Collection)_
Alongside the 'compact' trolleys built in workshops and intended solely for rail use, certain machines were converted from road armoured cars, such as the FAI-ZhD. There were two rail versions of the BA-64 ZhD, both based on the wide wheelbase variant. The first was designed by the Vyksinky factory in July 1942 and consisted of fastening rail wheels to the outside of the road wheels, a lengthy procedure similar to that used for the BA-20 ZhD. Although the forward speed was 85km/h (43mph), speed in reverse was only 13km/h (8mph), a derisory performance when high speed in both directions was required for a rail reconnaissance vehicle. In addition, the gearbox broke down after prolonged driving in reverse, the engine cooling was insufficient when moving backwards, and the machine continually fell off the rails due to the wheel rims being too small.
The shape of the FAI-ZhD was somewhat archaic, and even the wire wheels for use on rails appear fragile.
_(Illustration: All Rights Reserved)_
The first model BA 20M was rarely photographed by the Germans, being already very old by the time of 'Barbarossa'. It was easily identifiable by its cylindrical turret.
_(Photo: Paul Malmassari Collection)_
A production-model BA20 trolley with conical turret, in its road configuration, and the rail wheels attached to their standard fittings. Note the base of the movable antenna on the left-hand side.
_(Photo: Paul Malmassari Collection)_
On this BA 20M (recognisable by its frame antenna) we can clearly see the three attachment points for the wheels not in use: one on each side of the bonnet and a long axle rod with a hook at the rear, above the petrol tank.
_(Photo: Paul Malmassari Collection)_
This second BA-64B rail prototype from the GAZ factories was designed in June but only emerged from the Gorki works in November 1942.
_(Photo: All Rights Reserved)_
The second version had better on-rail stability but the problem of rearward driving remained, and no production models were built. However, in the Summer of 1944, the Moscow wagon repair depot did fit several BA-64 and BA-64B models with rail wheels for use with armoured trains.
A small production series of BA-6-ZhD models was produced in 1936, convertible by fastening rail wheels to the outside of four of the road wheels. This method was continued for the BA-10 armoured cars.
The BAD-2 ZhD was as interesting as it was bizzarre. It was developed from the original BAD ( _Brone Avto Drezine_ ) armoured car designed in 1932 at the 'Bolshevik' factory in Leningrad. Its boat-shaped hull was designed to give it amphibious capability, which was the subject of many research projects during the 1930s. The rail conversion was studied by the 'Izhorski' factory and was added to a well-armed vehicle, which could be considered as suitable for its proposed role. In fact, the machine was never adopted, despite operational trials in 1932–4.
A BA-10 ZhD on road wheels, with its four rail wheels fastened to the hull rear. Note the lengths of caterpillar tracks also carried above these wheels. The machine has just been hit, and a crew member was cut down as he tried to exit the vehicle.
_(Photo: Paul Malmassari Collection)_
This view of a BA-10 ZhD being turned shows to advantage the large diameter of the rail wheels which would be fastened to the outside of the road wheels, thus avoiding a lengthy wheel change. The trolley version ran on only four rail wheels, two at the front and two at the rear.
_(Photo: Maxim Kolomiets Collection)_
Among the wide range of different machines built to face the advancing Wehrmacht, we also find unidentified models of trolleys.
It is interesting to note several projects which were studied during the war. The MBV-2 railcar gave rise to a variant mounted on the same two-and three-axle bogies, but more lightly armed, as shown by the scale model at centre right on page 406.
One Soviet engineer even proposed building a railcar of exceptional size, with a very heavy armament. Three turrets armed with 76.2mm guns were to be mounted on the cylindrical hull. Each of these main turrets was to have carried a smaller turret on top, the sub-turrets at the ends to be armed with four anti-aircraft machine guns and the central one with a pair of 45mm anti-tank guns. Twelve machine guns were to be mounted in the hull sides, plus two flamethrowers in unspecified locations. The armour protection was to have been 25mm, 30mm on the turrets. The electric drive would produce 950hp, propelling the machine at up to 55km/h (34mph). This is illustrated by the scale model on page 406 (bottom).
The BAD-2 measured 5.28m (17ft 3¾in) long by 2m (6ft 6¾in) wide and 2.36m (7ft 9in) high. It weighed 4.6 tonnes, and was armed with a 37mm (Hotchkiss) cannon in the turret plus two 7.62mm machine guns. It was capable of maximum speeds of 65km/h (40mph) on rails and 50km/h (30mph) on roads.
_(Photo: All Rights Reserved)_
The rear turret armed with a 7.62mm machine gun could train over a wide field of fire. The propeller for amphibious operations is just visible beneath the hull.
_(Photo: All Rights Reserved)_
Among other design projects was one based on the NKVD D-2 railcars, but with four turrets, and an armament ranging from 76.2mm up to 127mm, on a total length of some 20m (65ft 7½in).
Two different views of a Soviet trolley captured and marked with large crosses in chalk. Note that the attached wagon differs in the two photos, which would indicate that the trolley has seen some use after being captured.
_(Photos: Paul Malmassari Collection)_
This machine was probably a front-line improvisation. The turret appears to belong to the BT-2 series of light tanks.
_(Photo: Paul Malmassari Collection) (Model by Paul Malmassari to 1:200th scale)_
Note the completely unarmoured radiator projecting from the hull side.
This proposed design would have measured 24m (78ft 8¾in) in length, weighing 145 tonnes, with a crew of thirty-four men. The cylindrical hull would have carried three T-28-type turrets, themselves carrying separately trainable subturrets. The ladders on the model give some idea of the gigantic propostions of the project, which however displays a streamlined modern shape.
_(Model by Paul Malmassari to 1:200th scale)_
### Armoured Trains from the Cold War to the Present Day
The end of the Great Patriotic War did not see armoured trains disappear from the Soviet inventory. An armoured train was active during the suppression of the Hungarian Uprising in 1956 and also, up until the 1960s, another was permanently parked in a tunnel in a suburb of Berlin, according to former East German railway workers. Three important periods mark the modern history of these trains: the Sino-Soviet conflict, the wars in Chechnya (1994–6 then 1999–2000), and since 2010, the maintenance of order in the face of the growing insecurity in the republics to the south of Russia (Chechnya, Daghestan and Ingushetia). In addition, the continuing latent rebellion in the Caucasus region requires that appropriate railway security measures remain in force.
Between the late 1950s and the early 1960s, tension between the Soviet Union and China mounted over the question of the deliniation of the frontier between the two countries, and in particular the status of the island of Damansky (Zhenbao to the Chinese) situated on the River Ussuri which separates the two countries. In March 1968, two weeks of fighting ended in a Soviet victory, but both sides continued to build up their forces for a future confrontation. On the Soviet side, the under-developed state of the region made the garrisons almost entirely dependent on the Transbaikal and Trans-Siberian railway lines, as much for resupply as for troop movement. The latter line is situated only some 100km (63 miles) from the frontier and is therefore vulnerable to a mass attack. With the whole railway network plus 1,200 sensitive points to protect, only armoured trains had the necessary firepower, flexibility and mobility.
Locomotive Design Bureau No 65 at the Kharkov factory, which had specialised in the production of T-64 tanks and locomotives since it was opened, was charged with the design work. Railway and armoured vehicle components were taken 'off the shelf', copying the ideas followed during the Great Patriotic War. Initially, the turrets were to come from T-55 tanks and ZSU 23-4 _Shilka_ anti-aircraft armoured vehicles, armed with four 23mm AZP-23 cannon. The use of a diesel locomotive circumvented the problems of electricity or alternatively water supply. The locomotive was built in Lioudinovo, and the armoured wagons in Kalinine and Marioupol. The train was ready in 1970 and was tested, but never entered service as the frontier tensions had decreased.
When tension once more increased, the employment of armoured trains was again considered during the establishment of the Far East central command structure in February 1979.
The new concept was modular: each armoured train was to comprise a central train and several autonomous units, with tanks embarked. Each of these armoured attack groups was to be formed with a TGM-14 armoured diesel shunter, positioned in between two flat wagons carrying T-55 or T-62 tanks. At the rear of each platform wagon, a demountable armoured casemate was intended for an infantry detachment, who could observe using periscopes, communicate by radio and fire through loopholes. Each train could include up to five groups of two tanks plus twenty-five men. Thus organised, a train could cover 500km (300 miles) of the rail network, each group covering 100km (60 miles).
One of the prototype tank transporter flat wagons. Note the two unloading ramps, made practicable by the central coupling gear and the lack of buffers.
_(Photo: Maxim Kolomiets Collection)_
The tank transporter wagon carrying a T-55 is being towed by a BTR40-ZhD. Here the armoured case is not intended for transporting troops.
_(Photo: Maxim Kolomiets Collection)_
One of the production tank transporter wagons with the lateral armoured panels hinged upwards, seen here with a T-62 fitted with side bars as protection against RPGs. Note the armoured casemate immediately behind the tank. The unloading ramps are clearly visible in front of the tank. In operational use, a guard rail would be fitted at the rear of the tank to prevent the turret from firing into the rest of the train.
_(Photo: Maxim Kolomiets Collection)_
Armoured TGM-14 diesel shunter which propels the attack group.
_(Photo: Athol Yates Collection)_
A still from the propaganda film _Heirs of Victory_ , in which three combat groups are seen on exercises, with the two tank transporters coupled in front of and behind the TGM-14 diesel locomotive.
_(Film still: All Rights Reserved)_
The central train was formed from an armoured TG-16 diesel locomotive, a command wagon protected against NBC (Nuclear Bacteriological and Chemical) effects, since it was thought these trains could enter contaminated zones in the event of a nuclear attack. The wagon was armed with two 23mm ZU 23-4. Additional anti-aircraft defence was provided by an armoured wagon equipped with either two ZU-23-4 or ZU-23-2 mounts. The reconnaissance element was provided by two flat wagons transporting PT-76 amphibious tanks which were protected by lateral armour plates 2m (6ft 6in) high, and able to disembark. The rail reconnaissance company was formed from eight BTR-40 ZhD vehicles, which could be carried over longer distances on flat wagons fitted with rails. In 1969, several BTR-40s were converted into trolleys by using the same method developed by GAZ for the wartime BA64-ZhD. Disembarking them took less than five minutes.
The flat wagon transporting the PT-76 opens at the front or rear to allow the tank to disembark. On the left is the anti-aircraft wagon.
_(Photo: Maxim Kolomiets Collection)_
The BTR-40 ZhD is the road-rail version of the 4x4 troop transport. The conversion, which is permanently fixed, consists of adapting two rail guide axles in front of and behind the driven wheels, which remain in contact with the track and provide the motive power. The two cutaway steel plates attached to the rear of the hull are devices which, when fastened to the track, form a small oblique ramp to facilitate mounting onto and descending from the rails.
_(Photo: Maxim Kolomiets Collection)_
The version A of the BTR-40 ZhD was armed with a twin-barrelled 14.5mm KPVT anti-aircraft mounting. It is not known how many of these conversions made in 1969 were attached to the armoured trains. This example is on display in the armour collection at Kubinka. The two rail versions of the BTR-40 remained in service up until 1991.
_(Photo: Paul Malmassari Collection)_
**BTR-40 ZhD Technical specifications:**
Length: | 5m (16ft 4¾in)
---|---
Width: | 1.9m (6ft 2¾in)
Height: | 1.75m (5ft 9in) without armament
Ground clearance: | 27.6cm (10.9in)
Wheelbase: | 2.7m (8ft 10¼in)
Weight: | 5.8 tonnes
Crew: | 10
Max speed (rails); | 65km/h (40mph)
Max speed (road): | 75km/h (47mph)
Range (road): | 430km (270 miles); probably x 3 on rails
Armour: | 4mm to 15mm
Armament: | 1 x 7.62mm SGMB machine gun
| (BTR-40-A): 2 x 14.5mm KPVT heavy machine guns
The four trains which were built never went into action, and were stored at Chita, being regularly used for exercises. One of the trains helped with clearing the track of derailed rolling stock in 1986. In January 1990 they were reactivated to go into action during the uprisings in Baku and Sumqayit, to keep open the two key routes linking the South Caucasus with Russia. They arrived on station after the recapture of Baku, but remained active to protect the railway convoys. At the end of their tour of duty, they were gradually dismantled, with the exception of the locomotives.
When the Chechen war began, the railway engineers put a certain number of specialised trains into service, incorrectly described as 'armoured trains', which were intended to maintain and repair the rail network and remove mines. It was only at the end of 2002 that four genuine armoured trains were employed, named _Amur_ , _Baikal_ , _Don_ and _Terek_. Only the last of these included armoured wagons from trains previously taken out of service.
Their composition was generally as follows, with variations in the number and order of the wagons:
– flat wagon with ZU-23-2.
– flat wagon with BMP-2.
– flat wagon with T-62.
– armoured wagon, with fixed turret, for infantry weapons and grenade launchers.
– equipment wagon.
– one or two coaches for the crew.
– two or three safety wagons (carrying sand or ballast).
– one or two flat wagons carrying a signals vehicle.
– locomotive.
These TGM-14 diesel shunters and TG-16 locomotives were photographed in storage in a military depot in the Zabaikalsk district, after the four armoured trains were taken out of service. Note that the diesel shunter in the foreground does not have an armoured cupola.
_(Photo: Athol Yates)_
Armoured Train _Baïkal_ in Chechnya. Note the makeshift nature of the armour with two turrets and lateral sponsons. The body has been hastily constructed and attached to a commercial bogie flat wagon.
_(Photo: Maxim Kolomiets Collection)_
The _Terek_ communications wagon is based on an armoured tank platform on top of which a ZIL radio truck is secured and protected with planks and makeshift armour, including concrete blocks. The tarpaulin is probably used to break up the silhouette and certainly provides the crew with protection from the elements.
_(Photo: Maxim Kolomiets Collection)_
As originally built, this command wagon was armed with two twin 23mm ZU-23-2 or quadruple 23mm ZU-23-4 mountings. In the absence of an air threat in the Caucasus, here the crew of _Terek_ has replaced the AA mountings with observation positions and embrasures for firing at ground targets. Note the ventilators on the roof.
_(Photo: Maxim Kolomiets Collection)_
Directly inspired by the anti-aircraft wagons of the Great Patriotic War, originally this armoured wagon also mounted 23mm cannon. These various wagons are all based on the same design of bogie flat wagon.
_(Photo: Maxim Kolomiets Collection)_
A view of the interior of an anti-aircraft wagon. Here the original multiple-barreled heavy weapon has been replaced by either an NSV 12.7mm heavy machine gun, or a Kord.
_(Photo: Maxim Kolomiets Collection)_
In October 2002 a fifth train, the _Cosima Minine_ , joined the base at Hankala, which served as the supply depot for the trains. It had been built by an OMON unit on the base of commercial rolling stock, armoured with all the materials that could be found on site. In particular it transported a BMP-2 with additional protection provided by sleepers and other materials, which were also used on the other wagons of the train.
The armoured trains in the Caucasus are credited with an impressive performance, such as the clearing of mines from 1000km (over 600 miles) of track, the escorting of 100 troop trains, and reconnaissance missions covering the 32,000km (20,000 miles) of track between Russia and Chechnya.
Since 2004, the Russian Army has had a specialised railway unit, the ZhDk ( _Zheleznodoroznhiki_ ), split into four railway corps, twenty-eight brigades and an unspecified number of units, in charge of military transportation, and responsible for their correct functioning and their protection. The two armoured trains in the North Caucasus (Ingushetia) were activated by the 76th ZhDk based at Volvograd.
With the return of insecurity in 2010, the _Cosima Minine_ , the sole armoured train deployed by the Interior Ministry, was reconstructed and fitted with modern equipment. For mine clearance work, it is equipped with an M4K Kamysh which interferes with the radio detonation of mines up to 20km (12.5 miles) away. Its anti-aircraft defence is provided by two ZPU-4 armoured vehicles, ten AGS-17 automatic chaff launchers and a number of machine guns. Firepower is provided by a 30mm 2A42 cannon, and the 9P135 M anti-tank missiles of a BMP-2 armoured vehicle carried on a flat wagon and protected by a side wall of sandbags. As necessary, one or two T-62 tanks (115mm gun) can be added to the train. On its return to service in around December 2013, it was stationed either at Hankala to the west of Grozny or at Mozdok in North Ossetia, along with other armoured trains.
The other trains were supposed to have been dismantled after the end of the operations in the Caucasus. At the time of writing that order has been rescinded, the Russian Defence Minister having announced their reactivation as part of the modernisation of the armed forces. Certain sources consider that, apart from their value in assymetric warfare, they could form excellent platforms for the transport and firing of self-propelled artillery pieces such as the brand-new 152mm 2S19 Msta-S howitzer.
On display outside the Auto Vaz technical museum in Togliatti, this type of armoured train is clearly intended to protect a military zone or base, as the height of the wagons and the anti-aircraft turret would preclude them from operating within the normal railway loading gauge.
_(Photo: All Rights Reserved)_
The great length of the wagon allows for the loading of an armoured intervention vehicle with the use of inclined ramps. The turret appears to be an automatic 2M-3, armed with two 25mm 110 PM cannon.
_(Photo: All Rights Reserved)_
For railway maintenance and repair missions in high-risk areas, in response to an order placed by the Gorki Railway company, the firm of Arzamas produced this GAZ-5603J based on the BTR80 troop transporter. In fact the system of auxiliary rollers is identical to those used on the road-rail vehicles which can be seen in every modern railway worksite.
_(Photo: Alain Dupouy Collection)_
This armoured wagon on display today in the Ukraine, in the Armed Forces Museum in Kiev, raises several queries. The height of the T-10 turrets and the lack of lower armour skirts leads one to think this is a training vehicle. Note the external ladders and the handgrips on the sides at the level of the open-topped infantry compartment.
_(Photo: Paul Malmassari Collection)_
A photo of the railway version No 2 with its inspection platform deployed. The same chassis has been offered as a fire engine by the same factory, under the designation GAZ-59402.
_(Photo: Alain Dupouy Collection)_
A modern reproduction of an armoured train of the Great Patriotic War. We can pick out the features of several wagons: the one behind the safety wagon is a mix of Baltic-type wagons with the small lateral turret, and Armoured Train _Khunkhuz_. The other wagons demonstrate the different combinations used at the time.
_(Photo: Private Collection)_
On 30 April 2015, to mark the 70th anniversary of the victory of 1945, Russia issued a set of postage stamps commemorating military equipment, of which four featured armoured trains. From top to bottom are: _Moskovski Metropoliten_ ('Moscow Metro', Type BP-43), _Moskvitch_ ('Muscovite', Type OB-3), _Istrebitel Nemetskikh Zakhvatchikov_ ('Destroyer of the German Invaders', Type OB-3) and the _Kuzma Minin_ ('Cosima Minine').
_(Stamp issue: Paul Malmassari Collection)_
**SOURCES:**
**Works partly covering armoured trains**
**Books:**
Body, Marcel, _Un Piano en bouleau de Carélie, Mes années de Russie 1917-1927_ (Paris: Hachette, 1981).
Bullock, D, _Armored Units of the Russian Civil War, Red Army_ (Oxford: Osprey Publishing Ltd, 2006).
_________, and Deryabin, A, _Armored Units of the Russian Civil War, White and Allied_ (Oxford: Osprey Publishing Ltd, 2003).
Dupouy, Alain, _Les Engins blindés à roues Tome I: historique_ (Grenoble: self-published, 1999).
____________, _Les Engins blindés à roues Tome II: automitrailleuses et autocanons_ (Grenoble: self-published, 1999).
____________, _Les Engins blindés à roues Tome III: le BTR-40 et le BTR-152_ (Grenoble: self-published, 1997).
____________, _Les Engins blindés à roues Tome VI: le BTR 70 et le BTR 80_ (Grenoble: self-published, 1997).
Kinnear, James, _Russian Armored cars 1930-2000_ (Darlington, MD: Darlington Productions, Inc., 2000).
Pasternak, Boris, _Doctor Zhivago_ (Paris: Gallimard, 1959).
Rostagno, Enrique, _Les Armées russes en Mandchourie_ (Ixelles-Bruxelles: A Beuer, 1909).
Vollert, Jochen, _KV-2 Soviet Heavy Breakthrough Tank of WWII_ (Erlangen: Tankograd Publishing, 2004).
Zaloga, Steven J, and Grandsen, James, _Soviet Tanks and Combat Vehicles of World War Two_ (London: Arms and Armour Press, 1984).
**Journal Articles:**
_L'Appel des Soviets_ No 13 (15 October 1929), cover page.
Vaucher, Robert, 'La Route de Petrograd', _L'Illustration_ No 3929 (22 June 1918), pp 607–9.
**Works exclusively or principally covering armoured trains**
**Books:**
Kolomiets, Maxim, _Sowieckie samochody pancerne vol. 1_ (Warsaw: Wydawnictwo Militaria, 2005).
_______________, _Sowieckie poci gi pancerne vol. 1 1930-1941_ (Warsaw: Wydawnictwo Militaria, 2006).
_______________, _Les Trains blindés de l'Armée rouge 1930-1941_ (in Russian) (Moscow: Frontline Illustration, 2006).
_______________, _Les Trains blindés de l'Armée rouge 1941-1945_ (in Russian) (Moscow: Frontline Illustration, 2007).
Kopenhagen, Wilfried, _Sowjetische Panzerzüge und Eisenbahngeschütze 1917-1945_ (Wölfersheim-Berstadt: Podzun-Pallas-Verlag, 1995).
**Journal Articles:**
Brauer, 'Do we need armoured trains?' (in Russian), _Τехника и снабжение красной армии_ ('Techniques and Supply of the Red Army') (August 1923), pp 27–9.
Koenig, Alan R, 'Glass-Jawed Goliaths: Red Army Artillery Armored trains in World War II', _The Journal of Slavic Military Studies_ Vol 14, No 4 (December 2001), pp 144–61.
'Le train blindé _Cosima Minine_ ', _Modelist Konstruktor_ (1980-5), pp 4–9.
McGregor. Andrew, 'Russian Interior Ministry Revives Its Armored Train in the North Caucasus', _Eurasia Daily Monitor_ Vol 10, Issue 91 (14 May 2013).
Malmassari, Paul, 'Les Trains blindés soviétiques', _39-45 Magazine_ No 45 (1989), pp 30–5.
Maurin, 'Installation of large calibre artillery pieces on armoured trains' (in Russian), _Τехника и снабжение красной армии_ ('Techniques and Supply of the Red Army') (September 1922), p 14.
Trojca, Halina and Waldemar, 'Der Panzertriebwagen Kirowski', _Modell-Fan_ 4/94, pp 53–5.
Zaloga, Steven, 'Soviet Armored Trains', _AFV News_ 17/2, pp 5–11.
Zhilin, Gennady, 'Baikal, Terek and Co.', _Tankomaster_ No 7 (2003), pp 2–14.
**Play:**
Vsevolod, Ivanov, _Le Train blindé n° 14-69_ (Paris: Librairie Gallimard, 1922).
**Film:**
_Heirs of Victory_ (1975), 60 minutes.
**Websites:**
<https://reibert.info/threads/bronepoezda-belyx-armij.116097/>
<http://en.zabmodels.mybb.ru/viewtopic.php?id=262>
. Armoured train = _Broniepoezd_.
. Armoured railcar = _Motorbronievagon_ (Self-propelled armoured wagon). Armoured trolley = _Broniedrezina_.
. Here we will use the description 'Russian' when referring to the Imperial Army then to the Army post-1991, 'Red', 'Bolshevik' or 'White' when referring to the Civil War period, and 'Soviet' for the period 1922 to 1991.
. _Neue Militärische Blätter_ , 26th Year, Vol 70 (17 February 1907), p 70.
. We are unsure whether he was the same Mescherinov who proposed a design in France in October 1924 (see the chapter on France).
. Vsevolod Viatcheslavovitch Ivanov (1895–1963).
. O = _osnovoÏ_ or 'principal engine', of 0-8-0 configuration. The letters 'b', 'v' or 'z' indicate a variant of the basic class.
. In total 106 wagons and fifty-three engines.
. ZhD = _Zheleznaya Doroga_ , road wheel/rail wheel.
. Here we will not be examining the twelve Molodets 15P961 ballistic missile trains which existed from 1987 to 1994, nor the new ballistic missile system being set up at the time of writing.
. In 1991 Russia under Boris Yeltsin recognised Chinese sovereignty over the island, which was retrospectively ceded to China.
. At that time no motorways existed between European Russia and the Far East.
. This was probably what inspired the artwork illustration in the article 'Panzerzug – Neuauflage' (in the East German journal _Armee Rundschau_ 8/1976) showing a modern train equipped with turrets from T-62 tanks and ZSU 23-4 armoured vehicles. We know of no photo of such an armoured train.
. ZU = _Zenitnaya Ustanovka_ , or anti-aircraft system. ZSU = _Zenitnaya Samokhodnaya Ustanovka_ , or self-propelled anti-aircraft system.
. The acronym comes from the names of designers G I Nikitin, Y S Sokolov and V I Volkov.
. Nicknamed 'Kuzma' by the troops.
. Sometimes written as 'Alkhan-Kala'.
. Otryad Mobilniy Osobogo Naznacheniya, or special missions mobile unit, reporting to the Interior Ministry.
. For an estimated cost of $635,000.
. A new town named in 1964 after Palmiro Toggliati, one of the founders of the Italian Communist Party, who passed away in the town in that year, while holidaying in the USSR. The former town, Stavropol-on-the-Volga, had been covered by the waters of a dam.
## SLOVAK REPUBLIC
### ARMOURED TRAIN _OROL_
Created following the dismantling of Czechoslovakia, the Slovak Republic under Monsignor Tiso briefly joined in the attack on Poland in September and October 1939. During the campaign the Slovaks put back into service _Bernolak_ , a former Austro-Hungarian armoured train. It appears that a second train was improvised at Zvolen for the same campaign. The latter unit was composed of locomotive No 310.422 and wagons numbered U-7,76290 and 7,17369. To date no photo of either armoured train has come to light.
On 23 June 1941, the Slovak Republic declared war on the Soviet Union, and in the occupied zone which comprised the northern part of the Ukraine and the southern part of Byelorussia, Slovak troops quickly came into conflict with communist partisans. The German armoured train PZ 25 was the main means of securing the zone of operations. Major Martin Strapak, commander of the 1st Battalion of the 102nd Slovak Infantry Regiment, was so impressed by the performance of the German train that he set about improvising a Slovak armoured train for the 'Orol' (Eagle) Security Division in the Spring of 1942. To protect his train, he used armour plate and turrets recovered from destroyed and abandoned Soviet tanks, plus a complete BT-5 cruiser tank.
The train immediately went into service on the line between Pinsk and Gomel, and its first major action took place in August 1942 in conjunction with PZ 25. _Orol_ was regularly targeted by partisan attacks, and they succeeded in derailing it several times, in particular following the withdrawal of PZ 25 which was sent to France. The Winter of 1942/43 was a period of relative calm, but on 22 March _Orol_ was seriously damaged in a derailment. Finally, on 27 May 1943, 3km (2 miles) to the north of Slavečna, it was irreparably damaged by the partisans.
This view showing the rear of the tank demonstrates the weak protection of _Orol_ in its initial form. The BT-5 was armoured to a maximum of 13mm at the front, but the sides and rear were much thinner. The partisans succeeded in blowing up the train at least three times.
_(Photo: Pavel Mičianik)_
_Orol_ in September 1942, in its initial configuration, with a Class BR 57 locomotive, and a lead wagon with a complete BT-5 Soviet tank protected by vertical armour plates at the leading end of the wagon only. This type of platform was also armed with 81mm mortars and a 37mm anti-tank gun.
_(Photo: Pavel Mičianik)_
In the Autumn of 1942, the train was rebuilt with improved armour protection, seen here in the workshops.
_(Photo: Martin Lacko)_
_Orol_ in its second configuration: the wagons had internal timber walls with the space between the inside and outside faces filled with stone ballast. The turret is from a T-28 or T-35 Soviet tank. Occasionally, individual wagons were detached from the complete train and coupled in supply trains.
_(Photo: Pavel Mičianik)_
The photos right and below show the armoured wagon completed and bearing the emblem of the Slovak Republic.
**SOURCES:**
Mičianik, Pavel, 'Improvizovaný pancierový vlak zaist'ovacej divízie "Orol"', _Vojenská história_ 4, 12 (2008), pp 10–19.
. In post-war literature also known as the Slovak State ( _Slovenský štát_ ).
. After the name of the Army Group.
. Crew: forty-six officers and men; armament: seven 7.92mm Schwarzlose Model 7/24 heavy machine guns, two 7.92mm ZB vz.26 LMGs, and one 37mm KPÚV vz.37 anti-tank gun.
. In Slovak: _Improvizovaný Pancierový Vlak_ (IPV).
## SOUTH AFRICA
### ARMOURED TRAINS AND TROLLEYS
Southern Africa was the scene of bitter fighting between the Boer Republics of the ZAR and the Orange Free State against the British from 1899 to 1902 during the Second Boer War. The armoured trains engaged in this conflict are described in the chapter on Great Britain. Having gained its independence under the South Africa Act of 31 May 1910, the Union of South Africa took part in the First World War. In 1939 the country once more went to war with Germany as part of the Commonwealth. On 31 May 1961, South Africa became an independent republic and left the British Commonwealth. The uprisings of the ANC and the nationalist movements against the apartheid policies of the white government which began in 1960 led to several declarations of a state of emergency. In 1966 fighting broke out on the frontiers of South Africa, and the state had to exert considerable effort to protect its infrastructure from attacks and sabotage by terrorists, at least up until 1989.
### The First World War and the Boer Rebellion
In 1914 South Africa joined in the First World War, attacking and capturing the German colony of South West Africa (SWA, present-day Namibia), and fighting alongside other Commonwealth forces in the Somme. In Africa several armoured trains, of which certain elements dated from the Second Boer War, were put into service on the country's narrow-gauge network (1067mm/3ft 6in). They were used to fight the German colonial troops, but first they had to protect rail transport during the Maritz Rebellion of a group of Afrikaners which took place between September 1914 and February 1915.
Armoured Train No 5 _Schrikmaker_ , built in Pretoria, which was used in German South West Africa. It was armed with an artillery piece, seen here surrounded by a group of officials and officers.
_(Photo: S.A.R.)_
This involved officers and men who had fought the British during the last Boer War, notably Brigadier-General Christiaan Frederick Beyers, the commander-in-chief of South African forces, who resigned his commission to lead the rebellion, and also many officers such as Generals de Wet, Kemp and Maritz, the latter lending his name to the movement. Repeated defeats led to the collapse of the uprising, the last _kommando_ surrendering on 8 February 1915.
Five armoured trains were built in 1914: _Trafalgar_ (His Majesty's Armoured Train No 1, completed on 22 October), _Scot_ (No 2, 6 November), _Erin_ (No 3, 9 November), _Karoo_ (No 4, 6 November) and _Schrikmaker_ (No 5, 18 November). However, at the time there was no rail link between South Africa and SWA. Huge efforts were expended between 15 August 1914 and 25 June 1915 on the construction of a rail link, including deviations and secondary lines, in order to deploy armoured trains. _Erin_ remained in reserve in South Africa, while the other four were used for patrol missions and for support of the ground troops. For this latter function seven armoured railway batteries were employed, often coupled to the armoured trains. But it appears that fire support by these batteries usually required their emplacement on the ground, as firing from the wagons proved impractical.
A modified version of the wagon shown below placed at the head of H. M. A. T. No 5 _Schrikmaker_ , with additional facilities to ensure the comfort of the crew, in the form of two timber shelters and a framework to hold a canvas covering to protect from the sun and rain. Nineteen such wagons were converted and divided between the Transvaal and the Orange Free State.
_(Photo: S.A.R.)_
A similar wagon, the sandbags providing both protection (descending behind the wagon sides) and also a rampart to support the weapons. The troops carry the SMLE (Short Magazine Lee Enfield) Mk III adopted in 1907 and are supported by a Lewis Gun at each end.
_(Photo: S.A.R.)_
The 12pdr artillery wagon of H. M. A. T. No 1 _Trafalgar_. Note the armoured side plates which hinge down to form the firing platform.
_(Photo: IWM)_
The three leading wagons of Armoured Train No 3 _Erin_. The composition of the armoured trains was relatively standard: for example AT No 5 comprised an armoured engine, an artillery wagon, a support wagon, three bogie wagons (one of which transported draught animals), a water tank wagon, and a short wheelbase wagon. Searchlights had to be purchased from the local mining companies to increase the effectiveness of night patrols.
_(Photo: S.A.R.)_
Armoured wagon built in Bloemfontein for _Erin_ at the end of 1914. Two similar wagons were also built, each coupled to an unarmoured engine to form an armoured reconnaissance train.
_(Photo: S.A.R.)_
A 6in naval gun mounted on a five-axle wagon: the two axles furthest from the camera are a locomotive leading truck and the other three are a tender chassis, seen in 1915.
_(Photo:_ Revue du Génie Civi _l_ )
### The Inter-War Period
Drawing on the experience of the First World War, it was decided to establish the Railways and Harbour Brigade (R & HB) to take charge of all forms of transport, including its two armoured trains, No 1 ( _Active_ ) based at the Cape, and No 2 at Johannesburg. In 1928, the R & HB was dissolved and the two armoured trains were transferred to the Active Citizen Force.
_Active_ at Johannesburg. The bogie wagons, although armed with captured German Maxim 08 MGs such as the one mounted on the right, and .303 calibre Lewis Guns (the barrel of one of which can be seen behind the head of the fourth officer from the right), do not present a formidable appearance, as their armour protection is hidden from view behind the side plating.
_(Photo: S.A.R.)_
### The Second World War
South Africa declared war on Germany on 6 September 1939. On 1 April 1940, the R & HB was reactivated: with its HQ at Johannesburg the Brigade comprised two infantry battalions, four armoured trains and an Engineers detachment (which would give rise to railway regiments and a regiment in charge of the ports). AT No 1 was based at the junction at Milner Park (Johannesburg) and No 2 at Durban, with volunteer crews manning them on a part-time basis. In August 1940, AT No 1 was moved 35km (28 miles) from its home base to Mapleton, which was also the training centre of the R & HB. In 1942, modernisation of the Brigade involved the dismantling of AT No 2. AT No 1 remained active up until 1 January 1946, when it was withdrawn from service.
Although the country was part of the Commonwealth, as in 1914 a large part of the white population did not support the declaration of war, and the government, fearing acts of rebellion and sabotage, decided to take steps to protect the rolling stock. Steam engine No 1554 was therefore partially armoured in August 1940, in order to haul an armoured train. Stationed at Mapleton with a view to patrols on the main line in Natal, this train, about which little information has come to light, was protected in a similar manner to the engine, by plates 25mm thick intended to resist small-arms fire. Its principal armament would have been a 18pdr QF field gun on a naval mounting, plus Vickers and Lewis machine guns. Later on in the war, this train was used to support the war effort by making runs from the Union of South Africa into Rhodesia, but it never saw action. Finally, the armour protection was removed from the engine and it returned to civilian use.
Class 4 engine No 1554, partially armoured.
_(Photo: Terry Hutson)_
_Active_ 's 18pdr Ordnance QF Mk II field gun on one of the two bogie wagons numbered 41101Z and 41102Z.
_(Photo: All Rights Reserved)_
An interesting document: cigarette card N° 17 from Hortors Ltd with a fair representation of the artillery wagon of this train. Despite the crew being out of proportion, the original shows the train in camouflage colours, in contrast to the engine and tender which are still painted in charcoal grey.
_(Card: Paul Malmassari Collection)_
In 1942, a Marmon-Herrington Mk I armoured car (No U1341) was converted to run on rails. No details of this machine are known, apart from a silhouette showing the unmistakable twin turret hatches, seen in the background of a photo of engine No 1554, and the fact that it was disposed of by auction at Lyttleton in 1952.
At the end of the Second World War, South African author and poet Roy Campbell penned the following lines, which show how much the armoured trains featured in the imagination of the country: 'Against a regiment I oppose a brain / And a dark horse against an armoured train'. These verses also inspired the 1954 painting by Alex Colville _Horse and train_.
### The Frontier War (South African Border War)
This conflict lasted more than 20 years (August 1966 – September 1980) and involved South West Africa (the future Namibia) and Angola, both supported by revolutionary independence movements (SWAPO in Namibia from 1962, and UNITA in Angola from 1966). These terrorist groups infiltrated South Africa to attack the economic and cultural infrastructure, and in particular the transport network, with increasing severity during the mid-1970s.
This background prompted several quite original armoured responses, comprising road/rail armoured vehicles and trains specially conceived for maintaining public order.
### The BOSPADDA convertible armoured vehicles
The two machines known as _Kobus_ (No SAS R 810494) and _Chris_ (No SAS R 810493) were used by the South African Rail Police (SAS: _Suid Afrika Spoorwegpolisie_ ) to protect the lines during crisis periods. Their conception and construction took place under the direction of Mr Chris van der Merwe in the Langlaagte workshops, based on the combined experience of the railway police, the Army Engineers, the South African Armed Forces and the CSIR. One of these vehicles was therefore baptised as _Chris_ , in honour of its designer, and the other as _Kobus_ , in honour of Dr Kobus Loubser, former president of the South African Railways.
_Chris_ and _Kobus_ were equipped with six-cylinder diesel engines, giving them a maximum speed of 60km/h (37mph) and a range of 1000km (620 miles) on rails and 750km (466 miles) on roads. Here one of the rail guide wheels is clearly visible in its lowered position.
_(Photo: S.A.R.)_
Here _Kobus_ is being presented to the authorities in 1978.
_(Photo: S.A.R.)_
One of the remarkable features of these machines is that all of the 6800 or so component parts which make up each one were designed and built in the workshops without any external help, during a period of severe international sanctions against South Africa.
_(Photo: S.A.R.)_
As designed, these machines were dual road-rail convertible configuration: during road travel the rail wheels were retracted underneath the hull; for rail travel they were hydraulically lowered onto the rails to act as guide wheels, traction on the rails being provided by the road wheels. At an unknown date, this system was removed due to supposed hydraulic problems (but possibly also the problem of using the road wheels as source of traction beside the track). Thereafter _Chris_ and _Kobus_ became simply armoured railcars mounted on traction bogies.
Today _Chris_ is preserved on display in front of the TransNamib Museum in Windhoek. _Kobus_ is still in working order, assigned to the Braamfontein Memorial Marshalling Yard.
In this photo of _Chris_ preserved in Windhoek, note the road mudguards are still in place, but the drive train has been converted from road wheels to rail bogies. The steps welded on the buffer beam at each end do not appear on _Kobus_.
_(Photo: All Rights Reserved)_
In comparison, _Kobus_ has been retained in full working order, and its protruding road mudguards have been removed. The road wheel arches have been covered by protective grills, again no doubt for health and safety reasons.
_(Photo: Petrus Botha)_
This frontal view of the machine taken in 1995 emphasises its aggressive appearance, which fits in well with its intended mission. It was designed to protect the crew from the explosion of a 7kg charge of TNT. The central knuckle allows for coupling wagons or for towing the machine in the case of breakdown.
_(Photo: Petrus Botha)_
A close-up of the driving bogie on _Kobus_.
_(Photo: Petrus Botha)_
Interior view of _Kobus_ at Braamfontein. Note the padding which covers much of the inside of the machine.
_(Photo: Johannes Botha)_
Right side view of _Kobus_ : the two sides of the machine are different as regards the lower central section, the doors are offset to the left on each side, and the front can be recognised by the motor cooling slots. The central observation windows, however, are symmetrical.
_(Photo: Petrus Botha)_
Left side view taken on 9 August 1996: Note that the square lamps have been moved from the roof to the front and rear hoods.
_(Photo: Petrus Botha)_
### The Inspection Trolleys
Several small inspection trolleys were built, some fitted with platforms. The latter were intended for inspection of the 3000-volt overhead catenary cables which powered the main lines and the depots, and to repair damaged sections when thieves had risked stealing the copper cables.
Turntable on the left-hand side of _Funkey_. Apparently this device was not automatically fitted to all of these machines.
_(Photo: Petrus Botha)_
One of them called _Funkey_ seems to have lent its name to all of these machines. Here we can make out painted on its sides the emblem of the South African Railways (Spoornet) during the 1990s.
_(Photo: Petrus Botha)_
### The Riot Trains: ('Ghost Trains')
During the 1960s, it was planned to build armoured trains, but the idea was dropped. On the other hand, four trains designed to control rioters were built, and partially armoured, in the 1970s. Generally, they were composed of the following units:
– a Type DZ-7 bogie wagon ballasted with gravel and equipped with cowcatchers.
– coaches for the riot police.
– a water tank and fire-fighting equipment.
– a diesel locomotive or steam engine.
– at the rear a second ballasted Type DZ-7 bogie wagon.
The inspection platforms were designed by the Electrification Department of Spoornet.
_(Photo: Petrus Botha)_
These trains could also be used for the transport of munitions, and to ensure their security the orders to move would be given only an hour prior to departure. When transporting munitions, the trains could be organised in the following formation, to provide maximum security to the personnel:
– diesel locomotive.
– ballasted Type DZ-7 wagon.
– the explosives transport wagon, followed by the second ballasted Type DZ-7.
One of the four 'Ghost Trains' powered by a Class 25 NC steam engine, preceded by its ballasted bogie wagon.
_(Photo: Petrus Botha)_
Two standard Class 38 dual power diesel-electrics double-heading this riot train and followed by two personnel coaches. Note the cowcatcher at the front of the Type DZ-7 bogie wagon.
_(Photo: Petrus Botha)_
The driving cab of this standard Class 38 diesel-electric prime mover is armoured against small-arms fire. The leading loco is 38-002 followed by 38-003.
_(Photo: Petrus Botha)_
Class 34 diesel-electric locomotive, which alternated with a Class 15 F steam engine on 'Ghost Trains' Nos 3 and 4. _(Photo: Petrus Botha)_
The Class 25 NC steam engines were modified to spray water to help fight fires and also to serve as a water cannon to repel rioters who approached too close to the engine, which is here N° 3475 _Braamfontein_. Class 15 steam engines were also employed on Trains 1, 2 and 4.
_(Photo: Petrus Botha)_
Close-up view of the hot water nozzle on the left side of the engine, and the long jet of steam it produced (below).
_(Photos: Petrus Botha)_
This Type X-17 water tank wagon has been modified with a water jet for use in fighting fires, with a nozzle similar to that on the steam engine fitted to the top of the central ladder. The wagon is in the orange and white livery of Spoornet.
_(Photo: Petrus Botha)_
Close-up of the front end of one of the Type DZE-7 bogie wagons. The cowcatcher reaches down quite far below the wagon and is fitted with reinforced rubber extensions.
_(Photo: Petrus Botha)_
No 9246, one of the self-propelled Class 2M1 electric units, converted into a riot coach. Note the circular ports for weapons in each of the armoured windows. When these coaches were used as motor units for suburban trains (note the folded pantograph), the driver's cab in this photo dating from 1996 would be on the right.
_(Photo: Petrus Botha)_
Internal view of one of the armoured coaches, the seated troops facing outwards towards attackers. Note the grills covering the windows. The armour protection consisted of 3mm steel plates on the outside of the wooden coach sides plus 5mm steel plates on the inside surface.
_(Photo: Petrus Botha)_
**SOURCES:**
**Book:**
Camp, Steve and Heitman, Helmoed-Römer, _Surviving the Ride_ (Johannesburg: 30° South Publishers (Pty) Ltd, 2014).
**Journal Articles:**
Bouch, Lieutenant R J, 'The Railway and the War Effort 1914-1915', _Militaria_ No 4/4 (1974), pp 1–14.
___________________, 'The Railway and the War Effort 1939-1945', _Militaria_ No 5/2 (1975), pages 66–75.
'E J', 'Capetown: A correspondant writes', _S.A. Railways & Harbour Magazine_ (May 1928), pp 848–50.
___, 'With the Armoured Train at Potchefstroom', _S.A. Railways and Harbour Magazine_ (May 1930), pp 697–9.
Harrigan, Anthony, 'The Armoured Train', _Commando_ (March 1963), pp 19–21.
_Revue du Génie Civil_ (23 October 1915).
Rhind, D M, 'The Mystery of 4AR No 1554', _World War Two Railway Study Group Bulletin_ Vol 8 No 1 (1998), pp 8.19–8.21.
'Veelsydige Pantserwa om Treindienste te Beskerm', _SASSAR_ (July 1978), pp 681–3.
. In Afrikaans _Pantsertrein_.
. The Defence Act of 1912 had created the South African Army or UDF (Union Defence Force) composed of the Permanent Force, a standing army of professional soldiers, and the Active Citizen Force, composed of recruits and volunteers.
. Ignatius Royston Dunnachie Campbell, (2 October 1901 – 22 April 1957). He supported the Nationalist side during the Spanish Civil War, then enlisted in the British Army during the Second World War.
. Art Gallery of Hamilton.
. German South West Africa was conquered in 1915 and was made a South African protectorate in 1920. After the Second World War, South Africa demanded the annexation of the territory. But the United Nations took SWA under its guardianship in 1966 and renamed it Namibia in 1968. From 1967 SWAPO began its guerrilla operations. In 1971 the International Court of Justice declared the South African presence in the territory to be illegal. Namibia finally achieved independence on 21 March 1990.
. 'Bush Frog' in Afrikaans.
. The railway police were absorbed into the national police in 1986.
. South of Johannesburg, in the Road Mechanical Vehicle Workshops of the SAR&H.
. Council for Scientific and Industrial Research.
. State-owned company responsible for rail freight, which became Transnet in July 2007.
. Not to be confused with the 'Phantom Trains' covered in the Belgian chapter, which were used as rams or indendiary trains.
## SOUTH KOREA
### ARMOURED TRAINS (1950–1953)
The North Korean Army began the invasion of the South on 25 June 1950. The US Army's 772nd Military Police Battalion (Railway Security) made up of four companies with a total complement of thirty-eight officers and 412 men, left its base in Maryland in September and landed at Wonsan. Their initial role was to help stop the advance of the North Korean divisions, and ensure the security of road communications. They also took charge of refugees and prisoners of war. In December, they handled security during the retreat of the United Nations Forces, faced with twelve Chinese divisions, up until the fall of Hamhung. At that point, the United Nations' lines of communication were being threatened by the presence of North Korean units as much as 150km (93 miles) behind the front lines. The 772nd Battalion, which had been evacuated to Pusan, was charged with the role of protecting the MSR, the principal supply route for the United Nations forces. Company D became responsible for protecting the railway line between Ulsan and Chechon, then from January 1951 as far as Seoul. In August 1951, the role of the battalion was changed, and all four Companies were dedicated to protecting the railway network, from their HQ in Taegu, under the overall command of the 3rd Transportation Military Rail System. Company A was posted to Taejon, Company B to Pusan, Company C to Tongdong-Po, and Company D remained at Yongchon. In all, they were responsible for the security of almost 1,700km (1,050 miles) of track.
Their rolling stock comprised bogie wagons reinforced internally with sandbags and nicknamed 'rolling foxholes'. Company B at least put back into service a Japanese armoured wagon, which ran in front of the locomotive and was itself preceded by a safety bogie wagon. The unit remained in Korea after the armistice of 27 July 1953, and was demobilised on 11 June 1955.
**SOURCES:**
**Book:**
Mesko, Jim, _Armor in Korea, a Pictorial History_ (Carollton, Texas: Squadron Signal Publications Inc. 1984).
**Websites:**
<http://www.military.com/HomePage/UnitPageHistory/1,13506,104826|797829,00.html>
<http://www.transportation.army.mil/museum/transportation%20museum/korearail.htm>
American and Korean members of Company B, 772nd MP Battalion (Railway Security) in front of their ex-Japanese armoured wagon.
_(Photo: Paul Malmassari Collection)_
The ex-Japanese armoured wagon and the rear of the safety wagon.
_(Photo: Paul Malmassari Collection)_
. With a strength equal to three divisions.
## SOUTH SUDAN
### ARMOURED TRAIN, 2001
South Sudan became independent of the North on 9 July 2011. At the time of writing the only railway line possessed by the South is the 248km (154 miles) stretch of the Babanousa line from the frontier to Wau, built between 1959 and 1962 to a gauge of 1067mm (3ft 6in).
A decade prior to the division of the country, the only mention of armoured trains is an Internet article by M. Brice Lalonde dated 3 September 2001, in which he mentions that each year an armoured train, escorted by militia cavalry, was despatched by the Khartoum Government to resupply the garrisons in Southern Sudan. Probably for security reasons, no photograph of this operation has come to light.
. French politician, former Secretary of State then Minister for the Environment from 1988 to 1992. He founded the Europe Ecology Party, of which he was the President at the time he wrote the article.
## SPAIN
### ARMOURED TRAINS
As with many of the other major European powers, Spain first employed armoured trains in its colonial empire (Cuba and Spanish Morocco), then afterwards at home during the Civil War of 1936–9. Although during the Carlist Wars of the nineteenth century certain railway stations had been protected by small fortifications, there is no evidence that armoured trains were used at that time.
### The Defence of Cuba
The transport network in Cuba comprised almost 1500km (930 miles) of railway lines, shared between sixteen small operators. During the Ten Years War (1868–78), which started with an uprising then the declaration of independence by the province of Oriente on 10 October 1868, armoured wagons were built and mustered in train rakes, to defend against sabotage. After several years of peace, on 24 February 1895, a new uprising led by a political exile named José Marti started with a landing by a small group of his followers at La Playitas de Cajobabo in the east of the island. Faced by a worsening of the situation, the authorities established a co-ordinating body, the _Sección de Intervención de la Intendencia Militar_. Patrol trains made up of troop coaches and several armoured wagons were assembled, and used on the defence line established by General Campos, backed by a network of small forts built along the tracks. These measures did not succeed in stopping the rebel advance, and in April 1898, following the controversial destruction of the battleship USS _Maine_ , the Americans decided to intervene. At the end of the ensuing Spanish-American War, under the Treaty of Paris signed on 10 December 1898, the Spanish gave up their colonial empire.
Numbered armoured wagons photographed at Saguä la Grande in Cuba on 5 March 1898. They appear to be of classic construction, well protected against small-arms fire.
_(Photo: All Rights Reserved)_
Armoured train in Cuba in 1898. Note the firing loopholes in the wooden sides of the wagon.
_(Photo: Archivo General Militar de Madrid, F.05933)_
### Operations in Spanish Morocco
The Rif War began on the morning of 17 July 1921 when a column of 200 troops was attacked by the fighters of Abd El Krim. There would be considerable fighting involving French and Spanish forces before the war ended with his surrender on 27 May 1926.
The Spanish railways in Morocco were operated by several companies: the 24km (15-mile) line of the Compañia de Minas del Rif (60cm/1ft 11½in gauge) ran between Melilla and Avanzamiento; the 30km (18.6-mile) line of the Compañia de Minas del Rif (metre/3ft 3¼in gauge) between Melilla and Afra; and finally the Linea des Estado (metre gauge) between Melilla and Tistutin, which ran for 36km (22.5 miles).
After the military disaster of Anoual on 21 July, the Spaniards tried to react. On 15 August 1921, the _1 st Regimento de Ferrocarriles_ was charged with extending the line from Melilla, and with constructing a platform for unloading equipment. As each night the Rif fighters dismantled the track, each following morning a repair team was put to work under the protection of an armoured train. The town of Nador was attacked on 17 September. Two armoured trains (one on the 60cm gauge and the other on the metre gauge) were in action in support of the troops. However, the 60cm gauge armoured train was stopped by demolitions. The second train managed to arrive in Nador, and another train for the metre gauge was built by cannibalising parts of the immobilised 60cm-gauge train. These two armoured trains were then used up until the end of December to reconquer territory as far as Avanzamiento and Titustin. We have no information on the technical details of these improvised trains, which apparently carried no artillery.
The ' _Tortillard'_ ('Local Train') on the Taza run. An armoured train was known to operate on the Taza run in July 1926, but it is not known whether it was the same as one recorded in 1921.
_(Photo: Via JMAM – Jacinto M Arévalo Molina)_
Card No 17 from an Orús (Barcelona) chocolate bar, showing one of the armoured trains in Spanish Morocco.
_(Card: Paul Malmassari Collection)_
The engine of the armoured train (60cm gauge) built to relieve the garrison at Zinatz.
_(Photo: via JMAM)_
The Spanish continued to lose ground to the rebels. In October 1924, an armoured train (60cm gauge) was assembled at Tetouan to relieve the besieged garrison at Zinatz. Two partially-armoured (front and sides) steam engines formed the head and tail of the train. In between were nine wagons protected on the sides with sandbags, carrying four machine guns, medical teams and signallers. During the retreat from Xauen in December 1924, it seems that an improvised armoured train was used.
### Revolt in the Asturias
In October 1934, a general strike declared in some regions of Spain turned into armed confrontations between the workers and the forces of order. The strike was quickly broken, except in Catalonia and in the Asturias. After several incidents of street fighting, the revolt ended in Catalonia, but the situation in the Asturias worsened to the point where the Army had to intervene. At least three armoured trains were used alongside armed trains. The first encounter took place on 7 October 1934, when a lightly-armoured train left the machinery depot of la Argañosa for the Norte Company station where the crew fought with the strikers. The most well-known of these trains was the one hauled by the steam engine _Grado_ on the metric gauge Vasco-Asturiano railway, which left the Vega factory on 9 October and was in action the following day against strikers in the suburb of Pelayo. Several days later, a broad-gauge train was in action at Vega del Rey Station but was hit in the boiler by a shell and was forced to withdraw. During the night of 14/15 October, the opponents of the Army put together an armoured train at Trubia to help the strikers in Grado.
The armoured train built at Oviedo on the Ferrocarril Vasco-Asturiano, with its steam engine _Grado_ , used in October 1934.
_(Photo: Paul Malmassari Collection)_
In the foreground is steam engine No 2544 _Cervera_ of the Northern Company. In front and behind the engine is a low-sided flat wagon, each one carrying a Landesa armoured tractor, with a ball mount for a 7mm Hotchkiss machine gun. If necessary, this train could act as an armoured train.
_(Photo: All Rights Reserved)_
### The Spanish Civil War
The Nationalist revolt began on 17 July 1936 in Spanish Morocco, led by Colonel Francisco Franco Bahamonde, commander of the troops in Morocco. Faced with the refusal of the Republican Government to issue arms to the general population, the people took advantage of those areas where the Army garrisons were weak to seize arms for themselves. Among the many emergency measures put in place by the Government from the very early days of the Army revolt was the construction of armoured trains, alongside many other types of improvised armoured vehicles. They were used almost exclusively by the Republican side. They operated either independently, or under the command of the local majority trade union or workers' committee. In late 1936, specialised units were created within the Madrid Army Corps, including a Railway Brigade which grouped together the Railway Militias, the Railway Shock Battalion, the armoured trains and the railway workshops. The Railway Brigade deployed its personnel as and when necessary to the construction of armoured trains, and when the _Ejercito Popular_ (Army of the People) was formed, the experienced and disciplined railway units were successfully integrated.
In fact, on 10 January 1937, a former trade unionist, Narciso Julián Sanz, was charged with regrouping all the armoured trains in a new unit. In Madrid, experienced soldiers were to train the various specialist crewmen: troops, railway workers, engine drivers, gunners, assault infantry, signallers, sappers to defuse mines and to repair the tracks, cooks, nurses etc. In February 1937, the Railway Brigade formed an independent unit in the Army of the Centre, then in May it became the Railway Battalion with a strength of 1798 men. This battalion, which for the whole period of the Civil War would be commanded by Sanz, was one of the formations under the overall command of Colonel Tomás Ardid, head of the Engineer Services of the Army of the Centre. If at the end of the Civil War, ten armoured trains remained operational, we know that a total of thirty had been built during the war, of which up to the present time twenty have been identified. However, the defeat of the Republican side, when the trains were all demobilised and the rolling stock was returned to commercial use, means that with rare exceptions they were never photographed.
The badge of the _Brigada Ferroviaria de Trenes Blindados y Especialidades_ printed as a title of a review published in June 1937. It is noticeable here, as on the game boards reproduced in Appendix 1, that a railway gun means more to the unin-formed observer than an armoured train with its less prominent characteristics.
_(Reconstruction by JMAM)_
Despite the very real existence of these well designed and assembled trains, and in some numbers, relevant documentation is sadly lacking, preventing a full description of their story, or indeed correct attribution of their identifying numbers and letters. The following outline description is based on the remarkable work undertaken by Sr. Jacinto M Arévalo Molina, as well as on the articles and reconstitutions of Sr. Francisco Cruzado Albert.
### The armoured trains of the Sierra de Guadarrama
Starting in Madrid, a railway line crossed the Sierra de Guadarrama and divided into two branches at the level of Villalba, one of which passed through a tunnel under the Alto del León and continued towards Segovia. The other branch passed by way of El Escorial, Robledo de Chavela and Las Navas del Marques and arrived in Avila. The first actions involving armoured trains took place on these two branches. On 23 July 1936 the first train, which was hastily protected with mattresses, tabletops, beams and steel plates, was put into service, and on the 26th it took part in the defence of Alto de Léon, but was a failure. On 5 August the first properly-constituted armoured train came out of the workshops of the Compańia del Norte. It had been designed by Engineer Lieutenant-Colonel D Ramón Valcárel, and comprised four wagons and a steam engine, all armoured, and armed with two 70mm guns, nine machine guns and eighty-nine rifles, considerable firepower for the period. It was designated _Tren blindado_ 'A', which was later changed to Armoured Train No 1 and finally by the end of the war, to Armoured Train No 5. This train, along with one or two motorised wagons used for reconnaissance, remained on this line for the whole of the war and patrolled from Torrelodones towards Cercedilla and El Escorial. A short time later, a similar train (Armoured Train 'B') was built, and after remaining on this front for a short time, moved to the Talavera line in October 1936.
A fine view of the engine of Armoured Train 'A' in August 1936, in Los Molinos Station, which shows off well the camouflage scheme and the armoured casemate at the front.
_(Photo: All Rights Reserved)_
Close-up of an end compartment of the artillery wagon of Armoured Train 'A', based on a Type MMG bogie well wagon of the Norte, before the inscriptions were painted on. (Note the outlines of the letters chalked on the metal as guidelines). It is armed with two 70mm guns. The red-yellow-red Spanish national flag hangs from one of the corner pillars. The photo was taken on 5 September 1936.
_(Photo: Archivo General de la Administración, AGA)_
The stamp used by Armoured Train 'A' showing the composition of the crew and their political affiliation.
_(Illustration: JMAM Collection)_
A photo apparently taken by a member of the Condor Legion in the Sierra de Guadarrama. The artillery wagon converted from a Type Rrf well wagon with six-axle bogies has obviously been damaged by fire, as there are smoke marks above the firing slits and the embrasure.
_(Photo: Paul Malmassari Collection)_
### The armoured trains of San Sebastián
There are a few brief details of the existence of two armoured trains during the short-lived fighting in the Basque Country. In August 1936, the Nationalist troops from Pamplona under General Beorlegui headed in the direction of Vera to capture Irún. A narrow-gauge train was quickly fitted with several steel plates, planks of wood and sandbags, and armed with machine guns. We know that it was in action on the 12, 15, 19, 20 and 26 August, before withdrawing into the town before it fell. In addition, there is some information concerning one or two armoured trains operating on the broad-gauge line to Oyarzun and Tolosa, used to transport ammunition and support troops with their machine guns.
2-6-0 Tank Engine _Zarauz_ , armoured in a simple manner but with protection certainly proof against light weapons. Note the armoured blockhouse carried inside the high-sided wagon marked 'Bidasoa'. The markings painted on by the trade unions are typical of armoured trains at the start of the Civil War.
_(Photo: Paul Malmassari Collection)_
### The armoured trains of Aragón
In his book _Diario de la guerra española_ (Paris: Ruedo Ibérico, 1963, and Editorial Akal, 1978), the Russian journalist Mikhail Koltsov relates how on his arrival in Tardienta on 13 August 1936, he saw his first armoured train. At the end of that month, it went into action against the Nationalist forces which were attacking the village, but without tangible results. On 28 August 1936 an armoured train built by the workers of the firm Construcciones Devis, S.A. of Valencia appeared. It was made up of an engine and two armoured wagons. It left for Teruel and then disappears from the records. Then in December, several newspapers mentioned the existence of a 'Phantom Train' in the area of Aragon. But then a long period passed without any information on these trains, apart from a photograph taken by a member of the Lincoln Brigade (15th International Brigade in the Quinto Zone) showing a well-built armoured train. Finally in March 1938 the town fell, and the Nationalists discovered two abandoned wagons and a broken-down tank.
This train (perhaps the 'Phantom Train') was possibly employed near Barcelona. Note it still bears the initials of the trade unionist political organisations, which would soon be in conflict inside the Republican faction. Despite the poor quality of the photo we can clearly make out two wagons fitted with a turret in front of the coach.
_(Photo: Puig Ferrán printed in_ La Vanguardia, _Barcelona, No 22692 [5 December 1936], p 4 and also in_ La Gaceta del norte, _Bilbao, No 12099 [30 December 1936], p 10 in the Hermeroteca Municipal de Madrid (HMM), via JMAM)_
The armoured train built in the workshops of the Devis Company in Valencia, seen on the day it was presented to the press.
_(Photo:_ Ahora _(Madrid) No 1771 [ND] via JMAM)_
Two photos taken on 13 August 1936 showing the armoured train built in Tardienta, in response to the advance of the Nationalist forces. The rustic construction of the armour protection is typical of the very first armoured trains, but the following trains would show astounding progress.
_(2 Photos: Fundación Tierra y Libertad, via JMAM)_
### The armoured trains of Talavera and the region to the south of Madrid
To the south of Madrid, three railway lines branched out towards Estremadura passing by way of Torrijos and Talavera de la Reina; towards Ciudad Real, and towards Cuenca by way of Aranjuez. One armoured train operated on each line. On 26 August 1936, in the face of the unstoppable advance of the rebel forces to the southwest, Armoured Train 'B' was transferred from the Sierra de Guadarrama line to Talavera de la Reina, a move given wide press coverage, and immediately entered Oropesa where it went into action for the first time. Meanwhile in Madrid, a series of armoured trains was being built, designated by a letter: we know of Armoured Trains 'H', 'I', 'J' and 'K', but there were several others which have not so far been identified.
A view of Armoured Train 'H' in October 1936 near Toledo on the approach to Talavera Station. The artillery wagon is the six-axle bogie type.
_(Photo: AGA)_
Armoured Train 'H' with a different armoured engine, this time propelling an artillery wagon converted from a four-axle bogie well wagon.
_(Photo: AGA)_
A clear view of the front of the engine of Train 'H', with an armoured cab. The usual slogans and initials of the political parties and trade unions on the Republican side are clearly visible.
_(Photo: AGA)_
The Republican forces lost control of Talavera de la Reina and pulled back towards Torrijos with the support of armoured trains which helped with the transport, made themselves useful, supported operations, but all in vain. When Toledo was captured in early November 1936, the line to Aranjuez was cut between Toledo and Algodor, then in November at Getafe when the Nationalists attacked Madrid, and finally to the south of Ciempozuelos during the Battle of the Jarama in February 1937, severely curtailing the actions of the train. On the other hand, the Algodor-La Flamenca-Aranjuez-Seseña line remained in the hands of the Republicans, and in that zone they had the use of two new armoured trains. The older armoured train, which was large and heavy, was replaced by two smaller, lighter trains which were more effective. Armoured Train No 10 (2nd Battalion, incorporated in III Army Corps) was stationed at the Farm of La Flamenca. Armoured Train No 11 (1st Battalion, incorporated in II Army Corps) was stationed at Aranjuez Racecourse. The high standards maintained in the Aranjuez workshops permitted these two trains to remain in good working order right up to the end of the war.
Armoured wagon captured at Griñón (to the south-west of Madrid) on 28 October 1936.
_(Photo: Diniz Salgado, via JMAM)_
A shot of one of the very first armoured trains of the Civil War, seen here at Aranjuez in October 1936. Note the impression of power and at the same time protection offered by the elaborate form of the armour, which however leaves the coupling rods of the engine exposed.
_(Photo: AGA)_
Armoured Train No 10, or the Train of Aranjuez. Little information is available on this train, which had a quite modern appearance.
_(Photo: Paul Malmassari Collection)_
### The trains of Oviedo
When the Civil War began, almost the whole of the Asturias remained loyal to the Government, except for the capital and a corridor joining it to Galicia, which meant that Oviedo found itself in a state of siege for several months. In September 1936 a rudimentary armoured train was built by the workers in the La Algodonera workshop depot near Oviedo, to bolster resistance against Nationalist attacks, especially from 21 February 1937 onward. A second train was also built, to operate on the Vasco-Asturiano metre-gauge network. The two trains were in action around Oviedo on several occasions. In early 1937 a new metre-gauge train was built (or indeed it may have been a conversion of the broad-gauge train). In May, the two trains went into the workshops for repairs, and no further trace of them is recorded.
Armoured train employed in the Asturias.
_(Photo:_ Ahora _(Madrid) [14 April 1937], p 12 in the Hemeroteca Municipal de Madrid (HMM), via JMAM)_
Armoured Train 'B' in January 1937 at Jadraque. The three safety flat wagons at the front of the train can be clearly seen, and the high visibility of a moving armoured train is amply demonstrated.
_(Photo: Narciso Julián via JMAM)_
### The trains of Guadalajara
In July 1936, the railway militia were transported by train to occupy the town of Sigüenza (Guadalajara) and took up position there. Clashes with the rebels coming from Saragossa along the line of the railway began several days later. The siege (known as the battle of Sigüenza) lasted from 7 September to 15 October and ended with the surrender of the defenders. The armoured train from the Talavera line, which at the time was under repair in Madrid, was hurriedly put back in service due to the urgency of the situation, and tried to support the besieged forces. It succeeded in helping a number of militiamen to escape.
After the fall of Sigüenza, the front line moved towards Jadraque where Armoured Train 'B', a more modern and more powerful unit, with artillery platforms on six-axle bogie wagons, was stationed. After the Battle of Guadalajara, the Republican front line recoiled even further near Humanes. This front was subsequently patrolled by Armoured Trains 'E' and 'K'. In June 1937 these two trains were re-designated Armoured Trains No 9 and No 10 respectively. Finally, beginning in mid-1938 and up until the end of the war, only Armoured Train No 7 remained on this line, along with railcars, one of which was lightly armoured to undertake reconnaissance missions, as well as artillery platform wagons used for firing trials.
### The trains at the siege of Madrid
In November 1936, the Nationalist forces arrived on the outskirts of Madrid, but despite the fact that they succeeded in creating a bridgehead in the University campus, they were unable to extend it, and the front lines remained virtually unchanged up until the end of the war in April 1939. Armoured trains operated on the following lines departing from Madrid:
– on the line of the Norte towards Villalba, which was cut quite close to the capital at the Pont des Français on the River Manzaranes, an armoured train operated throughout the entire war (firstly Armoured Train No 4 then later No 6). The train distinguished itself in the fighting on 8 November, then in April 1937 during the fighting at Cerro Garabitas.
– on the Almorox metre-gauge line, an armoured train (No 12) operated between Goya Station and the suburb of Aluche. In 1937, the train was hit by friendly fire from Republican artillery and was put out of action.
– the lines from Andalusia and Estremadure were cut a short distance from the capital, but at least three armoured trains operated on them near the suburbs of Delicias and Villaverde.
– on the line from Valencia, also cut a short distance from the capital, one train was in action for the entire duration of the war.
All of these trains were kept in operational condition during the last two years of the war, but they were gradually taken out of service, due principally to a lack of coal. Thus by February 1939 only a single unit of the Armoured Train Brigade remained in service, in the Northern Station.
### The armoured trains of Andalusia and Estremadura
From Madrid, a railway line ran towards Cabeza de Buey and Almorchón, then two branches continued towards Badajoz and Cordoba. Because the lines in the south of Estremadura and those of the north-west of Andalusia were quite close together, armoured trains constantly moved from one front to the other. The study of these trains is therefore treated as if they ran in one single zone.
In 1936 and early 1937, we know that an armoured train was in action in Andalusia, but we have no details of its composition, just as for a train which arrived from Madrid in September 1936 and was in action on the Oropesa and Talavera de la Reina front.
In early 1937, two trains were armoured at Águilas (Murcia), using two diesel shunting locomotives and wagons built as lightly as possible (because of the limited power of the shunters). Armoured Train No 7 was sent to Estremadura for the operation on the Tage in May 1937, and No 8 went to Andalusia. Shortly afterwards, they were employed paired with steam-hauled armoured trains.
Diesel shunter T.M. 2201.
_(Photo:_ MTZ-Motortechnische Zeitschrift, _Heft 12 [1942], p 489)_
Near Villanueva de la Serena, we also know of the actions of several special trains, on one of which members of the crew were trained for special operations such as the capture of prisoners – ideally officers to obtain intelligence from them. Nicknamed the 'Band of Crows' after their train, this unit was disbanded following unauthorised behaviour.
Another train was crewed by Catalan volunteers, controlled by the powerful 'National Railway Union' from the 9th (Barcelona) Zone. They conducted their own private war as they did not acknowledge the authority of the Armoured Trains Brigade. This situation was tolerated up until the end of 1937, when the Brigade Commander demanded that the command detachment of the train be relieved of duty and be replaced by an experienced team. The train thereafter became Armoured Train No 13Bis, and carried out its missions effectively.
The actions of the trains on the metre-gauge Peñarroya-Puertollano line deserve special attention and will be described later.
From the moment when Armoured Trains Nos 7 and 8 were sent to the Spanish Levant in mid-1938, up until the end of the war only Armoured Train No 3 stationed at Km Post 308.9 on the Madrid-Badajoz line, and Train No 4 stationed at Los Pedroches remained in the Andalusia /Estremadura Zone.
### Armoured Trains No 7 and No 8 (Diesel)
By the end of 1936, the workshops had acquired a certain amount of experience with armouring steam engines, and their limitations had been recognised, such as the lack of range due to the amount of fuel and water which could be carried on board, and their high visibility due to the smoke and steam from their chimneys. Tests carried out with 40- or 60-horsepower shunters revealed that they would be incapable of supporting the weight of the armour. Studies were then made into the possible use of 200-horsepower shunters, of which two examples were available. In early January 1937 the 210hp diesel locomotive No 2201 was sent to Águilas (Murcia), for conversion in the central railway workshops of Lorca in Baza. There it received its armour, which was also fitted on two mineral wagons chosen to be the lightest and smallest capable of carrying the required loads. The result was a train of reduced dimensions but heavily armed, capable of immediate intervention in a threatened area as it could be started up in several minutes, compared to the several hours needed to start a steam train. Its crew consisted of a captain, two lieutenants, two drivers, twenty-four militiamen, six gunners, two radio operators, three optical signallers, a doctor, two cooks, an ordnance specialist and an armourer. It was given the number 8, and was placed under the orders of the Tank Brigade. As its conversion was being completed, a second diesel shunter was taken in hand for armouring, becoming the future Armoured Train No 7.
Close-up of the safety chariot at the front of Armoured Train No 8 (Diesel), an arrangement which was unique in the history of armoured trains.
_(Photo:_ Mi Revista, _Barcelona [15 June 1937], HMM via JMAM)_
A rare profile shot of the complete Train No 8 (Diesel). Its well-designed layout in our opinion classes it among the most modern of its period. Note the armoured walkway between the two wagons.
_(Photo:_ Mi Revista, _Barcelona [15 June 1937], HMM via JMAM)_
The complete Armoured Train No 7 which sought refuge at La Tour de Carol in 1939. It would be interesting to know its ultimate fate: was it given back to Spain, as the different rail gauge prevented its use in France, or was it cut up for scrap?
_(Photo: L'Illustration, [4 March 1939])_
### The projected armoured train on the Peñarroya-Puertollano line
The metre-gauge line known as 'Peñarroya to Puertollano' ran to the north of the province of Córdoba. The war had cut it in two, with 90km (55 miles) on the Nationalist side and 140km (88 miles) on the Republican side. In mid-1937, the town of Pozoblanco became the base of the Eighth Army. A year later, a scantily-protected train was built using 2-8-0 tank engine No 22 at the town station, to which was coupled a wagon protected with wood, the latter armed with machine guns protected with sandbags. Even though this train saw little use, apart from patrol duties, it gave birth to a more ambitious project.
In this view, compared with the original design sketch used by the author, the armour of the engine is higher than that on the armoured wagon. As the turret was to have 360-degree traverse, it was therefore necessary to increase the height of the turret.
_(1/72nd scale model by Paul Malmassari)_
Another view of the 1/72nd scale model built by the author, which was intended to copy as closely as possible the characteristic features of the design sketch. Building in three dimensions meant correcting the approximations of the flat drawing. This was at the limit of this type of reconstruction, but shows it to advantage.
_(1/72nd scale model by Paul Malmassari)_
Captain A Cueto, a technician in the Armoured Trains Brigade, proposed the construction of a short train, of reduced dimensions but powerfully armed. Therefore engine No 22 would be completely covered by armour, formed of nickel-chrome plates 14mm thick on the exterior and 7mm on the interior, the 80mm space between the plates being filled with reinforced concrete. This armour would be inclined to increase the degree of protection. The engine would be coupled semi-rigidly to a short wagon, similarly armoured, designed to carry the main armament. The armour protection would weigh 7.4 tonnes for the engine and 11.15 tonnes for the artillery wagon. The armament was to be either a 70mm mountain gun or a 57mm naval gun. Two light machine guns were planned to be fitted at the front and the rear, and two 7.62mm heavy machine guns would be in ball mounts on the sides of the wagon. According to several eyewitnesses, this train was actually built and used up until the end of the war, but no surviving document produced by the Armoured Trains Brigade makes mention of it.
### The armoured trains of the Spanish Levant
At the start of the Civil War several trains transferred militiamen from the Levantine areas to the Aragon front, and the action of the armoured train built in Valencia has been already mentioned above in the paragraph dedicated to Aragon. Up until mid-1938, the region saw no military operations, apart from several air raids, but with the arrival of Nationalist troops at Vinaroz, the Republican zone had been cut in two, with Catalonia to the north and Valencia to the south.
A photo taken inside Armoured Train No 8 when it was part of an exhibition of captured equipment in Valencia Station, on 5 May 1939.
_(Photo: Eduardo Rubiales Rascón Collection, via Artemio Mortera)_
During the conquest of Valencia, which began with a powerful Nationalist offensive on several fronts and notably in the Province of Castellón, at least three armoured trains were in action: Armoured Train No 1 from the Army of the Centre (Madrid), Armoured Train No 8 (diesel) from the Estremadura-Andalusia front, and Armoured Train No 12, which was the most powerful and the most modern, having been built in the Sagonte steelworks. Fighting took place on the Sagonte-Teruel line and on the Valencia-Sagonte-Tortosa line, the trains changing from one sector to the other depending on the operational situation. One of the hardest fights took place at Alcalá de Chivert where Train No 8 was derailed and remained under enemy fire for two days before it could be recovered. This front was the subject of propaganda articles in the press, which reported the destruction of several trains. However, the supporting photos always showed the charred remains of wooden wagons, and in one case an engine, and none showed an actual armoured train.
Armoured Train No 8 had first been allocated to the Almorchón-Córdoba line, but it also fought near Toledo in early May. Armoured Train No 7 then rejoined the zone which extended as far as Peñarroya, La Granjuela and other peripheral zones where some hard fighting took place. In April 1938, Armoured Train No 8 rejoined the Valencia-Tarragona line and it was here, near Alcalá de Chivert that it was derailed as mentioned above. Armoured Train No 7 also intervened in that zone, including the battle of the Ebro where it was used to transport ammunition to the troops. The three armoured trains finished the war in this zone, Train No 7 withdrawing to the French frontier in early March 1939 (see the earlier photo taken at La Tour de Carol). Train No 8 remained in the province of Valencia after the bridge over the Ebro had been cut. Along with Train No 12 it was photographed in Valencia Station several days after the capitulation, in a display of captured enemy equipment.
### Armoured Train No 12
By mid-1937 the Popular Army of the Republic had gained valuable experience in the employment of armoured trains, and had developed new designs such as the diesel trains. A new project was undertaken in the factory at Sagonte (Fábrica de Guerra Número 15) which was extremely advanced as regards its protection as well as in its overall concept. The armour was to be sloped to obtain the greatest possible protection without too great an increase in weight, and the steel chosen was of the best quality, with thicknesses varying from 20mm to 23mm on the turrets, to 7mm to 14mm on the side panels.
A precise description was written by Political Commissar Manuel Rodriguez Bastante. According to him this train carried four Skoda 76mm guns in single turrets, two Vickers 40mm pompoms for anti-tank and anti-aircraft protection, behind armour 23mm thick, sixteen Maxim machine guns (made in Czechoslovakia) and a mortar at each end of the train. A command cupola was fitted between the engine and tender, with a modified submarine periscope. The crew was divided according to specialisations: a section of four groups of artillerymen, one section of mortar crews, two sections of machine-gunners and anti-aircraft gun crews, one section of infantry and one for repair work. These last two, armed with infantry weapons, would also form a ground assault unit.
The train came out of the factory on either 14 or 15 April 1938 and was to join the eastern front (Andalusia and Estremadura), but on the very same day the Nationalist forces cut communications between the Catalonia-Aragon region and the centre-south of Spain. The train therefore remained based at Sagonte, which was the junction of the two operational lines of the Centre-South Group of the Republican Army of the Levant: the Valencia-Barcelona line and the Valencia-Teruel line. As the line was cut at Vinaroz, the train went into action notably at Alcalá de Chivert, where its guns inflicted heavy losses on the Nationalist 4th 'Navarre' Brigade.
The construction of the train had been lengthy and difficult: the initial plans are dated July 1937 and the train not was completed until April 1938. For example, the original Type 400 engine of the Norte had to be replaced by a _Garraf_ ; also, the long recoil of the Skoda guns prevented their installation in the turrets as designed, and they had to be reworked. Again, differences between engineers as regards the technical aspects and tactical requirements had delayed the design work. However, in the end the completed armoured train, 50m (164ft) long and weighing 300 tonnes, was a success, and its fighting capacity far exceeded that of previous trains.
The original design from 1937 for Armoured Train No 12, showing the small planned turrets. The complete train weighed around 300 tonnes, and the 4-8-0 engine No 2.074 of the Central Aragon Railway was capable of hauling it at up to 115km/h (72mph).
_(Drawing via JMAM)_
One of the artillery wagons as built, with Skoda 80mm guns. Note how, compared with the original plan of 1937 shown above, the casemates carrying the turrets have been increased in width, because of the need to install larger turrets to cope with the guns' long recoil. Note also the inclined armour side walls.
_(Photo: Eduardo Rubiales Rascón Collection, via Artemio Mortera)_
The armoured engine of Train No 12 photographed in Valencia on 5 May 1939, during the display of captured Republican equipment. In the background is an artillery wagon, then elements of one of the diesel armoured trains, probably No 7.
_(Photo: Eduardo Rubiales Rascón Collection, via Artemio Mortera)_
### The armoured trains of Catalonia
Several armoured trains built in the workshops of _La Maquinista Terrestre y Maritima_ at San Andrés had operated in support of the anarchist columns which left Barcelona for Aragon and Estremadura during the initial months of the Civil War. At some date between late 1937 and early 1938 the construction of at least three more armoured trains had begun in the same workshops, intended to equip the Catalan Army (Catalonia, having declared its independence, had formed its own government and army). The known photographs of these trains, taken in or outside the workshops, shown semi-artistic flowing forms, with novel technical features such as periscopes or weapons in ball mounts. However, these trains never became part of the Armoured Trains Brigade, and in fact it is not certain whether any were used in combat, since no photo showing a complete train or one at the front has come to light.
We do know that Armoured Train No 7 (Diesel) arrived to support the troops on the Ebro (between July and November 1938) before withdrawing to seek refuge at La Tour de Carol in France at the time Catalonia fell to the Nationalists.
An armoured train photographed during the battle of the Ebro. Note what appears to be an armoured cupola on a four-wheel flat wagon in front of the steam engine, then a wagon with a turret resembling that of the 'Phantom Train' shown earlier. The engine is a 4-8-0 of the 1400 Series, from the MZA Company.
_(Photo: All Rights Reserved)_
Note the extremely elaborate camouflage scheme which effectively breaks up the outlines of the artillery wagons. In this photo we can see lower and upper rows of firing loopholes plus the machine-gun ball mount.
_(Photo: All Rights Reserved)_
Seen here in January 1938, this type of armoured wagon built in Barcelona seems to be the only design to have two cylindrical gun tubs. Note it carries a different style of camouflage to the two in the preceding photo, more akin to the 'speckled' scheme seen on engine No 4.069 in the following shots, and its machine-gun ball mounts are also the same type. Note how the vertical sides curve inwards at the ends to increase the machine guns' field of fire.
_(Photo:_ Mi Revista, _Barcelona, No 30, p 78 via JMAM)_
Two views of engine 4.029 of the Norte Company, photographed in the workshops of La Maquinista Terrestre y Maritima in Barcelona.
_(Photo: Luis del Valle Mendiburo, via Francisco Cruzado Albert)_
The camouflage scheme is highly elaborate. Note the well-finished rounded corners of the forward casemate which are evidence of a sophisticated industrial capability, together with the machine-gun ball mounts, each one paired with a sighting/observation aperture to its right
_(Photo: Luis del Valle Mendiburo, via Francisco Cruzado Albert)_
The tender fitted with a machine-gun turret as well as the installation of a machine-gun casemate at the front of certain engines are characteristic features of the trains of the Spanish Civil War.
_(Photo: Luis del Valle Mendiburo, via Francisco Cruzado Albert)_
### The Republican armoured trains as objects of propaganda
In the propaganda field, the following song was one of the success stories of the Spanish Civil War:
| Translation:
---|---
**El Treno Blindado** | **The Armoured Train**
_Yo me subí a un pino verde_ | I climbed a green pine tree
_Por ver si Franco llegaba_ | To see if Franco was coming
_Y sólo vi un tren blindado_ | And I only saw an armoured train
_Lo bien que tiroteaba_. | Its machine guns firing
_Anda jaleo, jaleo, jaleo_ , | Anda fuss, fuss, fuss
_Silba la locomotora_ | Whistled the engine
_Y Franco se va a paseo_ | And Franco went away
_Y Franco se va a paseo_. | And Franco went away
_Por tierras altas de Burgos_ | On the high ground of Burgos
_Anda Mola sublevado_ , | Away went Mola angry
_Ya veremos cómo corre_ | We clearly saw how he ran
_Cuando llegue el tren blindado_. | When came the armoured train
_Anda jaleo, jaleo, jaleo_ , | Anda fuss, fuss, fuss
_Silba la locomotora_ | Whistled the engine
_Y Mola se va a paseo_ | And Mola went away
_Y Mola se va a paseo_. | And Mola went away
_Yo me fui en el tren blindado_ | I went in the armoured train
_Camino de Andalucía_ | On the way to Andalusia
_Y vi que Queipo de Llano_ | And I saw how Queipo de Llano
_Al verlo retrocedía_ | At the sight of it ran away.
_Anda jaleo, jaleo, jaleo_ , | Anda fuss, fuss, fuss
_Silba la locomotora_ | Whistled the engine
_Y Queipo se va a paseo_ | And Queipo went away
_Y Queipo se va a paseo_. | And Queipo went away
A series of profile drawings all to the common scale of 1/400, which reproduce and compare all the historical Spanish armoured trains.
_(Document: Francisco Cruzado Albert)_
**SOURCES:**
**Archives:**
Archivio General Militar de Madrid (AGMM), Madrid, Spain.
Archivio General de la Administración (AGA), Alcalá de Henares, Madrid, Spain.
Hemeroteca Municipal de Madrid (HMM), Madrid, Spain.
SHD, 7 N 2755-EMA/2ème bureau.
**Books:**
Arévalo Molina, Jacinto M, _Los Trenes Blindados Espaňoles_ (Gijón: Ediciones Trea, S.L., 2003).
Cruzado Albert, Francisco, _Carros de combate y vehículos blindados de la guerra 1936-1939_ (Barcelona: Borrás ediciones, 1980).
Fernandez Sanz, Fernando, and Reder, Gustavo, _Historia de la tracción vapor en España. Tomo VI, 1936-1941_ (Madrid: Proyectos Editoriales S.L, 2014).
Kondratenko, R V, _Ispanso-Amerikanskaya Voína 1898 Goda_ (St Petersburg: Tsitadel 2000).
Mortera Pérez, Artemio, _Los Carros de combate 'TRUBIA' (1925-1939)_ (Valladolid: Quirón Ediciones, 1994).
Taylor, Thomás L, _Los Ferrocarriles en la Guerra_ (Barcelona: Administración de la revista científico-militar, 1885).
**Journal articles:**
Afán Alcáraz, Juan, 'Trenes Blindados en la Guerra Civil', _Carril_ No 14 (December 1985), pp 23–7.
Arévalo Molina, Jacinto M, 'El tren que nunca existió', _Revista Española de Historia Militar_ (September 2001), pp 109–11.
______________________, 'La Brigada de Trenes blindados 1936-1939', _Memorial del Arma de Ingenieros_ (December 2000), pp 99–110.
______________________, 'Los Ferrocarriles militares en la guerra de Cuba', _Memorial del Arma de Ingenieros_ (June 1999), pp 139–45.
______________________, 'Los Trenes blindados en la Guerra Civil Española', _Revista de Historia Militar_ No 88 (2000), pp 181–206.
Cruzado Albert, Francisco, 'España: Guerra Civil 1936/1939', _Hobby Tren_ No especial 150 (April 2006), pp 58–67.
_____________________, 'Tren Blindado, España: Guerra Civil 1936/1939 (I)', _Hobby Tren_ No 169, (November 2007), pp 66–75.
_____________________, 'Tren Blindado, España: Guerra Civil 1936/1939 (II)', _Hobby Tren_ No 170 (December 2007), pp 44–53.
_____________________, 'Trenes Blindados', _Trenmania_ No 7 (2001), pp 57–66.
Surlemont, Raymond, 'Republican Armoured Trains in the Spanish Civil War 1936-1939', _Tank TV_ No 6, (June 1994), pp 5–7.
**Sound recordings (partial list):**
_CNT. FAI. 1936. The Spanish Revolution_ , by The Ex, AK Press, San Francisco, 1997 (2 CDs).
_Chants de la Guerre d'Espagne_ , Le Chant du Monde, ref. LDX-S 4279, 1963 (vinyl).
_Espaňa en el Corazón_ , Bear Family Records GmbH, 2014 (CD + DVD).
. In Spanish: ' _Trenes Blindados_ '.
. He was killed in action on 19 May 1895.
. The Spanish gauge was wider than that in France: 1668mm (5ft 3¾in) as against 1435mm (4ft 8½in).
. Certain reports mention the existence of four Nationalist armoured trains, only one of which went into action, the other three lasting only a short time.
. The region to the north-west of Madrid.
. UHP = _Unión de Hermanos Proletarios_ , the Union of Proletariat Brothers; UGT = _Unión General de Trabajadores_ , the General Workers Union; CNT = _Confederación Nacional del Trabajo_ , National Working Confederation; AIT = _Asociación Internacional de los Trabajadore_ s, the International Workers Association.
. Capital of the Asturias.
. With a power output of only some 200hp.
. It is interesting to note that the French Military Attaché in Spain reported on the construction of this train in July 1937, and considered 'its form to be well-designed', but the armour protection failed badly: during trials the plates had resisted 20mm to 37mm shells fired at them, but shells from field guns 'shattered them like glass'. Lastly, he mentioned a French engineer as having participated in the design of the train, without naming him, but the Spanish archives give his name as a certain M. Lempereur (Letter by Colonel Morel No 502/A of 7 July 1937, 7 N 2755, SHD). In general, the Attaché considered the war as he observed it to be incomprehensible, for example because of the negligence of the belligerents in not destroying the tracks.
## SWEDEN
### ARMOURED TRAINS AND TROLLEYS 1905–1960
### The Crisis of the Union (1905)
As a consequence of the crisis of the Union in 1905, which obliged Sweden to take steps to defend its new frontier to the south-west with Norway, the railway network took on a new strategic importance. The task of guarding the line was given to the Wärmland frontier detachment under the command of Major Arvid Wester, who had served as an observer during the Boer War and who was therefore well aware of the capabilities of armoured trains. In addition to the fortifications he had built in the region of Eda and also Charlottenberg, he decided to construct an armoured wagon to provide a means of mobile defence. An old wagon from Göteborg was sent to Charlottenberg where it was fitted with 8mm-thick plates and armed with a Hotchkiss Model 1897 machine gun (known in Sweden as the ksp:/1900). It appears that neither this wagon nor any subsequent units actually entered service.
The 1905 armoured wagon as built.
_(Photo: All Rights Reserved)_
This view could depict the armour being either fitted or removed (but in our opinion probably the latter), showing the wooden planking at one end. The large number of fixation holes for the plates would indicate that they were hurriedly adapted from boiler plate or constructional panels.
_(Photo: Sveriges Järnvägs Museum)_
### 'Landsverk 320' Armoured Trolley
In 1931 the firm of Landsverk carried out a design study of an armoured rail trolley intended for reconnaissance and for guarding railway infrastructure such as bridges. Its main armament was to comprise a 20mm cannon and coaxial machine gun in each of two turrets. The description specified that the armament disposition allowed for end-on fire by three machine guns and a cannon, and lateral fire by both cannon plus five machine guns and small arms per side. The trolley design was symmetrical, and it was to be driven from the central armoured cupola where the vehicle commander/driver sat on a pivoting seat. In addition, it was proposed to attach anti-aircraft armament on top of the turrets. This design was offered to Ireland, but seems not to have been proceeded with.
**Technical specifications:**
Gauge | 1435mm (4ft 8½in)
---|---
Wheel diameter | 0.7m (2ft 3½in)
Overall length | 6.20m (20ft 4in)
Hull width | 2.025m (6ft 7¾in)
Overall width | 2.30m (7ft 6½in)
Wheelbase | 2.80m (9ft 2¼in)
Armament height | Swivelling MGs 2m (6ft 6¾in)
| 20mm cannon & coaxial MGs 2.5m (8ft 2½in)
Overall height | 3.05m (10ft)
Weight in working order | 13.2 tonnes
Motor | 6-cylinder 60/70hp at 1200/1400 rpm
| Electric starter
Range | 800km (500 miles)
Gearbox | 1st = 10.5km/h (6.5mph)
| 2nd = 20.5km/h (12.7mph)
| 3rd = 30.5km/h (19mph)
| 4th = 50km/h (31mph)
Minimum track radius | 65m (213ft 3in)
Armour protection | Sides and ends, turrets: 14mm
| Command cupola, access doors, cowcatchers: 10mm
| Roof: 6mm
### Armoured Trains _Boden_ and _Kiruna_
In 1940, General Douglas, commanding officer of the Great North Army Group, decided to build four armoured trains: _Kiruna_ , _Boden_ , _Malmö_ and _Österlund_ , all bearing the name of their home base, but the last two would not see the light of day. _Kiruna_ was built in the workshops of the LKAB Mining Company, using two Type Or flat wagons. The armour protection was 15mm thick (5mm for the roofs). The wagons of _Boden_ , built in the SJ workshops in Notviken, were of a quite different design. This train had three open-topped armoured wagons, with the anti-aircraft wagon being placed immediately in front of the engine. For both trains, the engines chosen were 2-6-4 types of Class J, partially armoured. _Kiruna_ was completed on 20 May 1940 and _Boden_ the following month.
_Kiruna_ patrolled the Kiruna-Narvik mineral line and _Boden_ the Boden-Haparanda line. There is very little surviving information on the actions of these trains, apart from 20 May 1940 when _Kiruna_ , in Vassijaure Station 7km (4.3 miles) from Narvik, and an anti-aircraft battery exchanged fire with a German aircraft. In the course of this action a Swedish soldier by the name of Sven Sjöberg was killed. In 1945 the two trains were demobilised, but they were maintained in reserve up until 1949, before being scrapped in around 1960.
The domes on the turrets had vision slits and the lateral loopholes allowed the use of personal weapons as well as one machine gun per side. The siting of the entry doors beside the offset turrets would appear to make for difficult access given the position of the gunner's seat, but this arrangement would permit the swivelling of the lateral machine gun on the opposite side.
_(Landsverk drawing: Paul Malmassari Collection)_
The central cupola was equipped with an emergency escape hatch. Note the horizontal fields of fire: 290 degrees for the turrets; 180 degrees for the corner casemates (by dismounting and repositioning the MGs); 90 degrees for the side-mounted MGs.
Crew member armed with an m/37-39 sub-machine gun, made by Husqvarna and modified to fire the 9x19mm Parabellum round.
_(Photo: Sveriges Järnvägs Museum)_
The importance given to these armoured trains can be gauged by the fact that in 1939 there were only twenty 57mm guns in service in the whole of Sweden.
_(Photo: Sveriges Järnvägs Museum)_
The 57mm gun on _Boden_ had a restricted firing embrasure allowing limited traverse and even less elevation. It had a range of 4000m (4375 yards).
_(Photo: Sveriges Järnvägs Museum)_
The engine of _Boden_ was Class J No 1390, with armour protecting only the coupling rods and the cab. The three wagons were built by placing armoured hulls on Type Mas 6-wheel flat wagons.
_(Photo: Sveriges Järnvägs Museum)_
The twin-handed 8mm Kulspruta m/36 Lv Dbl anti-aircraft machine guns on _Boden_. Note the fixed radio antenna behind the gun position.
_(Photos: Sveriges Järnvägs Museum)_
A fine profile shot of _Kiruna_ , showing the anti-aircraft mounting on the roof of the rear wagon. The engine is partially-armoured Class J No 1343.
_(Photo: F.M.W.)_
The 37mm gun which armed the leading wagon had a practical range of 4000m (4375 yards).
_(Photo: Sveriges Järnvägs Museum)_
In this shot the 37mm Bofors has not been mounted. Because the gun was offset to the left to allow space for the machine gun mounted in the front right corner embrasure to swivel, there was no room available for a corner embrasure on the front left. The armoured wagons were constructed using Type Or flat wagons.
_(Photo: Sveriges Järnvägs Museum)_
_Kiruna_ at Riksgränsen in 1941. Note the lack of lamps and also of cowcatchers beneath the buffer beam of the front wagon. The gun is the 37mm _pansarvärnskanon_ m/38 (or m/37), and its barrel is closely enveloped by the two sliding shutters when these are closed.
_(Photo: Sveriges Järnvägs Museum)_
**SOURCES:**
Berggren, Jan-Gunnar, 'Pansartåg, järnvägsartilleri och järnvâgsluftvärn', _Militärhistorisk Tidskrift_ (2004), pp 111–59 (translated by Captain Valérie Cagnard).
Furugård, Bo, 'Pansartåget Kiruna', in Hultstrand, Birger, _Kungl. Norrbottens regementes historia 1841-1966_ (Boden: Kungl. Norrbottens regementes kamratfören, 1972), pp 359–65.
'Pansansartagen Kiruna och Boden', _Pansar_ (1983/4), pp 16–19.
. The Union between Norway and Sweden was concluded on 4 November 1814. Sweden had forced Norway into a personal union with a common monarch and foreign policy, but the Norwegians resented the breakup of their previous union with Denmark which had lasted for 434 years. Disagreements between the two countries, notably over Norway's demand for separate consular services to oversee its large merchant marine, increased to the point where a plebiscite in August 1905 formally recognised that the Union had ceased to exist.
. In Swedish, _Pansar-Dressin_.
. Certain sources mention a Dornier Do 26, a four-engined flying boat armed with a 20mm cannon in a nose turret and several machine guns. Both the V1 and the V2 were operating in the Narvik area up to their destruction on 28 May 1940 by RAF Hurricanes.
. A town on the frontier with Norway, and 40km (25 miles) to the east of Narvik.
## SWITZERLAND
To the best of our knowledge, Switzerland has never employed armoured trains. On the other hand, a work dealing with the employment in Switzerland of railways for troop transportation and other military operations, inspired by the American Civil War and published in Basle in 1868, outlined proposals for the use of locomotives running light for reconnaissance missions by officers, and for wagons fitted with armour protection. The carriage of an assault team was also envisaged, for ground combat in the case of the train meeting a serious obstacle.
Analogous to the use of guns mounted in armoured trains to provide mobile firepower, we need to record the two platform wagons used at Fort Dailly between 1884 and the end of the Second World War. Running on rails in a cutting, the guns were on disappearing mountings, being reloaded beneath the armoured roof, rising in order to fire and retracting under recoil. When not in action they were housed in a tunnel with armoured doors.
**SOURCES:**
De Montet, Lt Col Jean, _Les Bouches à Feu de l'Artillerie Suisse 1919-1939_ (Lausanne: Editions du Centre d'Histoire, 1980). Hoffmann-Merian, Theodor, _Die Eisenbahnen zum Truppen-Transport und für den Krieg im Hinblick auf die Schweiz_ (Basle: Schweighauser, 1868).
The two disappearing mountings on a track at Fort Dailly, Emplacement E3.The guns were 12cm/L25 Krupp Model 1882s on Saint-Chamond coast-defence disappearing mountings. One gun and its mounting, without the wagon, is on display at the entrance to the fort.
_(Photo: Heer Kommando Festungswachtkorps, FWK Region 2)_
## THAILAND
Sulzer 450hp A1A-A1A locomotives, used in Siam from 1931 to the 1990s, were fitted with armour-plated cabs, possibly as early as the Second World War. From 1960 Thailand suffered continuous threats to its security, fomented by Communists, some being militants fleeing Malaysia and others being opponents of the Vietnam War, as between 1965 and 1975 Thailand was a base for the US Air Force. Several Wickham trolleys were obtained from Malaysia. The state of insecurity continued until just before the date of writing, notably in the South, with few details being released. Three armoured trolleys survive, No 50 at Thung Song, and two others in Bangkok at Bang Sue and Hua Lamphong.
A view of an armoured wagon preceded by a flat wagon loaded with a Vickers 6-Ton Mark E Type B tank, armed with a 47mm gun and a coaxial machine gun to the right of the main gun. Siam (renamed Thailand from 1939) possessed eighteen of these tanks prior to the Japanese invasion.
_Photo: All Rights Reserved)_
Before restoration, Wickham No 50 at the loco depot of Yhung Song, seen from the right-hand side.
_(Photo: All Rights Reserved)_
Several restorations later, and fitted with a fake gun, it has finally benefitted from a livery in Thai national colours, which detracts somewhat from its martial appearance.
_(Photo: All Rights Reserved)_
On this trolley seen from the front (with the driving position on the right), the .50 Cal machine gun is still in place, and there is a warning horn on the right-hand side of the turret.
_(Photo: All Rights Reserved)_
A trolley in a sorry state in Bang Sue Station (Bangkok).
_(Photo: All Rights Reserved)_
. The red symbolises the earth and the people, the white the religions and the blue the monarchy.
## TUNISIA
With the rise of nationalism, a 'Battle of the Rails' began in 1952, but it turned out to be less serious than the attacks on the railway network in Algeria. The first incident took place on 21 January when a section of rail was unbolted, resulting in traffic being held up for five days. From April 1952, the role of guarding the tracks was confined to 'security groups', but from May onward the running of trains at night was stopped. This measure continued up until July 1953 for freight trains and until January 1954 for passenger trains. In addition, armour protection was added to the motor units.
Following the war of independence, certain elements in Tunisia who supported the FLN in Algeria remained hostile to the continued French presence. On at least one occasion this anti-French sentiment led to the use of armed rail wagons.
In 1961 Air Base No 156 at Sidi-Ahmed was due to receive Mystère IV fighters to replace its force of Mistral fighter-bombers. From 13 June, threats to the security of the base increased to the point where, on the evening of 19 June, the 2nd RPIMa (Marine Infantry Parachute Regiment) dropped onto the base, which by then was surrounded and under fire from Tunisian artillery. The Tunis-Bizerte railway line which ran alongside the base allowed the Tunisians to install mortars in rail wagons. In the course of this operation, enemy fire caused a number of casualties, with two men killed and twenty-three wounded, and hit or destroyed five Noratlas transports.
**SOURCES:**
Bucher, Antoine, 'Mémoire des évènements de Bizerte vécus au sein de la compagnie de défense CD30 de la base de Sidi-Ahmed', _La Charte_ No 7 (November 1998), pp 21–2.
Patrick-Charles, Renaud, _La bataille de Bizerte (Tunisie)_ (Paris: Harmattan, 2011), p 20.
Railwaymen extend the bodyline red band around the frontal armour added to one of the seventeen Alsthom/Sulzer BB diesel-electric locomotives of the 'Overseas' type belonging to the Gafsa Phosphate & Railway Company in May 1953. The locomotives were numbered 201 to 217.
_United Press Photo: Paul Malmassari Collection)_
. We are dealing with the Tunisian Railways separately from those in France, as under the terms of the French Protectorate, the former came under Tunisian sovereignty.
. More commonly known as the Sfax-Gafsa line, abbreviated to S.G.
## UKRAINE
### ARMOURED TRAINS
The history of the Ukraine is complex, and requires a brief introduction in order to be able to understand the tortuous story of its armoured trains.
The territory of the Ukraine was fought over first by Germany and Austria-Hungary, then by the nations and various factions which were born or profited from the dismantling of the Russian and Austro-Hungarian Empires: Poland, Romania, Bolshevik Russia, Red Ukrainians, Nationalist Ukrainians, the White Russians, the Anarchist Black Army of Makhno, independent Cossacks and assorted atamans (warlords).
The Ukraine (less Galicia and the Crimea) declared its independence on 1 November 1917, while the Bolsheviks created their own republic in the east of the country, as did other local power groups. On 22 January 1918 the Rada (Ukrainian Parliament), under pressure from the Reds and the Black Anarchists under Makhno, was forced to leave Kiev. In addition, territorial claims based on the presence of large ethnic minorities led Romania to seize first Bessarabia then Bucovina in January 1918.
Following the capture of Kiev by the Germans on 1 March 1918, three different states coexisted: a Bolshevik government under Christian Rakowski, centred on Kharkov; a Popular Ukrainian Republic (Ukraine of the Dnieper) controlled by the warlord Symon Petlioura; and then from 1 November 1918 a Popular Republic of Western Ukraine with its capital at Lvov headed by Jevhen Petrouchevitch.
Conscription was introduced on 13 November 1918 to establish the Western Ukraine Army, in order to counter the Polish separatists in Lvov. In December 1918 an Allied force under French command landed on the shores of the Black Sea to counter Bolshevik progress. But in 1919, part of the Carpathians was given to Czechoslovakia, and on 14 February 1919 Galicia was made a part of Poland. By late 1919, the Ukraine, with the exception of the Crimea, was in the hands of the Bolsheviks. In February 1920, part of the Western Ukrainian Army was incorporated by force into the Red Army and became the Ukrainian Red Army of Galicia. In April 1920 two of its brigades surrendered to the Poles when Poland and the Ukraine signed a treaty to drive out the Bolsheviks. However, the Ukrainian forces were beaten in November 1921 and Poland signed a separate treaty with the Bolshevik Party of the Ukraine. Reduced to guerrilla operations only, the remaining Ukrainian forces were crushed by Bolshevik cavalry on 17 November 1921.
Armoured trains continue to play a major role in Ukrainian folklore. In September 2013, a tramcar was converted into a replica armoured train in honour of the train _Za Batkivshchnynu_ ('For the Mother Country') which saw combat in July 1942.
### Armoured Trains of the Ukrainian Army of Halych (UHA) or the Ukrainian Army of Galicia
During the First World War, Galicia was the scene of bitter fighting between Russia and the Central Powers. After having beaten the Austro-Hungarians in 1914, the Russians took over most of the region, but they were chased out by an Austro-German offensive between the Spring and Summer of 1915.
Fighting between Poles and Ukrainians started up again on the night of 31 October/1 November 1918 with attacks on Lvov by the Sich Riflemen and other units. In 1918 the western part of Galicia was incorporated in the new state of Poland which also absorbed the short-lived Ruthenian National Republic of the Lemkos. The Treaty of Riga signed on 18 March 1921 assigned Galicia to Poland.
The Galician railways used rolling stock left behind by the former German and Austro-Hungarian occupying forces to form their armoured trains. Many improvised trains were built in the industrial centres such as the Drohobycz Refinery or the railway workshops at Sambor. All the armoured trains of the UHA were captured by the Poles. The River Zbrucz marked the limit of the standard gauge, after which the Russian broad gauge applied, which prevented the Ukrainian armoured trains from retreating across the river with the rest of the army.
Armoured Train No 1 of III Corps of the UHA, near Lvov in December 1918.
_(Woodcut: Alexander Diedyk Collection via Krzysztof Margasinski)_
Austro-Hungarian wagon of an improvised armoured train of the UHA. This photo is of poor quality but interesting as it shows the exact moment of firing: the barrel of the 76.2mm field gun is seen at maximum recoil.
_(Photo: Alexander Diedyk Collection via Krzysztof Margasinski)_
A woodcut showing a similar gun on a UHA train, fighting an oncoming Polish armoured train.
_(Woodcut: Alexander Diedyk Collection via Krzysztof Margasinski)_
Armoured Train No 212 of I Corps of the UHA, halted and then captured by the Poles on 15 May 1919. Note the improvised protection consisting of trench shields fastened to the sides of the vans and wagons.
_(Photo: Mariusz Zimny Collection)_
A view of a Ukrainian armoured train, converted from German Type Om high-sided wagons, captured by the Poles on 9 July 1919 near D uryn (Buczacz region) during the Polish-Ukrainian War. Note the thickness of the protection and the plates extending above the wagon sides, probably trench shields.
_(Photo: CAW)_
### The Armoured Trains of the UHA in Transnistria (July 1919 – January 1920)
Despite its retreat behind the line of the Zbrucz, the UHA was not defeated. It regrouped in the Kamenets-Podolski region and formed three army corps. Along with about a hundred field guns and 390 machine guns, in late 1919 I Corps possessed an armoured train (Russian gauge), named _Halatschina_ , which the UHA had captured during its offensive towards Kiev in August of that year.
### The Armoured Trains (Russian Gauge) of the Army of Petlioura
On 23 June 1917, the National Ukrainian Republic was proclaimed. After the Russian Revolution, for a time it formed part of Russia. Several armoured trains were operated, and they ranged in quality from improvised wagons or units built in naval workshops such as in Odessa, to refined and well-armoured units captured from the Bolsheviks and Denikin's White forces.
The train in the photo below began life as Russian Armoured Train No 1 _Chunchuz_ , immobilised in No Man's Land by hits from Austro-Hungarian artillery on 24 September 1915. After repairs, it was used by the Bolsheviks, then became Ukrainian Armoured Train _Sichevik_ of the Petlioura Army. Captured by the Poles on 24 May 1920, it was used against the Russians under the name of _Krechowiak_ – as in the photo below – then later as _General Dowbór_. Then on 6 June 1920, it changed hands for the last time, being captured by the Red Cossacks of Budenny's First Cavalry Army. It appears to have suffered no serious damage, as its latest owners managed to repair it. It apparently remained in Russian service right up to the beginning of the Second World War.
Armoured train captured from the Whites by the Sich Riflemen at Kiev and then renamed _Sichovy Strilets_. The inscription ' _strilets'_ (riflemen) can be made out on the wagon's side. Note the fake firing slots painted in black to deceive enemy snipers.
_(Photo: All Rights Reserved)_
Armoured train _Krechowiak_ seen in May 1920.
_(Photo: CAW)_
Captured following the action by Colonel Wolf at Schepietovka in August 1919, this is the train christened _Wilna Ukraina_ ('Free Ukraine'). The design of the train is the same as several examples built in the railway workshops in Kiev, powered by Class O steam engines, such as Communist Korosthenskovo Rayona ('The Communists of the Korosten Region') and _Karl Liebknecht_.
_(Postcard: Paul Malmassari Collection)_
Bolshevik broad-gauge armoured train captured from the Petliura Army in 1919. Here its high-sided bogie wagon has been fitted with crude armour and a Canet naval gun.
_(Photo: Krzysztof Margasiński Collection)_
### Ukrainian Armoured Trains Co-operating with the Polish Army, 1920.
In the combat zone where the Polish forces and the Ukrainians of Petlioura operated side-by-side from April 1920, notably in Podolia, the railway network was dual gauge, both Russian broad gauge and European standard gauge.
Russian broad-gauge Armoured Train _Ukraine_ (note the inscription in Cyrillic and roman letters) seen in late 1920. The high-sided bogie wagon is fitted with a turret armed with a 76.2mm Model 1902 field gun.
_(Photo: Krzysztof Margasiński Collection)_
A meeting of two famous personalities, Józef Piłsudski of Poland and Symon Petliura of the Ukraine, at Stanislawow on 5 September 1920, on the occasion of the commissioning of the Ukrainian Armoured Train Кармелюк (Karmeluk), built in the local railway workshops.
_(Photo: Krzysztof Margasiński Collection)_
### The Modern Period
The Ukraine's desire for closer ties with the European Union, as opposed to its traditional ties with Russia, saw the sporadic reappearance of attempts to build armoured trains, such as this high-sided bogie wagon with roughly-cut firing embrasures, emplaced as a roadblock in the Lugansk region. Note the damage from a shell or RPG.
_(Photo: All Rights Reserved)_
**SOURCES:**
**Archives:**
Polish Historical Service (CAW).
**Books:**
Krotofil, Maciej, _Ukraińska Armia Halicka 1918-1920_ (Toruń: Wydawnictwo 'Adam Marszałek', 2002).
Tynchenko, Yaroslav, _Armored Trains and Armored cars in the War of Liberation 1917-1920_ (Kiev: Tempora, 2012).
**Journal articles:**
Diedyk, Alexander G, 'Armored Trains of the UHA. The war on railway tracks', _The Red Kalyna Chronicle_ No 6–7 (1992).
Wolos, Mariusz, 'Sortir de la guerre à Lvov', _Revue historique des armées_ [online] 251 (2008), put online 9 June 2008, URL : <http://rha.revues.org/323>
**Video:**
<http://ukstream.tv/en/videos/ukrayins_ki_viis_kovi_znishchili_broniepoyizd_iekstriemistiv_u_slov_ians_ku_05_05_2014#.VOcXtyybfc>
**Website:**
<http://www.encyclopediaofukraine.com/default.asp>
. Also known as the Ukrainian Army of Galicia – _Ukrayins'ka Halyts'ka Armiya_ (UHA). It was the regular army of the Western Ukrainian National Republic – _Zakhidnoukrayins'ka Narodna Respublyka_ (ZUNR). This army existed during and after the Polish-Ukrainian War.
. It should also be noted that a Red armoured train named _Ukrainski Revolutsija_ ('Ukrainian Revolution') was captured by the Finns near Antrea in late March 1918. This was obviously an honorific designation, as neither the train nor its crew had any connection with the Ukrainian Front.
. 5 December 1918 – 23 January 1919.
. Tributary of the Dniestr, in the western part of modern Ukraine, which marked the frontier between the former Austro-Hungarian and Russian Empires.
. Today situated in the north-west of modern Moldavia.
. Українська Народня Республіка (УНР), _Ukrayins'ka Narodnia Respublika_ (UNR).
. The name given to the members of the Sich Riflemen (derived from the term for a Cossack encampment).
. A region which became Polish in 1919 after having formed part of the Western Ukrainian Republic. The Soviets briefly occupied it during the Russo-Polish War.
## UNITED STATES OF AMERICA
### ARMOURED TRAINS, RAILCARS AND TROLLEYS
### Initial projects
In 1845, the _Journal des sciences militaires_ described a project by a contributor to the _United Service Magazine_ which fell halfway between railway artillery and armoured trains. He proposed defending the coastlines of the United States by means of a 'railway wide enough to allow the passage of wagons of large dimensions, similar as far as possible to the deck of a warship, open on the landward side and armed with cannons pointing out to sea'. The wagons were to be protected by an armoured side pierced by loopholes. A wall or dike of stones would be built to protect the railroad. Fortified stations set every 20 miles would enable the artillery wagons to intervene at any point on the coast within a maximum delay of fifteen minutes.
### The American Civil War (12 April 1861 – 9 May 1865)
(For the armoured rail vehicles used by the South during the Civil War, see the chapter on the Confederate States of America)
From the very beginning of the war, the employment of railway batteries in the form of guns placed at the head of trains came into use at several different locations on the front line, either on the initiative of the high command or of especially inventive local commanders. For example, in May 1861, in order to protect the network of the Baltimore & Ohio Railroad, Union General McClellan ordered the mounting of artillery at the head of troop trains. The _Dictator_ was another example, made famous during the siege of Petersburg between June 1864 and March 1865. This 13in coast-defence mortar lacked armour protection, and fired from a simple platform wagon. However, in this chapter we will confine ourselves to an examination of those armoured artillery batteries which demonstrated the modern aspects of the American Civil War, and which provided the inspiration for similar construction in many future conflicts, beginning with the Franco-Prussian War, until surpassed in ingenuity during the Boer War.
During the very first days of the war the Federal Government ordered the construction of an armoured wagon to protect the track workers on the Philadelphia, Wilmington & Baltimore Railroad. It was placed under the orders of General Herman Haupt, a renowned railroad engineer, but he refused to use it, considering the wagon to be a 'white elephant'. Nevertheless, the idea of armouring railway vehicles had taken root.
The Union Army built several armoured wagons. In the Summer of 1862, General Burnside ordered the construction of armoured wagons to counter the incursions of guerrillas and Southern raiders, but they were not meant to resist artillery. These wagons were mainly built in the workshops of the Baltimore & Ohio Railroad.
In 1862 a captain in the 23rd Massachusetts Volunteer Infantry Regiment designed an armoured artillery wagon which was built by the Atlantic & North Carolina Railroad and used for patrolling the line to the west of Newberne, where the Confederates were posted in some force. Propelled ahead of an engine with an armoured cab, this wagon bore the name _Monitor_. The wagon front, sides and rear were all inclined vertically inwards by some 15 degrees, and were painted black, with red firing loopholes. Its front end, pierced by an embrasure for a small naval gun, was armoured with vertical rails, and the sides and rear by boiler plate. The sides were bulletproof, and the front armour resisted projectiles from field guns. The roof was left open for ventilation and light, and covered by a tarpaulin. One Confederate artillery lieutenant expressed puzzlement and alarm at the first appearance of what the Southerners called the 'Yankee gunboat on wheels'.
One of many illustrations featuring the armoured wagon for the Philadelphia, Wilmington & Baltimore Railroad. This one shows the wagon parked in a station, while others show it from the same angle but in the countryside, demonstrating how much this new mechanised warfare held a fascination for the journalists and the readers of the period. The chase gun, with its muzzle swell, is likely a 10pdr Parrott rifle, capable of firing out of ports to each side as well as to the front. Note how the artist has exaggerated the width of the flat car used as the base.
_(Illustration: Paul Malmassari Collection)_
Another engraving, this time by William C Russell, showing a similar armoured artillery wagon, based on an eighteen-stave flatcar, with the Parrott rifle capable of forward and lateral fire. The sides of this wagon were trapezoidal, allowing for space alongside the gun for the gunners (shown under-scale!). The raised roof section allows light to enter and smoke to escape. The artist has represented a line of loopholes in the upper part of the sides, but the holes are too small to allow for sighting rifles. The weakest point on these trains was the engine's boiler and prominent smokestack.
_(Engraving: Paul Malmassari Collection)_
Faced by the cottonclad wagon of General Finegan (see the chapter on the Confederate States of America) during the Confederate attempt to recapture Jacksonville, in Union hands ever since 10 March 1863, the Northerners built their own armoured railway battery, armed apparently with a 10pdr Parrott rifle. The fighting between the two was the first example of combat between armoured railway wagons. The siege of Jacksonville would be lifted by the Union forces on 29 March.
In the same year, the _Scientific American_ described trials by the Northerners of an armoured engine named _Talisman_ , on which the cab and connecting rods were protected by an iron plate four-tenths of an inch (10mm) thick, on the advice of General Haupt. However, the trials showed that only small-arms projectiles would be stopped.
A Union armoured train was built by the Baltimore & Ohio Railroad with the aid of the 2nd Maryland Regiment, and was given the task of protecting the region around Cumberland. The train was arranged symmetrically on either side of the engine, which had an armoured cab. At front and rear there was an armoured battery protected by rails on three sides, the roof and rear of the wagon being left open, and then an armoured van with firing loopholes. In spite of its armour, a projectile in the boiler of the engine followed by a second striking an armoured wagon led to its destruction by the Confederates in July 1864.
This armoured wagon precedes and protects its train with a gun mounted so as to allow virtual all-round fire. This arrangement on the other hand has the inconvenience of exposing the gun crew to hostile fire when loading or when using their small arms. The armour protection would probably be constructed using inclined rails fastened to a wooden structure.
_(Engraving:_ Harper's Weekly, _1862)_
A close-up detail from an Andrew J Russell photo, showing the first train over the repaired Bull Run Bridge in the Spring of 1863, allows us a glimpse of an armoured artillery wagon, constructed on a twelve-stave railroad flatcar. Note the typical inset halfway up the armoured sides, and the gun emerging from hinged ports. It appears this was a two-gun wagon, so a similar piece would be mounted to fire from the front set of ports faintly visible in the photo (here probably trained to cover the opposite side of the track).
_(Photo: Library of Congress)_
The siege of Petersburg (June 1864–April 1865) saw the employment of railway artillery by the Union forces who wished to seize this strategic railroad centre where five major lines converged. The United States Military Railroad (USMR) which was by this time fully operational, deployed these weapons to such good effect that the Confederate Army was gradually cut off from outside aid. The town fell on 3 April 1865.
A 32pdr gun arms this battery used by the Union forces during the siege of Petersburg in 1864–5, mounted on seven axles. The use of wood for protection was widespread, and iron protection was much rarer.
_(Photo: Library of Congress)_
Alongside these units actually built, there existed a range of proposals put forward by enthusiastic citizens. For example, the project for a 'travelling battery' proposed by Charles Perley of New York, would have had the advantage of being able to move on rails (of different gauges) and on roads, the wheels being wide enough for these multiple roles. The inventor proposed to use such a wagon in front and to the rear of the engine. In the event of the wagon being uncoupled, the removable floor section would allow the crew to descend to rail or ground level and to push the vehicle, or even repair the tracks under cover. The armour protection was to consist of iron or steel plates fastened to a wooden frame. In addition to the light guns, firing loopholes were to pierce the sides, and four lengths of spare rail (marked No 4 on the plan) would be carried for track repair or replacement.
Plan attached to Patent 37.766, registered by Charles Perley, granted on 24 February 1863.
### Between the Civil War and the First World War
### Armoured trains in Panama, 1885 and 1903
Prior to the opening of the Panama Canal, the railway line linking Colón (Aspinwall to the Americans) in the north of the isthmus with Panama City in the south was of great strategic importance. To counter the attacks on the railway infrastructure of the Panama Railroad Company by revolutionaries struggling against the Colombian Government, the United States decided to intervene by sending by sea a contingent of 740 men (two battalions of Marines and sailors used to handling Gatling guns). The troops landed at Panama on 7 April 1885 then at Colón on 15 April. Between these two dates, on the night of the 10th/11th, two armed and armoured wagons were built under the supervision of Lieutenant Kimball, US Navy. From the 11th onward, order was gradually restored, and normal railway traffic could recommence, now under the protection of the armoured wagons.
American armoured wagon in Panama.
_(Engraving:_ Harper's Weekly, _30 May 1885)_
These wagons were armoured with steel plates 3ft 7¼in (1.10m) high and four-tenths of an inch (10mm) thick; each wagon was armed with a 37mm Hotchkiss QF gun, a short Gatling on its mounting, and a 12pdr smoothbore howitzer. The latter could be deployed in a ground role. The crew comprised forty-two US Marines and fifty-eight sailors.
In September 1902, the region was shaken by revolutionary movements, and in November 1903 a contingent of Marines and sailors landed once more, took up position in Colón and put into service armoured trains about which virtually no information is available.
Engraving attached to Patent 540.134 of 28 May 1895.
### Project by John Beck
In 1895, a native of Pennsylvania, a certain John Beck, obtained a patent for an armoured wagon armed with guns on the roof, aimed and fired by remote control. The upper halves of the armoured sides had panels which hinged upwards to allow salvo firing by the crew, while gunports in the lower halves allowed for firing small-calibre guns. Recoil was to be catered for by stabiliser legs at each corner of the vehicle. Surprising for such a late date, the small-calibre guns in the patent drawing would not have been out of place in the Civil War thirty years earlier. Probably the drawing was purely indicative, but they detract from the overall impression.
### Armoured cruiser on rails of the electoral campaign of William McKinley, Governor of Ohio, 1896
This tramcar converted into an armoured cruiser is purely anecdotal, and would have no place in the overall story of the armoured train had it not raised interest in the possible employment of such vehicles during civil disturbances.
To publicise the presidential election campaign of Republican candidate William McKinley in 1896, a tramcar had been converted into an armoured cruiser, using pasteboard according to some sources, or metal according to others. Designed by naval architect Henry P Lapointe, it was built and ran in the town of Fitchburg, Massachusetts. The idea originated with a supporters' club who set up a company to participate in the election campaign, and elected as its 'captain', a certain Major Charles K Darling. The 'warship' was 37ft (11.28m) long, 9ft (2.74m) wide and 12ft (3.65m) high. It was powered by two 30hp electric motors. The basic idea was to show that it would be possible to construct an armoured vehicle on tramway rails to intervene in urban riots. It could also be used to rapidly and securely transport a body of troops up to company size, plus artillery, between towns. This idea would be revived again in 1938, when 'a fleet of such trolleys, a new step in the progress towards mechanised warfare' was suggested. After McKinley's presidential election victory in 1896, certain sources indicate that the 'armoured cruiser' was put afloat on Lake Whalom, in a park belonging to the tramway company, while others claim it was left to fall to pieces.
In 1899, shortly after the Spanish-American War, the Americans decide to take control of the former Spanish colonies. In the Philippines, the Nationalists, with their capital at Manolos, refused to accept what they considered a new colonial yoke, and took up arms against the American forces concentrated in Manila. The latter advanced along the railway, using an improvised armoured train initially armed with a naval 6pdr gun and two Gatling guns firing to the sides. This armament was later augmented by a Hotchkiss revolver cannon. Their advance on Manolos was delayed by several lines of resistance but the town was taken. The rebels changed their tactics and began attacking the railway behind the American lines. On 25 April 1899 the armoured train was in action at Calumpit, pushed by Chinese workmen, in support of 400 troopers of the 4th Cavalry fighting dismounted. During that battle, it seems the firepower of the train was a major factor in inducing the Filipinos to withdraw. The war dragged out in the mountains, and the armoured train having no further useful employment, the individual wagons were probably returned to civilian use at the end of 1899.
The tramcar, loosely inspired by the armoured cruiser USS _Brooklyn_ , described as having a white hull, green superstructure (which in fact would have been buff yellow) and black armament and portholes.
_(Engraving:_ La Nature _No 1247 [24 April 1897], p 336)_
We have no information on this American armoured train design, which is probably intended for coast defence given the similarity of its components to those of warships. Stated to be a project dating from 1898, it could in fact be a revival of the original project of 1845.
_(Engraving: All Rights Reserved)_
An engraving showing the armoured train, made up of four wagons, the leading wagon armed with a 37mm Hotchkiss revolver and a Gatling gun. In the absence of a steam engine, it was pushed by hand by Chinese labourers during the fighting on the Bagbag River during the Battle of Calumpit.
_(Engraving: Paul Malmassari Collection)_
### The 'Bull Moose Special' Armoured Train of 1913
In West Virginia, coal miners went on a long drawn-out strike, lasting from 18 April 1912 to the end of July 1913. On one side were some 8000 strikers, demanding equality of pay with miners from the surrounding areas, an end to the practice of compulsory purchase in the company shops, and regulated coal-weighing procedures. They faced 300 private guards from the notorious Baldwin-Felts Detective Agency, brought in by the mining companies, supported by 1200 Federal troops. In order to protect strikebreakers, the Agency guards organised the construction of an armoured train in the workshops of the C&O Railroad Company at Huntington. The train consisted of a steam engine, a passenger coach and a van protected by steel plates. On the night of 7 February 1913, in retaliation for an attack on an ambulance and the depot near Mucklow, this train was used in a raid by private detectives, policemen and mine operators led by Kanawha County Sheriff Bonner Hill. They fired a hundred rounds from a Colt machine gun into the timber-framed house of a striker, Cesco Estep, killing him and wounding several others.
### Miners' armoured train, September 1913
Another dramatic incident took place during this period, when violent clashes broke out in Southern Colorado, in particular in a lengthy strike involving the coal mines owned by the Colorado Fuel & Iron Corporation, where the miners were stung by the murder of one of their number. On one occasion during a raid on the strikers' tent encampment by guards recruited by the company, the miners improvised an armoured train, and used it to attack strike-breakers. The strike continued into the Spring of 1914 and ended in the 'Ludlow Massacre' in which twenty-six miners along with several women and children perished.
Although not strictly speaking armoured, the train which had transported the Colorado Militia to attack the tent camp at Ludlow was deliberately halted by its driver in front of the Militia machine gun emplacements, thus covering the escape of many strikers and their families.
Orenstein Arthur Koppel Armoured Car No 1.
_(Photo: All Rights Reserved)_
In 1914 the US Division of the German firm Orenstein Arthur Koppel in Pittsburg built an armoured wagon with firing loopholes arranged in a quincunx layout, as used in the trains of the Boer War a dozen years earlier. As at that moment the US Army had no operational requirement for such a vehicle, it was probably sold to a foreign country, perhaps in South America.
### The Mexican Border Patrols
After troops under Pancho Villa had massacred Americans on a civilian train, then carried out the raid against the town of Columbus, New Mexico, on 9 March 1916, the USA decided to send a force under the command of General Pershing to eliminate the guerrilla menace. For this operation, in 1916 the American Army acquired some thirty Mack-Saurer trucks, known as 'Rikers' (from the name of their designer Andrew Riker). Several would be converted for use on rails, but were employed only in supply missions on the railway networks in New Mexico and Texas, since the Constitutionalist Government had forbidden American forces to use the Mexican railways.
An artist's impression showing the interior of the Standard Steel Co. patrol wagon. The machine guns shown here were the Machine Rifle Model of 1909 (Benet-Mercié Hotchkiss Portative), the unjustly maligned 'Daylight Gun' of the Pancho Villa raid on Columbus, New Mexico.
_(Illustration:_ Popular Science Monthly _Vol 89 [1916])_
Side elevation and end view of the patrol wagon.
_(Drawing: All Rights Reserved)_
The hulls of these two armoured railcars have a similar roof layout and lower armour protection to the 1916 Standard Steel armoured wagon. The lack of vertical T-section straps on the sides and driving positions in each corner follow the arrangement of the Hall-Scott Type 11.001 railcar. The gun in the nearer of the two wagons is not the US 3in, but the Model of 1917 (the British 18pdr converted to fire French 75mm ammunition), which entered service in February 1918, and .30 Cal Browning MGs are mounted in the gun well. This armament would suggest a date in the 1920s, and the railcars could conceivably be retained for Mexican Border patrols. Note the smoke from the roof exhaust pipe. A coloured version of this photo was issued as cigarette card No 99 by Lloyd Zigaretten.
_(Photo: El Paso Public Library)_
The Board of Engineers of the American Army had noted the armoured wagons built by the Villa forces, including an armoured version of the Riker truck (see the chapter on Mexico). So to secure the Mexican border during the crisis, the Engineers designed an armoured wagon, and gave the contract to the Standard Steel Company, which turned out the vehicle in just twenty-seven days. Its mission was to defend the railway lines and the nearby installations, rather than carry out offensive raids. The armour provided protection against small-arms fire only, and it was pierced by twenty firing loopholes at standing height for light machine guns and rifles. The central part held a stock of ammunition in its lower level, and the upper part formed a firing position for a 3in (76mm) field gun, served by three gunners. On patrol, the crew totalled a dozen men, who were provided with benches, a toilet and a tank of drinking water. The whole wagon weighed 44 tons. Although the cutaway illustration from _Popular Science Monthly_ shows the wagon being propelled by an armoured steam engine, in fact the latter was never built. An identical wagon mounting a searchlight was however built, and this was propelled by a rail trolley.
Similar in layout to the Standard Steel armoured wagon, but self-propelled and therefore more versatile, this is the Hall-Scott Type 11.001 Armoured Railcar. Note the driving positions at each corner, the centre of each end being taken up by a communicating armoured door when multiple units were coupled together.
_(Photo: All Rights Reserved)_
A second prototype armoured railcar was also commissioned by the US Army Corps of Engineers, and this time built by the General Electric Company. It is a more compact, traditional design, also mounted on bogies, but lacking a field gun.
_(Photo: All Rights Reserved)_
Drawing forming part of the patent granted to John Stankus on 5 October 1915.
### The Armoured Trains of the First and Second World Wars
### The First World War 1917–1918: Proposals imaginative and practical
Although the Americans only entered the First World War on 6 April 1917, several patents for armoured rail vehicles had been applied for since 1914, for example one by a certain Mr Bellamore of New York for a system of standardised armoured panels. In 1915, John Stankus of Pennsylvania proposed an armed and armoured road-rail vehicle. The conversion was effected by attaching rubber tyres on the rail wheels (US Patent 1,155,450). On 17 July 1918 Frederick W Wagner applied for a patent for an ambitious machine: armed with quick-firing guns, it travelled on the road, and was also equipped with tracks to cross wet ground. In addition, its wheels allowed it to travel on rails. The patent was granted on 21 January 1919, too late for the war, under Number US 1,292,170. It is illustrated below.
A more practical proposition, as planned in 1917. Note the curious representation of the machine guns.
_(Drawing: All Rights Reserved)_
In 1917, directives were issued laying down rules for the rapid conversion of armoured wagons in an emergency. The plan annexed to these proposals harked back to the wagons built during the Boer War, down to the roof-mounted searchlight and the arrangement of the firing loopholes in the armoured sides (drawing above).
Tractors for the 60cm gauge were built for service at the front, on the model of the British Simplex, and were used notably in the Meuse-Argonne offensive. They had a maximum speed of 8mph (12.9km/h) and a total weight of 6.35 tons.
The prototype of the Baldwin MM8 armoured tractor.
_(Photo: DeGolyer University)_
Baldwin built 126 narrow gauge Type MM8 tractors, with an output of 50hp, for use by the American army in France, but apparently only one example was armoured.
In 1919, the Americans intervened alongside the other Allies against Bolshevik Russia. The American Expeditionary Force (AEF) was in action in the Murmansk region where, to protect the rail network, it put into service at least one armoured train.
An improvised armoured train used by the American contingent in Russia in 1920.
_(Photo: IWM)_
The page from the Lionel Catalogue of 1917. The turret guns were fitted with red lights which flashed as the turret was turned.
_(Catalogue Page: via Bill Schmeelk of The Lionel Collectors' Club of America)_
Armoured trains featured prominently in the popular press during the early years of the First World War, so it was inevitable that an electric train set would be produced by the Lionel Company. The set complete with armoured locomotive (which presaged the form of the Crochat armoured tractors which would appear a year later) was first offered in the Lionel Catalogue of 1917, and remained on sale through 1919. It has recently been reissued by a modern American manufacturer.
During the Second World War, the Americans did not use armoured trains in an offensive role. On the other hand, they did employ passive protection, particularly on locomotives. Certain Whitcomb 65-DE-14 diesel locomotives were armoured, being the units deployed to the North African theatre (nineteen in 1942 and seventeen in early 1943). In all, in order to provide protection against air attack, fifty complete sets of armour were ordered from Whitcomb, to protect the driving cab and the ends of the machine.
Although the Americans did not use armoured trains (the special armoured coach built by the LNER for General Eisenhower is described in the chapter on Great Britain), armoured trains remained part of popular imagination, and continued to appear in toy form. Metal being in demand for war construction, card cutouts became very popular, as shown by this sheet issued in February 1941. Even if it is not based on any specific prototype, the camouflage scheme of green and earth upper surfaces is very British!
The card model from February 1941.
_(Sheet: Paul Malmassari Collection)_
### The Armoured Trains of the Cold War Period
Characteristic of the Cold War Period is the _'_ White Train' designed for the transport of nuclear material. The Safe Secure Railcar (SSR) wagons were built by the Thrall Car Company of Chicago, Illinois, by reinforcing and armouring modified bogie wagons. Design studies began in the 1950s and took two years to complete. Built initially for the transport of nuclear weapons, the older wagons were later used to carry military nuclear waste from the Rocky Flats site in Colorado to an underground repository in Idaho.
Eighty-three of the ATMX 500 Series were built, followed by fourteen ATMX 600 Series. They possessed several security measures to prevent terrorists from gaining access to the cargo. The inclined shape of the wagon ends is intended to minimise the results of a collision, by allowing the end of one wagon to slide up over the rear of the preceding one. Overall structural strength was also enhanced by the fact that loading took place through openings in the roof which were closed by riveted plates.
Running in complete designated rakes and not coupled in commercial trains, the nuclear wagons formed an armoured train rolling at up to 35mph (55km/h), stopping only to refuel the locomotives, and protected by armed guards aboard wagons at each end. The normal configuration was: locomotive/escort wagon/shock-absorbing wagon/nuclear munitions transport wagon/shock-absorbing wagon/escort wagon. Empty wagons would be coupled in with the loaded ones. The crew had at their disposal HF, VHF and CB Band radio equipment, and remained in constant communication with a network of intervention teams. The employment of each train was the responsibility of the Operations Bureau of the DOE (Department of Energy) in Albuquerque, which also controlled road movements. The eleven surviving wagons were preserved at the National Atomic Museum on Kirtland Air Base near Albuquerque, before being transferred to the Amarillo Railroad Museum.
**Technical details (ATMX-600 Series)**
Length: | 59ft 10in (18.24m)
---|---
Width: | 10ft 0in (3.05m)
Height: | 13ft 10in (4.22m)
Carrying capacity: | 45.95 tons
Loaded weight: | 99.79 tons
Nuclear Weapons Transport Car TSSX 557.
_(Photo: Amarillo Railroad Museum)_
Armoured Escort Wagon TSSX G-33, showing its openings, firing loopholes and radio antenna.
_(Photo: Amarillo Railroad Museum)_
### Special Vehicles
For the sake of completeness, we need to mention certain special armoured rail vehicles, such as the presidential carriage _Ferdinand Magellan_ , converted and armoured for President Franklin D Roosevelt, or armoured postal or cash transfer wagons, an American speciality which was the subject of many Patents between the late nineteenth and early twentieth centuries. Below is just one example, taken from 1888, which bears more than a passing resemblance to certain military contemporaries.
In 1919, a newspaper article described one of these protection wagons in great detail, probably to dissuade potential hijackers. At right we see a guard firing a pump-action shotgun, as used by prison guards, through an armoured embrasure. The same article was even copied in 1924 in a popular French review!
Finally, we note that an armoured railcar was put into service on the Metroliner network, but we have no details concerning it.
Armoured Whitcomb railcar belonging to the United Fruit Company, built in 1928 .
_(Photo: All Rights Reserved)_
**SOURCES**
**Archives:**
DeGoyler Library
Library of Congress
US National Archives
US Patents Office
**Books:**
Alexander, Edwin P, _Civil War Railroads & Models_ (New York: Clarkson N. Potter, Inc./Publishers 1977).
Drumm, Nelde K, and Harley, Margaret P, _Lunenburg – The Heritage of Turkey Hills 1718-1978_ (Lunenburg, MA: Lunenburg Historical Society, 1977).
Heimburger, Donald J, and Kelly, John, _Trains to Victory: America's Railroads in WWII_ (Forest Park, IL: Heimburger House Publishing Co, 2009). 380 pages.
Hodges, Robert R Jr., _American Civil War Railroad Tactics_ (Oxford: Osprey Publishing, 2009).
Koenig Alan R, _Ironclads on Rails: Railroad Weapons of the American Civil War, 1861-65_ , Doctoral History Thesis, University of Nebraska-Lincoln (E-U.), under the supervision of Dr Edward Homze, 1995.
**Journal articles:**
Hall, James D., 'Armored Trolley', _Railroad Magazine_ (1938), pp 93–4.
Stanitz, Jim, and Moon, Paul F, 'Safe Secure Rail Cars', _NMRA Bulletin_ (September 1980), pp 33–4.
Waite, Thornton, 'ATMX Covered Hoppers, a Special Car for Nuclear Shipments', _Mainline Modeler_ (August 2001), pp 69–72.
Walsh, Paul V, 'A US Armoured Train in the Philippines, 1899-1900', _AFV News_ 28/2 (May-August 1993), pp 10–11.
'A Trolley Man-of-War', _Literary Digest_ Vol XIV, No 10 (9 January 1897), pp 304–5.
'Emploi de l'artillerie sur un chemin de fer pour la défense des côtes [des USA]', _Journal des sciences militaires_ No 66, Third Series, Vol XXII (1845), p 304.
'Our First Armored Car', _Popular Science Monthly_ Vol 89 (1916), pp 388–9.
'Parades américaines, un navire de guerre à trolley', _La Nature_ No 1247 (24 April 1897), p 336.
'Trains blindés d'Amérique', Lecture pour tous (November 1924), pp 180–2.
'Trains, Boats and Guns–Armour in Panama, 1885', _Tank TV_ No 23 (September 2000), pp 1–4.
_Papers on Naval Operations_ , Chapter II, Navy Department, 1885.
_Fitchburg Daily Sentinel_ , 11 September 1896
_Harper's Weekly_ , 1862.
_Harper's Weekly_ , Vol XXIX, No 1484 (30 May 1885), p 349.
_Metal Trades_ (February 1919), pp 94–5.
_Modern Mechanics_ (February 1919).
**Websites:**
www.amarillorailmuseum.com
www.youtube.com/watch?feature=player_detailpage&v=kz54FcA4wqA
. 'Emploi de l'artillerie sur un chemin de fer pour la défense des côtes [des USA]', _Journal des sciences militaires_ No 66, Third Series, Vol XXII (1845), p 304.
. Who, from his famous side whiskers, popularised the fashion of 'sideburns'.
. By the Fitchburg & Leominster Street Railway Company.
. _The Fitchburg Daily Sentinel_ , 13 and 21 August 1896, p 6.
. All the sources consulted remain quite vague, but it is not the job of journalists to record history.
. So named from the mine owners' links with the Progressive Party of West Virginia, known as the 'Bull Moose Party' after the popular nickname of presidential candidate Theodore Roosevelt.
. The Chesapeake & Ohio Railroad, founded in 1869.
. Some sources quote a total of sixty-six deaths.
## VIETNAM, REPUBLIC OF
### ARMOURED TRAINS
Vietnam gradually regained its sovereignty during the War in Indochina, and the ARVN (Army of the Republic of Viet Nam) was created on 1 January 1949. Between June 1954 and October 1955, Vietnam was ruled by Emperor Bao Dai, who was deposed in a coup which created the Republic of Vietnam. Proclaimed on 26 October 1955, the Republic, also called South Vietnam, disappeared with the fall of Saigon on 30 April 1975.
Even before complete independence had been achieved, in 1953 the (French) armoured trains began to be transferred to the ARVN's 1st Armoured Cavalry Regiment, which was the successor to the 4th Dragoon Regiment. On 16 August 1954, the armoured train detachments of the 5th Cavalry Regiment (Armoured Train No 5, on the line to Loc Nonh) and of the 2nd Foreign Legion Infantry Regiment (Armoured Trains Nos 2 and 3, on the line to Nha Trang), were transferred to the 1st Escort Squadron Group (1er G.E.E.) of the ARVN. In about October 1954 this unit became the 1st Vietnamese Dragoon Regiment, and assumed the role of ensuring the security of the railway network.
Saluting the flag in Phan Thiet in October 1954, in front of Armoured Train No 3. The Vietnamese flag, yellow with three red bands is being hoisted.
_(Photo: Private Collection)_
Armoured wagon armed with the turret of a Coventry armoured car, seen during an exercise at Govap.
_(Photo: Private Collection)_
The crew of Armoured Train No 3 with its French officers in charge of handing over the equipment and training the Vietnamese. The insignia is that of the 1er G.E.E., also known as the 'Black Dragon Squadron'.
_(Photo: Private Collection)_
The wagons still carry their French names given to them by the 4th Dragoon Regiment.
_(Photo: Private Collection)_
Note the insignia of the 1er G.E.E. attached to the casemate of what is certainly the the wagon of the train commander.
_(Photos: Private Collection)_
During the Vietnam War, passenger and goods trains were protected by the insertion of armoured wagons in the rakes, manned by men drawn from eight companies of civilian guards. In addition, reconnaissance runs were carried out by Wickham armoured trolleys purchased from Malaysia in 1962.
As the war progressed, the railway network shrank to the point where, at the fall of Saigon, the only line still in use was the one linking the capital to Bien Hoa, a distance of just 30km (18.5 miles). Despite their chequered career, the French armoured wagons had remained in service for thirty years.
This is probably the all-metal Type GGy, which does not appear to have been modified – apart from the radio equipment – since its days in French service.
_(Photo: Critical Past)_
It is just possible that this wagon is the one named 'Paimpol', photographed twenty years earlier. One wonders what happened to these wagons. They were probably cut up for scrap or reconverted to goods traffic use. The armoured body of one has even been observed grounded for use as a guard post.
_(Photo: Critical Past)_
The overall condition of these trolleys owes much to the disastrous effect humidity has on modern equipment. The significance of the lettering 'DBD' is unknown. The third trolley in line shows that the drivers' positions were offset front and rear.
_(Photo: All Rights Reserved)_
Armoured wagon constructed on the chassis of a Type HHy bogie wagon. At the side we can see an extension to the casemate which allowed for observation and firing along the axis of the train.
_(Photo: Critical Past)_
Phu Bai, 1969. This shows the classic layout of two safety wagons preceding the train. The first of the two wagons has an observation cab. It appears that the locomotive is a General Electric Type U8B.
_(Photo: AWM)_
**SOURCES:**
**Archives:**
SHD (10 H 1276, 10 H 1729, 10 H 4477, 10 H4559).
Private archives.
**Videos:**
Military History Video: ' _Railroad Support Vietnam'_ (506th Field Depot, 1967, 45 minutes)
. Article 60 of the Constitution of the Fourth Republic stipulated that the French Union was formed, on the one hand by the French Republic, and on the other hand by the territories and states associated with France, among which were the three states of the Indochinese Union created in 1887.
. Unification of North and South Vietnam was proclaimed on 2 July 1976.
. Created in 1890. The gold symbolised the ruling dynasties and the three red bands, Tonkin, Annam and Cochinchina.
. Built in 1963, forty-eight units were delivered to the Vietnamese Railways. In 1975, they were re-designated as Type D9E.
## YUGOSLAVIA
### ARMOURED TRAINS 1918–1992
Yugoslavia was created by the Treaty of Versailles and broke up in 1992. In order to correctly allocate the armoured trains, this chapter will cover the Yugoslav trains up to the officially recognised disappearance of this state. Because of the various territorial partitions and accidents of history which affected the state of Yugoslavia, the Croatian armoured trains of the Independent State of Croatia (1941–5) and of the Croatian War of Independence (1991–5), plus the Serb armoured trains of the Republica Srpska (situated in Bosnia-Herzegovina) and the Serbian Republic of Krajina (situated in Croatia) are described separately.
### From the End of the Great War to the End of the Second World War
At the end of the First World War, it appears that only the Austro-Hungarian PZ V remained on the territory of the future Yugoslavia. It was taken over by the new Yugoslav Army, although no details of its use have come to light, apparently together with the artillery wagon from PZ I – but the only proof that this wagon was in Yugoslav hands is the photographic record. In March 1921 the French Military Attaché reported that '3 or 4 armoured trains could be formed'. On 27 October 1936, the new establishment of the Yugoslav Army included them in its 'special combat equipment'. However, there is no proof that these armoured trains had actually been put into service. At the time of the German invasion, several wagons were captured in Belgrade and from November 1941 were added to PZ 25. In addition, the pilot wagon of the ex-Austro-Hungarian PZ I was put back into service by the Wehrmacht, only to be lost on some unknown date.
Yugoslav armoured train captured in Belgrade in 1941. Note the modification to the wagon originally part of PZ V which now appears to have been fitted with a turret, possibly for anti-aircraft defence.
_(Photo: Wolfgang Sawodny Collection)_
Two views of the armoured artillery wagon from the old ex-Austro-Hungarian PZ I, left behind in Yugoslavia after 1918, fitted with buffering gear and brake hoses, and put back into service after the German invasion of Yugoslavia. Note that its 7cm gun has been removed: the wagon is now armed with an MG34.
_(Photos: Paul Malmassari Collection)_
During the Second World War, there were reports of a 'partisan armoured train', today preserved in the Narrow Gauge Railway Museum in Požega, situated in the Belgrade-Bar administrative district. It was used in the region of Uzice before that area was retaken by the Wehrmacht.
These two photos show the locomotive, on which only the cab is armoured, and a bogie low-sided wagon filled with sand, protecting a central open space. The collection also includes an armoured covered wagon with the same type of firing loopholes.
_(Photos: Philippe Tomatis)_
### After the Second World War
At the end of the Second World War a number of Croatian, German and Italian armoured trains and trolleys were captured, and some at least were put back into service. The majority of the units had been seized in Slovenia, and for the first year of the post-war period, they remained either in the zone where they had been captured, or otherwise were stored at the VTZ '21 October' in Kragujevac. On 24 May 1946, General Koca Popovic, Chief of the General Staff, gave orders to the commanders of the armoured and motorised units (KTJM), to place all the various scattered armoured rail units under the responsibility of the RVK, to report back on the numbers of units extant, and to evaluate their current state in order to establish a repair and maintenance programme. At that stage, in the zones of the First, Second, Fourth and Fifth Armies it was reported there were in existence a total of 242 armoured wagons and three armoured locomotives. However, of these some 60 per cent were unusable.
At the VTZ in Kragujevac alone there were around a hundred armoured wagons of which forty had concrete armour. After months of work at the VTZ, thirteen Steyr (in Serbian, _Štajer_ ) light trolleys (le.Sp) were considered ready for use along with seven Fiat trolleys. The VTZ also had several examples of heavy trolleys (s.Sp) and Italian LibLi (Ansaldo Fossati ALn56) railcars.
In August 1946 these units were sent to the central armoured workshops (CTR) to be fitted with the equipment they lacked, notably machine guns and radios. It was planned to form one squadron of light Steyr trolleys, then a second one with Fiat AB 41 trolleys. The towed armoured units were to be used by the Army battalions as command wagons, as troop transports or as workshops. At Sarajevo, where eighty-nine armoured wagons were concentrated, sixteen were selected to form a batallion for use on the narrow (76cm) gauge, with six wagons in combat configuration and the remainder in a support role. On the other hand, three armoured locomotives were transferred back to civilian use, as it was planned to use the Steyr trolleys as tractor units for the Narrow Gauge trains. In order to put the units in hand in a fit state to use, the KTMJ decided to cannibalise obsolete units and to produce or purchase the equipment which was missing. The batallions of armoured trains were to be attached to the Third, Fourth and Sixth Armies. The first formation was to be established at Sremska Kamenica.
The General High Command issued a notice which indicated that the armoured trains had as their 'principal mission to ensure transport, communications security and combat on the internal front'. It also laid down, however, that no new trains were to be built, and that repairs to existing trains should be carried out only where the end result justified the effort. Lastly it ordered the KTJM to constitute three narrow-gauge (76cm/30in) divisions at Belgrade (or Karlowitz), Zagreb and Sarajevo. The fate of the units in excess of these requirements (seventy-three wagons at Sarajevo, thirty-seven at Kragujevac and an undisclosed number at the VTZ '21st October') was to be decided by the Transport Ministry. No record exists, however, to prove that these armoured trains were ever formed, or that the proposed organisation had been set in motion. On the other hand, in July 1949 armoured trains featured in the inventory of the People's Corps for the Defence of Yugoslavia (KNOJ) and were deployed in four divisions for the purposes of internal security:
7th Division: two armoured trains made up of Fiat trolleys at Bosanski Samac and Bihac; two Steyr trolleys at Banja Luka.
11th Division: one platoon at Nis; two armoured trains made up of Steyr trolleys at Skopje.
27th Division: one platoon of three Steyr armoured trains at Batajnica.
16th Division: one Steyr platoon at Vinkovci; three Fiat armoured trains at Ljubljana, Ogulin and Zagreb.
PanzerZug (s.Sp) 201 destroyed in Cacini Station on 14 April 1945. Several of these heavy trolleys were recovered in working order by the new Yugoslav Army.
_(Photo: MRN via Bojan Dimitrijević)_
In 1950, an article in the _Chicago Daily Tribune_ described 'several armoured trains... One of which was on a storage siding outside Belgrade... '. In 1953, the KNOJ was dissolved and the armoured train units were integrated into the Yugoslav armoured forces, where the Department of Armoured and Motorised Units was charged with drawing up the doctrine for their emplyment. As the result of this reorganisation, the armoured trains were integrated into the various divisions as follows:
17th OKD: two armoured trains, one made up of five Steyr trolleys (three artillery and two MG units), and the other of three Steyr trolleys (two artillery and one MG units) based at Batajnica.
20th OKD: three Steyr trolleys (MG units) at Zagreb; two Fiat trolleys at Ljubljana.
26th OKD: three Fiat trolleys (including one without armament) at Nis (transferred to Batajnica in November 1953 in exchange for three Steyr trolleys); two Steyr trolleys (MG units) at Pristina; two Steyr trolleys (MG units) at Skopje.
In the 7th Military Region (Bosnia-Herzogovina and Montenegro, where no armoured divisions were stationed): six Steyr trolleys (MG units) equally divided between Sarajevo, Banja-Luka and Vinkovci. These latter units would eventually rejoin the 20th OKD in the 5th Military Region.
In mid-October 1954, the armoured trains were gathered together in Zagreb East Station, and on 22 November 1955 the order was given to withdraw all the armoured trains from active service. Their armament and motors were taken out and stored, the armaments at Zagreb (at VR No 69) and the motors at the TRZ at Bregana. Two years later, on 22 October 1957, it was decided to restore an s.Sp heavy trolley (the 75mm gun version) to working order, using the services of the armoured forces and the Army technical department. However, the lack of spare parts, and the recent manufacture of more modern arms and equipment, led to the abandonment of the project. All the armoured rail units were therefore scrapped.
One of the seven LiBli armoured railcars (known as _Panzertriebwagen_ ) Nos 30 to 35 and 38, captured in Slovenia in May 1945.
_(Photo: MRN via Bojan Dimitrijević)_
The first of three photos of captured German vehicles integrated into the Yugoslav armoured train units. Above is an alignment of ten s.Sp trolleys, of which at least four have a turret, photographed from a train passing in front of the CTR at Mladenovac, 56km (35 miles) to the south of Belgrade in 1946. Note the line of tanks in the background, among which are former French armoured vehicles.
_(Photo: Bojan Dimitrijević Collection)_
Two PanzerJägerWagen preceded by a Croat wagon.
_(Photo: Bojan Dimitrijević Collection)_
A German armoured artillery wagon with its distinctive turret. The Yugoslav Army was not interested in the complete armoured trains. In comparison the autorails and trolleys were felt to be more useful.
_(Photo: Bojan Dimitrijević Collection)_
**SOURCES:**
**Archives:**
SHD DAT 7 N 3200, 7 N 3202.
**Books:**
Dimitrijević, Bojan, _Modernizacija i intervencija, Jogoslovenske oklopne jedinice 1945-2006_ (Belgrade: Institut za savremenu istoriju, 2010).
________________ (with Savić, Dragan), _German Panzers and_
_Allied Armour in Yugoslavia in World War Two_ (Erlangen: Tankograd Publishing, 2013).
**Journal article:**
Grognet, Olivier, 'Les musées ferroviaires yougoslaves', _La Feuille_ , AJECTA newsletter No 87 (December 1997), pp 5–6.
. In Serbian: _Oklopni Voz, OKV_.
. The Principality of Serbia was created in 1815 and became independent from the Ottoman Empire in 1878. The Kingdom of Serbia was proclaimed in 1882, and then in 1918 the gathering of the Southern Slavs gave birth to the Kingdom of the Serbs, Croats and Slovenes, which became the Kingdom of Yugoslavia in 1929. During the Second World War its territory was divided up by the Axis powers, then in 1945 its territorial integrity was re-established as the _Federativna Narodna Republika Jugoslavija_ or FNRJ (Federal People's Republic of Yugoslavia). Following the war of 1991 to 1995, then the subsequent independence of Montenegro in 2006, Serbia inherited what was left of the old Yugoslavia.
. Unilaterally declared in May 1992 and officially recognised within Bosnia-Herzegovina on 14 December 1995 by the Dayton Accords.
. The 'Autonomous Serb Region of Krajina' seceded on 1 April 1991, transformed itself into the 'Serbian Republic of Krajina' on 19 December 1991, and was completely overrun by the Croats in early August 1995.
. For example: PZ (le.SP) 301 at Kraljevo on 11 November 1944, PZ (le.SP) 302 at Kosovo Polje on 12 November 1944, PZ (s.Sp) 201 at Čačincima on 15 April 1945, and PZ 6 destroyed in Serbia on 1 October 1944. At the capitulation the largest number of prizes seized was at Celje and Dravograd (on the Austro-Slovene frontier) when twelve armoured trains and various railcars surrendered, in particular PZ 73 which had been put back into service in the region of Gôrz. An extremely accurate list is given in Bojan Dimitrijevic's book G _erman Panzers and Allied Armour in Yugoslavia in World War Two_.
. VTZ = _Vojno Tehnički Zavod_ , Military Technical Institute.
. October 21st could be a reference to the massacre of 21 October 1941, when the German Army killed more than 6000 civilians in reprisal for Chetnik and Partisan actions against them in the area (the number varies according to the sources). It could also be a reference to 21 October 1944, day of the liberation of the city.
. KTMJ = _Komanda Tenkovskih I Mehanizovanih Jedinica_.
. RVK = _Rezerva Vrhovne Komande_ , Reserves High Command.
. CTR = _Centralna Tenkovska Radionica_.
. In reality, the Steyr trolleys were not defined as 'heavy' or 'light' in the archives, but instead were classified according to their armament. In certain cases it is impossible to be certain which type is mentioned.
. Today a suburb of Novi Sad.
. Created on 15 August 1944 to operate in liberated areas.
. Cass, Donn, 'Transport Poor in Russia and Balkan Lands', _Chicago Daily Tribune_ , 3 January 1950, p 4.
. OKD = _Oklopna Divizija_ , Armoured Division.
. VR = _Vojna Radionica_ , Military Workshop.
. TRZ = _Tehnicki Remontni Zavod_ , Technical Repair Workshops.
## APPENDIX 1
### ARMOURED TRAINS IN ART AND PROPAGANDA
Postcards were an excellent means of spreading a propaganda image, a role taken over today by postage stamps. Much rarer were commemorative objects such as this East German stylised model train of the Leuna Arbeiter uprising of 1919.
_(Photo: Paul Malmassari Collection)_
### AUSTRIA-HUNGARY
This section presents a series of classic postcards of the Great War period. The Austro-Hungarian armoured trains were more impressive than their German counterparts, and were the subject of a great many reproductions aimed at the general public.
_(Postcard: Paul Malmassari Collection)_
Type A armoured train in combat with Russians.
_(Postcard: Paul Malmassari Collection)_
A patriotic German postcard, using the image of an Austro-Hungarian Type B armoured train, which was evidently felt to be more impressive, and more symbolic of armoured trains in general, than their own. In actual fact French soldiers wearing blue and scarlet uniforms, typical of the early months of the war, never came into contact with Austro-Hungarian armoured trains. In addition, the artist has represented the observation cupola as a chimney.
_(Postcard: Paul Malmassari Collection)_
A fine composition showing a Type B PZ brushing aside Russian obstacles during the fight for Wilna. However, when the town did fall, on 19 September 1915, it was captured by German troops.
_(Postcard: Paul Malmassari Collection)_
Here PZ I / IX is the subject of a postcard which is strikingly faithful to the actual appearance of the train.
_(Postcard: Paul Malmassari Collection)_
A patriotic postcard, with three national flags behind the cartouche of the armoured train: German on the right, Ottoman in the centre and Austro-Hungarian on the left. The black and gold which were the colours of the House of Habsburg between 1804 and 1866 continued to be used when representing the Emperor.
_(Postcard: Paul Malmassari Collection)_
An illustration of a Austro-Hungarian armoured train used by the French popular press to portray the intervention of a German train. In truth the images of the German trains lacked the visual impact necessary for efficient propaganda. The resulting scenario is certainly aesthetic, but it contains numerous inaccuracies, notably the long-barrelled gun in the position where one would find the engine, and the common misconception that the observation cupola was a chimney.
_(_ L'Illustration National _No 42: Paul Malmassari Collection)_
An original watercolour signed Linebauer, which is perhaps unfinished, but which clearly shows one of the early Austro-Hungarian armoured trains. Note the rear armoured wagon depicted as having three lateral machine-gun positions but lacking a cupola.
_(Watercolour: Paul Malmassari Collection)_
A fine heroic engraving of fighting between Italian soldiers and troops disem-barked from an Austro-Hungarian armoured train. The action took place on the night of 12/13 September 1915, when the Austrians advancing from Gorizia attempted a surprise attack on Zagora. Note that the engine is not the actual type which would be used with these wagons.
_(Engraving:_ La Domenica del Corriere, _No 39, XVIIth Year [26th September–30 October 1915]: Paul Malmassari Collection)_
This small collectors' card (original size 5.8cm x 4.8cm/2¼in x just under 2in) faithfully depicts PZ II, but during its Czech period as Train No 1, with minor differences.
_(Card: Bilderdienst Schienen Wunder, Berlin, No 288: Paul Malmassari Collection)_
### BELGIUM
The impressive appearance of the Belgian armoured trains (as with their Austro-Hungarian contemporaries) inspired many artists, and in almost all types of media. The illustration on the right taken from a popular publication details the colour of the Belgian uniforms, with Royal Navy gunners manning the guns. The view on the left is an engraving which appeared in _La Domenica del Corriere_ dated 17 January 1915.
_(Both illustrations: Paul Malmassari Collection)_
A Heavy Armoured Train on a collectors' card painted by Nathan. It draws inspiration from an original photo which was widely printed in the contemporary press; this can be seen in the Belgian chapter, page 61.
_(Illustration: Paul Malmassari Collection)_
_Armoured Train in Action_ , by the Italian Futurist Gino Severini, 1915, oil on canvas, 115.8cm by 88.5cm.
_(Museum of Modern Art, New York)_
This postcard takes up the same view as the Belgian Army train depicted on page 61, but this time attributing the train to the German Army.
_(Postcard: Paul Malmassari Collection)_
### CAMBODIA
The insecurity of a period that required armouring locomotives featured on a Cambodian stamp issue of 1984. The date of '1966' refers to when these locomotives were first introduced rather than to the date they received their armoured cabs.
_(Paul Malmassari Collection)_
### ESTONIA
Patriotic postcard of the Estonian War of Independence, showing the action at Petserimaal in March 1919, near the end of the Bolshevik offensive.
_(Postcard: Paul Malmassari Collection)_
### FRANCE
A detail from _Asnières vue des bords de la Seine pendant l'insurrection le 22 mai 1871_ , by H Charles (Asnières seen from the banks of the Seine during the insurrection on 22 May 1871). The artist has deliberately omitted the roof of the railway battery on the right to show the interior details.
_(Painting: Collection du Ministre, 7 M B 335, SHD)_
A dramatic engraving showing the dangers which still threatened civilian trains in the 1920s in Algeria.
_(Cover of the_ Petit Journal _of 19 December 1920)_
### GERMANY
German South West Africa during the Herero revolt: railway workers repairing the track (note the detached rails lying on the left) covered by the armoured train and men of the _Schutztruppe_ on 13 January 1904.
_(Illustration: Paul Malmassari-DGEG Collection)_
Front cover of issue No 111 of the series _Heinz Brandt der Fremdenlegionär_ (up to No 80, Heinz Brandt, the hero of the story, was a French Foreign Legionnaire, but when the First World War broke out, he deserted and joined the German Army. Between 1914 and 1921 the series ran to 332 issues). This illustration demonstrates how the armoured train was recognised as part of the 'normal' armament of the countries of the period.
_(Cover: Paul Malmassari Collection)_
### GREAT BRITAIN
An example of British use of armed trains at the end of the nineteenth century is evoked by this postage stamp issued to commemorate the Alderney Railway's 1890 wagon armed with a QF gun for coastal defence, supplementing the fortifications built between 1847 and 1857. It appears there is a second such wagon partly obscured by the Queen's head.
An engraving from across the Atlantic which is a fine depiction of the Anglo-Belgian armoured trains.
_(Image:_ Scientific American, _Vol CXII, N° 18 of 1 May 1915)_
### HUNGARY
A postcard commemorating the Hungarian 'Red' Armoured Trains.
_(Postcard: Paul Malmassari Collection)_
### JAPAN
These two patriotic postcards illustrate the same theme in a contrasting serious and comical manner. Apart from their historical interest, they give an impression of the colours used in the camouflage schemes.
_(Two postcards: Paul Malmassari Collection)_
An example of the use of official photos to create postcards for the soldiers of the Emperor (the original photo can be found on page 293).
_(Postcard: Paul Malmassari Collection)_
Another postcard view inspired by the same train, this time including a rangefinder in the nearer artillery wagon.
_(Postcard: Paul Malmassari Collection)_
Here is an infantry wagon at the head of a train, with an understandably nervous officer bottom left, as they have no safety wagon preceding them.
_(Postcard: Paul Malmassari Collection)_
Two of the many propaganda postcards published during the war.
_(Two postcards: Paul Malmassari Collection)_
This illustration of a railway guard in winter kit and the engine of an armoured train is from the cover of a packet containing a set of patriotic postcards.
_(Illustration: Paul Malmassari Collection)_
### MEXICO
The striking appearance of the American-built armoured protection wagons inserted into passenger trains during the Mexican revolution made a big impression. Here they feature in a popular magazine of the 1920s. See page 321 for further details.
_(Illustration: Paul Malmassari Collection)_
### RUSSIA
Intended as publicity for their airships, this German postcard also features the Russian defences, and curiously uses identical turrets on both the fort and the train, probably inspired by a similar use of the German Gruson turrets.
_(Postcard: Paul Malmassari Collection)_
A heroic rendering of the capture of a White armoured train by Budenny's cavalry, in this contemporary engraving. The wagon is a mixture of 'White' and 'Red' train designs, not unusual during a period when the capture and return to service of the trains was commonplace.
_(Engraving: Paul Malmassari Collection)_
Wartime propaganda revived the myth of the armoured trains : here an OB-3 is saluted by the civilian population.
_(Postcard dated 1943: Paul Malmassari Collection)_
Even Stalin got in on the act: on this postcard dated 1942, he is seen (with his arm raised), supposedly commanding on the Tsaritsyn Front in 1918. The armoured train takes second place just behind him.
_(Postcard: Paul Malmassari Collection)_
An extremely odd train (perhaps intended to be a railcar) features on this postcard from 1942, with a chimney smoking in front of the armament, and the main cannon flanked by two others. But note the red star and red banner proudly displayed.
_(Postcard: Paul Malmassari Collection)_
This BTR which features on the cover of _Soviet Military Review_ N° 3 (1975) is rail-mounted. The date could correspond to a period of experimentation, but it could also be used as a means of training troops to mount and dismount from a moving vehicle.
_(Illustration: Paul Malmassari Collection)_
### SPAIN
An illustration included in American chewing gum packets, showing an episode from the Civil War.
_(From the Series 'Horrors of War', N° 215, Gum Inc., Philadelphia, Pennsylvania, 1938, Paul Malmassari Collection)_
These two illustrations show armoured trains in board games, the one on the right being a form of snakes and ladders, with symbols rarely found in such games: a head wearing a Phrygian bonnet (symbolising the Republic), or a crown (the Monarchy), and the initials and devices of political parties and trade unions. The one on the left celebrates the courage of the city of Madrid, 'Muy heroica cuidad'.
_(JMAM Collection)_
### Armoured Trains in Comic Books
There are as many genres of comic books as in 'classic' literature. From the past to the future, thus from history to science fiction, passing by way of politics, it is no surprise to find armoured trains represented, either to illustrate an actual historical event, or an adventure frozen in time, or to support a proposition. With rare exceptions, the armoured train is not an object of humour! In every case, it does not appear by accident in a cartoon strip: its impact is always linked to its impressive, even menacing aspect. And artists never hesitate to (deliberately?) exaggerate its dimensions or juggle with the chronology. The illustrations we have chosen, displayed chronologically in their order of appearance, are far from being exhaustive ( _Entremondes_ , or _Grêlé 7-13_ spring to mind among others), but are intended to give food for thought.
The accuracy of Hergé's drawings is evident in this image, despite the fact that this train of the time of the Manchurian Incident is actually Chinese (Fengtian Army) and not Japanese. However, the two did occasionally work together!
_(Le Lotus bleu, 1946)_.
In _Pâtée explosive_ (1971) the armoured train is a classic design and well represents the type used up until the end of the Second World War.
Even though many armoured trains appear in _Corto Maltese en Sibérie_ , we might grumble about their simplified representation – but the atmosphere of the 'end of the world' is well rendered (1971, p 51).
In 1977, this German armoured train inspired by the BP 42 type is doomed to meet its fate at the hands of a single sniper, in the spirit of the super-hero but fitting in well with the overall genre. _Warlord_ was published from 1974 to 1986.
Here is a faithful representation of the virtually unknown Spanish armoured trains, rendered by Antonio Hernandez Palacios in _Eloy_ (1981, p 40)
In _Rails_ ( _2. La Garde Blanche_ [1993], p 25) we see the gigantic aspects of science-fiction armoured trains, coming close to that of _La compagnie des glaces_.
In _L'Encyclo-B.D. des armes_ , Jacques Devos uses the comic strip for educational purposes: here are the first armoured trains rendered in humourous style (1985, p 59)
Because the story takes place in Russia, the armoured trains in _Harry Dickson, la conspiration fantastique_ (1999, p 19) are obviously Russian, though the tank-transporter wagon with the armoured cars unloading is clearly German. But then of course the Soviet trains of the 1970s had carried BTR 40 ZhDs and unloaded them in a similar manner! (See the chapters on Germany and Russia.)
In _Transperceneige_ , the train is armoured as much against some of its passengers as against an invincible enemy. The armament is the only element which disturbs the purity of its smooth outline. (2000, p 58).
In _YIU, premières missions, l'armée des néo-déchets_ , the train, menacingly armed and armoured since it is on the side of the 'baddies', is far removed from historical armoured train designs (2003, p 12).
An astounding mix of historical 'faction' and fascination for the nineteenth century of steam, wild inventions and unlikely machines, Volume 4 of _Hauteville House_ plunges us into an American Civil War even more modern than the 'real' version, and reminds us of the 1999 film _Wild Wild West_ by Barry Sonnenfeld (2007, cover illustration).
An armoured train the Confederates and Union forces could not have imagined in their wildest dreams... ( _Hauteville House_ Vol 4 [2007], p 12).
_Les Armées blanches 1917-1921_ (2008) faithfully depicts the impressive appearance of the armoured trains of the Russian Revolution and Civil War, the only contemporary land machines capable of moving over such enormous distances to rain fire and devastation. The idea of the 'moving fortress' is well rendered here.
In _Svoboda!_ , the armoured trains are the stars, but aesthetics wins out over chronology and geography: the Austro-Hungarian armoured trains, as impressive as they were, could not operate in Russia, given the distances to cover and the different rail gauge... (Vol 1 [2011], p 26).
As for the 6 August 1914 in Prague Station, the supposed date of the scene depicted, the Austro-Hungarian trains did not yet exist, and the train shown is one from the Russian Civil War... ( _Svoboda!_ Vol 1 [2011], p 29).
With _La Rafale_ , the cartoon strip depicts history, despite taking several liberties with the depiction of the train, and even with the title itself (see the chapter on France for the true meaning of the word 'Rafale' in Indochina), but captures well the essence of these trains. (2014, p 18).
### SUGGESTIONS FOR FURTHER STUDY:
Arnaud, G J, _La Compagnie des glaces_ , 15 volumes in 3 series (adapted from the eponymous novels) (Dargaud 2003–2009).
Chaboud, Jack, and Dupuis, Dominique, _Quai des Bulles – Le train dans la bande dessinée_ (Paris: La Vie du rail, 1985).
Chauvel, Simon, and Findakly, _Rails 1 à 4_ (Tournai: Guy Delcourt Productions, 1993).
Cothias, Patrick, Ordas, Patrice, and Winoc, _La Rafale_ (Charnay-Lès-Mâcon: Grand Angle/Bamboo Editions, 2012, 2013, 2014).
Devos, Jacques, _L'Encyclo-B.D. des armes_ (Paris: Editions Jean Dupuis, 1985).
Di Marco, 'L'Odyssée du convoi Apfelkern', _La Vie du rail_ , numéro hors-série (23 August 1964).
Duval, Gioux, Quet, Beau, _Hauteville House_ Vol 4 (Atlanta, Tournai: Guy Delcourt Productions, 2007).
Hergé, _Le Lotus bleu_ (Tournai: Casterman, 1946).
Hombourger, François, _Maknovtchina Ukraine 1919_ (Saint-Georges d'Oléron-Paris: Drapeau Noir, 1985).
Jacobs, Edgar P, _Le Secret de l'Espadon_ Volume 3 (Brussels: Le Lombard, 1950).
Joly, Octave, _Reporter et train blindé_ , Les belles histoires de l'Oncle Paul, _Spirou_ No 946 (Paris: Dupuis, 31 May 1956).
Lob, Jacques, and Rochette, Jean-Marc, _Le Transperceneige_ Vols 1–3 (Paris: Casterman, 1984, 1999 and 2000).
Palacios, Antonio Hernandez, _Eloy_ (Paris: Les Humanoïdes associés, 1981).
Pendanx, Jean-Denis and Kris, _Svoboda!_ Vols 1 and 2 (Paris: Futuropolis, 2011, 2012).
Pratt, Hugo, _Corto Maltese en Sibérie_ (Paris: Casterman, 1979).
Ray, Jean, Vanderhaeghe, Christian, and Zanon Pascal J, _Harry Dickson, la conspiration fantastique_ , Vol 6 (Paris: Dargaud, 1999).
Rochette and Legrand, _Transperceneige 2-L'Arpenteur_ (Tournai: Casterman, 1999).
'Sniper takes on an Armoured Train', _Warlord_ No 164 (12 November 1977).
Tehy, Vax, and Vee, _YIU, Premières missions, l'armée des néo-déchets_ (Toulon: Soleil Productions, 2003).
Temglit, Hadi, and Lehideux, Guy, _Les Armées blanches 1917 – 1921_ (Paris, Editions du Triomphe [collection Histoire], 2008).
Tillieux, _Gil Jourdan N°12 Pâtée explosive_ (Paris: Dupuis, 1971).
______, _Au pays du matin calme_ (Paris: Dupuis, 1986).
### Armoured trains in films
Several historical or fictional films, documentaries and cartoons, bring to the screen armoured trains, real or reconstructed or imagined for the needs of the script. The very fact that these films exist and the way the trains are depicted tells us much about the way the average filmgoer imagines armoured trains. As with comic books, the priority is the impression of power which they represent, and by so doing enhance the courage of their adversaries who have to face them.
In 1964, the images of the real armoured trains and in particular the train in _La Bataille du rail_ (1945) were still fresh in filmgoers' minds. This mock-up made for _The Train_ was directly inspired by the real thing as the German armoured wagon depicted here existed as part of PZ 32.
In 1965, _Doctor Zhivago_ marked generations of cinema fans. The scene when the hero comes face-to-face with Strelnikov's armoured train is a cult moment. The armoured wagon looked the part of a Bolshevik train, even though the coaches and engine would have severely restricted its fields of fire! A wonderful memory which feeds our imagination.
_Young Winston_ (1972) includes the incident when the future Prime Minister is on an armoured train in South Africa which the Boers attack and cause to derail. The same episode appears in Octave Joly's comic strip in _Spirou_ (listed above). Here, the steam engine is hauled into position for filming by a diesel, which the British would dearly have liked to possess in 1900!
_(Photo: Didcot Railway Centre via Frank Dumbleton)_
In _Goldeneye_ (1995) we are on the fringes of science-fiction. But the brutal-looking train which bears comparison with its Russian counterparts as described in the appropriate chapter, deserves a second glance from armoured train enthusiasts.
_(Photo: Nene Valley Railway via Angie Nurse)_
Two T-34 tank turrets are a classic icon of the Soviet armoured train, but even though there are few tunnels on the Steppes, the need to respect loading gauge limits to pass under over-bridges and other structures would have forbidden such a lofty construction! We can guess at the mineral wagon base beneath the 'armour'. ( _Stalingrad_ , 2001).
Viewed from this angle, the turrets and the armoured wagons of _The Last Armoured Train_ (2006) are really believable, and in fact the whole train is very convincing. After a period of 'artistic licence', it seems the film industry is once again becoming preoccupied with historical realism.
### SUGGESTIONS FOR FURTHER VIEWING:
_Bosna_ , Bernard-Henri Levy, Arte-Video, 1994. 117 mins.
_Castle in the Sky_ , dir. Hayao Miyasaki, Studio Ghibli, 1986. 124 mins.
_Cuba_ , dir. Richard Lester, United Artists,1979. 122 mins.
_Doctor Zhivago_ , dir. David Lean, Metro-Goldwyn-Mayer, 1965. 192 mins.
_Goldeneye_ , dir. Martin Campbell, EON Productions, 1995. 130 mins.
_La Bataille du rail_ , dir. René Clement, Coopérative Générale Française du cinéma, 1945. 90 mins.
_La Cour secrète des arcanes_ , dir. Pascal Morelli, Gebeka Films, 2002. 95 mins.
_Notre Train blindé_ (in Russian: Наш бронепоезд), Mikhail Ptachouk, 1988 (presented alongside the competition entries at the Russian Film Festival in Vyborg, 9 to 16 August 2003).
_Reds_ , dir. Warren Beatty, Paramount, 1981. 187 mins.
_Stalingrad_ , dir. Jean-Jacques Annaud, Pathé Distribution, 2001. 131 mins.
_The Last Armoured Train_ , dir. Zinovii Roizman, Belpartner TV, 2006. Four episodes of 52 mins.
_The Train_ , dir. John Frankenheimer, Associated Artists Productions, 1964. 133 mins.
_Young Winston_ , dir. Richard Attenborough, Columbia Pictures, 1972. 157 mins.
## APPENDIX 2
### SELECTED ORIGINAL FACTORY DRAWINGS OF ARMOURED TRAINS AND TROLLEYS
Profile view of the first series of Austro-Hungarian armoured trains, Type A, later re-classified as 'Light Armoured Trains'. Note the command cupola on the roof of the engine cab, and the different positions of the observation cupolas on the two machine-gun/infantry wagons.
_(Rajzalbum RA-581 01 19150804)_
Profile view of the later Type B Austro-Hungarian Heavy Armoured Trains built by MAVÁG, showing the telephone intercom wires connecting the units. Note the machine-gun embrasures moved further to the ends of the central wagon.
_(Rajzalbum RA-581 01 191509xx)_
Three-view drawing of an early S-Type machine-gun/infantry wagon, with the firing embrasures sloping inwards at the top. Note the central water tank (with coal locker underneath) and the offset observation cupola.
_(Rajzalbum RA-581 11 19141209)_
Three-view drawing of an S-Type wagon showing the braking system. Note the access ladder to the central observation cupola.
_(Rajzalbum RA-581 12 19141209)_
Complete set of original drawings for the artillery wagon of the Type B Heavy Armoured Trains. Note the braking system, with its armoured housing at the rear, and the system of travelling clamps to lock the rotating turret when not in action.
_(Rajzalbum RA-581 12 19150620)_
General arrangement sectioned drawings of the Drewry trolley ordered for the British Army in Mesopotamia. The plans which were almost 100 years old are slightly distorted, but give a good impression of this small machine, with a 9ft (2.736m) wheelbase. The gunners in the twin turrets had a Lewis Gun each, but would be obliged to perch on the leather strap hung from one side of the turret base to the other, just as on the Renault FT light tank of 1917.
_(Drawings: The Industrial Railway Society via Staffordshire Record Office)_
Factory drawing of the 1938 Drewry Light Trolley for Palestine, with 8ft 0in (2.438m) wheelbase
_(Plan: Industrial Railway Society via Staffordshire Record Office)_
**Sources**
Archives of the Hungarian Museum of Science, Technology and Transport, Budapest.
Staffordshire Record Office, Stafford, UK.
## ACKNOWLEDGEMENTS
This encyclopaedia represents more than thirty years of research. The assembling of such a vast collection of documents, photographs, drawings, technical details and personal reminiscences, from all the various original sources, would not have been possible without the support and help given by a large number of correspondents in many countries worldwide.
We would like to specially mention Mr Roger Branfill-Cook who has done much more than simply translate these texts, he is an armaments specialist always on the lookout for details hidden in photographs, an utter perfectionist and an uncoverer of secrets! Thanks must also go to our Editor, Mr Robert Gardiner, who with Roger Branfill-Cook insisted that this book, which initially we planned as just a simple updating of our 1989 edition, should be completely revised and expanded. My research efforts have been supported by historians and specialists in the realms of armoured trains and railway artillery, and by railway experts who have written about the rolling stock of their own country, or have created a specialised series of documents. In particular I must mention Messrs Illès András, Jacinto M Arévalo Molina, Peter Bagshawe, Carlos Stephani Bastos, Brian Baxter, Johan Botha, Petrus Botha, Jan de Bruin, Guy Chabot, Francisco Cruzado Albert, Bojan Dimitrijović, General Guy François, Daniele Guglielmi, Tomáš Jakl, Tony Hill, Adam Jońca, Alan Koenig, Maxim Kolomiets, the late Janusz Magnuski, Krzysztof Margasiński, Pavel Mičianik, Tiit Noormets, the late Nicola Pignato, Artur Przeczek, Wolfgang Sawodny, Tamara Štefanac, Marcel Verhaaf, Steven Zaloga and Mariusz Zimny. My thanks go to them all for their unfailing support.
We have also been able to count on the constant support and patience of Mme Laure Dubus, and on her expertise in international relations.
Our gratitude goes to the curators and archivists of the museums, archives and private companies, who have replied to our requests for information or have pointed us in the direction of contacts we would not otherwise have known about. Every effort has been made to correctly ascribe credit for the photographs and documents. Nonetheless, certain documents, the origin of which we have been unable to identify, have been used here because of their rarity or their historical interest. We trust their originators and owners will readily excuse us, and see in our use of them our recognition of the quality of these items.
We must also mention all the penfriends and correspondents who have helped us over the years and please accept our apologies in advance if anyone has been accidentally omitted: Alain Alvarez, Reginaldo Bacchi, John Batwell, the late Yves Bernard, Luc Binet, Captain Valérie Caniart, Colonel Fillipo Capellano, Frédéric Carbon, Jean-Christophe Carbonel, Emmanuelle Chanteranne, Peter Cooke, Paul Coterell, Pascal Danjou, Stephen Dartnell, the late Yves Debay, Henry Dropsy, Rob Dickinson, Marcel Duflot, the late Alain Dupouy, Patricia Durrieu, Matthew Ecker, Barba Ekmane, Konstantin Fedorov, Tony Ford, the late Andrew Gillitt, Florian Grupp, Frederic Guelton, Olaf Güttler, Georges Handrinos, Michael Hansson, David Hills, Stuart Jefferson, the late Jean-Gabriel Jeudy, John Jolly, Jacques Jost, Philip Jowett, Hans Kohit, Bas Koster, Günther Kraus, Martin Lacko, Eric Laugier, Colonel (Hon) Dominique Loiseau, Denis MacCarthy, Walter McGrath, Wawrzyniec Markowski, the late Georges Mazy, Jürgen Meister, Chen Melling, Candice Menat, André Meyer, Paul Middleton, Albert Mroz, John Murphy, Paul Napier, Général Pierre Nicolas-Vullierme, Kevin Patience, Walter Piringer, Lieutenant-Colonel Rémy Porte, Gérard Pouilé, Michel Protat, Uzi Raviv, Werner Regenberg, Charles Rickwood, Stuart Robinson, John L Rue, Max Schiavon, Bill Schmeelk, Horst Schobesberger, Aleksandar Smiljanić, Prakash Tendulkar, Philippe Tomatis, Gerry Van Tonder, Véronique De Touchet, Pierre Touzin, François Vauvillier, Jochen Vollert, Paul V Walsh, Hal Walters, Athol Yates and Chen Yichuan.
We dedicate this book to all the crews of armoured trains, who carried on the railway war which was as difficult and as dangerous as those of their comrades in arms in other branches, without however receiving the accolades that armoured trains so richly deserved. Our hope is therefore that this book will open up new and multiple avenues of research, and we remain open to all constructive criticism.
| {
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Willi Goetschel (* 1958 in Zürich) ist ein schweizerisch-kanadischer Literaturwissenschaftler und Professor für Philosophie und Germanistik an der University of Toronto.
Goetschel studierte Philosophie und Germanistik in der Schweiz und den USA. An der Universität Zürich erwarb er 1982 das Lizenziat in Philosophie, promoviert wurde er 1989 in Germanistik an der Universität Harvard.
Seine Forschungsgebiete umfassen Jüdische Geisteswelt, Kritische Theorie sowie Aufklärung und Idealismus im deutschsprachigen Raum.
Goetschel ist Herausgeber der Werkausgabe von Hermann Levin Goldschmidt in neun Bänden im Wiener Passagen-Verlag und war bis 2020 leitender Herausgeber von The Germanic Review.
Er ist Präsident der Stiftung Dialogik. 2020 erhielt er den Moses Mendelssohn Preis der Stadt Dessau-Roßlau.
Schriften (Auswahl)
Kant als Schriftsteller. Passagen, Wien 1990 ISBN 978-3-900767-61-7
Constituting Critique: Kant's Writing as Critical Praxis. Duke University Press, Durham 1994
Spinoza's Modernity: Mendelssohn, Lessing, and Heine. University of Wisconsin Press, Madison 2003 ISBN 978-0-299-19084-2
The Discipline of Philosophy and the Invention of Modern Jewish Thought. Fordham University Press, New York 2012
Heine and Critical Theory. Bloomsbury Academic, London 2019 ISBN 978-1-350-08729-3
Einzelnachweise
Website
Willi Goetschel auf der Website der University of Toronto
Germanist
Literaturwissenschaftler
Hochschullehrer (University of Toronto)
Schweizer
Kanadier
Geboren 1958
Mann | {
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The lighter nights are on their way – and hopefully soon there will be a hint of Spring in the air! So there is no better time to venture down to the Community Centre and try out one of our strength and balance classes. Active Seniors exercise classes continue to be popular both on Tuesday and Thursday afternoons and it's great to see so many local people coming along to exercise with us each week. We would love a few more locals – especially some men as we have more ladies than gents! - do come along and try out a class – but be quick because after a busy start to 2018 we now only have a few spaces available in the classes.
We have classes to suit all – a couple of very active and lively classes at 3.15pm on Tuesday and Thursday and for those who need a little less challenging class we can find a just couple of spots in our earlier classes at 1.45pm. So if you feel that you would like to be stronger, or find your balance isn't as good as it was, or perhaps you just want to feel a bit fitter then give us a call on 07512 546480 to have a chat about which class might suit you and to book a FREE taster session.
If you are interested in our very popular Tai Chi for health class at 4.30 on Tuesday afternoons then please ring for a chat as numbers in this class are very limited.
We hope to hear from you soon. Angela & Kim Ring Angela or Kim on 07512 546480 or email us.
If you are Kim why not edit this page? | {
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Over the years I've tried numerous ways to get girls involved in my technical classes…not easy to do. Some courses, like drafting, seemed to draw more girls than, say, auto shop. When engineering was introduced to our department I thought I'd see a rise in the number of girls enrolled. This wasn't the case, it seemed for some reason they were just as intimidated to sign up for engineering as they were other tech classes. I had heard from some of my students that there were girls who wanted to sign up but for whatever reason didn't. I wanted to figure out what was going on so I went directly to the source…the girls in my class. We discussed the issues and decided that the intimidation factor of being in a class with mostly boys was probably the number one detractor. Also misinformation about the class, particularly the curriculum, also surfaced. What we decided to do was form a "Girls in Engineering" club. The girls developed flyers to post and got permission from math and science teachers to give a short presentation in their classes and invited the girls to a monthly meeting. At that meeting they discussed everything from what they were doing in class to opportunities for women in engineering. They went to seminars in the area designed to encourage girls to explore engineering. Our numbers the following year tripled!
Let's continue this dialogue — if you have a technique you've used to encourage girls to your program that's been successful, please post it here and let us know! | {
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\section{Introduction}
\label{sec:Intro}
Understanding expressiveness and generalization of deep models is essential for robust performance of NNs. Recently, the optimization analysis for a general NN architecture was related to \emph{gradient similarity} kernel \cite{Jacot18nips}, whose properties govern NN expressivity level, generalization and convergence rate. Under various considered conditions \cite{Jacot18nips,Lee19arxiv}, this NN kernel converges to its steady state and is invariant along the entire optimization, which significantly facilitates the analyses of Deep Learning (DL) theory \cite{Jacot18nips,Lee19arxiv, Basri19arxiv,Bietti19arxiv,Hayou19arxiv,Arora19arxiv}.
Yet, in a typical realistic setting the \emph{gradient similarity} kernel is far from being constant, as we empirically demonstrate in this paper. Moreover, its spectrum undergoes a very specific change during training, aligning itself towards the target function that is learned by NN. This kernel adaptation in its turn improves the optimization convergence rate, by decreasing a norm of the target function within the corresponding reproducing kernel Hilbert space (RKHS) \cite{Arora19arxiv}. Furthermore, these \emph{gradient similarity} dynamics can also explain the expressive superiority of deep NNs over more shallow models.
Hence, we argue that understanding the \emph{gradient similarity} of NNs beyond its time-invariant regime is a must for full comprehension of NN expressiveness power.
To encourage the onward theoretical research of the kernel, herein we report several strong empirical phenomena and trends of its dynamics. To the best of our knowledge, these trends neither were yet reported nor they can be explained by DL theory developed so far. We argue that accounting for the presented below phenomena can lead to a more complete learning theory of complex hierarchical models like modern NNs.
To this end, in this paper we perform an empirical investigation of fully-connected (FC) NN, its \emph{gradient similarity} kernel and the corresponding Gramian at training data points during the entire period of a typical learning process. Our main empirical contributions are:
\begin{enumerate}[(a)]
\item We show that Gramian serves as a NN memory, with its \topp eigenvectors changing to align with the learned target function. This improves the optimization performance since the convergence rate along kernel \topp eigenvectors is typically higher.
\item During the entire optimization NN output is located inside a sub-space spanned by these \topp eigenvectors, making the eigenvectors to be a basis functions of NN.
\item Deeper NNs demonstrate a stronger alignment, which may explain their expressive superiority. In contrast, shallow wide NNs with a similar number of parameters achieve a significantly lower alignment level and a worse optimization performance.
\item We show additional trends in kernel dynamics as a consequence of learning rate decay. Specifically, after each decay the information about the target function, that is gathered inside \topp eigenvectors, is spread to a bigger number of \topp eigenvectors. Likewise, kernel eigenvalues grow after each learning rate drop, and an eigenvalue-learning-rate product is kept around the same value for the entire optimization.
\item Experiments over various FC architectures and real-world datasets are performed. Likewise, several \supp and \unsupp learning algorithms and number of popular optimizers were evaluated. All experiments showed the mentioned above spectrum alignment.
\end{enumerate}
The paper is structured as follows. In Section \ref{sec:Nottn} we define necessary notations for first-order NN dynamics. In Section \ref{sec:FIMSec} we relate \emph{gradient similarity} with Fisher information matrix (FIM) of NN and in Section \ref{sec:L2Loss} we provide more insight about NN dynamics on L2 loss example. In Section \ref{sec:RelWork} the related work is described and in Section \ref{sec:Expr} we present our main empirical study. Later, conclusions are discussed in Section \ref{sec:Concl}. Further, additional derivations
placed in the Appendix. Finally, more visual illustrations of NN spectrum and additional experiments are placed in the separate Supplementary Material (SM) \cite{Kopitkov19dm_Supplementary} due to the large size of involved graphics.
\section{Notations}
\label{sec:Nottn}
Consider a NN $f_{\theta}(X): \RR^d \rightarrow \RR$ with a parameter vector $\theta$, a typical sample loss $\ell$ and an empirical loss $L$, training samples $D = \left[ \pmb{\mathcal{X}} = \{ X^i \in \RR^d \}_{i = 1}^{N}, \pmb{\mathcal{Y}} = \{ Y^i \in \RR \}_{i = 1}^{N} \right]$ and loss gradient $\nabla_{\theta} L$:
\begin{equation}
L(\theta, D)
=
\frac{1}{N}
\sum_{i = 1}^{N}
\ell
\left[
X^i,
Y^i,
f_{\theta}(X^i)
\right]
,
\quad
\nabla_{\theta} L(\theta, D)
=
\frac{1}{N}
\sum_{i = 1}^{N}
\ell'
\left[
X^i,
Y^i,
f_{\theta}(X^i)
\right]
\cdot
\nabla_{\theta}
f_{\theta}(X^i)
.
\label{eq:GeneralLoss}
\end{equation}
The above formulation can be extended to include \unsupp learning methods in \cite{Kopitkov19arxiv} by eliminating labels $\pmb{\mathcal{Y}}$ from the equations. Further, techniques with a model $f_{\theta}(X)$ returning multidimensional outputs are out of scope for this paper, to simplify the formulation.
Consider a GD optimization with learning rate $\delta$, where parameters change at each discrete optimization time $t$ as $d\theta_{t} \triangleq \theta_{t + 1} - \theta_{t} = - \delta \cdot \nabla_{\theta} L(\theta_{t}, D)$.
Further, a model output change at any $X$ according to first-order Taylor approximation is:
\begin{multline}
d f_{\theta_{t}}(X)
\triangleq
f_{\theta_{t + 1}}(X)
-
f_{\theta_{t}}(X)
=
d\theta_{t}^T
\cdot
\int_{0}^{1}
\nabla_{\theta}
f_{\theta_{s}}(X)
ds
\approx\\
\approx
\nabla_{\theta}
f_{\theta_{t}}(X)^T \cdot d\theta_{t}
=
-
\frac{\delta}{N}
\sum_{i = 1}^{N}
g_{t}(X, X^i)
\cdot
\ell'
\left[
X^i,
Y^i,
f_{\theta_{t}}(X^i)
\right]
,
\label{eq:FDff}
\end{multline}
where $\theta_s \triangleq (1-s)\theta_{t} + s\theta_{t+1}$ and $\int_{0}^{1}
\nabla_{\theta}
f_{\theta_{s}}(X)
ds$ is a gradient averaged over the straight line between $\theta_{t}$ and $\theta_{t + 1}$. Further,
$g_{t}(X, X') \triangleq \nabla_{\theta}
f_{\theta_t}(X)^T \cdot \nabla_{\theta}
f_{\theta_t}(X')$ is a \emph{gradient similarity} - the dot-product of gradients at two different input points also known as NTK \cite{Jacot18nips}, and where $\ell'
\left[
X^i,
Y^i,
f_{\theta_{t}}(X^i)
\right]
\triangleq
\nabla_{f_{\theta}} \ell
\left[
X^i,
Y^i,
f_{\theta_{t}}(X^i)
\right]
$.
In this paper we mainly focus on optimization dynamics of $f_{\theta}$ at training points. To this end, define a vector $\bar{f}_{t} \in \RR^{N}$ with $i$-th entry being $f_{\theta_{t}}(X^i)$. According to Eq.~(\ref{eq:FDff}) the discrete-time evolution of $f_{\theta}$ at testing and training points follows:
\begin{equation}
d f_{\theta_{t}}(X)
\approx
-
\frac{\delta}{N}
\cdot
g_{t}(X, \pmb{\mathcal{X}})
\cdot
\bar{m}_{t}
,
\quad
d \bar{f}_{t}
\triangleq
\bar{f}_{t + 1}
-
\bar{f}_{t}
\approx
-
\frac{\delta}{N}
\cdot
G_{t}
\cdot
\bar{m}_{t}
,
\label{eq:FVecDff}
\end{equation}
where $G_{t} \triangleq g_{t}(\pmb{\mathcal{X}}, \pmb{\mathcal{X}})$ is a $N \times N$ Gramian with entries $G_{t}(i,j) = g_{t}(X^i, X^j)$ and $\bar{m}_{t} \in \RR^{N}$ is a vector with the $i$-th entry being
$\ell'
\left[
X^i,
Y^i,
f_{\theta_{t}}(X^i)
\right]
$
. Likewise, denote eigenvalues of $G_{t}$, sorted in decreasing order, by $\{ \lambda_{i}^t \}_{i = 1}^{N}$, with $\lambda_{max}^{t} \triangleq \lambda_{1}^{t}$ and $\lambda_{min}^{t} \triangleq \lambda_{N}^{t}$. Further, notate the associated orthonormal eigenvectors by $\{ \bar{\upsilon}_{i}^t \}_{i = 1}^{N}$. Note that $\{ \lambda_{i}^t \}_{i = 1}^{N}$ and $\{ \bar{\upsilon}_{i}^t \}_{i = 1}^{N}$ also represent estimations of eigenvalues and eigenfunctions of the kernel $g_{t}(X, X')$ (see Appendix \ref{sec:AppSp} for more details). Below we will refer to large and small eigenvalues and their associated eigenvectors by \topp and \btm terms respectively.
Eq.~(\ref{eq:FVecDff}) describes the first-order dynamics of GD learning, where $\bar{m}_{t}$ is a functional derivative of any considered loss $L$, and the global optimization convergence is typically associated with it becoming a zero vector, due to Euler-Lagrange equation of $L$.
Further, $G_t$ translates a movement in $\theta$-space into a movement in a space of functions defined on $\pmb{\mathcal{X}}$.
\section{Relation to Fisher Information Matrix}
\label{sec:FIMSec}
NN Gramian can be written as $G_t = A_t^T A_t$ where $A_t$ is $|\theta| \times N$ Jacobian matrix with $i$-th column being $\nabla_{\theta} f_{\theta_{t}}(X^i)$. Moreover, $F_t = A_t A_t^T$ is known as the empirical FIM of NN\footnote{In some papers \cite{Sagun17arxiv} FIM is also referred to as a Hessian of NN, due to the tight relation between $F_t$ and the Hessian of the loss. See Appendix \ref{sec:AppA} for more details}
\cite{Park00nn,Ollivier15iai,Karakida18arxiv} that approximates the second moment of model gradients $\frac{1}{N} F_t \approx \mathbb{E}_X \left[\nabla_{\theta} f_{\theta_{t}}(X) \nabla_{\theta} f_{\theta_{t}}(X)^T \right]$. Since $F_t$ is dual of $G_t$, both matrices share same non-zero eigenvalues $\{ \lambda_i^t \neq 0 \}$. Furthermore, for each $\lambda_i^t$ the respectful eigenvector $\bar{\omega}_{i}^t$ of $F_t$ is associated with appropriate $\bar{\upsilon}_{i}^t$ - they are left and right singular vectors of $A_t$ respectively. Moreover, change of $\theta_t$ along the direction $\bar{\omega}_{i}^t$ causes a change to $\bar{f}_{t}$ along $\bar{\upsilon}_{i}^t$ (see Appendix \ref{sec:AppB} for the proof). Therefore, spectrums of $G_t$ and $F_t$ describe principal directions in function space and $\theta$-space respectively, according to which $\bar{f}_{t}$ and $\theta_t$ are changing during the optimization. Based on the above, in Section \ref{sec:RelWork} we relate some known properties of $F_t$ towards $G_t$.
\section{Analysis of L2 Loss For Constant Gramian}
\label{sec:L2Loss}
To get more insight into Eq.~(\ref{eq:FVecDff}),
we will consider L2 loss with $\ell
\left[
X^i,
Y^i,
f_{\theta}(X^i)
\right]
=
\half
\left[
f_{\theta}(X^i) - Y^i
\right]^2
$. In such a case we have $\bar{m}_{t} = \bar{f}_{t} - \bar{y}$, with $\bar{y}$ being a vector of labels. Assuming $G_t$ to be fixed along the optimization (see Section \ref{sec:RelWork} for justification), NN dynamics can be written as (see the Appendix \ref{sec:AppC} for a proper derivation):
\begin{equation}
\bar{f}_{t}
=
\bar{f}_{0}
-
\sum_{i = 1}^{N}
\left[
1 -
\left[
1 -
\frac{\delta}{N}
\lambda_i
\right]^t
\right]
<\bar{\upsilon}_{i}, \bar{m}_{0}>
\bar{\upsilon}_{i}
,
\label{eq:L2DynamicsF}
\end{equation}
\begin{equation}
\bar{m}_{t}
=
\sum_{i = 1}^{N}
\left[
1 -
\frac{\delta}{N}
\lambda_i
\right]^t
<\bar{\upsilon}_{i}, \bar{m}_{0}>
\bar{\upsilon}_{i}
.
\label{eq:L2DynamicsM}
\end{equation}
Further, dynamics of $f_{\theta_{t}}(X)$ at testing point $X$ appear in the Appendix \ref{sec:AppC_test} since they are not the main focus of this paper.
Under the stability condition $\delta < \frac{2N}{\lambda_{max}}$, the above equations can be viewed as a transmission of a signal from $\bar{m}_{0} = \bar{f}_{0} - \bar{y}$ into our model $\bar{f}_{t}$ - at each iteration $\bar{m}_{t}$ is decreased along each $\{\bar{\upsilon}_{i}: \lambda_i \neq 0\}$ since $\lim\limits_{t \rightarrow \infty} \left[
1 -
\frac{\delta}{N}
\lambda_i
\right]^t = 0$. Furthermore, the same information decreased from $\bar{m}_{t}$ in Eq.~(\ref{eq:L2DynamicsM}) is appended to $\bar{f}_{t}$ in Eq.~(\ref{eq:L2DynamicsF}).
Hence, in case of L2 loss and for a constant Gramian matrix, conceptually GD transmits information packets from the residual $\bar{m}_{t}$ into our model $\bar{f}_{t}$ along each axis $\bar{\upsilon}_{i}$. Further, $s_i^t \triangleq 1 - |1 -
\frac{\delta}{N}
\lambda_i|$ governs a speed of information flow along $\bar{\upsilon}_{i}$. Importantly, note that for a high learning rate (i.e. $\delta \approx \frac{2N}{\lambda_{max}}$) the information flow is slow for directions $\bar{\upsilon}_{i}$ with both very large and very small eigenvalues $\lambda_i$, since in former the term $1 -
\frac{\delta}{N}
\lambda_i$ is close to $-1$ whereas in latter - to $1$. Yet, along with the learning rate decay, performed during a typical optimization, $s_i^t$ for very large $\lambda_i$ is increased. However, the speed along a direction with small $\lambda_i$ is further decreasing with the decay of $\delta$.
As well, in case $\lambda_{min} > 0$, at the convergence $t \rightarrow \infty$ we will get from Eq.~(\ref{eq:L2DynamicsF})-Eq.~(\ref{eq:L2DynamicsM}) the global minima convergence: $\bar{f}_{\infty}
=
\bar{f}_{0}
- \bar{m}_{0} = \bar{y}$ and $\bar{m}_{\infty} = \bar{0}$.
Under the above setting, there are two important key observations.
First, due to the restriction over $\delta$ in practice the information flow along small $\lambda_i$ can be prohibitively slow in case a conditional number $\frac{\lambda_{max}}{\lambda_{min}}$ is very large. This implies that for a faster convergence it is desirable for NN to have many eigenvalues as close as possible to its $\lambda_{max}$ since this will increase a number of directions in the function space where information flow is fast.
Second, if $\bar{m}_{0}$ (or $\bar{y}$ if $\bar{f}_{0} \approx 0$) is contained entirely within \topp eigenvectors, small eigenvalues will not affect the convergence rate at all. Hence, the higher alignment between $\bar{m}_{0}$ (or $\bar{y}$) and \topp eigenvectors may dramatically improve overall convergence rate. The above conclusions and their extensions towards the testing loss are proved in formal manner in \cite{Arora19arxiv,Oymak19arxiv} for two-layer NNs. Further, the generalization is also shown to be dependent on the above alignment.
In Section \ref{sec:Expr} we support these conclusions experimentally.
\section{Related Work}
\label{sec:RelWork}
First-order NN dynamics can be understood by solving the system in Eq.~(\ref{eq:FVecDff}). However, its solution is highly challenging due to two main reasons - non-linearity of $\bar{m}_{t}$ w.r.t. $\bar{f}_{t}$ (except for the L2 loss) and intricate and yet not fully known time-dependence of Gramian $G_t$.
Although \emph{gradient similarity} $g_{t}(X, X')$ and corresponding $G_t$
achieved a lot of recent attention in DL community \cite{Jacot18nips,Lee19arxiv}, their properties are still investigated mostly only for limits under which $G_t$ becomes time-constant. The first work in this direction was done in \cite{Jacot18nips} where $g_{t}(X, X')$ was proven to converge to Neural Tangent Kernel (NTK) in infinite width limit. Similarly, in \cite{Lee19arxiv} $G_0$ was shown to accurately explain NN dynamics when $\theta_{t}$ is nearby $\theta_{0}$ during the entire optimization. The considered case of constant Gramian facilitates solution of Eq.~(\ref{eq:FVecDff}), as demonstrated in Section \ref{sec:L2Loss}, which otherwise remains intractable. Moreover, GD over NN with constant Gramian/kernel is identical to kernel methods where optimization is solved via kernel gradient descent \cite{Jacot18nips}, and hence theoretical insights from kernel learning can be extrapolated towards NNs.
Yet, in practical-sized NNs the spectrum of $G_t$ is neither constant nor it is similar to its initialization. Recent several studies explored its adaptive dynamics \cite{Woodworth19arxiv,Dou19arxiv,Williams19arxiv}, although most of the work was done for single or two layer NNs. Further, in \cite{Dyer19arxiv,Huang19arxiv} mathematical expressions for NTK dynamics were developed for a general NN architecture. Likewise, in the Appendix \ref{sec:AppD} we derive similar dynamics for the Gramian $G_t$.
Yet, the above derivations produce intricate equations and it is not straightforward to explain the actual behavior of $G_t$ along the optimization, revealed in this paper. Particularly, in Section \ref{sec:Expr} we empirically demonstrate that \topp spectrum of $G_t$ is dramatically affected by the learning task at hand, aligning itself with the target function. To the best of our knowledge, the presented NN kernel trends were not investigated in such detail before.
Further, many works explore properties of FIM $F_t$ both theoretically and empirically \cite{Sagun17arxiv,Gur18arxiv,Karakida18arxiv,Oymak19arxiv}. Specifically, most of these works come to conclusion that in typical NN an absolute majority of FIM eigenvalues are close to zero, with only small part of them being significantly strong. According to Section \ref{sec:FIMSec} the same is also true about eigenvalues of $G_t$.
Furthermore, in \cite{Arora19arxiv,Oymak19arxiv} authors showed for networks with a single hidden layer that NN learnability strongly depends on alignment between labels vector $\bar{y}$ and \topp eigenvectors of $G_t$. Intuitively, it can be explained by fast convergence rate along $\bar{\upsilon}_{i}$ with large $\lambda_i$ vs impractically slow one along directions with small $\lambda_i$, as was shortly described in Section \ref{sec:L2Loss}. Due to most of the eigenvalues being very small, the alignment between $\bar{y}$ and \topp eigenvectors of $G_t$ defines the optimization performance. Moreover, in \cite{Oymak19arxiv} authors also noted the increased aforementioned alignment comparing NN at start and end of the training. This observation was shortly made for ResNet convolutional NN architecture, and in Section \ref{sec:Expr} we empirically investigate this alignment for FC architecture, in comprehensive manner for various training tasks.
Furthermore, the picture of information flow from Section \ref{sec:L2Loss} also explains what target functions are more "easy" to learn. The \topp eigenvectors of $G_t$ typically contain low-frequency signal, which was discussed in \cite{Arora19arxiv} and proved in \cite{Basri19arxiv} for data uniformly distributed on a hypersphere. In its turn, this explains why low-frequency target functions are learned significantly faster as reported in \cite{Zhang16arxiv,Rahaman18arxiv,Arora19arxiv}. Combined with early stopping such behavior is used by DL community as a regularization to prevent fitting high-frequency signal affiliated with noise; this can also be considered as an instance of commonly known Landweber iteration algorithm \cite{Landweber51ajm}.
We support findings of \cite{Basri19arxiv} also in our experiments below, additionally revealing that for a general case the eigenvectors/eigenfunctions of the \emph{gradient similarity} are not spherical harmonics considered in \cite{Basri19arxiv}.
Finally, in context of kernel methods a lot of effort was done to learn the kernels themselves \cite{Varma09aicml,Gonen11jmlr,Wang15air,Wilson16ais}. The standard 2-stage procedure is to first learn the kernel and latter combine it with the original kernel algorithm, where the first stage can involve search for a kernel whose kernel matrix is strongly aligned with the label vector $\bar{y}$ \cite{Gonen11jmlr,Wang15air}, and the second is to solve a data fitting task (e.g. L2 regression problem) over RKHS defined by the new kernel. Such 2-stage adaptive-kernel methods demonstrated an improved accuracy and robustness compared to techniques with pre-defined kernel \cite{Varma09aicml,Gonen11jmlr,Wilson16ais}. In our experiments we show that NNs exhibit a similar alignment of $g_{t}(X, X')$ during the optimization, and hence can be viewed as an adaptive-kernel method where both kernel learning and data fitting proceed in parallel.
\section{Experiments}
\label{sec:Expr}
In this section we empirically study Gramian dynamics along the optimization process. Our main goal here is to illustrate the alignment nature of the \emph{gradient similarity} kernel and verify various deductions made in Section \ref{sec:L2Loss} under a constant-Gramian setting for a real learning case. To do so in detailed and intuitive manner, we focus our experiments on 2D dataset where visualization of kernel eigenfunctions is possible.
We perform a simple regression optimization of FC network via GD, where a learning setup\footnote{Related code can be accessed via a repository \url{https://bit.ly/2kGVHhG}} is similar to common conventions applied by DL practitioners. \textbf{All} empirical conclusions are also validated for high-dimensional real-world data, which we present in SM \cite{Kopitkov19dm_Supplementary}.
\paragraph{Setup}
\begin{figure}
\centering
\begin{tabular}{ccccc}
\subfloat[\label{fig:LearningDetails-a}]{\includegraphics[width=0.11\textwidth]{0.png}}
&
\subfloat[\label{fig:LearningDetails-b}]{\includegraphics[width=0.11\textwidth]{1.jpg}}
&
\subfloat[\label{fig:LearningDetails-c}]{\includegraphics[width=0.125\textwidth]{2.pdf}}
&
\subfloat[\label{fig:LearningDetails-d}]{\includegraphics[width=0.233\textwidth]{3.pdf}}
&
\subfloat[\label{fig:LearningDetails-e}]{\includegraphics[width=0.22\textwidth]{4.pdf}}
\end{tabular}
\protect
\caption{(a) Mona Lisa target function for a regression task. (b) NN $f_{\theta}(X)$ at convergence. (c) $10^4$ sampled training points.
(d) Accuracy of first order dynamics in Eq.~(\ref{eq:FVecDff}). Depicted is $error_t = \frac{\norm{d \tilde{f}_{t} - d \bar{f}_{t}}}{\norm{d \tilde{f}_{t}}}$, where $d \bar{f}_{t} = -
\frac{\delta_t}{N}
\cdot
G_{t}
\cdot
\bar{m}_{t}$ is the first-order approximation of a real differential $d \tilde{f}_{t} \triangleq \bar{f}_{t + 1}
-
\bar{f}_{t}
$; $\cos \left( \alpha_t \right)$ is cosine of an angle between $d \tilde{f}_{t}$ and $d \bar{f}_{t}$.
As observed, Eq.~(\ref{eq:FVecDff}) explains roughly $90 \%$ of NN change.
(e) Learning rate $\delta_t$ and its upper stability boundary $\frac{2N}{\lambda_{max}^{t}}$ along the optimization. We empirically observe a relation $\lambda_{max}^{t} \propto \frac{1}{\delta_t}$.
}
\label{fig:LearningDetails}
\end{figure}
To provide a better intuition, we specifically consider a regression
of the target function $y(X)$ with $X \in [0, 1]^2 \subseteq \RR^2$ depicted in Figure \ref{fig:LearningDetails-a}. We approximate this function with Leaky-Relu FC network via L2 loss, using $N = 10000$ training points sampled uniformly from $[0, 1]^2$ (see Figure \ref{fig:LearningDetails-c}). Training dataset is normalized to an empirical mean 0 and a standard deviation 1. NN contains 6 layers with 256 neurons each, with $|\theta| = 264193$, that was initialized via Xavier initialization \cite{Glorot10aistats}. Such large NN size was chosen to specifically satisfy an over-parametrized regime $|\theta| \gg N$, typically met in DL community. Further, learning rate $\delta$ starts at $0.25$ and is decayed twice each $10^5$ iterations, with the total optimization duration being $6 \cdot 10^5$. At convergence $f_{\theta}(X)$ gets very close to its target, see Figure \ref{fig:LearningDetails-b}. Additionally, in Figure \ref{fig:LearningDetails-d} we show that first-order dynamics in Eq.~(\ref{eq:FVecDff}) describe around 90 percent of the change in NN output along the optimization, leaving another 10 for higher-order Taylor terms. Further, we compute $G_{t}$ and its spectrum along the optimization, and thoroughly analyze them below.
\paragraph{Eigenvalues}
\begin{figure}
\centering
\begin{tabular}{cccc}
\subfloat[\label{fig:EigvalsEv-a}]{\includegraphics[width=0.179\textwidth]{5.pdf}}
&
\subfloat[\label{fig:EigvalsEv-b}]{\includegraphics[width=0.179\textwidth]{6.pdf}}
&
\subfloat[\label{fig:EigvalsEv-c}]{\includegraphics[width=0.179\textwidth]{7.pdf}}
&
\subfloat[\label{fig:EigvalsEv-d}]{\includegraphics[width=0.18\textwidth]{8.pdf}
\includegraphics[width=0.176\textwidth]{9.pdf}}
\end{tabular}
\protect
\caption{(a) Eigenvalues $\{ \lambda_{i}^t \}_{i = 1}^{N}$ for different $t$. (b) Individual eigenvalues along $t$. As observed, eigenvalues monotonically grow along $t$, with growing boost at times of the learning rate drop.
(c) The information flow speed $s_i^t$ discussed in Section \ref{sec:L2Loss} for several \topp eigenvectors. For first 8 eigenvectors, roughly, this speed is increased at learning rate drop. (d) $\frac{\delta_t}{N}
\lambda_i^t$ along time $t$, for various $i$.
}
\label{fig:EigvalsEv}
\end{figure}
In Figures \ref{fig:EigvalsEv-a}-\ref{fig:EigvalsEv-b} it is shown that each eigenvalue is monotonically increasing along $t$. Moreover, at learning rate decay there is an especial boost in its growth. Since $\frac{\delta_t}{N}
\lambda_i^t$ also defines a speed of movement in $\theta$-space along one of FIM eigenvectors (see Section \ref{sec:FIMSec}), such behavior of eigenvalues suggests an existence of mechanism that keeps a roughly constant movement speed of $\theta$ within $\RR^{|\theta|}$. To do that, when $\delta_t$ is reduced, this mechanism is responsible for increase of $\{ \lambda_{i}^t \}_{i = 1}^{N}$ as a compensation. This is also supported by Figure \ref{fig:EigvalsEv-d} where
each $\frac{\delta_t}{N}
\lambda_i^t$ is balancing, roughly, around the same value along the entire optimization. Furthermore, in Figure \ref{fig:LearningDetails-e} it is clearly observed that an evolution of $\lambda_{max}^t$ stabilizes\footnote{Trend $\lambda_{max}^t \rightarrow \frac{2 N}{\delta_t}$ was consistent in FC NNs for a wide range of initial learning rates, number of layers and neurons, and various datasets (see SM \cite{Kopitkov19dm_Supplementary}), making it an interesting venue for a future theoretical investigation} only when it reaches value of $\frac{2 N}{\delta_t}$, further supporting the above hypothesis.
\paragraph{Neural Spectrum Alignment}
\begin{figure}
\centering
\newcommand{\width}[0] {0.23}
\begin{tabular}{cc}
\subfloat[\label{fig:NNSpectrum1.0-a}]{\includegraphics[width=\width\textwidth]{10.pdf}
\includegraphics[width=\width\textwidth]{11.pdf}}
&
\subfloat[\label{fig:NNSpectrum1.0-b}]{\includegraphics[width=\width\textwidth]{12.pdf}
\includegraphics[width=\width\textwidth]{13.pdf}}
\\
\subfloat[\label{fig:NNSpectrum1.0-c}]{\includegraphics[width=\width\textwidth]{14.pdf}
\includegraphics[width=\width\textwidth]{15.pdf}}
&
\subfloat[\label{fig:NNSpectrum1.0-d}]{\includegraphics[width=\width\textwidth]{16.pdf}
\includegraphics[width=\width\textwidth]{17.pdf}}
\end{tabular}
\begin{tabular}{c}
\subfloat[\label{fig:NNSpectrum1.0-e}]{\includegraphics[width=\width\textwidth]{18.pdf}
\includegraphics[width=\width\textwidth]{19.pdf}}
\end{tabular}
\protect
\caption{(a) For different $k$, relative energy of the label vector $\bar{y}$ in \topp $k$ eigenvectors of $G_t$, $E_t(\bar{y}, k)$, along the optimization time $t$. (b) Relative energy of NN output, $E_t(\bar{f}_{t}, k)$.
(c) Relative energy of the residual, $E_t(\bar{m}_{t}, k)$.
(d) Relative energy of the differential $d \bar{f}_{t} = -
\frac{\delta_t}{N}
\cdot
G_{t}
\cdot
\bar{m}_{t}$, $E_t(d \bar{f}_{t}, k)$.
(e) Relative energy of NN output, $E_t(\bar{f}_{t}^{test}, k)$, with both $G_t$ and $\bar{f}_{t}^{test}$ computed at $10^4$ testing points.
Dashed vertical lines depict time $t$ at which learning rate $\delta$ was decayed (see Figure \ref{fig:LearningDetails-e}).
}
\label{fig:NNSpectrum1.0}
\end{figure}
Notate by $\cos \left[ \alpha_t \left( \bar{\phi}, k \right) \right] \triangleq \sqrt{\frac{\sum_{i = 1}^{k}
<\bar{\upsilon}_{i}^t, \bar{y}>^2}{\norm{\bar{\phi}}_2^2}}$ the cosine of an angle $\alpha_t \left( \bar{\phi}, k \right)$ between an arbitrary vector $\bar{\phi}$ and its projection to the sub-space of $\RR^N$ spanned by $\{ \bar{\upsilon}_{i}^t \}_{i = 1}^{k}$.
Further, $E_t(\bar{\phi}, k) \triangleq \cos^2 \left[ \alpha_t \left( \bar{\phi}, k \right) \right]$ can be considered as a \emph{relative energy} of $\bar{\phi}$, the percentage of its energy $\norm{\bar{\phi}}_2^2$ located inside $span \left( \{ \bar{\upsilon}_{i}^t \}_{i = 1}^{k} \right)$. In our experiments we will use $E_t(\bar{\phi}, k)$ as an alignment metric between $\bar{\phi}$ and $\{ \bar{\upsilon}_{i}^t \}_{i = 1}^{k}$.
Further, we evaluate alignment of $G_t$ with $\bar{y}$ instead of $\bar{m}_{0}$ since $\bar{f}_{0}$ is approximately zero in the considered FC networks.
In Figure \ref{fig:NNSpectrum1.0-a} we depict relative energy of the label vector $\bar{y}$ in \topp $k$ eigenvectors of $G_t$, $E_t(\bar{y}, k)$.
As observed, 20 \topp eigenvectors of $G_t$ contain 90 percent of $\bar{y}$ for almost all $t$. Similarly, 200 \topp eigenvectors of $G_t$ contain roughly 98 percent of $\bar{y}$, with rest of eigenvectors being practically orthogonal w.r.t. $\bar{y}$. That is, $G_t$ aligns its \topp spectrum towards the ground truth target function $\bar{y}$ almost immediately after starting of training, which improves the convergence rate since the information flow is fast along \topp eigenvectors as discussed in Section \ref{sec:L2Loss} and proved in \cite{Arora19arxiv,Oymak19arxiv}.
Further, we can see that for $k < 400$ the relative energy $E_t(\bar{y}, k)$ is decreasing after each decay of $\delta$, yet for $k > 400$ it keeps growing along the entire optimization. Hence, the \topp eigenvectors of $G_t$ can be seen as NN memory that is learned/tuned toward representing the target $\bar{y}$, while after each learning rate drop the learned information is spread more evenly among a higher number of different \topp eigenvectors.
Likewise, in Figure \ref{fig:NNSpectrum1.0-b} we can see that NN outputs vector $\bar{f}_{t}$ is located entirely in a few hundreds of \topp eigenvectors.
In case we consider $G_t$ to be constant, such behavior can be explained by Eq.~(\ref{eq:FVecDff}) since each increment of $\bar{f}_{t}$, $d \bar{f}_{t}$, is also located almost entirely within \topp 60 eigenvectors of $G_t$ (e.g. see $E_t(d \bar{f}_{t}, 60)$ in Figure \ref{fig:NNSpectrum1.0-d}). Yet, for a general NN with a time-dependent kernel the theoretical justification for the above empirical observation is currently missing.
Further, similar relation is observed also at points outside of $\pmb{\mathcal{X}}$ (see Figure \ref{fig:NNSpectrum1.0-e}),
leading to the empirical conclusion that \topp eigenfunctions of \emph{gradient similarity} $g_{t}(X, X')$ are the basis functions of NN $f_{\theta}(X)$.
\paragraph{Residual Dynamics}
Further, a projection of the residual $\bar{m}_{t}$ onto \topp eigenvectors, shown in Figure \ref{fig:NNSpectrum1.0-c}, is decreasing along $t$, supporting Eq.~(\ref{eq:L2DynamicsM}). Particularly, we can see that at $t = 600000$ only 10\% of $\bar{m}_{t}$'s energy is located inside \topp 4000 eigenvectors, and thus at the optimization end 90\% of its energy is inside \btm eigenvectors. Moreover, in Figure \ref{fig:NNSpectrum3-a} we can observe that the projection of $\bar{m}_{t}$ along \btm 5000 eigenvectors almost does not change during the entire optimization. This may be caused by two main reasons - the slow convergence rate associated with \btm eigenvectors and a single-precision floating-point (float32) format used in our simulation. The latter can prevent the information flow along the \btm spectrum due to the numerical precision limit. No matter the case, we empirically observe that the information located in the \btm spectrum of $G_t$ was not learned, even for a relatively long optimization process (i.e. $600000$ iterations). Furthermore, since this spectrum part is also associated with high-frequency information \cite{Basri19arxiv}, $\bar{m}_{t}$ at $t = 600000$ comprises mostly the noise, which is also evident from Figures \ref{fig:NNSpectrum3-b}-\ref{fig:NNSpectrum3-c}.
Moreover, we can also observe in Figure \ref{fig:NNSpectrum1.0-c} a special drop of $E_t(\bar{m}_{t}, k)$ at times of $\delta$ decrease. This can be explained by the fact that a lot of $\bar{m}_{t}$'s energy is located inside first several $\{\bar{\upsilon}_{i}^t\}$ (see $E_t(\bar{m}_{t}, 5)$ in Figure \ref{fig:NNSpectrum1.0-c}). When learning rate is decreased, the information flow speed $s_i^t \triangleq 1 - |1 -
\frac{\delta_t}{N}
\lambda_i^t|$, discussed in Section \ref{sec:L2Loss}, is actually increasing for a few \topp eigenvectors (see Figure \ref{fig:EigvalsEv-c}). That is, terms $\frac{\delta_t}{N}
\lambda_i^t$, being very close to 2 before $\delta$'s decay, are getting close to 1 after, as seen in Figure \ref{fig:EigvalsEv-d}. In its turn this accelerates the information flow along these first $\{\bar{\upsilon}_{i}^t\}$, as described in Eq.~(\ref{eq:L2DynamicsF})-(\ref{eq:L2DynamicsM}), leading also to a special descend of $E_t(\bar{m}_{t}, k)$ and of the training loss in Figure \ref{fig:NNSpectrum1.1-b}.
\paragraph{Eigenvectors}
\begin{figure}
\centering
\newcommand{\imagepath}[0] {Figures/FC_NN_6L/time_00595000}
\newcommand{\width}[0] {0.091}
\begin{tabular}{cccc}
\subfloat[\label{fig:NNSpectrum3-a}]{\includegraphics[width=0.19\textwidth]{20.pdf}}
&
\subfloat[\label{fig:NNSpectrum3-b}]{\includegraphics[width=0.17\textwidth]{21.pdf}}
&
\subfloat[\label{fig:NNSpectrum3-c}]{\includegraphics[width=0.15\textwidth]{22.pdf}}
&
\subfloat[\label{fig:NNSpectrum3-d}]{\includegraphics[width=\width\textwidth]{23.jpg}
\includegraphics[width=\width\textwidth]{24.jpg}
\includegraphics[width=\width\textwidth]{25.jpg}
\includegraphics[width=\width\textwidth]{26.jpg}}
\end{tabular}
\protect
\caption{(a) Spectral projections of the residual $\bar{m}_{t}$, $<\bar{\upsilon}_{i}^t, \bar{m}_{t}>^2$, at $t = 20000$ and $t = 600000$; (b) and (c) Fourier Transform of $\bar{m}_{t}$ at $t = 20000$ and $t = 600000$ respectively. The high frequency is observed to be dominant in (c). (d) a linear combination $\bar{f}_{t, k} \triangleq \sum_{i = 1}^{k}
<\bar{\upsilon}_{i}^t, \bar{f}_{t}>
\bar{\upsilon}_{i}^t
$ of first $k = \{ 10, 100, 200, 500 \}$ eigenvectors at $t = 600000$. Each vector $\bar{f}_{t, k}$ was interpolated from training points $\{ X^i \}_{i = 1}^{N}$ to entire $[0, 1]^2$ via a linear interpolation.
}
\label{fig:NNSpectrum3}
\end{figure}
\begin{figure}
\centering\offinterlineskip
\newcommand{\imagepath}[0] {Figures/FC_NN_6L/time_00595000}
\includegraphics[width=0.166\linewidth]{27.pdf}%
\includegraphics[width=0.166\linewidth]{28.pdf}%
\includegraphics[width=0.166\linewidth]{29.pdf}%
\includegraphics[width=0.166\linewidth]{30.pdf}%
\includegraphics[width=0.166\linewidth]{31.pdf}%
\includegraphics[width=0.166\linewidth]{32.pdf}%
\\
\includegraphics[width=0.15\linewidth]{33.pdf}%
\hspace{0.01\linewidth}
\includegraphics[width=0.15\linewidth]{34.pdf}%
\hspace{0.01\linewidth}
\includegraphics[width=0.15\linewidth]{35.pdf}%
\hspace{0.01\linewidth}
\includegraphics[width=0.15\linewidth]{36.pdf}%
\hspace{0.01\linewidth}
\includegraphics[width=0.15\linewidth]{37.pdf}%
\hspace{0.01\linewidth}
\includegraphics[width=0.15\linewidth]{38.pdf}%
\\
\includegraphics[width=0.166\linewidth]{39.pdf}%
\includegraphics[width=0.166\linewidth]{40.pdf}%
\includegraphics[width=0.166\linewidth]{41.pdf}%
\includegraphics[width=0.166\linewidth]{42.pdf}%
\includegraphics[width=0.166\linewidth]{43.pdf}%
\includegraphics[width=0.166\linewidth]{44.pdf}%
\\
\includegraphics[width=0.15\linewidth]{45.pdf}%
\hspace{0.01\linewidth}
\includegraphics[width=0.15\linewidth]{46.pdf}%
\hspace{0.01\linewidth}
\includegraphics[width=0.15\linewidth]{47.pdf}%
\hspace{0.01\linewidth}
\includegraphics[width=0.15\linewidth]{48.pdf}%
\hspace{0.01\linewidth}
\includegraphics[width=0.15\linewidth]{49.pdf}%
\hspace{0.01\linewidth}
\includegraphics[width=0.15\linewidth]{50.pdf}%
\protect
\caption{Eigenvectors of Gramian $G_{t}$ at $t = 600000$. First two rows: from left-to-right, 6 first eigenvectors and their Fourier Transforms (see the Appendix \ref{sec:AppF} for details). Last two rows: 10-th, 100-th, 500-th, 1000-th, 2000-th and 4000-th eigenvectors, and their Fourier Transforms. As observed, a frequency of signal inside of each eigenvector increases when moving from large to small eigenvalue.
}
\label{fig:NNSpectrum1}
\end{figure}
\begin{figure}
\centering\offinterlineskip
\newcommand{\imagepath}[0] {Figures/FC_NN_6L/time_00020000}
\includegraphics[width=0.166\linewidth]{51.pdf}%
\includegraphics[width=0.166\linewidth]{52.pdf}%
\includegraphics[width=0.166\linewidth]{53.pdf}%
\includegraphics[width=0.166\linewidth]{54.pdf}%
\includegraphics[width=0.166\linewidth]{55.pdf}%
\includegraphics[width=0.166\linewidth]{56.pdf}%
\\
\includegraphics[width=0.166\linewidth]{57.pdf}%
\includegraphics[width=0.166\linewidth]{58.pdf}%
\includegraphics[width=0.166\linewidth]{59.pdf}%
\includegraphics[width=0.166\linewidth]{60.pdf}%
\includegraphics[width=0.166\linewidth]{61.pdf}%
\includegraphics[width=0.166\linewidth]{62.pdf}%
\protect
\caption{First line: from left-to-right, 6 first eigenvectors of Gramian $G_{t}$ at $t = 20000$. Second line: 10-th, 100-th, 500-th, 1000-th, 2000-th and 4000-th eigenvectors.
}
\label{fig:NNSpectrum4}
\end{figure}
We further explore $\{\bar{\upsilon}_{i}^t\}$ in a more illustrative manner, to produce a better intuition about their nature. In Figure \ref{fig:NNSpectrum3-d} a linear combination of several \topp eigenvectors at $t = 600000$ is presented, showing that with only 100 vectors we can accurately approximate the NN output.
Furthermore, in Figure \ref{fig:NNSpectrum1} several eigenvectors are interpolated to entire $[0, 1]^2$. We can see that \topp $\{\bar{\upsilon}_{i}^t\}$ obtained visual similarity with various parts of Mona Lisa image and indeed can be seen as basis functions of $f_{\theta}(X)$ depicted in Figure \ref{fig:LearningDetails-b}. Likewise, we also demonstrate the Fourier Transform of each $\bar{\upsilon}_{i}^t$. As observed, the frequency of the contained information is higher for smaller eigenvalues, supporting conclusions of \cite{Basri19arxiv}. More eigenvectors are depicted in SM.
Likewise, in Figure \ref{fig:NNSpectrum4} same eigenvectors are displayed at $t = 20000$. At this time the visual similarity between each one of first eigenvectors and the target function in Figure \ref{fig:LearningDetails-a} is much stronger. This can be explained by the fact that the information about the target function within $G_t$ is spread from first few towards higher number of \topp eigenvectors after each learning rate drop, as was described above. Hence, before the first drop at $t = 100000$ this information is mostly gathered within first few $\{\bar{\upsilon}_{i}^t\}$ (see also $E_t(\bar{y}, 10)$ in Figure \ref{fig:NNSpectrum1.0-a}).
\paragraph{Alignment and NN Depth / Width}
Here we further study how a width and a depth of NN affect the alignment between $G_t$ and the ground truth signal $\bar{y}$. To this purpose,
we performed the optimization under the identical setup, yet with NNs containing various numbers of layers and neurons. In Figure \ref{fig:NNSpectrum1.1-a} we can see that in deeper NN \topp eigenvectors of $G_t$ aligned more towards $\bar{y}$ - the relative energy $E_t(\bar{y}, 400)$ is higher for a larger depth. This implies that more layers, and the higher level of non-linearity produced by them, yield a better alignment between $G_t$ and $\bar{y}$. In its turn this allows NN to better approximate a given target function, as shown in Figures \ref{fig:NNSpectrum1.1-b}-\ref{fig:NNSpectrum1.1-c}, making it more expressive for a given task. Moreover, in evaluated 2-layer NNs, with an increase of neurons and parameters the alignment rises only marginally.
\begin{figure}
\centering
\newcommand{\width}[0] {0.23}
\begin{tabular}{ccc}
\subfloat[\label{fig:NNSpectrum1.1-a}]{\includegraphics[width=\width\textwidth]{63.pdf}}
&
\subfloat[\label{fig:NNSpectrum1.1-b}]{\includegraphics[width=\width\textwidth]{64.pdf}}
&
\subfloat[\label{fig:NNSpectrum1.1-c}]{\includegraphics[width=\width\textwidth]{65.pdf}}
\end{tabular}
\begin{tabular}{c}
\subfloat[\label{fig:NNSpectrum1.1-d}]{\includegraphics[width=\width\textwidth]{66.pdf}
\includegraphics[width=\width\textwidth]{67.pdf}}
\end{tabular}
\protect
\caption{(a) For NNs with a different number of layers and of neurons, relative energy of the label vector $\bar{y}$ in \topp $400$ eigenvectors of $G_t$, $E_t(\bar{y}, 400)$, along the optimization time $t$; (b) training loss and (c) testing loss of these models. \textbf{L} and \textbf{W} stand for number of layers and number of neurons respectively.
(d) For different $i$, relative energy of $\bar{\upsilon}_{i}^{600000}$ in spectrum of $G_{20000}$, $E_{20000}(\bar{\upsilon}_{i}^{600000}, k)$, as a function of $k$, with horizontal axes being log-scaled. As seen, 10 first \topp eigenvectors at final time $t = 600000$ are located also in the \topp spectrum of $G_{20000}$, hence the \topp Gramian spectrum was preserved along the optimization. Yet, \btm eigenvectors are significantly less stable.
}
\label{fig:NNSpectrum1.1}
\end{figure}
\paragraph{Spectrum Preservation}
Next, we examine how stable are eigenvectors of $G_t$ along $t$. For this we explore the relative energy of $G_{600000}$'s eigenvectors, final eigenvectors of the optimization, within spectrum of $G_{20000}$. Note that we compare spectrums at $t = 600000$ and $t = 20000$ to skip first several thousands of iterations since during this bootstrap period the change of $G_t$ is highly notable.
In Figure \ref{fig:NNSpectrum1.1-d} we depict $E_{20000}(\bar{\upsilon}_{i}^{600000}, k)$ as a function of $k$, for various $\{ \bar{\upsilon}_{i}^{600000} \}$. As observed, 10 first \topp eigenvectors of $G_{600000}$ are also located in the \topp spectrum of $G_{20000}$ - the function $E_{20000}(\bar{\upsilon}_{i}^{600000}, k)$ is almost 1 for even relatively small $k$. Hence, the \topp Gramian spectrum was preserved, roughly, along the performed optimization.
Further, eigenvectors of smaller eigenvalues (i.e. with higher indexes $i$) are significantly less stable, with large amount of their energy widely spread inside \btm eigenvectors of $G_{20000}$. Moreover, we can see a clear trend that with higher $i$ the associated eigenvector is less preserved.
\paragraph{Scope of Analysis}
The above empirical analysis was repeated under numerous different settings and can be found in SM \cite{Kopitkov19dm_Supplementary}. We evaluated various FC architectures, with and without shortcuts between the layers and including various activation functions. Likewise, optimizers GD, stochastic GD and Adam were tested on problems of regression (L2 loss) and density estimation (noise contrastive estimation \cite{Gutmann10aistats}). Additionally, various high-dimensional real-world datasets were tested, including MNIST and CIFAR100. \textbf{All} experiments exhibit the same alignment nature of kernel towards the learned target function.
\section{Discussion and Conclusions}
\label{sec:Concl}
In this paper we empirically revealed that during GD \topp eigenfunctions of \emph{gradient similarity} kernel change to align with the target function $y(X)$ learned by NN $f_{\theta}(X)$, and hence can be considered as a NN memory tuned during the optimization to better represent $y(X)$. This alignment is significantly higher for deeper NNs, whereas a NN width has only a minor effect on it.
Moreover, the same \topp eigenfunctions represent
a \emph{neural spectrum} - the $f_{\theta}(X)$ is a linear combination of these eigenfunctions during the optimization. As well, we showed various trends of the kernel dynamics as a result of the learning rate decay, accounting for which we argue may lead to a further progress in DL theory. The considered herein optimization scenarios include various \supp and \unsupp losses over various high-dimensional datasets, optimized via several different optimizers. Several variants of FC architecture were evaluated. The results are consistent with our previous experiments in \cite{Kopitkov19arxiv}.
The above revealed behavior leads to several implications. First, our empirical study suggests that the high approximation power of deep models is produced by the above alignment capability of the \emph{gradient similarity}, since the learning along its \topp eigenfunctions is considerably faster. Furthermore, it also implies that the family of functions that a NN can approximate (in reasonable time) is limited to functions within the \topp spectrum of the kernel. Recently, it was proved in \cite{Arora19arxiv,Basri19arxiv,Oymak19arxiv}. Thus, it leads to the next main question - how the NN architecture and optimization hyper-parameters affect this spectrum, and what is their optimal configuration for learning a given function $y(X)$. Moreover, NN dynamics behavior beyond first-order Taylor expansion is still unexplored. We shall leave it for a future exciting research.
\section{Acknowledgments}
The authors thank Daniel Soudry and Dar Gilboa for discussions on dynamics of a Neural Tangent Kernel (NTK).
This work was supported in part by the Israel Ministry of Science \& Technology (MOST) and Intel Corporation. We gratefully acknowledge the support of NVIDIA Corporation with the donation of the Titan Xp GPU, which, among other GPUs, was used for this research.
| {
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Q: Get column names with zero variance using dplyr I'm trying to find any variables in my data that have zero variance (i.e. constant continuous variables). I figured out how to do it with lapply but I would like to use dplyr as I'm trying to follow tidy data principles. I can create a vector of just the variances using dplyr but its the last step where I find the values not equal to zero and return the variable names that confusing me.
Here's the code
library(PReMiuM)
library(tidyverse)
#> ── Attaching packages ───────────────────────────────────────────────────────────────────────────────────── tidyverse 1.2.1 ──
#> ✔ ggplot2 2.2.1 ✔ purrr 0.2.4
#> ✔ tibble 1.4.2 ✔ dplyr 0.7.4
#> ✔ tidyr 0.7.2 ✔ stringr 1.2.0
#> ✔ readr 1.2.0 ✔ forcats 0.2.0
#> ── Conflicts ──────────────────────────────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
#> ✖ dplyr::filter() masks stats::filter()
#> ✖ dplyr::lag() masks stats::lag()
setwd("~/Stapleton_Lab/Projects/Premium/hybridAnalysis/")
# read in data from analysis script
df <- read_csv("./hybrid.csv")
#> Parsed with column specification:
#> cols(
#> .default = col_double(),
#> Exp = col_character(),
#> Pedi = col_character(),
#> Harvest = col_character()
#> )
#> See spec(...) for full column specifications.
# checking for missing variable
# df %>%
# select_if(function(x) any(is.na(x))) %>%
# summarise_all(funs(sum(is.na(.))))
# grab month for analysis
may <- df %>%
filter(Month==5)
june <- df %>%
filter(Month==6)
july <- df %>%
filter(Month==7)
aug <- df %>%
filter(Month==8)
sept <- df %>%
filter(Month==9)
oct <- df %>%
filter(Month==10)
# check for zero variance in continuous covariates
numericVars <- grep("Min|Max",names(june))
zero <- which(lapply(june[numericVars],var)==0,useNames = TRUE)
noVar <- june %>%
select(numericVars) %>%
summarise_all(var) %>%
filter_if(all, all_vars(. != 0))
#> Warning in .p(.tbl[[vars[[i]]]], ...): coercing argument of type 'double'
#> to logical
#> Warning in .p(.tbl[[vars[[i]]]], ...): coercing argument of type 'double'
#> to logical
#> Warning in .p(.tbl[[vars[[i]]]], ...): coercing argument of type 'double'
#> to logical
#> Warning in .p(.tbl[[vars[[i]]]], ...): coercing argument of type 'double'
#> to logical
#> Warning in .p(.tbl[[vars[[i]]]], ...): coercing argument of type 'double'
#> to logical
#> Warning in .p(.tbl[[vars[[i]]]], ...): coercing argument of type 'double'
#> to logical
#> Warning in .p(.tbl[[vars[[i]]]], ...): coercing argument of type 'double'
#> to logical
#> Warning in .p(.tbl[[vars[[i]]]], ...): coercing argument of type 'double'
#> to logical
#> Warning in .p(.tbl[[vars[[i]]]], ...): coercing argument of type 'double'
#> to logical
#> Warning in .p(.tbl[[vars[[i]]]], ...): coercing argument of type 'double'
#> to logical
#> Warning in .p(.tbl[[vars[[i]]]], ...): coercing argument of type 'double'
#> to logical
#> Warning in .p(.tbl[[vars[[i]]]], ...): coercing argument of type 'double'
#> to logical
#> Warning in .p(.tbl[[vars[[i]]]], ...): coercing argument of type 'double'
#> to logical
#> Warning in .p(.tbl[[vars[[i]]]], ...): coercing argument of type 'double'
#> to logical
#> Warning in .p(.tbl[[vars[[i]]]], ...): coercing argument of type 'double'
#> to logical
#> Warning in .p(.tbl[[vars[[i]]]], ...): coercing argument of type 'double'
#> to logical
#> Warning in .p(.tbl[[vars[[i]]]], ...): coercing argument of type 'double'
#> to logical
#> Warning in .p(.tbl[[vars[[i]]]], ...): coercing argument of type 'double'
#> to logical
#> Warning in .p(.tbl[[vars[[i]]]], ...): coercing argument of type 'double'
#> to logical
#> Warning in .p(.tbl[[vars[[i]]]], ...): coercing argument of type 'double'
#> to logical
A: With a reproducible example, I think what you are aiming for is below. Please note that as pointed out by Colin, I have not dealt with the issue of you selecting variables with a character variable. See his answer for details on that.
# reproducible data
mtcars2 <- mtcars
mtcars2$mpg <- mtcars2$qsec <- 7
library(dplyr)
mtcars2 %>%
summarise_all(var) %>%
select_if(function(.) . == 0) %>%
names()
# [1] "mpg" "qsec"
Personally, I think that obfuscates what you are doing. One of the following using the purrr package (if you wish to remain in the tidyverse) would be my preference, with a well written comment.
library(purrr)
# Return a character vector of variable names which have 0 variance
names(mtcars2)[which(map_dbl(mtcars2, var) == 0)]
names(mtcars2)[map_lgl(mtcars2, function(x) var(x) == 0)]
If you'd like to optimize it for speed, stick with base R
# Return a character vector of variable names which have 0 variance
names(mtcars2)[vapply(mtcars2, function(x) var(x) == 0, logical(1))]
A: You have two problems.
1. Passing names of columns as a variable to select()
The vignette about that is here. programming with dplyr. The solution here is to use the select_at() scoped variant of the select function.
2. Variance equals 0
noVar <- june %>%
select_at(.vars=numericVars) %>%
summarise_all(.funs=var) %>%
filter_all(any_vars(. == 0))
A: Select columns if unique count is 1 then get column names, using @Benjamin's example data mtcars2:
mtcars2 %>%
select_if(function(.) n_distinct(.) == 1) %>%
names()
# [1] "mpg" "qsec"
A: The answers here are all good, but
as dplyr 1.0.0 deprecated the scoped variants (e.g. select_if, select_at, filter_all), here is an update using the same repex data given by @Benjamin:
mtcars2 <- mtcars
mtcars2$mpg <- mtcars2$qsec <- 7
mtcars2 %>%
map_df( ~ var(.)) %>%
select(where( ~ . == 0))
gives
# A tibble: 1 x 2
mpg qsec
<dbl> <dbl>
1 0 0
or after %>% names:
[1] "mpg" "qsec"
| {
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} | 3,963 |
Courage in the Face of Despair | Mark 15:39-47
By Cole Newton — 4 weeks ago
We know that death did not defeat Christ but that death was defeated by Christ through His dying. Like Christ's substitutional atoning for our sins, His humiliation was also finished upon the cross. To those looking on, His burial seemed to be the most disappointing in a long stream of would-be messiahs, but in reality, His burial, His descent to the dead, was the beginning of His eternal exaltation. Although Saturday must have been the longest Sabbath the disciples ever felt, the new week began with Jesus' resurrection, which Paul calls the first fruit. Christ's resurrection is a foretaste and a guarantee of the great resurrection of all God's people still to come.
And when the centurion, who stood facing him, saw that in this way he breathed his last, he said, "Truly this man was the Son of God!"
There were also women looking on from a distance, among whom were Mary Magdalene, and Mary the mother of James the younger and of Joses, and Salome. When he was in Galilee, they followed him and ministered to him, and there were also many other women who came up with him to Jerusalem.
And when evening had come, since it was the day of Preparation, that is, the day before the Sabbath, Joseph of Arimathea, a respected member of the council, who was also himself looking for the kingdom of God, took courage and went to Pilate and asked for the body of Jesus. Pilate was surprised to hear that he should have already died. And summoning the centurion, he asked him whether he was already dead. And when he learned from the centurion that he was dead, he granted the corpse to Joseph. And Joseph bought a linen shroud, and taking him down, wrapped him in the linen shroud and laid him in a tomb that had been cut out of the rock. And he rolled a stone against the entrance of the tomb. Mary Magdalene and Mary the mother of Joses saw where he was laid.
Mark 15:39-47 ESV
COVID-19 was an apocalypse. Now, I mean that in the technical sense of the word. Apocalypse means revelation or unveiling, and any crisis inevitably leads to a kind of revealing, especially of people's hearts. One immediate effect of the pandemic has been a greater societal awareness of illnesses. Many headlines warn to beware of a tripledemic of Covid, flu, and RSV. Winter, however, has always been a season of viruses, particularly respiratory, and some seasons are inevitably worse or better than others. That has not changed, but our awareness has.
Yet, in my opinion, the greatest unveiling of the Covid pandemic was its exposure and amplification of a psychological epidemic of despair that had been growing long before 2020. For instance, suicide rates and the desperate pleas for euthanasia were certainly present before Covid, but the pandemic and the lockdowns have certainly brought them to the surface and even heightened them. Being forced to face our own mortality did not settle well on our secular society, and it exposed that most people simply cannot face the reality of death. That is why we sedate ourselves against reality as much as possible with drugs and entertainment, and when the sedation no longer works, we would rather take death into our own hands rather than embrace the uncertainly of life. We are a culture in despair.
We would do well to consider intently this passage of Mark because His followers were certainly faced with despair in the wake of Jesus' death. You see, even though Jesus told His disciples three times that He would both die and rise, we have also seen repeatedly that they did not yet have eyes to see that blessed promise. Rather, the Christ who they hoped would restore the kingdom of Israel had been crucified, ridiculed by men and cursed by God, and His disciples had abandoned Him in His suffering. During His life, Jesus made it seem as if God's kingdom really was at hand, but with His death, it never felt more distant. The sun may have begun to shine again with Jesus' death, but an even greater darkness loomed over the hearts of the faithful. Though the greatest victory of all time had been accomplished, they could only see the most savage of all defeats.
Yet in the midst of this despair, Mark records for us three examples of courage (a confession, discipleship, and an act of love) from the three unexpected places. We will look at each individually before considering their collective exhortation for us today who likewise live between the cross and the resurrection.
Truly This Man Was the Son of God! // Verses 39
Although the priests and bystanders were not able to understand the sign of the darkness around because of the darkness within them, a ray of light pierced through the most unlikely person imaginable at the foot of the cross.
Although there were other Roman soldiers at the crucifixion, this centurion was their commander. He was responsible for overseeing the execution of Jesus and the two robbers on either side of Him. Timothy Keller notes:
Centurions were not aristocrats who got military commissions; they were enlisted men who had risen through the ranks. So this man had seen death, and had inflicted it, to a degree that you and I can hardly imagine.
Here was a hardened, brutal man. Yet something had penetrated his spiritual darkness. He became the first person to confess the deity of Jesus Christ.[1]
Indeed, Mark explicitly notes that the centurion saw Christ's divinity through His manner of death. He saw how Jesus breathed His last breath, and a fountain deep within the centurion's violence-stained heart broke open. As a dealer of death, he knew it very well. He brought the curse of Adam upon others for a living, so he was no doubt intimately familiar with how it snatched up the strong and the weak alike, both old and young, men and women, slave and free. He knew firsthand that all living would be dragged down into that everlasting darkness called the grave.
Yet Jesus was different. Death did not fall upon Jesus; He gave Himself over to it. Even while hanging from the tree, mocked by men and forsaken in our place by the Father, Jesus was still Lord. As both God and the only sinless man, death had no claim over Him; therefore, His life could never be taken from Him. He could only lay it down. I doubt that the centurion could have expressed his thoughts and emotions very well, but I believe that this is what he saw. As the one presiding over the crucifixion, I think he understood that even from the cross Jesus was really in command of the proceedings. Jesus' death was so unlike normal deaths that the centurion could only conclude that Jesus was indeed divine. Indeed, as Keller said, he is the first human to confess Jesus' divinity in Mark's Gospel, and he is the first to confess the second part of Jesus' twofold confession of Jesus: that He is the Son of God.
Now, we do not know the degree of the centurion's faith past this point. Did he become a Christian? Perhaps; perhaps not. We will never know on this side of the river. We should, however, commend both his faith and his courage. We can safely assume that the centurion did not have everything in mind that we as Christians do today whenever we talk about the Son of God. I do not think, for example, that he was miraculously given understanding of the Trinity. Instead, the phrase 'son of god' was an honorific title given to humans who were deemed to have ascended to divinity. Most notably, it was a title used by Caesar, that is, the centurion's king and commander. He was, therefore, making a very dangerous confession. He was, at the very least, confessing Jesus to be as equally divine as Caesar.
Also, we should note with wonder and joy that this centurion Gentile is only a foretaste of the salvation that Christ's death would bring to all nations.
Revealed Under the Cross // Verses 40-41
The second example of faith and courage in the face of despair is not an individual but a group of women:
There were also women looking on from a distance, among whom were Mary Magdalene, and Mary the mother of James the younger and of Joses, and Salome. When he was in Galilee, they followed him and ministered to him, and there were also many other women who came up with him from Jerusalem.
Though all the disciples fled from Jesus and did not have the courage to follow Him to Golgotha (John being the only exception), this small crowd of women did. Just as they had followed Jesus in Galilee, they now followed Him as He went to His death. They were likely forced to do so from a distance because the soldiers would not let them nearer.
I find it significant that Mark makes the revelation of how these women followed and minister to Jesus throughout His ministry immediately after His death while His body still hung upon the cross. In most of the events that we studied in this Gospel, these women were there as eye witnesses. Hearing His words, and seeing His wonders. Yet we are only told of their presence here. I would imagine that their ministry to Jesus was largely unnoticed by the other disciples as well. Luke tells us that it was women like Joanna and Susanna that financially supported Jesus' ministry, yet their mention is almost like a footnote. They served in the background, until this moment when the more prominent disciples fell away in fear. This again is a picture in miniature of what Jesus taught. The proud will be humbled, while the humble shall be exalted. The servant of all is counted the greatest in the kingdom. The first become last, and the last become first.
Why "Turn Your Eyes Upon Jesus" is the Best Advice During Difficulty
By Michael Kelley — 10 months ago
Christian, you may or may not be feeling rightly today. Regardless, make sure you are "looking" rightly. No matter what you're feeling, turn your eyes upon Jesus. And find that those things of earth which might be making you feel this way or that will slowly but surely grow strangely dim.
Helen Howarth Lemmel wrote the lyrics to "Turn Your Eyes Upon Jesus" in 1922. She loved music her entire life and even studies vocal music in Germany for a time. But by the time she was 55, she had become blind, been abandoned by her wealthy husband, and suffered various other tribulations. And that's when she came across a little tract that deeply impressed her. The pamphlet read:
"So then, turn your eyes upon Him, look full into His face and you will find that the things of earth will acquire a strange new dimness."
And Helen Lemmel responded with a song:
O soul are you weary and troubledNo light in the darkness you seeThere's light for a look at the SaviorAnd life more abundant and free
Turn your eyes upon JesusLook full in his wonderful faceAnd the things of earth will grow strangely dimIn the light of his glory and grace
It's a wonderful song, but it's even better counsel. It is, in fact, very counsel we could receive during times of difficulty. During those days – during dark days – we will find that our feelings are spiraling out of control. And it's during days like that which we must remember that even when we can't make ourselves feel better, we can always control where our focus is. We can't control how we feel but we can always control where we're looking. And where we're looking is actually more important than what we are feeling. Here's why:
We cannot trust our feelings to tell us the truth:
The heart is more deceitful than anything else,and incurable—who can understand it? (Jer. 17:9).
This is indeed an uncomfortable truth. It's a decidedly different truth than the version of truth we find anywhere else in the world. While movies, Hollywood, and self-help gurus will tell us to follow our own hearts, the Bible says we should follow Jesus.
Why Almost Nobody Knows Anything about Critical Race Theory
By James E. Hanley — 1 year ago
Written by James E. Hanley |
CRT is just a sophisticated legal theory taught only in law schools and graduate schools. Others say that CRT is the simple factual truth about the history of race and politics in the U.S. and conservative opponents are trying to block teaching that in public schools. These two claims cannot both be true. A complexly sophisticated idea taught only in graduate school cannot simultaneously be a simple idea taught in elementary and high schools. One need not even critique CRT to agree to this. So why do its defenders contradict themselves?
In recent months defenders of Critical Race Theory have given two conflicting stories. Some tell us that the flap over critical race theory (CRT) in K-12 education is a strawman because CRT is just a sophisticated legal theory taught only in law schools and graduate schools. Others say that CRT is the simple factual truth about the history of race and politics in the U.S. and conservative opponents are trying to block teaching that in public schools. These two claims cannot both be true. A complexly sophisticated idea taught only in graduate school cannot simultaneously be a simple idea taught in elementary and high schools. One need not even critique CRT to agree to this. So why do its defenders contradict themselves?
In our search for a reason, we should look for an explanation that is both charitable and grounded. By charitable, I mean we assume CRT's defenders are not consciously trying to deceive. By grounded, I mean one that easily fits known facts and theories, without need for special pleading. Collectively, these two principles are the foundation of Hanlon's razor, which warns us to never assume malice when ignorance is an adequate explanation.
In the case of CRT, I believe we can explain its defenders' confusion through the simple lens of costs and benefits. Put simply, acquiring knowledge is costly, and thinking logically is costly, but feeling morally righteous or smugly superior is psychologically valuable and attained at low cost. Just as any of us prefer a good meal we don't have to pay for, we face a temptation to latch on to the feelings of moral or intellectual superiority without paying the costs of gaining real knowledge and engaging in careful thinking.
Let's begin with those who say critical race theory is just a high-level academic theory. They clearly err, because no influential academic theory remains only at the law school and graduate school level for decades. Although CRT originated in law schools, legal scholarship is not hermetically sealed off from the rest of academia. Some social science and humanities scholars found the ideas of CRT useful for their scholarly pursuits and adopted them. Blossoming scholars then learned these ideas in graduate school and applied them in their own scholarly thinking, and then, when they got academic jobs, in their undergraduate courses.
That sophisticated scholarly ideas sometimes get watered down in undergrad courses is no secret. So the CRT a student learns in an undergraduate Sociology or African-American Studies course may be incomplete in the same way that undergrads get an incomplete version of Plato or Marx. That doesn't make it not critical theory. And if some of these undergrads go on to teach in elementary or high schools, some likely will introduce some of these ideas, likely in an even more watered-down way.
Book Review: Typology by Dr. James M. Hamilton Jr.
By Camron Hyde — 5 months ago
It was definitely a book I had to read slowly, but it's also a book I'm grateful to have read. It is certainly one I will return to for reference in my preaching and teaching! Typology is a useful tool to help us better understand the Bible as well as to help others see it come alive. Dr. Hamilton has provided a great resource to help us all grow deeper in our walk with Christ.
This review has been a long time coming. I'm a huge fan of Dr. James M. Hamilton Jr. Discovering his teaching on biblical theology truly changed my life and the Bible Talk podcast he's on is something I'm trying to get everyone to listen to because it will blow your mind. Dr. Hamilton pastors Kenwood Baptist Church in Louisville, KY and he's the Professor of Biblical Theology at The Southern Baptist Theological Seminary.
His new book, Typology: Understanding the Bible's Promise-Shaped Patterns took me awhile to work through. Part of it is that it's academic in nature and the other is that I have three small children and my reading time is limited. Even so, it is a book that is worth your time. It is a book I will reference over and over again.
Dr. Hamilton says, "I will be arguing in this book that God's promises shaped the way the biblical authors perceived, understood, and wrote. As this happens again and again across the Scriptures, from account to account, book to book, author to author, patterns begin to be discerned, patterns that have been shaped by promises: promise-shaped patterns." | {
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\section{Introduction}
In this paper we continue the exploration of Poisson-Lie duals of $\eta$-deformed sigma models initiated in \cite{Hoare:2017ukq}.
In \cite{Hoare:2017ukq} we investigated the Poisson-Lie duals \cite{Klimcik:1995ux,Klimcik:1995jn} of the $\eta$-deformation \cite{Klimcik:2002zj,Klimcik:2008eq,Delduc:2013fga} of the bosonic symmetric space sigma model on $\grp{G}/\grp{H}$ \cite{Eichenherr:1979ci,Eichenherr:1979hz} for compact groups $\grp{G}$.
Here we focus on the $\eta$-deformation of the $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ superstring.
To study this model we consider the semi-symmetric space sigma model \cite{Metsaev:1998it,Zhou:1999sm,Berkovits:1999zq,Zarembo:2010sg} on the supercoset
\begin{equation}\label{eq:supercoset}
\frac{\grp{PSU}(1,1|2)}{\grp{SO}(1,1)\times\grp{SO}(2)} ~,
\end{equation}
and its $\eta$-deformation \cite{Delduc:2013qra,Delduc:2014kha}.
The bosonic part of this model is the symmetric space sigma model on the coset
\begin{equation}
\frac{\grp{SU}(1,1)}{\grp{SO}(1,1)} \times \frac{\grp{SU}(2)}{\grp{SO}(2)} ~,
\end{equation}
that is with target space $\geom{AdS}_2 \times \geom{S}^2$.
The semi-symmetric space sigma model then describes a truncation of the type II Green-Schwarz superstring \cite{Green:1983wt,Green:1983sg,Witten:1985nt,Grisaru:1985fv} on certain $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ supergravity backgrounds \cite{Sorokin:2011rr}.
This truncation is well-understood for both the two-dimensional worldsheet sigma model and the supergravity background.
To define a particular $\eta$-deformation of the semi-symmetric space sigma model, we first need to specify an antisymmetric operator $R$ satisfying the non-split modified classical Yang-Baxter equation on the superalgebra $\alg{psu}(1,1|2)$.
We will take this R-matrix to be given by the canonical Drinfel'd-Jimbo solution associated to a particular Dynkin diagram and Cartan-Weyl basis of the superalgebra.
\unskip\footnote{The relation between $\eta$-deformations corresponding to inequivalent Cartan-Weyl bases and the associated Drinfel'd-Jimbo R-matrices is not fully understood.
These can exist for non-compact real forms of bosonic Lie algebras and have been partially investigated for the $\eta$-deformations of the sigma model on $\geom{AdS}_5$, for which the relevant Lie algebra is $\alg{so}(2,4)$, in \cite{Delduc:2014kha,Hoare:2016ibq,Araujo:2017enj}.
They can also exist for Lie superalgebras, for which there exist different Dynkin diagrams.}
For such a choice of R-matrix the manifest symmetry algebra of the deformed model is broken to the Cartan subalgebra.
Together with the remaining charges, which are hidden, the isometry algebra is $q$-deformed \cite{Delduc:2013fga,Delduc:2014kha,Delduc:2016ihq,Delduc:2017brb,Arutyunov:2013ega} with $q \in \mathds{R}$ depending on the string tension and the deformation parameter $\eta$.
The Poisson-Lie duals of the $\eta$-deformed $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ superstring can be studied starting from a model on the complexified double
\begin{equation}
\frac{\grp{PSL}(2|2;\mathds{C})}{\grp{SO}(1,1)\times\grp{SO}(2)} ~,
\end{equation}
following the general construction of \cite{Klimcik:1995dy,Klimcik:1996nq}, which is extended to coset spaces in \cite{Klimcik:1996np,Squellari:2011dg,Sfetsos:1999zm}.
The model is constructed such that on integrating out the degrees of freedom associated to an appropriate Borel subalgebra (that correlates with the R-matrix) we recover the $\eta$-deformation of interest.
Following the results of \cite{Hoare:2017ukq}, for subalgebras $\alg{g}_0$ of $\alg{psu}(1,1|2)$ corresponding to sub-Dynkin diagrams we can construct subalgebras of the complexified double $\alg{psl}(2|2;\mathds{C})$ whose associated degrees of freedom can be integrated out to give the Poisson-Lie dual of the $\eta$-deformed $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ superstring with respect to $\alg{g}_0$.
Any additional Cartan generators not covered by the sub-Dynkin diagram can also be included in $\alg{g}_0$.
It is likely that this is not a complete list of possible Poisson-Lie duals of the $\eta$-deformed $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ superstring (see, for example, \cite{Lust:2018jsx}).
In this paper we mostly work with the Dynkin diagram $\mbox{\wasyfamily\char35} - \otimes - \mbox{\wasyfamily\char35}$.
A discussion of the other possible Dynkin diagrams is given in \@ifstar{\namedref{Appendix}}{\namedref{app.}}{app:Different_Dynkin}.
Let us briefly outline three possible Poisson-Lie duals that one can consider based on this choice:
\begin{enumerate}
\item First, one can consider the Poisson-Lie dual with respect to the full $\alg{psu}(1,1|2)$ superalgebra.
This model is conjectured \cite{Vicedo:2015pna,Hoare:2015gda,Sfetsos:2015nya,Klimcik:2015gba,Hoare:2017ukq,Driezen:2018glg} to be an analytic continuation of the $\lambda$-deformation of the $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ superstring \cite{Hollowood:2014qma} (generalising the bosonic $\lambda$-deformed models of \cite{Sfetsos:2013wia,Hollowood:2014rla}), which, following the terminology of \cite{Hoare:2017ukq} we refer to as the $\lambda^\star$-deformed model.
\item Second, one can take the sub-Dynkin diagram formed of the two bosonic nodes.
This corresponds to dualising with respect to the full bosonic subalgebra $\alg{su}(1,1) \oplus \alg{su}(2)$.
The bosonic part of this model coincides with the $\lambda^\star$-deformed model, however they differ in the fermionic part.
\item Finally, one can consider just the $\alg{u}(1) \oplus \alg{u}(1)$ subalgebra associated to the two Cartan generators.
This model is conjectured to be equivalent to taking the two-fold T-dual of the $\eta$-deformed $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ superstring.
\end{enumerate}
There is substantial evidence \cite{Alvarez:1994np,Elitzur:1994ri,Tyurin:1995bu,Bossard:2001au,VonUnge:2002xjf,Hlavaty:2004jp,Hlavaty:2004mr,Jurco:2017gii} that a Weyl anomaly is associated to integrating out the degrees of freedom of a non-unimodular algebra, that is when the trace of the structure constants is non-vanishing, $f_{ab}{}^b \neq 0$.
In this case, rather than solving the standard supergravity equations, the background solves a generalisation thereof \cite{Arutyunov:2015mqj,Wulff:2016tju} (as discussed in the context of non-abelian duality in \cite{Hoare:2016wsk,Hong:2018tlp,Wulff:2018aku}).
These generalised supergravity equations are equivalent to the $\kappa$-symmetry of the Green-Schwarz superstring \cite{Wulff:2016tju}.
They are also related to the standard supergravity equations by T-dualising a supergravity background in a $\grp{U}(1)$ isometry, $y \to y + c$, which is a symmetry of all the fields except the dilaton, $\Phi ~ \sim y + \ldots$ \cite{Arutyunov:2015mqj}.
The relation with dualities has been explored further in the context of generalised geometry, double field theory and exceptional field theory \cite{Sakatani:2016fvh,Baguet:2016prz,Sakamoto:2017wor,Fernandez-Melgarejo:2017oyu,Lust:2018jsx,Sakamoto:2018krs}.
The $\eta$-deformation of $\geom{S}^2$ \cite{Delduc:2013fga,Arutyunov:2013ega} is equivalent \cite{Hoare:2014pna} to the sausage model of \cite{Fateev:1992tk}.
A proposal for the $\eta$-deformation of the $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ supergravity background solving the generalised supergravity equations is given in app.~F of \cite{Arutyunov:2015mqj} (see also \cite{Borsato:2016ose,Bakhmatov:2017joy,Araujo:2018rbc}).
This is consistent as the Borel subalgebra, whose degrees of freedom we integrate out to give the $\eta$-deformed $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ superstring, is not unimodular.
For the three duals listed above the subalgebras whose degrees of freedom we integrate out are all unimodular, and hence the corresponding backgrounds are expected to solve the standard supergravity equations.
Note that, since all three models involve dualising in a timelike direction, these solutions may actually be of type II or II$^\star$ supergravity \cite{Hull:1998vg}.
For the Poisson-Lie dual with respect to the full $\alg{psu}(1,1|2)$ superalgebra, assuming the conjectured relation to the $\lambda$-deformation \cite{Vicedo:2015pna,Hoare:2015gda,Sfetsos:2015nya,Klimcik:2015gba}, this is indeed the case \cite{Borsato:2016zcf}.
It is also true for the two-fold T-dual \cite{Hoare:2015gda,Hoare:2015wia,Arutyunov:2015mqj}.
For the remaining case, we recall that an alternative, arguably simpler, embedding of the metric of the $\lambda$-deformed model in supergravity to that of \cite{Borsato:2016zcf} is given in \cite{Sfetsos:2014cea}.
The analytic continuation of this background therefore provides a natural conjecture for the Poisson-Lie dual of the $\eta$-deformed $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ superstring with respect to the full bosonic subalgebra.
The main result of this paper is to confirm this proposal.
That the same metric and B-field can be supported by different RR fluxes is known in the literature.
Indeed, it is the case for the different embeddings of the metric of the $\lambda$-deformed model on $\geom{AdS}_2 \times \geom{S}^2$ \cite{Sfetsos:2014cea,Borsato:2016zcf} and is also discussed in \cite{Lunin:2014tsa} in the context of the $\eta$-deformed models.
Here, one mechanism by which this may happen, that is duality transformations with respect to different subalgebras, is studied.
The layout of this paper is as follows.
In \@ifstar{\namedref{Section}}{\namedref{sec.}}{sec:PLduality} we review the model on the Drinfel'd double and the formalism for constructing Poisson-Lie dual sigma models.
We then focus on the $\eta$-deformation of the $\geom{AdS}_2 \times \geom{S}^2$ supercoset in \@ifstar{\namedref{Section}}{\namedref{sec.}}{sec:etadeformation}, writing its action in a manifestly Poisson-Lie symmetric form.
Using these results, in \@ifstar{\namedref{Section}}{\namedref{sec.}}{sec:PLdualityBosonic} the background of the Poisson-Lie dual with respect to the full bosonic subalgebra is derived.
In \@ifstar{\namedref{Appendix}}{\namedref{app.}}{app:Different_Dynkin} we discuss the different Dynkin diagrams of $\alg{psu}(1,1|2)$ in the context of $\eta$-deformations and Poisson-Lie duality.
In \@ifstar{\namedref{Appendix}}{\namedref{app.}}{app:sl_generators} and \@ifstar{\namedref{Appendix}}{\namedref{app.}}{app:gamma_matrices} we give our conventions for the superalgebras $\alg{psu}(1,1|2)$ and $\alg{pb}(1,1|2)$ and 4-dimensional and 32-dimensional gamma matrices respectively, while \@ifstar{\namedref{Appendix}}{\namedref{app.}}{app:field_redef} contains technical details of the derivation of the background of the Poisson-Lie dual with respect to the full bosonic subalgebra.
\section{Poisson-Lie duality and the Drinfel'd double}
\label{sec:PLduality}
\paragraph{The Drinfel'd double.}
Poisson-Lie duality \cite{Klimcik:1995ux,Klimcik:1995jn} is a generalisation of non-abelian duality to certain backgrounds that do not necessarily possess manifest isometries.
The underlying algebraic structure is a Drinfel'd double, defined as a $2n$-dimensional real connected Lie group $\grp{D}$ whose Lie algebra $\alg{d} = \Lie(\grp{D})$ can be decomposed as
\[
\label{eq:decompo_dgtg}
\alg{d} = \alg{g} \oplus \tilde{\alg{g}} ~,
\]
where $\alg{g}$ and $\tilde{\alg{g}}$ are two $n$-dimensional real Lie subalgebras, maximally isotropic with respect to a non-degenerate ad-invariant inner product $\beta(\cdot , \cdot )$ on $\alg{d}$,
\[
\beta(\alg{g}, \alg{g})=0~, \qquad \beta(\tilde{\alg{g}}, \tilde{\alg{g}}) =0~.
\]
When $\alg{d}$, $\alg{g}$ and $\tilde{\alg{g}}$ are Lie superalgebras, the $\mathds{Z}_2$ grading allows one to decompose them as
\[
\alg{d} = \alg{d}_\Boson \oplus \alg{d}_\Fermion~, \qquad \alg{g} = \alg{g}_\Boson \oplus \alg{g}_\Fermion~, \qquad \tilde{\alg{g}} = \tilde{\alg{g}}_\Boson \oplus \tilde{\alg{g}}_\Fermion~,
\]
where $\alg{d}_\Boson$ and $\alg{d}_\Fermion$ contain the elements of grade zero and one respectively.
The inner product should also be consistent with the $\mathds{Z}_2$ grading, supersymmetric
\[
\beta(X,Y) & = \beta(Y,X) = 0 ~, & \qquad X \in \alg{d}_\Boson, Y \in \alg{d}_\Fermion ~,
\\
\beta(X,Y) & = \beta(Y,X) ~, & \qquad X,Y \in \alg{d}_\Boson ~,
\\
\beta(X,Y) & = - \beta(Y,X) ~, & \qquad X,Y \in \alg{d}_\Fermion ~,
\]
and ad-invariant
\[
\beta( [X,Y\}, Z ) = \beta( X, [Y,Z\}) ~, \qquad X,Y,Z \in \alg{d} ~,
\]
where $[\cdot, \cdot \}$ is the $\mathds{Z}_2$-graded commutator.
\paragraph{First-order action on the Drinfel'd double.}
As for abelian and non-abelian duality, dual models can be obtained starting from an action for a dynamical field in the Drinfel'd double and integrating out half the degrees of freedom.
To define this first-order action on the Drinfel'd double we extend the definition of the inner-product to the Grassmann envelope of the superalgebra as
\[
\< X, Y\> &\equiv \beta(X, Y) ~, & \qquad X,Y &\in \alg{d}_\Boson ~, \\
\<\theta_1 X, \theta_2 Y \> &\equiv \textsf{c} \, \theta_1 \theta_2 \, \beta( X, Y) ~, & \qquad X, Y &\in \alg{d}_\Fermion ~, \\
\< X, \textsf{c} \,\theta_1 \theta_2 Y \> &\equiv \textsf{c} \,\theta_1 \theta_2 \, \beta(X, Y)~, & \qquad X, Y &\in \alg{d}_\Boson ~, \\
\]
and so on, where $\theta_1, \theta_2$ are real Grassmann variables and $ \textsf{c} \in \mathds{C}$ is such that $|\textsf{c}|=1$ and $ \textsf{c}\, \theta_1 \theta_2 \in \mathds{R}$.
If $c$ is a complex number with complex conjugate $c^\star$, then we take the conjugation operation on Grassmann variables to be given by
\[\label{eq:conjugation}
(c\theta)^\star = c^\star \theta^\star~, \qquad (\theta^\star)^\star=\theta~, \qquad (\theta_1 \theta_2)^\star = \theta_2^\star \theta_1^\star~,
\]
and correspondingly
\[ \label{eq:cei} \textsf{c} = i ~.\]
The inner product between two elements of different grading vanishes.
The first-order action for the dynamical field $l \in \grp{D}$ that gives the Poisson-Lie dual models is \cite{Klimcik:1995dy,Klimcik:1996nq}
\[\label{eq:action_double}
\mathcal{S}_\grp{D}(l) = \int \mathrm{d} \tau \mathrm{d} \sigma \, \Big[ \sfrac{1}{2} \< l^{-1} \partial_\sigma l , l^{-1} \partial_\tau l \> - \sfrac{1}{2} K(l^{-1} \partial_\sigma l ) \Big] +\mathrm{WZ}(l)~,
\]
where
\[
\mathrm{WZ}(l) = - \sfrac{1}{12} \int \, \mathrm{d}^{-1} \< l^{-1} \mathrm{d} l , \com{l^{-1} \mathrm{d} l}{l^{-1} \mathrm{d} l} \>~,
\]
is the standard Wess-Zumino term.
The quadratic form $K$, whose explicit form is discussed below, is model dependent and acts on the current, which takes values in the Grassmann envelope of the algebra $\alg{d}$.
Henceforth, we will use $\alg{d}$, $\alg{g}$, $\tilde{\alg{g}}$ and so on to refer to both the algebra and its Grassmann envelope.
\paragraph{Canonical Poisson-Lie duality.}
Starting from the action \eqref{eq:action_double} and using the decomposition of the Drinfel'd double \eqref{eq:decompo_dgtg}, where we recall both $\alg{g}$ and $\tilde{\alg{g}}$ are subalgebras, we recover the Poisson-Lie dual models on $\grp{G}$ and $\tilde{\grp{G}}$ by integrating out the degrees of freedom associated to $\tilde{\alg{g}}$ and $\alg{g}$ respectively \cite{Klimcik:1995dy,Klimcik:1996nq}.
To obtain the explicit form of the dual models we need to specify the action of the bilinear form $K$ on an arbitrary element $x \in \alg{d}$.
Such an element admits a unique decomposition $x = y+z$ where $y \in \alg{g}$ and $z \in \tilde{\alg{g}}$.
Without loss of generality one may then define the action of the bilinear form as
\[
K(x) = \< z, G_0 z \> + \< (y+B_0 z), G_0^{-1} (y+B_0 z) \>~,
\]
where $G_0$ and $B_0$ are the symmetric and antisymmetric parts of some operator $F_0: \tilde{\alg{g}} \rightarrow \alg{g}$ with respect to the inner product $\< \cdot , \cdot \>$.
To integrate out the degrees of freedom associated to $\tilde{\alg{g}}$, we parametrise the field $l \in \grp{D}$ as $l=\tilde{g} g$, where $\tilde{g} \in \tilde{\grp{G}}$ and $g \in \grp{G}$.
Taking $x = l^{-1} \partial_\sigma l = g^{-1} \partial_\sigma g + \Ad_g^{-1} \tilde{g}^{-1} \partial_\sigma \tilde{g}$ we then have
\[
y & = \Proj{\alg{g}} \, g^{-1} \partial_\sigma g + \Proj{\alg{g}} \Ad_g^{-1} \Proj{\tilde{\alg{g}}}\, \tilde{g}^{-1} \partial_\sigma \tilde{g} ~, \\
z & = \Proj{\tilde{\alg{g}}} \Ad_g^{-1} \Proj{\tilde{\alg{g}}}\, \tilde{g}^{-1} \partial_\sigma \tilde{g} ~,
\]
where $\text{P}_\alg{g}$ (respectively $\text{P}_{\tilde{\alg{g}}}$) takes an element of the Drinfel'd double and projects it onto $\alg{g}$ (respectively $\tilde{\alg{g}}$).
The operator $\Proj{\tilde{\alg{g}}} \Ad_g^{-1} \Proj{\tilde{\alg{g}}}$ is invertible on $\tilde{\alg{g}}$ and hence it is possible to eliminate $y$ in favour of $z$,
\[
y = \Proj{\alg{g}} \, g^{-1} \partial_\sigma g + \Proj{\alg{g}} \Ad_g^{-1} \Proj{\tilde{\alg{g}}} ( \Proj{\tilde{\alg{g}}} \Ad_g^{-1} \Proj{\tilde{\alg{g}}} )^{-1} z ~.
\]
The action then becomes quadratic in $z$, which can be integrated out to give
\[\label{eq:dual_actions}
\mathcal{S}_{\grp{G}}(g) = \frac{1}{2} \int \extder^2 \sigma \, \< g^{-1} \partial_+ g , (F_0 + \Pi(g))^{-1} \, g^{-1} \partial_- g \> ~, \qquad \Pi(g) = \text{P}_{\alg{g}} \Ad_g^{-1} \text{P}_{\tilde{\alg{g}}} \Ad_g \text{P}_{\tilde{\alg{g}}}~,
\]
where the worldsheet light-cone coordinates are defined as
\[\label{eq:wslcg}
\sigma^\pm = \frac{1}{2}(\tau \pm \sigma) ~, \qquad \partial_\pm = \partial_\tau \pm \partial_\sigma~, \qquad \extder^2 \sigma = \mathrm{d} \tau \mathrm{d} \sigma = 2 \mathrm{d} \sigma^+ \mathrm{d} \sigma^- ~.
\]
To obtain the dual model, we parametrise the field $l \in \grp{D}$ as $l=g \tilde{g} $ and integrate out the degrees of freedom associated to $\alg{g}$.
After exchanging the role of $\alg{g}$ and $\tilde{\alg{g}}$ in the above derivation one obtains the dual sigma model
\[
\label{eq:dual_actions_2}
\mathcal{S}_{\tilde{\grp{G}}}(\tilde{g}) = \frac{1}{2} \int \extder^2 \sigma \, \< \tilde{g}^{-1} \partial_+ \tilde{g} , (F_0^{-1} + \tilde{\Pi}(\tilde{g}))^{-1} \, \tilde{g}^{-1} \partial_- \tilde{g} \> ~, \qquad \tilde{\Pi}(\tilde{g}) &= \text{P}_{\tilde{\alg{g}}} \Ad_{\tilde{g}}^{-1} \text{P}_{\alg{g}} \Ad_{\tilde{g}} \text{P}_{\alg{g}}~.
\]
The two sigma models \eqref{eq:dual_actions} and \eqref{eq:dual_actions_2} are described by the same set of equations after appropriate non-local field and parameter redefinitions.
The model corresponding to the action \eqref{eq:dual_actions_2} is said to be the dual of \eqref{eq:dual_actions} with respect to $\alg{g}$.
Non-abelian duality is a special case of Poisson-Lie duality, and corresponds to the case in which the dual algebra $\tilde{\alg{g}}$ is abelian and hence $\Pi(g)=0$.
\paragraph{Poisson-Lie duality with respect to a subalgebra.}
Besides the canonical decomposition $\alg{d}=\alg{g} \oplus \tilde{\alg{g}}$ of \eqref{eq:decompo_dgtg}, it is also possible to consider more general maximally isotropic decompositions of the Drinfel'd double of the type $\alg{d} = \alg{k} \oplus \tilde{\alg{k}}$ where $\alg{k}$ is not necessarily an algebra \cite{Klimcik:1995dy,Klimcik:1996nq,Klimcik:2002zj,Klimcik:2015gba}.
On the other hand, $\tilde{\alg{k}}$ is still a subalgebra of $\alg{d}$ and its associated degrees of freedom can be integrated out to yield a model on the coset space $\tilde{\grp{K}}\backslash\grp{D}$.
Starting with the field $l \in \grp{D}$ parametrised as $l=\tilde{k} k$, where $\tilde{k} \in \tilde{\grp{K}}= \exp[\tilde{\alg{k}}]$ and $k \in \tilde{\grp{K}}\backslash \grp{D}$, and integrating out the degrees of freedom associated to $\tilde{\alg{k}}$ following the steps outlined above, we find the following Lorentz-invariant action for the field $k$
\[\label{eq:actionS1}
\mathcal{S}_{\tilde{\grp{K}}\backslash\grp{D}}(k) = \frac{1}{2} \int \extder^2 \sigma \, \< k^{-1} \partial_+ k, (\sfrac{1}{2} \Proj{\tilde{\alg{k}}}^\mathrm{rot} - \sfrac{1}{2} \Proj{\alg{k}}^\mathrm{rot} + \Proj{\tilde{\alg{k}}}^\mathrm{rot} ({\En^\prime}+\Pi(k))^{-1} \, \Proj{\alg{k}}^\mathrm{rot}) k^{-1} \partial_- k \> + \mathrm{WZ}(k) ~,
\]
where
\[
\Pi(k)= \text{P}_{\alg{k}} \Ad_k^{-1} \text{P}_{\tilde{\alg{k}}} (\text{P}_{\tilde{\alg{k}}} \Ad_k^{-1} \text{P}_{\tilde{\alg{k}}})^{-1}~, \qquad \Proj{\alg{k}}^\mathrm{rot} = \Proj{\alg{k}} - \Pi(k) \Proj{\tilde{\alg{k}}}~, \qquad \Proj{\tilde{\alg{k}}}^\mathrm{rot} = \Proj{\tilde{\alg{k}}} + \Pi(k) \Proj{\tilde{\alg{k}}}~.
\]
The operator ${\En^\prime}: \tilde{\alg{k}} \rightarrow \alg{k}$ is related to $F_0:\tilde{\alg{g}} \rightarrow \alg{g}$ via the non-linear transformation
\[\label{eq:E0t}
{\En^\prime} = (\text{P}_{\tilde{\alg{g}}} (\mathds{1} + F_0^{-1} \text{P}_{\alg{g}}) \text{P}_{\alg{k}})^{-1} (\text{P}_{\tilde{\alg{g}}}(\mathds{1} + F_0^{-1} \text{P}_{\alg{g}}) \text{P}_{\tilde{\alg{k}}}) ~.
\]
In the particular case where the intersection of $\tilde{\alg{k}}$ with $\alg{g}$ defines a common subalgebra $\alg{g}_0$ and one has the decomposition \cite{Hoare:2017ukq,Lust:2018jsx}
\[
\label{eq:decomposition_gk}
\alg{g} & = \alg{g}_0 \oplus \alg{m} ~, & \qquad \tilde{\alg{g}} & = \tilde{\alg{g}}_0 \oplus \tilde{\alg{m}} ~,
\\
\alg{k} & = \tilde{\alg{g}}_0 \oplus \alg{m} ~, & \qquad \tilde{\alg{k}} & = \alg{g}_0 \oplus \tilde{\alg{m}} ~,
\]
we can interpret \eqref{eq:actionS1} as the Poisson-Lie dual of the model on $\grp{G}$ with respect to $\alg{g}_0$.
The requirement that $\tilde{\alg{k}}$ forms an algebra imposes restrictions with respect to which subalgebras it is possible to dualise.
\section{The \texorpdfstring{$\eta$}{eta}-deformed \texorpdfstring{$\geom{AdS}_2 \times \geom{S}^2$}{AdS2 x S2} supercoset}
\label{sec:etadeformation}
In this section we turn our attention to the $\eta$-deformed $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ superstring and its Poisson-Lie duals.
To this end we consider the $\eta$-deformed semi-symmetric space sigma model \cite{Metsaev:1998it,Zhou:1999sm,Berkovits:1999zq,Zarembo:2010sg,Delduc:2013qra,Delduc:2014kha} on the supercoset
\[\label{eq:sc}
\frac{\grp{PSU}(1,1|2)}{\grp{SO}(1,2) \times \grp{SO}(2)} ~,
\]
which we will refer to as the $\eta$-deformed $\geom{AdS}_2 \times \geom{S}^2$ supercoset model, and investigate Poisson-Lie duals with respect to various subalgebras of $\alg{psu}(1,1|2)$.
We start by explaining how to write the $\eta$-deformed semi-symmetric space sigma model in the manifestly Poisson-Lie symmetric form \eqref{eq:dual_actions}.
For this we need to specify the Drinfel'd double together with its invariant inner product, as well as the specific form of the operator $F_0$.
We then specialise to the supercoset \eqref{eq:sc}, discussing the possible Poisson-Lie duals of the $\eta$-deformed $\geom{AdS}_2 \times \geom{S}^2$ supercoset model.
\subsection{The \texorpdfstring{$\eta$}{eta}-deformed semi-symmetric space sigma model}
\paragraph{The action of the deformed model.}
Let $g$ be an element of a supergroup $\grp{G}$ whose corresponding Lie superalgebra $\alg{g}$ is basic and admits a $\mathds{Z}_4$ grading consistent with the commutation relations
\[
\alg{g} = \alg{g}^{(0)} \oplus \alg{g}^{(1)} \oplus \alg{g}^{(2)} \oplus \alg{g}^{(3)}~, \qquad
\com{\alg{g}^{(k)}}{\alg{g}^{(l)}} \subset \alg{g}^{(k+l \mod 4)}~.
\]
The $\mathds{Z}_4$ grading follows from the existence of a linear automorphism of the complexified superalgebra $\Omega: \alg{g}^\mathds{C} \rightarrow \alg{g}^\mathds{C}$ satisfying
\[
\Omega^4 = \mathds{1} ~, \qquad \Omega(\alg{g}^{(k)})= i^k \alg{g}^{(k)}~.
\]
The bosonic subalgebra of $\alg{g}$ is given by $\alg{g}^{(0)} \oplus \alg{g}^{(2)}$, while the fermionic generators belong to either $\alg{g}^{(1)}$ or $\alg{g}^{(3)}$.
We introduce the projectors $P_k \, \alg{g} = \alg{g}^{(k)}$, $k=0,1,2,3$, and denote the group corresponding to the grade 0 subalgebra by $\grp{H}=\grp{G}^{(0)}=\exp[\alg{g}^{(0)}]$.
The $\eta$-deformed model describes a deformation of the semi-symmetric space sigma model on the supercoset $\grp{G}/\grp{H}$.
Its action is \cite{Delduc:2013qra}
\[
\label{eq:eta_deformation}
\mathcal{S}_\eta(g) = T \int \extder^2 \sigma \, \STr \Big( g^{-1} \partial_+ g , P \frac{1}{\mathds{1} - \frac{2\eta}{1-\eta^2} R_g P} g^{-1} \partial_- g\Big) ~,
\]
where the supertrace $\STr$ denotes an ad-invariant and $\mathds{Z}_4$ invariant bilinear form on $\alg{g}$, which is symmetric (respectively antisymmetric) on the bosonic (respectively fermionic) subspace of $\alg{g}$ and hence it is symmetric on the Grassmann envelope.
The operators $P$ and $R_g$ are given by
\[
P= P_2 + \frac{1-\eta^2}{2} ( P_1 -P_3) ~, \qquad R_g = \Ad_g^{-1} R \Ad_g ~,
\]
where the operator $R$ satisfies the non-split modified classical Yang Baxter equation
\[
\com{R X}{R Y} - R(\com{X}{R Y} + \com{R X}{Y} ) = \com{X}{Y} ~, \qquad X,Y \in \alg{g} ~,
\]
and is antisymmetric with respect to the supertrace $\STr( X, R Y ) = - \STr ( R X, Y )$.
We will take this R-matrix to be given by the canonical Drinfel'd-Jimbo solution associated to a particular Dynkin diagram and Cartan-Weyl basis of $\alg{g}$.
The overall coupling constant $T$ plays the role of the effective string tension and $\eta$ is the deformation parameter, flipping the sign of which is equivalent a parity transformation.
The global left-acting $\grp{G}$ symmetry is broken to the Cartan subgroup, while the right-acting gauge symmetry, $g \rightarrow g h$, where $h$ belongs to $\grp{H}$, is preserved.
\medskip
\paragraph{Poisson-Lie symmetric action.}
To write the action of the $\eta$-deformed semi-symmetric space sigma model in a manifestly Poisson-Lie symmetric form, we recall that for the $\eta$-deformed models the relevant Drinfel'd double is the complexified Lie algebra $\alg{d}=\alg{g}^\mathds{C}$ \cite{Klimcik:2002zj,Vicedo:2015pna}, which as a real vector space admits the decomposition
\[
\alg{g}^\mathds{C} = \alg{g} \oplus \tilde{\alg{g}}~,
\]
where $\tilde{\alg{g}}$ is the Borel subalgebra, formed by the Cartan generators and the positive roots of $\alg{g}^\mathds{C}$.
More precisely, if $\set{h_i}$ ($i=1,\ldots,\rank \alg{d}$), $\set{e_\ind{M}}$ and $\set{f_\ind{M}}$, ($M=1,\ldots, \sfrac{1}{2}(\dim_\mathds{C} \alg{d}-\rank \alg{d})$) are the Cartan generators, positive and negative roots respectively, then the Borel subalgebra is spanned by $\tilde{\alg{g}}=\set{h_i, e_\ind{M}, ie_\ind{M}}$.
Furthermore, the action of the Drinfel'd Jimbo R-matrix on the Cartan-Weyl basis is given by
\[
\label{eq:DrinfeldRmatrix}
R(h_i) = 0 ~, \qquad R(e_\ind{M}) = - i e_\ind{M} ~, \qquad R(f_\ind{M}) = i f_\ind{M} ~.
\]
To specify the operator $F_0$ we introduce bases of $\alg{g}$ and $\tilde{\alg{g}}$, denoting the generators of $\alg{g}$ (respectively $\tilde{\alg{g}}$) by $T_\ind{A}$, $A = 1, 2, \ldots , \dim \grp{G}$ (respectively $\tilde{T}^\ind{A}$).
We further assume that we have an inner product $\< \cdot, \cdot \>$ on $\alg{g}^\mathds{C}$ with respect to which the two subalgebras are isotropic, $\<T_\ind{A}, T_\ind{B}\> = \<\tilde{T}^\ind{A}, \tilde{T}^\ind{B} \>=0$ and that provides a canonical pairing, that is $\<T_\ind{A}, \tilde{T}^\ind{B}\>=\delta_\ind{A}^\ind{B}$ for bosonic generators and $\<\theta_1 T_\ind{A}, \theta_2 \tilde{T}^\ind{B}\> = i \, \theta_1 \theta_2 \delta_\ind{A}^\ind{B}$ for fermionic ones.
Introducing $\kappa_\ind{AB} = \STr(T_\ind{A} T_\ind{B})$ and the auxiliary operator
\[
P_\epsilon : \left\{ \begin{aligned}
& T_\ind{A} \rightarrow \epsilon \kappa_\ind{BA} \tilde{T}^\ind{B}~, \quad &T_\ind{A} &\in \alg{g}^{(0)}~, \\
& T_\ind{A} \rightarrow -\sfrac{i}{2}(1-\eta^2)\kappa_\ind{BA} \tilde{T}^\ind{B}~, \quad &T_\ind{A} &\in \alg{g}^{(1)}~, \\
& T_\ind{A} \rightarrow \kappa_\ind{BA} \tilde{T}^\ind{B}~, \quad &T_\ind{A} &\in \alg{g}^{(2)} ~, \\
& T_\ind{A} \rightarrow \sfrac{i}{2}(1-\eta^2) \kappa_\ind{BA} \tilde{T}^\ind{B}~, \quad & T_\ind{A} &\in \alg{g}^{(3)} ~,
\end{aligned} \right.
\]
we define the operators $F_\ind{\text{P}} : \tilde{\alg{g}} \rightarrow \alg{g}$ and $F_\ind{\text{R}} : \tilde{\alg{g}} \rightarrow \alg{g}$ by
\[\label{eq:g0def}
F_\ind{\text{P}}^{-1} &= -\frac{2 \eta}{1-\eta^2} \lim_{\epsilon \rightarrow 0} P_\epsilon~, \]
and
\[\label{eq:b0def}
F_\ind{\text{R}}(\tilde{T}^\ind{B})&= F_\ind{\text{R}}^\ind{AB} T_\ind{A}~, \qquad &F_\ind{\text{R}}^\ind{AB} &= R^\ind{A}{}_\ind{C} \kappa^\ind{CB} ~, &\qquad T_\ind{A} &\in \alg{g}^{(0)}+\alg{g}^{(2)}~,\\
F_\ind{\text{R}}(\theta \tilde{T}^\ind{B})&= F_\ind{\text{R}}^\ind{AB}\theta T_\ind{A}~, \qquad &F_\ind{\text{R}}^\ind{AB} &= i R^\ind{A}{}_\ind{C} \kappa^\ind{CB} ~, &\qquad T_\ind{A} &\in \alg{g}^{(1)}+\alg{g}^{(3)} ~,
\]
where $R(T_\ind{A}) = R^\ind{B}{}_\ind{A} T_\ind{B}$ and $\kappa^\ind{AB} \kappa_\ind{BC} = \delta^\ind{A}_\ind{C}$.
These operators preserve the $\mathds{Z}_2$ grading of the superalgebra.
The action \eqref{eq:eta_deformation} of the $\eta$-deformation is then equivalent to
\[
\mathcal{S}_\eta(g) &= - T \frac{1-\eta^2}{2 \eta} \int \extder^2 \sigma\,\< g^{-1} \partial_+ g , F_\ind{\text{P}}^{-1} \frac{1}{ \text{P}_{\alg{g}} + (F_\ind{\text{R}} + \Pi(g)) F_\ind{\text{P}}^{-1}} g^{-1} \partial_- g \>~,
\]
which is of the form \eqref{eq:dual_actions} with $F_0 = F_\ind{\text{P}} + F_\ind{\text{R}}$.
\subsection{Poisson-Lie duals of the \texorpdfstring{$\eta$}{eta}-deformed \texorpdfstring{$\geom{AdS}_2 \times \geom{S}^2$}{AdS2 x S2} supercoset}
\paragraph{The complex Drinfel'd double.}
The isometry algebra of the $\geom{AdS}_2 \times \geom{S}^2$ supercoset \eqref{eq:sc} is $\alg{g}=\alg{psu}(1,1|2)$, the bosonic subalgebra of which is $\alg{su}(1,1) \oplus \alg{su}(2)$.
As discussed above, the relevant Drinfel'd double for the $\eta$-deformed model is the complexified Lie superalgebra $\alg{d}=\alg{g}^\mathds{C}= \alg{psl}(2|2 ; \mathds{C})$.
The Drinfel'd double can be decomposed into two real subalgebras
\[
\alg{d} = \alg{psl}(2|2 ; \mathds{C}) = \alg{psu}(1,1|2) \oplus \alg{pb}(1,1|2) ~,
\]
where $\alg{pb}(1,1|2)$ is the projected Borel subalgebra spanned by the Cartan generators and positive roots of $\alg{psl}(2|2;\mathds{C})$.
It will often be convenient for us to work with the superalgebra $\alg{sl}(2|2;\mathds{C})$.
The superalgebra $\alg{psl}(2|2;\mathds{C})$ is then obtained by quotienting out the $\alg{u}(1)$ ideal, that is we identify elements of $\alg{sl}(2|2; \mathds{C})$ that differ by the central element.
At this point let us make a brief comment on the different Dynkin diagrams of $\alg{sl}(2|2;\mathds{C})$.
In general, for Lie superalgebras there are inequivalent choices for the set of Cartan generators and simple roots, where the latter can either be bosonic or fermionic.
Since the Drinfel'd Jimbo R-matrix \eqref{eq:DrinfeldRmatrix} is defined by its action on the Cartan generators and roots, it is possible that different choices of Dynkin diagrams and Cartan-Weyl bases define inequivalent deformations.
The three Dynkin diagrams of $\alg{sl}(2|2;\mathds{C})$ are $\mbox{\wasyfamily\char35}- \otimes- \mbox{\wasyfamily\char35}$, $\otimes-\mbox{\wasyfamily\char35}-\otimes$ and $\otimes-\otimes-\otimes$, where $\mbox{\wasyfamily\char35}$ represents a bosonic root and $\otimes$ a fermionic root.
In this paper we will focus on the distinguished Dynkin diagram $\mbox{\wasyfamily\char35}-\otimes-\mbox{\wasyfamily\char35}$.
A discussion of the other choices is given in \@ifstar{\namedref{Appendix}}{\namedref{app.}}{app:Different_Dynkin}.
\paragraph{Matrix realisation.}
For calculations we will use a given matrix realisation of the superalgebras $\alg{psu}(1,1|2; \mathds{C})$ and $\alg{pb}(1,1|2; \mathds{C})$, which is presented explicitly in \@ifstar{\namedref{Appendix}}{\namedref{app.}}{app:sl_generators}.
The generators of the grade 0 subalgebra $\alg{h}=\alg{so}(1,1)\oplus \alg{so}(2)$ are denoted $J_{01}$ and $J_{23}$ respectively, while the remaining bosonic generators are denoted $P_a$, with $a=0,1$ for $\alg{su}(1,1)$ and $a=2,3$ for $\alg{su}(2)$.
The supercharges are denoted by $Q^{\ind{I} \check{\alpha} \hat{\alpha}}$ where $I=1,2$ is the grading, $\check{\alpha}=1,2$ is the $\alg{su}(1,1)$ index and $\hat{\alpha}=1,2$ the $\alg{su}(2)$ index.
The dual generators $\tilde{P}^a, \tilde{J}^{ab}, \tilde{Q}^{\ind{I} \check{\alpha} \hat{\alpha}}$ are then identified using the inner product
\[\label{eq:innerproduct}
\< \cdot , \cdot \> = -\Im \STr (\cdot,\cdot) ~.
\]
The positive roots span the upper triangular matrices such that on an arbitrary $4 \times 4$ matrix $M$, the Drinfel'd Jimbo R-matrix \eqref{eq:DrinfeldRmatrix} acts as
\[
R(M)_{ij} = -i \epsilon_{ij} M_{ij}~, \qquad \epsilon_{ij} = \left\{ \begin{aligned} 1 &\text{ if } i < j \\ 0 &\text{ if } i = j \\ -1 &\text{ if } i > j \end{aligned}\right.~.
\]
\paragraph{Poisson-Lie duals and unimodularity.}
The background of the $\eta$-deformed $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ superstring has a non-vanishing, albeit closed, B-field, together with a three-form and five-form RR flux \cite{Arutyunov:2015mqj,Araujo:2018rbc}.
\unskip\footnote{Note that in the explicit formulae given in app.~F of \cite{Arutyunov:2015mqj} a gauge transformation has been used to set the B-field to vanish.}
This background does not solve the standard supergravity equations, rather a generalisation thereof \cite{Arutyunov:2015mqj,Wulff:2016tju}.
In the context of the first-order action on the Drinfel'd double and duality, the corresponding Weyl anomaly is expected to be associated to integrating out the degrees of freedom of a non-unimodular algebra, that is when the trace of the structure constants is non-vanishing, $f_{ab}{}^b \neq 0$.
Indeed, when starting from the first-order action on the Drinfel'd double, the $\eta$-deformed model is obtained by integrating out the degrees of freedom associated to the projected Borel algebra $\alg{pb}(1,1|2)$, which is indeed non-unimodular.
As the background of the $\eta$-deformed $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ superstring solves the generalised supergravity equations, the Weyl anomaly is of a particularly special type.
As a result, the background of the $\eta$-deformed model is expected to be related to solutions of the standard supergravity equations by Poisson-Lie duality.
These dual models are given by integrating out the degrees of freedom of unimodular algebras in the model on the Drinfel'd double.
We finish this section by listing three examples of such Poisson-Lie duals of the $\eta$-deformed $\geom{AdS}_2 \times \geom{S}^2$ supercoset and describe the associated unimodular subalgebras of $\alg{psl}(2|2;\mathds{C})$.
\begin{enumerate}
\item First, it is possible to dualise with respect to the full superalgebra $\alg{psu}(1,1|2)$.
In this case one integrates out the degrees of freedom associated to $\alg{psu}(1,1|2)$, a unimodular algebra.
In the terminology of \cite{Hoare:2017ukq} this gives the $\lambda^\star$-deformed model and is conjectured to be an analytic continuation of the $\lambda$-deformation \cite{Vicedo:2015pna,Hoare:2015gda,Sfetsos:2015nya,Klimcik:2015gba,Hoare:2017ukq,Driezen:2018glg}.
The background of the $\lambda$-deformation of the $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ superstring has been derived in \cite{Borsato:2016zcf}.
It has a vanishing B-field and the metric is supported by a RR five-form flux and dilaton giving a solution of the standard supergravity equations.
\item Second, as we are considering the distinguished Dynkin diagram $\mbox{\wasyfamily\char35} - \otimes - \mbox{\wasyfamily\char35}$, the results of \cite{Hoare:2017ukq} tell us that we can dualise with respect to the full bosonic subalgebra of $\alg{psu}(1,1|2)$, that is $\alg{su}(1,1) \oplus \alg{su}(2)$, by considering the sub-Dynkin diagram formed of the two bosonic nodes.
In this case the degrees of freedom that are integrated out are associated to the algebra $\tilde{\alg{k}}=\alg{su}(1,1) \oplus \alg{su}(2) \oplus \set{\tilde{Q}^{\ind{I}\check{\alpha} \hat{\alpha}}}$, where $\set{\tilde{Q}^{\ind{I} \check{\alpha} \hat{\alpha}}}$ are the dual fermionic generators, that is the positive fermionic roots.
Since this is also a unimodular algebra we expect the resulting background to again solve the standard supergravity equations.
The bosonic part of this model, and hence the metric and B-field, coincides with the $\lambda^\star$-deformation.
However, they differ in the fermionic part.
In \cite{Sfetsos:2014cea} an alternative embedding of the metric of the $\lambda$-deformed $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ superstring in supergravity was given.
The metric is again supported by a RR five-form flux and dilaton, however these are different to those found in \cite{Borsato:2016zcf}.
In \@ifstar{\namedref{Section}}{\namedref{sec.}}{sec:PLdualityBosonic} we show that this background corresponds to an analytic continuation of the Poisson-Lie dual of the $\eta$-deformed $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ superstring with respect to the full bosonic subalgebra.
\item Finally, we consider the two-fold T-dual of the $\eta$-deformed $\geom{AdS}_2 \times \geom{S}^2$ supercoset, equivalent to dualising with respect to the $\alg{u}(1) \oplus \alg{u}(1)$ Cartan subalgebra of $\alg{psu}(1,1|2)$.
As discussed in detail for the bosonic case in \cite{Hoare:2017ukq}, one can show that the algebra whose degrees of freedom are integrated out is unimodular.
Accordingly, the background of the two-fold T-dual of the $\eta$-deformed $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ superstring solves the standard supergravity equations, again supported by a RR five-form flux and dilaton \cite{Hoare:2015gda,Hoare:2015wia,Arutyunov:2015mqj}.
As shown in \cite{Hoare:2015gda} and \cite{Borsato:2016zcf} respectively, the two-fold T-dual can be found by analytically continuing and taking a scaling limit of the backgrounds of \cite{Sfetsos:2014cea} and \cite{Borsato:2016zcf}.
The analytic continuation amounts to considering the reality conditions relevant for the $\eta$-deformed models, and hence the two-fold T-dual should be given by a real scaling limit of the two Poisson-Lie duals of the $\eta$-deformed $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ superstring discussed above.
\end{enumerate}
These three examples of Poisson-Lie duals of the $\eta$-deformed $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ superstring all involve dualising in a timelike direction.
Abelian T-duality in a timelike direction maps solutions of type II supergravity to solutions of type II$^\star$ \cite{Hull:1998vg}.
As Poisson-Lie duality is a generalisation of abelian T-duality, the corresponding backgrounds are expected to solve the standard type II$^\star$ supergravity equations.
\section{Poisson-Lie duality with respect to the full bosonic subalgebra}
\label{sec:PLdualityBosonic}
In this section we derive the background of the Poisson-Lie dual of the $\eta$-deformed $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ superstring with respect to the full bosonic subalgebra $\alg{su}(1,1) \oplus \alg{su}(2)$.
We start from the first-order action on the Drinfel'd double \eqref{eq:action_double} with $F_0 = F_\ind{\text{P}} + F_\ind{\text{R}}$ defined in eqs.~\eqref{eq:g0def} and \eqref{eq:b0def}.
We then consider the decomposition \eqref{eq:decomposition_gk} with
\[
\alg{g}_0 = \alg{g}_\Boson=\alg{su}(1,1) \oplus \alg{su}(2)~, \qquad \alg{m}=\alg{g}_\Fermion = \set{Q_{\ind{I} \check{\alpha} \hat{\alpha}} } ~,
\]
and integrate out the degrees of freedom associated to the algebra $\tilde{\alg{k}} = \alg{g}_0 \oplus \tilde{\alg{m}}$, where $\tilde{\alg{m}}$ is spanned by the positive fermionic roots.
These degrees of freedom are associated to a unimodular algebra and hence the corresponding background is expected to solve the standard supergravity equations.
Expanding the action \eqref{eq:actionS1} to quadratic order in fermions, we rewrite it in Green-Schwarz form and extract the background fields.
The resulting background indeed solves the standard supergravity equations and, as conjectured, is given by an analytic continuation of that constructed in \cite{Sfetsos:2014cea}.
\subsection{Parametrisation}
In order to Poisson-Lie dualise with respect to the full bosonic subalgebra $\alg{g}_\Boson = \alg{su}(1,1) \oplus \alg{su}(2)$ we need to find a suitable parametrisation of the field $k \in \tilde{\grp{K}} \backslash \grp{D} / \grp{H}$ appearing in the action.
Starting with a group-valued field $k \in \grp{D}=\grp{PSL}(2|2; \mathds{C})$ and using the fermionic part of the left-acting $\tilde{\grp{K}}$ gauge symmetry we partially gauge fix
\[
k= \tilde{g}_0 \exp[ \theta^{\ind{I} \check{\alpha} \hat{\alpha}} Q_{\ind{I} \check{\alpha} \hat{\alpha}}]~,
\]
where
\[
\tilde{g}_0 \in \grp{G}_\Boson \backslash \grp{D}_\Boson / \grp{H} = (\grp{SU}(1,1) \times \grp{SU}(2))\backslash (\grp{SL}(2;\mathds{C}) \times \grp{SL}(2;\mathds{C})) / (\grp{SO}(1,1) \times \grp{SO}(2)) ~.
\]
To gauge fix $\tilde{g}_0$ we write $\tilde{g}_0 = \check{g}_0 \oplus \hat{g}_0$, where $\check{g}_0$ corresponds to the $\geom{AdS}_2$ factor and $\hat{g}_0$ to the $\geom{S}^2$ factor and gauge fix in each sector separately.
\paragraph{Gauge fixing in the $\geom{S}^2$ sector.}
Let us introduce the generators $S_\ind{A}$ and $\tilde{S}^\ind{A}$, $A=4,5,6$, defined in terms of the Cartan generator $h=\sigma_3$ and the simple roots $e=\sigma_+$, $f=\sigma_-$ of $\alg{sl}(2;\mathds{C})$ as
\[
S_4 &= i(e+f)~, & \qquad S_5 &= -(e-f)~, & \qquad S_6 &= ih~, \\
\tilde{S}^4 &= (e+f)/2~, &\qquad \tilde{S}^5 &= -i(h-e+f)/2~, &\qquad \tilde{S}^6 &= (h-e+f)/2 ~.
\]
The right-acting gauge symmetry is generated by $S_4$, the adjoint action of which rotates $\tilde{S}^5$ and $\tilde{S}^6$ amongst themselves.
Therefore, using this right-acting gauge symmetry together with the left-acting gauge symmetry generated by $\set{S_4,S_5,S_6}$, we can partially gauge fix
\[
\hat{g}_0 \in \exp[\set{S_5,\tilde{S}^4,\tilde{S}^6}] \in \grp{SO}(2) \backslash \grp{SL}(2;\mathds{R}) ~,
\]
where the residual left-acting gauge symmetry is generated by $S_5$.
Using this residual gauge freedom we choose the familiar parametrisation of this coset
\[
\hat{g}_0= \exp[\phi_5 e] \exp[\phi_4 h/2] ~,
\]
which in terms of the generators $\{\tilde P^2, \tilde P^3, \tilde J^{23}\}$ defined in \@ifstar{\namedref{Appendix}}{\namedref{app.}}{app:sl_generators} is given by
\[
\hat{g}_0= \exp[- \phi_5 \tilde{J}^{23}] \exp[-\phi_4 \tilde{P}^2] ~.
\]
\paragraph{Gauge fixing in the $\geom{AdS}_2$ sector.}
For the $\geom{AdS}_2$ sector we introduce the following generators $\set{S_\ind{A}, \tilde{S}^\ind{A}}$, $A=1,2,3$, of $\alg{sl}(2;\mathds{C})$
\[
S_1 &= -(e+f)~, & \qquad S_2 &= i(e-f)~, & \qquad S_3 &= ih~, \\
\tilde{S}^1 &= i(e+f)/2~, &\qquad \tilde{S}^2 &=i(h-i(e-f))/2~, &\qquad \tilde{S}^3 &= -(h+i(e-f))/2~.\\
\]
Here the right-acting gauge symmetry is generated by $S_1$, the adjoint action of which hyperbolically rotates $\tilde{S}^2$ and $\tilde{S}^3$ amongst themselves, while the left-acting gauge symmetry is generated by $\set{S_1,S_2,S_3}$.
Following the same logic as for the $\geom{S}^2$ sector we find it is possible to gauge fix
\[
\check{g}_0= \exp[\phi_2 ie] \exp[\phi_1 h/2] ~,
\]
which in terms of the generators $\set{\tilde P^0, \tilde P^1, \tilde J^{01}}$ defined in \@ifstar{\namedref{Appendix}}{\namedref{app.}}{app:sl_generators} is given by
\[
\check{g}_0 = \exp[-\phi_2 \tilde{J}^{01}] \exp[\phi_1 \tilde{P}^0] ~.
\]
\paragraph{Full parametrisation.}
Finally, our parametrisation of the field $k \in \tilde{\grp{K}} \backslash \grp{D} / \grp{H}$ is given by
\[
\label{eq:param_gen}
k= \tilde{g}_0 \exp[ \theta^{\ind{I} \check{\alpha} \hat{\alpha}} Q_{\ind{I} \check{\alpha} \hat{\alpha}}]~,
\]
with
\[
\label{eq:paramg0}
\tilde{g}_0 = \exp[-\phi_2 \tilde{J}^{01}] \exp[\phi_1 \tilde{P}^0] \oplus \exp[- \phi_5 \tilde{J}^{23}] \exp[-\phi_4 \tilde{P}^2] ~.
\]
\subsection{NSNS background}\label{ssec:nsns}
The NSNS fields (the metric and the B-field) are obtained by setting the fermions in the action \eqref{eq:actionS1} to zero and considering the bosonic Lagrangian
\unskip\footnote{In our conventions the bosonic part of the action is related to the metric by
\begin{equation*}
\mathcal{S} = \int \extder^2 \sigma \, \mathcal{L}^0 = \int \extder^2 \sigma \, G_\ind{MN} \partial_+ X^\ind{M} \partial_- X^\ind{N} ~,
\end{equation*}
and the line element is $\mathrm{d} s^2 = G_\ind{MN} \mathrm{d} X^\ind{M} \mathrm{d} X^\ind{N}$.
That is the tension $T$ is included in the metric.}
\[
\mathcal{L}^0 = - \frac{T}{\kappa} \< \tilde{g}_0^{-1} \partial_+ \tilde{g}_0, (F_0^{-1} + \Pi(\tilde{g}))^{-1} \tilde{g}_0^{-1} \partial_- \tilde{g}_0 \> ~,
\]
which corresponds to the Lagrangian of the $\lambda^\star$-deformation of the bosonic sigma model on $\geom{AdS}_2 \times \geom{S}^2$ and we have introduced the deformation parameter \cite{Arutyunov:2013ega}
\[ \kappa = \frac{2 \eta}{1-\eta^2} ~. \]
Using the parametrisation \eqref{eq:paramg0} we find the following metric
\[
2 T^{-1} \mathrm{d} s^2 = & \frac{1}{\kappa^2} \Big(- \mathrm{d} \phi_1^2 + \frac{4(e^{2 \phi_1} \kappa^2 - \phi_2^2)}{(1-e^{2 \phi_1} - \phi_2^2)^2} \mathrm{d} \phi_2^2 - \frac{4 \phi_2 \mathrm{d} \phi_1 \mathrm{d} \phi_2}{1-e^{2 \phi_1} - \phi_2^2} \Big) \\
&+ \frac{1}{\kappa^2} \Big(\mathrm{d} \phi_4^2 + \frac{4(e^{2 \phi_4} \kappa^2 + \phi_5^2)}{(1-e^{2 \phi_4} + \phi_5^2)^2} \mathrm{d} \phi_5^2 - \frac{4 \phi_5 \mathrm{d} \phi_4 \mathrm{d} \phi_5}{1-e^{2 \phi_4}+\phi_5^2} \Big)~,
\]
The B-field vanishes.
After the coordinate redefinition
\unskip\footnote{The redefinitions $\phi_1 = \log |\check{p}+\sqrt{\check{p}^2+\check{q}^2-1}|$ and $\phi_4 = \log|\hat{p}+\sqrt{\hat{p}^2-\hat{q}^2-1}|$ give the same result.}
\[
\label{eq:coord_redef}
\phi_1 &= \log |\check{p}-\sqrt{\check{p}^2+\check{q}^2-1}|~, & \qquad \phi_2 &= \check{q}~, & \qquad \check{p}^2 + \check{q}^2 > 1~, \\
\phi_4 &= \log|\hat{p}-\sqrt{\hat{p}^2-\hat{q}^2-1}|~, & \qquad \phi_5 &= \hat{q}~, & \qquad \hat{p}^2 - \hat{q}^2 > 1~,
\]
the metric becomes conformally flat,
\[\label{eq:cfmet}
2 T^{-1} \mathrm{d} s^2 = \frac{1}{\kappa^2} \frac{1}{\check{p}^2+\check{q}^2-1} \Big( - \mathrm{d} \check{p}^2 + \kappa^2 \mathrm{d} \check{q}^2 \Big) + \frac{1}{\kappa^2} \frac{1}{\hat{p}^2-\hat{q}^2-1} \Big( \mathrm{d} \hat{p}^2 + \kappa^2 \mathrm{d}\hat{q}^2 \Big) ~.
\]
We also introduce the vielbein
\[\label{eq:vielbein}
&E_{\check{p} \, 0} = \frac{1}{\kappa} \sqrt{\frac{T}{2} } \frac{1}{\sqrt{\check{p}^2 + \check{q}^2 -1}} ~, \qquad E_{\check{q}\, 1} = \sqrt{\frac{T}{2} } \frac{1}{\sqrt{\check{p}^2 + \check{q}^2 -1}} ~, \\
&E_{\hat{p}\, 2} = \frac{1}{\kappa} \sqrt{\frac{T}{2} }\frac{1}{\sqrt{\hat{p}^2 - \hat{q}^2 -1}} ~, \qquad E_{\hat{q}\, 3} = \sqrt{\frac{T}{2} } \frac{1}{\sqrt{\hat{p}^2 - \hat{q}^2 -1}} ~,
\]
satisfying $G_\ind{MN} = E_{\ind{M}a} E_{\ind{N}b} \eta^{ab}$.
The spin connection, which we will need to obtain the RR fields, is given in terms of the vielbein
\[
\omega_{\ind{M} ab} = & \frac{1}{2} E^\ind{N}{}_b (\partial_\ind{M} E_{\ind{N} a} - \partial_\ind{N} E_{\ind{M} a})
\\ & -\frac{1}{2} E^\ind{N}{}_{a} (\partial_\ind{M} E_{\ind{N} b} - \partial_\ind{N} E_{\ind{M} b} )+ \frac{1}{2} E^\ind{R}{}_a E^\ind{S}{}_b (\partial_\ind{R} E_{\ind{S} c} - \partial_\ind{S} E_{\ind{R} c}) E_\ind{M}{}^c ~,
\]
and has the following non-vanishing components
\[
\omega_{\check{p} 01} = +\frac{1}{\kappa} \frac{\check{q}}{\check{p}^2+\check{q}^2-1}~, \qquad \omega_{\check{q} 01} = +\kappa \frac{\check{p}}{\check{p}^2+\check{q}^2-1}~, \\
\omega_{\hat{p} 23} = -\frac{1}{\kappa} \frac{\hat{q}}{\hat{p}^2-\hat{q}^2-1}~, \qquad \omega_{\hat{q} 23} = -\kappa \frac{\hat{p}}{\hat{p}^2-\hat{q}^2-1}~.
\]
\paragraph{Relation to the metric of the $\lambda$-deformed model on $\geom{AdS}_2 \times \geom{S}^2$.}
The metric \eqref{eq:cfmet} is related to the metric of the $\lambda$-deformed model on $\geom{AdS}_2 \times \geom{S}^2$ by an analytic continuation of both the parameters and the coordinates \cite{Hoare:2015gda,Klimcik:1996np,Sfetsos:1999zm}.
Applying the transformation rules of \cite{Hoare:2015gda}
\[
\label{eq:transfo_rules}
T = \frac{k \kappa}{i \pi}~,\qquad \kappa = i\frac{1-\lambda^2}{1+\lambda^2} ~, \qquad \check{q} \rightarrow i \check{q}~, \qquad \hat{q} \rightarrow i \hat{q}~,
\]
we find the following metric
\[
2 \pi k^{-1} \mathrm{d} s^2 = & \frac{1}{1-\check{p}^2+\check{q}^2} \Big( - \frac{1+\lambda^2}{1-\lambda^2} \mathrm{d} \check{p}^2 + \frac{1-\lambda^2}{1+\lambda^2} \mathrm{d} \check{q}^2 \Big)
\\ & + \frac{1}{1-\hat{p}^2-\hat{q}^2} \Big( \frac{1+\lambda^2}{1-\lambda^2} \mathrm{d} \hat{p}^2 + \frac{1-\lambda^2}{1+\lambda^2} \mathrm{d}\hat{q}^2 \Big) ~.
\]
This is precisely the metric of the $\lambda$-deformed model on $\geom{AdS}_2 \times \geom{S}^2$ given in \cite{Sfetsos:2014cea},
\[
\label{eq:metricS}
\mathrm{d} s^2 &= \tilde{k} \Big( \frac{1-\tilde{\lambda}}{1+\tilde{\lambda}} (-\coth^2 \rho \, \mathrm{d} t^2 + \mathrm{d} \rho^2) + \frac{4 \tilde{\lambda}}{1-\tilde{\lambda}^2} (\cosh t \, \mathrm{d} \rho + \sinh t \coth \rho \, \mathrm{d} t)^2 \Big) \\
&+ \tilde{k} \Big( \frac{1-\tilde{\lambda}}{1+\tilde{\lambda}} (\cot^2 \omega \, \mathrm{d} \phi^2 + \mathrm{d} \omega^2) + \frac{4 \tilde{\lambda}}{1-\tilde{\lambda}^2} (\cos \phi \, \mathrm{d} \omega + \sin \phi \cot \omega \, \mathrm{d} \phi)^2 \Big)~,
\]
where
\[\label{eq:kl}
\tilde{k} = \frac{k}{2\pi} ~, \qquad \tilde{\lambda} = \lambda^2 ~.
\]
and the coordinates are related as
\[
\check{p} = \cosh \rho \cosh t ~, \qquad \check{q} = \cosh \rho \sinh t ~, \qquad
\hat{p} = \cos \omega \cos \phi ~, \qquad \hat{q} = \cos \omega \sin \phi ~.
\]
\subsection{RR background}\label{ssec:RR}
To obtain the RR fluxes we rewrite the deformed $\geom{AdS}_2 \times \geom{S}^2$ supercoset sigma model in Green-Schwarz form.
The supercoset sigma model has 4 bosonic and 8 fermionic fields compared to the 10 bosonic and 32 fermionic of the type II Green-Schwarz superstring sigma model.
In this subsection we describe a consistent truncation of the latter that can be matched with the former to quadratic order in fermions.
This in turn allows us to derive the RR fluxes of the Poisson-Lie dual of the $\eta$-deformed $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ superstring with respect to the full bosonic subalgebra $\alg{su}(1,1) \oplus \alg{su}(2)$.
\subsubsection{Truncation of the Green-Schwarz action}
To embed the 4 dimensions of the $\lambda^\star$-deformed model on $\geom{AdS}_2 \times \geom{S}^2$ \eqref{eq:cfmet} into 10 dimensions we take the remaining six dimensions to simply be a flat torus, $\geom{T}^6$, so that the full 10-dimensional metric is ($i = 4,5,6,7,8,9$)
\[\label{eq:fullmet}
\mathrm{d} s^2 = \frac{T}{2 \kappa^2} \frac{1}{\check{p}^2+\check{q}^2-1} \Big( - \mathrm{d} \check{p}^2 + \kappa^2 \mathrm{d} \check{q}^2 \Big) + \frac{T}{2 \kappa^2} \frac{1}{\hat{p}^2-\hat{q}^2-1} \Big( \mathrm{d} \hat{p}^2 + \kappa^2 \mathrm{d}\hat{q}^2 \Big) + \mathrm{d} X_i \mathrm{d} X^i ~.
\]
For the truncation of the fermionic fields \cite{Sorokin:2011rr,Borsato:2016zcf} let us start with the action of the type IIB Green-Schwarz superstring at quadratic order in fermions
\unskip\footnote{Since we are primarily interested in extracting the RR background fields we only consider the action of the Green-Schwarz superstring up to quadratic order in the fermions.
Note that the overall factor is proportional to $\sqrt{T}$ as the metric \eqref{eq:cfmet} and vielbein \eqref{eq:vielbein} contain a factor of $T$ and $\sqrt{T}$ respectively.}
\[
\label{eq:GSaction}
\mathcal{S} = \frac{i}{2}\sqrt{\frac{T}{2} }\int \extder^2 \sigma \, \bar{\Theta}^\ind{I} \big(\sigma_1^{\alpha \beta} \delta^\ind{IJ} + \epsilon^{\alpha \beta} \sigma_3^\ind{IJ} \big) E_{\alpha \ind{A}} \Gamma^\ind{A} D_\beta^\ind{JK} \Theta^\ind{K} ~,
\]
where
\[
D_\beta^\ind{JK} = \delta^\ind{JK} \Big( \partial_\beta - \frac{1}{4} \omega_\beta{}_\ind{AB} \Gamma^\ind{AB} \Big) + \frac{1}{8} \sigma_3^\ind{JK} E_{\beta \ind{A}} H^\ind{ABC} \Gamma_\ind{BC} +\frac{1}{8} S^\ind{JK} E_{\beta \ind{A}} \Gamma^\ind{A}~,
\]
\[
S^\ind{JK} = -e^\Phi\big(\epsilon^\ind{JK} \Gamma^\ind{A} F_\ind{A} + \frac{1}{3!} \sigma_1^\ind{JK} \Gamma^\ind{ABC} F_\ind{ABC} + \frac{1}{2 \cdot 5!} \epsilon^\ind{JK} \Gamma^\ind{ABCDE} F_\ind{ABCDE} \big)~.
\]
The action is written in conformal gauge with $\alpha,\beta = +,-$ and the worldsheet light-cone coordinates defined in eq.~\eqref{eq:wslcg}.
The (rescaled) conformal gauge metric and two-index antisymmetric tensor are given by $\sigma_1^{+-}=\sigma_1^{-+}=\epsilon^{+-}=-\epsilon^{-+}=1$.
$E_{\alpha \ind{A}}$ and $\omega_{\alpha \ind{AB}}$ are the pullbacks of the vielbein and corresponding spin connection to the worldsheet, $H$ is the field strength of the B-field, $\Phi$ is the dilaton and $F_\ind{A}$, $F_\ind{ABC}$ and $F_\ind{ABCDE}$ are the RR fluxes.
It is useful to split the tangent space index $A=0,1,2, \dots, 9$ into an index $a=0,1,2,3$ covering the $\geom{AdS}_2 \times \geom{S}^2$ directions and an index $i=4,5,6,7,8,9$ covering the torus directions.
As we are considering the type IIB superstring, the two 32-components spinors $\Theta^\ind{I}$, $I=1,2$ are both Weyl spinors of the same chirality ($\Gamma^{11} \Theta^1 = \Gamma^{11} \Theta^2$) and satisfy the Majorana condition
\unskip\footnote{See \@ifstar{\namedref{Appendix}}{\namedref{app.}}{app:gamma_matrices} for the definitions and properties of the gamma matrices and the charge conjugation matrix $\mathcal C$.}
\[
\label{eq:MWcondition}
\bar{\Theta}^\ind{I} = (\Theta^\ind{I})^\dagger \Gamma^0 = (\Theta^\ind{I})^t \mathcal{C}~.
\]
The deformed supercoset sigma model has 8 fermionic fields compared to the 32 of the Green-Schwarz action.
In order to rewrite the action in Green-Schwarz form we embed two 4-component fermions $\hat{\theta}^\ind{I}$ into the two 32-component spinors
\[
\label{eq:relation10d4dfermions}
\Theta^\ind{I} &= \begin{pmatrix} 1 \\ 0 \end{pmatrix} \otimes \hat{\theta}^\ind{I} \otimes \begin{pmatrix} a_\ind{(I)} \\ b_\ind{(I)} \\ c_\ind{(I)} \\ d_\ind{(I)} \end{pmatrix}~, \qquad
\bar{\Theta}^\ind{I} = \begin{pmatrix} 0 & 1 \end{pmatrix} \otimes \bar{\hat{\theta}}^\ind{I} \otimes \begin{pmatrix} a_\ind{(I)}^\star & b_\ind{(I)}^\star & c_\ind{(I)}^\star & d_\ind{(I)}^\star \end{pmatrix}~,
\]
where the complex numbers $a_\ind{(I)}$, $b_\ind{(I)}$, $c_\ind{(I)}$ and $d_\ind{(I)}$ may take different values depending on the grading.
Note that for our choice of gamma matrices the 32-component spinors are of negative chirality, $\Gamma^{11} \Theta^\ind{I} = - \Theta^\ind{I}$.
A priori, there is a non-trivial coupling between the spinors and the torus directions giving rise to terms such as $\bar \Theta \partial X^i \Theta$.
Such terms should not survive the truncation since they do not appear in the deformed supercoset sigma model.
Requiring that this is indeed the case constrains the complex numbers $a_\ind{(I)}$, $b_\ind{(I)}$, $c_\ind{(I)}$ and $d_\ind{(I)}$.
To find the complex numbers we assume that the deformed model is supported only by a self-dual RR five-form flux of the form
\[
\label{eq:five_form_flux}
F_5 = \frac{1}{2} (1+\star) F_2 \wedge \Re \Omega_3~,
\]
where $\Omega_3 = \epsilon_{\tilde\imath\tilde\jmath\tilde{k}} dZ^{\tilde{\imath}} \wedge dZ^{\tilde{\jmath}} \wedge dZ^{\tilde{k}}$ is the holomorphic three-form on the torus,
\unskip\footnote{The complex coordinates are chosen to be $Z^1 = X^4 + i X^5$, $Z^2 = X^6 + i X^7$ and $Z^3 = X^8 + i X^9$.}
$F_2 = \sfrac{1}{2} F_{ab} E^a \wedge E^b$ and $\star$ is the 10-dimensional Hodge dual
\unskip\footnote{The Hodge dual is defined such that
\begin{equation*}
\star ( \mathrm{d} X^\ind{A_0} \wedge \mathrm{d} X^\ind{A_1} \wedge \mathrm{d} X^\ind{A_2} \wedge \mathrm{d} X^\ind{A_3} \wedge \mathrm{d} X^\ind{A_4}) = \epsilon^\ind{A_0A_1A_2A_3A_4A_5A_6A_7A_8A_9} \mathrm{d} X_\ind{A_5} \wedge \mathrm{d} X_\ind{A_6} \wedge \mathrm{d} X_\ind{A_7} \wedge \mathrm{d} X_\ind{A_8} \wedge \mathrm{d} X_\ind{A_9}~,
\end{equation*}
with $\epsilon^{0123456789}=+1$.}
squaring to one, $\star^2 =+1$.
With this ansatz
\[
S^\ind{IJ} = - \frac{1}{2 \cdot 5!} \epsilon^\ind{IJ} e^\Phi F_\ind{ABCDE} \Gamma^\ind{ABCDE} = - \frac{1}{2} \epsilon^\ind{IJ} e^\Phi F_{ab} \Gamma^{ab} \Gamma^{468} \mathcal P_4 (\mathds{1} + \Gamma^{11}) ~,
\]
where
\[
\mathcal P_4 = \frac{1}{4} (\mathds{1} - \Gamma^{4567} - \Gamma^{4589} - \Gamma^{6789}) ~,
\]
is a projector, $(\mathcal P_4)^2 = \mathcal P_4$, that can be used to decompose the 32-component spinors
\[
\Theta_\perp^\ind{I} = (\mathds{1} - \mathcal P_4) \Theta^\ind{I}~, \qquad \Theta_\parallel^\ind{I} = \mathcal P_4 \Theta^\ind{I} ~.
\]
The additional properties
\[
\mathcal P_4^t = \mathcal P_4~, \quad \com{\mathcal P_4}{\mathcal C}=0~, \quad \com{\mathcal P_4}{\Gamma^a}=0~, \quad \com{\mathcal P_4}{\Gamma^{468}}=0~, \quad \com{\mathcal P_4}{\Gamma^{11}}=0~,\quad \mathcal P_4 \Gamma^{i} \mathcal P_4 =0~,
\]
then imply that there are no linear terms in $\set{\Theta_\perp,X^i}$ in the Green-Schwarz action.
It thus follows that setting $X^i = \Theta_\perp^\ind{I}=0$ is a consistent truncation.
As can be seen from the explicit form of $\mathcal P_4$
\[
\mathcal P_4 = \frac{1}{4} \mathds{1} \otimes \mathds{1} \otimes \mathds{1} \otimes (\mathds{1} \otimes \mathds{1} - \sum_{\iota=1,2,3} \sigma_\iota \otimes \sigma_\iota)~,
\]
setting $\Theta_\perp^\ind{I} =0$ imposes conditions on the complex numbers $a_\ind{(I)}$, $b_\ind{(I)}$, $c_\ind{(I)}$ and $d_\ind{(I)}$.
In particular, these are satisfied when $a_\ind{(I)}=d_\ind{(I)}=0$, $c_\ind{(I)}=-b_\ind{(I)}$.
Henceforth, we will consider this truncation and take the 32-component spinors and their Dirac conjugates to be
\[
\Theta^\ind{I} &= b_\ind{(I)} \begin{pmatrix} 1 \\ 0 \end{pmatrix} \otimes \hat{\theta}^\ind{I} \otimes \begin{pmatrix} 0 \\ +1 \\ -1 \\ 0 \end{pmatrix}~, \qquad
\bar{\Theta}^\ind{I} = b_\ind{(I)}^\star \begin{pmatrix} 0 & 1 \end{pmatrix} \otimes \bar{\hat{\theta}}^\ind{I} \otimes \begin{pmatrix} 0 & +1 & -1 & 0 \end{pmatrix}~.
\]
Using the 32-dimensional gamma matrices given in \@ifstar{\namedref{Appendix}}{\namedref{app.}}{app:gamma_matrices} we have
\[
\label{eq:TGTeqtgt}
\bar{\Theta}^\ind{I} \Gamma^a \Theta^\ind{J} &= 2 b_\ind{(I)}^\star b^{\vphantom{\star}}_\ind{(J)} \bar{\hat{\theta}}^\ind{I} \gamma^a \hat{\theta}^\ind{J} ~, \qquad & \bar{\Theta}^\ind{I} \Gamma^a \Gamma^{bc} \Theta^\ind{J} &= 2 b_\ind{(I)}^\star b^{\vphantom{\star}}_\ind{(J)} \bar{\hat{\theta}}^\ind{I}\gamma^a \gamma^{bc} \hat{\theta}^\ind{J}~, \\ \bar{\Theta}^\ind{I} \Gamma^i \Theta^\ind{J}&=0~, & \bar{\Theta}^\ind{I} \Gamma^i \Gamma^{bc} \Theta^\ind{J}&=0~,
\]
and the Lagrangian of the Green-Schwarz action can be rewritten
\[
\label{eq:4dGS}
\hat{\mathcal{L}}_{GS} & = i \sqrt{\frac{T}{2} } b^\star_\ind{(I)} b^{\vphantom{\star}}_\ind{(J)} \bar{\hat{\theta}}^\ind{I} (\sigma_1^{\alpha \beta} \delta^\ind{IJ} + \epsilon^{\alpha \beta} \sigma_3^\ind{IJ} ) E_{\alpha a} \gamma^a \Big(\partial_\beta - \frac{1}{4} \omega_{\beta bc} \gamma^{bc}\Big) \hat{\theta}^\ind{J} \\
& \quad - \frac{i}{16} \sqrt{\frac{T}{2} }\bar{\Theta}_\parallel^\ind{I} (\sigma_1^{\alpha \beta} \delta^\ind{IJ} + \epsilon^{\alpha \beta} \sigma_3^\ind{IJ} ) \epsilon^\ind{JK} e^\Phi E_{\alpha a} \Gamma^a F_{bc} \Gamma^{bc} \Gamma^{468} E_{\beta d}\Gamma^d \Theta_\parallel^\ind{K}~.
\]
Finally, let us comment on the reality condition satisfied by the 4-dimensional fermions $\hat{\theta}^\ind{I}$.
The Majorana condition \eqref{eq:MWcondition} implies
\[
\label{eq:MWcondition_theta}
(\hat{\theta}^\ind{I})^\dagger = \frac{b_\ind{(I)}}{b_\ind{(I)}^\star} (\hat{\theta}^\ind{I})^t~.
\]
The two fermions can thus have different reality conditions depending on the choice of the complex numbers $b_\ind{(I)}$.
We will choose to work with
\[
\label{eq:choice_b}
b_\ind{(1)}= \frac{i}{\sqrt{2}}~, \qquad b_\ind{(2)}=\frac{1}{\sqrt{2}},
\]
such that the Majorana condition becomes
\[
\label{eq:MWcondition_theta_choice_b}
(\hat{\theta}^{1})^\dagger = - (\hat{\theta}^{1})^t~, \qquad (\hat{\theta}^{2})^\dagger = (\hat{\theta}^{2})^t~.
\]
\subsubsection{Field redefinitions}
To match the form of the Green-Schwarz Lagrangian \eqref{eq:4dGS} we start by parametrising the field $k$ of the deformed supercoset sigma model as in eq.~\eqref{eq:param_gen} and expand the action \eqref{eq:actionS1} up to quadratic order in the fermions.
We also use the Polyakov-Wiegmann identity to reduce the Wess-Zumino term to a two-dimensional integral.
The resulting Lagrangian
\[
\mathcal{L} = \mathcal{L}^0 + \mathcal{L}^\partial + \mathcal{L}^m + \mathcal{L}^{\partial \partial}~,
\]
consists of four distinct parts: $\mathcal{L}^0 \sim \partial X \partial X$ is the bosonic Lagrangian giving rise to the metric of the $\lambda^\star$-deformed model and is discussed in \namedref{subsec.}{ssec:nsns}, $\mathcal{L}^\partial \sim \partial X \theta \partial \theta$ contains the terms with one derivative acting on the fermions, $\mathcal{L}^m \sim \partial X \partial X \theta \theta$ are the fermion ``mass'' terms and finally $\mathcal{L}^{\partial \partial} \sim \partial \theta \partial \theta$.
Field redefinitions are needed to rewrite $\mathcal{L}^\partial$, $\mathcal{L}^m$ and $\mathcal{L}^{\partial \partial}$ in Green-Schwarz form, in particular matching the consistent truncation \eqref{eq:4dGS}.
In \@ifstar{\namedref{Appendix}}{\namedref{app.}}{app:field_redef} we show that $\mathcal{L}^{\partial \partial}$ is a total derivative and thus can be ignored.
We then focus on two types of transformations, namely shifts of the bosons $X \rightarrow X + \theta s(X) \theta$ and rotations of the fermions $\theta \rightarrow r(X) \hat{\theta}$, which lead to the following modifications
\[
\mathcal{L}^0 \rightarrow \mathcal{L}^0 + (\delta \mathcal{L}^0)^\partial + (\delta \mathcal{L}^0)^m~, \qquad
\mathcal{L}^\partial \rightarrow \hat{\mathcal{L}}^\partial + (\delta \mathcal{L}^\partial)^m~, \qquad \mathcal{L}^m \rightarrow \hat{\mathcal{L}}^m~.
\]
Therefore, we would like to find functions $s(X)$ and $r(X)$ such that
\begin{equation}\begin{gathered}
\label{eq:conditions_rs}
\hat{\mathcal{L}}^\partial + (\delta \mathcal{L}^0)^\partial = \hat{\mathcal{L}}_{GS}^\partial~, \qquad \hat{\mathcal{L}}^m + (\delta \mathcal{L}^0)^m + (\delta \mathcal{L}^\partial)^m = \hat{\mathcal{L}}_{GS}^m~,
\end{gathered}\end{equation}
where the equalities hold up to total derivatives.
In order to find the exact functions $s(X)$ and $r(X)$ satisfying these conditions we follow the procedure outlined in \cite{Arutyunov:2015qva}.
All terms quadratic in the fermions contributing to the Lagrangian can be classified according to their symmetry properties under the exchange of the two fermions.
At quadratic order in fermions the Lagrangian can be written as $\mathcal{L} = \mathcal{L}_+ + \mathcal{L}_-$, where $\mathcal{L}_+$ and $\mathcal{L}_-$ contain the terms with the symmetry property
\[
\label{eq:sym_prop}
\mathcal{L}_\pm \supset \theta^\ind{I} f_\pm^\ind{IJ} \lambda^\ind{J} = \pm \lambda^\ind{I} f_\pm^\ind{IJ} \theta^\ind{J}~.
\]
In the above expression the sum over the spinor indices is understood: $f_\pm^\ind{IJ}$ are $4 \times 4$ matrices depending on the bosons.
In particular, this decomposition can be applied to the terms containing one derivative acting on the fermions, $\mathcal{L}^\partial = \mathcal{L}_+^\partial + \mathcal{L}_-^\partial$.
In the Green-Schwarz Lagrangian we have that $\hat{\mathcal{L}}_{GS\,+}^\partial=0$, that is the Lagrangian only contains terms with the symmetry property
\[
\theta^\ind{I} f_-^\ind{IJ} \partial \theta^\ind{J} = - \partial \theta^\ind{I} f_-^\ind{IJ} \theta^\ind{J}~.
\]
Having identified the contributions to $\mathcal{L}_\pm ^\partial$ we use a field redefinition to set $\mathcal{L}_+^\partial$ equal to zero.
Observing that rotating the fermions does not affect the symmetry property,
\[
\mathcal{L}_+^\partial \rightarrow \hat{\mathcal{L}}_+^\partial~, \qquad \mathcal{L}_-^\partial \rightarrow \hat{\mathcal{L}}_-^\partial~,
\]
this can only be achieved with a shift of the bosons and fixes for us the function $s(X)$.
Finally, the rotation of the fermions is implemented to rewrite the remaining terms in $\mathcal{L}^\partial$ in Green-Schwarz form.
More details, including the exact field redefinitions $r(X)$ and $s(X)$, are presented in \@ifstar{\namedref{Appendix}}{\namedref{app.}}{app:field_redef}.
After using the field redefinitions we find that the conditions \eqref{eq:conditions_rs} are satisfied, the Lagrangian takes precisely the form of the Green-Schwarz Lagrangian \eqref{eq:4dGS} and we can easily read off the RR fluxes, or more precisely the combination $e^\Phi F$.
\subsubsection{RR Fluxes}
Comparing with the form of the Green-Schwarz Lagrangian \eqref{eq:4dGS} we find that the only necessary components of the two-form $F_2$ in eq.~\eqref{eq:five_form_flux} are
\[
\sqrt{\frac{T}{2} } F_{12} = -\sqrt{\frac{T}{2} } F_{21} = -2i \sqrt{1+\kappa^2} e^{-\Phi}~,
\]
which leads to the following RR five-form flux
\[
\label{eq:RRflux}
\sqrt{\frac{T}{2} } F_5 = -i \sqrt{1+\kappa^2} e^{-\Phi} (1+\star) \, E^1 \wedge E^2 \wedge \Re \Omega_3~.
\]
This flux is imaginary, a consequence of the fact that we have dualised in a timelike direction and are now strictly speaking in type IIB$^\star$ supergravity \cite{Hull:1998vg}.
Since the two spinors $\Theta^\ind{I}$ satisfy the Majorana condition, this implies that the corresponding action of the Green-Schwarz superstring is not real.
However, the Poisson-Lie dual of the $\eta$-deformed $\geom{AdS}_2 \times \geom{S}^2$ supercoset has a real action.
This discrepancy comes from the rotation of the fermions $\theta^\ind{I} = U^\ind{IJ} \hat{\theta}^\ind{J}$, where $\theta^\ind{I}$ are the real 4-dimensional fermions appearing in the deformed supercoset model via the parametrisation \eqref{eq:param_gen}, $U^\ind{IJ}$ is the rotation matrix used to rewrite the action in Green-Schwarz form and the 4-dimensional fermions $\hat{\theta}^\ind{I}$ are related to the 32-components spinors $\Theta^\ind{I}$ as in eq.~\eqref{eq:relation10d4dfermions}.
When choosing the particular coefficients \eqref{eq:choice_b} the Majorana condition implies the reality conditions \eqref{eq:MWcondition_theta_choice_b} for the 4-dimensional fermions $\hat{\theta}^\ind{I}$: $\hat{\theta}^1$ is imaginary and $\hat{\theta}^2$ is real.
However, the rotation matrix $U^\ind{IJ}$ defined in eq.~\eqref{eq:rotation} has only real entries and thus we identify a real and an imaginary fermion, thereby breaking the reality condition.
Implementing the transformation rules \eqref{eq:transfo_rules} and \eqref{eq:kl} we find
\[
\sqrt{\tilde{k}} F_5 = - \sqrt{\frac{4 \tilde{\lambda}}{1-\tilde{\lambda}}} \frac{e^{-\Phi}}{\sqrt{\check{p}^2 - \check{q}^2 -1} \sqrt{\hat{p}^2 + \hat{q}^2 -1}} (1+\star ) \, \mathrm{d} \check{q} \wedge \mathrm{d} \hat{p} \wedge \Re \Omega_3 ~,
\]
which is precisely the RR five-form flux supporting the metric of the $\lambda$-deformed model on $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ found in \cite{Sfetsos:2014cea}.
In conclusion, the Poisson-Lie dual of the $\eta$-deformed $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ superstring with respect to the full bosonic subalgebra $\alg{su}(1,1) \oplus \alg{su}(2)$, with metric \eqref{eq:fullmet} and RR five-form flux \eqref{eq:RRflux}, solves the standard supergravity equations with the dilaton given by \cite{Sfetsos:2014cea}
\[
e^{\Phi} = \frac{1}{\sqrt{\check{p}^2 + \check{q}^2 - 1}\sqrt{\hat{p}^2 - \hat{q}^2 -1}} ~.
\]
\section{Concluding comments}
In this paper we have investigated Poisson-Lie duals of the $\eta$-deformed $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ superstring.
While the background of the $\eta$-deformed $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ superstring satisfies a generalisation of the standard supergravity equations, here we have discussed three Poisson-Lie duals, with respect to \textit{(i)} the full $\alg{psu}(1,1|2)$ superalgebra, \textit{(ii)} the full bosonic subalgebra and $(iii)$ the Cartan subalgebra, for which the corresponding backgrounds are expected to satisfy the standard supergravity equations.
Focusing on the second case we explicitly derived the background, showing agreement with the embedding of the metric of the $\lambda$-deformed model on $\geom{AdS}_2 \times \geom{S}^2$ in supergravity given in \cite{Sfetsos:2014cea} up to an analytic continuation.
There are various interesting open questions extending and developing the results presented here.
Firstly, it would also be useful to confirm some of the remaining conjectures summarised in this paper and extend the results to other backgrounds.
This includes explicitly checking that Poisson-Lie dualising with respect to the full $\mathfrak{psu}(1,1|2)$ superalgebra gives the background of \cite{Borsato:2016zcf} up to analytic continuation and dualising with respect to the Cartan subalgebra gives the two-fold T-dual of \cite{Hoare:2015gda,Hoare:2015wia,Arutyunov:2015mqj}.
Furthermore, candidates for the background of the Poisson-Lie dual of the $\eta$-deformed $\geom{AdS}_3 \times \geom{S}^3 \times \geom{T}^4$ and $\geom{AdS}_5 \times \geom{S}^5$ superstrings with respect to the full bosonic subalgebras are given in \cite{Sfetsos:2014cea} and \cite{Demulder:2015lva} respectively, up to analytic continuation.
It is highly probable that the backgrounds discussed in this paper define integrable 2-dimensional sigma models.
The results of \cite{Severa:2017kcs} together with the integrability of the $\eta$-deformed principal chiral, symmetric space sigma and semi-symmetric space sigma models \cite{Klimcik:2008eq,Delduc:2013qra,Delduc:2013fga} suggest that their Poisson-Lie duals are also integrable.
It is important to point out that the semi-symmetric space sigma model on the supercoset \eqref{eq:supercoset} is a truncation of the type II Green-Schwarz superstring on certain $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ backgrounds.
The integrability of the latter was demonstrated to quadratic order in fermions in \cite{Wulff:2014kja}.
In principle, for a complete analysis of integrability, this analysis should be extended to the deformed backgrounds.
As well as exploring deformations of other $\geom{AdS}_2$ integrable string backgrounds \cite{Zarembo:2010sg,Wulff:2015mwa}, it would be interesting to consider some of the ways integrability has been used to study the $\eta$- and $\lambda$-deformed $\geom{AdS}_5 \times \geom{S}^5$ superstrings in the context of the $\eta$-deformed $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ superstring and its Poisson-Lie duals.
This includes the light-cone gauge S-matrix \cite{Beisert:2008tw,Hoare:2011wr,Arutyunov:2013ega,Arutyunov:2015qva}, which should be a deformation of the S-matrix of \cite{Hoare:2014kma}, and the associated finite-size spectrum \cite{Arutyunov:2012zt,Arutyunov:2012ai,Arutynov:2014ota,Klabbers:2017vtw}.
Another direction would be to investigate how the analysis of the solitons in the $\lambda$-deformed $\geom{AdS}_5 \times \geom{S}^5$ superstring \cite{Appadu:2017xku} is modified when considering the Poisson-Lie dual of the $\eta$-deformation with respect to either the full superalgebra (that is the $\lambda^\star$-deformed model, an analytic continuation of the $\lambda$-deformed model) or the full bosonic subalgebra.
This is of relevance to both the $\geom{AdS}_5 \times \geom{S}^5$ and $\geom{AdS}_2 \times \geom{S}^2 \times \geom{T}^6$ cases.
One could also ask how the $q$-deformed symmetry of the $\eta$-deformed model \cite{Delduc:2013fga,Delduc:2014kha,Delduc:2016ihq,Delduc:2017brb,Arutyunov:2013ega} and the contraction limits (that is the maximal deformation, $\eta \to 1$, limit) of \cite{Arutynov:2014ota,Arutyunov:2014cra,Pachol:2015mfa} behave under Poisson-Lie duality.
Finally, while there has been much study of quantum aspects of Poisson-Lie duality, as well as its interplay with supergravity and generalised geometry, including, for example, \cite{Tyurin:1995bu,Bossard:2001au,VonUnge:2002xjf,Hlavaty:2004jp,Hlavaty:2004mr,Jurco:2017gii,Alekseev:1995ym,Valent:2009nv,Sfetsos:2009dj,Avramis:2009xi,Sfetsos:2009vt,Hlavaty:2012sg,Hassler:2017yza,Lust:2018jsx}, a systematic understanding of the model on the Drinfel'd double in the path integral and the Weyl anomaly associated to integrating out the degrees of freedom of a non-unimodular algebra, as given for non-abelian duality in \cite{Alvarez:1994np,Elitzur:1994ri}, remains to be found.
\pdfbookmark[1]{Acknowledgements}{ack}
\section*{Acknowledgements}
We thank A.~Tseytlin for comments on the draft.
This work is supported by grant no.~615203 from the European Research Council under the FP7.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,344 |
R. Hakan Arslan
Kerem Yükseloğlu
Muratcan Gökçe
Burcu Güçük
Ahmet Kenan Bilgiç
Ceyda Yüceer
Ali Atay
Müge Duygun
Recep Usta
Erdem Kaynarca
Melissa Değer
İpek Erden
Osman was assigned to finish a blood feud by his family. As he hits the road, he spots a snail on the windshield and avoids using the wipers even when it's raining. On the way he picks up hitchhikers who end up guiding him to find his own way in life. Bartu and Güneş are two youths who are trying to live in nature. Another hitchhiker Esin has quit her job as a singer at the nightclub because her boss wanted her to work as a hostess. She is the only person that Osman confesses his current task of murder. Muzo is the last hitchhiker Osman picks up and he is carrying a bag full of drugs. When the police stop them, Osman finds a way to live his life with a clear conscience.
Kerem Yükseloğlu graduated from Istanbul Kültür University Art Management Department. He shot his first short film Rastlantılar Oteli in 2014. His last film Rüzgâr Bizi Götürecek was shown at many festivals.
R. Hakan Arslan graduated from Ege University Radio-TV and Cinema Department in 2009. While he was a student in 2007, he also started photography. He worked as a director and cinematographer in music videos and fashion films. In 2017, he completed his music documentary, I'm Actually. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,190 |
Ilie Văduva () a fost un demnitar comunist român care a servit ca Ministru al Afacerilor Externe al României din 1985 până în 1986, Ministrul Comerțului Exterior și Cooperării Internaționale din 26 august 1986 până în mai 1988 și consilier al lui Nicolae Ceaușescu din decembrie 1988 până în decembrie 1989. El a fost unul dintre cei arestați după căderea regimului comunist din 1989. A fost membru al Partidului Comunist Român din anul 1961. Ilie Văduva a fost deputat în Marea Adunare Națională în sesiunile (1980 - 1985) și (1985 - 1989).
Viață și carieră politică
El a fost un membru supleant al Comitetului Central al Partidul Comunist Român din 1979 și a devenit membru cu drepturi depline în 1984. Ilie Văduva, care l-a sfătuit pe Nicolae Ceaușescu în probleme economice și nu a avut cunoștință de relații internaționale, a fost considerat protejatul lui Elena Ceaușescu. Ilie Văduva l-a înlocuit pe ministrul Ștefan Andrei. Ilie Văduva a servit ca ministru al Afacerilor Externe de la 11 noiembrie 1985 până la 26 august 1986.
El a fost îndepărtat pentru ineficiența lui în domeniul afacerilor internaționale și a fost numit ministru al Comerțului Exterior și Cooperare Internațională. El a deținut acest post până la 21 mai 1988, când a fost demis de conducerea română pentru rolul său în stocarea de deșeuri toxice în Marea Neagră, la portul Sulina, provocând un scandal de mediu și ultraj. Cu toate acestea, câteva luni mai târziu, în decembrie 1988, el a fost numit consilier, o poziție de rang înalt.
Studii
Școala medie tehnică financiară din Târgu-Jiu (1950–1954)
Facultatea de Finanțe, Credit și Contabilitate la Academia de Studii Economice (1954–1958)
Specializare în Elveția în domeniul informaticii economice (1968–1970)
Doctorat în Științe economice (1971).
Note
Nașteri în 1934
Decese în 1998
Comuniști români
Deputați români în Marea Adunare Națională
Membri ai Comitetului Central al Partidului Comunist Român
Politicieni români din secolul al XX-lea
Decorați cu Ordinul Muncii
Miniștri comuniști români
Membri ai Partidului Muncitoresc Român
Decese în București | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,384 |
\section{Introduction}
Cataclysmic Variables (CVs) are semidetached binary systems
formed by a white dwarf (WD) primary accreting
matter from a Roche lobe-filling secondary, usually a low mass main
sequence star.
The WD is surrounded by an accretion disk, unless
its magnetic field is strong enough to partially or totally
control the accretion geometry; these two cases correspond to the
{\it Intermediate Polar} systems and the
{\it Polar} systems, respectively.
CVs are thought to lose angular momentum through
magnetic braking and gravitational radiation.
The shrinking of the Roche lobe of the secondary produces the
mass overflow through the inner Lagrangian point and accretion
onto the WD. Thus, CVs are generally evolving towards shorter orbital
periods and less massive secondaries.
The luminosity of a CV is mainly produced by the thermalization of
the potential energy released by the accretion stream.
Very few objects have been observed at orbital periods in the range
2-3 h, called the period gap (PG). This is generally
explained by the disrupted magnetic braking model (Rappaport, Verbunt
\& Joss 1983; Spruit \& Ritter 1983). When
the orbital period gets close to 3 h, the mass losing secondary
becomes fully convective and the efficiency of the magnetic braking
suddenly decreases.
As the mass transfer rate drops, the secondary tends to recover
its thermal equilibrium shrinking inside its Roche lobe and
the CV is {\it switched off}.
Mass transfer would then start again only when angular
momentum losses due to gravitational radiation have brought the secondary
back in contact with its Roche lobe, which typically occurs
at approximately 2 h of orbital period.
\smallskip
Not only does the history of the mass transfer rate of a CV
characterize its secular evolution,
but it also characterizes the behavior of some subclasses of CVs.
For example, dwarf novae (DN) have relatively low accretion
rates so their disks can be thermally unstable and produce
cyclic instability phenomena.
Old novae and nova-like systems, instead, are systematically
brighter than DN suggesting that their accretion disks are
powered by larger mass transfer rates. In this case, the higher
temperatures of the accretion disks would
in most cases prevent the onset of the instability phenomenon.
However, the most important difference between novae and dwarf novae
is represented by the requirement that the primaries of nova systems
must have masses larger than $\sim 0.5 M_{\odot}$ in order to produce
ejecta (Livio 1992).
The spread of the observed mass transfer rates in CVs and, perhaps,
also the existence of various subclasses at any given orbital period,
might have several causes. The presence of magnetic cycles
of activity in the secondaries (Bianchini 1987, 1990; Warner 1988;
Richman, Applegate \& Patterson 1994) account only for
luminosity changes of a few tenths of a magnitude.
More important mechanisms could be a variable efficiency of the envelope
chaotic dynamo combined with that of the boundary layer dynamo
(Zangrilli, Tout \& Bianchini 1997), secular mass transfer cycles
excited by the irradiation of the secondary by the primary
(King et al. 1996), and/or the hibernation scenario
for classical novae proposed by Shara et al. (1986).
\smallskip
A CV emerging from common envelope (CE) evolution (Paczynski 1976) must
experience stable mass transfer from the Roche lobe filling secondary
on to the WD primary.
As continuous mass loss perturbs the thermal equilibrium of the
secondaries, they are slightly smaller or larger than MS
stars when they are predominantly radiative or convective,
respectively (e.g. Whyte \& Eggleton 1980, Stehle, Ritter \& Kolbe 1996,
Baraffe \& Kolbe 2000).
Generally speaking, the stability of mass transfer is
determined by the change in radius of the secondary due to
adjustment of its convective outer layers
(dynamical stability) and internal structure (thermal stability) in
response to mass loss, compared with the
changes of the Roche lobe radius induced by both the mass exchange and
the angular momentum losses by the system.
We define three exponents, $\xi_{ad}$, $\xi_{the}$
and $\xi_{RL2}$, for the adiabatic, thermal equilibrium and Roche-lobe
mass-radius relations of low-mass MS stars, respectively.
Since the time derivative of the radius can be
written in the form
\begin{equation}
\frac{\dot R}{R}= \xi\frac{\dot M_2}{M_2}
\end{equation}
the binary will be adiabatically and thermally stable against mass
transfer only if we have
\begin{equation}
\xi_{ad}~-~\xi_{RL2} > 0
\end{equation}
and
\begin{equation}
\xi_{the}~-~\xi_{RL2} > 0
\end{equation}
respectively.
Alternatively, a second CE episode would quickly drive the two
components of the newborn CV to cohalescence.
The $M_2-\xi_{ad}$ and $M_2-\xi_{the}$ profiles for stable
mass transfer were discussed by Schenker, Kolb \& Ritter (1998).
They can be easily transformed into two relations between
$M2$ and the critical mass ratio $q_{critic}=(M_2/M_1)_{critic}$
as described by de Kool (1992) and King et al. (1994).
The critical q-profiles for adiabatic and thermal equilibrium
stable mass transfer can be described as follows.
For secondaries below $\sim$0.45 $M_\odot$, the deep convective
envelope tends to expand adiabatically in response to mass loss
on a dynamical time scale.
In this case, the dynamical stability criterion is the most
restrictive one and the mass ratios should satisfy the condition
$q<q_{dyn}=0.63$.
For masses above $\sim$0.75$M_\odot$, the mass in the convective
envelope is too small to produce adiabatic expansion, and the secondary
even tends to shrink. As a consequence, dynamical stability is
guaranteed even for larger mass ratios while the
thermal stability criterion $q<q_{therm}=1.25$ suddenly
becomes the more restrictive one.
All CVs are then expected to have mass ratios
that are roughly consistent with these stability criteria
although exceptions are possible (see next section 2).
\bigskip
In this paper we explore the effects of magnetic fields
on the critical $q_{dyn}$ profile of lower mass
secondaries.
In section 2 we present systems that apparently
deviate from the theoretical stability criteria.
In section 3 we try to evaluate how magnetic fields modify
the critical $q_{dyn}$ profile.
The effects of the presence of solar-type magnetic cycles on the mass
transfer rate is discussed in section 4.
Conclusions are given in section 5.
\section{The q-profile of the observed CVs}
The Ritter \& Kolb (2005) on-line catalogue
(hereafter RK2005) reports the masses and the mass ratios for
about 102 CVs.
The mass transfer stability criteria described by de Kool (1992),
King et al. (1994) and Shenker, Kolb \& Ritter (1998)
roughly state that, for mass companions below 0.45$M_\odot$,
the dynamical stability criterion is the most
restrictive one and it must be $q<0.63$, while, for masses above
0.75$M_\odot$, as the dynamical stability is achieved even for
very large mass ratios, the prescription for thermal
stability $q<1.25$ dominates.
The critical $q(M_2)$ values for the dynamically and
thermally unstable mass transfer are sketched in the $q-M_2$
plane of Fig. 1 by the solid line ($q_{dyn}$) and the dashed
line ($q_{therm}$), respectively.
The $M_2$ and $q$ values of the selected sample of CVs
are plotted in Fig. 1 using different symbols for different subclasses.
Polar and Intermediate Polar systems are circled
by open circles and open squares, respectively.
Looking at Fig. 1, we first notice that $M_2$ and $q$ are
linearly correlated, as predicted by standard CV models.
We also observe that some of the
data points are not below the critical $q_{dyn}$
line as requested by the stability criterion.
In fact, six CVs fall inside the thermally stable but
dynamically unstable region; they are V1043 Cen, LX Ser, HY Eri, AT Ara,
CM Del and V347 Pup. We should have also included UX UMa
for which RK2005 report $M_1=M_2=0.47 M_\odot$ (Baptista et al. 1995).
However, from new radial velocity curves Putte et al. (2003) derived
$M_1=0.78\pm 0.13 M_\odot$ and $q=0.60\pm0.09$ that places UX UMa
just below the limit for mass transfer stability.
Five objects almost coincide with the $q_{dyn}$ line; they are
the old novae T Aur, HR Del, and DQ Her, the magnetic system V1309 Ori
and the nova-like RW Tri.
Finally, the recurrent nova CI Aql (Lederle \& Kimeswenger 2003)
and the dwarf nova EY Cyg (Tovmassian et al. 2002) even appear both
thermally and dynamically unstable, but having rather long orbital
periods they probably host evolved secondaries. In particular,
G\"ansicke et al. (2003) suggested that EY Cyg might have passed
through a phase of (unstable) thermal timescale mass transfer
that produced a CNO-enriched secondary stripped of its outer layers.
Pollution of the secondary of CY Cyg caused by an unrecorded nova
explosion was also suggested by Sion et al. (2004).
Somewhat evolved secondaries might also exist in short orbital
period systems and, in any case, secondaries are mass losing stars
out of thermal equilibrium. Thus, the theoretical prescriptions
for the dynamical stability of actual CVs are probably different
from those predicted for MS secondaries.
In this paper we suggest that the critical q-profile could be also
modified by the magnetic fields produced in the convective envelopes of
the secondaries.
\smallskip
Fig. 2 plots $M_2$ {\it versus} $M_1$.
Filled circles represent masses that have been determined
spectroscopically; open circles, instead, refer to mass estimates
obtained from empirical correlations. These two classes of
data points are indistinguishable in the diagram.
The errorbars of the suspected unstable objects are shown.
Only V1043 Cen and LX Ser can be considered unstable at a 95$\%$
confidence level.
The six systems that fall inside the dynamically unstable region are
characterized by $M_{2(mean)}=0.38 \pm 0.1 M_\odot$ and
$M_{1(mean)}=0.55\pm 0.1 M_\odot$.
We notice that these 'unstable objects' are dynamically but not
thermally unstable (see Fig. 2). The only exception is the peculiar
dwarf nova EY Cyg discussed above.
The weak correlation between the masses of the
two components observed in Fig 2 is probably only due to the
selection effects introduced by the thermal stability criterion.
Fig 2 suggests that apparently unstable CVs tend to cluster around
massess of the secondaries that correspond to orbital periods above
the period gap.
Since the masses of the primaries are very weakly correlated with
the orbital period because they have only to obey to the mass ratio
limits for stability, unstable systems must also select the less
massive primaries.
\smallskip
In order to investigate the nature of these apparently dynamically
unstable CVs, we plot in Fig. 3 the mass-period diagram.
Different symbols are like in Fig. 2 and basically show the same
statistics.
Empirical mass-period relationships were given, amongst others,
by Warner (1995a,b), Smith \& Dhillon (1998), Howell \& Skidmore (2000),
and Patterson et al. (2003).
Smith \& Dhillon (1998) found that the secondary stars in CVs with
periods below 7-8 h are indistinguishable from main-sequence stars.
As an example, we show in Fig. 3 how data points are fitted by the
Patterson et al.'s correlation (dashed line).
The solid line represents the evolutionary track of a
1.0 ${M_\odot}$ secondary obtained using the two-dynamos evolutionary
code developed by Zangrilli, Tout \& Bianchini (1997).
The fit is particularly significant around and through the period gap,
especially for filled circles.
With the exception of V1309 Ori and AT Ara, the unstable
systems candidates (labelled by crosses) that apparently possess
unevolved secondaries do not follow any distinctive pattern and fall
in the range $3<P_{orb}<6$ h, corresponding to masses of the
secondaries in the range $0.3-0.7 M_\odot$.
\smallskip
It is however possible that mass transfer stability condition (2),
also sketched in Fig. 1, is not applicable to the secondaries
of some CVs because their convective shells follow a mass-radius
relation that implies larger $\xi_{ad}$ exponents.
Actually, the adopted stability criteria might be uncertain,
the masses of the two components could be poorly determined,
and a significant fraction of short-period, angular momentum-driven
CVs seem to have a somewhat evolved donor star (e.g. Kolb \& Baraffe 2000,
Kolb \& Williems 2005).
\smallskip
In all cases, in the next paragraph we will focus our attention on
the role played by the magnetic fields produced in the
convective envelopes of the secondaries in changing
the $\xi_{ad}$ exponent and the critical $q_{dyn}$-profile.
\section{How magnetic fields in the secondaries modify the
critical q-profile of CVs}
It is widely recognized that magnetic fields, increasing the
critical Rayleigh number, inhibit convection (see, for example,
van den Borght 1969).
The possibility that convection inside stars might be suppressed
by strong magnetic fields of simple geometry, namely, poloidal
and/or toroidal, was discussed by Gough \& Tayler (1966) and
Moss \& Tayler (1969, 1970).
A detailed solar model containing a large-scale
''magnetic perturbation'' to mimic the strong fields
associated with an $\alpha-\Omega$-type solar dynamo was constructed
by Lyndon \& Sofia (1995). They found that the changes in the
temperatures and the adiabatic gradient produced by the magnetic
perturbation lead to quite large decreases in the
convective velocities above the perturbed region and to considerable
increases of the convective turnover time.
\smallskip
Even neglecting boundary-layer dynamos, which are
responsible for the large scale structure of the stellar
poloidal field, chaotic envelope-dynamos
driven by convective turbulence are sufficient to produce
magnetic energy densities comparable to the kinetic energy, that is
at a level close to global equipartition (Thelen \& Cattaneo 2000).
Liao \& Bi (2004) found that turbulent
magnetic fields can also inhibit the generation of convection.
We might then think that if magnetic fields can reduce the efficiency of
convection, they should also reduce their adiabatic response
to mass loss.
However, since the prescription for dynamical stability is
$\xi_{ad}~-~\xi_{RL2} > 0$, we should mainly investigate whether
magnetic fields can modify the adiabatic mass-radius
exponent $\xi_{ad}$.
\smallskip
For stars with extended convective layers, that means for masses
$\le0.5 M_\odot$, an approximated expression of the mass-radius
adiabatic exponent given by Paczy\'nski (1965) is
\begin{equation}
\xi_{ad}=\frac{\gamma-2}{3\gamma-4}
\end{equation}
where $\gamma = c_p/c_v$ is the polytropic exponent for an adiabatic
transformation and $c_p$ and $c_v$ are the specific heats.
The $\xi_{ad}$-vs-$\gamma$ diagram is shown in Fig. 4.
For an ideal gas and isotropic turbulence we have $\gamma = 5/3$
and $\xi_{ad}=-1/3$, which, in Fig. 1, corresponds to the
$q=0.63$ critital mass ratio for the dynamical stability
of secondaries below 0.5$M_\odot$.
From Fig. 4 we may see that, if we chose $\gamma$ values
below 4/3 or above 5/3, we obtain $\xi_{ad}>-1/3$ and thus
steeper mass-radius relations that lead to less restrictive
critical $q-$profiles for low mass secondaries.
\smallskip
The corrections to the thermodynamical variables due to
the presence of a turbulent magnetic field derived by
Liao \& Bi (2004) are
\begin{equation}
\Delta c_v= \beta_m \frac{k}{\mu m_u}
\end{equation}
\begin{equation}
\Delta c_p= 2\beta_m \frac{k}{\mu m_u}
\end{equation}
\begin{equation}
\Delta \gamma= \frac{1}{c_v}\Delta c_p - \frac{c_p}{c_v^2}\Delta c_v
(2- \gamma) \frac{\Delta c_v}{c_v}
\end{equation}
where $\beta_m$ is the ratio of magnetic pressure to gas pressure,
while $k$, $\mu$ and $m_u$ have their usual meaning.
As we can see, a turbulent magnetic field tends to increase
the specific heats and $\gamma$. Assuming an initial $\gamma=5/3$,
the increment of the polytropic exponent can be written as
$\Delta \gamma\sim(0.33/c_v)\beta_m k/(\mu m_u)$.
Fig. 5 plots the mass-radius exponent $\xi_{ad}$ derived
from eq. (4) as a function of $\beta_m$, for complete
and partial hydrogen ionization, assuming unperturbed
specific heats $c_v/(\frac{3}{2}N_0k)=2$
and $c_v/(\frac{3}{2}N_0k)=35$, respectively (Clayton 1983,
table 2-4), $N_0$ being the Avogadro number.
If we focus on the full ionization line in Fig. 5 we find for
$\beta_m=0.01$ an increase $\Delta \gamma/\gamma =1.6\times10^{-3}$,
which is in good agreement with the numerical results obtained by
Mollikutty, Das \& Tandon (1989) when we use the values of the
specific heats listed in their Tables 1 and 2.
We conclude that chaotic dynamos can produce critical q-profiles
above the minimum standard value $q_{dyn}=0.63$ for low mass secondaries
(see Fig. 1), but probably not much above $q\sim0.7$ even for
large $\beta_m$'s. This result shows that the
modified critical q-profile accounts for the stability
of the border line systems of Fig 1.
\smallskip
If we consider large-scale, geometrically structured magnetic fields,
like those generated by $\alpha-\Omega$-type dynamos, then
the magnetic extra pressure is no more a simple scalar and
$\gamma$ will strongly depend on the field geometry.
Since the magnetic force component along the magnetic field is zero,
in that direction a magnetically controlled gas will show $\gamma=1$,
while, perpendicular to the field, it will be
$\gamma=2$. For fields tangled on distance scales of interest
$\gamma=4/3$, as for a relativistic gas (Endal, Sofia \& Twigg 1985).
Thus, $\gamma$ represents the ratio of specific heats for the
applied perturbation.
In practice, the effective polytropic exponent of a convective envelope
should be calculated for any given field geometry, distribution and intensity
and averaged over the whole convective shell.
In particular, as stellar structures mainly depend on the radial variations
of the total pressure, we will only consider the radial dependence
of the magnetic pressure and the polytropic exponent.
Lyndon \& Sofia (1995) studied the effects on the solar structure
produced by localized large-scale magnetic fields with no radial component,
i.e. a toroidal field with a radial pressure component,
and assumed $\gamma=2$.
Similarly, the toroidal fields rising from the overshoot regions
of secondaries with masses between 0.3 and 0.5 $M_\odot$ might also
produce strong localized magnetic perturbations with $5/3<\gamma<2$.
Poloidal fields, instead, appear radial only at large
latitudes and could, in principle, produce perturbations
with $1<\gamma<5/3$. We recall that radial fields should much more strongly
inhibit convection (Moss \& Tayler 1969).
\smallskip
However, since magnetic pressure is, on the average, a small
fraction of gas pressure, the effective polytropic exponent of the
convective shell should not greately differ from the
unperturbed value $\gamma=\frac{5}{3}$.
Looking at Fig. 4, we see that, for small changes of
$\gamma$, the initial value of the adiabatic exponent $\xi_{ad}=-\frac 13$
can increase or decrease whether the geometry of the magnetic
perturbation corresponds to $\gamma=2$ or to $\gamma=1$, respectively.
However, the $\gamma=2$ geometry very likely dominates
most of the stellar envelope because large-scale poloidal fields are
weaker than the toroidal ones and because they become radial only near
the magnetic poles.
Thus, we may roughly describe the effects of large scale
fields using the same approach as for turbulent fields,
assuming $\beta_m$ as the ratio of the radial component of the combined
toroidal and poloidal magnetic pressure, $ B^2_{tot}/8\pi$, to gas pressure.
According to Applegate (1992), the magnetic torques which are active in
the outer convective regions of the secondaries should be produced by
fields of several kilogauss. Toroidal fields of some $10^4$ G
produced by $\alpha-\omega$ dynamo models were suggested by Zangrilli,
Tout \& Bianchini (1997) in CVs just above the period gap.
Since equipartition, i.e. $\beta_m=1$, in the envelopes of low mass
secondaries typically requires fields of $\sim10^8$ G, the ratio
of magnetic to gas pressure is $\beta_m\sim 10^{-4}$.
This small value however becomes $\sim 100$ times larger
at the photosphere (Applegate \& Patterson 1987).
Assuming $\beta_m\sim 10^{-4}$, equations 5-7 yield
$\Delta\gamma\sim 3\times10^{-5}$, while from eq. 4 we obtain
$\Delta\xi_{ad}\sim5\times10^{-5}$.
We conclude that large-scale toroidal and poloidal
fields should not significantly contribute to increase the stability of
fully, or almost fully convective secondaries, their effects being smaller
than those produced by chaotic fields.
\smallskip
Possible effects due to the presence of magnetic torques in
the outer convective regions should also be investigated.
Applegate (1992) explained that the field lines rising from
the magnetic dynamo in the overshoot region produce a negative
torque in the outer envelope trying
to spin down the tidally locked outer layers of the secondary.
In this case, an observer corotating with the binary would see
the surface of the star rotate in a retrograde sense.
The consequent change in the quadrupole moment of the star
would then produce the orbital period modulations observed
in some CVs during magnetic cycles.
Richman, Applegate \& Patterson (1994) have
shown that a consequence of the decreased rotation of the outer
envelope is the appearence of an inward directed Coriolis acceleration.
Following these authors, we find that for orbital periods
around $4$ h and $\sim 0.45$ $M\odot$ secondaries, the
mean extra-gravity due to Coriolis forces is
$\sim 10^2~~ cm~ s^{-2}$.
Since this is only $10^{-3}$ times the surface gravity,
some effects could be seen only in the photosphere and the
thin radiative layer above.
Another consequence is that the energy stored and dissipated
in the convective zone, where a peak of differential rotation
is cyclically set up by magnetic cycles, will produce a modulation
of the stellar luminosity of the order of $\Delta L/L\sim 0.1$,
corresponding to changes in the effective temperature
$\Delta T_{eff}/T_{eff}\sim 0.025$.
In Applegate's model, the release of the stored torque
energy should heat not only the stellar surface, but most of
the convective shell as well.
Since in most of the convective region the temperatures are above
the HeII ionization limit, the Rosseland mean is dominated
by Kramers' law. Thus, inside the convective shell, a $3\%$
increment of the temperature should produce a $\sim 10\%$
decrease in the opacity coefficient. The result should be a less
developed convection zone and a hotter photosphere, the effect being
more pronounced as the mass of the secondary increases
(Pizzolato et al. 2001).
Instead, in the cool atmospheres, small temperature increments
should determine substantial increases of the mean opacity
and the atmospheric radiative gradient.
As a result, the photospheric radius should increase.
However, whether the combined effects of all these mechanisms will
result in a steeper mass-radius relation with a
larger $\xi_{ad}$ could be understood only by performing
numerical simulations with full stellar models.
\section{The effects of magnetic cycles on the mass transfer rate}
Since $\alpha-\Omega$-type dynamos are
characterized by periodic solutions (magnetic cycles), we wonder
whether the presence of weakly variable $\gamma$ and $\xi_{ad}$ might
represent an additional/alternative mechanism
modulating the mass transfer rate within the binary system.
Following Osaki (1985), Warner (1988) and Richman, Applegate \& Patterson
(1994), we may express the fractional change in the accretion rate as
\begin{equation}
\Delta\dot M_2/\dot M_2 = \Delta R/H
\end{equation}
where $H$ is the photospheric pressure scale height that, for a lower
main sequence star, is $\sim3200$ times smaller than the radius $R$,
and $\Delta R$ is here assumed as the variation of the
stellar radius produced by a change of $\xi_{ad}$.
We may then rewrite expression 8 as
\begin{equation}
\Delta\dot M_2/\dot M_2 \sim 3200 \times \Delta R/R
\end{equation}
and, since
\begin{equation}
\Delta R/R \sim lnM\Delta\xi_{ad}
\end{equation}
we obtain, for a 0.5 $M_\odot$ secondary, $\Delta\dot M_2/\dot M_2 \sim 0.1$.
Actually, this is the order of magnitude of the observed long-term luminosity
variations of CVs which are usually ascribed to the presence in the
secondaries of solar-type cycles (Bianchini 1987, 1990; Warner 1988;
Richman, Applegate \& Patterson 1994).
\section{Conclusions }
A few CVs with orbital periods in the range 3.5-7 h have
mass ratios that would define them as thermally stable
but dynamically unstable (Fig. 1). Assuming that the masses of the
two companions are fairly well determined and the secondaries are MS stars,
the commonly adopted criteria do not explain the stability of these
systems against mass tansfer.
However, we found another effect since cahotic and large-scale
magnetic fields produced in the convective shells of the secondaries
modify the polytropic $\gamma$ exponent,
the mass-radius adiabatic exponent $\xi_{ad}$
and, consequently, the critical $q$-profile for stable
mass transfer.
We demonstrated that large $\beta_m$'s turbulent magnetic
fields might produce critical q-profiles 10\% higher than the
usually adopted minimum critical value $q_{dyn}=0.63$ for
low mass secondaries.
We found that the contribution by large-scale toroidal and poloidal
fields could be smaller. Thus, magnetic fields alone
cannot account for the stability of all the anomalous CVs
identified in Fig. 1 and other explanations must be investigated.
During this study, we found another important effect due to the magnetic
fields of the secondaries. In fact, since toroidal and poloidal fields are
produced by $\alpha-\Omega$-type dynamos, their intensities
should vary throughout magnetic cycles, inducing periodic changes in
the mass-radius adiabatic exponent $\xi_{ad}$.
We have demonstrated that these variations, though small,
are sufficient to explain the cyclic mass transfer rate
variations observed in a number of CVs.
\section*{ACKNOWLEDGEMENTS}
A.B. wishes to thank the people of the Department of Physics and
Astronomy of the University of Wyoming for their friendship and support.
We acknowledge Cesare Chiosi, Franca D'Antona, Alvio Renzini and
Marina Orio for helpful discussions.
This research was supported by NASA Cooperative Agreement NCC 5-578 to
the Wyoming EPSCoR Program and by the Italian MURST.
| {
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Retro Review: Wonder Woman #93 (January 1995)
By Matthew Peterson on August 5, 2018 0 Comments
Legends say that Princess Diana defeated all the other Amazons in a competition to become their ambassador to the outside world. But that wasn't the ONLY time she had to earn her role… Your Major Spoilers (Retro) Review of Wonder Woman #93 awaits!
WONDER WOMAN #93
Writer: William Messner-Loebs
Artist: Mike Deodato, Jr.
Colorist: Patricia Mulvihill
Letterer: John Costanza
Editor: Paul Kupperberg
Current Near-Mint Pricing: $6.00
Previously in Wonder Woman: Centuries ago, the Amazon tribes split, with one group staying on Themiscyra and another moving to Egypt, where they founded the Bana-Mighdall tribe. By the 20th century, their greatest warrior was Artemis, a six-foot redhead whose ideas on justice are much more visceral than Diana's. After seeing visions of a terrible death for Wonder Woman, Queen Hippolyta called for a new competition in the hopes of saving her daughter from death, leading to Diana being bested in combat by Artemis in the previous issue. As this adventure opens, Artemis is gifted with the tools she will use as Wonder Woman: Gauntlets of Atlas to increase her strength tenfold, and the Sandals of Hermes, allowing high-speed flight…
The real story of this series of events is a bit more mercenary: The Death of Superman replaced the Man of Steel with several other Supermen, boosting the sales and getting the attention of fans in a way that the staid DC heroes hadn't been in those heady post-Image debut days. It wasn't long before Batman was replaced with a new Dark Knight, just a few months before this issue, leading to another bump in sales and interest, leading to Diana's turn in the "replacement hero" spotlight. Back in the story proper, an angry Diana confronts her mother, still unaware that Hippolyta is trying to protect her, angrily trying to figure out what her mother is playing at (and also fearing that rumors that her true father was Hercules are true, which would mean her mother has been lying to her all her life) before storming off in a huff. Returning home to Boston, Wonder Woman just wants to get back to her normal life, but since Artemis has now taken over a major part of that life, things go poorly. After a week, a super-villain attack in the city brings out its protector, Wonder Woman!
Version 2.0, mind you…
I'm going to be honest here, it's REALLY hard to figure out what's happening in the pages of Wonder Woman #93, as Deodato's layouts are focused on doing wild, weird stuff without enough fundamentals to keep it all focused. Some of the full-page spreads are quite pretty thought, and the basic gist is a team of super-villains blowing things up while Artemis kicks the bajeezus out of them, until a giant rock-creature pops up to attack. Then, it becomes clear that Artemis isn't working alone.
I admit it, that's a pretty impressive page, even with the questionable proportions of Diana, and as dated as the biker-bikini look is, it's not a bad looking suit. (At least, not a bad looking suit by 1995 standards.) Then, we get a weird moment wherein AFTER having gone into action for the first time, Wonder Woman is gifted the costume she just wore into battle by her friends.
While the old Wonder Woman worries about money, the new Wonder Woman moves to New York and signs up with a PR firm to get the news about the new take on the Amazons' mission for peace with Man's World. In a nice bit of foreshadowing of Artemis' ideas on justice and violence, we get to watch this on a screen covered in blood…
This ends up being because Wonder Woman's aforementioned private investigator friend is being beaten senseless by thugs. When Diana arrives, they mock her for her peaceful mission, only to have her kick the hell out of them in a rage before telling Micah the private eye that she is going to partner with him, in return for fifty percent of the take. Wonder Woman #93 is a book that starts awkwardly AND ends abruptly but has some nice moments in between, muted by an artist focused on channeling Jim Lee's work on WildCATS rather than storytelling, earning an unsuccessful-but-not-terrible 2 out of 5 stars overall. The idea is a sound one, though, and I wonder what might have come of Artemis with a different art team or fewer echoes of Jean-Paul Valley as Batman.
Artemis dc comics Mike Deodato Jr. Retro Review Review William Messner Loebs Wonder Woman
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[First Look] The Flash #88
[First Look] Superman: Villains #1
[First Look] The Green Lantern: Season Two #1 | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,455 |
{"url":"https:\/\/rgitools.readthedocs.io\/en\/latest\/dems.html","text":"# The RGI-TOPO dataset (beta release)\u00b6\n\nRGI-TOPO provides a local topography map for each single glacier in the RGI.\n\nWe gathered and processed topography data for each glacier in the RGI V6 and for each Data sources we are aware of. These data are released in a beta version and are provided here for feedback and testing purposes only, i.e. they are not (yet) an official RGI product. In particular, the various topography data are provided \u201cas is\u201d, i.e. without recommendation on which data source to use. Note also that RGI-TOPO cannot be used for glacier change assessment: its aim is to provide a baseline for glacier modelling and other data analysis efforts.\n\nNote\n\nWe will include the final topography and hypsometry data in the next official RGI release (V7) scheduled for release by end of 2020.\n\nThe data is available at https:\/\/cluster.klima.uni-bremen.de\/data\/gdirs\/dems_v0\/RGI62\/b_010\/L1\/\n\nSee Data format and How to cite these data for more information.\n\n## Data sources\u00b6\n\nUnfortunately, there is no gap-free, global DEM available to date. For most regions several data sources are available, each with various acquisition dates and data quality issues. As of today (Jan 08 2020), the data sources supported by OGGM\/rgitools are:\n\n\u2022 the Shuttle Radar Topography Mission (SRTM) 90m Digital Elevation Database v4.1 freely available for all locations in the [60\u00b0S; 60\u00b0N] range. Date of acquisition: February 2000\n\u2022 the Greenland Mapping Project (GIMP) Digital Elevation Model covering Greenland (for RGI region 05). Date of acquisition: February 2003 - October 2009\n\u2022 the Radarsat Antarctic Mapping Project (RAMP) Digital Elevation Model, Version 2 covering the Antarctic continent (for RGI region 19 with the exception of the peripheral islands). Date of acquisition: 1940-1999 (mostly 1980s and 1990s)\n\u2022 the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) ASTER Global Digital Elevation Model (GDEM) Version 3 (ASTGTM) covering the entire globe but with consequent artefacts (not tagged as invalid data). Date of acquisition: 2000 - 2013\n\u2022 the Viewfinder Panoramas DEM3 products, a global DEM based on various of the above listed sources, manually merged and corrected, sometimes from cartographical data. Date of acquisition: variable, depending on original source.\n\u2022 the TanDEM-X 90m DEM, newly released and covering the entire globe. Date of acquisition: December 2010 - January 2015\n\u2022 the Arctic DEM newly released in version 7 and covering the northern latitudes at various resolutions (we picked 100m for a start). Date of acquisition: 2007-2018\n\u2022 the REMA Antarctic DEM newly released and covering the Antarctic continent at various resolutions (we picked 100m for a start). Date of acquisition: 2009 - 2017 (mostly 2015-2016)\n\u2022 the ALOS World 3D - 30mx (AW3D30) global digital surface model from the Japanese space agency JAXA. Date of acquisition: 2006-2011\n\u2022 the AWS terrain tiles data hosted on Amazon Web Services and maintained by Mapzen. This is a bundle of various data-sources but very flexible in use. Date of acquisition: variable, depending on original source\n\n## Examples\u00b6\n\nThese graphics and statistics were generated with a freely available Jupyter notebook. You can run this notebook online (without any installation) by following this link (the online server may take a couple of minutes to start).\n\n## Data format\u00b6\n\nThe data is sorted into regional folders (one per RGI region). Each tar file stores 1000 glaciers (RGI60-01.00.tar contains glacier IDs from RGI60-01.00001 to RGI60-01.00999, RGI60-01.01.tar contains glacier IDs from RGI60-01.01000 to RGI60-01.01999, etc.).\n\nEach glacier data comes in a single folder named after its RGI ID. A glacier folder contains the following data files:\n\n\u2022 glacier_mask.tif: a raster mask of the RGI glacier at the same resolution than the associated DEMs (geotiff format).\n\u2022 outlines.tar.gz: the RGI vector outlines for this glacier\n\u2022 intersects.tar.gz: the vector lines of the boundaries between this glacier and possible neighbors\n\u2022 glacier_grid.json: information about the grid and map projection\n\u2022 diagnostics.json, log.txt: files used by OGGM\/rgitools (not relevant here)\n\u2022 one folder per available DEM source, containing a dem.tif file (geotiff format) and the data source and citation information in dem_source.txt (text file).\n\nThe topography data is bilinearily interpolated from the DEM source to a local tranverse mercator map projection (similar to the well known UTM, but with projection parameters centered on the glacier). Most modern GIS packages are able to read the projection information out of the geotiff files.\n\nThe spatial resolution of the target local grid depends on the size of the glacier. We use a square relation to the glacier size ($$dx=aS^{\\frac{1}{2}}$$, with a=14 and S the area of the glacier in $$\\text{km}^{2}$$), clipped to a minimum (10\u2009m) and maximum (200\u2009m) value.\n\nThe map size is chosen so that it is larger than the glacier of about 10 grid points (a future release of the data will also ship with larger map extents).\n\n## How to cite these data\u00b6\n\nWarning\n\nIMPORTANT: RGI-TOPO does NOT generate any new topography data. We use freely available data and interpolate it to a local glacier map. If you make use of these data for a publication, presentation or website, it is mandatory to refer to the original data provider as given in the dem_source.txt file found in each DEM folder.\n\nWe are very thankful to the institutions providing these data, and we ask our users to acknowledge the original contributions according to their respective license (sometimes unclear, unfortunately).\n\nRGI-TOPO itself (i.e., the compilation of data) is licensed under a CC BY 4.0 license, i.e. you can use, share and adapt it under the conditions stated by the license and by acknowledging the rgitools contributors as well as the original data sources (as explained above). The name of the rgitools contributors cannot be used to endorse any product or result derived from RGI-TOPO without prior approval.\n\nNote\n\nIf you wish to acknowledge the data processing work that was necessary to generate these data in a scientific publication, we suggest the following citation: \u201cThe glacier dem data was processed with the rgitools and OGGM software packages (Maussion et al., 2019 doi: 10.5194\/gmd-12-909-2019).\u201d\n\n## How to provide feedback\u00b6\n\nBefore the official release with the next RGI version, we aim to:\n\n\u2022 make sure that we didn\u2019t miss any important data source\n\u2022 ensure that there is no bug in our processing chain, i.e. that the data is properly parsed, reprojected, and documented\n\u2022 decide on the data format which is most suitable for the majority of users\n\u2022 publish a detailed report about the quality and data availability of each data source\n\u2022 decide on a \u201cstandard\u201d data source for each glacier, which will provide the reference hypsometry for future RGI versions\n\nYour help on any of these objectives is very welcome! Contact us if you want to provide feedback.\n\nRegarding the choice of the default data source for the RGI, we currently formulate the following criteria:\n\n1. robust and gap-free datasets are preferred over more accurate or recent but incomplete DEMS. Indeed, we have to keep in mind that any kind of glacier bed inversion or glacier simulation based on ice-dynamics cannot deal with topographical artefacts.\n2. the acquisition date of the DEM must be as close as possible to the acquisition date of the glacier outline (which is targeted to be around 2000 in RGI V7).\n3. preferably, the DEM source should be the same for neighboring glaciers. This implies that ideally, a single DEM source should be chosen at the region or sub-region level.\n\nCurrently, we are most confident in SRTM for all latitudes between 60\u00b0 N and S. Almost gap free, the SRTM data aquisition date is also very concordant with the target date of the RGI outlines.\n\nFor all other regions, more investigation is needed and your feedback is welcome.\n\n## Global data availability\u00b6\n\nThe following section shows a more detailed analysis of all the above mentioned DEMs with respect to the different RGI regions.\n\nTable 1 gives a summary for the RGI regions with respect to the different DEMs. For this and all further analysis a DEM is only attributed as available to a individual glacier if the glacier centered cutout has less than 10% missing data points in this DEM. This threshold obviously only covers actual voids in the DEM source but does not state anything about the quality or accuracy of the none-void data points.\n\n RGI region # total ARCTICDEM ASTER AW3D30 DEM3 GIMP MAPZEN RAMP REMA SRTM TANDEM 01: Alaska 27108 75% 100% 76% 100% \u2013 100% \u2013 \u2013 47% 99% 02: Western Canada and USA 18855 4% 100% 94% 100% \u2013 100% \u2013 \u2013 93% 98% 03: Arctic Canada, North 4556 99% 98% 63% 99% 15% 100% \u2013 \u2013 \u2013 100% 04: Arctic Canada, South 7415 97% 100% 44% 98% \u2013 100% \u2013 \u2013 1% 100% 05: Greenland Periphery 20261 95% 98% 70% 99% 100% 99% \u2013 \u2013 \u2013 99% 06: Iceland 568 97% 100% 27% 100% \u2013 100% \u2013 \u2013 \u2013 100% 07: Svalbard and Jan Mayen 1615 99% 100% 32% 100% \u2013 100% \u2013 \u2013 \u2013 99% 08: Scandinavia 3417 92% 100% 24% 100% \u2013 100% \u2013 \u2013 2% 100% 09: Russian Arctic 1069 98% 99% 7% 99% \u2013 100% \u2013 \u2013 \u2013 100% 10: Asia, North 5151 48% 99% 85% 99% \u2013 99% \u2013 \u2013 67% 100% 11: Central Europe 3927 \u2013 100% 100% 100% \u2013 100% \u2013 \u2013 100% 93% 12: Caucasus and Middle East 1888 \u2013 100% 100% 100% \u2013 100% \u2013 \u2013 100% 98% 13: Asia, Central 54429 \u2013 100% 100% 100% \u2013 100% \u2013 \u2013 100% 98% 14: Asia, South West 27988 \u2013 100% 100% 100% \u2013 100% \u2013 \u2013 100% 95% 15: Asia, South East 13119 \u2013 100% 100% 100% \u2013 100% \u2013 \u2013 100% 94% 16: Low Latitudes 2939 \u2013 100% 100% 100% \u2013 100% \u2013 \u2013 100% 99% 17: Southern Andes 15908 \u2013 99% 99% 99% \u2013 100% \u2013 \u2013 99% 98% 18: New Zealand 3537 \u2013 100% 100% 100% \u2013 100% \u2013 \u2013 100% 85% 19: Antarctic and Subantarctic 2752 \u2013 78% 24% 78% \u2013 99% 49% 18% 24% 87% All RGI regions 216502 28% 99% 87% 99% 9% 99% \u2013 \u2013 73% 97%\n\nThe following barplot shows again the availability of particular DEMs for RGI region.\n\nIn the section Details for RGI subregions you can find similar statistics but broken down into the RGI Subregions.\n\n## Code availability\u00b6\n\nThese data where generated with OGGM version 1.2. This tutorial (interactive version) documents how to create local topography maps yourselves.\n\n## Contact\u00b6\n\nRGI-TOPO authors: Matthias Dusch and Fabien Maussion.\n\nFor feedback, please use the github issue tracker (requires a github account) or send us an email.\n\n## Acknowledgements\u00b6\n\nWe acknowledge financial support from the International Association of Cryospheric Sciences (Matthias Dusch) and from the University of Innsbruck (Fabien Maussion).","date":"2020-02-21 12:20:19","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.2536756098270416, \"perplexity\": 5035.540120382988}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-10\/segments\/1581875145529.37\/warc\/CC-MAIN-20200221111140-20200221141140-00102.warc.gz\"}"} | null | null |
{"url":"http:\/\/fractaledmind.com\/articles\/page\/2\/","text":"\u2022 ### The Word of God\n\n##### 04 September 2017\n\nWhat does the phrase Word of God mean?\n\n\u2022 ### On Antinomies and Paradoxes\n\n##### 02 September 2017\n\nShould the central tenets of Christian theology be best understood as antinomies, or paradoxes, or both?\n\n\u2022 ### Degrees of Separation\n\n##### 25 August 2017\n\nWhen talking about God, I\u2019m not so certain that we have a great understanding of what we can and cannot say properly, or what we can and cannot understand properly.\n\n\u2022 ### I am but a water glass\n\n##### 24 August 2017\n\nI am but a water glass,\na container for my life.\nLife osmoses through me\nforming droplets of moments\nthat ruin rivulet-like to the tabletop.\n\n\u2022 ### Portrait of Pain II\n\n##### 20 August 2017\n\nI had felt it for a while, though even then I didn\u2019t know it. I didn\u2019t know that I knew. It\u2019s odd when truth gnaws at your gut, but you stubbornly ignore it. It is odd because, on the one hand, you know it, but on the other, you don\u2019t. It\u2019s odd and...\n\n\u2022 ### Time in Ruby and ActiveRecord\n\n##### 20 August 2017\n\nHow does the Ruby Time class relate to the ActiveRecord time column type?\n\n\u2022 ### Typecasting in Ruby and Rails\n\n##### 19 August 2017\n\nI recently had the need to typecast string values passed as query parameters to a controller action to their appropriate type. In solving this problem, I've learned a lot about Rails' typecasting layer, Ruby's typecasting methods, as well as a handful of edge cases. The result was a typecasting function that I think has a lot to offer.\n\n\u2022 ### Recalling my earliest deep regret\n\n##### 18 August 2017\n\nA recollection of rocks, regret, and Snickers.\n\n\u2022 ### Encoding the Logic of Sets\n\n##### 16 August 2017\n\nHow can procedures be used to encode the logic of both infinite and finite sets?\n\n\u2022 ### On Death and Life\n\n##### 15 August 2017\n\nA short meditation on death and life.","date":"2018-06-21 21:52:08","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.21353857219219208, \"perplexity\": 5560.774156250374}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-26\/segments\/1529267864300.98\/warc\/CC-MAIN-20180621211603-20180621231603-00054.warc.gz\"}"} | null | null |
{"url":"https:\/\/www.zbmath.org\/authors\/?q=ai%3Aschenkel.alexander","text":"# zbMATH \u2014 the first resource for mathematics\n\n## Schenkel, Alexander\n\nCompute Distance To:\n Author ID: schenkel.alexander Published as: Schenkel, A.; Schenkel, Alexander External Links: MGP \u00b7 ORCID\n Documents Indexed: 35 Publications since 2004\nall top 5\n\n#### Co-Authors\n\n 2 single-authored 12 Benini, Marco 6 Dappiaggi, Claudio 6 Szabo, Richard J. 3 Barnes, Gwendolyn E. 3 Hack, Thomas-Paul 3 Ohl, Thorsten 3 Uhlemann, Christoph F. 2 Aschieri, Paolo 2 Becker, Christian 2 Murro, Simone 2 Woike, Lukas 1 Bieliavsky, Pierre 1 Fewster, Christopher J. 1 Gimperlein, Heiko 1 Hanisch, Florian 1 Koslowski, Tim A. 1 Pagani, Chiara 1 Rejzner, Kasia 1 Schreiber, Urs 1 Schweigert, Christoph 1 Zahn, Jochen\nall top 5\n\n#### Serials\n\n 7 Communications in Mathematical Physics 5 Annales Henri Poincar\u00e9 3 General Relativity and Gravitation 3 Letters in Mathematical Physics 3 Journal of Geometry and Physics 2 Journal of High Energy Physics 2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Classical and Quantum Gravity 1 Journal of Mathematical Physics 1 Reviews in Mathematical Physics 1 Theory and Applications of Categories 1 Advances in Theoretical and Mathematical Physics 1 International Journal of Geometric Methods in Modern Physics 1 Oberwolfach Reports\nall top 5\n\n#### Fields\n\n 28 Quantum Theory\u00a0(81-XX) 13 Relativity and gravitational theory\u00a0(83-XX) 10 Differential geometry\u00a0(53-XX) 5 Associative rings and algebras\u00a0(16-XX) 5 Category theory, homological algebra\u00a0(18-XX) 5 Topological groups, Lie groups\u00a0(22-XX) 5 Algebraic topology\u00a0(55-XX) 5 Global analysis, analysis on manifolds\u00a0(58-XX) 4 Algebraic geometry\u00a0(14-XX) 4 Functional analysis\u00a0(46-XX) 3 Nonassociative rings and algebras\u00a0(17-XX) 3 Mechanics of particles and systems\u00a0(70-XX) 2 Geometry\u00a0(51-XX) 1 General mathematics\u00a0(00-XX) 1 Number theory\u00a0(11-XX) 1 $K$-theory\u00a0(19-XX) 1 Partial differential equations\u00a0(35-XX) 1 General topology\u00a0(54-XX) 1 Manifolds and cell complexes\u00a0(57-XX) 1 Classical thermodynamics, heat transfer\u00a0(80-XX)","date":"2019-10-18 21:13:49","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.2324310541152954, \"perplexity\": 9925.68541339294}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-43\/segments\/1570986684854.67\/warc\/CC-MAIN-20191018204336-20191018231836-00082.warc.gz\"}"} | null | null |
{"url":"http:\/\/physics.stackexchange.com\/questions?page=3&sort=newest","text":"# All Questions\n\n446 views\n\n### Can an elliptical orbit take the same time as a circular obit?\n\nIn the picture below you can see two orbits of potential pbjects. The main aspect of the orbits is that they have a collision point at the maximum of the elliptical orbit. My question is, could the ...\n21 views\n\n### Question about time of charge of a battery [on hold]\n\nif I have a 24kWh lithium-ion battery made of 192 cells in two parallel strings of 96 in parallel with 66.2 Ah; and I want to charge it using a solar panel with 3000W and 48V. What are the ...\n56 views\n\n### Bug riding on a ball moving at almost the speed of light [on hold]\n\nA ball with a bug on it is thrown at almost the speed of light. The bug looks back and observes the thrower throwing the ball. In the context of special relativity, what is the weight and the height ...\n75 views\n\n### Expanding a ket in the position basis?\n\nMy textbook says that to find the ket $|\u03c8\\rangle$ in the same position basis as the ket $|\u00f8\\rangle$ we do the following: $$|\u03c8\\rangle=\\int d\u00f8|\u00f8\\rangle \\langle \u00f8|\u03c8\\rangle$$ Firstly can $|\u00f8\\rangle$ be ...\n574 views\n\n### Why are silicon-silicon bonds weak?\n\nIf carbon\u2013carbon bonds are reasonably strong and silicon and carbon are both in the same column of the periodic table meaning they have the same amount of valence electrons, also seeing as its bonding ...\n32 views\n\n### Spontaneous breaking of a discrete non-Abelian symmetry\n\nCan someone give an example of an one dimensional local gapped quantum lattice model with a discrete non-Abelian global internal symmetry that is spontaneously broken in the ground state? In ...\n108 views\n\n### How do heated showers\/faucets work? [on hold]\n\nI'm not sure if this question is for Physics SE, but I'd go ahead and ask. I was wondering how the heated showers work (the ones with the hot and cold knobs). I have always been curious and this may ...\n92 views\n\n### How do instantons cause vacuum decay?\n\nFrom what I read about on instantons (Zee, QFT in a Nutshell, pg 309-310), an instanton is a vacuum solution that maps $S^3 \\rightarrow S^3$ (the boundary of Euclideanized spacetime), which comes from ...\n55 views\n\n### Geodesics in Kerr\n\nI'm interested in plotting the trajectories of null geodesics near an uncharged rotating black hole (described by the Kerr solution) which involves a system of first order differential equations. Kerr ...\n68 views\n\n### Could the universe have non-vanishing net colour charge?\n\nI've heard that the strong force doesn't decrease in strength with increasing distance, and that's why quarks must be confined within hadrons. But could there be, say, a single quark out there, so ...\n48 views\n\n### Is wireless power viable? [on hold]\n\nI had a quick read over the Wikipedia article for wireless power. It gives an overview of different methods of wireless power transmission, but doesn't elaborate as to its current usage or efficiency. ...\n47 views\n\n### Definition of causality relation\n\nIt seems to me that special relativity has a weird definition of the causality relation. In that theory, the only thing that matters is the space-time distance between events. But I don't think this ...\n17 views\n\n### Why do these papers show the wrong concavity to the conductivity near the percolation threshold?\n\nI'm looking at two papers in particular: A. L. Efros and B. I. Shklovskii, Critical Behaviour of Conductivity and Dielectric Constant near the Metal-Non-Metal Transition Threshold, Phys. Status Solidi ...\n26 views\n\n### Given two events such that either one of them is 'on the light cone' of the other, do they constitute a 'null interval'?\n\nOne basic part of determining a metric (or applicable generalization) of a given set $\\cal S$ of events (up to an arbitrary non-zero constant) is to determine to which pairs among those events, ...\n148 views\n\n### Redshift of Cosmic Microwave Background\n\nDoes the cosmic microwave background radiation have a red shift parameter z? If so what is the value for z?\n119 views\n\n### Is it possible to produce images of pair production in home-made cloud chamber?\n\nThere are some nice pictures on the web showing the counter-spiralling paths of an electron positron pair produced in a bubble chamber with a uniform magnetic field, for example:- Would it be ...\n40 views\n\n### Length contraction and simultaneous length measurements\n\nI am just working through an argument from Halliday Resnick to derive the Lorentz contraction (see quote below). Some paragraphs before this, the authors note that: If the rod is moving, ...\n112 views\n\n### Moon's orbit period as seen from a spaceship traveling at 0.8c\n\nI am studying special relativity and I am trying to figure out the following small problem which occurred to me: An observer, the pilot of a spaceship flying to or from earth at v = 0.8c, is ...\n40 views\n\n27 views\n\n### Formula to find angle of projectile motion [on hold]\n\nI want to be able to modify the angle at which the bullet follows projectile motion in order to hit the object which is moving horizontally (from right to left) and the projectile motion is starting ...\n19 views\n\n### What is the symmetry of the Penrose tiling? [migrated]\n\nWhat is the symmetry of the Penrose tiling? Simply C5 or bigger? Any simple proof that the tiling is a complete cover of the plane?\n36 views\n\n### Noncommutative Field Quantization\n\nI'm studying noncommutative (quantum) field theory, and I have confusion need to be clear. I'm reading Szabo's and Douglas's .pdf of noncommutative QFT. As I understand, in the book they just ...\n51 views\n\n### velocity of light [on hold]\n\nWe have assumed in the last 100 years or so, due to great minds and their diligent attitude, that nothing surpasses velocity of light. But nature knows no barriers. Exceeding that velocity transcends ...\n41 views\n\n### Ghosts in theories of gravity and holographic theories\n\nI want to understand when a theory leads to ghosts in gravity. Is there any relation between ghosts and non-linear higher order theories? Ghost is a clasical or quantum field concept?\n51 views\n\n### Positive charges \u201cmove\u201d from higher to lower potential [on hold]\n\nIt's my understanding that whenever an object gains or loses electric charge this actually corresponds to losing\/gaining electrons (protons do not move). 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Many scientific experiments I've come across use segmented electrodes (like in ...\n30 views\n\n### Compactification and off-diagonal terms of the metric tensor\n\nIn standard 3+1 dimensional spacetime, the metric tensor is of order 4 and had ten independent coefficients, hence there are 6 terms off the diagonal in the corresponding $4\\times 4$ real symmetric ...\n50 views\n\n### Is static friction an impulsive force?\n\nFor example: let's consider a static sphere on an horizontal rough surface. I apply an impulse $J$ parallel to the ground and in the middle of the sphere. If, like my book says, the friction is not an ...\n40 views\n\n### Do randomness and indeterminacy in Quantum Physics mean the same?\n\nI have been trying to learn about the randomness in Quantum Physics. But of the many sources I referred to, some say about \"Randomness in Quantum physics\" and some others say about \"Quantum ...\n397 views\n\n### Thoughts on the ice cube from orbit problem\n\nLet's say we have a really exquisite cocktail party somewhere in New Mexico, and we just ran out of ice cubes. To the rescue comes this new service provided by Orbital Glacier Inc. They provide ice ...\n69 views\n\n### The Eigenstate Existence Problem in Dirac's 'Principles of Quantum Mechanics'\n\nIn Chapter II of Dirac's Principles of Quantum Mechanics, Dirac explains that in general it is very difficult to know whether, for a given real linear operator, that any eigenvalues\/eigenvectors exist ...\n32 views\n\n### Reference Request: Fluid dynamics\/Elasticity via Lagrangians\n\nWould there be a book that does what Landau does in Fluid Mechanics and Theory of Elasticity using Lagrangian's\/Action-principles, analogous to the presentation in Landau's mechanics? I have only ...\n36 views\n\n### Traces in different representation\n\nI am actually working with Green-Schwarz anomaly cancellation mechanism in which I have came across a strange formula which relates trace in the adjoint representation (Tr) to trace in fundamental ...\n37 views\n\n### If space-time continuum exists in nature then where is mass? [on hold]\n\nIf space-time continuum exists in nature then what is its relation to mass? Does mass exist unaffected in S-T continuum, or , does the S-T exist without affecting the mass in any way. If gravity ...\n81 views\n\n### Why does the action have to be hermitian?\n\nThe hermiticity of operators of observables, e.g. the Hamiltonian, in QM is usually justified by saying that the eigenvalues must be real valued. I know that the Lagrangian is just a Legendre ...\n100 views\n\n### What is the analogy of $|x\\rangle$ in quantum field theory?\n\nLet me start from path integral formulation in quantum mechanics and quantum field theory. In QM, we have $$U(x_b,x_a;T) = \\langle x_b | U(T) |x_a \\rangle= \\int \\mathcal{D}q e^{iS} \\tag{1}$$ ...\n4k views\n\n### Which ball touches the ground first?\n\nThis is a very well known problem, but I can't find an answer in the specific case I'm looking for. Let's consider two balls : Ball 1 weighs 10 kg Ball 2 weighs 1 kg Balls have identical volumes ...\n49 views\n\n### CPT invariance of Dirac equation\n\nWe know that Dirac equation is $$( i \\partial _\\mu \\gamma ^\\mu - m ) \\psi ~=~0.$$ How can we show that Dirac equation is invariant under CPT transformation?\n51 views\n\n### Aharonov-Bohm Effect electricity generation\n\nThis question is based on highly intuitive picture of the Aharonov-Bohm effect (perhaps a naive one). From what I have read, the current explanation of the AB effect is that although the electron ...\n19 views\n\n### Energy comparison, evaporate water vs compress air, same mass\n\nI would like to compare the energy requirements of the 2 following tasks: Total energy to evaporate 1 litre of water at normal atmospheric pressure at normal temperature? Total energy to compress ...\nThe viscous Burgers' equation: $$q_{t}+q\\:q_{x}~=~\\nu\\:q_{xx}, \\mbox{ where } \\:\\:\\nu >0,$$ combines the nonlinear propagation of $q(x,t)$ and the diffusion. What is this equation for? (in ...","date":"2014-07-26 03:13:59","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 1, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8972845673561096, \"perplexity\": 822.9784465162649}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2014-23\/segments\/1405997894976.0\/warc\/CC-MAIN-20140722025814-00035-ip-10-33-131-23.ec2.internal.warc.gz\"}"} | null | null |
Q: Verificar arquivos que possuem determinada palavra - Python (Biblioteca os) Tenho o código abaixo ao qual eu acesso uma determinada pasta e trago o nome de todos os arquivos com extensão .asp.
import glob
import os
os.chdir('G:\PASTA\SUBPASTA')
for file in glob.glob('*.asp'):
print(file)
Preciso melhorar esse código da seguinte forma:
Acessar arquivo por arquivo contido na pasta e identificar quais arquivos possuem uma determinada palavra dentro dele.
Exemplo:
Quais arquivos possuem a palavra bench e em seguida trazer a lista encontrada, tal como:
G:\PASTA\SUBPASTA\Arquivo.asp
G:\PASTA\SUBPASTA\ArquivoXPTO.asp
A: Você precisa abrir o conteúdo do arquivo primeiramente e depois realizar uma leitura verificando se a palavra deseja está dentro do arquivo.
Como abrir arquivo em Python ?
Para abrir um arquivo em Python utilize a função open().
Nessa função você deverá passar o caminho do arquivo (só é necessário o nome caso o arquivo esteja no mesmo diretório do seu programa ) e o modo de abertura.
Como ler arquivos em Python ?
Após abrir o arquivo você precisará ler o conteúdo. Para isso existem três métodos que você pode usar: read(), readline() e readlines().
No seu caso, eu recomendo utilizar o read() para agilizar tudo.
Fechando o arquivo.
Depois de abrir e fazer a leitura do arquivo, você deverá fechá-lo utilizando o método close(). Após utilizar este método, você não poderá mais acessar o conteúdo deste arquivo até que o mesmo seja aberto novamente.
Como ficaria meu código após isso tudo ?
import glob
import os
key = "<Digite a palavra aqui>"
os.chdir('G:\PASTA\SUBPASTA')
for filename in glob.glob('*.asp'):
print("Verificando o arquivo",filename,"...")
file = open(filename)
if key in file.read():
print("A palavra",key,"existe no arquivo",filename+"!")
file.close()
Eu recomendo que você estude mais sobre o open(), pois existem muito mais coisas nele que podem ser úteis para você.
| {
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Particle and vapor emissions from vat polymerization desktop-scale 3-dimensional printers
A. B. Stefaniak, L. N. Bowers, A. K. Knepp, T. P. Luxton, D. M. Peloquin, E. J. Baumann, J. E. Ham, J. R. Wells, A. R. Johnson, R. F. LeBouf, F.-C. Su, S. B. Martin (+1 others)
2019 Figshare
https://web.archive.org/web/20200209204634/https://s3-eu-west-1.amazonaws.com/pstorage-tf-iopjsd8797887/15168794/uoeh_a_1612068_sm7421.pdf
Little is known about emissions and exposure potential from vat polymerization additive manufacturing, a process that uses light-activated polymerization of a resin to build an object. Five vat polymerization printers (three stereolithography (SLA) and two digital light processing (DLP) were evaluated individually in a 12.85 m3 chamber. Aerosols (number, size) and total volatile organic compounds (TVOC) were measured using real-time monitors. Carbonyl vapors and particulate matter were more » ... for offline analysis using impingers and filters, respectively. During printing, particle emission yields (#/g printed) ranged from 1.3 ± 0.3 to 2.8 ± 2.6 x 108 (SLA printers) and from 3.3 ± 1.5 to 9.2 ± 3.0 x 108 (DLP printers). Yields for number of particles with sizes 5.6 to 560 nm (#/g printed) were 0.8 ± 0.1 to 2.1 ± 0.9 x 1010 and from 1.1 ± 0.3 to 4.0 ± 1.2 x 1010 for SLA and DLP printers, respectively. TVOC yield values (µg/g printed) ranged from 161 ± 47 to 322 ± 229 (SLA printers) and from 1281 ± 313 to 1931 ± 234 (DLP printers). Geometric mean mobility particle sizes were 41.1–45.1 nm for SLA printers and 15.3–28.8 nm for DLP printers. Mean particle and TVOC yields were statistically significantly higher and mean particle sizes were significantly smaller for DLP printers compared with SLA printers (p < 0.05). Energy dispersive X-ray analysis of individual particles qualitatively identified potential occupational carcinogens (chromium, nickel) as well as reactive metals implicated in generation of reactive oxygen species (iron, zinc). Lung deposition modeling indicates that about 15–37% of emitted particles would deposit in the pulmonary region (alveoli). Benzaldehyde (1.0–2.3 ppb) and acetone (0.7–18.0 ppb) were quantified in emissions from four of the printers and 4-oxopentanal (0.07 ppb) was detectable in the emissions from one printer. Vat polymerization printers emitted nanoscale particles that contained potential carcinogens, sensitizers, and reacti [...]
doi:10.6084/m9.figshare.8138861 fatcat:mdqnyluuh5gapd2nkolpwvwvjm
figshare.com
A. B. Stefaniak, L. N. Bowers, A. K. Knepp, T. P. Luxton, D. M. Peloquin, E. J. Baumann, J. E. Ham, J. R. Wells, A. R. Johnson, R. F. LeBouf, F.-C. Su, S. B. Martin, M. A. Virji. "Particle and vapor emissions from vat polymerization desktop-scale 3-dimensional printers." Figshare (2019) | {
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Q: Check if any array inside another array contains a value from another array I have an array of arrays aa = [[value, value2], [value3, value4]]
and I need to check if my new array a = [value2, value7]
includes any value from aa
I had tried this code and then i tried with adding .every to the aa but doesnt work. what should i do
a.some(r=> aa.includes(r))
a.some(r=> aa.every.includes(r))
A: Since you are using a nested array, you will want to use Array.prototype.flat on the aa array first. This will convert:
[[value, value2], [value3, value4]]
...to:
[value, value2, value3, value4]
See proof-of-concept below:
const aa = [[1, 2], [3, 4]];
const a = [2, 7];
// Flatten nested arrays
const aaFlat = aa.flat();
console.log(a.some(x => aaFlat.includes(x)));
| {
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Q: Omnetpp .ned file default value of parameter I'm trying to get familiar with Omnetpp, so I'm doing the TicToc example. But there I found a point I do not understand: Why does the default value of limit not work? Limit is always set to 5, only if I set it to an other value like I did it in Toc5.
Here my log from Txc5::initialize
Initializing module Tictoc5, stage 0
Tictoc5.tic: Initializing module Tictoc5.tic, stage 0
Tictoc5.tic: limit is 10
Tictoc5.tic: tic's counter is set to 10
Tictoc5.tic: Sending initial message
Tictoc5.toc: Initializing module Tictoc5.toc, stage 0
Tictoc5.toc: limit is 5
Tictoc5.toc: toc's counter is set to 5
Here you can see, tic's counter was set to 10, this is ok, but toc's counter is to 5.
I do not understand why its not set to 20, like I have said in int limit = default(20);
I have tictoc5.ned:
simple Txc5
{
parameters:
bool sendMsgOnInit = default(false);
int limit = default(20);
@display("i=block/routing");
gates:
input in;
output out;
}
simple Tic5 extends Txc5
{
parameters:
@display("i=,cyan");
sendMsgOnInit = true;
limit = 10;
}
simple Toc5 extends Txc5
{
parameters:
@display("i=,gold");
}
network Tictoc5
{
submodules:
tic: Tic5;
toc: Toc5;
connections:
tic.out --> { delay = 100ms; } --> toc.in;
tic.in <-- { delay = 100ms; } <-- toc.out;
}
and I have txc5.cc
#include <string.h>
#include <omnetpp.h>
class Txc5 : public cSimpleModule
{
private:
int counter;
protected:
virtual void initialize();
virtual void handleMessage(cMessage *msg);
};
Define_Module(Txc5);
void Txc5::initialize()
{
counter = par("limit");
EV << "limit is " << (int)par("limit") << " \n";
EV << getName() << "'s counter is set to " << counter << "\n";
if (par("sendMsgOnInit").boolValue() == true)
{
// The `ev' object works like `cout' in C++.
EV << "Sending initial message\n";
cMessage *msg = new cMessage("tictocMsg");
send(msg, "out");
}
}
void Txc5::handleMessage(cMessage *msg)
{
counter--;
if(counter == 0) {
EV << getName() << "'s counter reached zero, deleting message \n";
} else {
EV << getName() << "'s counter is " << counter << "\n";
EV << "Received message `" << msg->getName() << "', sending it out again\n";
send(msg, "out");
}
}
A: The default value of parameter is taken from NED provided that there is no matched entry for this parameter in omnetpp.ini file (and the parameter isn't hardcoded - explanation later). In omnetpp.ini for Tictoc5 example there is following entry: **.limit = 5
Therefore for Toc5 limit is equal to 5.
However, in definition of Tic5 in NED line: limit = 10 means that the value of limit parameter is hardcoded to 10. And according to OMNeT++ Manual hardcoded parameter:
*
*cannot be overwritten by value from omnetpp.ini
file
*doesn't take default value anymore
| {
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La Symphonie en do mineur op. 29 est la seconde des trois symphonies écrites par Alexandre Scriabine.
Elle est achevée en 1901, soit un an après sa première symphonie. La première a été donnée à Saint-Pétersbourg le sous la direction de Anatoli Liadov. L'accueil fut un échec.
Elle se compose de cinq mouvements et son exécution demande un peu plus de quarante minutes.
Andante
Allegro
Andante
Tempestuoso
Maestoso
Notes et références
Liens externes
Scriabine|02
2 | {
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.background{
width: 100%;
height: 100%;
position: fixed;
top: 0;
left: 0;
z-index: -1;
opacity: 0.6;
background: url('~Static/building-1245986_1920.jpg') no-repeat center center fixed;
background-attachment: fixed;
-webkit-background-size: cover;
-moz-background-size: cover;
-o-background-size: cover;
background-size: cover;
}
/*from url no-repeat until the end is optional, only to keep img fixed as background cover*/ | {
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The PER42UDOOR is a 42U Door for the PER1216 AV Equipment Rack. It features a mesh front, and literally snaps in place. A Lock built-in and includes 2 sets of keys. Can be installed front or back, and can also swing out left or right. | {
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Q: Getting started with Google-App-Engine Java Servlets I am doing my first GAE project using Eclipse Lunar. On the GAE server I shall have 3 datastore objects as follows:
*
*Registry
*RegistrationNumbers
*Subscriptions
I have designed 18 commands to service these 3 datastore objects. Each command shall be implemented as a Java Servlet where most will have a 'session' object in the 'HttpServletRequest' parameters. The command Servlets shall be used from a Web Page [HTML] or from a Java stand alone applications...
I shall build one GAE application with an Eclipse Project name of 'MyServlets' and a package name of 'myServlets'. The 'MyServlets' GAE application shall contain the 18 Java Servlets...
I need help getting started. I am not building a Web App. I am looking for the best way to create, debug and deploy the 18 command Servlets to the GAE server. I have successfully loaded the GAE and GWT Eclipse Plugins although I do not think I need the GWT capability.
Questions :
1) I am at the point where I need advice on what Eclipse Project should I use to build the .war file I need to deploy my servlets to the GAE server?
2) in my attempt to setup the Eclipse Lunar system for this effort I have several plugins that I don't think I need. If I delete them from the eclipse-Lunar/plugins folder are they gone entirely or is there a better way to get rid of them?
A:
I am doing my first GAE project using Eclipse Lunar. On the GAE server I > shall have 3 datastore objects as follows:
Registry
RegistrationNumbers
Subscriptions
I now understand that a datastore should be considered as a collection of HashMaps. All my datastore HashMap keys shall commence with a GAE ID assigned to my account. The above datastore objects shall be implemented as individual HashMaps with the following codes concatenated to the GAE ID:
"R" - Registry; "N" - RegistrationNumbers; "S" - Subscriptions...
Next, a HashMap Unique ID is appended to each key...
1) I am at the point where I need advice on what Eclipse Project should I > use to build the .war file I need to deploy my servlets to the GAE
server?
After loading the GAE Eclipse Plugins I used the Eclipse menu to navigate to the new/Google/New Web ApplicationProject wizard. During the creation process, I Uncheck the "Use Google Web Toolkit" checkbox...
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,253 |
Republic Plaza es un rascacielos en Denver (Colorado, Estados Unidos). Con 218 metros es el edificio más alto de la ciudad de Denver, del estado de Colorado y toda la región de las Montañas Rocosas. El Republic Plaza se sitúa actualmente como el ciento noveno edificio más alto de los Estados Unidos.
Fue construido en 1984 y tiene 56 pisos, la mayoría de los cuales se utilizan como espacio de oficinas. Diseñado por Skidmore, Owings & Merrill fue construido de hormigón armado revestido en granito sardo.
El 27 de octubre de 2007, los 20 pisos superiores del edificio fueron iluminados de color morado con las gigantescas letras "C" y "R" en blanco, para celebrar el debut de los Colorado Rockies.
Véase también
Anexo:Edificios más altos de Estados Unidos por estado
Galería de imágenes
Enlaces externos
Republic Plaza, página web oficial
Obras de Skidmore, Owings and Merrill
Edificios de oficinas de Estados Unidos de los años 1980
Rascacielos de oficinas de Denver
Arquitectura de Estados Unidos de 1984
Rascacielos de Estados Unidos entre 200 y 249 metros
Rascacielos inaugurados en 1984 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,202 |
{"url":"http:\/\/www.caam.rice.edu\/~lc55\/SFEMaNS\/html\/doc_SFEMaNS_condlim_sigma_bar_in_fourier_space.html","text":"SFEMaNS \u00a0version 4.1 (work in progress) Reference documentation for SFEMaNS\nThe function sigma_bar_in_fourier_space\n\nIt is used to define a stabilization term $$\\overline{\\sigma}(r,z)$$ for multiphase problems where the electrical conductivity varies between the fluids considered. We refer to the section Extension to multiphase flow problem for more information on the formulation of the Navier-Stokes equations in SFEMaNS.\n\nThis function defines a scalar function depending only of the radial and vertical coordinates. It is defined on the nodes of the finite element mesh.\n\n### Inputs and outputs\n\nThe input of this function the mesh H_mesh where the magnetic field is approximated.\n\nThe output of this function is a real valued tabular vv of dimension SIZE(H_meshrr,2). It is equal to the number of nodes, H_mesh%np, of the finite element mesh used to approximate the magnetic field.\n\nRemark:\n\n1. The electrical conducitivites of the fluids are set in the data as follows.\n===Conductivity of fluid 0, fluid 1, ...\n1.d0 2.d0\n2. These electrical conductivities are stored in the variable inputs%sigma_fluid. It is a real valued tabular of dimension the number of fluids considered.\n\n### Exemple\n\nHere is an exemple where we set the stabilization term $$\\overline{\\sigma}$$ to half of the minimum of the fluids electrical conductivities.\n\nThe corresponding code lines are written as follows.\n\nvv=0.5d0*MINVAL(inputs%sigma_fluid)\nRETURN\n\nWe refer to the sections Examples with manufactured solutions and Examples on physical problems for more examples.","date":"2018-01-22 04:22:28","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8373315930366516, \"perplexity\": 917.7191874682036}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-05\/segments\/1516084890991.69\/warc\/CC-MAIN-20180122034327-20180122054327-00086.warc.gz\"}"} | null | null |
LIFT OFF - Robin Pawlak is launching his first book Space Cadets for readers at Gateway Christian School on Feb 28th. Michelle Falk/Red Deer Express
Retired Red Deer teacher launches first book for kids
Space Cadets takes kids on an imaginative journey into space
Robin Pawlak, a teacher in Red Deer, who's taught for 31 years, is launching his first book Space Cadets for readers at Gateway Christian School on Feb 28th.
"When I retired in the summer of 2016, it was to pursue the dream of a second career as an author," Pawlak said.
He credits his Language Arts students at Grandview Elementary School and Gateway Christian School for encouraging him in persuing his writing career.
"They loved the story and kept telling me to get it published," Pawlak said of his students.
Pawlak has been reading the novel to students since he completed the first draft 19 years ago.
Space Cadets is the story of Simon, a daydreamer, and his twin sister Casey, who prefers to stay grounded in reality. The pair winds up on a wild adventure in space after being zapped by an invention they discover in their father's off-limits workshop. Their dad's invention turns Simon's imaginings into their new reality.
The twins are taken prisoner by aliens and have to fight for freedom and face danger, but still enjoy laughs along the way as they struggle to escape their captors or be trapped in space forever.
Pawlak has a real edge as a writer because he worked closely with his target audience for so long.
He said something that he saw a lot of with traditional publishing is books that adults think kids will like, but not books that were actually things kids wanted to read.
The 12-year-old protagonists in the book are true to life and believable because of Pawlak's career teaching pre-teens.
Now re-inventing himself as an author, Pawlak is open about the fact that he still feels most at home in schools.
He enjoys sharing his book with students and looks forward to his book tour where he will visit schools around the province.
Pawlak is also sharing his insights as a teacher and writer with other teachers, speaking at teacher's conferences on the value of story and how to use it in the classroom and giving practical tips for teaching students how to write.
The book will be offically launched at Gateway Christian School, where Pawlak finished his teaching career.
"I have remained connected to the very supportive school community at Gateway since retiring," he said.
Pawlak has done about six author visits to the school leading up to the book launch, and over 100 copies of Space Cadets have already been pre-ordered.
"It has been a treat to interact with these very enthusiastic children," Pawlak said. "The youngest ones only know me as an author, but the older ones as their former teacher—their support has been overwhelming."
After his book tour, he plans to jump right into working on his next novel.
Pawlak's novel Space Cadets is available for purchase on Amazon.
Lacombe Police uncover 779 grams of suspected cocaine
Green Carts rolling out in Red Deer this week | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 6,414 |
/*
TODO:
add destroy method to terminal (cmd alrady have it)
add support for - $(...).each(function() { ... });
$.fn.pluginname = function(options) {
var settings = $.extend({}, $.fn.pluginname.defaultOptions, options);
return this.each(function() {
var $this = $(this);
});
$.fn.pluginname.defaultOptions = {
};
};
distinguish between paused and disabled
paused should block keydown in terminal it should disable command line
disable
*/
// return true if value is in array
Array.prototype.has = function(val) {
"use strict";
for (var i = this.length; i--;) {
if (this[i] === val) {
return true;
}
}
return false;
};
// debug function
function get_stack(caller) {
"use strict";
if (caller) {
return [caller.toString().match(/.*\n.*\n/)].concat(get_stack(caller.caller));
} else {
return [];
}
}
(function($, undefined) {
"use strict";
// ----------------------------------------
// START Storage plugin
// ----------------------------------------
// Private data
var isLS = typeof window.localStorage !== 'undefined';
// Private functions
function wls(n, v) {
var c;
if (typeof n === 'string' && typeof v === 'string') {
localStorage[n] = v;
return true;
} else if (typeof n === 'object' && typeof v === 'undefined') {
for (c in n) {
if (n.hasOwnProperty(c)) {
localStorage[c] = n[c];
}
}
return true;
}
return false;
}
function wc(n, v) {
var dt, e, c;
dt = new Date();
dt.setTime(dt.getTime() + 31536000000);
e = '; expires=' + dt.toGMTString();
if (typeof n === 'string' && typeof v === 'string') {
document.cookie = n + '=' + v + e + '; path=/';
return true;
} else if (typeof n === 'object' && typeof v === 'undefined') {
for (c in n) {
if (n.hasOwnProperty(c)) {
document.cookie = c + '=' + n[c] + e + '; path=/';
}
}
return true;
}
return false;
}
function rls(n) {
return localStorage[n];
}
function rc(n) {
var nn, ca, i, c;
nn = n + '=';
ca = document.cookie.split(';');
for (i = 0; i < ca.length; i++) {
c = ca[i];
while (c.charAt(0) === ' ') {
c = c.substring(1, c.length);
}
if (c.indexOf(nn) === 0) {
return c.substring(nn.length, c.length);
}
}
return null;
}
function dls(n) {
return delete localStorage[n];
}
function dc(n) {
return wc(n, '', -1);
}
/**
* Public API
* $.Storage.set("name", "value")
* $.Storage.set({"name1":"value1", "name2":"value2", etc})
* $.Storage.get("name")
* $.Storage.remove("name")
*/
$.extend({
Storage: {
set: isLS ? wls : wc,
get: isLS ? rls : rc,
remove: isLS ? dls : dc
}
});
// ----------------------------------------
// END Storage plugin
// ----------------------------------------
// START jQuery Timers
// ----------------------------------------
jQuery.fn.extend({
everyTime: function(interval, label, fn, times, belay) {
return this.each(function() {
jQuery.timer.add(this, interval, label, fn, times, belay);
});
},
oneTime: function(interval, label, fn) {
return this.each(function() {
jQuery.timer.add(this, interval, label, fn, 1);
});
},
stopTime: function(label, fn) {
return this.each(function() {
jQuery.timer.remove(this, label, fn);
});
}
});
jQuery.extend({
timer: {
guid: 1,
global: {},
regex: /^([0-9]+)\s*(.*s)?$/,
powers: {
// Yeah this is major overkill...
'ms': 1,
'cs': 10,
'ds': 100,
's': 1000,
'das': 10000,
'hs': 100000,
'ks': 1000000
},
timeParse: function(value) {
if (value === undefined || value === null) {
return null;
}
var result = this.regex.exec(jQuery.trim(value.toString()));
if (result[2]) {
var num = parseInt(result[1], 10);
var mult = this.powers[result[2]] || 1;
return num * mult;
} else {
return value;
}
},
add: function(element, interval, label, fn, times, belay) {
var counter = 0;
if (jQuery.isFunction(label)) {
if (!times) {
times = fn;
}
fn = label;
label = interval;
}
interval = jQuery.timer.timeParse(interval);
if (typeof interval !== 'number' ||
isNaN(interval) ||
interval <= 0) {
return;
}
if (times && times.constructor !== Number) {
belay = !!times;
times = 0;
}
times = times || 0;
belay = belay || false;
if (!element.$timers) {
element.$timers = {};
}
if (!element.$timers[label]) {
element.$timers[label] = {};
}
fn.$timerID = fn.$timerID || this.guid++;
var handler = function() {
if (belay && this.inProgress) {
return;
}
this.inProgress = true;
if ((++counter > times && times !== 0) ||
fn.call(element, counter) === false) {
jQuery.timer.remove(element, label, fn);
}
this.inProgress = false;
};
handler.$timerID = fn.$timerID;
if (!element.$timers[label][fn.$timerID]) {
element.$timers[label][fn.$timerID] = window.setInterval(handler, interval);
}
if (!this.global[label]) {
this.global[label] = [];
}
this.global[label].push(element);
},
remove: function(element, label, fn) {
var timers = element.$timers, ret;
if (timers) {
if (!label) {
for (var lab in timers) {
if (timers.hasOwnProperty(lab)) {
this.remove(element, lab, fn);
}
}
} else if (timers[label]) {
if (fn) {
if (fn.$timerID) {
window.clearInterval(timers[label][fn.$timerID]);
delete timers[label][fn.$timerID];
}
} else {
for (var _fn in timers[label]) {
if (timers[label].hasOwnProperty(_fn)) {
window.clearInterval(timers[label][_fn]);
delete timers[label][_fn];
}
}
}
for (ret in timers[label]) {
if (timers[label].hasOwnProperty(ret)) {
break;
}
}
if (!ret) {
ret = null;
delete timers[label];
}
}
for (ret in timers) {
if (timers.hasOwnProperty(ret)) {
break;
}
}
if (!ret) {
element.$timers = null;
}
}
}
}
});
if (jQuery.browser.msie) {
jQuery(window).one('unload', function() {
var global = jQuery.timer.global;
for (var label in global) {
if (global.hasOwnProperty(label)) {
var els = global[label], i = els.length;
while (--i) {
jQuery.timer.remove(els[i], label);
}
}
}
});
}
// ----------------------------------------
// START CROSS BROWSER SPLIT
// ----------------------------------------
var split;
// Avoid running twice; that would break the `nativeSplit` reference
split = split || function (undef) {
var nativeSplit = String.prototype.split,
compliantExecNpcg = /()??/.exec("")[1] === undef, // NPCG: nonparticipating capturing group
self;
self = function (str, separator, limit) {
// If `separator` is not a regex, use `nativeSplit`
if (Object.prototype.toString.call(separator) !== "[object RegExp]") {
return nativeSplit.call(str, separator, limit);
}
var output = [],
flags = (separator.ignoreCase ? "i" : "") +
(separator.multiline ? "m" : "") +
(separator.extended ? "x" : "") + // Proposed for ES6
(separator.sticky ? "y" : ""), // Firefox 3+
lastLastIndex = 0,
// Make `global` and avoid `lastIndex` issues by working with a copy
separator2, match, lastIndex, lastLength;
separator = new RegExp(separator.source, flags + "g");
str += ""; // Type-convert
if (!compliantExecNpcg) {
// Doesn't need flags gy, but they don't hurt
separator2 = new RegExp("^" + separator.source + "$(?!\\s)", flags);
}
/* Values for `limit`, per the spec:
* If undefined: 4294967295 // Math.pow(2, 32) - 1
* If 0, Infinity, or NaN: 0
* If positive number: limit = Math.floor(limit); if (limit > 4294967295) limit -= 4294967296;
* If negative number: 4294967296 - Math.floor(Math.abs(limit))
* If other: Type-convert, then use the above rules
*/
// ? Math.pow(2, 32) - 1 : ToUint32(limit)
limit = limit === undef ? -1 >>> 0 : limit >>> 0;
while (match = separator.exec(str)) {
// `separator.lastIndex` is not reliable cross-browser
lastIndex = match.index + match[0].length;
if (lastIndex > lastLastIndex) {
output.push(str.slice(lastLastIndex, match.index));
// Fix browsers whose `exec` methods don't consistently return `undefined` for
// nonparticipating capturing groups
if (!compliantExecNpcg && match.length > 1) {
match[0].replace(separator2, function () {
for (var i = 1; i < arguments.length - 2; i++) {
if (arguments[i] === undef) {
match[i] = undef;
}
}
});
}
if (match.length > 1 && match.index < str.length) {
Array.prototype.push.apply(output, match.slice(1));
}
lastLength = match[0].length;
lastLastIndex = lastIndex;
if (output.length >= limit) {
break;
}
}
if (separator.lastIndex === match.index) {
separator.lastIndex++; // Avoid an infinite loop
}
}
if (lastLastIndex === str.length) {
if (lastLength || !separator.test("")) {
output.push("");
}
} else {
output.push(str.slice(lastLastIndex));
}
return output.length > limit ? output.slice(0, limit) : output;
};
// For convenience
String.prototype.split = function (separator, limit) {
return self(this, separator, limit);
};
return self;
}();
// -----------------------------------------------------------------------
/*
function decodeHTML(str) {
if (typeof str === 'string') {
str = str.replace(/&/g, '&');
str = str.replace(/</g, '<').replace(/>/g, '>');
str = str.replace(/	/g, '\t');
str = str.replace(/<br\/?>/g, '\n').replace(/ /g, ' ');
return str;
} else {
return '';
}
}
*/
//split string to array of strings with the same length
function str_parts(str, length) {
var result = [];
var len = str.length;
if (len < length) {
return [str];
}
for (var i = 0; i < len; i += length) {
result.push(str.substring(i, i + length));
}
return result;
}
// -----------------------------------------------------------------------
var format_split_re = /(\[\[[bius]*;[^;]*;[^\]]*\][^\]\[]*\])/g;
var format_re = /\[\[([bius]*);([^;]*);([^\]]*)\]([^\]\[]*)\]/g;
var color_hex_re = /#([0-9A-Fa-f]{3}|[0-9A-Fa-f]{6})/;
function encodeHTML(str) {
if (typeof str === 'string') {
// don't escape entities
str = str.replace(/&(?!#[0-9]+;|[a-zA-Z]+;)/g, '&');
str = str.replace(/</g, '<').replace(/>/g, '>');
// I don't think that it find \n
str = str.replace(/\n/g, '<br/>');
str = str.replace(/ /g, ' ');
str = str.replace(/\t/g, ' ');
//support for formating foo[[u;;]bar]baz[[b;#fff;]quux]zzz
var splited = str.split(format_split_re);
//console.log($.json_stringify(splited));
if (splited.length > 1) {
str = $.map(splited, function(text) {
if (text === '') {
return text;
} else if (text.substring(0,1) === '[') {
// use substring for IE quirks mode - [0] don't work
return text.replace(format_re, function(s,
style,
color,
background,
text) {
if (text === '') {
return '<span> </span>';
}
var style_str = '';
if (style.indexOf('b') !== -1) {
style_str += 'font-weight:bold;';
}
var text_decoration = 'text-decoration:';
if (style.indexOf('u') !== -1) {
text_decoration += 'underline ';
}
if (style.indexOf('s') !== -1) {
text_decoration += 'line-through';
}
if (style.indexOf('s') !== -1 ||
style.indexOf('u') !== -1) {
style_str += text_decoration + ';';
}
if (style.indexOf('i') !== -1) {
style_str += 'font-style:italic; ';
}
if (color.match(color_hex_re)) {
style_str += 'color:' + color + ';';
}
if (background.match(color_hex_re)) {
style_str += 'background-color:' + background;
}
str = '<span style="' + style_str + '">' + text +
'</span>';
return str;
});
} else {
return '<span>' + text + '</span>';
}
}).join('');
}
return str;
} else {
return '';
}
}
// -----------------------------------------------------------------------
//split string to array of strings with the same length and keep formatting
function get_formatted_lines(str, length) {
var array = str.split(/\n/g);
var re_format = /(\[\[[bius]*;[^;]*;[^\]]*\][^\]\[]*\]?)/g;
var re_begin = /(\[\[[bius]*;[^;]*;[^\]]*\])/;
var re_last = /\[\[[bius]*;?[^;]*;?[^\]]*\]?$/;
var formatting = false;
var in_text = false;
var braket = 0;
var prev_format = '';
var result = [];
for (var i = 0, len = array.length; i < len; ++i) {
if (prev_format !== '') {
if (array[i] === '') {
result.push(prev_format + ']');
continue;
} else {
array[i] = prev_format + array[i];
prev_format = '';
}
} else {
if (array[i] === '') {
result.push('');
continue;
}
}
var line = array[i];
var first_index = 0;
var count = 0;
for (var j=0, jlen=line.length; j<jlen; ++j) {
if (line[j] === '[' && line[j+1] === '[') {
formatting = true;
} else if (formatting && line[j] === ']') {
if (in_text) {
formatting = false;
in_text = false;
} else {
in_text = true;
}
} else if ((formatting && in_text) || !formatting) {
++count;
}
if (count === length || j === jlen-1) {
var output_line = line.substring(first_index, j+1);
if (prev_format) {
output_line = prev_format + output_line;
if (output_line.match(']')) {
prev_format = '';
}
}
first_index = j+1;
count = 0;
var matched = output_line.match(re_format);
if (matched) {
var last = matched[matched.length-1];
if (last[last.length-1] !== ']') {
prev_format = last.match(re_begin)[1];
output_line += ']';
} else if (output_line.match(re_last)) {
var line_len = output_line.length;
var f_len = line_len - last[last.length-1].length;
output_line = output_line.replace(re_last, '');
prev_format = last.match(re_begin)[1];
}
}
result.push(output_line);
}
}
}
return result;
}
// -----------------------------------------------------------------------
function skipFormattingCount(string) {
return string.replace(format_re, '$4').length;
}
// -----------------------------------------------------------------------
function formattingCount(string) {
return string.length - skipFormattingCount(string);
}
// -----------------------------------------------------------------------
// CYCLE DATA STRUCTURE
// -----------------------------------------------------------------------
function Cycle(init) {
var data = init ? [init] : [];
var pos = 0;
$.extend(this, {
rotate: function() {
if (data.length === 1) {
return data[0];
} else {
if (pos === data.length - 1) {
pos = 0;
} else {
++pos;
}
return data[pos];
}
},
length: function() {
return data.length;
},
set: function(item) {
for (var i = data.length; i--;) {
if (data[i] === item) {
pos = i;
return;
}
}
this.append(item);
},
front: function() {
return data[pos];
},
append: function(item) {
data.push(item);
}
});
}
// -----------------------------------------------------------------------
// :: BCYCLE DATA STRUCTURE // Two way cycle
// -----------------------------------------------------------------------
function BCycle(init) {
var data = init instanceof Array ? init : init ? [init] : [];
var pos = 0;
$.extend(this, {
left: function() {
if (pos === 0) {
pos = data.length - 1;
} else {
--pos;
}
return data[pos];
},
right: function() {
if (pos === data.length - 1) {
pos = 0;
} else {
++pos;
}
return data[pos];
},
current: function() {
return data[pos];
},
data: function() {
return data;
},
length: function() {
return data.length;
},
reset: function() {
pos = 0;
},
append: function(item) {
data.push(item);
this.reset();
}
});
}
// -----------------------------------------------------------------------
// :: STACK DATA STRUCTURE
// -----------------------------------------------------------------------
function Stack(init) {
var data = init ? [init] : [];
$.extend(this, {
size: function() {
return data.length;
},
pop: function() {
if (data.length === 0) {
return null;
} else {
var value = data[data.length - 1];
data = data.slice(0, data.length - 1);
return value;
}
},
push: function(value) {
data = data.concat([value]);
return value;
},
top: function() {
return data.length > 0 ? data[data.length - 1] : null;
}
});
}
// serialize object myself (biwascheme or prototype library do something
// wiked with JSON serialization for Arrays)
$.json_stringify = function(object, level) {
var result = '', i;
level = level === undefined ? 1 : level;
var type = typeof object;
switch (type) {
case 'function':
result += object;
break;
case 'boolean':
result += object ? 'true' : 'false';
break;
case 'object':
if (object === null) {
result += 'null';
} else if (object instanceof Array) {
result += '[';
var len = object.length;
for (i = 0; i < len - 1; ++i) {
result += $.json_stringify(object[i], level + 1);
}
result += $.json_stringify(object[len - 1], level + 1) + ']';
} else {
result += '{';
for (var property in object) {
if (object.hasOwnProperty(property)) {
result += '"' + property + '":' +
$.json_stringify(object[property], level + 1);
}
}
result += '}';
}
break;
case 'string':
var str = object;
var repl = {
'\\\\': '\\\\',
'"': '\\"',
'/': '\\/',
'\\n': '\\n',
'\\r': '\\r',
'\\t': '\\t'};
for (i in repl) {
if (repl.hasOwnProperty(i)) {
str = str.replace(new RegExp(i, 'g'), repl[i]);
}
}
result += '"' + str + '"';
break;
case 'number':
result += String(object);
break;
}
result += (level > 1 ? ',' : '');
// quick hacks below
if (level === 1) {
// fix last comma
result = result.replace(/,([\]}])/g, '$1');
}
// fix comma before array or object
return result.replace(/([\[{]),/g, '$1');
};
// -----------------------------------------------------------------------
// :: HISTORY CLASS
// -----------------------------------------------------------------------
function History(name) {
var enabled = true;
if (typeof name === 'string' && name !== '') {
name += '_';
}
var data = $.Storage.get(name + 'commands');
var bc = new BCycle(data ? eval('(' + data + ')') : ['']);
$.extend(this, {
append: function(item) {
if (enabled && bc.current() !== item) {
bc.append(item);
$.Storage.set(name + 'commands', $.json_stringify(bc.data()));
}
},
data: function() {
return bc.data();
},
next: function() {
return bc.right();
},
last: function() {
bc.reset();
},
previous: function() {
return bc.left();
},
clear: function() {
bc = new BCycle();
$.Storage.remove(name + 'commands');
},
enable: function() {
enabled = true;
},
disable: function() {
enabled = false;
}
});
}
// -----------------------------------------------------------------------
// :: COMMAND LINE PLUGIN
// -----------------------------------------------------------------------
$.fn.cmd = function(options) {
var self = this;
self.addClass('cmd');
self.append('<span class="prompt"></span><span></span>' +
'<span class="cursor"> </span><span></span>');
var clip = $('<textarea/>').addClass('clipboard').appendTo(self);
if (options.width) {
self.width(options.width);
}
var num_chars; // calculates by draw_prompt
var prompt_len;
var reverse_search = false;
var reverse_search_string = '';
var reverse_search_position = null;
var backup_prompt;
var mask = options.mask || false;
var command = '';
var position = 0;
var prompt;
var enabled = options.enabled;
var name, history;
var cursor = self.find('.cursor');
function blink(i) {
cursor.toggleClass('inverted');
}
function draw_reverse_prompt() {
prompt = "(reverse-i-search)`" + reverse_search_string + "': ";
draw_prompt();
}
function clear_reverse_state() {
prompt = backup_prompt;
reverse_search = false;
reverse_search_position = null;
reverse_search_string = '';
}
// if next is not defined or false it search for first item from the end
// if true it search for next item
function reverse_history_search(next) {
var history_data = history.data();
var regex = new RegExp('^' + reverse_search_string);
var len = history_data.length;
if (next && reverse_search_position > 0) {
len -= reverse_search_position;
}
for (var i=len; i--;) {
if (regex.test(history_data[i])) {
reverse_search_position = history_data.length - i;
position = 0;
self.set(history_data[i], true);
redraw();
break;
}
}
}
function change_num_chars() {
var W = self.width();
var w = cursor.innerWidth();
num_chars = Math.floor(W / w);
}
function str_repeat(str, n) {
var result = '';
for (var i = n; i--;) {
result += str;
}
return result;
}
function get_splited_command_line(string) {
/*
string = str_repeat('x', prompt_len) + string;
var result = get_formatted_lines(string);
result[0] = result[0].substring(prompt_len);
return result;
*/
var first = string.substring(0, num_chars - prompt_len);
var rest = string.substring(num_chars - prompt_len);
return [first].concat(str_parts(rest, num_chars));
}
var redraw = (function(self) {
var before = cursor.prev();
var after = cursor.next();
function draw_cursor_line(string, position) {
var len = string.length;
if (position === len) {
before.html(encodeHTML(string));
cursor.html(' ');
after.html('');
} else if (position === 0) {
before.html('');
//fix for tilda in IE
cursor.html(encodeHTML(string.slice(0, 1)));
//cursor.html(encodeHTML(string[0]));
after.html(encodeHTML(string.slice(1)));
} else {
var before_str = encodeHTML(string.slice(0, position));
before.html(before_str);
//fix for tilda in IE
var c = string.slice(position, position + 1);
//cursor.html(string[position]));
cursor.html(c === ' ' ? ' ' : encodeHTML(c));
if (position === string.length - 1) {
after.html('');
} else {
after.html(encodeHTML(string.slice(position + 1)));
}
}
}
function div(string) {
return '<div>' + encodeHTML(string) + '</div>';
}
function lines_after(lines) {
var last_ins = after;
$.each(lines, function(i, line) {
last_ins = $(div(line)).insertAfter(last_ins).
addClass('clear');
});
}
function lines_before(lines) {
$.each(lines, function(i, line) {
before.before(div(line));
});
}
var count = 0;
return function() {
var string = mask ? command.replace(/./g, '*') : command;
var i, first_len;
self.find('div').remove();
before.html('');
// long line
if (string.length > num_chars - prompt_len - 1 ||
string.match(/\n/)) {
var array;
var tabs = string.match(/\t/g);
var tabs_rm = tabs ? tabs.length * 3 : 0;
//quick tabulation hack
if (tabs) {
string = string.replace(/\t/g, '\x00\x00\x00\x00');
}
// command contain new line characters
if (string.match(/\n/)) {
var tmp = string.split("\n");
first_len = num_chars - prompt_len - 1;
// empty character after each line
for (i=0; i<tmp.length-1; ++i) {
tmp[i] += ' ';
}
// split first line
if (tmp[0].length > first_len) {
array = [tmp[0].substring(0, first_len)];
array = array.concat(str_parts(tmp[0].substring(first_len), num_chars));
} else {
array = [tmp[0]];
}
// process rest of the lines
for (i=1; i<tmp.length; ++i) {
if (tmp[i].length > num_chars) {
array = array.concat(str_parts(tmp[i], num_chars));
} else {
array.push(tmp[i]);
}
}
} else {
array = get_splited_command_line(string);
}
if (tabs) {
array = $.map(array, function(line) {
return line.replace(/\x00\x00\x00\x00/g, '\t');
});
}
first_len = array[0].length;
//cursor in first line
if (position < first_len) {
draw_cursor_line(array[0], position);
lines_after(array.slice(1));
} else if (position === first_len) {
before.before(div(array[0]));
draw_cursor_line(array[1], 0);
lines_after(array.slice(2));
} else {
var num_lines = array.length;
var offset = 0;
if (position < first_len) {
draw_cursor_line(array[0], position);
lines_after(array.slice(1));
} else if (position === first_len) {
before.before(div(array[0]));
draw_cursor_line(array[1], 0);
lines_after(array.slice(2));
} else {
var last = array.slice(-1)[0];
var from_last = string.length - position;
var last_len = last.length;
var pos = 0;
if (from_last <= last_len) {
lines_before(array.slice(0, -1));
pos = last_len === from_last ? 0 : last_len-from_last;
draw_cursor_line(last, pos+tabs_rm);
} else {
// in the middle
if (num_lines === 3) {
before.before('<div>' + encodeHTML(array[0]) +
'</div>');
draw_cursor_line(array[1], position-first_len-1);
after.after('<div class="clear">' +
encodeHTML(array[2]) +
'</div>');
} else {
// more lines, cursor in the middle
var line_index;
var current;
pos = position;
for (i=0; i<array.length; ++i) {
var current_len = array[i].length;
if (pos > current_len) {
pos -= current_len;
} else {
break;
}
}
current = array[i];
line_index = i;
// cursor on first character in line
if (pos === current.length) {
pos = 0;
current = array[++line_index];
}
draw_cursor_line(current, pos);
lines_before(array.slice(0, line_index));
lines_after(array.slice(line_index+1));
}
}
}
}
} else {
if (string === '') {
before.html('');
cursor.html(' ');
after.html('');
} else {
draw_cursor_line(string, position);
}
}
};
})(self);
var draw_prompt = (function() {
var prompt_node = self.find('.prompt');
return function() {
if (typeof prompt === 'string') {
prompt_len = skipFormattingCount(prompt);
prompt_node.html(encodeHTML(prompt));
} else {
prompt(function(string) {
prompt_len = skipFormattingCount(string);
prompt_node.html(encodeHTML(string));
});
}
//change_num_chars();
};
})();
// paste content to terminal using hidden textarea
function paste() {
clip.focus();
//wait until Browser insert text to textarea
self.oneTime(1, function() {
self.insert(clip.val());
clip.blur().val('');
});
}
function keydown_event(e) {
if (options.keydown && options.keydown(e) === false) {
return false;
}
if (enabled) {
var pos, len, result;
// arrows / Home / End / ENTER
if (reverse_search && (e.which === 35 || e.which === 36 ||
e.which === 37 || e.which === 38 ||
e.which === 39 || e.which === 40 ||
e.which === 66 || e.which === 13 ||
e.which === 27)) {
clear_reverse_state();
draw_prompt();
if (e.which === 27) { // ESC
command = '';
}
redraw();
// finish reverse search and execute normal event handler
keydown_event.call(this, e);
} else if (e.altKey) {
// Chrome on Windows set ctrlKey and altKey for alt
// need to check for alt first
//if (e.which === 18) { // press ALT
if (e.which === 68) { //ALT+D
var regex = /[^ ]+ |[^ ]+$/;
self.set(command.slice(0, position) +
command.slice(position).replace(regex, ''),
true);
// chrome jump to address bar
return false;
}
return true;
} else if (e.keyCode === 13) { //enter
if ((history && command) &&
((options.historyFilter &&
options.historyFilter(command)) ||
!options.historyFilter)) {
if (history.data().slice(-1)[0] !== command) {
history.append(command);
}
}
history.last();
var tmp = command;
self.set('');
if (options.commands) {
options.commands(tmp);
}
if (typeof prompt === 'function') {
draw_prompt();
}
} else if (e.which === 32) { //space
if (reverse_search) {
reverse_search_string += ' ';
draw_reverse_prompt();
} else {
self.insert(' ');
}
} else if (e.which === 8) { //backspace
if (reverse_search) {
reverse_search_string = reverse_search_string.slice(0, -1);
draw_reverse_prompt();
} else {
if (command !== '' && position > 0) {
command = command.slice(0, position - 1) +
command.slice(position, command.length);
--position;
redraw();
}
}
} else if (e.which === 9 && !(e.ctrlKey || e.altKey)) { // TAB
self.insert('\t');
} else if (e.which === 46) {
//DELETE
if (command !== '' && position < command.length) {
command = command.slice(0, position) +
command.slice(position + 1, command.length);
redraw();
}
return true;
} else if (history && e.which === 38 ||
(e.which === 80 && e.ctrlKey)) {
//UP ARROW or CTRL+P
self.set(history.previous());
} else if (history && e.which === 40 ||
(e.which === 78 && e.ctrlKey)) {
//DOWN ARROW or CTRL+N
self.set(history.next());
} else if (e.which === 37 ||
(e.which === 66 && e.ctrlKey)) {
//CTRL+LEFT ARROW or CTRL+B
if (e.ctrlKey && e.which !== 66) {
len = position - 1;
pos = 0;
if (command[len] === ' ') {
--len;
}
for (var i = len; i > 0; --i) {
if (command[i] === ' ' && command[i+1] !== ' ') {
pos = i + 1;
break;
} else if (command[i] === '\n' && command[i+1] !== '\n') {
pos = i;
break;
}
}
self.position(pos);
} else {
//LEFT ARROW or CTRL+B
if (position > 0) {
--position;
redraw();
}
}
} else if (e.which === 82 && e.ctrlKey) { // CTRL+R
if (reverse_search) {
reverse_history_search(true);
} else {
backup_prompt = prompt;
draw_reverse_prompt();
command = '';
redraw();
reverse_search = true;
}
} else if (e.which === 39 ||
(e.which === 70 && e.ctrlKey)) {
//RIGHT ARROW OR CTRL+F
if (e.ctrlKey && e.which !== 70) {
// jump to beginig or end of the word
if (command[position] === ' ') {
++position;
}
var match = command.slice(position).match(/\S[\n\s]{2,}|[\n\s]+\S?/);
if (!match || match[0].match(/^\s+$/)) {
position = command.length;
} else {
if (match[0][0] !== ' ') {
position += match.index + 1;
} else {
position += match.index + match[0].length - 1;
if (match[0][match[0].length-1] !== ' ') {
--position;
}
}
}
redraw();
} else {
if (position < command.length) {
++position;
redraw();
}
}
} else if (e.which === 123) { //F12 - Allow Firebug
return true;
} else if (e.which === 36) { //HOME
self.position(0);
} else if (e.which === 35) {
//END
self.position(command.length);
} else if (e.ctrlKey || e.metaKey) {
if (e.shiftKey) { // CTRL+SHIFT+??
if (e.which === 84) {
//CTRL+SHIFT+T open closed tab
return true;
}
//} else if (e.altKey) { //ALT+CTRL+??
} else {
//NOTE: in opera charCode is undefined
if (e.which === 65) {
//CTRL+A
self.position(0);
} else if (e.which === 69) {
//CTRL+E
self.position(command.length);
} else if (e.which === 88 || e.which === 67 ||
e.which === 87 || e.which === 84) {
//CTRL+X CTRL+C CTRL+W CTRL+T
return true;
} else if (e.which === 86) {
//CTRL+V
paste();
return true;
} else if (e.which === 75) {
//CTRL+K
if (position === 0) {
self.set('');
} else if (position !== command.length) {
self.set(command.slice(0, position));
}
} else if (e.which === 85) { // CTRL+U
self.set(command.slice(position, command.length));
self.position(0);
} else if (e.which === 17) { //CTRL+TAB switch tab
return true;
}
}
} else {
return true;
}
return false;
} /*else {
if ((e.altKey && e.which === 68) ||
(e.ctrlKey && [65, 66, 68, 69, 80, 78, 70].has(e.which)) ||
// 68 === D
[35, 36, 37, 38, 39, 40].has(e.which)) {
return false;
}
} */
}
$.extend(self, {
name: function(string) {
if (string !== undefined) {
name = string;
history = new History(string);
} else {
return name;
}
},
history: function() {
return history;
},
set: function(string, stay) {
if (string !== undefined) {
command = string;
if (!stay) {
position = command.length;
}
redraw();
if (typeof options.onCommandChange === 'function') {
options.onCommandChange(command);
}
}
},
insert: function(string, stay) {
if (position === command.length) {
command += string;
} else if (position === 0) {
command = string + command;
} else {
command = command.slice(0, position) +
string + command.slice(position);
}
if (!stay) {
position += string.length;
}
redraw();
if (typeof options.onCommandChange === 'function') {
options.onCommandChange(command);
}
},
get: function() {
return command;
},
commands: function(commands) {
if (commands) {
options.commands = commands;
} else {
return commands;
}
},
destroy: function() {
$(document.documentElement).unbind('.commandline');
self.find('.prompt').remove();
},
prompt: function(user_prompt) {
if (user_prompt === undefined) {
return prompt;
} else {
if (typeof user_prompt === 'string' ||
typeof user_prompt === 'function') {
prompt = user_prompt;
} else {
throw 'prompt must be a function or string';
}
draw_prompt();
// we could check if command is longer then numchars-new prompt
redraw();
}
},
position: function(n) {
if (typeof n === 'number') {
position = n < 0 ? 0 : n > command.length ? command.length : n;
redraw();
} else {
return position;
}
},
show: (function() {
var show = self.show;
return function() {
show.apply(self, []);
redraw();
draw_prompt();
};
})(),
resize: function(num) {
if (num) {
num_chars = num;
} else {
change_num_chars();
}
redraw();
},
enable: function() {
if (!enabled) {
cursor.addClass('inverted');
self.everyTime(500, 'blink', blink);
enabled = true;
}
},
isenabled: function() {
return enabled;
},
disable: function() {
if (enabled) {
self.stopTime('blink', blink);
cursor.removeClass('inverted');
enabled = false;
}
},
mask: function(display) {
if (typeof display === 'boolean') {
mask = display;
redraw();
} else {
return mask;
}
}
});
// INIT
self.name(options.name || '');
prompt = options.prompt || '> ';
draw_prompt();
if (options.enabled === undefined || options.enabled === true) {
self.enable();
}
// Keystrokes
//document.documentElement
var object;
if ($.browser.msie) {
object = document.documentElement;
} else {
object = window;
}
$(object).keypress(function(e) {
var result;
if (e.ctrlKey && e.which === 99) {
return true;
}
if (!reverse_search && options.keypress) {
result = options.keypress(e);
}
if (result === undefined || result) {
if (enabled) {
if ([38, 32, 13, 0, 8].has(e.which) &&
e.keyCode !== 123 && // for F12 which === 0
//!(e.which === 40 && e.shiftKey ||
!(e.which === 38 && e.shiftKey)) {
return false;
} else if (!e.ctrlKey && !(e.altKey && e.which === 100)) {
// TODO: this should be in one statement
if (reverse_search) {
reverse_search_string += String.fromCharCode(e.which);
draw_reverse_prompt();
reverse_history_search();
} else {
self.insert(String.fromCharCode(e.which));
}
return false;
} else if (e.altKey) {
if (reverse_search) {
reverse_search_string += String.fromCharCode(e.which);
draw_reverse_prompt();
reverse_history_search();
} else {
self.insert(String.fromCharCode(e.which));
}
}
}
} else {
return result;
}
}).keydown(keydown_event);
// characters
return self;
};
// -----------------------------------------------------------------------
// JSON-RPC CALL
// -----------------------------------------------------------------------
$.jrpc = function(url, id, method, params, success, error) {
var request = $.json_stringify({
'jsonrpc': '2.0', 'method': method,
'params': params, 'id': id});
return $.ajax({
url: url,
data: request,
success: success,
error: error,
contentType: 'application/json',
dataType: 'json',
async: true,
cache: false,
//timeout: 1,
type: 'POST'});
};
// -----------------------------------------------------------------------
// :: TERMINAL PLUGIN CODE
// -----------------------------------------------------------------------
var version = '0.4.17';
var copyright = 'Copyright (c) 2011 Jakub Jankiewicz <http://jcubic.pl>';
var version_string = 'version ' + version;
//regex is for placing version string aligned to the right
var reg = new RegExp(" {" + version_string.length + "}$");
var signatures = [
['jQuery Terminal', '(c) 2011 jcubic'],
['jQuery Terminal Emulator v. ' + version,
copyright.replace(/ *<.*>/, '')],
['jQuery Terminal Emulator version ' + version_string,
copyright],
[' _______ ________ __',
' / / _ /_ ____________ _/__ ___/______________ _____ / /',
' __ / / // / // / _ / _/ // / / / _ / _/ / / \\/ / _ \\/ /',
'/ / / // / // / ___/ // // / / / ___/ // / / / / /\\ / // / /__',
'\\___/____ \\\\__/____/_/ \\__ / /_/____/_//_/ /_/ /_/ \\/\\__\\_\\___/',
' \\/ /____/ '.replace(reg, '') +
version_string,
copyright],
[' __ _____ ________ __',
' / // _ /__ __ _____ ___ __ _/__ ___/__ ___ ______ __ __ __ ___ / /',
' __ / // // // // // _ // _// // / / // _ // _// // // \\/ // _ \\/ /',
'/ / // // // // // ___// / / // / / // ___// / / / / // // /\\ // // / /__',
'\\___//____ \\\\___//____//_/ _\\_ / /_//____//_/ /_/ /_//_//_/ /_/ \\__\\_\\___/',
' \\/ /____/ '.replace(reg, '') +
version_string,
copyright]
];
// for canceling on CTRL+D
var requests = [];
var terminals = new Cycle(); //list of terminals global in this scope
$.fn.terminal = function(init_eval, options) {
var self = this;
var lines = [];
var output;
var terminal_id = terminals.length();
var num_chars; // numer of chars in line
var command_list = []; // for tab completion
var settings = {
name: '',
prompt: '> ',
history: true,
exit: true,
clear: true,
enabled: true,
cancelableAjax: true,
login: null,
tabcompletion: null,
historyFilter: null,
onInit: null,
onExit: null,
keypress: null,
keydown: null
};
if (options) {
if (options.width) {
self.width(options.width);
}
if (options.height) {
self.height(options.height);
}
$.extend(settings, options);
}
var pause = !settings.enabled;
if (self.length === 0) {
throw 'Sorry, but terminal said that "' + self.selector +
'" is not valid selector!';
}
// register ajaxSend for cancel requests on CTRL+D
self.ajaxSend(function(e, xhr, opt) {
requests.push(xhr);
});
// terminal already exist
if (self.data('terminal')) {
return self.data('terminal');
}
output = $('<div>').addClass('terminal-output').appendTo(self);
self.addClass('terminal').append('<div/>');
function haveScrollbars() {
return self.get(0).scrollHeight > self.innerHeight();
}
//calculate numbers of characters
function get_num_chars() {
var cursor = self.find('.cursor');
var cur_width = cursor.width();
var result = Math.floor(self.width() / cur_width);
if (haveScrollbars()) {
// assume that scrollbars are 20px - in my Laptop with
// Linux/Chrome they are 16px
var margins = self.innerWidth() - self.width();
result -= Math.ceil((20 - margins / 2) / (cur_width-1));
}
return result;
}
function escape_brackets(string) {
return string.replace(/\[/g, '[').replace(/\]/g, ']');
}
// display Exception on terminal
function display_exception(e, label) {
var message;
if (typeof e === 'string') {
message = e;
} else {
if (typeof e.fileName === 'string') {
message = e.fileName + ': ' + e.message;
} else {
message = e.message;
}
}
self.error('[' + label + ']: ' + message);
self.pause();
if (typeof e.fileName === 'string') {
//display filename and line which throw exeption
$.get(e.fileName, function(file) {
self.resume();
var num = e.lineNumber - 1;
var line = file.split('\n')[num];
if (line) {
self.error('[' + e.lineNumber + ']: ' + line);
}
});
}
}
//validating if object is string or function, call that function and
//display exeption if any
function validate(label, object) {
try {
if (typeof object === 'function') {
object(function() {
// don't care
});
} else if (typeof object !== 'string') {
var msg = label + ' must be string or function';
throw msg;
}
} catch (e) {
display_exception(e, label.toUpperCase());
return false;
}
return true;
}
function scroll_to_bottom() {
var scrollHeight = self.prop ? self.prop('scrollHeight') :
self.attr('scrollHeight');
self.scrollTop(scrollHeight);
}
function draw_line(string) {
string = typeof string === 'string' ? string : String(string);
var div, i, len;
if (string.length > num_chars) {
// string can have line break
//var array = string.split('\n');
// TODO: the way it should work
var array = get_formatted_lines(string, num_chars);
div = $('<div></div>');
for (i = 0, len = array.length; i < len; ++i) {
if (array[i] === '' || array[i] === '\r') {
div.append('<div> </div>');
} else {
$('<div/>').html(encodeHTML(array[i])).appendTo(div);
}
}
} else {
div = $('<div/>').html(encodeHTML(string));
}
output.append(div);
div.width('100%');
scroll_to_bottom();
return div;
}
function show_greetings() {
if (options.greetings === undefined) {
self.echo(self.signature);
} else if (options.greetings) {
self.echo(options.greetings);
}
}
function is_scrolled_into_view(elem) {
var docViewTop = $(window).scrollTop();
var docViewBottom = docViewTop + $(window).height();
var elemTop = $(elem).offset().top;
var elemBottom = elemTop + $(elem).height();
return ((elemBottom >= docViewTop) && (elemTop <= docViewBottom));
}
// ----------------------------------------------------------
// TERMINAL METHODS
// ----------------------------------------------------------
$.extend(self, {
clear: function() {
output.html('');
command_line.set('');
lines = [];
self.attr({ scrollTop: 0});
return self;
},
paused: function() {
return pause;
},
pause: function() {
if (command_line) {
self.disable();
command_line.hide();
}
return self;
},
resume: function() {
//console.log('resume on ' + options.prompt + '\n' +
// get_stack(arguments.callee.caller).join(''));
if (command_line) {
self.enable();
command_line.show();
scroll_to_bottom();
}
return self;
},
cols: function() {
return num_chars;
},
rows: function() {
return lines.length;
},
history: function() {
return command_line.history();
},
next: function() {
if (terminals.length() === 1) {
return self;
} else {
var offsetTop = self.offset().top;
var height = self.height();
var scrollTop = self.scrollTop();
if (!is_scrolled_into_view(self)) {
self.enable();
$('html,body').animate({scrollTop: offsetTop-50}, 500);
return self;
} else {
terminals.front().disable();
var next = terminals.rotate().enable();
// 100 provides buffer in viewport
var x = next.offset().top - 50;
$('html,body').animate({scrollTop: x}, 500);
return next;
}
}
},
focus: function(toggle) {
//console.log('focus on ' + options.prompt + '\n' +
// get_stack(arguments.callee.caller).join(''));
// TODO: one terminal should go out of focus
// TODO: add onFocus and onBlur
self.oneTime(1, function() {
if (terminals.length() === 1) {
if (toggle === false) {
self.disable();
} else {
self.enable();
}
} else {
if (toggle === false) {
self.next();
} else {
terminals.front().disable();
terminals.set(self);
self.enable();
}
}
});
return self;
},
enable: function() {
//console.log('enable: ' + options.prompt + '\n' +
// get_stack(arguments.callee.caller).join(''));
if (num_chars === undefined) {
//enabling first time
self.resize();
}
if (pause) {
if (command_line) {
command_line.enable();
pause = false;
}
}
return self;
},
disable: function() {
if (command_line) {
pause = true;
command_line.disable();
}
return self;
},
enabled: function() {
return pause;
},
signature: function() {
var cols = self.cols();
var i = cols < 15 ? null : cols < 35 ? 0 : cols < 55 ? 1 : cols < 64 ? 2 : cols < 75 ? 3 : 4;
if (i !== null) {
return signatures[i].join('\n') + '\n';
} else {
return '';
}
},
version: function() {
return version;
},
/* COMMAND LINE FUNCTIONS */
get_command: function() {
return command_line.get();
},
insert: function(string) {
if (typeof string === 'string') {
command_line.insert(string);
return self;
} else {
throw "insert function argument is not a string";
}
},
set_prompt: function(prompt) {
if (validate('prompt', prompt)) {
if (prompt.constructor === Function) {
command_line.prompt(function(command) {
prompt(command, self);
});
} else {
command_line.prompt(prompt);
}
interpreters.top().prompt = prompt;
}
return self;
},
get_prompt: function() {
return interpreters.top().prompt;
// command_line.prompt(); - can be a wrapper
//return command_line.prompt();
},
set_command: function(command) {
command_line.set(command);
return self;
},
set_mask: function(display) {
command_line.mask(display);
return self;
},
get_output: function(raw) {
if (raw) {
return lines;
} else {
return $.map(lines, function(i, item) {
return typeof item === 'function' ? item() : item;
}).get().join('\n');
}
},
resize: function(width, height) {
if (width && height) {
self.width(width);
self.height(height);
}
num_chars = get_num_chars();
command_line.resize(num_chars);
var o = output.detach();
output.html('');
$.each(lines, function(i, line) {
draw_line(line.constructor === Function ? line() : line);
});
self.prepend(o);
scroll_to_bottom();
return self;
},
echo: function(line) {
lines.push(line);
return draw_line(typeof line === 'function' ? line() : line);
},
error: function(message) {
//echo red message
self.echo('[[;#f00;]' + escape_brackets(message) + ']');
},
scroll: function(amount) {
var pos;
if (self.prop) {
if (amount > self.prop('scrollTop') && amount > 0) {
self.prop('scrollTop', 0);
}
pos = self.prop('scrollTop');
self.prop('scrollTop', pos + amount);
return self;
} else {
if (amount > self.attr('scrollTop') && amount > 0) {
self.attr('scrollTop', 0);
}
pos = self.attr('scrollTop');
self.attr('scrollTop', pos + amount);
return self;
}
},
logout: settings.login ? function() {
while (interpreters.size() > 1) {
interpreters.pop();
}
logout();
return self;
} : function() {
throw "You don't have login function";
},
token: settings.login ? function() {
var name = settings.name;
return $.Storage.get('token' + (name ? '_' + name : ''));
} : null,
login_name: settings.login ? function() {
var name = settings.name;
return $.Storage.get('login' + (name ? '_' + name : ''));
} : null,
name: function() {
return settings.name;
},
push: function(_eval, options) {
if (!options.prompt || validate('prompt', options.prompt)) {
if (typeof _eval === 'string') {
_eval = make_json_rpc_eval_fun(options['eval'], self);
}
interpreters.push($.extend({'eval': _eval}, options));
prepare_top_interpreter();
}
return self;
},
pop: function(string) {
if (string !== undefined) {
echo_command(string);
}
if (interpreters.top().name === settings.name) {
if (settings.login) {
logout();
if (typeof settings.onExit === 'function') {
settings.onExit(self);
}
}
} else {
var current = interpreters.pop();
prepare_top_interpreter();
if (typeof current.onExit === 'function') {
current.onExit(self);
}
}
return self;
}
});
//function constructor for eval
function make_json_rpc_eval_fun(url, terminal) {
var id = 1;
var service = function(method, params) {
terminal.pause();
$.jrpc(url, id++, method, params, function(json) {
if (!json.error) {
if (typeof json.result === 'string') {
terminal.echo(json.result);
} else if (json.result instanceof Array) {
terminal.echo(json.result.join(' '));
} else if (typeof json.result === 'object') {
var string = '';
for (var f in json.result) {
if (json.result.hasOwnProperty(f)) {
string += f + ': ' + json.result[f] + '\n';
}
}
terminal.echo(string);
}
} else {
terminal.error('[RPC] ' + json.error.message);
}
terminal.resume();
}, function(xhr, status, error) {
terminal.error('[AJAX] ' + status +
' - Server reponse is: \n' +
xhr.responseText);
terminal.resume();
});
};
//this is eval function
return function(command, terminal) {
if (command === '') {
return;
}
var method, params;
if (!command.match(/[^ ]* /)) {
method = command;
params = [];
} else {
command = command.split(/ +/);
method = command[0];
params = command.slice(1);
}
if (!settings.login || method === 'help') {
service(method, params);
} else {
var token = terminal.token();
if (token) {
service(method, [token].concat(params));
} else {
//should never happen
terminal.error('[AUTH] Access denied (no token)');
}
}
};
}
//display prompt and last command
function echo_command(command) {
var prompt = command_line.prompt();
if (command_line.mask()) {
command = command.replace(/./g, '*');
}
if (typeof prompt === 'function') {
prompt(function(string) {
self.echo(string + command);
});
} else {
self.echo(prompt + command);
}
}
// wrapper over eval it implements exit and catch all exeptions
// from user code and display them on terminal
function commands(command) {
try {
var interpreter = interpreters.top();
if (command === 'exit' && settings.exit) {
if (interpreters.size() === 1) {
if (settings.login) {
logout();
} else {
var msg = 'You can exit from main interpeter';
echo_command(command);
self.echo(msg);
}
} else {
self.pop('exit');
}
} else {
echo_command(command);
if (command === 'clear' && settings.clear) {
self.clear();
} else {
interpreter['eval'](command, self);
}
}
} catch (e) {
display_exception(e, 'USER');
self.resume();
throw e;
}
}
// functions change prompt of command line to login to password
// and call user login function with callback that set token
// if user call it with value that is true
function login() {
var user = null;
command_line.prompt('login: ');
// don't stor logins in history
if (settings.history) {
command_line.history().disable();
}
command_line.commands(function(command) {
try {
echo_command(command);
if (!user) {
user = command;
command_line.prompt('password: ');
command_line.mask(true);
} else {
command_line.mask(false);
self.pause();
if (typeof settings.login !== 'function') {
throw "Value of login property must be a function";
}
var passwd = command;
settings.login(user, passwd, function(token) {
if (token) {
var name = settings.name;
name = (name ? '_' + name : '');
$.Storage.set('token' + name, token);
$.Storage.set('login' + name, user);
//restore commands and run interpreter
command_line.commands(commands);
// move this to one function init.
initialize();
} else {
self.error('Wrong password try again');
command_line.prompt('login: ');
user = null;
}
self.resume();
if (settings.history) {
command_line.history().enable();
}
});
}
} catch (e) {
display_exception(e, 'LOGIN', self);
throw e;
}
});
}
//logout function remove Storage, disable history and run login function
//this function is call only when options.login function is defined
//check for this is in self.pop method
function logout() {
var name = settings.name;
name = (name ? '_' + name : '');
$.Storage.remove('token' + name, null);
$.Storage.remove('login' + name, null);
if (settings.history) {
command_line.history().disable();
}
login();
}
//function enable history, set prompt, run eval function
function prepare_top_interpreter() {
var interpreter = interpreters.top();
var name = '';
if (interpreter.name !== undefined &&
interpreter.name !== '') {
name += interpreter.name + '_';
}
name += terminal_id;
command_line.name(name);
if (interpreter.prompt.constructor === Function) {
command_line.prompt(function(command) {
interpreter.prompt(command, self);
});
} else {
command_line.prompt(interpreter.prompt);
}
if (settings.history) {
command_line.history().enable();
}
command_line.set('');
if (typeof interpreter.onStart === 'function') {
interpreter.onStart(self);
}
}
function initialize() {
prepare_top_interpreter();
show_greetings();
if (typeof settings.onInit === 'function') {
settings.onInit(self);
}
}
var tab_count = 0;
var scrollBars = haveScrollbars();
function key_down(e) {
var i;
// after text pasted into textarea in cmd plugin
self.oneTime(5, function() {
if (scrollBars !== haveScrollbars()) {
// if scollbars appearance change we will have different
// number of chars
self.resize();
scrollBars = haveScrollbars();
}
});
if (!self.paused()) {
if (settings.keydown && settings.keydown(e, self) === false) {
return false;
}
if (e.which !== 9) { // not a TAB
tab_count = 0;
}
if (e.which === 68 && e.ctrlKey) { // CTRL+D
if (command_line.get() === '') {
if (interpreters.size() > 1 ||
settings.login !== undefined) {
self.pop('');
} else {
self.resume();
self.echo('');
}
} else {
self.set_command('');
}
return false;
} else if (settings.tabcompletion && e.which === 9) { // TAB
// TODO: move this to cmd plugin
// add tabcompletion = array | function
++tab_count;
var command = command_line.get();
if (!command.match(' ')) { // complete only first word
var reg = new RegExp('^' + command);
var commands = interpreters.top().command_list;
var matched = [];
for (i=commands.length; i--;) {
if (reg.test(commands[i])) {
matched.push(commands[i]);
}
}
if (matched.length === 1) {
self.set_command(matched[0]);
} else if (matched.length > 1) {
if (tab_count >= 2) {
echo_command(command);
self.echo(matched.join('\t'));
tab_count = 0;
}
}
}
return false;
} else if (e.which === 86 && e.ctrlKey) { // CTRL+V
self.oneTime(1, function() {
scroll_to_bottom();
});
return true;
} else if (e.which === 9 && e.ctrlKey) { // CTRL+TAB
if (terminals.length() > 1) {
self.focus(false);
}
return false;
} else if (e.which === 34) { // PAGE DOWN
self.scroll(self.height());
} else if (e.which === 33) { // PAGE UP
self.scroll(-self.height());
} else {
self.attr({scrollTop: self.attr('scrollHeight')});
}
} else {
// cancel ajax requests
if (settings.cancelableAjax) {
if (e.which === 68 && e.ctrlKey) { // CTRL+D
for (i=requests.length; i--;) {
var r = requests[i];
if (4 !== r.readyState) {
try {
r.abort();
} catch(e) {
self.error('error in aborting ajax');
}
}
}
self.resume();
return false;
}
}
}
}
// INIT CODE
var url;
if (settings.login && typeof settings.onBeforeLogin === 'function') {
settings.onBeforeLogin(self);
}
if (init_eval.constructor === String) {
url = init_eval; //url variable is use when making login function
init_eval = make_json_rpc_eval_fun(init_eval, self);
} else if (init_eval.constructor === Array) {
throw "You can't use array as eval";
} else if (typeof init_eval === 'object') {
// top commands
for (var i in init_eval) {
if (init_eval.hasOwnProperty(i)) {
command_list.push(i);
}
}
init_eval = (function make_eval(object) {
// function that maps commands to object methods
// it keeps terminal context
return function(command, terminal) {
if (command === '') {
return;
}
command = command.split(/ +/);
var method = command[0];
var params = command.slice(1);
var val = object[method];
var type = typeof val;
if (type === 'function') {
val.apply(self, params);
} else if (type === 'object' || type === 'string') {
var commands = [];
if (type === 'object') {
for (var m in val) {
if (val.hasOwnProperty(m)) {
commands.push(m);
}
}
val = make_eval(val);
}
self.push(val, {
prompt: method + '> ',
name: method,
command_list: commands
});
} else {
self.error("Command '" + method + "' Not Found");
}
};
})(init_eval);
} else if (typeof init_eval !== 'function') {
throw 'Unknow object "' + String(init_eval) + '" passed as eval';
}
// create json-rpc authentication function
if (url && (typeof settings.login === 'string' || settings.login)) {
settings.login = (function(method) {
var id = 1;
return function(user, passwd, callback) {
self.pause();
$.jrpc(url,
id++,
method,
[user, passwd],
function(response) {
self.resume();
if (!response.error && response.result) {
callback(response.result);
} else {
callback(null);
}
}, function(xhr, status, error) {
self.resume();
self.error('[AJAX\ Response: ' +
status + '\n' +
xhr.responseText);
});
};
//default name is login so you can pass true
})(typeof settings.login === 'boolean' ? 'login' : settings.login);
}
if (validate('prompt', settings.prompt)) {
var interpreters = new Stack({
name: settings.name,
'eval': init_eval,
prompt: settings.prompt,
command_list: command_list,
greetings: settings.greetings
});
var command_line = self.find('.terminal-output').next().cmd({
prompt: settings.prompt,
history: settings.history,
historyFilter: settings.historyFilter,
width: '100%',
keydown: key_down,
keypress: settings.keypress ? function(e) {
return settings.keypress(e, self);
} : null,
onCommandChange: function(command) {
if (typeof settings.onCommandChange === 'function') {
settings.onCommandChange(command, self);
}
scroll_to_bottom();
},
commands: commands
});
//num_chars = get_num_chars();
terminals.append(self);
if (settings.enabled === true) {
self.focus();
} else {
self.disable();
}
$(window).resize(self.resize);
self.click(function() {
self.focus();
});
if (self.token && !self.token() && self.login_name &&
!self.login_name()) {
login();
} else {
initialize();
}
if (typeof $.fn.init.prototype.mousewheel === 'function') {
self.mousewheel(function(event, delta) {
//self.echo(dir(event));
if (delta > 0) {
self.scroll(-40);
} else {
self.scroll(40);
}
return false;
}, true);
}
}
self.data('terminal', self);
return self;
}; //terminal plugin
})(jQuery);
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,161 |
package whisk.core.cli.test
import org.junit.runner.RunWith
import org.scalatest.junit.JUnitRunner
import common.TestHelpers
import common.TestUtils._
import common.TestUtils
import common.Wsk
import common.WskAdmin
import common.WskProps
import common.WskTestHelpers
/**
* Tests for testing the CLI "api" subcommand. Most of these tests require a deployed backend.
*/
@RunWith(classOf[JUnitRunner])
class ApiGwTests
extends TestHelpers
with WskTestHelpers {
implicit val wskprops = WskProps()
val wsk = new Wsk
val (cliuser, clinamespace) = WskAdmin.getUser(wskprops.authKey)
behavior of "Wsk api"
it should "reject an api commands with an invalid path parameter" in {
val badpath = "badpath"
var rr = wsk.api.create(basepath = Some("/basepath"), relpath = Some(badpath), operation = Some("GET"), action = Some("action"), expectedExitCode = ANY_ERROR_EXIT)
rr.stderr should include (s"'${badpath}' must begin with '/'")
rr = wsk.api.delete(basepathOrApiName = "/basepath", relpath = Some(badpath), operation = Some("GET"), expectedExitCode = ANY_ERROR_EXIT)
rr.stderr should include (s"'${badpath}' must begin with '/'")
rr = wsk.api.list(basepathOrApiName = Some("/basepath"), relpath = Some(badpath), operation = Some("GET"), expectedExitCode = ANY_ERROR_EXIT)
rr.stderr should include (s"'${badpath}' must begin with '/'")
}
it should "verify successful creation of a new API" in {
val testName = "CLI_APIGWTEST1"
val testbasepath = "/"+testName+"_bp"
val testrelpath = "/path"
val testnewrelpath = "/path_new"
val testurlop = "get"
val testapiname = testName+" API Name"
val actionName = testName+"_action"
try {
println("cli user: "+cliuser+"; cli namespace: "+clinamespace)
var rr = wsk.api.create(basepath = Some(testbasepath), relpath = Some(testrelpath), operation = Some(testurlop), action = Some(actionName), apiname = Some(testapiname))
rr.stdout should include("ok: created API")
rr = wsk.api.list(basepathOrApiName = Some(testbasepath), relpath = Some(testrelpath), operation = Some(testurlop))
rr.stdout should include("ok: APIs")
rr.stdout should include regex (s"/${clinamespace}/${actionName}\\s+${testurlop}\\s+${testapiname}\\s+")
rr.stdout should include(testbasepath + testrelpath)
val deleteresult = wsk.api.delete(basepathOrApiName = testbasepath)
deleteresult.stdout should include("ok: deleted API")
}
finally {
val deleteresult = wsk.api.delete(basepathOrApiName = testbasepath, expectedExitCode = DONTCARE_EXIT)
}
}
it should "verify get API name " in {
val testName = "CLI_APIGWTEST3"
val testbasepath = "/"+testName+"_bp"
val testrelpath = "/path"
val testnewrelpath = "/path_new"
val testurlop = "get"
val testapiname = testName+" API Name"
val actionName = testName+"_action"
try {
var rr = wsk.api.create(basepath = Some(testbasepath), relpath = Some(testrelpath), operation = Some(testurlop), action = Some(actionName), apiname = Some(testapiname))
rr.stdout should include("ok: created API")
rr = wsk.api.get(basepathOrApiName = Some(testapiname))
rr.stdout should include(testbasepath)
rr.stdout should include(s"${actionName}")
}
finally {
val deleteresult = wsk.api.delete(basepathOrApiName = testbasepath, expectedExitCode = DONTCARE_EXIT)
}
}
it should "verify delete API name " in {
val testName = "CLI_APIGWTEST4"
val testbasepath = "/"+testName+"_bp"
val testrelpath = "/path"
val testnewrelpath = "/path_new"
val testurlop = "get"
val testapiname = testName+" API Name"
val actionName = testName+"_action"
try {
var rr = wsk.api.create(basepath = Some(testbasepath), relpath = Some(testrelpath), operation = Some(testurlop), action = Some(actionName), apiname = Some(testapiname))
rr.stdout should include("ok: created API")
rr = wsk.api.delete(basepathOrApiName = testapiname)
rr.stdout should include("ok: deleted API")
}
finally {
val deleteresult = wsk.api.delete(basepathOrApiName = testbasepath, expectedExitCode = DONTCARE_EXIT)
}
}
it should "verify delete API basepath " in {
val testName = "CLI_APIGWTEST5"
val testbasepath = "/"+testName+"_bp"
val testrelpath = "/path"
val testnewrelpath = "/path_new"
val testurlop = "get"
val testapiname = testName+" API Name"
val actionName = testName+"_action"
try {
var rr = wsk.api.create(basepath = Some(testbasepath), relpath = Some(testrelpath), operation = Some(testurlop), action = Some(actionName), apiname = Some(testapiname))
rr.stdout should include("ok: created API")
rr = wsk.api.delete(basepathOrApiName = testbasepath)
rr.stdout should include("ok: deleted API")
}
finally {
val deleteresult = wsk.api.delete(basepathOrApiName = testbasepath, expectedExitCode = DONTCARE_EXIT)
}
}
it should "verify adding endpoints to existing api" in {
val testName = "CLI_APIGWTEST6"
val testbasepath = "/"+testName+"_bp"
val testrelpath = "/path2"
val testnewrelpath = "/path_new"
val testurlop = "get"
val testapiname = testName+" API Name"
val actionName = testName+"_action"
val newEndpoint = "/newEndpoint"
try {
var rr = wsk.api.create(basepath = Some(testbasepath), relpath = Some(testrelpath), operation = Some(testurlop), action = Some(actionName), apiname = Some(testapiname))
rr.stdout should include("ok: created API")
rr = wsk.api.create(basepath = Some(testbasepath), relpath = Some(newEndpoint), operation = Some(testurlop), action = Some(actionName), apiname = Some(testapiname))
rr.stdout should include("ok: created API")
rr = wsk.api.list(basepathOrApiName = Some(testbasepath))
rr.stdout should include("ok: APIs")
rr.stdout should include regex (s"/${clinamespace}/${actionName}\\s+${testurlop}\\s+${testapiname}\\s+")
rr.stdout should include(testbasepath + testrelpath)
rr.stdout should include(testbasepath + newEndpoint)
}
finally {
val deleteresult = wsk.api.delete(basepathOrApiName = testbasepath, expectedExitCode = DONTCARE_EXIT)
}
}
it should "verify successful creation with swagger doc as input" in {
// NOTE: These values must match the swagger file contents
val testName = "CLI_APIGWTEST7"
val testbasepath = "/"+testName+"_bp"
val testrelpath = "/path"
val testurlop = "get"
val testapiname = testName+" API Name"
val actionName = testName+"_action"
val swaggerPath = TestUtils.getTestApiGwFilename("testswaggerdoc1")
try {
var rr = wsk.api.create(swagger = Some(swaggerPath))
rr.stdout should include("ok: created API")
rr = wsk.api.list(basepathOrApiName = Some(testbasepath), relpath = Some(testrelpath), operation = Some(testurlop))
println("list stdout: "+rr.stdout)
println("list stderr: "+rr.stderr)
rr.stdout should include("ok: APIs")
// Actual CLI namespace will vary from local dev to automated test environments, so don't check
rr.stdout should include regex (s"/[@\\w._\\-]+/${actionName}\\s+${testurlop}\\s+${testapiname}\\s+")
rr.stdout should include(testbasepath + testrelpath)
}
finally {
val deleteresult = wsk.api.delete(basepathOrApiName = testbasepath, expectedExitCode = DONTCARE_EXIT)
}
}
it should "verify adding endpoints to two existing apis" in {
val testName = "CLI_APIGWTEST8"
val testbasepath = "/"+testName+"_bp"
val testbasepath2 = "/"+testName+"_bp2"
val testrelpath = "/path2"
val testnewrelpath = "/path_new"
val testurlop = "get"
val testapiname = testName+" API Name"
val actionName = testName+"_action"
val newEndpoint = "/newEndpoint"
try {
var rr = wsk.api.create(basepath = Some(testbasepath), relpath = Some(testrelpath), operation = Some(testurlop), action = Some(actionName), apiname = Some(testapiname))
rr.stdout should include("ok: created API")
rr = wsk.api.create(basepath = Some(testbasepath2), relpath = Some(testrelpath), operation = Some(testurlop), action = Some(actionName), apiname = Some(testapiname))
rr.stdout should include("ok: created API")
// Update both APIs - each with a new endpoint
rr = wsk.api.create(basepath = Some(testbasepath), relpath = Some(newEndpoint), operation = Some(testurlop), action = Some(actionName))
rr.stdout should include("ok: created API")
rr = wsk.api.create(basepath = Some(testbasepath2), relpath = Some(newEndpoint), operation = Some(testurlop), action = Some(actionName))
rr.stdout should include("ok: created API")
rr = wsk.api.list(basepathOrApiName = Some(testbasepath))
rr.stdout should include("ok: APIs")
rr.stdout should include regex (s"/${clinamespace}/${actionName}\\s+${testurlop}\\s+${testapiname}\\s+")
rr.stdout should include(testbasepath + testrelpath)
rr.stdout should include(testbasepath + newEndpoint)
rr = wsk.api.list(basepathOrApiName = Some(testbasepath2))
rr.stdout should include("ok: APIs")
rr.stdout should include regex (s"/${clinamespace}/${actionName}\\s+${testurlop}\\s+${testapiname}\\s+")
rr.stdout should include(testbasepath2 + testrelpath)
rr.stdout should include(testbasepath2 + newEndpoint)
}
finally {
var deleteresult = wsk.api.delete(basepathOrApiName = testbasepath, expectedExitCode = DONTCARE_EXIT)
deleteresult = wsk.api.delete(basepathOrApiName = testbasepath2, expectedExitCode = DONTCARE_EXIT)
}
}
it should "verify successful creation of a new API using an action name using all allowed characters" in {
val testName = "CLI_APIGWTEST9"
val testbasepath = "/"+testName+"_bp"
val testrelpath = "/path"
val testnewrelpath = "/path_new"
val testurlop = "get"
val testapiname = testName+" API Name"
val actionName = testName+"_a-c@t ion"
try {
println("cli user: "+cliuser+"; cli namespace: "+clinamespace)
var rr = wsk.api.create(basepath = Some(testbasepath), relpath = Some(testrelpath), operation = Some(testurlop), action = Some(actionName), apiname = Some(testapiname))
rr.stdout should include("ok: created API")
rr = wsk.api.list(basepathOrApiName = Some(testbasepath), relpath = Some(testrelpath), operation = Some(testurlop))
rr.stdout should include("ok: APIs")
rr.stdout should include regex (s"/${clinamespace}/${actionName}\\s+${testurlop}\\s+${testapiname}\\s+")
rr.stdout should include(testbasepath + testrelpath)
val deleteresult = wsk.api.delete(basepathOrApiName = testbasepath)
deleteresult.stdout should include("ok: deleted API")
}
finally {
val deleteresult = wsk.api.delete(basepathOrApiName = testbasepath, expectedExitCode = DONTCARE_EXIT)
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,481 |
The Ancient Chinese Libertarian Tradition
by Murray N. Rothbard
The first libertarian intellectual was Lao-tzu, the founder of Taoism. Little is known about his life, but apparently he was a personal acquaintance of Confucius in the late sixth century BC and like the latter came from the state of Sung and was descended from the lower aristocracy of the Yin dynasty.
Unlike the notable apologist for the rule of philosopher-bureaucrats, however, Lao-tzu developed a radical libertarian creed. For Lao-tzu the individual and his happiness was the key unit and goal of society. If social institutions hampered the individual's flowering and his happiness, then those institutions should be reduced or abolished altogether. To the individualist Lao-tzu, government, with its "laws and regulations more numerous than the hairs of an ox," was a vicious oppressor of the individual, and "more to be feared than fierce tigers."
Government, in sum, must be limited to the smallest possible minimum; "inaction" was the proper function of government, since only inaction can permit the individual to flourish and achieve happiness. Any intervention by government, Lao-tzu declared, would be counterproductive, and would lead to confusion and turmoil. After referring to the common experience of mankind with government, Lao-tzu came to this incisive conclusion: "The more artificial taboos and restrictions there are in the world, the more the people are impoverished….The more that laws and regulations are given prominence, the more thieves and robbers there will be."
The wisest course, then, is to keep the government simple and for it to take no action, for then the world "stabilizes itself." As Lao-tzu put it, "Therefore the Sage says: I take no action yet the people transform themselves, I favor quiescence and the people right themselves, I take no action and the people enrich themselves…"
Lao-tzu arrived at his challenging and radical new insights in a world dominated by the power of Oriental despotism. What strategy to pursue for social change? It surely was unthinkable for Lao-tzu, with no available historical or contemporary example of libertarian social change, to set forth any optimistic strategy, let alone contemplate forming a mass movement to overthrow the State. And so Lao-tzu took the only strategic way out that seemed open to him, counseling the familiar Taoist path of withdrawal from society and the world, of retreat and inner contemplation.
I submit that while contemporary Taoists advocate retreat from the world as a matter of religious or ideological principle, it is very possible that Lao-tzu called for retreat not as a principle, but as the only strategy that in his despair seemed open to him. If it was hopeless to try to disentangle society from the oppressive coils of the State, then he perhaps assumed that the proper course was to counsel withdrawal from society and the world as the only way to escape State tyranny.
That retreat from the State was a dominant Taoist objective may be seen in the views of the great Taoist Chuang-tzu (369 BC – 286 BC) who, two centuries after Lao-tzu, pushed the master's ideas of laissez faire to their logical conclusion: individualist anarchism.
The influential Chuang-tzu, a notable stylist who wrote in allegorical parables, was a highly learned man in the state of Meng, and also descended from the old aristocracy. A minor official in his native state, Chuang-tzu's fame as a writer spread far and wide throughout China, so much so that King Wei of the Ch'u kingdom sent an emissary to Chuang bearing great gifts and urging him to become Wei's chief minister of state. Chuang-tzu's scornful rejection of the king's offer is one of the great declarations in history on the evils underlying the glittering trappings of State power; it was a fitting declaration from the man who was perhaps the world's first anarchist.
A thousand ounces of gold is indeed a great reward, and the office of chief minister is truly an elevated position. But have you, sir, not seen the sacrificial ox awaiting the sacrifices at the royal shrine of state? It is well cared for and fed for a few years, caparisoned with rich brocades, so that it will be ready to be led into the Great Temple. At that moment, even though it would gladly change places with any solitary pig, can it do so? So, quick and be off with you! Don't sully me, I would rather roam and idle about in a muddy ditch, at my own amusement, than to be put under the restraints that the ruler would impose. I will never take any official service, and thereby I will satisfy my own purposes.
Chuang-tzu reiterated and embellished Lao-tzu's devotion to laissez faire and opposition to state rule: "There has been such a thing as letting mankind alone; there has never been such a thing as governing mankind [with success]." In fact, the world simply "does not need governing; in fact it should not be governed." Chuang-tzu was also the first to work out the idea of "spontaneous order," developed particularly by Proudhon in the nineteenth and by F. A. Hayek of the Austrian School in the twentieth Century: "Good order results spontaneously when things are let alone."
Chuang-tzu, moreover, was perhaps the first theorist to see the State as a brigand writ large: "A petty thief is put in jail. A great brigand becomes a ruler of a State." Thus the only difference between State rulers and out-and-out robber chieftains is the size of their depredations. This theme of ruler-as-robber was to be repeated, independently of course, by Cicero and then by St. Augustine and other Christian thinkers in the Middle Ages.
Editor's Note: Murray N. Rothbard (1926-1995) was dean of the Austrian School. This article is taken from the first section of "Concepts of the Role of Intellectuals in Social Change Toward Laissez Faire," The Journal of Libertarian Studies, Vol IX No. 2 (Fall 1990). You can download a PDF version of the original paper here.
If you enjoyed this essay, be sure to procure the latest book by Lin Yutang, The Importance of Living. This book is a wry, witty antidote to the dizzying pace of the modern world. Lin Yutang's prescription is the classic Chinese philosophy of life: Revere inaction as much as action, invoke humor to maintain a healthy attitude, and never forget that there will always be plenty of fools around who are willing-indeed, eager-to be busy, to make themselves useful, and to exercise power while you bask in the simple joy of existence.
Find your joy at The Daily Reckoning's Bookstore:
3 Signs Black Friday Was a Bust
By Craig Wilson Posted November 30, 2016
Economic confidence in America is at an all time high yet Black Friday sales were a total let down. Here are 3 signs Black Friday has met a slow death. Craig Wilson reports… | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,147 |
\section{Introduction}
In this paper we employ machinery of deterministic random walks
to produce an improved strategy in the pathological liar game
with a linearly bounded liar. We also provide
discrepancy bounds of independent interest for a discretized
random walk which we call the ``liar machine''. Liar games,
introduced by R\'enyi and Ulam \cite{R61,U76}, are played by a
questioner and responder, whom we can Paul and Carole,
respectively, according to tradition; they model search in the
presence of error. The original variant is like ``twenty
questions'' to identify a distinguished element of the search
space, except with lies; while in the pathological variant,
Carole lies as much possible, and Paul tries to preserve at
least one element of the search space. Winning strategies in
liar games correspond to adaptive codes, introduced by
Berlekamp \cite{B64}. A primary objective in developing
winning strategies for liar games is to optimize the size of a
search space that can be processed given the number of
questions Paul can ask and a constraint on how Carole may lie.
Translated into coding theory language, this objective is to optimize
the size of a message set that can be handled given the number
of bits to be transmitted and a constraint on how noise can
corrupt the transmission. Berlekamp's codes in \cite{B64} are
adaptive packing codes for error-correction, corresponding to
the original liar game, whereas the pathological liar game,
introduced by the second author and Yan \cite{EY04},
corresponds to adaptive covering codes. For both the liar game
and adaptive coding viewpoints there is a theoretical size
limit on the search space, called the sphere bound, that
provides the target for optimization, often in terms of a
multiple of the sphere bound.
We combine two ideas to improve the best-known winning strategy
for the pathological liar game with Yes-No questions and a
linearly bounded liar. The first idea is to reduce the
pathological liar game to a chip-moving machine on the integer
line, which we call the liar machine, introduced implicitly by Spencer and
Winkler for the original liar game \cite{SW92}. The second is
to adapt the analysis of deterministic random walks on the
integers, developed by the first author, Doerr, Spencer, and
Tardos \cite{CDST07}, to the time-evolution of the liar
machine, and confirm a winning strategy in the pathological
liar game. Our main results are pointwise and interval
discrepancy bounds on the time-evolution of the liar machine as
compared to random walks on the integers, in Theorems
\ref{thm:ptwiseupperbound} and \ref{thm:intervalupperbound};
and an improved upper bound on the size of the search space for
which Paul can win the pathological liar game with Yes-No
questions and a linearly bounded liar, in Corollary
\ref{thm:pathGameBound}.
\section{Definitions and main results}
\subsection{The liar game and pathological variant}
The R\'enyi-Ulam liar game is an $n$-round 2-person
question-and-answer game on a search space
$[M]:=\{1,\ldots,M\}$. A fixed integer parameter $e\geq 0$ is
the maximum number of {\em lies} an element of the search space
can accumulate before being disqualified, and the game begins
with an initial function $\ell:\{1,\ldots,M\}\rightarrow
\{0,1,\ldots,e\}$, representing the initial assignment of up to
$e$ lies to each $y\in [M]$.
As elements of $M$ are distinguished only by their number of
lies, we may ignore element labels and consider instead the
initial state vector $x_0=(x_0(0),x_0(1),\ldots,x_0(e))$, where
$x_0(i)=|\{y\in [M]:\ell(y)=i\}|$ is the number of elements of
$[M]$ initialized with $i$ lies. Most often we set
$x_0=(M,0,\ldots,0)$. Paul and Carole play an $n$-round game in
which Paul attempts to discover a distinguished element
$z\in[M]$ of the search space. To start each round, Paul weakly
partitions $[M]$ into two parts by choosing a {\em question}
$(A_0,A_1)$ such that $[M]=A_0\ensuremath{\mathaccent\cdot\cup} A_1$, where $\ensuremath{\mathaccent\cdot\cup}$
denotes disjoint union. We interpret this choice as the
question, ``Is $z\in A_0$?''. Carole completes the round by
responding with her {\em answer}, an index $j\in \{0,1\}$. For
each $y\in [M]$, if $y\in A_j$, no additional lie is assigned
to $y$, but if $y\in A_{1-j}$, one additional lie is assigned
to $y$. Any $y\in [M]$ accumulating $e+1$ lies is {\em
disqualified}. We interpret Carole's answer of $j=0$ as ``Yes''
and of $j=1$ as ``No''. Analogous to the definition of $x_0$,
for each $s=1,\ldots,n$, let the state vector
$x_s=(x_s(0),\ldots, x_s(e))$ record the number of elements
$x_s(i)$ that have $i$ lies after the end of round $s$. Paul's
question $(A_0,A_1)$ in round $s$ corresponds to a question
vector $a_s=(a_s(0),\ldots,a_s(e))$ with $0\leq a_s(i)\leq
x_{s-1}(i)$ for all $0\leq i\leq e$, by letting $a_s(i)$ count
the number of elements in $A_0$ that have $i$ lies at the end
of round $s-1$. Define the right-shift operator $R$ on any
vector $x=(x(0),\ldots,x(e))$ by $R(x)=(0,x(0),\ldots,x(e-1))$.
Given $x_{s-1}$ and $a_s$,
define \\
\begin{eqnarray*}
Y(x_{s-1},a_s) & := & a_s+R(x_{s-1}-a_s), \\
N(x_{s-1},a_s) & := & x_{s-1}-a_s + R(a_s);
\end{eqnarray*}
and for each $s=1,\ldots,n$, set $x_s=Y(x_{s-1},a_s)$ if Carole
responds $j=0$ (``Yes'') in round $s$, and otherwise
$x_s=N(x_{s-1},a_s)$ if Carole responds $j=1$ (``No'') in round
$s$. Elements $y\in [M]$ that accumulate $e+1$ lies are shifted
out to the right and may be ignored for the rest of the game.
Paul wins the original liar game if
$\sum_{i=0}^{e}x_n(i)\leq 1$, that is, if all but at most one
element are disqualified after $n$ rounds; he wins the
pathological liar game if $\sum_{i=0}^{e}x_n(i)\geq 1$, that
is, if at least one element survives after $n$ rounds. We are
primarily interested in the pathological variant, which may be
interpreted as having a capricious Carole lying to eliminate
elements as quickly as possible, while Paul forms questions to
prevent all elements from being disqualified. We summarize the
pathological liar game as follows.
\begin{definition}
Let $n,M,e\geq 0$ be integers, and let $x=(x(0),x(1),\ldots,x(e))$
be a nonnegative integer vector with $\sum_{i=0}^{e} x(i)=M$.
Define the $(x,n,e)^*_2$-game to be the $n$-round pathological
liar game with Yes-No questions, initial configuration $x$,
and $e$ lies. We say that Paul can win the $(x,n,e)^*_2$-game
provided there exists a winning strategy for Paul regardless of
Carole's responses.
\end{definition}
In the notation $(x,n,e)^*_2$, use of the asterisk indicates the
pathological variant of the liar game rather than the original.
The subscript 2 means that questions are binary and symmetric
with respect to replacing $a_s$ with $x_{s-1}-a_s$ while preserving
the same two vectors as candidates for $x_s$. This corresponds in
coding theory to the binary symmetric channel assumption; see \cite{EN09}
for a much broader class of
channel assumptions.
\subsection{The liar machine and the linear machine\label{sec:liarLinearDef}}
We define the ``liar machine'' as follows. Start with some
configuration of chips on the even or odd integers (but not both). Number the chips
$c_1,c_2,\ldots$ left-to-right. At each location with, say,
$k$ chips, send $\floor{k/2}$ of the chips one step left, and
$\floor{k/2}$ one step right. If one chip remains
(because $k$ is odd) we break the tie by sending the highest-indexed $c_j$ one step
left if $j$ is even or one step right if $j$ is odd.
Formally, define the ``starting configuration'' to be a map
$f_0 : {\mathbb Z} \rightarrow {\mathbb N}$ with finite support lying in $2{\mathbb Z}$ or $2{\mathbb Z}+1$. Then, given
$f_t : {\mathbb Z} \rightarrow {\mathbb N}$, define $\chi_t : {\mathbb Z} \rightarrow
\{-1,0,1\}$ by
\begin{equation} \label{eq:chidef}
\chi_t(j) = \left \{ \begin{array}{ll} 0 & \textrm{ if } f_j \equiv 0 \pmod{2} \\ (-1)^{\sum_{i<j} \chi_t(i)} & \textrm{ if } f_j \equiv 1 \pmod{2}. \end{array} \right .
\end{equation}
Then we define
$$
f_{t+1}(j) = \frac{ f_t(j-1) + f_t(j+1)+ \chi_t(j-1) - \chi_t(j+1) }{2}.
$$
Now, we define the ``linear machine'' by taking $g_0 : {\mathbb Z}
\rightarrow {\mathbb N}$ to be any function. Let the operator ${\mathcal L} :
{\mathbb Z}^{\mathbb Z} \rightarrow {\mathbb Z}^{\mathbb Z}$ be defined by
$$
{\mathcal L} g(j) = \frac{g(j-1)}{2} + \frac{g(j+1)}{2},
$$
and define $g_{t+1} = {\mathcal L} g_t$. Then $g_t(j)$ is just the
expected number of chips at location $j$ after a simple random
walk on ${\mathbb Z}$ starting from the configuration $g_0$. In
particular, we expect $g_t$ and $f_t$ to be relatively close to
one another if $g_0 \equiv f_0$. Also, define the operator
$\Delta: {\mathbb Z}^{\mathbb Z} \rightarrow {\mathbb Z}^{\mathbb Z}$ by
$$
\Delta f(j) = f(j-1).
$$
It is easy to see that ${\mathcal L}$ and $\Delta$ are linear, and they
commute with each other. We write $\delta_j \in {\mathbb Z}^{\mathbb Z}$ for the
function which is $1$ at $j$ and $0$ elsewhere. In order to
consider intervals in a configuration, for a set $S \subset {\mathbb Z}$
and a function $h : {\mathbb Z} \rightarrow {\mathbb R}$, define $h(S) = \sum_{i
\in S} h(i)$.
\subsection{Main results}
Our first two main results are a pointwise and an interval discrepancy bound
in the time-evolution of the liar machine versus the linear machine starting
with the same initial configuration.
\begin{theorem} \label{thm:ptwiseupperbound}
Let $f_0 \equiv g_0$, and define $f_t$ and $g_t$ according to
the evolution of the liar machine and linear machine, respectively, as
described above. Then
$$
|f_t(j) - g_t(j)| < 12 \log t
$$
for all $t \geq 2$, $j \in {\mathbb Z}$.
\end{theorem}
\begin{theorem} \label{thm:intervalupperbound}
Let $I=[a,b] \subset {\mathbb Z}$ and $f_0 \equiv g_0$, and define
$f_t(I)$ and $g_t(I)$ according to the evolution of the liar
machine and linear machine, respectively, as described above. Then
$$
|f_t(I) - g_t(I)| \leq c^\prime \cdot \left \{
\begin{array}{ll} \sqrt{t} & \textrm{ if } B > \sqrt{t}/2 \\
B \log (t/B^2) & \textrm{ if } B \leq \sqrt{t}/2, \end{array} \right .
$$
where $B = b-a$ and $c^\prime$ is an absolute constant.
\end{theorem}
In Corollary \ref{cor:mainlowerbound} we prove that Theorems
\ref{thm:ptwiseupperbound} and \ref{thm:intervalupperbound} are
tight up to a constant multiple for a general initial
configuration $f_0$. Corollary \ref{cor:liarGameToLiarMachine}
allows extraction of a winning strategy for the pathological
liar game from the time-evolution of the liar machine, yielding
the following improved bound for the pathological liar game.
\begin{theorem}\label{thm:pathGameBound}Let
$M=\frac{2^n}{\binom{n}{\leq \lfloor fn\rfloor}}
(4/(1-2f))c'\sqrt{\log \log n}(1+o(1))$, where $c'$ is the
constant from Theorem \ref{thm:intervalupperbound}. Then for
$n$ sufficiently large, Paul can win the
$((M,0,\ldots,0),n,\lfloor fn\rfloor)^*_2$-pathological liar
game with $M$ elements and $\lfloor fn\rfloor$ lies on the
binary symmetric channel.
\end{theorem}
We now discuss the improvement provided by Theorem
\ref{thm:pathGameBound}. The previous best known bound on $M$
for $f\in (0,1/2)$ is Theorem 1 of \cite{DP86}, which in our
language bounds the smallest $M$ for which Paul can win the
$((M,0,\ldots,0),n,\lfloor f n \rfloor)_2^*$-game with a
restricted strategy (called ``non-adaptive'' in the literature)
of selecting all questions before any responses from Carole are
available.
\begin{theorem}[Delsarte and Piret]\label{thm:DelsartePiret}
Let $f\in (0,1/2)$. The minimum $M$ for which Paul can win the
$((M,0,\ldots,0),n,\lfloor fn \rfloor)_2^*$-game with the restriction
that all $n$ questions must be formed before any responses from Carole
are available is bounded by
$$
M \leq \left\lceil \frac{2^n}{\binom{n}{\leq \lfloor fn\rfloor}} n
\log 2\right\rceil.
$$
\end{theorem}
The quantity $2^n/\binom{n}{\leq \lfloor fn\rfloor}$ is called the sphere bound,
and so Theorem \ref{thm:pathGameBound} provides an improved {\em density} in the
best-known minimum $M$, from a linear to sub-logarithmic factor in $n$ times the
sphere bound. The sphere bound is an immediate lower bound on $M$;
this can be seen by defining an appropriate weight function on the liar game
state which Carole greedily minimizes (cf.~\cite[Lemma 3]{EPY05}).
In Theorem \ref{thm:DelsartePiret}, the ``spheres'' are Hamming balls of radius
$\lfloor fn \rfloor$ that are used to cover the binary discrete hypercube
(Hamming space) of dimension $n$. The equivalence of
wining strategies in the pathological liar game to coverings of
Hamming space by objects of size $\binom{n}{\leq \lfloor fn\rfloor}$ is
proved in Theorem 3.7 of \cite{EN09}.
We conclude the section by outlining the rest of the paper.
Section \ref{sec:liarMachineProofs} contains the proofs of the
liar machine discrepancy bounds: Theorems
\ref{thm:ptwiseupperbound} and \ref{thm:intervalupperbound},
and Corollary \ref{cor:liarGameToLiarMachine}. Section
\ref{sec:distribution} proves several technical distributional
facts about the binomial and hypergeometric distributions
needed to bound the distribution of chips in the liar machine
(via discrepancy from the linear machine). Section
\ref{sec:reduction} reduces a strategy for Paul in the
pathological liar game to the liar machine and blends the
preceding results into Theorem \ref{thm:pathGameBound}. Section
\ref{sec:conclusion} contains open questions and closing
remarks.
\section{Proofs of liar machine discrepancy bounds\label{sec:liarMachineProofs}}
The proofs of Theorems \ref{thm:ptwiseupperbound} and
\ref{thm:intervalupperbound} flow directly from the definitions
in Section \ref{sec:liarLinearDef}, and resemble the arguments in \cite{CDST07}. A bound on, and the
bimodality in space of, a term that tracks the discrepancy
between the liar machine and the linear machine is deferred
until Lemma \ref{lemma:painful}. Next, Lemma
\ref{lem:parityForce} shows that the parity of the number of
chips in the liar machine can be pre-selected for an arbitrary
product of intervals in space and time, by choosing an
appropriate initial configuration. This leads to a
complementary lower bound in Corollary \ref{cor:mainlowerbound}
on discrepancy for a general initial configuration. We adopt the convention, here and throughout, that $\binom{a}{b}$ is zero unless $a$ and $b$ are nonnegative integers and $b \leq a$.
\begin{proof}[Proof of Theorem \ref{thm:ptwiseupperbound}] Evidently,
$$
f_{t+1} = {\mathcal L} f_t + \frac{1}{2} (\Delta - \Delta^{-1}) \chi_t.
$$
Therefore, by the linearity of ${\mathcal L}$ and the fact that it commutes with $\Delta$,
$$
f_t = {\mathcal L}^{t} f_0 + \frac{1}{2} \sum_{s = 0}^{t-1}
(\Delta - \Delta^{-1}) {\mathcal L}^{s} \chi_{t-1-s}.
$$
Since $g_t = {\mathcal L}^t g_0 = {\mathcal L}^t f_0$,
\begin{align*}
2|f_t - g_t| &= \left | \sum_{s = 0}^{t-1} (\Delta - \Delta^{-1}) {\mathcal L}^{s}
\chi_{t-1-s} \right | \\
& \leq 2 + \sum_{s = 1}^{t-1} \left | (\Delta - \Delta^{-1}) {\mathcal L}^{s} \chi_{t-1-s} \right |.
\end{align*}
Consider a fixed $s$. Denote by $z_i$ the $i^\textrm{th}$
element of the support of $\chi_{t-1-s}$, with $z_0$ its
minimal element and $z_{i+1} > z_i$ for each $i$. Note that the $z_i$ all have the same parity, by our assumption that the chips occupy only even or only odd integers. Then
\begin{align}
\nonumber (\Delta - \Delta^{-1}) {\mathcal L}^{s} \chi_{t-1-s} &= (\Delta - \Delta^{-1}) {\mathcal L}^{s} \sum_{i} (-1)^i \delta_{z_i} \\
\nonumber &= \sum_{i} (-1)^i (\Delta - \Delta^{-1}) {\mathcal L}^{s} \delta_{z_i} \\
\nonumber &= \sum_{i} (-1)^i (\Delta - \Delta^{-1}) {\mathcal L}^{s} \Delta^{z_i} \delta_0 \\
\label{eq:sum1} &= \sum_{i} (-1)^i \Delta^{z_i} (\Delta - \Delta^{-1}) {\mathcal L}^{s} \delta_0.
\end{align}
Note that
$$(\Delta - \Delta^{-1}) {\mathcal L}^{s}
\delta_0(j) = 2^{-s} \left ( \binom{s}{(s+j-1)/2} - \binom{s}{(s+j+1)/2} \right ).
$$
Therefore, by Lemma \ref{lemma:painful}, $(\Delta - \Delta^{-1}) {\mathcal L}^{s}
\delta_0$ is bimodal on its support. This means that the alternating sum
$\sum_{i} (-1)^i \Delta^{z_i} (\Delta - \Delta^{-1}) {\mathcal L}^{s}
\delta_0$ is bounded by at most four times the maximum (in absolute
value) of the quantity $(\Delta - \Delta^{-1}) {\mathcal L}^{s}
\delta_0$, since the $z_i$ all have the same parity. This maximum, by Lemma
\ref{lemma:painful}, is at most $3/s$.
Therefore,
\begin{align*}
|f_t - g_t| &\leq \frac{1}{2} \left ( 12 \sum_{s = 1}^{t-1} \frac{1}{s} + 2 \right ) \\
&\leq 12 \log t.
\end{align*}
\end{proof}
\begin{proof}[Proof of Theorem \ref{thm:intervalupperbound}] Without loss of generality, $I = \{1,\ldots,B\}$. We may also assume that $B$ is even. Evidently,
$$
f_{t+1}(I) = \left ( {\mathcal L} f_t(I) + \frac{1}{2} (\Delta - \Delta^{-1}) \chi_t(I) \right ).
$$
Therefore, by the linearity of ${\mathcal L}$ and the fact that it commutes with $\Delta$,
$$
f_t(I) = \sum_{i = 1}^B \Delta^i {\mathcal L}^{t} f_0(I) + \frac{1}{2}
\sum_{s = 0}^{t-1} (\Delta - \Delta^{-1}) {\mathcal L}^{s} \chi_{t-1-s}(I).
$$
Since $g_t(I) = {\mathcal L}^t g_0(I) = {\mathcal L}^t f_0(I)$,
\begin{align*}
2|f_t(I) - g_t(I)| &= \left | \sum_{s = 0}^{t-1} (\Delta - \Delta^{-1}) {\mathcal L}^{s} \chi_{t-1-s}(I) \right | \\
& \leq 2 + \sum_{s = 1}^{t-1} \left | (\Delta - \Delta^{-1}) {\mathcal L}^{s} \chi_{t-1-s}(I) \right |.
\end{align*}
Denote by $z_i$ the $i^\textrm{th}$ element of the support of $\chi_{t-1-s}$, with $z_0$ its minimal element and $z_{i+1} > z_i$ for each $i$. Then
\begin{align}
\nonumber (\Delta - \Delta^{-1}) {\mathcal L}^{s} \chi_{t-1-s}(I) &= (\Delta - \Delta^{-1}) {\mathcal L}^{s} \sum_{i} (-1)^i \delta_{z_i}(I) \\
\nonumber &= \sum_{i} (-1)^i (\Delta - \Delta^{-1}) {\mathcal L}^{s} \delta_{z_i}(I) \\
\nonumber &= \sum_{i} (-1)^i (\Delta - \Delta^{-1}) {\mathcal L}^{s} \Delta^{z_i} \delta_0(I) \\
\nonumber &= \sum_{i} (-1)^i \Delta^{z_i} (\Delta - \Delta^{-1}) {\mathcal L}^{s} \sum_{k=1}^B \Delta^{k} \delta_0 \\
\nonumber &= \sum_{i} (-1)^i \Delta^{z_i} \sum_{k=1}^B \Delta^{k} (\Delta - \Delta^{-1}) {\mathcal L}^{s} \delta_0 \\
\nonumber &= \sum_{i} (-1)^i \Delta^{z_i} (\Delta^{B+1} + \Delta^B - \Delta - 1) {\mathcal L}^{s} \delta_0 \\
\label{eq:sum2} &= \sum_{i} (-1)^i \Delta^{z_i} (\Delta + 1)(\Delta^{B} - 1) {\mathcal L}^{s} \delta_0.
\end{align}
Note that ${\mathcal L}^s \delta_0(j) = 2^{-s} \binom{s}{(s+j)/2}$, so that
$$
(\Delta^B - 1) {\mathcal L}^{s} \delta_0(j) = 2^{-s} \left ( \binom{s}{(s+j-B)/2} - \binom{s}{(s+j)/2} \right ).
$$
By Lemma \ref{lemma:painful}, when $B = \Omega(\sqrt{s})$, the maximum possible value of the right-hand side is $\Theta(1/\sqrt{s})$; when $B = o(\sqrt{s})$, it is of order
$$
2^{-s} B \cdot \max_{j} \left ( \binom{s}{(s+j-1)/2} - \binom{s}{(s+j+1)/2} \right ) = \Theta(B/s).
$$
Since an alternating sum over a bimodal function like $(\Delta + 1)(\Delta^{B} - 1) {\mathcal L}^{s} \delta_0$ is bounded by four times the maximum absolute value of that function,
\begin{align*}
|f_t(I) - g_t(I)| &\leq c \sum_{s = 1}^{t-1} \frac{\min(\sqrt{s},B)}{s+1} \\
&\leq c^\prime \cdot \left \{ \begin{array}{ll} \sqrt{t} & \textrm{ if } B > \sqrt{t}/2 \\
B \log (t/B^2) & \textrm{ if } B \leq \sqrt{t}/2, \end{array} \right .
\end{align*}
for some absolute constants $c$ and $c^\prime$.
\end{proof}
\begin{lemma} \label{lemma:painful} There exists constants $c_1$, $c_2$, $c_3$, and $c_4$ so that the following holds for all $s \geq 1$ and even $B > 0$. Define
$$
h_B(j) = 2^{-s} \left ( \binom{s}{(s+j-B)/2} - \binom{s}{(s+j)/2} \right ).
$$
Then, when $B \geq \sqrt{s}$,
$$
\frac{c_1}{\sqrt{s}} \leq \max_j \left |h_B(j) \right |\leq \frac{c_2}{\sqrt{s}},
$$
where the left-hand inequality holds for all $s \geq S$, some absolute constant. When $B \leq \sqrt{s}$,
$$
\frac{c_3B}{s} \leq \max_j \left |h_B(j) \right |\leq \frac{c_4B}{s}.
$$
Furthermore, $h_B(j)$ is bimodal on its support.
\end{lemma}
\begin{proof} It is easy to see that
$$
h_2(j) = 2^{-s} \frac{j-1}{s+1} \binom{s+1}{(s+j)/2}.
$$
Therefore,
$$
\frac{h_2(j)}{\Delta^2 h_2(j)} = \frac{(j-1)(s-j+4)}{(j-3)(s+j)},
$$
which equals one when $j^2 - 4j - (s-2) = 0$, i.e., $j = 2 \pm \sqrt{s+2}$. Then the maximum of $|h_2(j)|$ can be bounded by
\begin{align*}
2^{-s} \frac{|j_{\max}|-1}{s+1} \max_j \binom{s+1}{(s+j)/2} & \leq \frac{1 + \sqrt{s+2}}{s+1} \cdot \frac{1}{\sqrt{3(s+1)/2}} \\
& \leq \frac{1 + 2}{(s+1)\sqrt{2}} < \frac{3}{s}.
\end{align*}
Since $h_B(j) = \sum_{i=0}^{B/2-1} h_2(j-2i)$, it immediately follows that
$$
\max_j \left | h_B(j)\right | \leq \frac{B}{2} \max_j \left | h_2(j) \right | < \frac{3B}{2s},
$$
so we may take $c_4 = 3/2$. Now, it is clear that
\begin{align*}
\max_j \left |h_B(j)\right | &< \max_j 2^{-s} \cdot \binom{s}{(s+j)/2} \\
&< \frac{1}{\sqrt{s}},
\end{align*}
so we may take $c_2 = 1$.
On the other hand, by a version of the Local Central Limit
Theorem (see, e.g., \cite[Thm.~1.2.1]{L91}), $2^{-s}
\binom{s}{(s+j)/2} = \sqrt{\frac{2}{\pi s}} \cdot e^{-j^2/2s} +
O(s^{-3/2})$, so that we have
$$
h_B(j) = \sqrt{\frac{2}{\pi s}} \cdot e^{-(j-B)^2/2s} - \sqrt{\frac{2}{\pi s}} \cdot e^{-j^2/2s} + O(s^{-3/2}).
$$
Hence, when $B \geq \sqrt{s}$,
\begin{align*}
\max_j \left | h_B(j) \right | &\geq |h_B(0)| \\
&= \left | \sqrt{\frac{2}{\pi s}} \cdot e^{-B^2/2s} -
\sqrt{\frac{2}{\pi s}} +O(s^{-3/2})\right | \\
&\geq \sqrt{\frac{2}{\pi s}} \left | e^{-1/2} - 1 \right | + O(s^{-3/2})\\
&> \frac{1+o(1)}{4 \sqrt{s}},
\end{align*}
so we may take $c_1 = 1/4$ and $S$ sufficiently large. Note that the error term $O(s^{-3/2})$ is uniform in $j$ and therefore the $o(1)$ does not depend on $B$.
When $B < \sqrt{s}$,
\begin{align*}
2^s h_B(j) &= \binom{s}{(s+j-B)/2} - \binom{s}{(s+j)/2} \\
&= \binom{s}{(s+j)/2} \left ( \prod_{i=1}^{B/2} \frac{s+j-B+2i}{s-j+2i} - 1 \right ) \\
&= \binom{s}{(s+j)/2} \left ( \prod_{i=1}^{B/2} \left ( 1 + \frac{2j-B}{s-j+2i} \right ) - 1 \right ),
\end{align*}
so we have
\begin{align*}
\max_j h_B(j) &\geq h_B(\sqrt{s}) \\
&= 2^{-s} \binom{s}{(s+\sqrt{s})/2} \left ( \prod_{j=1}^{B/2} \left ( 1 + \frac{2 \sqrt{s}-B}{s-\sqrt{s}+2j} \right ) - 1 \right ) \\
&\geq 2^{-s} \binom{s}{(s+\sqrt{s})/2} \left ( \left ( 1 + \frac{\sqrt{s}}{s} \right )^{B/2} - 1 \right ) \\
&\geq \frac{c_0}{\sqrt{s}} \cdot \frac{B}{2\sqrt{s}} = \frac{c_0 B}{2 s},
\end{align*}
so we can take $c_3 = c_0/2$.
Finally, we have
\begin{align*}
2^s(h_B(j-2) - h_B(j)) &= \binom{s}{(s+j-B)/2-1} - \binom{s}{(s+j-B)/2} \\
& \qquad - \binom{s}{(s+j)/2-1} + \binom{s}{(s+j)/2} \\
&= 2^s (h_2(j-B) - h_2(j))\\
&= \frac{j-B-1}{s+1} \binom{s+1}{(s+j-B)/2} - \frac{j-1}{s+1} \binom{s+1}{(s+j)/2}.
\end{align*}
This quantity is positive when
$$
(j-B-1) \binom{s+1}{(s+j-B)/2} > (j-1) \binom{s+1}{(s+j)/2},
$$
i.e.,
$$
(j-B-1) \prod_{i=1}^{B/2} (s+j-2i+2) > (j-1) \prod_{i=1}^{B/2} (s-j+2i+2).
$$
(We may assume that each term of both products is nonnegative.) When $1 \leq j \leq B+1$, this inequality cannot be satisfied, since the left-hand side is nonpositive and the right-hand side is nonnegative. When $j > B+1$, the inequality is the same as
$$
\left (1-\frac{B}{j-1} \right ) \prod_{i=1}^{B/2} (s+j-2i+2) > \prod_{i=1}^{B/2} (s-j+2i+2).
$$
The left-hand side is nondecreasing in $j$ and the right-hand side is nonincreasing in $j$, so $h_B(j-2) - h_B(j)$ has at most one change of sign in this regime. When $j < 1$, we have the condition
$$
\prod_{i=1}^{B/2} (s+j-2i+2) < \left (1 + \frac{B}{j-B-1} \right ) \prod_{i=1}^{B/2} (s-j+2i+2),
$$
where again the left-hand side is nondecreasing in $j$ and the right-hand side is nonincreasing in $j$, so $h_B(j-2) - h_B(j)$ has at most one more change of sign. Therefore, $h_B(j)$ is bimodal on its support.
\end{proof}
\begin{lemma}\label{lem:parityForce} For each function
$g : \{0,\ldots,N-1\} \times \{0,\ldots,T-1\} \rightarrow \{0,1\}$,
there exists a chip-assignment function $f_0 : {\mathbb Z} \rightarrow {\mathbb N}$
so that, for all $0 \leq n < N$ and $0 \leq t < T$,
$$
f_t(n) \equiv g(n,t) \pmod{2},
$$
where $f_t$ is the state of the liar machine at time $t$ if $f_0$
is its initial state (i.e., at time $t=0$).
\end{lemma}
\begin{proof} We proceed by induction. For $T = 1$, the result is immediate: we simply set $f_0 \equiv g(\cdot,0)$. Suppose that the claim holds for $T$, i.e., there exists an $f_0$ so that $f_t$ agrees with $g(\cdot,t)$ in parity for each $t \in \{0,\ldots,T-1\}$. Now we perform a second induction (on $n$) to show the following claim:
\begin{claim*} For each $n \in \{0,\ldots,N-1\}$, there exists a chip-assignment function $f^{(n)}_0 : {\mathbb Z} \rightarrow {\mathbb N}$ so that, for all pairs $(n^\prime,t)$ with $0 \leq n^\prime < N$ and $0 \leq t < T$ or $0 \leq n^\prime < n$ and $t = T$,
$$
f^{(n)}_t(n^\prime) \equiv g(n^\prime,t) \pmod{2},
$$
where $f^{(n)}_t$ is the state of the liar machine at time $t$ if
$f^{(n)}_0$ is its initial state.
\end{claim*}
Again, the claim is immediate for $n=0$ (given the inductive
hypothesis), since we can just let $f^{(0)}_0 = f_0$ from the top-level induction.
Suppose it holds for $n$. If $f^{(n)}_T(n) \equiv g(n,T) \pmod{2}$,
then setting $f^{(n+1)}_0 = f^{(n)}_0$ clearly suffices to prove
the claim for $n+1$. If, however, $f^{(n)}_T(n) \not\equiv g(n,T)
\pmod{2}$, then define $f^{(n+1)}_0$ by
$$
f^{(n+1)}_0 (k) = \left \{ \begin{array}{ll} f^{(n)}_0(k)
& \textrm{if } k \neq n+T \\ f^{(n)}_0(k) + 2^T
& \textrm{if }k=n+T. \end{array} \right .
$$
Then $f^{(n+1)}_t(k) \equiv f^{(n)}_t(k) \pmod{2}$ for $t < T$ and $0 \leq k < N$, since
the ``new'' $2^T$ chips placed at site $n+T$ at time $t = 0$ are split
exactly in half at each time $t < T$, so that
$2 | 2^{T-t} | f^{(n+1)}_t(k) - f^{(n)}_t(k)$ for all $t < T$. For
$t = T$ and $k < n$, $f^{(n+1)}_t(k) = f^{(n)}_t(k)$, since the ``new''
chips can only occupy sites in $[n+T-t,n+T+t]$ at time $t$, which
for $T=t$ is the interval $[n,n+2T]$ not containing $k$. Finally,
there is one chip added to site $n$ at time $T$, i.e.,
$f^{(n+1)}_T(n) = f^{(n)}_T(n) + 1$, because exactly one of the $2^T$
``new'' chips makes it to site $n$ after $T$ steps. This means,
in particular, that $f^{(n+1)}_T(n) \equiv g(n,T) \pmod{2}$, completing
the induction.
\end{proof}
This ``parity forcing'' lemma implies that it is possible
to set the function $\chi_t(j)$ for any finite space-time interval to whatever we wish.
We may then conclude that Theorems \ref{thm:ptwiseupperbound} and
\ref{thm:intervalupperbound} are tight.
\begin{cor} \label{cor:mainlowerbound} Fix $T$, a nonnegative integer, and $N$, and integer.
There exists an $f_0 : {\mathbb Z} \rightarrow {\mathbb N}$ so that, letting
$g_0 \equiv f_0$, and defining $f_t$ and $g_t$ according to the
evolution of the liar machine and linear machine, respectively, we have
$$
|f_T(N) - g_T(N)| = \Omega(\log T).
$$
Fix an interval $I$ of any given length $B$. Then there exists
an $f^\prime_0 : {\mathbb Z} \rightarrow {\mathbb N}$ so that, letting $g^\prime_0 \equiv f^\prime_0$,
and defining $f^\prime_t$ and $g^\prime_t$ according to the evolution of the
liar machine and linear machine, respectively, we have
$$
|f^\prime_T(I) - g^\prime_T(I)| = \Omega \left( \left \{
\begin{array}{ll} \sqrt{T} & \textrm{ if } B > \sqrt{T}/2 \\
B \log (T/B^2) & \textrm{ if } B \leq \sqrt{T}/2 \end{array} \right .\right).
$$
\end{cor}
\begin{proof}
The same argument applies for both claims: we can set the
number of chips at each location and time so that the sums in
the proof of Theorems \ref{thm:ptwiseupperbound} and
\ref{thm:intervalupperbound} are maximized, in view of the lower bounds given by Lemma 6. In the first case, let
$\chi : \{N-T,\ldots,N+T\} \times \{0,\ldots,T-1\} \rightarrow
\{-1,0,1\}$ be chosen to maximize the sum (\ref{eq:sum1}); in the second case, let $\chi : \{\min(I)-T,\ldots,\max(I)+T\} \times \{0,\ldots,T-1\} \rightarrow \{-1,0,1\}$ be chosen to maximize the sum (\ref{eq:sum2}). Note that this
requires that $\chi$ alternate in sign on the support of its first
argument. Let $m_t$ be the minimum element of the support of
$\chi(\cdot,t)$. Define
$$
g(k,t) = \left \{ \begin{array}{ll}
\frac{1 - \chi(m_t,t)}{2} & \textrm{if }k = N-T-1 \\
|\chi(k,t)| & \textrm{if }N-T \leq k \leq N+T \\
0 & \textrm{otherwise},
\end{array} \right .
$$
in the first case, or else
$$
g(k,t) = \left \{ \begin{array}{ll}
\frac{1 - \chi(m_t,t)}{2} & \textrm{if }k = \min(I)-T-1 \\
|\chi(k,t)| & \textrm{if }\min(I)-T \leq k \leq \max(I)+T \\
0 & \textrm{otherwise},
\end{array} \right .
$$
in the second case. Then, we may obtain the desired $f_0$ by
applying the preceding lemma to $g$. Since the (possible) chip
at $k = N-T-1$ or $k = \min(I)-T-1$ can never even reach the
site $N$ or any of $I$ before time $T$, the relevant sums are
unaffected by this small modification. However, the presence
of such a chip when appropriate ensures that $\chi_t(j) =
\chi(j,t)$ for each $(j,t) \in \{N-T,\ldots,N+T\} \times
\{0,\ldots,T-1\}$ or $(j,t) \in \{\min(I)-T,\ldots,\max(I)+T\}
\times \{0,\ldots,T-1\}$ (where $\chi_t(j)$ is as defined in
(\ref{eq:chidef})).
\end{proof}
\section{Liar machine distributional bound\label{sec:distribution}}
We need several technical facts to obtain to obtain lower
bounds for the configuration of chips in the time-evolution of
the liar machine. Lemma \ref{cutoffLemma} shows that the
cumulative distribution of the binomial random variable drops
off sharply just below where it is evaluated.
Lemma \ref{lem:relativeCDF} shows that the ratio of the
evaluations at the same relative position of the cumulative
distributions of binomial random variables with a similar
number of trials is not too small. This is needed to bound the
left tail of the liar machine from below.
Because for Theorem \ref{ref:liarMachineBound} we will run $n$
steps of the liar machine in two stages of $n_1$ and $n_2$
steps, respectively, terms of a hypergeometric distribution
arise. Theorem \ref{thm:hyperGeom} quotes a result on the
closeness of the median to the mean of a generalized
hypergeometric distribution from \cite{Si01}, specialized to
the hypergeometric distribution in Corollary \ref{mmCor}. Then
in Proposition \ref{halfprop} we show that for $r$ sufficiently
close to but below the mean $\mu$, asymptotically almost half
of the hypergeometric distribution lies below $r$. This allows
transferring from a partial sum of hypergeometric distributions
in $n_1$ and $n_2$ to that of the binomial distribution in $n$,
in Proposition \ref{prop:HyperGeomApprox}. This last result is
critical for Theorem \ref{ref:liarMachineBound} in negotiating
a lower bound on the number of chips between two stages in the
time-evolution of the liar machine, so that at least one chip
survives in a prescribed interval after $n$ rounds.
Throughout the section, we use the following notation. Let $n
\rightarrow \infty$, fix $f \in (0,1/2)$, and set
$$
n_1 = n - \floor{\frac{4}{(1 - 2f)^2} \log \log n}
$$
and $n_2 = n - n_1$. The numbers of rounds in the first and
second stages of the $n$-round liar machine, are $n_1$ and
$n_2$, respectively.
Define $F=\lfloor f n\rfloor$, $F_1 = \lfloor f n_1\rfloor$,
and $F_2 = F-F_1$.
\begin{lemma} \label{cutoffLemma}
For any integer sequence $n_3 = n_3(n) \rightarrow \infty$,
there is a function $\epsilon(n,f)$ with $\lim_{n \rightarrow
\infty} \epsilon(n,f) = 0$ so that
$$
\sum_{i = F - n_3}^{F} \frac{\binom{n}{i}}{\binom{n}{\leq F}}
\geq 1 - \epsilon(n,f).
$$
\end{lemma}
\begin{proof}
Note that
\begin{align*}
\frac{\binom{n}{F - t}}{\binom{n}{F}} &= \frac{F!(n-F)!}{(F-t)!(n-F+t)!} \\
&\leq \frac{F^t}{(n-F+1)^t}\\
&\leq \frac{(fn)^t}{((1-f)n)^t} = \left ( \frac{f}{1-f} \right)^t.
\end{align*}
Therefore,
\begin{align*}
\sum_{i = 0}^{F-n_3} \binom{n}{i} & \leq \sum_{i = 0}^{F-n_3}
\binom{n}{F} \left ( \frac{f}{1-f} \right)^{F-i} \\
&\leq \binom{n}{F} \sum_{j = n_3}^{\infty} \left ( \frac{f}{1-f}
\right)^j \\
&\leq \binom{n}{\leq F} \left ( \frac{f}{1-f} \right)^{n_3}
\cdot \frac{1-f}{1-2f}.
\end{align*}
It follows that
\begin{align*}
\sum_{i = F-n_3}^F \frac{\binom{n}{i}}
{\binom{n}{\leq F}} &= 1 - \sum_{i = 0}^{F-n_3-1}
\frac{\binom{n}{i}}{\binom{n}{\leq F}}\\
& \geq 1 - \left ( \frac{f}{1-f} \right)^{n_3} \cdot \frac{1-f}{1-2f},
\end{align*}
which clearly tends to $1$ as $n \rightarrow \infty$, since $f < 1/2$ implies $f/(1-f) < 1$.
\end{proof}
\begin{lemma}\label{lem:relativeCDF}
There exists a function $\delta(n,f)$ with
$\lim_{n \rightarrow \infty} \delta(n,f) = 0$ so that
$$
\frac{2^n}{\binom{n}{\leq \floor{fn}}}
\cdot \frac{\binom{n_1}{\floor{fn_1}}}{2^{n_1}}
\geq (\log n)^{2 - \delta(n,f)}.
$$
\end{lemma}
\begin{proof} First of all, note that
\begin{align*}
\frac{2^n}{\binom{n}{\leq F}} \cdot \frac{\binom{n_1}{F_1}}{2^{n_1}} =
2^{n-n_1} \frac{\binom{n_1}{F_1}}{\binom{n}{F}}
\cdot \frac{\binom{n}{F}}{\binom{n}{\leq F}}.
\end{align*}
Denote by $A$, $B$, and $C$ the three factors on the right-hand
side. Since
$$
n - n_1 = \floor{\frac{4}{(1-2f)^2} \log \log n} \geq
\frac{4}{(1-2f)^2} \log \log n -1,
$$
we have
$$
A \geq \frac{1}{2} (\log n)^{4 \log 2/(1-2f)^2}.
$$
Then, applying the estimates from the proof of Lemma
\ref{cutoffLemma},
\begin{align*}
\binom{n}{\leq F} &= \binom{n}{F} \sum_{t = 0}^F
\frac{\binom{n}{F-t}}{\binom{n}{F}} \\
&\leq \binom{n}{F} \sum_{t = 0}^\infty \left (\frac{f}{1-f}
\right )^t = \binom{n}{F} \cdot \frac{1-f}{1-2f},
\end{align*}
so that $C \geq \frac{1-2f}{1-f}$. Now, we use the fact that
$\binom{n}{\alpha n} = 2^{H(\alpha)n + O(1)}/\sqrt{n}$, where
$H(x) = -x \log_2 x - (1-x) \log_2 (1-x)$ is the entropy
function. We may therefore write $B$ as
\begin{align*}
\frac{\binom{n_1}{F_1}}{\binom{n}{F}}
&= 2^{H(f)(n_1 - n) + O(1)} \cdot \frac{\sqrt{n}}{\sqrt{n_1}}\\
&\geq \beta \left ( 2^{\frac{-4 H(f)}{(1-2f)^2} \log \log n} \right )\\
&= \beta (\log n)^{-\frac{4 H(f)\log 2}{(1-2f)^2}},
\end{align*}
where $\beta>0$ is an absolute constant. Combining these
bounds, we have
\begin{align*}
ABC \geq \frac{\beta}{2} \frac{1-2f}{1-f} (\log n)^{\frac{4 \log 2}
{(1-2f)^2}(1-H(f))}.
\end{align*}
It is easy to check that $\frac{4 \log 2}{(1-2f)^2}(1-H(f)) > 2$ for all $f \in (0,1/2)$, from which the desired bound follows.
\end{proof}
\begin{lemma}
$$ \log \binom{n}{\leq \floor{fn}} = \Theta(n),$$
where the implicit constant depends on $f$.
\end{lemma}
\begin{proof} This follows immediately from the estimate
$$
\binom{n}{\floor{fn}} = 2^{H(f) n + O(\log n)}
$$
as in the proof of Lemma \ref{lem:relativeCDF}.
\end{proof}
The following result appears in \cite{Si01}.
\begin{theorem}\label{thm:hyperGeom}
Let an urn contain $R$ red balls and $B$ black balls.
Suppose each red ball has weight $w_\circ$ and each black has weight
$w_\bullet$. Suppose that the balls are selected one-by-one without
replacement where each as yet unselected ball is given a probability
of being selected at the next round that equals its current fraction
of the total weight of all unselected balls. Suppose $r$ and $b$
satisfy $r = R(1 - e^{-w_\circ \rho})$ and $b = B(1 - e^{-w_\bullet \rho})$,
for some fixed $\rho > 0$. Let $r + b$ balls be drawn from the urn
as prescribed. Let $X_\circ$ be the number of red balls selected
by this random process, and let $X_\bullet$ be the number of black,
so that $X_\circ + X_\bullet = r + b$. Then $r^\prime = \ceil{r}$
or $\floor{r}$ and $b^\prime = \ceil{b}$ or $\floor{b}$ are the
medians of $X_\circ$ and $X_\bullet$, respectively.
\end{theorem}
By taking $w_\circ = w_\bullet$, i.e., $r/b = R/B$, this result
gives the median of the hypergeometric distribution. If we let
$r+b = T$ be the total number of balls drawn, then this gives
$b = BT/(R+B)$, i.e., the mean of $X_\circ$. Hence, we have
the following Corollary.
\begin{cor} \label{mmCor} If $\mu$ is the mean and $m$ the median
of a hypergeometric distribution, then $m = \ceil{\mu}$ or $m = \floor{\mu}$.
\end{cor}
\begin{prop} \label{halfprop} Let $0 \leq r \leq fn_2$. Suppose
that $fn_1 + r$ elements are drawn uniformly at random (without
replacement) from a set $S = S_1 \ensuremath{\mathaccent\cdot\cup} S_2$ with
$|S_1| = n_1$ and $|S_2| = n_2$. Let $X$ denote the number of
such elements in $S_2$. If $n_1,n_2 \rightarrow \infty$, there
is some function $h: {\mathbb N} \rightarrow {\mathbb N}$ with $h = \omega(1)$ so
that, for $r \geq fn_2 - h(n)$, we
have
$$
\Pr \left ( X \leq r \right ) \geq 1/2 - o(1).
$$
\end{prop}
\begin{proof} $X$ follows a hypergeometric distribution with parameters $n = n_1 + n_2$, $n_2$, and $R = fn_1 + r$. Its expectation is therefore given by $\mu = \frac{n_2}{n}(fn_1+r) = n_2 R/n$. Writing $p(k)$ for the probability that $X = k$, note that
\begin{align*}
p(k) &= \frac{\binom{n_2}{k}\binom{n_1}{R-k}}{\binom{n}{R}}.
\end{align*}
When $k = \mu + \Delta$, we have
\begin{align*}
\frac{p(k)}{p(k-1)} &= \frac{\binom{n_2}{k}\binom{n-n_2}{R-k}}{\binom{n_2}{k-1}\binom{n-n_2}{R-k+1}} \\
&= \frac{(k-1)!(n_2-k+1)!(R-k+1)!(n-n_2-R+k-1)!}{k!(n_2-k)!(R-k)!(n-n_2-R+k)!} \\
&= \frac{(n_2-k+1)(R-k+1)}{k(n-n_2-R+k)} \\
&= \frac{(n_2 - \frac{Rn_2}{n} - \Delta + 1)(R - \frac{Rn_2}{n} - \Delta + 1)}{(\frac{Rn_2}{n} + \Delta)(n - n_2 - R + \frac{Rn_2}{n} + \Delta)}\\
&= \frac{(1 - \frac{R}{n} + \frac{1-\Delta}{n_2})(1 - \frac{n_2}{n}+\frac{1-\Delta}{R})}{(1 - \frac{n_2}{n} - \frac{R}{n} + \frac{Rn_2}{n^2} + \frac{\Delta}{n})(1 + \frac{\Delta n}{Rn_2})}.
\end{align*}
Then,
\begin{align*}
\frac{p(k)}{p(k-1)} - 1 &= \frac{(1 - \frac{R}{n} + \frac{1-\Delta}{n_2})(1 - \frac{n_2}{n}+\frac{1-\Delta}{R})}{(1 - \frac{n_2}{n} - \frac{R}{n} + \frac{Rn_2}{n^2} + \frac{\Delta}{n})(1 + \frac{\Delta n}{Rn_2})} - 1\\
&= \frac{O ( \Delta n^2)}{n_2Rn (1 - \frac{n_2}{n} - \frac{R}{n} + \frac{Rn_2}{n^2} + \frac{\Delta}{n})(1 + \frac{\Delta n}{Rn_2})}.
\end{align*}
Since $n_1+n_2=n$, it follows that $n_2 + R \leq n$. Therefore,
\begin{align*}
\frac{p(k)}{p(k-1)} - 1 &=O( \Delta ) \frac{n^2}{n_2Rn (\frac{Rn_2}{n^2}+ \frac{\Delta}{n})(1 + \frac{\Delta n}{Rn_2})} \\
&= O( \Delta ) \cdot \frac{n^2}{(n_2R + \Delta n)^2}\\
&= O( \Delta ) \cdot \left ( \frac{1}{\Delta + n_2R/n} \right )^2.
\end{align*}
The quantity $z/(z+a)^2$ is maximized when $z = a$, i.e, $z/(z+a)^2 = (4a)^{-1}$, so
$$
\frac{p(k)}{p(k-1)} - 1 = O \left ( \frac{n}{n_2R} \right ) = O \left ( \frac{n}{n_2n_1} \right ) = o(1).
$$
Therefore, as $n \rightarrow \infty$, the number of $k$'s so that $p(k)$ is within $1+o(1)$ of $p(\mu)$ grows without bound. This implies that $p(k) = O(1/g(n))$ for some function $g : {\mathbb N} \rightarrow {\mathbb N}$ with $g = \omega(1)$ and all $k$. If we let $h(n) = \sqrt{g(n)}$, the total probability that $r \leq X \leq \mu$ is $O(1/\sqrt{g(n)}) = o(1)$. Since, by Corollary \ref{mmCor}, $\ceil{\mu}$ or $\floor{\mu}$ is the median of the hypergeometric distribution, this implies that $\Pr(X \leq r) \geq 1/2 + o(1)$.
\end{proof}
\begin{prop}\label{prop:HyperGeomApprox}
For $n$ tending to infinity and a fixed $f \in (0,1/2)$,
$$
\sum_{k=F_1}^{F} \sum_{s=F_1}^{k} \binom{n_1}{s}
\binom{n_2}{k-s} = \left ( \frac{1}{2} + o(1) \right )
\sum_{k=0}^{F} \binom{n}{k}
$$
\end{prop}
\begin{proof}
Let $n_3 = \lceil \sqrt{2 F_2}\rceil$. By Proposition
\ref{halfprop}, we have
$$
\frac{\sum_{s=F_1}^{k} \binom{n_1}{s}\binom{n_2}{k-s}}
{ \binom{n}{k}} \geq \frac{1}{2} - o(1),
$$
for $k \in [F-n_3,F]$ since the left-hand quantity represents
the probability, if a set of $k = F_1 + r$ elements is drawn
uniformly at random, $F_2 - n_3 \leq r \leq F_2$, that at most
$r$ of the points will be taken from the last $n_2$ of all $n =
n_1 + n_2$ elements. Therefore, by the above and then by Lemma
\ref{cutoffLemma},
\begin{align*}
\sum_{k=F_1}^{F} \sum_{s=F_1}^{k} \binom{n_1}{s}
\binom{n_2}{k-s} &= \sum_{k=F-n_3}^{F} \sum_{s=F_1}^{k}
\binom{n_1}{s}\binom{n_2}{k-s} \\
& \qquad + \sum_{k=F_1}^{F-n_3-1} \sum_{s=F_1}^{k}
\binom{n_1}{s}\binom{n_2}{k-s}\\
& \geq \left ( \frac{1}{2} - o(1) \right ) \sum_{k=F-n_3}^{fn}
\binom{n}{k} \\
& \geq \left ( \frac{1}{2} - o(1) \right ) \left ( 1 - o(1) \right )
\sum_{k=0}^{F} \binom{n}{k} \\
& \geq \left ( \frac{1}{2} - o(1) \right ) \sum_{k=0}^{F} \binom{n}{k}.
\end{align*}
\end{proof}
\section{Reduction from liar machine to the pathological
liar game\label{sec:reduction}}
We now consider the alternating-question strategy for Paul, and
show that Carole has no better response strategy than always
assigning a lie to each of the odd-numbered chips. The
time-evolution of the chips under these question-and-response
strategies is equivalent, by
Cor.~\ref{cor:liarGameToLiarMachine}, to the liar machine. We
then combine results of the previous sections to prove Theorem
\ref{thm:pathGameBound} on parameters for which Paul can win.
\begin{definition}[Position vector]
Given the state vector $x=(x(0),\ldots,x(e))$ of a liar game
with $M$ elements,
the {\em position vector} $u=u(x)=(u(1),u(2),\ldots,u(M))$
corresponding to $x$ is defined by
$$ u(j):=\min\left\{k:\sum_{i=0}^k x(i)\geq j\right\}. $$
\end{definition}
\begin{exm}
The position vector of a state vector essentially labels the
$M$ elements tracked by the state vector from left to right,
and records as $u(j)$ the number of lies associated with the
$j$th element.
\begin{eqnarray*}
\mathrm{If}\quad x & = & (2,0,1,3,0), \quad \mathrm{then}\\
u=u(x) & = & (0,0,2,3,3,3).
\end{eqnarray*}
\end{exm}
Position vectors are monotonic increasing, and provided the
maximum number of lies is available (from context, for
example), the state vector can be recovered from the position
vector.
We analyze the round-by-round evolution of state vectors by
comparing their corresponding position vectors under the weak
majorization partial order, presented for analysis of the
original liar game by \cite{SW92}.
\begin{definition}[Partial order on position vectors] Let
$M\in\mathbb{Z}^+$, and let
$$U=\{(u(1),\ldots,u(M))\in
\mathbb{N}^M:u(1)\leq \cdots \leq u(M)\}$$
be the set of position vectors with $M$ entries. For $u,v\in
U$, we define the partial order $u\leq v$ provided for all
$1\leq k\leq M$, $\sum_{j=1}^k u(j)\leq \sum_{j=1}^k v(j)$.
\end{definition}
\begin{exm}
The partial order on position vectors gives $(0,2,2)\leq
(1,1,2)\leq (1,2,2)\leq (2,2,2)$.
\end{exm}
In order to analyze position vectors within the partial order,
it will be convenient to continue tracking disqualified
elements, with position at least $e+1$, in the position vector.
We do this with the understanding that disqualified elements
are dropped when converting back to the state vector. The {\em
alternating question} for Paul puts all elements tracked by an
even (odd) index in the position vector $u$ into $A_0$ ($A_1$).
The number of lies associated with each element is easily read
from the position vector. Carole's response either assigns an
additional lie to the elements indexed by the odd positions, to
obtain the new position vector $\ensuremath{\textsc{odd}}(u)$, or assigns an
additional lie to the elements indexed by the even positions,
to obtain the new position vector $\ensuremath{\textsc{even}}(u)$.
\begin{definition}[$\ensuremath{\textsc{odd}}(u)$ and $\ensuremath{\textsc{even}}(u)$]\label{def:oeu}
Given the position vector $u=(u(1),\ldots,u(M))$, define the
position vector $\ensuremath{\textsc{odd}}(u)$ to be the result of sorting
$(u(1)+1,u(2),u(3)+1,u(4),\ldots,u(M)+(M\mod 2))$ in
nondecreasing order, and define the position vector $\ensuremath{\textsc{even}}(u)$
to be the result of sorting
$(u(1),u(2)+1,u(3),u(4)+1,\ldots,u(M)+(M+1\mod 2))$ in
nondecreasing order.
\end{definition}
The following two properties appear in the proof of Lemma 2 of
\cite{SW92}. There is a minor error in the proof of the second
property which we describe and correct after stating the lemma.
\begin{lemma}\label{lem:eUeV}
Let $u$ and $v$ be position vectors of liar games with the same
number of elements on the
binary symmetric channel. Then\\
\noindent (1) \ $\ensuremath{\textsc{even}}(u) \leq \ensuremath{\textsc{odd}}(u)$, and\\
\noindent (2) \ If $u\leq v$, then $\ensuremath{\textsc{even}}(u)\leq \ensuremath{\textsc{even}}(v)$.
\end{lemma}
The proof of (1) is a straightforward verification. We defer
the proof of (2) until after describing how to transform $u$
into $v$ in manageable steps.
Close inspection will reveal that the proof in \cite{SW92} does
not find a transformation from $u=(0,1,2)$ to $v=(1,1,1)$; a
successful procedure is as follows.
\begin{alg}
\label{alg:uTov} (Transformation of $u\rightarrow u' \leq v$
with $u<u'$.)
\noindent Input: Position vectors $u=(u(1),\ldots,u(M))$ and
$v=(v(1),\ldots,v(M))$ with $u < v$.\\
Output: A position vector $u'$ with $u<u'\leq v$.\\
\noindent 0. \ Initialize $u'=u$.\\
\noindent 1. \ If $\sum_{i=1}^M u(i) < \sum_{i=1}^M v(i)$, then
set $u'(M)=u(M)+
\sum_{i=1}^M v(i) - \sum_{i=1}^M u(i)$.\\
\noindent 2. \ Otherwise, if $\sum_{i=1}^M u(i) = \sum_{i=1}^M v(i)$:\\
\phantom{mmm}\noindent 2a. \ Maximize $j$ such that $u(j)<v(j)$.\\
\phantom{mmm}\noindent 2b. \ Minimize $k>j$ such that $u(k)>v(k)$.\\
\phantom{mmm}\noindent 2c. \ Set $u'(j)=u(j)+1$ and $u'(k)=u(k)-1$.\\
(By design of $j$ and $k$, $u(j)<v(j),
u(j+1)=v(j+1),\ldots,u(k-1)=v(k-1),u(k)>v(k)$. Furthermore,
$u'$ is already in nondecreasing order.)
\end{alg}
\begin{proof}
The algorithm is easy to verify for $u'$ produced by Step 1.
Suppose Step 2 is executed. Step 2a certainly produces a
maximum $j$: $u<v$ implies that
$\sum_{i=1}^{\ell}u(i)<\sum_{i=1}^{\ell}v(i)$ for some $\ell$,
and so at least one choice for $j$ with $u(j)<v(j)$ exists.
Step 2b produces a minimum $k$: using the $j$ from Step 2a and
combining the inequalities $\sum_{i=1}^{j-1}u(i)\leq
\sum_{i=1}^{j-1}v(i)$, $u(j)<v(j)$, and
$\sum_{i=1}^Mu(i)=\sum_{i=1}^M v(i)$ yields
$\sum_{i=j+1}^Mu(i)>\sum_{i=j+1}^Mv(i)$; and so there is at
least one choice of $k$ for which $u(k)>v(k)$. For all indices
$i$ strictly between $j$ and $k$, $u(i)<v(i)$ is impossible by
maximality of $j$, and $u(i)>v(i)$ is impossible by minimality
of $k$. The middle entries of $u$ and $v$ are as follows:
\begin{equation}\label{eqn:relationString}
u(j)<v(j),
u(j+1)=v(j+1),\ldots,u(k-1)=v(k-1),u(k)>v(k).
\end{equation}
It remains to verify that $u<u'\leq v$ for $u'$ constructed in
Step 2c. Already $u'$ is in nondecreasing order, by definition
of $u'$, inspection of \eqref{eqn:relationString}, and noting
that $u(j)<u'(j)\leq v(j)$ and $v(k)\leq u'(k)<u(k)$.
Furthermore, for $1\leq \ell\leq j-1$,
$\sum_{i=1}^{\ell}u(i)=\sum_{i=1}^{\ell}u'(i)\leq
\sum_{i=1}^{\ell}v(i)$. With $u(j)+1=u'(j)\leq v(j)$, we have
$1+\sum_{i=1}^{j}u(i)=\sum_{i=1}^{j}u'(i)\leq
\sum_{i=1}^{j}v(i)$. Since $u(i)=u'(i)=v(i)$ for all $j+1\leq
i\leq k-1$, we have $1+\sum_{i=1}^{\ell}u(i)=
\sum_{i=1}^{\ell}u'(i)\leq \sum_{i=1}^{\ell}v(i)$ for all
$j+1\leq \ell\leq k-1$. With $v(k)\leq u'(k)=u(k)-1$, we have
$\sum_{i=1}^{k}u(i)= \sum_{i=1}^{k}u'(i)\leq
\sum_{i=1}^{k}v(i)$. Since $u\leq v$ and $u'(i)=u(i)$ for
$i>k$, $\sum_{i=1}^{\ell}u(i)=\sum_{i=1}^{\ell} u'(i)\leq
\sum_{i=1}^{\ell}v(i)$ for $k+1\leq \ell\leq M$.
\end{proof}
\begin{proof}[Proof of Lemma \ref{lem:eUeV} Part (2)]
Iterative application of Algorithm \ref{alg:uTov} produces a
sequence of position vectors $u=u_0<u_1<\cdots<u_t=v$. The
sequence terminates because there are a bounded number of
position vectors satisfying the precondition $\sum_{i=1}^M u(i)
= \sum_{i=1}^M v(i)$ to execute Step 2 of the algorithm. Now
let $0\leq s<t$ and consider $u_s<u_{s+1}$. If $u_{s+1}$ was
created by applying Step 1 of the algorithm to $u_s$ (thereby
forcing $s=0$), then $\ensuremath{\textsc{even}}(u_s)\leq \ensuremath{\textsc{even}}(u_{s+1})$ is easy to
verify.
Otherwise Step 2 created $u_{s+1}$ from $u_s$. Inspection of
\eqref{eqn:relationString} reveals that
$u_s(j)<u_{s+1}(j)=u_s(j)+1\leq u_{s+1}(k)=u_s(k)-1<u_s(k)$.
Ignoring for a moment the $j$th and $k$th entries of $u_s$ and
$u_{s+1}$, and applying $\ensuremath{\textsc{even}}$ to all other entries and then
resorting, we have the following identical structure for
$\ensuremath{\textsc{even}}(u_s)$ and $\ensuremath{\textsc{even}}(u_{s+1})$:
$$
\begin{array}{cc|ccc|cc}
\cdots & \leq u_s(j)+\chi_{2|j}
& \geq u_s(j)+1 +\chi_{2|j}
& \cdots & \leq u_s(k)-1 + \chi_{2|k}
& \geq u_s(k) + \chi_{2|k} & \cdots\, .
\end{array}
$$
Here, $\chi_{2|j}$ ($\chi_{2|k}$) equals 1 if 2 divides $j$
($k$) and equals 0 otherwise; the vertical separators denote
that smaller entries lie to the left and larger to the right.
Now we can see that $\ensuremath{\textsc{even}}(u_s)$ is the same as inserting
$u_s(j)+\chi_{2|j}$ and $u_s(k)+\chi_{2|k}$ from left to right
at the two separators without need for resorting. Similarly,
$\ensuremath{\textsc{even}}(u_{s+1})$ is the same as inserting $u_s(j)+1+\chi_{2|j}$
and $u_s(k)-1+\chi_{2|k}$ from left to right at the two
separators without need for resorting. With this observation it
is simple to verify that $\ensuremath{\textsc{even}}(u_s) < \ensuremath{\textsc{even}}(u_{s+1})$.
Since $s$ was arbitrary in the preceding argument, we have
$\ensuremath{\textsc{even}}(u)=\ensuremath{\textsc{even}}(u_0)<\ensuremath{\textsc{even}}(u_1)<\cdots<\ensuremath{\textsc{even}}(u_t)=\ensuremath{\textsc{even}}(v)$,
and so combined with the case $t=0$ for which
$\ensuremath{\textsc{even}}(u)=\ensuremath{\textsc{even}}(v)$, Part (2) of the lemma holds.
\end{proof}
\begin{cor}\label{cor:oUoV}
Let $u$ and $v$ be position vectors of liar games with the same
number of elements on the binary symmetric channel. If $u\leq
v$, then $\ensuremath{\textsc{odd}}(u)\leq \ensuremath{\textsc{odd}}(v)$.
\end{cor}
\begin{proof}
We use a trick to piggyback on Lemma \ref{lem:eUeV} Part (2).
Set $u'=(-2,u(1),\ldots,u(M))$ and $v'=(-2,v(1),\ldots,v(M)$
and observe that $u\leq v$ implies $u'\leq v'$. The first
entry of $u'$ and of $v'$ is sufficiently separated, and so
$\ensuremath{\textsc{even}}(u')=(-2,\ensuremath{\textsc{odd}}(u))$ and $\ensuremath{\textsc{even}}(v')=(-2,\ensuremath{\textsc{odd}}(v))$. Applying
Lemma \ref{lem:eUeV} to $u'$ and $v'$ yields $\ensuremath{\textsc{even}}(u')\leq
\ensuremath{\textsc{odd}}(v')$. As $\ensuremath{\textsc{even}}(u')(1)=\ensuremath{\textsc{even}}(v')(1)=-2$, this forces
$\ensuremath{\textsc{odd}}(u)\leq \ensuremath{\textsc{odd}}(v)$.
\end{proof}
Next we show that when Paul's strategy is to always ask the
alternating question, Carole's best possible response strategy
in the pathological liar game is to move the odd-numbered
elements. This will provide an upper bound on the minimum
number of elements required for Paul to have a winning strategy
in the $(x,n,e)^*_2$-game.
\begin{theorem}\label{thm:CaroleStrat}
Let $x$ be an initial state vector, and $n,e\in \mathbb{N}$.
Assume that Paul always asks the alternating question. In the
$(x,n,e)^*_2$-game, Carole's best strategy is to move the
odd-numbered elements.
\end{theorem}
\begin{proof}
Let $u_s$ be the position vector after $s$ rounds of the game,
where $u_0$ is the position vector corresponding to the initial
state vector $x$. Carole wins the $(x,n,e)^*_2$-game iff
$u_n(1)>e$. Consider the $2^n$ leaves of the strategy tree of
the game determined by every possible length $n$ sequence of
choices for Carole to select $\ensuremath{\textsc{odd}}(u_s)$ or $\ensuremath{\textsc{even}}(u_s)$ to
complete round $s+1$. Thus $\ensuremath{\textsc{odd}}^n(u_0)$ is the leaf
corresponding to Carole always moving the odd elements. It
suffices to show that $\ensuremath{\textsc{odd}}^n(u_0)\geq v$ for all other leaves
$v$ of the strategy tree. We prove this by induction on $n$.
The base case $n=1$ is provided by Lemma \ref{lem:eUeV} Part
(1). Now let $0<s<n$, assume that $v$ is a position vector
after $s$ rounds, and assume that $v\leq \ensuremath{\textsc{odd}}^s(u_0)$. By
Corollary \ref{cor:oUoV}, $\ensuremath{\textsc{odd}}(v)\leq
\ensuremath{\textsc{odd}}(\ensuremath{\textsc{odd}}^s(u_0))=\ensuremath{\textsc{odd}}^{s+1}(u_0)$, and by Lemma \ref{lem:eUeV}
Part (1) and transitivity, $\ensuremath{\textsc{even}}(v)\leq \ensuremath{\textsc{odd}}^{s+1}(v)$. All
position vectors after $s+1$ rounds are obtained by applying
$\ensuremath{\textsc{odd}}$ or $\ensuremath{\textsc{even}}$ to a position vector after $s$ rounds, and so
the induction succeeds.
\end{proof}
By a simple transformation, Carole's odd response strategy is
equivalent to the time-evolution of the liar machine.
\begin{cor}\label{cor:liarGameToLiarMachine}
Let the liar machine have initial configuration $f_0$ with $M$
chips at the origin and none elsewhere. If
$\sum_{i=-n}^{-n+2e}f_n(i)\geq 1$, then Paul can win the
$((M,0,\ldots,0),n,e)_2^*$-game.
\end{cor}
\begin{proof}
Let $u_s$ and $x_s$ be the position and state vectors,
respectively at the end of round $s$, of the
$((M,0,\ldots,0),n,e)_2^*$-game in which Paul always asks the
alternating question, and Carole always chooses
$u_{s+1}=\ensuremath{\textsc{odd}}(u_s)$. By Theorem \ref{thm:CaroleStrat}, we need
only transform $\ensuremath{\textsc{odd}}^s(u_0)$ into $f_s$, where $u_0$ is the
position vector corresponding to the initial state vector
$(M,0,\ldots,0)$. By definition of $\ensuremath{\textsc{odd}}(u)$ and of one step
of the liar machine, this is accomplished by observing that
$x_s(i)
=f_s(-s+2i)$ for all $0\leq i\leq s$. Consequently
$\ensuremath{\textsc{odd}}^n(u_0)(1)\leq e$ iff $\sum_{i=0}^ef_n(-n+2i)\geq 1$.
\end{proof}
The converse is not true. For some games the alternating
question strategy is not optimal, so that Paul has a winning
strategy, but $\ensuremath{\textsc{odd}}^n(u_0(1))>e$. For example, Paul can win the
$((1,11),4,1)^*_2$-game (as the reader can readily verify --
the first question is $(1,4)$), but the progression of
configurations given by the liar machine is $(1,11)\rightarrow
(0,7)\rightarrow (0,3)\rightarrow (0,1)\rightarrow (0,0)$.
We again use the following notation. Let $n \rightarrow
\infty$, fix $f \in (0,1/2)$, and set $ n_1 = n -
\floor{\frac{4}{(1 - 2f)^2} \log \log n}$ and $n_2 = n - n_1$.
Define $F=\lfloor f n\rfloor$, $F_1 = \lfloor f n_1\rfloor$,
and $F_2 = F-F_1$.
\begin{theorem}\label{ref:liarMachineBound}
Let $n,M\in \mathbb{Z}^+$. Let
$f_0:\mathbb{Z}\rightarrow\mathbb{N}$ be the initial
configuration of the liar machine defined by $f_0(0)=M$, and
$f_0(j)=0$ otherwise.
For $n$ sufficiently large, if
$$
M \geq \frac{2^n}{\binom{n}{\leq F}}
(2+o(1))c'\sqrt{n_2}
,
$$
where $c'$ is the constant from Theorem
\ref{thm:intervalupperbound}, then $\sum_{i=F_1}^{F} f_n(-n+2i)
\geq 1$.
\end{theorem}
\begin{proof}
Set $g_0=f_0$ and let $g_s$ be the chip distribution in the
linear machine after $s$ rounds. Then for $F_1 \leq j \leq F$,
the number of chips at position $-n_1+2j$ in the linear machine
after $n_1$ rounds is
\begin{equation}\label{eqn:n1Linear}
g_{n_1}(-n_1+2j) = \frac{\binom{n_1}{j}}{2^{n_1}}
\frac{2^{n}}{\binom{n}{\leq F}}(2+o(1))c'\sqrt{n_2}
.
\end{equation}
Since $F<n_1/2$ for $n$ sufficiently large, the minimum occurs
at $j=F_1$, and is $\omega(\log n)$ by Lemma
\ref{lem:relativeCDF}.
Applying Theorem \ref{thm:ptwiseupperbound}, for $F_1\leq j\leq
F$ we have
\begin{equation}\label{eqn:n1Liar}
f_{n_1}(-n_1+2j) \geq
\frac{\binom{n_1}{j}}{2^{n_1}}
\frac{2^{n}}{\binom{n}{\leq F}}(2+o(1))c'\sqrt{n_2}.
\end{equation}
Now for $F_1 \leq j \leq F$, define $h_{n_1}(-n_1+2j)$ to be
the right-hand side of \eqref{eqn:n1Liar}, and $h_{n_1}(j)=0$
elsewhere. Thus $h_{n_1}$ is obtained from $f_{n_1}$ by
removing chips outside of the interval $[-n_1+2F_1,-n_1+2F]$.
We run the linear machine with initial state $h_{n_1}$ for
$n_2$ rounds, and obtain for $F_1 \leq i \leq F$ that
$$
h_n(-n+2i) \geq
\sum_{j=F_1}^{i}
\frac{\binom{n_1}{j}}{2^{n_1}}
\frac{2^{n}}{\binom{n}{\leq F}}(2+o(1))c'\sqrt{n_2}
\frac{\binom{n_2}{i-j}}{2^{n_2}},
$$
as for $i$ and $j$ fixed, the contribution to $h_n(-n+2i)$ from
$h_{n_1}(-n+2j)$ is $h_{n_1}(-n+2j)\binom{n_2}{i-j}/2^{n_2}$.
Summing $h_n(-n+2i)$ over $i$ and applying Proposition
\ref{prop:HyperGeomApprox},
$$
\sum_{i=F_1}^{F}
h_n(-n+2i)\geq c'\sqrt{n_2}(1+o(1)).
$$
Noting that $\sqrt{n_2} = o(F-F_1)$ and applying Theorem
\ref{thm:intervalupperbound} to $h_{n_1}$, we obtain
$\sum_{i=F_1}^{F} f_n(-n+2i) \geq 1 $ as desired.
\end{proof}
\begin{proof}[Proof of Theorem \ref{thm:pathGameBound}]
Corollary \ref{cor:liarGameToLiarMachine} reduces the
$((M,0,\ldots,0),n,e)_2^*$-game to the liar machine with
winning condition $\sum_{i=-n}^{-n+2e}f_n(i)\geq 1$, which
Theorem \ref{ref:liarMachineBound} shows is satisfied for the
given form of $M$.
\end{proof}
\section{Concluding remarks\label{sec:conclusion}}
The major open question is whether the time-evolution of the
liar machine with $M$ elements at the origin and zero elsewhere
can be given in closed form, or at least whether the leftmost
chip can be tracked more tightly. Either case would yield an
improvement by decreasing the minimum $M$ for which Paul can
win the $((M,0,\ldots,0),n,e)^*_2$-game. We suppose that the
best hope is for the optimal $M$ to be asymptotically a
constant multiple above the sphere bound. Similarly, by the
reduction in \cite{SW92} from the $((M,0,\ldots,0),n,e)_2$-game
(original liar game) to the linear machine, improved tracking
of the leftmost chip could provide an alternative proof of
Theorem 3 of \cite{Z76}, which is equivalent to a lower bound
on $M$ for which Paul can win the original liar game.
Optimistically, the bound in \cite{Z76} on $M$ might be
improved to a constant multiple below the sphere bound.
We thank Joel Spencer for discussions that helped to
crystallize the ideas for this paper -- with the first author
during an extended collaboration on deterministic random walks,
and with the second author at a conference in 2004 on alternate
viewpoints for the liar game.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,579 |
\section{Introduction}
Modular architectures for quantum information processing envision a scale-up of quantum devices from elementary building blocks interconnected by coherent quantum links \cite{Kimble2008,Duan2010,Nickerson2014,Monroe2014}. A modular quantum processor is structured as an `on-chip' local-area quantum network, with small quantum computers as nodes of the network, and where quantum states are transferred between nodes via quantum channels \cite{Northup2014,Reiserer2015}. Remarkable progress has been made during the last years in demonstrating some of the basic elements of such modular architectures. In atomic physics quantum computers and quantum simulators involving several tens of individually controlled qubits have been built along with quantum logic entangling operations \cite{Labuhn2016,Bernien2017,Zhang2017,Friis2018}. Deterministic and probabilistic protocols for entanglement generation \cite{Haas2014}, as well as quantum state transfer between distant atomic qubits \cite{Ritter2012} have been demonstrated experimentally using cavity-QED interfaces, with optical photons as carriers of quantum information. A basic requirement and remaining challenge, however, is to develop high-speed photonic quantum links allowing for high-fidelity quantum communication and entanglement distribution in on-chip quantum networks.
The paradigmatic and conventional setup of a photonic quantum link is built around strong coupling of atoms to photonic nanostructures or nanofibers as 1D waveguides \cite{Tiecke2014,Hood2016,Corzo2016,Solano2017}, or to cavities \cite{Ritter2012,McConnell2015}. In Fig.~\ref{fig:chiralQO}(d), we sketch an example of photonic quantum link between two atomic qubits, based on an interface between a two-level atom and an optical fiber. In such setups protocols can be applied to deterministically transfer a quantum state from the first to the second atomic `stationary' qubit via a photonic `flying' qubit propagating as wavepacket in a 1D optical waveguide. Achieving a high-fidelity transfer requires the following two key ingredients. First, we need to achieve routing of the photon wavepacket emitted by the first atom. This necessitates a \textit{chiral} atom-fiber interface, i.e. with unidirectional photon emission (and absorption) \cite{Lodahl2017}. The second ingredient is the 1D character of the fiber modes guiding the wavepacket, which is essential in achieving efficient reabsorption of the photon and thus restoration of the qubit in the second atom. Recent experiments have demonstrated such {chiral} quantum interfaces with atoms trapped close to optical nanofibers~\cite{Mitsch2014,LeFeber2015}. Significant challenges remain, however, in resolving the conflicting requirements of trapping atoms close to dielectric surfaces, while achieving the strong-coupling regime where the interaction between atoms and confined modes dominates losses such as spontaneous emission to free-radiating modes. These challenges have so far limited demonstrations of photon mediated remote entanglement of matter qubits
to rates of at most 30 $s^{-1}$ with neutral atoms \cite{Ritter2012},
trapped ions \cite{Hucul2014}, or NV centers \cite{Kalb2017}. To address these challenges, we propose below a chiral photonic quantum link, where effective 1D (paraxial) \textit{free-space} modes of the electromagnetic field provide a photonic quantum channel connecting atomic qubits --- therefore eliminating the requirement for 1D nanofibers or photonic nanostructures. Combining the demonstrated capability for creating local entanglement on a few $\mu$s timescale via
Rydberg interactions \cite{Maller2015,Jau2015} with a high efficiency chiral channel
we project realization of remote entanglement at rates above $10^4~\rm s^{-1}$, which will speed
development of modular quantum processing networks.
\begin{figure*}[t]
\includegraphics[width=1\linewidth]{Fig1} \caption{\textit{Free-space chiral quantum optics.} (a)~A master atom (qubit) is coupled
to a bilayer atomic array of $N_{\rm a}=N_\perp\times N_\perp \times 2$ atoms as `quantum antenna' achieving
unidirectional photon emission. (b)~Spatial distribution of the emitted
field $|\vec{\varphi}(\vec{r}\,)|$ (see text) for two master atoms as qubits interacting via a paraxial mode, with $2z_0=90\lambda_0$, $N_\perp=17$, $\delta_\perp=0.7\lambda_0$.
(c)~Basic model
of the antenna: level schemes of the qubit off-resonantly coupled
to a two-level antenna atom. (d) Chiral coupling in waveguide-QED, with two atomic qubits coupling to right-propagating modes with rate $\gamma_{R}$, and to non-guided modes with rate ${\gamma'}$. (e) Fidelity for Quantum State Transfer between atomic qubits, with interatomic spacing $\delta_\perp=0.8\lambda_0$, and various $N_\perp$. The red curve corresponds to $N_\perp\to\infty$ (see text). Inset: corresponding infidelity for $z_0\to0$, with $50/N_\perp^4$ in dashed black for reference. }
\label{fig:chiralQO}
\end{figure*}
The setup describing the `free-space' photonic quantum link is outlined in Figs.~\ref{fig:chiralQO}(a-c). The key element is the coupling of the atom representing the qubit, in an engineered laser-assisted process, to a regular array of atoms with sub-wavelength separation $\delta_\perp<\lambda_0$ (with $\lambda_0$ the wavelength of the light), which acts as a \textit{phased-array} antenna for photon emission and absorption. We make this interface \textit{chiral} by employing a bilayer atomic array, where the desired unidirectionality is guaranteed by interference. We can view the composite object consisting of the qubit atom coupled to the atomic array as an artificial two-level atom, where the `excited state' decays to the `ground state' while coherently emitting an optical photon into a given well-defined localized and directed (1D) mode of the electromagnetic field. This chiral photonic quantum interface for `free-space' atomic qubits then becomes the building block for a `free-space' photonic quantum link. We illustrate this in Fig.~\ref{fig:chiralQO}(c) for the example of an array of $N_\perp \times N_\perp$ atoms (here $17 \times 17$) with $N_z=2$ layers acting as antenna. This example demonstrates the generation of a free-space Gaussian mode as photonic quantum link connecting two atomic arrays. For a given transverse array size $L_\perp \sim \lambda_0 N_\perp$, this link can cover a distance $L\sim L_\perp ^2 /\lambda_0 \sim N_\perp L_\perp$ between sending and receiving node.
The achievable communication range can be further extended with lenses inserted between the sending and receiving antenna.
Remarkably, running the standard quantum state transfer protocol on this setup gives fidelities close to unity for such distances, as shown in Fig.~\ref{fig:chiralQO}(e). For atomic arrays of much smaller size, the light emitted from the antenna remains unidirectional, albeit divergent as illustrated in Fig.~\ref{fig:setup}(a)
\section{Chiral quantum optics}
\label{sec:chiralQO}
\label{sec:chiralQO}
We wish to implement a `free-space' chiral light-matter
interface (discussed in Sec.~\ref{sec:Model}), and a `free-space' photonic quantum link
(discussed in Sec.~\ref{sec:chiralnetworks}) in a 3D environment, analogous to the 1D models of
chiral quantum optics. Thus, for reference below, we find it worthwhile
to first summarize the basic dynamical equations of 1D chiral quantum optics
and cascaded quantum systems.
A minimal model for a chiral interface
coupling two-level atoms to a waveguide is shown in Fig.~\ref{fig:chiralQO}(d).
Here, two quantum emitters %
\mbox{%
$(a=1,2)$%
} as two-level atoms with ground states $\ket{G}_{a}$ and excited
states $\ket{E}_{a}$, respectively, are coupled to an open 1D waveguide
as bosonic bath. The dynamics of this system is governed by the Hamiltonian $H_{1D}=H_{0A}+H_{0F}+H_{AF}$.
Here the free Hamiltonian for the waveguide can be written as %
\mbox{%
$H_{0F}=\int dk\omega_{k}\left({b_{k}^{R}}^{\dagger}b_{k}^{R}+{b_{k}^{L}}^{\dagger}b_{k}^{L}\right)$%
}, where $\omega_{k}$ is the waveguide dispersion relation, which
we assume linear ($\omega_{k}\approx ck$ with $k$ the momentum and
$c$ the speed of light in the waveguide), and ${b_{k}^{R(L)}}$ is
the annihilation operator for photons propagating in the right (left)
direction in the waveguide, with momentum $k$, which satisfy bosonic
commutation relations %
\mbox{%
$\left[b_{k}^{\alpha},{b_{k'}^{\beta}}^{\dagger}\right]=\delta(k-k')\delta_{\alpha,\beta}$%
}. On the other hand, the free atomic Hamiltonian is %
\mbox{%
$H_{0A}=\omega_{0}\sum_{a=1}^{2}\sigma_{a}^{+}\sigma_{a}^{-}$%
}, with $\omega_{0}$ the atomic transition frequency and $\sigma_{a}^{-}\equiv\ket{G}_{a}\!\bra{E}$,
possibly along with an additional term accounting for external driving
fields. Finally, the interaction Hamiltonian between atoms and photons
reads
\begin{equation}
\begin{aligned}H_{AF}=i & \sum_{a=1}^{2}\sqrt{\frac{\gamma_{R,a}}{2\pi}}\int dk\left(e^{-ikz_{a}}{b_{k}^{R}}^{\dagger}\sigma_{a}^{-}-\text{h.c.}\right)\\
+ & i\sum_{a=1}^{2}\sqrt{\frac{\gamma_{L,a}}{2\pi}}\int dk\left(e^{ikz_{a}}{b_{k}^{L}}^{\dagger}\sigma_{a}^{-}-\text{h.c.}\right),
\end{aligned}
\end{equation}
where $z_{a}$ is the atomic position along the waveguide, with $d\equiv z_{2}-z_{1}>0$,
and $\gamma_{R(L),a}$ is the \emph{spontaneous decay rate} of atom
$a$ for the emission of photons propagating to the right (left).
Broken left-right symmetry manifests itself in the couplings $\gamma_{R,a}\ne\gamma_{L,a}$,
and we are particularly interested in unidirectional coupling $\gamma_{R,a}\gg\gamma_{L,a}\rightarrow0$.
The master equation obtained by integrating out the radiation field
in a Born-Markov approximation for two atoms and $\gamma_{R,a}\ne\gamma_{L,a}$
is
\begin{equation}
\frac{d}{dt}{\rho}=-i\left[H_{\text{eff}}{\rho}-{\rho}H_{\text{eff}}^{\dagger}\right]+\mathcal{J}{\rho},\label{eq:mastereq1D}
\end{equation}
with non-hermitian Hamiltonian
\begin{equation}
H_{\text{eff}}=-i\sum_{a=1}^{2}\frac{\gamma_{a}}{2}s_{a}^{+}s_{a}^{-}-ie^{i\omega_{0}d/c}\Big(\gamma_{L}s_{1}^{+}s_{2}^{-}+\gamma_{R}s_{2}^{+}s_{1}^{-}\Big).\label{eq:Hchir1D}
\end{equation}
written here in a rotating frame. The first term in Eq.~(\ref{eq:Hchir1D}) describes the individual decay of atomic excitations, with the total
decay rate of atom $a$ defined as %
\mbox{%
$\gamma_{a}=\gamma_{R,a}+\gamma_{L,a}+\gamma'_{a}$%
}. Here we added an additional decay channel with rate $\gamma'_{a}$
accounting for losses due to coupling of the atoms to non-guided modes.
The second term of Eq.~(\ref{eq:Hchir1D}) on the other hand describes
non-reciprocal atomic effective interactions. The rate \mbox{$\gamma_{L}\equiv\sqrt{\gamma_{L,1}\gamma_{L,2}}$}
denotes the rate of interaction mediated by photons propagating to
the left from atom $2$ to $1$, while $\gamma_{R}\equiv\sqrt{\gamma_{R,1}\gamma_{R,2}}$
corresponds to photons propagating to the right from atom $1$ to
$2$. Finally, the last term in Eq.~(\ref{eq:mastereq1D})
expresses as
\begin{eqnarray}
\mathcal{J}{\rho}= & & \sum_{a=1}^{2}\gamma_{a}s_{a}^{-}{\rho}s_{a}^{+}+e^{i\omega_{0}d/c}\left(\gamma_{R}s_{1}^{-}{\rho}s_{2}^{+}+\gamma_{L}s_{2}^{-}{\rho}s_{1}^{+}\right)\nonumber \\
& & +e^{-i\omega_{0}d/c}\left(\gamma_{L}s_{1}^{-}{\rho}s_{2}^{+}+\gamma_{R}s_{2}^{-}{\rho}s_{1}^{+}\right).
\end{eqnarray}
In the unidirectional case ($\gamma_{L}=0$), the above equation reduces
to the cascaded master equation as derived in Ref.~\cite{Gardiner1993}. We note that in
this case atom 1 can only talk to atom 2 downstream, while there is
no backaction of atom 2 to atom 1. This cascaded master equation has
been the starting point to discuss quantum state transfer of a qubit
as superposition state, from the first to the second atom, realizing %
\mbox{%
$\left(\alpha\ket{G}_{1}+\beta\ket{E}_{1}\right)\otimes\ket{G}_{2}\to\ket{G}_{1}\otimes\left(\alpha\ket{G}_{2}+\beta\ket{E}_{2}\right)$%
} \cite{Cirac1997}.
We show below that the `free-space' chiral photonic quantum link of
Sec.~\ref{sec:chiralnetworks} can be described by a chiral master equation of the form of Eq.~\eqref{eq:mastereq1D} and we derive
explicit expressions for $\gamma_{R,a}\gg\gamma_{L,a}$ in terms of coupling coefficients to free-space radiation modes. The
setup of Figs.~\ref{fig:chiralQO}(a-c) thus provides a faithful implementation of chiral
quantum optics in a free space environment.
\section{`Free-space' Chiral Atom-Light Interface\label{sec:Model}}
The basic setup of an atom coupled to a quantum antenna as directional
quantum emitter is illustrated in Figs.~\ref{fig:chiralQO}(a-c).
We consider a two-level atom represented by a pair of long lived atomic
states $\ket{G},\ket{E}$ (e.g.~hyperfine states in an atomic ground
state manifold), dubbed 'master atom' or qubit, which we assume trapped
in free space. We wish to design an effective `decay' from the excited
state to the ground state $\ket{E}\rightarrow\ket{G}$ as a laser-assisted
spontaneous emission process, analogous to an optical pumping process,
with the property that the optical photon is emitted into a specified
target mode of the electromagnetic field, written as an outgoing wave
packet \mbox{$\left\vert \psi^{\text{targ}}\left(t\right)\right\rangle \equiv\sum_{\lambda}\int d^{3}k\psi_{\vec{k},\lambda}^{\text{targ}}(t)b_{\vec{k},\lambda}^{\dagger}\ket{\textrm{vac}}$},
with $\ket{\textrm{vac}}$ the vacuum state. Here $b_{\vec{k},\lambda}^{\dagger}$
creates a photon with momentum $\vec{k}$ and polarization $\lambda$,
with \mbox{$[b_{\vec{k},\lambda},b_{\vec{k}'\lambda'}^{\dagger}]=\delta_{\lambda,\lambda'}\delta(k-k')$},
and $\psi_{\vec{k},\lambda}^{\text{targ}}$ specifies the target mode
in momentum space (e.g.~a Gaussian mode).
We design this `decay' of the master atom with the optical photon
emitted into the target mode as a two-step process via a nearby atomic array with subwavelength spacing (as investigated in recent theoretical studies \cite{Bettles2016,Facchinetti2016,Shahmoon2017,Asenjo-Garcia2017,Manzoni2017,Perczel2017}). This ensemble consists
of two-level atoms $\left\{ \ket{g}_{i},\ket{e}_{i}\right\} $ located
at positions $\vec{r}_{i}$ ($i=1,...,N_{a}$) trapped in free-space (e.g. with optical traps \cite{Bloch2012,Lester2015,Xia2015,Endres2016,Barredo2016}). In a first step the
atomic excitation of the master atom is swapped in a laser assisted
process to a \emph{delocalized} electronic excitation of the ensemble,
\begin{equation}
s^{+}\ket{\Omega}\rightarrow\sum_{i=1}^{N_{a}}e^{i\phi_{i}}\sigma_{i}^{+}\ket{\Omega}/\sqrt{N_{a}}.\label{eq:transfer}
\end{equation}
Here $\ket{\Omega}\equiv\ket{G}\{\ket{g}_{i}\}\ket{\textrm{vac}}$,
and we have defined %
\mbox{%
$s^{+}\equiv\ket{E}\bra{G}$%
} and %
\mbox{%
$\sigma_{i}^{+}\equiv\ket{e}_{i}\bra{g}$%
}. This delocalized electronic excitation in the atomic ensemble then
decays back to the ground state $\ket{e}_{i}\rightarrow\ket{g}_{i}$
by emission of an optical photon. The key idea is to design phases
$\phi_{i}$ in the laser-assisted first step, so that the atomic ensemble
acts as a holographic or \textit{phased-array antenna} for directed spontaneous emission into the target mode (in analogy to classical phased-array antennas \cite{He2009,Sun2013,Stokes2015}). That is,
directionality of emission comes from interference between the emitting
atomic dipoles \cite{Clemens2003,Saffman2005,Scully2006,Miroshnychenko2013,Slepyan2013,Wiegner2015,Bhatti2016,Paris-Mandoki2017}. We first assume the system to operate in the Lamb-Dicke regime, such that photon recoil and motional effects, e.g. due to temperature, can be neglected \cite{gardiner2015}.
There are
various ways of implementing the process (\ref{eq:transfer}) in quantum
optics with atoms; as an example we discuss below a transfer with
long-range laser-assisted Rydberg interactions \cite{Saffman2010,Browaeys2016},
where spatially dependent phases $\phi_{i}$ can be written via laser
light, akin to synthetic gauge fields for cold atoms \cite{Goldman2016}.
We emphasize that the overall process preserves quantum coherence
and entanglement, such that, for instance, for an initial qubit superposition
state $c_{g}\left\vert G\right\rangle +c_{e}\left\vert E\right\rangle $
(with $c_{g}$ and $c_{e}$ complex numbers) the outgoing photonic
state will read $c_{g}\left\vert \text{vac}\right\rangle +c_{e}\left\vert \psi^{\text{targ}}\left(t\right)\right\rangle $.
\begin{figure}[t]
\includegraphics[width=1\linewidth]{Fig2} \caption{\textit{Few-atom quantum antenna.} (a)~Spatial distribution of the emitted
field $|\vec{\varphi}(\vec{r}\,)|$ (see text) for antenna configurations
as bilayer $\protect\smash{2 \times 2}$, $\protect\smash{3 \times 3}$
and $\protect\smash{8 \times 8}$ regular arrays. The field can be interfaced with optical lenses. (b)~Emission to a superposition of two
focussing modes, and mode matching to an optical fiber,
with bilayer $\protect\smash{17 \times 17}$ atomic arrays as antennas.}
\label{fig:setup}
\end{figure}
Below we will be interested in various geometries of the few-atom
antenna, with the goal of optimizing the directionality of emission.
We will consider bilayer and multilayer regular arrays of $N_{{\rm a}}$
atoms, where %
\mbox{%
$N_{{\rm a}}=N_{\perp} \times N_{\perp} \times N_{z}$%
} with $N_{z}$ and $N_{\perp}$ being the number of atoms in longitudinal
and transversal directions, respectively. The corresponding interatomic
spacings are denoted as $\delta_{z(\perp)}$, while the overall spatial
extent of the antenna is $L_{z(\perp)}=\delta_{z(\perp)}N_{z(\perp)}$.
For comparison, we also assess the case of atoms with random positions
characterized by their density $n_{{\rm a}}$. As an illustration
of results derived below, we show in Fig.~\ref{fig:setup}(a) spatial
photon emission patterns for ${2\times2\times2}$, ${3\times3\times2}$
and ${8\times8\times2}$ bilayer regular arrays, assuming
subwavelength spacings $\delta_{z}=0.75\lambda_{0}$ and $\delta_{\perp}=0.7\lambda_{0}$, which is necessary in order to avoid Bragg resonances.
It is remarkable that rather directed spontaneous emission can be
obtained with very small atom numbers. We will quantify this below
as a Purcell factor $\beta$ for emission into a paraxial mode of
interest, and show that $\beta$ close to 1 can be achieved.
For transverse sizes $L_{\perp}\gg\lambda_{0}$, the antenna can emit
photons in several spatial modes, as illustrated in the upper panel
of Fig.~\ref{fig:setup}(b). Photons can also be emitted in directional
modes focussing at a distance $z_{0}$ outside the antenna, which
could be used to match the mode of an optical fiber, as represented
in the lower panel of Fig.~\ref{fig:setup}(b). The focussing distance
achievable in this way is limited by diffraction as $z_{0}\lesssim L_{\perp}^{2}/\lambda_{0}$.
\subsection{Model of Quantum Optical Antenna}
A quantum optical description for the setup in Fig.~\ref{fig:chiralQO}(a)
starts from a Hamiltonian \mbox{$H_{3D}=H_{0A}+H_{0F}+H_{AF}$}, which we write
as sum of an atomic Hamiltonian, the free radiation field, and the
atom - radiation field coupling in the dipole approximation. We find
it convenient to work in an interaction picture with respect to $H_{0F}$,
and transform to a rotating frame eliminating optical frequencies.
Thus we write for the atomic Hamiltonian (with $\hbar=1$)
\begin{equation}
H_{0A}=-\Delta\sum_{i}\sigma_{i}^{+}\sigma_{i}^{-}+s^{-}\sum_{i}J_{i}\sigma_{i}^{+}+\text{h.c}.\label{eq:H0A}
\end{equation}
with $\Delta$ the detuning in the laser-assisted transfer from the
master atom to ensemble due to long-range couplings $J_{i}\!=\!|J_{i}|e^{i\phi_{i}}$.
For the atom-radiation field coupling we have
\begin{equation}
H_{AF}(t)=-d\sum_{i}\sigma_{i}^{+}\vec{p}^{\,*}\vec{{\cal E}}^{\left(+\right)}\left(\vec{r}_{i},t\right)+\text{h.c.}\label{eq:HAF}
\end{equation}
with $\vec{d}= d \vec{p}$ the atomic dipole matrix element with amplitude $d$ and unit vector $\vec p$, which for concreteness we will assume circularly polarized along $z$, and
\begin{equation}\label{eq:expE}
\vec{{\cal E}}^{\left(+\right)}\left(\vec{r},t\right)=i\sum_{\lambda}\int d^{3}{k}\sqrt{\frac{\omega_{k}}{2(2\pi)^{3}\varepsilon_{0}}}b_{{\vec{k}},\lambda}e^{i{\vec{k}}{\vec{r}}}e^{-i(\omega_{\vec{k}}-\omega_{0})t}{\vec{e}}_{\lambda,{\vec{k}}}
\end{equation}
the positive frequency part of the electric field operator (in the
rotating frame), with $\omega_{0}\equiv ck_{0}\equiv2\pi c/\lambda_{0}$
the optical frequency, ${\vec{e}}_{\lambda,{\vec{k}}}$ the polarization
vector.
The effective decay of the master atom via the ensemble is described
in a Wigner-Weisskopf ansatz as
\begin{equation}
\begin{aligned}\ket{\Psi({t})}=\Big( & \!s\left(t\right)s^{+}\!+\!\sum_{i}{\cal P}_{i}\left(t\right)\sigma_{i}^{+}\\
& +\sum_{\lambda}\!\int d^{3}k\psi_{\vec{k},\lambda}\left(t\right)b_{k,\lambda}^{\dagger}\!\Big)\ket{\Omega},
\end{aligned}
\label{eq:WW}
\end{equation}
with initial condition $s(0)=1$, ${\cal P}_{i}\left(0\right)=\psi_{\vec{k},\lambda}\left(0\right)=0$,
and our aim is to obtain a photon in the specified target mode $\psi_{\vec{k},\lambda}\left(t\right)\rightarrow\psi_{\vec{k},\lambda}^{\text{targ}}(t)$
for times $t\rightarrow\infty$. In the Born-Markov approximation
we can eliminate the radiation field and find
\begin{align}
\frac{d}{dt}s & =-i\sum_{i}J_{i}^{*}{\cal P}_{i},\quad\frac{d}{dt}{\cal P}_{i}=-iJ_{i}s-i\sum_{j}\left(H_{nh}\right)_{i,j}{\cal P}_{j}.\label{eq:S_P}
\end{align}
This describes the transfer of the excitation from the master atom
to the ensemble atoms according to the couplings $J_{i}$. The last
equation contains the non-hermitian effective atomic Hamiltonian \mbox{$H_{nh}\equiv-\Delta\mathbb{I}-i(\gamma_{e}/2)\left(\mathbb{I}+\mathbb{G}\right)$}
with detuning $\Delta$ and atomic decay rate $\gamma_{e}\equiv k_0^3 d^2/(3\pi\varepsilon_0)$, and the
hopping of the atomic excitation within the ensemble due to dipole-dipole
interaction induced by photon exchanges. Here we have defined
\mbox{%
$\mathbb{G}_{i,j}\equiv\vec{p}^{\,*}\hat{G}\left(\vec{r}_{j}-\vec{r}_{i}\right)\vec{p}$%
}, where in our notations the dyadic Green's tensor is a solution of
\mbox{$\vec{\nabla}\times\vec{\nabla}\times\hat{G}(\vec{r})-k_{0}^{2}\hat{G}(\vec{r})=-(6\pi i/k_0)\delta(\vec{r})\,\mathbb{I}$},
and expresses as \cite{Lehmberg1970,James1993}
\begin{equation}
\begin{aligned}{\hat{G}}({\vec{r}})=\frac{3e^{ik_{0}r}}{2i(k_{0}r)^{3}}\Big[ & \left((k_{0}r)^{2}+ik_{0}r-1\right)\mathbb{I}\\
& +\left(-(k_{0}r)^{2}-3ik_{0}r+3\right)\frac{\vec{r}\otimes\vec{r}}{r^{2}}\Big].
\end{aligned}
\end{equation}
To obtain the spatial profile of the emitted light, we define the
(normalized) single photon distribution as %
\mbox{%
$\vec{\psi}\left(\vec{r},t\right)\equiv-i\sqrt{{2\varepsilon_{0}}/{\omega_{0}}}\bra{\Omega}\vec{{\cal E}}^{\left(+\right)}\left(\vec{r}\right)\ket{\Psi\left(t\right)}$%
}. By integrating Maxwell equation we find
\[
\vec{\psi}\left(\vec{{r}},t\right)=\sqrt{\frac{\gamma_{e}}{6\pi c}}k_{0}\sum_{i}\hat{G}\left(\vec{r}-\vec{r}_{i}\right)\vec{p}\,{\cal P}_{i}\left(t-\frac{|\vec{r}-\vec{r}_{i}|}{c}\right),
\]
with the emitted field as radiation of interfering atomic dipoles.
For simplicity we discuss below the limit of perturbative $J_{i}$,
where we eliminate the atomic ensemble coupled to the radiation field
as an effective quantum reservoir. We obtain for the effective decay
of the master atom
\begin{align}
\frac{d}{dt}s & =\Big(i\sum_{i,j}{J_{i}}^{*}\left(H_{nh}^{-1}\right)_{i,j}{J_{j}}\Big)s\equiv\Big(-i\epsilon-\frac{1}{2}\gamma_{\text{tot}}\Big)s,\label{eq:full_gamma}
\end{align}
with $\gamma_{\text{tot}}$ the \emph{total emission rate} (into $4\pi$
solid angle). The spatio-temporal profile of the emitted photon wavepacket
can thus be written as $\vec{\psi}\left(\vec{r},t\right)=\vec{\varphi}(\vec{r}\,)s\left(\tau\right)$
with geometric factor
\begin{equation}
\vec{\varphi}(\vec{r}\,)=-\sqrt{\frac{\gamma_{e}}{6\pi c}}k_{0}\sum_{i,j}\hat{G}\left(\vec{r}-\vec{r}_{i}\right)\vec{p}\left(H_{nh}^{-1}\right)_{i,j}J_{j}.\label{eq:phi}
\end{equation}
Here $s(\tau)=e^{-\gamma_{\text{tot}}\tau/2}$ represents the exponentially
decaying atomic state with retarded time $\tau=t\!-\!|\vec{r}\,|/c\ge0$.
We note that the above discussion generalizes to time-dependent couplings
$J_{j}\rightarrow J_{j}(t)\equiv J_{j}f(t)$, allowing a temporal
shaping of the outgoing wavepacket.
In our antenna design, we wish to optimize the directionality of emission
with an appropriate choice of phases $J_{j}=|J_{j}|e^{i\phi_{j}}$,
for a given antenna geometry and atomic parameters. In Figs.~\ref{fig:chiralQO} and \ref{fig:setup}
we have already presented corresponding results from numerical evaluation
of $\vec{\varphi}(\vec{r}\,)$ for various few-atom configurations.
We present both analytical and numerical studies of this optimization
problem in the following two sections.
\begin{figure*}[t]
\includegraphics[width=1\linewidth]{Fig3}\caption{\emph{Performance of a `few-atom' antenna.} Effective optical depth
(a) and corresponding Purcell factor $\beta$ {[}inset~(a){]} for
an optimal Gaussian mode $n_{0}$, for an antenna consisting of $N_{{\rm a}}$
atoms. Regular arrays with $N_{z}=2,4,8$ are shown in blue, orange,
and green solid lines, respectively (transversal sizes of $N_{\perp}=2,3,4$
are highlighted by different markers as shown in the legend). A lattice
imperfection modeled as classical randomization of atomic positions
with normal distribution with dispersion $\sigma_\text{th}=0.01\lambda_{0}$ ($\sigma_\text{th}=0.02\lambda_{0}$)
is shown in dashed (resp. dotted dashed) lines with the corresponding
color code. Results for randomly distributed atoms with the atomic
density of the regular arrays $n_{a}=2/\lambda_{0}^{3}$ are shown
with black dotted line. (b) Statistics of optimal Gaussian mode waists
$w_{0}$ (blue dots) versus $L_{\perp}$ for all configurations of
$N_{\perp}$ and $N_{z}$ up to $\protect\smash{16 \times 16 \times 8}$.
Fitted linear dependence (blue dashed line) of $w_{0}$ and the corresponding
opening angle $\theta$ of the Gaussian beam (in red). (c) Statistics
of optimal interatomic distances $\delta_{\perp}$ versus $N_{\perp}$.
(d-f) Imperfections for arrays with $N_{z}=2,4,8$ and $N_{\perp}=10$.
Purcell factor as a function of (d) percentage of defects, (e) Gaussian
dispersion $\sigma_\text{th}$ of randomized atomic positions, and (f) detuning
from resonance for two-level atoms. }
\label{fig2}
\end{figure*}
\subsection{Quantum Antenna in Paraxial Approximation\label{subsec:Parxial}}
An analytical insight for optimizing emission to a given spatial mode
of the radiation field can be obtained in the paraxial approximation
for $\vec{\psi}(\vec{r},t)$. This approximation is valid for strongly
directional emission, and for atomic antenna configurations with $L_{\perp}\gg\lambda_{0}$
{[}as illustrated in Figs.~\ref{fig:setup}(b,d){]}. In the paraxial
description the target mode is specified as a desired paraxial mode
of interest, e.g. as a Laguerre-Gauss mode. The paraxial formulation
given below will not only allow us to quantify the directionality
in terms of a Purcell $\beta$-factor for emission into the desired
mode, but also to show that the optimal phases for the master atom
- ensemble couplings $J_{j}$ are naturally generated by Laguerre-Gauss
laser beams driving the transfer from master atom to atomic ensemble.
In the paraxial approximation the photon wavepacket, propagating dominantly
along a given direction (chosen in the following as the $z$-axis
in Figs.~\ref{fig:chiralQO} and \ref{fig:setup}), can be expanded in the form %
\mbox{%
$\vec{\psi}(\vec{\rho},z,t)=\sum_{n}\psi_{n}(t-z/c)u_{n}\left(\vec{\rho},z\right)\vec{p}\,e^{ik_{0}z}$%
}, where we denote $(\vec{\rho},z)\equiv\vec{r}$. Here $u_{n}\left(\vec{\rho},z\right)$
is a complete set of (scalar) modes solving $\left(\partial_{z}-\frac{i}{2k_{0}}\nabla_{\perp}^{2}\right)u_{n}\left(\vec{\rho},z\right)=0,$
and satisfying for a given~$z$ the orthogonality condition %
\mbox{%
$\int d^{2}{\vec{\rho}}\,u_{n}^{*}\left(\vec{\rho},z\right)u_{m}\left(\vec{\rho},z\right)=\delta_{nm}$%
} \footnote{In practice, the range of $n$ is limited by the condition that the spectral distribution of $u_n(\vec \rho,z)$ takes non-vanishing values only for momenta $|\vec q|\ll k_0$. }. Examples of paraxial modes include the Laguerre-Gauss modes $LG_{p}^{l}(\vec{\rho},z)$
with radial and azimuthal indices $p$ and $l$. The LG modes are
implicitly parametrized by the beam waist $w_{0}$, and the focal
point $z_{0}$, as summarized in Appendix \ref{sec:-Laguerre-Gauss-(LG)}.
Expanding the field emitted from the antenna into a set of paraxial
modes allows to decompose the spontaneous decay rate $\gamma_{{\rm tot}}$
of the master atom as $\gamma_{{\rm tot}}=\sum_{n}\gamma_{n}+\gamma^{\prime}$.
Here $\gamma_{n}$ is the spontaneous emission rate into the paraxial
mode $u_{n}(\vec{\rho},z)$, while $\gamma^{\prime}$ denotes the
emission into the remaining modes in $4\pi$ solid angle. In Appendix
\ref{sec:Emission-rate-into} we derive
\begin{equation}
\gamma_{n}=\frac{3\pi\gamma_{e}}{2k_{0}^{2}}\Big|\sum_{i,j}u_{n}^{*}\left(\vec{\rho}_{i},z_{i}\right)e^{-ik_{0}z_{i}}\left(H_{nh}\right)_{i,j}^{-1}J_{j}\Big|^{2}\label{eq:gamman}
\end{equation}
which is essentially the spontaneous emission rate according to Fermi's
golden rule with the emitted field pattern $\vec{\varphi}(\vec{r}\,)$
projected on the paraxial modes $u_{n}(\vec{\rho},z)$. This leads
us to define a Purcell factor
\begin{equation}
\beta_{n}\equiv\frac{\gamma_{n}}{\gamma_{{\rm tot}}},\label{eq:beta_of_delta}
\end{equation}
as the fraction of the total emission into each paraxial mode $n$
($0\le\beta_{n}\le1$). Our aim is thus to find a set of couplings
$\{J_{j}\}$ which optimizes emission into a given directed mode —
say a target mode $n_{0}$ — ideally with $\beta_{n_{0}}\rightarrow1$.
Purcell factors close to unity for a given mode can be achieved for
off-resonant transfer $\Delta\gg\gamma_{e}$. In this limit we have
\mbox{%
$H_{nh}^{-1}\approx-\Delta^{-1}\mathbb{I}+i\gamma_{e}/\left(2\Delta^{2}\right)\left(\mathbb{I}+\mathbb{G}\right)$%
} up to second order in $1/\Delta$, and dipolar flip-flops in the
atomic ensemble are suppressed as higher order terms in a large detuning
expansion. We then find
\begin{align}
\gamma_{n} & = \left|g_n\right|^2,\ \ \ \ \ g_n=\frac{\sqrt{3\pi\gamma_{e}}}{\sqrt{2}\Delta k_{0}}\sum_{j}u_{n}^{*}\left(\vec{\rho}_{j},z_{j}\right)e^{-ik_{0}z_{j}}J_{j},\label{eq:gamma_n_large_Delta}\\
\gamma_{{\rm tot}} & =\frac{\gamma_{e}}{\Delta^{2}}\sum_{i,j}J_{i}^{*}\left(\mathbb{I}+{\rm Re}[\mathbb{G}]\right)_{ij}J_{j}.\label{eq:gamma_tot_large_Delta}
\end{align}
From this expression we see that the emission rate $\gamma_{n_{0}}$
to the target mode of interest $n_{0}$ is maximized under the prescription
\begin{equation}
J_{j}\sim e^{ik_{0}z_{j}}u_{n_{0}}\left(\vec{\rho}_{j},z_{j}\right),\label{eq:Jj_choice}
\end{equation}
while other $\gamma_{n\ne n_{0}}$ are strongly suppressed, as a consequence
of the orthogonality condition of the paraxial modes in a discrete
approximation. This is a manifestation of the Huygens-Fresnel principle, where the atomic emission interferes constructively in the desired direction. We emphasize that these couplings are naturally implemented
in the physical setup of Fig.~\ref{fig:chiralQO}(a,c), when the laser driving
the master atom --- ensemble couplings is chosen with the spatial mode
$u_{n_{0}}$. Under the prescription \eqref{eq:Jj_choice}, we obtain for the effective decay rate of Eq.~\eqref{eq:gamma_n_large_Delta} \mbox{$\gamma_{n_0}=3\pi \gamma_e \bar J^2 N_z/(2\Delta^2k_0^2\delta_\perp^2)$}, where $\bar J\equiv \sqrt{\sum_j|J_j|^2}$. As an example, for $\bar J\sim 0.15 \Delta$, $N_z=2$ and $\delta_\perp=0.7\lambda_0$, this corresponds to $\gamma_{n_0}\sim 10^{-2} \gamma_e$, which for $\gamma_e$ in the MHz range represents timescales of the order of $10^{-4}$ s.
We note that in the limit $\Delta\gg\gamma_{e}$ of off-resonant excitation
the atoms representing the quantum antenna are only virtually excited,
i.e. the atomic ensemble acts as a \emph{virtual quantum memory}.
This is in contrast to \emph{real quantum memory} for quantum states
of light in atomic ensembles \cite{Hammerer2010}, where an incident
photon is absorbed and stored in a long-lived spin excitation, and
is read out after some storage time in a Raman process.
In the following section we will present a numerical study for various
antenna geometries, including ensembles as regular atomic arrays,
and for randomly positioned atoms. Analytical results for Purcell
factors can be obtained in the limit of a large number of randomly
distributed atoms, and assuming the choice of phases as given by \eqref{eq:Jj_choice}.
In Appendix~\ref{sec:purcell random} we show that for such a `random'
ensemble with atomic density $n_{a}$ and optical depth $\smash{\mathcal{O}_{d}=3\lambda_{0}^{2}n_{a}L_{z}/(2\pi)}$,
the Purcell factor can be written as $\beta_{n_{0}}=\mathcal{O}_{d}/\left(4+\mathcal{O}_{d}\right)$.
This is consistent with the expression for readout efficiency of ensemble
based atomic quantum memories \cite{PhysRevA.76.033805,Saffman2005}. Thus $\beta_{n_{0}}\rightarrow1$
is achievable in the limit of large optical depth, i.e. large number
of atoms. Remarkably, as shown in the following section, the number
of atoms required can be significantly relaxed for regular arrays
with subwavelength spacing.
\subsection{Numerical Study of Few-Atom Arrays\label{subsec:Few-atom-antenna}}
We now turn to a numerical study for characterizing and optimizing
the geometry of the quantum antenna. We will show in particular that
regular atomic arrays, due to their periodic structure, can significantly
suppress spontaneous emission into non-forward propagating modes and
this will allow us to achieve large Purcell factors even for a few-atom
antenna. In our study below we choose as target mode a Gaussian beam
$u_{n_{0}\equiv(0,0)}(\vec{\rho},z)\equiv LG_{0}^{0}(\vec{\rho},z)$
(for notation see Appendix~\ref{sec:-Laguerre-Gauss-(LG)}) with a
beam waist $w_{0}$ and the antenna located at the focal point $z_{0}=0$
{[}see Fig.~\ref{fig:setup}(b){]}\footnote{Such modes can be further transformed by optical lenses to interface
the master atom with another system of interest, such as an optical
fiber, a nanophotonic device, an extra master atom, etc.}. Furthermore, we assume that phases are chosen as fixed according
to the prescription \eqref{eq:Jj_choice}, i.e. as $J_{j}\sim e^{ik_{0}z_{j}}LG_{0}^{0}(\vec{\rho}_{j},z_{j})$.
Let us consider an antenna with a configuration characterized by a
transverse atom number $N_{\perp}$, a number of layers $N_{z}$,
and thus a total atom number \mbox{$N_{{\rm a}}=N_{\perp}\times N_{\perp}\times N_{z}$}.
In the following we fix the distance between the layers as $\delta_{z}=\lambda_{0}(2N_{z}-1)/(2N_{z})$,
which provides maximum destructive interference and thus suppression
of emission in the backward direction, but we leave open the transverse
distance $\delta_{\perp}$ as a parameter to be varied. The quantity
to be optimized is the Purcell factor for the Gaussian mode. We find
the maximum value of $\beta_{n_{0}}(w_{0},\delta_{\perp})$, denoted
$\beta$, by varying the waist parameter $w_{0}$ and the transverse
spacing $\delta_{\perp}$.
Our results are shown in the inset of Fig.~\ref{fig2}(a), which
shows $\beta$ as a function of~$N_{{\rm a}}$ for \emph{perfectly
regular arrays} with $N_{z}=2,4,8$ in blue, orange, and green lines,
respectively. Remarkably, a large Purcell factor of $\beta\approx0.94$
can be reached with just two layers of $\smash{4 \times 4}$ arrays
of atoms as antenna (blue square marker on the blue curve), and we
see rapid convergence to 1 with increasing atom number. We note that for the \emph{perfect} arrays considiered here, the efficiency decreases with increasing $N_z$ at fixed $N_\perp$, which is a consequence of the divergence of the paraxial mode increasing with the longitudinal antenna size, such that the optimal configuration is $N_z=2$.
The corresponding
waists $w_{0}$ are shown in blue circles in Fig.~\ref{fig2}(b),
as a function of transverse antenna size $L_{\perp}\equiv N_{\perp}\delta_{\perp}$,
for all configurations of $N_{\perp}$ and $N_{z}$ up to $\smash{16 \times 16 \times 8}$.
The dashed blue line indicates the linear dependence of the optimal
mode waists $w_{0}\sim L_{\perp}$ on the transverse antenna size
(as long as $w_{0}\gtrsim\lambda_{0}$). The optimization routine
identifies the largest mode waist supported by the antenna, as the
Purcell factor for regular arrays increases with the growth of the
transverse mode size, as we discuss below. The red dashed curve in
Fig.~\ref{fig2}(b) shows the corresponding opening angle of the
Gaussian mode as given by $\theta=\tan^{-1}[\lambda_{0}/(\pi w_{0})]$.
The optimal interatomic spacings $\delta_{\perp}$ are presented in
Fig.~\ref{fig2}(c) and indicate a slow growth with the increase
of the transverse antenna size. This is a consequence of the fact
that the transverse spatial spectrum of the target mode becomes narrower
for larger antennas and, according to the sampling theorem, the antenna
can properly couple to the mode even with an increasing interatomic
spacing $\delta_{\perp}$.
To compare regular arrays and `random' atomic ensembles, and to reveal
the antenna performance scaling with its size, we find it convenient
to define an effective optical depth for regular arrays as $\mathcal{O}_{d}^{{\rm eff}}=4\beta/(1-\beta)$,
corresponding to the optical depth for a `random' ensemble achieving
the same Purcell factor. This effective optical depth is shown in
Fig.~\ref{fig2}(a) for regular perfect arrays with $N_{z}=2,4,8$
in blue, orange, and green solid lines, respectively. For comparison,
results for an antenna with randomly distributed atoms, with atomic
density equivalent to the one of regular arrays, are shown in black
dotted line.
The performance of the $\smash{4 \times 4}$ bilayer
array mentioned above is highlighted by the optical depth $\mathcal{O}_{d}^{{\rm eff}}\approx70$
(blue square marker). The scaling of the optical depth with the number
of atoms shows a striking difference between regular arrays and `random'
atomic ensembles. This is due to the fact that even though the emission
rate $\gamma_{n_{0}}$ into a target mode given by Eq.~\eqref{eq:gamma_n_large_Delta}
is similar, the total emission rate, which for the optimized couplings
choice reads $\gamma_{{\rm tot}}\approx\gamma_{n_{0}}+\gamma'$, is
defined mainly by the scattering into non-paraxial modes $\gamma'$.
An ensemble of randomly distributed atoms emits almost equally well
into all non-paraxial modes, although the ratio $\gamma'/\gamma_{n_{0}}$
is suppressed by the number of atoms. For regular atomic arrays, however,
the sideward scattering is totally suppressed for target modes with
large transverse extent. In addition, paraxial backward emission is
significantly suppressed by means of the destructive interference
with the proper choice of longitudinal spacing $\delta_{z}$ given
above. This results in Purcell factors for regular arrays, which are
far superior to the one of a `random' ensemble.
In Appendix~\ref{app:Od_lattice} we show that the effective optical
depth for a lattice emitting into a mode with transverse size $w$
grows as $(w/\lambda_{0})^{4}$, which is equivalent to %
\mbox{%
$\mathcal{O}_{d}^{{\rm eff}}\sim(N_{{\rm a}}/N_{z})^{2}$%
} since $w/\lambda_{0}\sim N_{\perp}$. More precisely, for a Gaussian
mode with waist $w_{0}$ focussed inside an antenna of size $L_{\perp}\gg w_{0}$
we have %
\mbox{%
$\mathcal{O}_{d}^{{\rm eff}}\leq8+32(w_{0}^{4}/\sigma^{2})$%
} for a two layer antenna with $\delta_{z}=(3/4)\lambda_{0}$, where
$\sigma=3\lambda_{0}^{2}/(2\pi)$ is the scattering cross section
of a two-level atom, where the upper bound corresponds to the probability
of emitting forwards. This analytical result is shown in black dot-dashed
line in Fig.~\ref{fig2}(a), where we have converted the antenna
size $N_{{\rm a}}$ into a mode waist $w_{0}$ using the linear dependence
of the optimal mode waist on the transverse antenna size {[}blue dashed
line in Fig.~\ref{fig2}(b){]}. This scaling is in contrast to the
`random' ensemble optical depth, which grows like $\mathcal{O}_{d}\sim(N_{{\rm a}})^{1/2}$
for an ensemble geometry optimized for a Gaussian beam~\footnote{The optimal overlap with a Gaussian beam is achieved for an ensemble
of length $2z_{R}\equiv2\pi w_{0}^{2}/\lambda_{0}$ (i.e. twice the
Rayleigh length) and section $S=\pi w_{0}^{2}$. This ensemble contains
$N_{{\rm a}}=2n_{{\rm a}}Sz_{R}=2n_{{\rm a}}S^{2}/\lambda_{0}$ atoms,
such that $\mathcal{O}_{d}\equiv(\sigma/S)N_{{\rm a}}=\sigma(2n_{{\rm a}}N_{{\rm a}}/\lambda_{0})^{1/2}$
with $\sigma$ the resonant scattering cross section of a two-level
atom.}. This scaling is shown in black dotted line in Fig.~\ref{fig2}(a).
\begin{comment}
The analytical calculation is performed for an emission forward into
a solid angle, therefore, it is an upper bound for the numerical estimations
of the effective optical depth corresponding to emission into a Gaussian
mode shown in Fig.~\ref{fig2}(a) with color lines.
The fact that efficiency of the lattice antenna grows simply with
the transverse size $w_{0}$ of the emission mode can be seen in Fig.~\ref{fig2}(b)
where $w_{0}$ (blue dots) of optimal Gaussian modes for all antenna
configurations (up to %
\mbox{%
$16 \times 16 \times 8$%
}) linearly depend on the transverse size $L_{\perp}$ of the antenna.
The optimization routine basically chooses the largest mode waist
supported by the antenna, almost irrespective of the number of atomic
layers $N_{z}$.
\end{comment}
The effect of imperfections in atomic arrays is shown in Figs.~\ref{fig2}(d,e,f).
Panel (d) illustrates the decrease of Purcell factor $\beta$ due
to a finite percentage of defects (i.e. missing atoms) for an array
with $N_{z}=2,4,8$ layers. Panel (e) shows the effect of temperature,
which is modeled as a classical randomization of atomic positions
normally distributed with variance $\sigma_\text{th}^2\equiv 2n_\text{th}/(m\omega_m)$, where $n_\text{th}$ is the average thermal occupation of motional states, $m$ the atomic mass and $\omega_m$ the vibrational frequency. This is also shown in Fig.~\ref{fig2}(a) with dashed and dot-dashed
lines corresponding to $\sigma_\text{th}=0.01\lambda_{0},\,0.02\lambda_{0}$,
respectively (the color indicates $N_{z}$ as described above). Clearly,
an antenna consisting of larger number of layers $N_{z}$ is less
prone to imperfections since it has more emitters to support the destructive
interference for the backward scattering. Finally, in panel (f) we
study the Purcell factor $\beta$ {[}without the approximations of
Eqs.~\eqref{eq:gamma_n_large_Delta}, \eqref{eq:gamma_tot_large_Delta}{]}
as a function of the detuning $\Delta$ from the resonance for two-level
atoms. One can see that a detuning of the order of the natural linewidth $\gamma_{e}$
is sufficient to reach optimal Purcell factors.
\section{Chiral Photonic quantum Link}
\label{sec:chiralnetworks}
Quantum antennas can be used as a light-matter interface to form \emph{chiral} photonic quantum networks in free-space, with several distant master atoms strongly interacting via a common 1D free space photonic mode [see Fig.~\ref{fig:chiralQO}(b)]. We illustrate the efficiency of this `quantum link' with simulations of deterministic Quantum State Transfer protocols. We then express the dynamics of a more generic photonic network, including possibly many-photon states, in terms of a Quantum Stochastic Schr\"odinger Equation.
\begin{figure}
\includegraphics[width=1\columnwidth]{Fig4}\caption{\emph{Free-space quantum link}. (a)~Purcell factor $\beta$ as a function of the distance $z_0$ from each antenna to the focussing point of the gaussian mode for various $N_\perp$, with $\delta_\perp=0.75\lambda_0$. Inset: corresponding optimal waists. The dotted-dashed curves have analytical expressions (see text). (b,c)~State transfer fidelity, for $N_\perp=10$ and (b)~$\delta_z=0.75\lambda_0$, (c)~$\delta_\perp=0.8\lambda_0$. }
\label{qsse}
\end{figure}
\subsection{Chiral Master Equation with Quantum Antennas}\label{sec:QLink}
We consider a minimal network consisting of two nodes separated by a distance $L=2z_0$ [see Fig.~\ref{fig:chiralQO}(b)], where each master atom \mbox{$(a=1,2)$} has a ground state $\ket{G}_a$ and an excited state $\ket{E}_a$, with $s_a^-\equiv\ket{G}_a\!\bra{E}$ and is coupled to an array of $N_{\rm a}$ atoms. We denote the hopping rates as $J_{j,a}$ with $j=1,...,2N_{\rm a}$, where $J_{j,1}$ ($J_{j,2}$) takes non-zero values only for $j\leq N_{\rm a}$ (resp. $j>N_{\rm a}$). We assume that each array acts as a quantum antenna with a common paraxial target mode $n_0$, with the waist of this mode located halfway between the two nodes \footnote{One can alternatively use optical lenses to couple paraxial modes with waists located at the position of each antenna}. As represented in Fig.~\ref{qsse}(a), a good photon emission and absorption into this mode, characterized by $\beta\approx1$, is realized when $L_\perp\gtrsim\sqrt{\lambda_0 z_0}$, a condition set by the diffraction limit. The dashed-dotted curve represents \mbox{$\int_{|x|,|y|<L_\perp/2} d^2\rho \left|u_{n_0}\left(\vec \rho,z_1\right)\right|^2=\text{erf}\left[\sqrt{L_\perp^2\pi/(4z_0\lambda_0)}\right]^2$}, with $z_1$ the position of the first antenna along $z$, which is the maximum value for $\beta$ achievable with an antenna with transverse surface $L_\perp^2$. This corresponds to the limit $N_\perp\to\infty$, and already for $N_\perp=10$ the curve is almost indistinguishable from this limit.
The corresponding optimal waists are shown in the inset of Fig.~\ref{qsse}(a), where the black curve represents the waist minimizing the mode width at the position of the antenna, and is given by $w_0=\sqrt{z_0L/\pi}$. For discrete arrays with finite $N_\perp$, the optimal waist is given by a trade-off between minimizing this mode width in order to diminish finite-size effects of the layers, and increasing the number of atoms emitting in the mode in order to improve the effective optical depth. This results in a saturation of $w_0\sim L_\perp$ for low values of $z_0$.
In order to characterize the efficiency of the quantum link between the two qubits, we first express the dynamics in terms of a master equation for the density matrix $\rho$ for the master atoms. Assuming that (i) the photonic field is initially in the vacuum state, (ii) the couplings are perturbative (i.e.,~$J_{j,a}\ll\Delta$), and (iii) the time-delay in the photon propagation between the two antennas is negligible (i.e.,~Markov approximation), we eliminate antenna atoms and radiation field as an effective reservoir for master atoms, and obtain a chiral master equation analogous to Eq.~\eqref{eq:mastereq1D},
where now the effective non-hermitian Hamiltonian reads (see Appendix~\ref{sec:chiralmasterequationderiviation})
\begin{equation}
\begin{aligned}
H_{\text{eff}} = & \sum_{a=1}^2\left(\epsilon_{a}-i\frac{\gamma_{\text{tot},a}}{2}\right)s_{a}^{+}s_{a}^{-}
\\ &-i\left(\gamma_{L}e^{i\phi_L}s_{1}^{+}s_{2}^{-}+\gamma_{R}e^{i\phi_R}s_{2}^{+}s_{1}^{-}\right).
\label{eq:Hchir}
\end{aligned}
\end{equation}
Here %
\mbox{%
$\epsilon_{a}-i\gamma_{\text{tot},a}/2\equiv-\sum_{i,j}J_{i,a}^{*}(H_{nh}^{-1})_{i,j}J_{j,a}$%
}, where $\epsilon_{a}$ is a frequency shift for each qubit \footnote{$\epsilon_a$ can be cancelled e.g. using additional AC Stark
shifts.}, while $\gamma_{a}$ is their total effective decay rate, similarly to Eq.~\eqref{eq:full_gamma}.
We note that due to the symmetry of the system and of the target mode, we have here $\gamma_{\text{tot},1}=\gamma_{\text{tot},2}\equiv\gamma$.
On the other hand, the rates of interaction between qubits and the associated phases are given by
\begin{eqnarray}
\label{eq:gammaRphiR}\gamma_{R}e^{i\phi_{R}}= & - & i\sum_{i,j=1}^{2N_{\rm a}}J_{i,2}^{*}(H_{nh}^{-1})_{i,j}J_{j,1},\\
\label{eq:gammaLphiL}\gamma_{L}e^{i\phi_{L}}= & - & i\sum_{i,j=1}^{2N_{\rm a}}J_{i,1}^{*}(H_{nh}^{-1})_{i,j}J_{j,2},
\end{eqnarray}
and the decay to unwanted non-paraxial modes expresses as $\gamma'\equiv\gamma-\gamma_R-\gamma_L$.
Finally, the recycling terms express as
\begin{eqnarray}
\mathcal{L}_{\text{eff}}{\rho} & = & \sum_{a=1}^2\gamma_{\text{tot},a}s_{a}^{-}{\rho}s_{a}^{+}+\left(\gamma_{R}e^{i\phi_R}+\gamma_{L}e^{-i\phi_L}\right)s_{1}^{-}{\rho}s_{2}^{+}\nonumber \\
& & +\left(\gamma_{R}e^{-i\phi_R}+\gamma_{L}e^{i\phi_L}\right)s_{2}^{-}{\rho}s_{1}^{+},\label{eq:Lchir}
\end{eqnarray}
The rate $\gamma_{R}$ ($\gamma_{L}$) in Eq.~\eqref{eq:Hchir} corresponds to the effective long-range coupling from the first qubit to the second one (second to first, respectively), which in general is not reciprocal (i.e.,~$\gamma_R\neq\gamma_L$). In analogy to Eq.~\eqref{eq:gamma_n_large_Delta}, assuming $k_0z_0\gg 1$, we obtain in the paraxial approximation and to lowest order in $\gamma_e/\Delta$
\begin{equation}
\gamma_{R}e^{i\phi_R}\!=\! \frac{3\pi\gamma_e}{2\Delta^2 k_0^2}\! \sum_{n,i,j}\!e^{ik_0(z_i-z_j)}\!J^*_{i,2}u_n(\vec{\rho}_i,z_i)
u^*_n(\vec{\rho}_j,z_j)J_{j,1},
\end{equation}
while $\gamma_Le^{i\phi_L}$ can be expressed in a similar way by replacing $J_{j,a}\to J_{j,a}^*$. This assumes a decomposition of left-propagating modes on a similar paraxial basis, with the same waist location as for the right-propagating modes. In particular, using Eq.~\eqref{eq:Jj_choice} for the couplings, in the limit $\beta\to 1$ we have the expression \mbox{$\gamma_R\to 3\pi \gamma_e \bar J_1\bar J_2 N_z/(2\Delta^2k_0^2\delta_\perp^2)$}, where $\bar J_a\equiv\sqrt{\sum_i |J_{i,a}|^2}$ denotes the coupling rate between master atom $a$ and its antenna, while $(\gamma_L,\phi_R)\to0$ and $\phi_L\to 4k_0z_0$.
We thus obtain almost ideal unidirectional couplings between qubits, thus forming a {cascaded} quantum system as discussed in Sec.~\ref{sec:chiralQO}. We illustrate this here with the application of deterministic Quantum State Transfer (QST) protocols.
To realize QST, we first remark that the various decay rates in Eq.~\eqref{eq:Hchir} can be taken time-dependent by adding a temporal modulation in the laser-assisted hopping rates $J_{j,a}\to f_a(t) J_{j,a}$, such that \mbox{$\gamma_{\text{tot},a}\to f_a(t)^2 \gamma_{\text{tot},a}$} and $\gamma_{R/L}\to f_1(t)f_2(t)\gamma_{R/L}$. The functions $f_1(t)$ and $f_2(t)$ are chosen such that in the ideal scenario (i.e.,~\mbox{$\gamma_{R}=\gamma$}) the total excitation of the two qubits is conserved~\footnote{Analytical expressions for $f_1(t)$ and $f_2(t)$ can be obtained by requiring the temporal shape of photons emitted by the first array to be symmetric, in which case a solution is $f_2(t)\equiv f_1(-t)$.}.
With imperfect couplings ($\gamma_R<\gamma$), the QST fidelity is given by \mbox{$\mathcal F=\gamma^2_R/\gamma^2$}, assuming $\gamma_L\ll\gamma_R$ (see Appendix~\ref{sec:pulseshapingQST} for details).
Fig.~\ref{fig:chiralQO}(e) represents the range of values for $\mathcal F$ accessible in our model, which are obtained by evolving the dynamics of the master atom density matrix $\rho$ from the chiral master equation, and shows that the typical achievable inter-array separations $2z_0$ grows linearly with the surface $L_\perp^2$. The dashed curve represents a numerical estimation for the maximum fidelity achievable in the paraxial limit, and corresponds to the limit of $N_\perp\to\infty$. In the inset, we show that the saturation value decreases like $1/N_\perp^4$, which is equivalent to the scaling of $\mathcal O_d^\text{eff}\sim(N_{\rm a}/N_z)^2$ as discussed in Sec.~\ref{subsec:Few-atom-antenna}. As an example, with $N_\perp=20$ we obtain $\mathcal F \approx 0.88$ for $2z_0=150\lambda_0$, demonstrating the efficiency of atomic arrays for building optical interconnects with mesoscopic distances. For small $z_0$, Fig.~\ref{qsse}(b) shows that $\delta_\perp$ can take a broad range of values, as long as $\delta_\perp\lesssim0.9\lambda_0$. As $z_0$ increases, this range diminishes as we need a larger surface $L_\perp^2\sim z_0 \lambda_0$. Conversely, by varying $\delta_z$, a spatial periodicity of $\lambda_0/2$ appears when $\delta_z\neq\lambda_0(1\pm1/4)$ [see Fig.~\ref{qsse}(c)], arising from the fact that $\gamma_L$ is not properly cancelled, which induces a back-action on the first qubit depending in general on the propagation phase as $\phi_R+\phi_L= 4k_0z_0$.
Finally, we note that for fidelities $\mathcal{F}$ close to $1$, several strategies for quantum error correction can be applied to our situation to further improve the fidelity. This can be realized by coupling several qubits to each atomic array, rather than a single one, to implement redundant
qubit codes correcting for the photon losses arising from $\beta<1$. For instance, following a protocol described in Ref.~\cite{Vermersch2017}, the qubit state can first be redundantly encoded in an atomic ensemble, using entangled states with multiple atomic excitations for the logical qubit, such as cat or binomial states~\cite{Michael2016}. Coupling the ensemble to the atomic array will produce a propagating quantum error correcting photonic code rather than a single photon, which can then be transferred to a second distant ensemble, using the same protocol as described above. Provided the probability of error is small enough, single photon losses can be detected and corrected in the second ensemble. On the other hand, when the fidelity $\mathcal F$ is too low for error correction, probabilistic protocols become advantageous, and atomic arrays can be used to achieve high repetition rates.
\subsection{Quantum Stochastic Schr\"odinger Equation Formulation}\label{sec:QSSE}
In Sec.~\ref{sec:Model} we studied the spontaneous emission process of a single photon from a single master atom, which we described using a Wigner-Weisskopf ansatz. In Sec.~\ref{sec:QLink} we then considered a system of two nodes, whose generic dynamics was provided by a master equation, obtained under the assumptions that the radiation was initially in the vacuum state, and that time-delays in the photon propagation between the nodes was negligible (Markov approximation).
In the following we extend these formalisms to account for such possible delays, and to allow for the description of any initial photonic field state.
\subsubsection{Single emitter}
We start with the description of a single node of master atom and quantum antenna.
Beyond the Wigner-Weisskopf treatment presented in Sec.~\ref{sec:Model}, the dynamics, including possibly many-photon states, is conveniently formulated in the framework of quantum stochastic calculus, in terms of a Quantum Stochastic Schr\"odinger Equation (QSSE) \cite{gardiner2015}. Our description is obtained in the limit $\Delta\gg\gamma_e$ by adiabatically eliminating excitations in the antenna in an Holstein-Primakoff approximation. For details on the derivation of the QSSE and formal definition of the field modes we refer the reader to Appendix~\ref{app:qsse}. We obtain
\begin{equation}\label{eq:qssedef}
i\frac d {dt}\ket{\Psi(t)}=\left[H_\text{sys}+V(t)\right]\ket{\Psi(t)},
\end{equation}
describing the dynamics of a pure state $\ket{\Psi(t)}$ including master atom and photonic field,
where the interaction Hamiltonian expresses as
\begin{equation}\label{eq:QSSE_Vdef}
V(t)=i\Big[\sum_n\left(g^R_n {b^R_n}^\dagger(t)+g^L_n {b^L_n}^\dagger(t)\right)
+g'{b'}^\dagger(t)\Big] s^-+\text{h.c.}
\end{equation}
Here $b^{R/L}_n(t)$ represent quantum noise annihilation operators for photons in the paraxial 1D mode $n$ propagating in the right/left direction, and interacting with the master atom at time $t$, while $b'(t)$ corresponds to unwanted modes propagating in 3D, satisfying \mbox{$[b^{p}(t),{b_n^q}^\dagger(t')]=\delta_{p,q}\delta(t-t')$} with $p,q\in\{R,L,'\}$.
The effective coupling of the master atom to right-propagating modes $g_n^R$ expresses as $g_n$ in Eq.~\eqref{eq:gamma_n_large_Delta}, while $g_n^L$ can be expressed as in Eq.~\eqref{eq:gamma_n_large_Delta} by replacing $u_{n}\left(\vec{\rho}_{j},z_{j}\right)e^{ik_{0}z_{j}} \to u_{n}^{*}\left(\vec{\rho}_{j},z_{j}\right)e^{-ik_{0}z_{j}}$. The coupling $g'$ on the other hand expresses from Eq.~\eqref{eq:gamma_tot_large_Delta} as \mbox{$g'=\sqrt{\gamma_\text{tot}-\sum_n(|g_n^R|^2+|g_n^L|^2)}$}. For generality sake we also added a term $H_\text{sys}$, accounting for eventual additional operations on the master atom which needs not conserve the number of excitations, e.g. for an external coherent drive \mbox{$H_\text{sys}=\Omega_\text{R}(s^-+s^+)-\Delta_\text{R} s^+s^-$} with Rabi frequency $\Omega_\text{R}$ and detuning $\Delta_\text{R}$ \footnote{The QSSE can be interpreted according to quantum Stratonovich calculus and integrated to obtain a master equation for the master atom depending on the state of the input fields.}.
The dynamics generated by Eq.~\eqref{eq:QSSE_Vdef} is in exact analogy to that of a qubit with {chiral} coupling ($g^L_n\neq g^R_n$) to a multimode 1D waveguide, where each $n$ corresponds to an orthogonal degenerate waveguide mode, achieving ideal coupling in the limit $g'\to0$.
\subsubsection{Two emitters}
We now consider the case of two nodes as studied in Sec.~\ref{sec:QLink}.
The interaction Hamitonian in Eq.~\eqref{eq:QSSE_Vdef} expresses here as $V(t)=V_1(t)+V_2(t)$, where (see Appendix~\ref{app:qsse})
\begin{eqnarray}
V_a(t)=i\Big[g_a'{b_a'}^\dagger(t)+\sum_n &&\Big(g^R_{n,a}e^{-i\omega_0\tau_a}{b^R_n}^\dagger(t-\tau_a)\label{eq:QSSE_V2def}
\\+&&g^L_{n,a}e^{i\omega_0\tau_a}{b^L_n}^\dagger(t+\tau_a)\Big)\Big]s_a^- +\text{h.c.},\nonumber
\end{eqnarray}
with $\tau_1=0$, and $\tau_2\equiv\tau= 2z_0/c$ the time-delay in the propagation of a photon between the two nodes. Here ${b_{1,2}'}(t)$ denote annihilation operators for photons in non-paraxial modes, which we assume independent with $[{b_1'}(t),{b_2'}^\dagger(t')]=0$, and $g'_{1,2}$ denote the effective coupling rates of the master atoms to these modes. On the other hand $b^{R}_n(t)$ represent bosonic operators for a continuous string of harmonic oscillators interacting consecutively with the first and second master atom, while $b^{L}_n(t)$ represent harmonic oscillators interacting consecutively with the second and first atom.
In some cases, the time-delay $\tau$ in the label of field operators of Eq.~\eqref{eq:QSSE_V2def} can be formally set to \mbox{$0^+$}, such that the QSSE can be integrated. This is the case when the time-delay is shorter than the typical timescale of the atomic dynamics (Markov approximation, i.e.~\mbox{$|g'_a|^2+\sum_n(|g^R_{n,a}|^2+|g^L_{n,a}|^2)\ll1/\tau$}), or for purely cascaded systems (i.e.,~$\sum_n|g^L_{n,a}|^2\ll \sum_n|g^R_{n,a}|^2$), where photons flow from the first to second node without back-action. In the case of vacuum initial state for the photonic field we obtain the chiral master equation of Sec.~\ref{sec:QLink}, in the paraxial approximation, where we identify \mbox{$\gamma_Re^{i\phi_R}=\sum_n g^R_{n,1} \left(g^R_{n,2}\right)^*$} and \mbox{$\gamma_L e^{i\phi_L}=\sum_n g^L_{n,2}\left(g^L_{n,1}\right)^*$}. When the delay cannot be neglected however, numerical techniques can be used to solve the QSSE, such as matrix-product-state methods.
\section{Atomic Implementation \label{sec:Atomic-Implementations}}
Quantum antennas can be realized in various microscopic systems. The
basic requirements for the physical realization of the model of the
previous section, as master atom (qubit) coupled to a quantum antenna,
are the following. (i) Excitations must be transferred \emph{coherently}
from master atom (qubit) to the antenna atoms. For a quantum antenna
built as large atomic arrays this requires long-range couplings. (ii)
The spatial distribution of the corresponding couplings $J_{i}$,
in particular the required phases for directional emissions, can be
\emph{engineered}, for instance using laser-assisted processes {[}see
Eq.~\eqref{eq:Jj_choice}{]}. (iii) Antenna atoms can emit photons
via an optical dipole transition.
\begin{figure}
\includegraphics[width=1\columnwidth]{Fig5}\caption{\emph{Rydberg implementation}. (a) Atomic level schemes, with the
relevant states for our implementation in blue. (b,c) Probability
of emission in a Gaussian mode (b) as a function of the distance $z_{m}$
between master atom and antenna {[}dashed line: value for two-level
model, see Fig.~\ref{fig2}(a){]}, and (c) as a function of the number
of atoms for the optimal $z_{m}$, using dressing laser with a LG
profile (blue), or with an optimized spatial distribution of $\Omega_{d}(\vec{r}_{i})$
(orange). We consider an ensemble of $10\times10\times2$ atoms with
$\delta_{\perp}=0.7\lambda_{0}$, $\delta_{z}=1.25\lambda_{0}$, $\Omega_{c}=2\pi\times2.5\,\text{MHz}$,
$|\Omega_{d}/\Delta_{d}|\leq0.02$.}
\label{impln-1}
\end{figure}
Here we present an implementation
with neutral atoms employing laser-assisted Rydberg interactions.
This builds on the recent experimental progress in loading atoms in
regular optical lattices, using e.g. optical trapping techniques,
and the possibility to laser excite atoms to Rydberg states to induce
and control long-range dipolar interactions.
We remark that our model can also be realized in various other atomic
physics setups. For very small antenna sizes, e.g. the minimal antenna
$\smash{2 \times 2 \times 2}$, we can use the physics of atomic
Hubbard models (including synthetic gauge fields~\cite{Goldman2016})
to implement the model of Sec.~\ref{sec:Model}. In addition, for
neutral atoms~\cite{Lahaye2009,Browaeys2016,Glaetzle2017} and molecules~\cite{Micheli2006}
long range coupling are available as magnetic and electric dipolar
interactions. Finally, these ideas can also be translated to a solid-state
context, using quantum dots~\cite{Lodahl2015} or NV centers~\cite{Cai2013}.
This also includes interfacing superconducting qubits~\cite{Houck2012}
stored in strip line cavities with bilayer atomic ensembles acting
as quantum antenna.
The atomic level structure we have in mind is shown in Fig.~\ref{impln-1}(a).
For concreteness, we consider optically trapped atoms in a bilayer
($\smash{N_{z}=2}$) configuration, where the master atom is a $^{133}\text{Cs}$
atom and the antenna is made of $^{87}\text{Rb}$ atoms \footnote{The scheme can be adapted for systems with single atomic species.}. The state
of the master atom is encoded in two Rydberg states $\ket{G}=\ket{28S_{1/2},m_{j}=\frac{1}{2}}$
and $\ket{E}=\ket{27P_{3/2},m_{j}=\frac{3}{2}}$, with microwave transition
frequency $\omega_{\mathrm{Cs}}$ (the quantization axis is set by
an external magnetic field along $z$). Antenna atoms can be excited
to four electronic levels, including two Rydberg states $\ket{R'}_{i}=\ket{26P_{1/2},m_{j}=-\frac{1}{2}}$
and $\ket{R}_{i}=\ket{26S_{1/2},m_{j}=\frac{1}{2}}$, with transition
frequency $\omega_{\mathrm{Rb}}$~\footnote{The nuclear spin $m_{I}=3/2$ can be considered as spectator due to
the small hyperfine interactions between Rydberg levels.}. Our particular choice of Rydberg states is motivated by the small
energy difference $\tilde{\Delta}\equiv\omega_{\mathrm{Cs}}-\omega_{\mathrm{Rb}}=2\pi\times1.74(2)$
GHz between the two Rydberg transitions due to a Förster resonance~\cite{Walker2008}.
Finally, we choose two hyperfine stretched states, a ground state
$\ket{g}_{i}=\ket{5S_{1/2},F=2,m_{F}=2}$ and an excited state $\ket{e}_{i}=\ket{5P_{3/2},F=3,m_{F}=3}$,
in order to generate optical photons with $\lambda_{0}=780$ nm (D2-line).
In our model, we operate in the frozen gas regime \cite{Browaeys2016},
where the motion of the atoms can be neglected for the timescales
associated with our model.
While the complete atomic physics details are presented in Appendix~\ref{sec:Details-of-Rydberg},
we describe here the main elements allowing this setup to behave as
quantum antenna. First, the antenna atoms are subject to a laser beam
coupling off-resonantly, with spatial Rabi frequencies $\Omega_{d}(\vec{r}_{i})$,
and detuning $\Delta_{d}$, $\ket{g}_{i}$ to $\ket{R'}_{i}$. In
the dressing regime, $\Omega_{d}(\vec{r}_{i}),V_{\mathrm{dd}}\ll\Delta_{d}$,
where $V_{\mathrm{dd}}$ is the dipole-dipole coupling between Rydberg
states (see Fig.~\ref{impln-1}), we obtain an effective coherent
`flip-flop' interaction $\smash{\ket{E}\ket{g}_{i}\to\ket{G}\ket{R}_{i}}$
between master atom and antenna, which can be controlled externally
via $\Omega_{d}(\vec{r}_{i})$, i.e we can use the dressing laser
to write the required phases on the antenna atoms. Second, emission
of optical photons from $\ket{R_{i}}$ is assisted by a control laser
with Rabi frequencies $\Omega_{c}(\vec{r}_{i})$, and detuning $\Delta_{c}$.
To show that good directionality can be achieved with realistic configurations,
we now present numerical simulations showing the Purcell factor $\beta$
for emission of a single photon to a Gaussian mode, which include
unwanted dipole-dipole couplings between antenna atoms, and finite
Rydberg states lifetimes. To complement this analysis, we also present
in Appendix~\ref{sec:Details-of-Rydberg} a mapping to Eq.~\eqref{eq:S_P},
which is valid under the condition of the electromagnetically induced
transparency \textbf{ $\Omega_{c}(\vec{r_{i}})\gg J_{i},\gamma_{r}$},
and $\Delta_{c}=0$, with $\gamma_{r}$ being the Rydberg decay rate.
In Fig.~\ref{impln-1} (b,c) we show the Purcell factor $\beta$
for the emission to Gaussian modes. Panel (b) shows that an almost
perfect fidelity of coupling to a Gaussian target mode can be reached
at a certain optimal qubit-antenna distance $z_{m}$. The latter results
from a tradeoff between an exaggerated inhomogeneity of the dipole-dipole
couplings $J_{i}$ at small $z_{m}$ and the predominance of unwanted
losses from the Rydberg states at large $z_{m}$. In panel (c) we
show that the effect of inhomogeneity can be significantly mitigated
by using an optimized spatial distribution of Rabi frequencies $\Omega_{d}(\vec{r}_{i})$
(instead of LG mode). This shows that the atomic antenna based on
Rydberg atoms can be realized with state-of-art technology and with
realistic parameters.
\section{Outlook}
In the present work we propose a scheme for implementing high-efficiency quantum links in free-space, using phased atomic arrays as chiral atom-light optical interface. Our setup realizes the paradigmatic model of chiral quantum optics, with distant atoms interacting via emission and absorption of unidirectional photons. This allows for the implementation of modular architectures for quantum information processing in free space, without use of dielectric nanostructures or cavities.
In particular, we show that strong connectivity can be achieved even for moderate antenna sizes, allowing for high-fidelity state transfer between atomic qubits.
Quantum antennas as a free-space quantum light matter interface can be extended to incorporate `built-in' modules for quantum information processing.
Beyond the case of quantum state transfer with single photons discussed here, quantum antennas can be used for instance to generate, emit and absorb photonic states with can error correct for single photon losses~\cite{Michael2016}, and thus increase the free-space link connectivity.
\emph{Note added ---} Since our first submission arXiv:1802.05592v1, the Rydberg coupling between a master atom and an atomic ensemble was also discussed for directional single-photon sources in arXiv:1806.07094v1.
\begin{acknowledgments}
We thank M.~Saffman and F.~Robicheaux for discussions on the Rydberg implementation and valuable feedback on the manuscript, and we acknowledge discussions with R.~Blatt, T.~Monz, M.~Lukin and J.~I.~Cirac. The parameters for the Rydberg simulations were obtained
using the ARC library~\cite{Sibalic2017}. This work was supported
by the Army Research Laboratory Center for Distributed Quantum Information
via the project SciNet, the ERC Synergy Grant UQUAM and the SFB FoQuS
(FWF Project No. F4016-N23).
\end{acknowledgments}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,738 |
\section{INTRODUCTION}
In magnetic resonance imaging (MRI), the k-space data are samples from the continuous Fourier transform of the underlying image. Physical and physiological limits (e.g., gradient slew rate and nerve stimulation) impede MRI acquisition efficiency, leading to long acquisition times, especially for applications that require a large corpus of k-space data such as volumetric, dynamic, or high-resolution imaging. The long acquisition time can compromise patient comfort, reduce throughput, and increase motion artifacts. Therefore, image reconstruction using less data but without losing image quality has been an active research area for three decades.
Image recovery from partially sampled k-space is typically facilitated by parallel MRI (pMRI), which is available on almost all clinical scanners. In pMRI, each of several receive coils provides k-space samples of the image modulated by a corresponding spatial sensitivity map. Sensitivity Encoding (SENSE) \cite{pruessmann1999sense} and GeneRalized Autocalibrating Partial Parallel Acquisition (GRAPPA) \cite{griswold2002generalized} are the most commonly used pMRI reconstruction methods. SENSE uses the coil sensitivity maps to solve for the image via linear least-squares; however, SENSE reconstruction assumes sensitivity maps are known, which typically requires the acquisition of a separate scan or a fully sampled auto-calibration signal (ACS) region.
By leveraging the linear dependence of one k-space sample on its neighboring samples from all coils, GRAPPA
employs interpolation kernels learned from the ACS region to fill the missing k-space.
Iterative Self-consistent Parallel Imaging Reconstruction from Arbitrary K-space (SPIRiT) \cite{lustig2010spirit}, a generalization of GRAPPA, reorganizes interpolators into annihilating kernels.
Parallel Reconstruction Using Null Operations (PRUNO) \cite{zhang2011parallel} generalizes GRAPPA to use a nullspace spanned by multiple annihilating kernels extracted from the ACS region.
To enable higher acceleration rates and increase flexibility in sampling pattern design, image-based \cite{ying2007joint,trzasko2011calibrationless,holme2019enlive} and k-space-based \cite{shin2014calibrationless,haldar2016p} calibrationless MRI (Cl-MRI) methods have been proposed and validated in research settings. Most k-space-based methods treat the recovery as a structured low-rank matrix completion problem with respect to a convolutional matrix constructed from the original k-space or weighted k-space samples. The rank deficiency results from the shift-invariant linear dependence of one k-space sample on its neighboring samples from all coils. This linear dependence originates from several sources, including multi-coil data structure \cite{griswold2002generalized,shin2014calibrationless,ying2010parallel}, limited image support \cite{shin2014calibrationless, haldar2014}, slowly varying image phase \cite{haldar2014,haldar2020linear}, multi-shot imaging \cite{mani2020improved}, piece-wise polynomial image content \cite{liang1989high,ongie2017fast}, and other transform domain sparsity \cite{jin2016general}.
Although k-space-based low-rank matrix completion methods all leverage rank deficiency, each may employ a specific optimization formulation or adopt a different optimization algorithm. For example, Simultaneous Auto-calibrating and K-space Estimation (SAKE) \cite{shin2014calibrationless} minimizes the data mismatch subject to a hard rank constraint on the convolutional matrix using Cadzow's algorithm \cite{Cadzow1988}. Low-rank Modeling of Local K-space Neighborhoods (LORAKS) \cite{haldar2014} minimizes the sum of the squared tail singular values of the convolutional matrix with hard data consistency using the majorize-minimize (MM) algorithm \cite{haldar2014}; soft data consistency and slowly varying image phase are also optional constraints in LORAKS. For k-space based Cl-MRI methods, large memory requirement and enormous computation burden have been identified as challenges. Several algorithms aim to address these issues. For example, Generic Iterative Reweighted Annihilation Filter (GIRAF) \cite{ongie2017fast} extracts spectral information from the Gram matrix built from the convolution operator instead of directly computing a singular value decomposition of a large block-Hankel matrix. Moreover, a ``half-circulant'' padding approximation and fast Fourier transform (FFT) increase the speed of GIRAF. Using a synthetic ACS strategy combined with SENSE, LORAKS has been extended to 3D static imaging \cite{kim2019wave} with reduced memory and computation requirements. Likewise, through the use of slice-by-slice reconstruction in the readout direction, Annihilating Filter-Based Low Rank Hankel Matrix Approach (ALOHA) \cite{jin2016general} has been extended to 2D cine (2D+t) imaging \cite{lee2016acceleration}. Despite these computational advances, the clinical application of k-space based Cl-MRI methods is still limited by a computation complexity that is not competitive with regularized SENSE-based methods. In this work, we present a new numerical procedure, called HIgh-dimensional fast ConvolUtional framework (HICU, pronounced $`\text{h}\overline{\text{\i}} \ \text{k} \overline{\text{oo}}$) that offers these advantages: (i) small memory footprint; (ii) fast computation that is competitive with SENSE-based imaging; (iii) seamless scalability to many MRI applications, regardless of the number of data dimensions arising from space, time, coils, or encodings; (iv) and, better reconstruction quality than SENSE-based compressed sensing (CS) reconstruction
\section{THEORY}
A wealth of parallel imaging methods exploits the linear dependence of one k-space sample on its neighboring samples from all coils. These correlations arise both from the multi-channel interrogation of a single image using spatially smooth coil sensitivity maps \cite{griswold2002generalized,shin2014calibrationless} and from image structure itself \cite{liang1989high,haldar2014,haldar2020linear}. The dependencies yield rank deficiency in a multi-dimensional convolution matrix formed from the data, and hence the existence of annihilating kernels for the multi-dimensional k-space data. Let $\mathbb{X}$ denote the multi-dimensional array of k-space samples, and $\bm{x}$ denote the $N$-by-$1$ vectorization of the complex-valued entries in $\mathbb{X}$. For example, for a 2D+t application, the size of the four dimensional array $\mathbb{X}$ is $[ N_x,\, N_y,\, N_t,\, N_c]$, representing $N_x$ frequency encoding samples, $N_y$ phase encoding samples, $N_t$ time frames, and $N_c$ coils. Let $\mathbb{K}$ be a $\{ 0,1\}$-valued mask indicating the support of an annihilating kernel, with values on the support of $\mathbb{K}$ vectorized into the $n$-by-$1$ list $\bm{v}$. Let $\mathcal{H}_{\mathbb{K}}\{\mathbb{X}\}$ denote the $m$-by-$n$ multi-level Hankel matrix generated from the k-space array $\mathbb{X}$ such that multiplication $\mathcal{H}_{\mathbb{K}}\{\mathbb{X}\} \bm{v}$ is the vectorization of the valid convolution of $\mathbb{X}$ with multi-dimensional kernel described by $\bm{v}$. In contrast to circular and linear convolutions, valid convolution generates only those output points that do not depend on any boundary conditions. Thus, the data array $\mathbb{X}$ is lifted to a much larger, multi-level Hankel matrix, and rank of the matrix becomes a powerful implicit modeling tool \cite{haldar2020linear,JacobMagazine2020}. For accelerated imaging, only a fraction of the elements of $\mathbb{X}$ are observed; let $\mathbb{X}_0$ be the array of observed data zero-filled to match the array size of $\mathbb{X}$.
We pose recovery of the unobserved k-space samples as a structured low-rank matrix completion problem.
Many approaches relax the non-convex rank constraint, $\text{rank} \left\{ \mathcal{H}_{\mathbb{K}} \left( \mathbb{X} \right) \right\} \leq r$, to the nuclear norm minimization, which equals to minimizing the sum of all singular values
\cite{Majumdar2012,Fazel_hankel_2013,ChenChiIT,otazo2015low,mani2017}.
Instead, we choose as a cost function the squared distance
of the completed multi-level Hankel matrix to the set of matrices with rank not exceeding $r$:
\begin{equation}
\label{eq:l2tail}
J( {\bm{x}} ) = \sum_{k > r} \sigma^2_k \left\{ \mathcal{H}_{\mathbb{K}} \left( \mathbb{X} \right) \right\} ,
\end{equation}
where $\sigma_k \{ {\bm{A}} \}$ denotes the $k^{\text{th}}$ largest singular value of a matrix $\bm{A}$.
This cost function was introduced in the LORAKS framework \cite{haldar2014} and is the sum of squares of the tail singular values, $\sigma_k$ for $k>r$,
of the multi-level Hankel matrix formed from the k-space array, $\mathbb{X}$.
This cost may be minimized subject to constraints, $f_i ({\bm{x}}) = 0$, $i=1, ... , c$. An example constraint is data fidelity, $f_1 ( {\bm{x}}) = \| \mathbb{M} \circ \mathbb{X} - \mathbb{X}_0\|_\textsf{F}^2$, where $\mathbb{M}$ is the $\{ 0,1\}$-valued mask indicating observed k-space locations, $\circ$ denotes element-wise multiplication, and $\| \cdot \|_\textsf{F}$ denotes the Frobenius norm.
In general, the constrained minimizer, ${\bm{x}}_{\star}$, yields $J({\bm{x}}_{\star})>0$, and the matrix completion is only approximately rank $r$.
Given annihilating kernel mask $\mathbb{K}$, we adopt for the $m$-by-$n$ multi-level Hankel matrix the shorthand notation ${\bm{H}}({\bm{x}}) = \mathcal{H}_{\mathbb{K}}\left( \mathbb{X} \right) $, and use ${\bm{H}}^{\prime}({\bm{x}})$ to denote the conjugate transpose. The cost, $J( {\bm{x}} )$, in \eqref{eq:l2tail} is readily seen to be equivalent to
$ \min_{ {\bm{Q}}} \sum_{j=r+1}^{n} \| {\bm{H}}({\bm{x}}) {\bm{Q}} \|_\textsf{F}^2$, with ${\bm{Q}}^{\prime} {\bm{Q}} = {\bm{I}}$.
Each of the $n-r$ orthonormal columns of $\bm{Q}$ specifies an approximate
annihilating filter, and $J(\bm{x})$ is the residual energy, after valid convolution, summed across all $n-r$ approximate annihilating kernels. Thus, in HICU the matrix completion task is formulated as the optimization
\begin{equation}
\label{eq:hicu_cost2}
\min_{{\bm{x}}, {\bm{Q}}} \ \|{\bm{H}}({\bm{x}}) {\bm{Q}} \|_\textsf{F}^2 + \sum_{i=1}^{c} \lambda_i f_i({\bm{x}}) , \quad {\bm{Q}}^{\prime} {\bm{Q}} = {\bm{I}},
\end{equation}
with Lagrange multipliers, $\lambda_i$ \cite{haldartechreport}. We adopt the familiar alternating minimization strategy for optimizing
over $\bm{x}$ and $\bm{Q}$: first update the nullspace basis, $\bm{Q}$, then update the unobserved k-space samples, $\bm{x}$. We demonstrate that this cost function pairs quite amicably with four numerical techniques that, taken together, yield both fast computation and low memory requirement. The proposed iteration, dubbed HICU, is given in Algorithm~\ref{alg:h2_new}.
We note that by
choosing an annihilating kernel of size $N_c$ in the coil dimension, valid convolution affects a sum across all coils, while maintaining the conceptual simplicity of a single multi-dimensional convolution.
Consider now the four numerical techniques we adopt in Algorithm~\ref{alg:h2_new}. First, we use randomization
to efficiently compute a nullspace basis.
To this end, we use the randomized singular value decomposition (rSVD) \cite{Tropp2011}
to compute the $n$-by-$r$ matrix, ${\bm{V}}^{(i)}$, corresponding to the principal $r$ right singular values
of ${\bm{H}} ( {\bm{x}}^{(i-1)} )$; the update to ${\bm{Q}}^{(i)}$ is then completed from ${\bm{V}}^{(i)}$ using $r$ Householder reflections. So, ${\bm{Q}}^{(i)}$ minimizes [\ref{eq:hicu_cost2}] subject to ${\bm{Q}}^{\prime} {\bm{Q}} = {\bm{I}}$ for fixed ${\bm{x}}^{(i-1)}$.
The rSVD can compute the $r$ principal right singular vectors, ${\bm{V}}^{(i)}$, to high precision using only $\frac{3}{2}r$ applications of the multi-dimensional valid convolution, ${\bm{H}} ( {\bm{x}}^{(i-1)} )$, and its conjugate transpose,
${\bm{H}}^{\prime} ( {\bm{x}}^{(i-1)} )$, which is itself a valid convolution operation. Thus, rSVD avoids explicit construction of both the large multi-level Hankel matrix and its Gram matrix, sidestepping the associated memory requirement and computation time. Compared to other truncated SVD techniques, such as Lanczos bidiagonalization algorithm \cite{larsen1998lanczos} found in PROPACK \cite{larsen2004propack}, rSVD is more stable and inherently amenable to parallel computing \cite{Tropp2011}. Recent studies have shown that rSVD methods can be significantly faster compared to the truncated SVD implementation in PROPACK \cite{feng2018faster}.
Next, we make a number, $G^{(i)}$, of gradient descent steps on $\bm{x}$ for fixed ${\bm{Q}}^{(i)}$. A gradient descent step updates the unobserved k-space points to reduce the energy in the set of annihilator outputs, as constrained by the costs $\lambda_i f_i({\bm{x}})$. The number of steps can be chosen to balance computational cost between the rSVD to update $\bm{Q}^{(i)}$ and the total collection of $G^{(i)}$ gradient descent steps to update ${\bm{x}}^{(i)}$. Only a few gradient steps are required, and computation does not benefit from full convergence for a fixed nullspace estimate, ${\bm{Q}}^{(i)}$.
Exact computation of the gradient of $\| {\bm{H}} ({\bm{x}}^{(i-1)}) {\bm{Q}}^{(i)} \|_\textsf{F}^2$ for fixed ${\bm{Q}}^{(i)}$ requires a sum over all annihilating kernels of the composition of two convolutions. So, at each gradient step we adopt a second numerical technique for speed while preserving the correct mean gradient direction: motivated by the random mixing of dimension reduction in the Johnson-Lindenstrauss (JL) Lemma \cite{JL1984,BaraniukJL}, we reduce ${\bm{Q}}^{(i)}$ to $p$ columns. Specifically, before computing a gradient direction, we use an $n$-by-$p$ matrix, ${\bm{P}}^{(i,j)}$, of i.i.d.\ zero-mean Gaussian entries with variance $1/p$ to project ${\bm{Q}}^{(i)}$ to a smaller $p$-dimensional nullspace, $\widetilde{\bm{Q}}^{(i,j)}={\bm{Q}}^{(i)} {\bm{P}}^{(i,j)}$.
Compared to randomly sampling $p$ columns from ${\bm{Q}}^{(i)}$,
the JL compression
provides implicit preconditioning.
Third, exact line search (ELS) can be efficiently implemented for $J({\bm{x}})$ paired with many choices of $f_i$, providing the minimum of the cost function in [\ref{eq:hicu_cost2}] in the direction of the negative of the gradient and obviating any need for a step-size heuristic or iterative line search. The step size at Step 9 of Algorithm~\ref{alg:h2_new} is found via one convolution with each of the $p$ small annihilating kernels in $\widetilde{{\bm{Q}}}^{(i,j)}$.
Fourth, the region of k-space, $\mathbb{S}^{(i)}$, on which the valid convolution
is computed in Steps 2 and 8 does not affect the $n$-by-$r$ matrix of principal right singular vectors in the idealized noiseless case. Therefore, invoking shift invariance across the spatial frequency dimensions in k-space, the region may be restricted to small subsets of the full k-space. In this manner, a high signal-to-noise ratio (SNR), under-sampled, small region at the center of k-space may be used to rapidly determine an approximate solution
for ${\bm{Q}}^{(i)}$. Subsequent iterations can use more or all of the k-space to both refine ${\bm{Q}}^{(i)}$ and estimate the full k-space data array, $\mathbb{X}$.
We refer to this strategy as center-out (CO). A similar use of the center of k-space is found,
for example, in SAKE \cite[p.~968]{shin2014calibrationless} and Wave-LORAKS \cite{kim2019wave} where an auto-calibration region is synthesized as a pre-processing step to a SENSE reconstruction. In Algorithm~\ref{alg:h2_new}, the abbreviated notation ${\bm{H}}^{(i)}\left( {\bm{x}}^{(i-1)} \right)$ is used to denote this potentially much smaller multi-level Hankel matrix constructed using a portion, $\mathbb{S}^{(i)}$, of the full k-space at iteration $i$.
Let $s=|\mathbb{S}^{(i)}|$ be the number of output points from the valid convolution region at iteration $i$. Recall $n=| \mathbb{K}|$ is the number of convolution kernel samples, and $r$ is the rank; note $r < n < s$. The complexity of gradient computation with ELS is roughly $3nps$, and the rSVD complexity is roughly $3nrs$. Note that $r$ generally grows with number of dimensions in the data array, $\mathbb{X}$. Thus, for high dimensional problems, the ratio $r/p$ grows large, leaving the rSVD much more costly than a single gradient descent step. The memory requirement is approximately $N$, the size of k-space array $\mathbb{X}$, plus $1.5rs$.
The combination of the optimization objective \eqref{eq:hicu_cost2} and four numerical techniques adopted here---CO, rSVD, JL, ELS---
provides significant savings in computation time for memory-efficient completion of a multi-level Hankel matrix with approximate rank deficiency.
The moniker ``HIgh-dimensional fast ConvolUtional framework'' refers to the simple and exclusive reliance in Algorithm~\ref{alg:h2_new} on multi-dimensional convolutions, ${\bm{H}}^{(i)} \left( {\bm{x}}^{(i-1)} \right)$
and ${\bm{H}}^{(i) \prime} \left( {\bm{x}}^{(i-1)} \right)$, at each step of the alternating minimization, and the name points to the attendant scalability of memory and computation to large k-space arrays, $\mathbb{X}$.
Below, we present numerical results for HICU computation for the case of exact data matching; this allows direct comparison with publicly available code for SAKE \cite{shin2014calibrationless,bart-toolbox} and coincides with one specific cost function found in the LORAKS 2.1 suite \cite{haldartechreport}, namely C-based LORAKS with hard data constraint. To achieve data matching in HICU, we simply set, in Step 8 of Algorithm~\ref{alg:h2_new}, the gradient of $J(\bm{x})$ equal to zero at observed k-space locations.
\section{METHODS}
We evaluated HICU using four in vivo studies: 2D static imaging of the brain (Study I), 2D+t imaging of the heart (Study II), 3D imaging of the knee (Study III), and MSDWI of the brain (Study IV).
\subsection{MR acquisition}
In Study I, six T2-weighted pMRI brain datasets, $B1, B2, \cdots, B6$, were taken from the New York University fastMRI database \cite{zbontar2018fastmri}. All datasets were fully sampled and collected in an axial orientation on $3$\,T scanners using a T2-weighted turbo spin-echo sequence. Other imaging parameters included: TE 113~ms, TR 6,000---6,570~ms, TI 100~ms, field-of-view (FOV) 220~mm$ \times$ 227~mm, slice thickness 7.5~mm, matrix size 384$\times$384, number of receive coils 16---20, and flip angle 149---180 degrees. The center slice from each dataset was used. The 2D datasets were retrospectively undersampled using a variable density sampling pattern, $S1$, at rates $R=3$ and $R=5$, as shown in Figure~\ref{Figure_nD_Sampling_Pattern}. The pattern $S1$ had at most two contiguous readouts at $R=3$ and no contiguous readouts at $R=5$.
In Study II, seven fully sampled 2D+t cardiac datasets $C1, C2, \cdots, C7$ were collected from seven healthy volunteers using a balanced steady-state free precession sequence under breath-hold with prospective triggering.
The data were collected at The Ohio State University and Nationwide Children's Hospital, with the ethical approval for recruitment and consent given by an Internal Review Board (2005H0124). Three short-axis oriented and four long-axis oriented fully sampled segmented datasets were collected on $3$\,T scanners (MAGNETOM Prisma, Siemens Healthineers, Erlangen, Germany). Other imaging parameters included: TE 1.48---1.53~ms, TR 2.95---3.05~ms, FOV 380---400~mm $\times$ 285---325~mm, slice thickness 8~mm, matrix size 176---384 $\times$ 132---156, number of frames 16---25, temporal resolution 36.6---38.35~ms, number of receive coils 20---34, and flip angle 33---42 degrees. The 2D+t datasets were retrospectively undersampled at $R=6$ and $R=8$ using a variable density pseudo-random sampling pattern $S2$ shown in Figure~\ref{Figure_nD_Sampling_Pattern}. ALOHA reconstruction requires sampling of the center phase encoding line; therefore, for the ALOHA method only we added an additional line to the sampling pattern for each frame, resulting in slightly lower acceleration rates of $R= 5.77$ and $R=7.61$.
In Study III, five 3\,T 3D knee datasets, $D1, D2, \cdots, D5$ from www.mridata.org were used. The spin-echo imaging parameters included: receiver bandwidth 50~kHz, number of coils $N_c=8$, FOV 160 mm $\times$ 160 mm $\times$ 153.6 mm, matrix size $320 \times 320 \times 256$, repetition time 1,550~ms, echo time $25$~ms, and flip angle~$90$\,degrees. The datasets were retrospectively undersampled along the phase encoding dimensions using 2D random sampling patterns $S3$ and $S4$ shown in Figure~\ref{Figure_nD_Sampling_Pattern}. Pattern $S4$ is 2D random sampling with rate $R=5$, while $S3$ augments $S4$ with a $32 \times 32$ fully sampled center region to yield $R=4.86$.
In Study IV, one ten-slice dataset was provided courtesy of the University of Iowa. The data were acquired from a healthy volunteer on a 3~T GE Discovery MR750W (GE Healthcare, Waukesha) using a four-shot ($N_s=4$) dual spin echo diffusion sequence. Parameters included: partial Fourier $59\%$, TE $84$ ms for $b$-value of $700~\text{s/mm}^2$, FOV $210 \times 210$\,mm, sampling matrix $256 \times 152$, slice thickness $4$\,mm, slice number $10$, $\text{NEX}=2$, $32$ coils, one non-diffusion image, and $60$ diffusion directions. The prospective sampling pattern for four shots is $S5$ with acceleration rate $R=6.74$, as shown in Figure~\ref{Figure_nD_Sampling_Pattern}. Detailed description of the dataset is provided in~\cite{mani2020improved}
\subsection{MR reconstruction and analysis}
In Study I, the datasets were compressed to $N_c=8$ virtual coils before reconstruction \cite{zhang2013coil}. For comparison, we include three reconstruction methods: SAKE using the authors' publicly available Matlab code \cite{SPIRiTV(0.3New):2020},
LORAKS 2.1 using the authors' publicly available Matlab code \cite{haldartechreport};
and, Image Reconstruction by Regularized Nonlinear Inversion (NLINV) \cite{uecker2008image} using compiled C code from the Berkeley Advanced Reconstruction Toolbox (BART) \cite{bart-toolbox}. To allow uniform comparison to SAKE, the C-based version of LORAKS was used, and kernels for HICU and LORAKS were restricted to rectangular support of size $[5,5, N_c]$. The sixth dataset, $B6$ at ($S1, R=5$), was used to tune the rank for SAKE, LORAKS, and HICU manually to maximize reconstruction signal-to-error ratio (SER). SER is defined as $\text{SER} = 20\log ( \|\mathbb{X}\|_\textsf{F} / \| \hat{\mathbb{X}}-\mathbb{X}\|_\textsf{F})$ \cite{erdogmus2004image}. The remaining five datasets were then used for performance evaluation at one hour execution time. Coincidentally, SAKE, LORAKS, and HICU all shared the same best rank, $r=30$. For LORAKS, algorithm choices were set for consistent comparison to SAKE, i.e., hard data consistency and no virtual conjugate coils. Additionally, the multiplicative half-quadratic algorithm using FFT approximation was chosen with LORAKS for execution speed. From computed results, the SER versus time for SAKE, LORAKS, and HICU was averaged over $B1, B2, \cdots, B5$. For NLINV, the input zero-filled k-space was scaled to have the Frobenius norm equal to $100$.
The number of iterations for NLINV was tuned to maximize the SER for ($B6,S1,R=3$) and ($B6,S1,R=5$).
SER for NLINV at each iteration is not available from the compiled code; thus, only the final SER is reported for NLINV. For the first stage of HICU,
the size of the CO region was set at $\frac{1}{4}N_x \times \frac{1}{4}N_y \times N_c$, with $p=N_c=8$ and $G^{(i)} = 5$ gradient steps per update of the nullspace. For the second stage, the full k-space was used with $p = 4N_c=32$ and $G^{(i)} = 10$. From the tuning results, the number of iterations for the first stage was set at $50$ for $R=3$ and $200$ for $R=5$. Coil images were combined via square-root sum of squares (SSoS) \cite{larsson2003snr}.
For all four methods, the mean and standard deviation were computed for four metrics: k-space SER in dB, high frequency error norm (HFEN) \cite{ravishankar2010mr} in dB, structural similarity index (SSIM), which was averaged across all coil magnitude images, and the time, T$_c$, to reach within $0.1$\,dB of the SER achieved at one hour (except for NLINV). For NLINV, T$_c$ corresponds to the computation time to run $14,\,15$ iterations for $R=3,\,5$. To illustrate the effect of $p$ in HICU, the SER curves for ($B1, S1, R=3$) were computed for six values of $p$ ranging from $1$ to $n-r=170$. To illuminate the separate and joint effects of CO and JL strategies in HICU, the SER curves for ($B1, S1, R=5$) were computed for all four combinations of using or omitting the strategies.
In Study II, the data were compressed to $N_c=12$ virtual coils before reconstruction. For comparison, we included four reconstruction methods: ALOHA \cite{lee2016acceleration, ALOHA}; total-variation (TV) penalty using MFISTA \cite{tan2014smoothing}; soft-thresholding of non-decimated wavelet transform (NWT) using balanced FISTA \cite{ting2017fast}; and low-rank plus sparse (L+S) \cite{otazo2015low, L+S2018}. The seventh dataset $C7$ at ($S3, R=8$) was withheld to determine the tuning parameters. For all methods, the initialization was the time-averaged k-space; if a phase encoding point was not sampled across all frames, then zero filling was used. For TV, NWT, and L+S, the number of iterations was $150$, and
the sensitivity maps were estimated from time-averaged k-space using the method by Walsh et al.\ \cite{walsh2000adaptive}. The number of iterations and tolerance for two stages of ALOHA were set to $[500,\, 500]$ and $[10^{-2},\, 10^{-3}]$; the ALOHA kernel size was $[5,\, 5]$. For HICU, the kernel size was $\left[ 5,\,5,\,5,\,N_c\right]$, rank $r=130$, $p = N_c = 12$, and the total number of iterations $I=101$. For the first $100$ HICU iterations, $\mathbb{S}^{(i)}$ was the center $\frac{1}{4}N_x \times \frac{1}{4}N_y \times N_t \times N_c$ and $G^{(i)}=5$; $\mathbb{S}^{(101)}$ was the full k-space and $G^{(101)} = 100$. In HICU computation, the convolution in the time dimension was circular, rather than valid. We consistently observed $0.2$ to $0.3$\,dB SER gain with circular convolution along time, compared to valid convolution. For the three SENSE-based methods, the reconstruction results were converted into coil images via pixel-wise multiplication of the reconstructed image with the sensitivity maps. For all five methods, the mean and standard deviation were computed for four metrics: k-space SER, HFEN, SSIM, and compute time.
In Study III, we compared HICU to two reconstruction methods: SENSE-based reconstruction with regularization of wavelet transform (WT) sparsity using BART \cite{bart-toolbox}; and, NLINV using BART \cite{bart-toolbox}. The fifth dataset $D5$ was withheld to determine the tuning parameters. For HICU and NLINV, the parameters were based on sampling pattern $S5$ and used for both $S4$ and $S5$. For WT, one set of coil sensitivity maps was extracted using ESPIRiT \cite{uecker2014espirit}; parameters were $\lambda=0.01$ and $150$ FISTA iterations. For NLINV, the observed k-space was scaled to have Frobenius norm $25,600$, and the number of iterations was set at $18$. For HICU, the kernel size was $\left[ 5,\,5,\,5,\,N_c\right]$, rank $r=150$, $p = N_c = 8$, and $I=11$. For the first ten iterations, $\mathbb{S}^{(i)}$ was $\frac{1}{4}N_x \times \frac{1}{4}N_y \times \frac{1}{4}N_z \times N_c$ and $G^{(i)}=5$. $\mathbb{S}^{(11)}$ was the full k-space, and $G^{(11)}=20$. For all five methods, the mean and standard deviation were computed for four metrics: k-space SER, HFEN, SSIM, and computing time.
In Study IV, reconstruction for each slice was performed separately after compressing to $N_c = 8$ virtual coils. IRLS MUSSELS with conjugate symmetry \cite{mani2020improved} was used for comparison. For IRLS MUSSELS, the coil sensitivity map was extracted using ESPIRiT \cite{uecker2014espirit} based on the sum of the $4$ shots for the non-diffusion image. The kernel size was $[5,\,5]$; execution employed $10$ outer iterations and $8$ inner iterations, with regularization parameter $\lambda = 0.005$. HICU was applied separately for each $b$ value because the phase modulation due to multi-shot varies with diffusion weighting. To better accommodate the uniform downsampling, the nullspace was augmented $[{\bf Q}\,|\,{\bf Q}_+]$ in Step 3 of Algorithm \ref{alg:h2_new} using information from the non-diffusion ($b0$) measurement. Forty null vectors, ${\bf Q}_0$, were computed using the sum of the four shots at $b0$. Then, ${\bf Q}_+$ is a block diagonal matrix, with four repetitions of ${\bf Q}_0$ along the diagonal.
For HICU, the kernel size was $\left[ 5,\,5,\,N_c,\,N_s\right]$, rank $r=45$, $p = N_c = 8$, and $I=51$. For the first 50 iterations, $\mathbb{S}^{(i)}$ was center $\frac{1}{4}N_x \times \frac{1}{4}N_y \times N_c \times N_s$ and $G^{(i)}=5$;
$\mathbb{S}^{(51)}$ was the partial Fourier sampled region of k-space, with $G^{(51)} = 100$. HICU matrix completion was followed by homodyne partial Fourier reconstruction \cite{noll1991homodyne}.
In absence of fully sampled data, no quantitative metrics were computed.
For all studies, processing was conducted in Matlab 2020a (Mathworks, Natick, MA, US) on an Alienware Aurora Ryzen\texttrademark~desktop, equipped with an AMD Ryzen 3950X CPU and 64\,GB memory. The Matlab code for HICU is provided at \url{https://github.com/OSU-CMR/HICU}.
\section{RESULTS}
For the first three studies, Table \ref{Tab:nD SER SSIM HFEN} reports the mean and standard deviation of quantitative metrics for all datasets, sampling patterns, and accelerations. Figure \ref{Figure_nD_SER} shows the SER for each dataset.
For Study I, the memory requirements for SAKE, LORAKS, NLINV, and HICU were approximately $450$\,MB, $450$\,MB, $130$\,MB, and $18$\,MB, respectively. Figure \ref{Figure_2D_SER_vs_Time} shows the average SER versus runtime for SAKE, LORAKS, and HICU for ($S1,R=3$) and ($S1,R=5$). Time in seconds is plotted logarithmically to illuminate computing time ratios and simultaneously view time on the scale of hours, minutes, and seconds. Figure \ref{Figure_2D_All_Module_Effect} shows SER versus runtime for six choices of $p$ with CO disabled to explore the effect of the JL projection dimension, $p$, for ($B1,S1,R=3$); this figure also shows SER versus runtime for four HICU variants with and without the CO and JL numerical strategies for ($B1,S1,R=5$). Figure \ref{Figure_2D_Images} shows the SSoS reconstruction images for ($B4,S1,R=3$) and ($B1,S1,R=5$), the two datasets that yielded the highest and lowest SER from Figure~\ref{Figure_nD_SER}.
For Study II reported in Table~\ref{Tab:nD SER SSIM HFEN}, HICU yields the highest average SER, SSIM, and HFEN. For display of representative images, we selected the two combinations of dataset, sampling pattern, and acceleration rate that yielded the highest and lowest SER values in Figure~\ref{Figure_nD_SER}.
Videos of all frames and error maps for ($C5, S3, R=6$, $C2, S3, R=8$) are found in the Supporting Information Videos S\ref{video 1} and S\ref{video 2}.
For Study III reported in Table~\ref{Tab:nD SER SSIM HFEN}, HICU yields the highest average SER, SSIM, and HFEN. Figure \ref{Figure_3D_Images} shows the reconstruction results from $D3$ and $D1$, which had the
highest and lowest average k-space SER in Figure~\ref{Figure_nD_SER}. For Study IV, Figure~\ref{Figure_MSDWI_Image} shows the SSoS of all coils and shots for the first six $b$ values. The results from the 6$^\text{th}$ slice are shown. From Table \ref{Tab:nD SER SSIM HFEN}, HICU is over $5$ times faster than SENSE-based IRLS MUSSELS with conjugate symmetry.
\section*{DISCUSSION}
HICU provides a fast and memory-efficient computational procedure for structured low-rank matrix completion. Using 2D brain images, Study I suggests, from Table \ref{Tab:nD SER SSIM HFEN} and Figure~\ref{Figure_2D_SER_vs_Time}, that HICU can provide over an order of magnitude speedup compared to SAKE and LORAKS while providing comparable image quality across all metrics and significantly reduced memory requirement. Likewise, Figure~\ref{Figure_2D_Images} shows qualitatively very similar converged reconstruction results for SAKE, LORAKS, and HICU; the similarity is expected in that all three methods exploit the rank deficiency of the Hankel data matrix. The annihilating kernel support used in Study I was rectangular to conform with SAKE implementation \cite{bart-toolbox}; however, LORAKS and HICU can support circumscribing circular or spherical kernel masks that have been observed to yield SER gains \cite{haldar2014}. NLINV produced much lower image quality in this application than the other methods and required $1.5$ to $4$ times more computation time than HICU.
From Figure~\ref{Figure_2D_SER_vs_Time}, SAKE and HICU exhibit a decline in SER as iterations proceed past the point of maximum SER. This has been previously observed \cite{lustig2010spirit} and may be attributed to the high SER central k-space region used in the CO strategy. High SER of the nullspace can lead to noise amplification in the recovered k-space; this seemingly paradoxical effect has been studied for GRAPPA \cite{DingParadox2015}. The presence of a time dimension in the 2D+t images of Study II ameliorates this behavior.
Figure~\ref{Figure_2D_All_Module_Effect} explores the choice of JL dimension, $p$, for the datasets in Study I. The effects of $p$ on both the computation cost per iteration and the SER benefit per iteration combine to yield very similar performance across the range $0.5 N_c \leq p \leq 2N_c$. Note that even when $p=1$, HICU still manages to reconstruct. This implies that randomness through JL projection can efficiently capture most of the information in the large nullspace. The bottom panel in Figure~\ref{Figure_2D_All_Module_Effect} suggests that the impact of the CO strategy slightly exceeds the impact of JL on computing time, and that the two speedup factors are approximately multiplicative when the two numerical strategies are adopted jointly.
For 2D+t images in Study II, Figures~\ref{Figure_nD_SER} and \ref{Figure_2D_T_Images} show that HICU can provide consistently better SER than SENSE-based methods. The SER gain may be attributed to a low-rank model better capturing the multi-coil structure than do the sensitivity maps extracted from the time-averaged ACS region. The average computing times in Study II of the fastest SENSE-based method, NWT, and HICU are $78.5$\,s and $350.5$\,s. Yet, to achieve only the same average SER of the best SENSE-based method, L+S, HICU can compute in $77.7$\,s using only $I=16$ iterations. ALOHA reconstructions averaged $4.1$\,dB less SER and required over $13$ times longer computation than HICU. The ALOHA reconstruction in Figure~\ref{Figure_2D_T_Images} shows banding artifacts, whereas others do not; this difference may be attributed to the slice by slice processing in ALOHA.
For 3D knee images in Study III, Figures~\ref{Figure_nD_SER} and \ref{Figure_3D_Images} show that HICU can provide, on average, $0.68$\,dB improvement in SER and $23\%$ less computation time than the SENSE-based methods reported.
Thus, in both Study II and the volumetric imaging application in Study III, HICU matrix completion enables calibrationless imaging to exceed SENSE-based CS imaging in both SER and computing speed. In Study IV, HICU is demonstrated for multi-shot diffusion weighted imaging on a large k-space array of $74.7$\,million samples. Figure~\ref{Figure_MSDWI_Image} demonstrates qualitatively similar results to IRLS MUSSELS, with five times shorter computation time.
The optimization task addressed by HICU is found in LORAKS \cite{haldar2014} and is similar to many other calibrationless parallel imaging approaches. Consequently, the numerical techniques (rSVD, JL, CO) employed in HICU could likewise accelerate algorithms used to optimize other variations of cost functions. For example, for the case of ($S1$, $R=3$) in Study I, the use of rSVD (with projection dimension $3r$) reduces average computation time, T$_c$, for SAKE from $239.1 \pm 71.7$\,s to $111.9 \pm 32.7$\,s, without any performance loss. Moreover, various forms of regularization may be used as the functions $f_i(\bm{x})$ found in [\ref{eq:hicu_cost2}] but are not considered in the results presented here. For example, in addition to a soft data consistency function, the $\ell_1$ norm of a linear sparsifying transform of $\mathbb{X}$ results in a simple soft-thresholding after Step 8 of Algorithm \ref{alg:h2_new}. Similarly, a learned plug-in denoiser could be employed \cite{AhmadPNP, zhao2020calibrationless}. In either case, this additional regularizer operates on the premise that multi-coil image structure not captured by the low-rank linear dependence assumption can be exploited via a nonlinear denoising step. For the least-squares subproblem, gradient descent with ELS is observed faster than LSQR and conjugate gradient descent in our sparse and rectangular linear system.
Although they attempt to optimize different cost functions, HICU and GIRAF algorithmically share much in common. Instead of the cost in [\ref{eq:l2tail}], GIRAF seeks to minimize the smoothed Schatten-$q$ quasi-norm,
\begin{equation}
\label{eq:giraf_cost}
J_{\text{G}} ( \bm{x} ) = \sum_{k =1}^{n}
\left( \sigma^2_k \left\{ \mathcal{H}_{\mathbb{K}} \left( \mathbb{X} \right) \right\} + \epsilon \right)^{q/2}.
\end{equation}
In its iterative reweighted least-squares computation \cite{Sullivan1987,Fornasier2011,mohan}, GIRAF uses weighted right singular vectors of $\bm{H}(\bm{x})$ as annihilating kernels; the $k^{\text{th}}$ singular vector is weighted by $w_k = (\sigma_k + \epsilon )^{-(1-q/2)/2}$, $0 \leq q \leq 1$. Seen in this framework, HICU uses weights $w_k=0$ for $k\leq r $ and $w_k=1$ for $r+1 \leq k \leq n$. GIRAF requires computation of the full set of $m$ singular values at each iteration, whereas HICU only requires
the $r$ principal right singular vectors, from which a null space basis is found via Householder reflections. Therefore, HICU can benefit from rSVD versus SVD of the Gram matrix. For Study I, we did not observe appreciable difference in computing time between rSVD and SVD of Gram matrix. However, rSVD was significantly faster than SVD of the Gram matrix for larger applications considered in Studies II, III, and IV. For example, for Study II, when rSVD was replaced with SVD of Gram matrix, the average computation time increased by $52\%$.
The current implementation of HICU has several limitations. HICU requires, like related Cl-MRI algorithms, several tuning parameters, including: rank, kernel support, size of the central region in CO, and the number of iterations or, equivalently, a stopping criterion. An automated selection of these parameters, especially $r$, is a direction for future work.
\section{CONCLUSION}
A variety of physical features contribute to the approximate linear dependence among neighboring k-space samples. This dependence has been leveraged to yield many existing algorithms to recover unobserved k-space samples. We build on this rich literature to present a computational approach, HICU, that is simple, fast, memory efficient, and directly extensible to imaging in higher dimensions. For structured low-rank matrix completion, HICU iteratively estimates unknown annihilating kernels and k-space samples to minimize the tail sum of squared singular values. Computational speed is achieved by random projection, at each iteration, of the annihilating kernel space to a lower-dimensional subspace and employing a small, high-SNR center of k-space to quickly build initial estimates of nullspace vectors. Results from 2D brain imaging show that HICU can offer over an order of magnitude speedup compared to existing algorithms. Results from 2D+t and 3D imaging show that HICU can make calibrationless imaging computationally comparable to SENSE-based CS methods while providing improved reconstruction SER. Results from 2D, 2D+t, 3D, and MSDWI demonstrate that HICU can generalize to various MRI applications.
\section{ACKNOWLEDGMENTS}
This work was funded in part by NIH project R01HL135489. The authors are grateful to Merry Mani and Mathews Jacob for providing the DWI dataset and code used in Study IV and thank Kaiying Xie and Chong Chen for valuable discussions. The authors are also thankful to Martin Uecker and Christian Holme for assistance in optimizing parameters in the NLINV code. In memory of FEMD, 1927-2020.
\clearpage
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,614 |
EDUCATIONAL CENTER OF LTSNU "DONBAS-UKRAINE"
EDUCATIONAL CENTER of LTSNU "DONBAS-UKRAINE": admission to the university WITHOUT CERTIFICATES of the EXTERNAL INDEPENDENT EVALUATION for graduates of 2018 and past years
from the territory of the antiterrorist operation and settlements located on the contact line, which:
do not have a Ukrainian document on education;
did not pass the External Independent Evaluation;
have a Ukrainian document on education;
passed the External Independent Evaluation and have the corresponding certificates of 2017 or 2018.
The educational center "Donbas-Ukraine" was created for graduates of 2018 and the last years, the place of residence of which is the territory of the antiterrorist operation and the settlements located on the contact line, according to the Law on Amendments to Some Laws of Ukraine on Ensuring the Right to Education of Individuals , whose place of residence is the territory of the antiterrorist operation."
Such persons can obtain a document on full general secondary education in a simplified procedure at the educational center "Donbas-Ukraine" at the State Institution "Luhansk Taras Shevchenko National University" and enter the University without certificates of the External Independent Evaluation based on the results of the entrance examinations.
According to the results of the entrance examinations, the right to enter without certificates of the EIE is obtained by persons who have completed the receipt of full general secondary education in the settlements located on the territory of the antiterrorist operation where it is impossible to ensure the implementation of Ukrainian educational standards and / or a stable educational process (list of cities and villages) as well as persons who moved from the ATO zone after January 1, 2018.
The Educational Center will work from June 4 to September 30, 2018. The whole procedure together with passing the entrance examinations to the university for applicants for the chosen specialty (the list of examinations in the specialties) will last 1 – 2 days. Applicants (if necessary with parents) will be provided with free accommodation in the hostel.
Applicants, who already have a document on full general secondary education of the state sample, immediately submit documents to the University Admission Committee and pass the entrance examinations in accordance with the admission rules in the State Institution "Luhansk Taras Shevchenko National University" for the chosen specialty.
The algorithm of actions for applicants who do not have a certificate of secondary education of the state sample:
Seek advice from the Educational Center "Donbas-Ukraine".
Submit your application to the Educational Center "Donbas-Ukraine" in a timely manner.
Fill in the educational declaration.
Pass the annual assessment and the state final certification of the Ukrainian language and history of Ukraine at the Educational Center "Donbas-Ukraine" and get a certificate.
Submit documents to the Admission Committee of the State Institution "Luhansk Taras Shevchenko National University" from 07.2018 to 27.07.2018 (for admission to full-time tuition for state budget funds), until September 28, 2013 (for training for individuals or legal entities).
Pass the entrance examination in the subject (the list of examinations in the specialties), which is defined by the Rules of Admission to LTSNU for the chosen specialty from 07.2018 to 27.07.2018 (for admission to the full-time form of education for state budget funds), until 28.09.2018 (for training for the funds of individuals or legal entities) or provide certificates of External Independent Evaluation in 2017 – 2018.
In the 3-month period, replace the certificate on the passage of the annual assessment and the state final attestation on the document on the total secondary education and its annex; obtain a passport of a citizen of Ukraine, if it is necessary.
The algorithm of actions for applicants with a certificate of secondary education of the state sample, but did not pass the External Independent Evaluation in 2017 – 2018:
Submit documents to the Admission Committee of the State Institution "Luhansk Taras Shevchenko National University" from 07.2018 to 27.07.2018 (for admission to full-time training for state budget funds), until September 28, 2013 (for training for the funds of individuals or legal entities).
Pass the entrance examination in the subjects (the list of examinations in the specialties), which are determined by the Rules of admission to the State Institution "Luhansk Taras Shevchenko National University" for the chosen specialty from 07.2018 to 27.07.2018 (for admission to the full-time training for state budget funds), until 28.09. 2018 (for training for the funds of individuals or legal entities).
Features of the submission of documents to the Educational Center "Donbas-Ukraine":
Documents must be submitted in person.
The fact of living in the territory where the ATO is carried out is confirmed by a stamp in the passport about the place of registration in the village in accordance with the approved list.
A birth certificate can be submitted by persons regardless of their age (a passport of one of the parents must be provided to confirm the fact of residence in the ATO zone).
In the admissions office, you can submit a certificate and an application on the total secondary general education of a state sample or a certificate from the Educational Center about the successful completion of the final certification. The certificate should be replaced with a document on the total secondary education and its annex.
Certificate of passage of the External Independent Evaluation in 2017-2018 in one, two or more subjects can be submitted to the Admission Committee.
The schedule of the Educational Center "Donbas-Ukraine" of the State Institution "Luhansk Taras Shevchenko National University":
from 04.06.2018 to 30.09.2018 – from 08:00 to 17:00, Saturday and Sunday from 09:00 to 15:00.
The address:
Educational Center "Donbas-Ukraine", educational building No. 1
1 Gogol Square, the city of Starobilsk.
E-mail: m19050829@gmail.com
For information, please contact:
0507671066, 0960231434, 0999444268, 0937791554
(mobile phone, Viber, Messenger).
Page in social networks: | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,399 |
Adam Lindgren (born 28 March 1993), known by his handle Armada, is a Swedish professional Super Smash Bros. player from Gothenburg. He is widely considered one of the greatest Super Smash Bros. Melee players of all time and the greatest Melee Peach player of all time. Lindgren has won several major tournaments: he is a three-time champion of GENESIS, two-time champion of EVO, two-time champion of Apex and one-time champion of The Big House. Considered one of the "Five Gods" of Melee, alongside Jason "Mew2King" Zimmerman, Joseph "Mango" Marquez, Juan "Hungrybox" DeBiedma, and Kevin "PPMD" Nanney, Lindgren was ranked one of the top two Melee players in the world every year from the beginning of formal rankings in 2013 until his retirement from singles tournaments in 2018, with Lindgren ranked as the number one Melee player in the world in 2015 and 2016. A 2021 list by PGstats ranked Lindgren as the second-greatest Melee player of all time. Lindgren retired from professional Melee singles tournaments in September 2018, citing declining interest in the game, although he still occasionally enters doubles tournaments teaming with his brother Andreas "Android" Lindgren. He also runs a YouTube channel with over 125,000 subscribers.
He uses Peach and Fox, and formerly used Young Link as a secondary character. Lindgren rose to fame playing Peach exclusively, but he added Fox as a secondary in early 2015 in order to deal with a select few opponents. He is also considered one of the best doubles players in the world and is famous for teaming with both of his brothers Andreas "Android" and Alexander "Aniolas" Lindgren, as well as with Mew2King. Lindgren has also played Super Smash Bros. Ultimate and Project M competitively, primarily playing Inkling in the former and Peach and Pit in the latter. Lindgren has been nicknamed the Swedish Sniper.
Since 2019, Lindgren has shifted his focus entirely away from competition. Since 2020, he has instead focused on speedrunning the game Super Mario 64 and livestreaming on Twitch.
Gaming career
Competitive Smash Bros. career
Lindgren started his gaming career in 2003 competing in the Swedish Nintendo Championship.
Armada came to prominence in 2007 finishing 4th at The Renaissance of Smash 4, his first national tournament. Seven months later, he finished 3rd at Epita Smash Arena 2, the largest tournament in Europe at the time, defeating top ranked Japanese player, Masashi, before losing to Ryota "Captain Jack" Yoshida.
In 2009, Lindgren had firmly established himself as the strongest player in Europe and decided to enter GENESIS, a tournament held in Antioch, California which was attended by the best players in the larger and more prominent American community. Many Americans did not expect Armada to do well, but he shocked the country by reaching the finals of the tournament, upsetting top American players such as Mew2King and Mang0. Armada would eventually lose in Grand Finals to Mang0, but GENESIS established Armada as a legitimate contender for best in the world and was the start of a prolific rivalry between Armada and Mang0.
Each passing year, Lindgren was ranked progressively higher. In July 2011, Armada won the major tournament at the time, GENESIS 2, defeating number one ranked player, Mang0. Lindgren remained undefeated worldwide for two years until EVO 2013 where he lost the title and 1st rank back to Mang0.
After Apex 2013, Armada announced his retirement from competitive Melee although he did return to compete in EVO 2013, where he placed 4th, losing to PPMD 0–2 in winners' bracket and being eliminated by Mang0 0–2 in losers' semis. He returned to the scene a year later, with B.E.A.S.T, a tournament held in his hometown of Gothenburg which he helped to organize, as his first tournament back.
Lindgren also had a fairly short-lived, but very successful career in Project M, winning Apex 2014's Project M title by defeating Mew2King in grand finals. On 6 November 2014 he left Empire Arcadia and became sponsored by professional gaming team Alliance.
Lindgren initially showed some interest in Super Smash Bros. for Wii U stating that he found it considerably different from Melee and felt that he needed to spend more time playing it, but has not publicly practiced or competed in the game since a short time after its release. Since 2015, Armada has switched from using only Peach to both Peach and Fox in tournaments. He cites Fox's ability to put mental pressure on opponents as a reason for this change. Armada faced PPMD in the Grand Finals of Apex 2015, while coming from the losers bracket, but eventually lost after forcing a bracket reset. Armada was the EVO 2015 Melee champion after defeating Hungrybox in the Finals. By winning EVO, Lindgren received the largest single prize ever awarded in a Melee tournament at that time.
After winning EVO 2015, Melee It On Me (MIOM) ranked Armada as the best Melee player for the 2015 Summer SSBMRank, ahead of Leffen and Mang0.
At The Big House 5 in Dearborn, Michigan, Armada and his Europe crew lost to SoCal, placing 2nd. In doubles, Armada won with his brother Android, beating Mew2King and Hungrybox in Grand Finals. In Singles, he beat Hungrybox 3–2 in Grand Finals to win the tournament.
Armada was ranked the number one player in the world on the Melee it On Me (MIOM) year end SSBMRank for 2015.
Armada continued his tournament success in 2016 and 2017, winning events such as GENESIS 3, Dreamhack Winter 2016, GENESIS 4, and EVO 2017 as well as a multitude of doubles events with his teammate and brother Android. In addition, Armada won the first four iterations of the highly prestigious invitational tournament series Smash Summit. In doing so, Armada became the first Melee player to win the same major tournament series three and four times consecutively.
Armada's lowest placing in his entire Melee career, excluding tournaments which he forfeit or did not seriously compete, is 5th place at both Paragon Orlando 2015 and Get On My Level 2016.
Armada retired from competing in Melee singles on 18 September 2018.
Speedrunning career
Armada began speedrunning the 70 star category of Super Mario 64 in 2020 and currently places 20th in the world.
Personal life
Lindgren has 10 siblings, two of whom, Alexander "Aniolas" and Andreas "Android", also play Melee competitively. Lindgren formerly worked as a substitute teacher in Gothenburg, but now dedicates his time fully to competing, producing YouTube videos, and streaming on Twitch.
Armada is one of the subjects of the sequel of the documentary The Smash Brothers by producer Travis "Samox" Beauchamp, and its sequel entitled Metagame, which was released on 11 December 2020. The project raised over 30,000 on Kickstarter.
Notable tournament placings
Only Majors and Supermajors are listed.
Super Smash Bros. Melee
Project M
Super Smash Bros. for Wii U
References
External links
1993 births
Living people
Swedish esports players
Super Smash Bros. Melee players
Twitch (service) streamers
Video game speedrunners
People from Gothenburg
Alliance (esports) players
Empire Arcadia players
Team Razer players
Project M players | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,566 |
Q: Report performance optimization How can I get only once signature picture from UserSetup in DataSet?
DataItem Integer in the end doesn't work when I print two or more documents with different signatures.
A: The usual tactics is to clear BLOB with a picture after the first row has been generated, e.g. in AfterGetRecord of document lines.
An example with more details can be found here:
http://www.softwareanswers.co.uk/software_answers/2015/01/outofmemoryexception-when-running-dynamics-nav-reports.html
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,104 |
Fouad may refer to:
People with the single name
Fuad I of Egypt (1868-1936), also spelled Fouad, sultan and later king of Egypt
Fuad II of Egypt (born 1952), deposed infant king of Egypt
Fictional characters
Fouad (Family Guy), character in American animated comedy series
People with the surname
Amina Fouad (born 1980), Egyptian volleyball player
Ceet Fouad (born 1971), Algerian muralist
Hala Fouad (1958-1992), Egyptian film and TV actress
Mohamed Fouad (born 1961), Egyptian singer and actor
Muharram Fouad (1934-2002), Egyptian singer and film star
Nagwa Fouad (born 1943), Egyptian-Palestinian belly-dancer
Yasmine Fouad, Egyptian politician
Tamino-Amir Moharam Fouad (born 1996), Belgian-Egyptian singer and model, grandson of Egyptian singer Muharram Fouad
People with the given name
Fouad (given name), includes list of holders of the name Fouad or Fuad
Other uses
See also
Includes people with the given name | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,246 |
Герб комуни Вестерос () — символ шведської адміністративно-територіальної одиниці місцевого самоврядування комуни Вестерос.
Історія
Від XІV століття місто Вестерос використовувало герб. Він був зафіксований на міській печатці 1307 року. На гербі Вестероської єпископії було зображення Богородиці.
Герб міста Вестерос отримав королівське затвердження 1939 року.
Після адміністративно-територіальної реформи, проведеної в Швеції на початку 1970-х років, муніципальні герби стали використовуватися лишень комунами. Цей герб був 1971 року перебраний для нової комуни Вестерос.
Герб комуни офіційно зареєстровано 1974 року.
Опис (блазон)
У срібному полі синій сигль «М» з дашком (марійська монограма), під ним — червона троянда.
Зміст
Синій сигль М з дашком є монограмою Діви Марії. Ця монограма є злиттям літер «A» та «M» — «Ave Maria». Вестероський собор був присвячений Богородиці з ХІІІ століття. Вважається, що стилізована квітка являє собою троянду, ймовірно, це стосується Христа та його чеснот.
Див. також
Вестерос (комуна)
Джерела
Heraldiskt register
Nevéus C. Ny svensk vapenbok. — Stockholm: Streiffert, 1992. — S. 161—162.
Герби комун лену Вестманланд | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,150 |
\section{Introduction}
Let $(X,d)$ be a metric space.
By euclidean space we mean $\mathbb{R}^k$ equipped with the standard euclidean metric.
Given $\lambda > 0$ a map $f: X \rightarrow \mathbb{R}^k$ gives a $\lambda$-bilipschitz embedding of $(X,d)$ into euclidean space if:
$$ \frac{1}{\lambda} d(x,x') \leq \| f(x) - f(x') \| \leq \lambda d(x,x') \quad \text{for all } x,x' \in X. $$
The map $f$ is a bilipschitz embedding if it is a $\lambda$-bilipschitz embedding for some $\lambda > 0$.
Bilipschitz embeddings are injective, so the term ``embedding'' is justified.
The map $f$ is an isometric embedding if it is a $1$-bilipschitz embedding.
Given $0 < r < 1$, the $r$-snowflake of $(X,d)$ is the metric space $(X,d^r)$.
We say that $(X,d^r)$ is a snowflake of $(X,d)$.
Let $K > 0$, we say that $(X,d)$ is $K$-doubling if every open ball of radius $t$ contains at most $K$ pairwise disjoint open balls of radius $\frac{1}{2}t$.
The metric space $(X,d)$ is said to be doubling if it is $K$-doubling for some $K > 0$.
It is easy to see that the following facts hold:
\begin{itemize}
\item Euclidean space is doubling.
\item Any metric space which admits a bilipschitz embedding into euclidean space is doubling.
\item A snowflake of a doubling metric space is doubling.
\end{itemize}
The following marvelous theorem, due to Assouad, gives a kind of converse to the simple facts listed above:
\begin{Thm}[Assouad]
Suppose that $(X,d)$ is doubling and $0 < r < 1$.
Then the $r$-snowflake of $(X,d)$ admits a bilipschitz embedding into some euclidean space.
\end{Thm}
It is natural to wonder when snowflakes admit isometric embeddings into euclidean space.
In this paper we show that this is generally not the case:
\begin{Thm}\label{Thm:it}
Suppose that $(X,d)$ has positive Hausdorff dimension and $0 < r < 1$.
Then the $r$-snowflake of $(X,d)$ does not admit an isometric embedding into euclidean space.
\end{Thm}
We thank Enrico le Donne for useful correspondence on this topic and Samantha Xu for providing an excellent working environment.
\section{Preliminaries}
Our proof depends on some basic geometric facts which we gather in this section.
We begin with an elementary lemma:
\begin{Lem}\label{Lem:general}
Let $x_1,\ldots, x_{l+1} \in \mathbb{R}^{l}$ be in general position.
Then the map $\sigma: \mathbb{R}^{l} \rightarrow \mathbb{R}^{l + 1}$ given by
$$ \sigma(y) = ( \| y - x_1 \|, \ldots, \|y - x_{l+1}\|) $$
is injective.
\end{Lem}
\begin{proof}
We suppose otherwise towards a contradiction.
Suppose that $y,y' \in \mathbb{R}^{l}$ are such that $y \neq y'$ and $\sigma(y) = \sigma(y')$.
Let $H$ be the set of $x \in \mathbb{R}^{l}$ such that $\| x - y \| = \| x - y' \|$.
So $x_1,\ldots,x_{l+1} \in H$.
However, as $H$ is a hyperplane of codimension one, this implies that $x_1,\ldots, x_{l+1}$ are not in general position.
\end{proof}
We let $D \subseteq \mathbb{R}^{l+1}$ be the image of $\sigma$ and let $\tau: D \rightarrow \mathbb{R}^{l}$ be the compositional inverse of $\sigma$.
That is, if $\bar{t} = (t_1,\ldots,t_{l+1}) \in D$ then $\tau(\bar t)$ is the unique $y \in \mathbb{R}^{l}$ such that:
$$ \| y - x_i \| = t_i \quad \text{for all } 1 \leq i \leq l+1. $$
We make use of the following:
\begin{Lem}\label{Lem:decomp}
There are smooth submanifolds $D_1,\ldots,D_m \subseteq \mathbb{R}^{l+1}$ such that $D = D_1 \cup \ldots \cup D_m$ and the restriction of $\tau$ to each $D_i$ is smooth.
\end{Lem}
\begin{proof}
It is presumably easy to prove Lemma~\ref{Lem:decomp} in an elementary way.
However, the present author is a logician.
Therefore, we give a very general proof using semialgebraic geometry.
A set $A \subseteq \mathbb{R}^k$ is semialgebraic if it is a finite union of sets of the form
$$ \{ \bar x \in \mathbb{R}^k : p(\bar x) \geq 0\} \quad \text{ for polynomial $p$.} $$
A function $f: A \rightarrow B$ between semialgebraic subsets $A,B \subseteq \mathbb{R}^k$ is semialgebraic if its graph is a semialgebraic subset of $\mathbb{R}^k \times \mathbb{R}^k$.
We refer to \cite{bcr} for information about semialgebraic geometry.
It is well known that every semialgebraic subset of euclidean space is a finite union of smooth submanifolds of euclidean space and if $A \subseteq \mathbb{R}^k$ and $f: A \rightarrow \mathbb{R}^n$ are semialgebraic then $A$ can be written as a finite union of smooth submanifolds of $\mathbb{R}^k$ in such a way that the restriction of $f$ to every submanifold is smooth.
It is an immediate consequence of Tarski-Seidenberg quantifier elimination that $D \subseteq \mathbb{R}^{l+1}$ and $\tau: D \rightarrow \mathbb{R}^l$ are both semialgebraic.
Lemma~\ref{Lem:decomp} follows.
\end{proof}
\begin{Lem}\label{Lem:raise}
Let $A \subseteq D$.
The Hausdorff dimension of $\tau(A)$ is no greater then the Hausdorff dimension of $A$.
\end{Lem}
Lemma~\ref{Lem:raise} is a straightforward consequence of Lemma~\ref{Lem:decomp} and a few standard facts about Hausdorff dimension which can be found in \cite{mattila} or other places.
We let $\dim$ be the Hausdorff dimension.
\begin{proof}
Let $D_1,\ldots, D_m$ be as in the statement of Lemma~\ref{Lem:decomp}.
Then:
$$ \dim(A) = \max\{ \operatorname{dim} (D_i \cap A) : 1 \leq i \leq m \}$$
and
$$ \operatorname{dim}( \tau(A)) = \max\{ \operatorname{dim}(\tau(D_i \cap A)) : 1 \leq i \leq m \}. $$
Smooth maps do not raise Hausdorff dimension, therefore:
$$ \operatorname{dim}(\tau(D_i \cap A)) \leq \operatorname{dim}(D_i \cap A) \quad \text{for all } 1 \leq i \leq m. $$
\end{proof}
\section{Proof}
In this section we prove Theorem~\ref{Thm:it}.
We let $(X,d)$ be a metric space with positive Hausdorff dimension and $0 < r< 1$.
Let $D$ and $\tau$ be as in the previous section and let $\operatorname{dim}$ be the Hausdorff dimension.
We suppose toward a contradiction that $\iota: X \rightarrow \mathbb{R}^l$ gives an isometric embedding of $(X,d^r)$ into euclidean space.
We may suppose that $\iota(X)$ contains $l+1$ points $y_1,\ldots, y_{l + 1}$ in general position.
If this is not the case then $\iota(X)$ is contained in a hyperplane with positive codimension, and we replace $\iota$ with an isometric embedding into a euclidean space with smaller dimension.
We let $x_1,\ldots, x_{l+1} \in X$ be such that
$$ \iota(x_i) = y_i \quad \text{for all } 1 \leq i \leq l+1. $$
It follows from Lemma~\ref{Lem:general}
that for all $x \in X$, $\iota(x)$ is the unique $y \in \mathbb{R}^l$ such that
$$ \| y_i - y \| = d(x_i, x)^r \quad \text{for all } 1 \leq i \leq l+1. $$
Let $X' = X \setminus \{x_1,\ldots, x_{l+1}\}$.
Let $U$ be the open subset of $\mathbb{R}^{l+1}$ consisting of elements with positive coordinates.
Let $f: X' \rightarrow U$ be given by
$$ f(x) = ( d(x_1,x),\ldots, d(x_{l+1},x))$$
and $g: U \rightarrow U$ be given by
$$ g(t_1,\ldots, t_{l+1}) = (t_1^r, \ldots, t_{l+1}^r) $$
Note that $g \circ f$ maps $X'$ into $D$.
The restriction of $\iota$ to $X'$ can be factored as the composition
$$ X' \stackrel{f}{\longrightarrow} U \stackrel{g}{\longrightarrow} U \stackrel{\tau}{\longrightarrow} \mathbb{R}^l. $$
As $f$ gives a lipschitz map $(X',d) \rightarrow U$ we have $\operatorname{dim} f(X') \leq \operatorname{dim}(X',d)$.
As $g$ is smooth it does not raise Hausdorff dimension so $\operatorname{dim} (g \circ f)(X') \leq \operatorname{dim}(X',d)$ as well.
It follows from Lemma~\ref{Lem:raise} that $\operatorname{dim} (\tau \circ g \circ f)(X') \leq \operatorname{dim}(X',d)$.
Therefore $\operatorname{dim} \iota(X') \leq \operatorname{dim}(X',d)$.
As $X \setminus X'$ is finite we have $ \operatorname{dim} \iota(X) \leq \operatorname{dim}(X,d)$.
As $\iota(X)$ is isometric to $(X,d^r)$ this implies that $\operatorname{dim}(X,d^r) \leq \operatorname{dim}(X,d)$.
However, it follows immediately from the definition of Hausdorff dimension that $\operatorname{dim}(X,d^r) = \frac{1}{r}\operatorname{dim}(X,d)$.
This yields a contradiction as $\frac{1}{r} > 1$ and $\operatorname{dim}(X,d) > 0$.
\bibliographystyle{alpha}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,415 |
{"url":"https:\/\/socratic.org\/questions\/how-do-you-differentiate-y-arctan-x-sqrt-1-x-2#279526","text":"# How do you differentiate y= arctan(x - sqrt(1+x^2))?\n\nJun 20, 2016\n\nd\/dx tan^-1(x-sqrt(1+x^2)) = (1-(x\/sqrt(1+x^2)))\/(1+(x-sqrt(1+x^2))^2\n\n#### Explanation:\n\n$\\frac{d}{\\mathrm{dx}} {\\tan}^{-} 1 \\left(x\\right) = \\frac{1}{1 + {x}^{2}}$\n\nNow, treat $x - \\sqrt{1 + {x}^{2}}$ as $x$ in the above definition.\n\nThat would give us,\nd\/dx tan^-1(x-sqrt(1+x^2)) = 1\/(1+(x-sqrt(1+x^2))^2\n\nDon't forget the chain rule though!\n\nThe derivative of $x - \\sqrt{1 + {x}^{2}}$ is $1 - \\left(\\frac{x}{\\sqrt{1 + {x}^{2}}}\\right)$\n\nMultiplying the derivative would give us,\n\nd\/dx tan^-1(x-sqrt(1+x^2)) = (1-(x\/sqrt(1+x^2)))\/(1+(x-sqrt(1+x^2))^2","date":"2022-01-28 00:14:13","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 8, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6925617456436157, \"perplexity\": 11567.89062693258}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-05\/segments\/1642320305317.17\/warc\/CC-MAIN-20220127223432-20220128013432-00560.warc.gz\"}"} | null | null |
{"url":"http:\/\/lilibiju.com.br\/novidades\/flexible-correct-in-addition-to-trustworthy-measurement-technology-38404\/","text":"# Flexible, Correct in addition to Trustworthy Measurement Technology\n\n\u2022 GPS situation and velocity sizing\u2019s revise the task as well as swiftness estimates ( $$\\vec^$$ in addition to $$\\vec^$$ )\n\u2022 Magnetometers and\/or Navigation heading data format this perp-frame having legitimate or permanent magnet north ( $$) \u2022 The Nation\u2019s Aeronautics as well as Room web page gives a finish information involving scalar\u2019s and also vectors, together with examples and in what way one can use them. \u2022 The Country\u2019s Aeronautics plus Place web page gives a finish explanation regarding scalar\u2019s and also vectors, as well as examples and in what way they are utilized. \u2022 GPS situation in addition to speed dimensions update the career plus speed estimates ( \\(\\vec^$$ and $$\\vec^$$ )\n\u2022 Speed as well as temps : A pair of more commonly used scalar quantities inside physical measurements will be quickness and also heat. Provided they are usually not of a typical online mobility, they continue to be scalar volumes. As an illustration, this way of measuring connected with speed in mls or maybe kilometers-per-hour or measurement on the temp on the method each continue to be scalar levels once they may not be belonging to the path on the medium\u2019s travel.\n\u2022 Velocity ( space ) The particular measurement in the amount of which a product variations posture is a vector amount. For example:\n\u2022 the xy-plane aspect and\n\nAlong with FlexRay coach relationship, the program offers gain access to and to Could FD bus techniques. Vector sustains people inside the progress, examination and also optimisation with digital vehicle networks plus ECUs with some other hardware pieces. Regardless of methods fast an object goes, your track in the movements needs to be defined in the pace vector which include \u201crightwards\u201d or \u201cforward.\u201d This program features a rapid USB2.Zero interface which is manipulated by the high-performance 32-bit processor chip. Adjustment from the magnets arena statistic intended for hard\/soft-iron agitations can be executed using the pursuing picture: To get RMS EVM, greatest EVM, plus X-percentile EVM, the output estimations reveal the particular normalization process.\n\n#### Which rating is actually a vector volume?\n\nAlso at large quantities of info, numerous gadgets can be utilized concurrently with brief response times, that is especially effective for your study associated with band position-dependent processes plus high-load testing. A new pace associated with -20 a long way for every Just one http:\/\/kissmyessay.org\/research-paper-help minute indicates getting off the original source time a two-dimensional way of measuring for a price involving Twenty mile after mile per Just one next. Inside true-north NED-frame that isn\u2019t the way it is; a magnetic declination direction corrects due to this. The EVM Description obstruct measures this won\u2019t vector degree (EVM), that is an indicator with modulator as well as demodulator effectiveness. With regard to RMS EVM, highest EVM, in addition to X-percentile EVM, this end result data reveal a normalization system. The re-training of ECUs or even the enactment with analysis programs will be managed by just one electronics gadget. On the 1st product run, simulate and produce signal.\n\n### WELCOME So that you can VECTOR SOLUTIONS\n\nFor that reason, quickness could be the degree involving Acceleration.\n\nThe sheer numbers of elements inside the subsequent measurement is bound with Several. The following force features a route for the center of the The planet in addition to a benefit, which will we all get in touch with excess weight, assessed in some units, such as kilograms. Panel Yards, Electric powered Transducer, MFT Panel Meters, Electrical power Keeping track of Software program. Vector Answers created itself that year The year 2013 as being a Relationship business in the business.You can expect a unique product selection along with excess top quality. The VN8900 system slot is often a modular intended screen equipment with some other feasible direct blends to get Can certainly FD, LIN, FlexRay, J1708 along with K-Line.\n\nTypes of I\/O programs are the ECU\u2019s outcome intended for preventing any headlamp or knowledge allowing you to connect a new lighting sensor \/ probe. Scalar in addition to vector quantities are a couple of of them types of description equipment. This will make it the right application for evaluating your fault dealing with associated with nodes. Static jiggle plus toss prices are usually based on noting that gravitational forces is actually regular within the N-Frame (perp-Frame):\n\n#### WELCOME So that you can VECTOR SOLUTIONS\n\nEtherCAT is surely an proven process intended for quick and synchronous dimension from analyze counter computing equipment. To become more details pertaining to all of our equipment including Cables and also Adaptors, Vector PCMCIA, CardBus plus ExpressCard Devices or Extras intended for GL Loggers and also CANlog, please click on the website link that follows. Measurement apps that need increased bandwidths need a quickly communication flow together with facts throughputs that are beyond your Could bus can offer. Normalizes EVM rating by the optimum constellation energy. Difficult and also soft-iron results are usually close to it and can be included; outer subject disorder are not corrected. To test ECUs diligently, it\u2019s not only important to be connected your communication systems on the examination system, it is additionally important to link a I\/O connects. The particular setting application as a result stipulates as a result of which could mail messages and ways in which some of the rating valuations will be sent on the Might shuttle bus.\n\nTop lens Push fitted (Avoids unfastened fitting) and many others., Roll plus toss prices will be computed from the accelerometer indicate. Heading measurements are driven through the next: To evaluate any scalar is to identify just the value, normally, as a selection. Vector Controllers tend to be ECUs to use broadly intended for automobile conversation.\n\n### How vector is scalar?\n\nBy way of example, pace is often a scalar and, to determine that, we have to designate its cost (ourite.gary the gadget guy. The VN4610 interface is actually a special option intended for IEEE 802.11p which enables it to (FD) dependent applications. The CANextender is usually a automatic input\/output machine for Could systems that can be used where analog and digital sizes must be bought and also transported to your Can easily tour bus via May announcements. Were the cutting edge vendor,individual plus dealer in our product range out of Chennai, Tamil Nadu (China). CANlog Three in addition to CANlog 4 record the info transmission regarding May along with LIN programs. The idea makes simpler the particular installation with analyze benches and HIL exam techniques greatly, since it incorporates virtually all world components had to connect a strong I\/O route a single component.\n\nIn addition to FlexRay coach bus relationship, the particular interface supplies gain access to and also to Might FD shuttle bus techniques. For example, any speed of any motor vehicle on the road is a vector throughout two-dimensional living space, while the pace connected with an air is often a vector within three-dimensional place. For this specific purpose, the CANextender flows with electronic digital in addition to analog alerts plus measures these folks based on some sort of setting system created by you. The highest EVM presents this worst-case EVM value each rush. There\u2019re excellent for immediate continuing development of practical examples and make use of throughout small line shows. The actual go delinquent can be 1 hundred .\n\nNext a couple of coordinates of this endpoint absolutely explain both direction and expense in our vector. The vector is usually a range (way of measuring) certainly where an course is critical. Please note: because of this evaluation the actual magnetometer disposition is definitely missed; thought being negligible or perhaps lumped along with the particular hard-iron. By distinction, vector is a blend of a new way and cost, although scalar can be characterized exclusively simply by worth. Static throw along with toss beliefs are dependant upon observing that gravity is definitely constant within the N-Frame (perp-Frame): The GL loggers tend to be specific car data camera which can be employed throughout test out cars or trucks or maybe upon test out benches.\n\n## High-Voltage Way of measuring Systems\n\nIt really is established coming from sensor \/ probe measurements:. Static roll along with pitch valuations are generally dependant upon observing this gravitational forces is actually consistent while in the N-Frame (perp-Frame): The program kinds your user interface relating to the Eu and a statistic and standardization device including CANape. Enables a great productivity X-percentile EVM description. Scalar volumes, spoken about above, would be the size that firmly consult this value with the medium sized. Within the true-north NED-frame this is simply not the way it is; a permanent magnetic declination point of view corrects in this. XCP-on-Ethernet can be a normal project intended for on-board ECU technological innovation inside automobile arena.\n\nA few communications now decoded from the IMU381\/OpenIMU firmware present true planning by using announcements listed in Dining room table Half-dozen. this individual solution actually starts to weaken since the move plus presentation increase. The prohibit has a couple knowledge indicators: a new acquired indicator along with, optionally, some sort of reference transmission. The hinder will accept double, single, and also fixed-point information styles. Your scalar is actually a amount certainly where an route matters not. Expanding a phrase ends up with the following: While in the true-north NED-frame that isn\u2019t the way it is; any permanent magnet declination position adjusts in this.\n\nThe particular parameter non-payments on the 95th percentile. To test ECUs extensively, it is not just vital to connect this communicating cpa affiliate networks for the test system, it is usually vital to hook up a I\/O interfaces. The particular VN1630 journal delivers added saving usefulness. CANlog 3 or more and CANlog Five history the details conversation involving May along with LIN systems. Below noise circumstances, proportions expressed by a accelerometer is composed only regarding the law of gravity and indicator racket. Your scalar is really a sum wherein a path makes no difference. A vector variety is a measurement that has a way.\n\n\u2022 Time \u2013 Scalar portions typically consult time period; a rating of a long time, many months, 2 or 3 weeks, times, a long time, min\u2019s, mere seconds, and also milliseconds.\n\u2022 GPS Velocity\n\u2022 the xy-plane ingredient and\n\u2022 Magnetometers\n\u2022 The Country wide Aeronautics plus Space web page provides for a complete criteria with scalar\u2019s plus vectors, in conjunction with good examples and in what way they are acustomed.\n\u2022 Magnetometers and\/or Gps system likely information align the actual perp-frame having true or even magnet south ( \\( )\n\nThe CAN\/LIN multi-level connects VN1530 and VN1531 are usually ultimately designed for getting at Could along with LIN sites from the PCIe program. The GL loggers will be particular automotive info recorders which may be employed with exam motor vehicles or with test out benches. This kind of parameter just is accessible in the event you arranged Normalize RMS mistake vector to help High constellation electrical power . Interestingly, we could think about a two-dimensional vector as a pair of scalars, when we introduce a Cartesian technique involving coordinates within our two-dimensional area plus connect any vector using a online segment with the source involving matches to some position. Difficult and also soft-iron results are usually close to it and can be included; outer subject disorder are not corrected. Expanding the appearance brings about the examples below:\n\n Reliable Might testing instruments Datasheet (Pdf file)","date":"2020-09-21 02:01:47","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.28940078616142273, \"perplexity\": 4514.1462097778685}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-40\/segments\/1600400198887.3\/warc\/CC-MAIN-20200921014923-20200921044923-00399.warc.gz\"}"} | null | null |
\section{Introduction}
Transition metal oxides, in many cases, consist of the basic unit of
octahedron where a metal is surrounded by six oxygens.
One of the famous families is the perovskite
such as high-$T_{\rm C}$ cuprates and CMR manganites,
in which octahedra form two-dimensional (2D) or three-dimensional (3D)
network by sharing oxygens at their corner.
Another typical geometry is the edge-sharing network of octahedra.
An old but still intriguing example is the spinel
in which octahedra form 3D edge-sharing network.
A 2D example is found in the sodium cobaltite
which has a triangular lattice of Co cations.
There, a large thermoelectric effect or superconductivity
is recently attracting much interests.
In this paper, we present our recent theoretical efforts
to understand remarkable properties in several edge-sharing materials
with focusing on a keen competition among spin, orbital and lattice degrees of freedom.
In the octahedral coordinate, the fivefold energy levels of $d$ electrons
of transition metals
split into lower threefold $t_{2g}$ levels and higher twofold $e_g$ levels.
Here, we consider the systems in which
electrons in the $t_{2g}$ levels play a central role.
In the $t_{2g}$ electron systems, it is known that
the Jahn-Teller interaction is rather weak compared to the $e_g$ systems.
Therefore, it is expected that the energy scales in
spin, orbital and lattice degrees of freedom become closer to each other and
that a keen competition among them seriously affects
physical properties of the system.
This paper is organized as follows.
In Sec.~\ref{sec:spin-orbital}, we mainly address the interplay
between spin and orbital degrees of freedom.
In Sec.~\ref{sec:V-spinel}, we discuss the mechanism of lifting the degeneracy
due to the geometrical frustration in vanadium spinels.
We remark how the magnetic ordering pattern is changed
depending on the sign of the third-neighbor spin coupling.
In Sec.~\ref{sec:Ti-pyroxene}, we discuss the non spin-Peierls mechanism
of the spin-singlet formation in titanium pyroxenes.
We observe an interesting phase competition
between different spin-orbital orderings.
In Sec.~\ref{sec:Cr-spinel}, we discuss the interplay
between spin and lattice degrees of freedom in chromium spinels
to understand the unusual magnetization process under the external magnetic field.
\section{Interplay between spin and orbital}
\label{sec:spin-orbital}
\subsection{Vanadium spinels}
\label{sec:V-spinel}
Vanadium spinels $A$V$_2$O$_4$ with nonmagnetic $A$ cations
such as Zn, Mg or Cd have 3D edge-sharing network of VO$_6$ octahedra,
and consequently, magnetic V cations form
the geometrically frustrated pyrochlore lattice.
In general, the geometrical frustration results in
(nearly) degenerate ground states and
suppresses a long-range ordering.
Nevertheless, these compounds exhibit two successive transitions
at low temperatures:
One is the structural transition at $T_{\rm c1} \simeq 50$K
from high-temperature cubic phase to low-temperature tetragonal phase, and
the other is the antiferromagnetic (AF) transition at $T_{\rm c2} \simeq 40$K.
\cite{Ueda1997}
The issue is the microscopic mechanism of these two transitions, that is,
how the frustration is reduced and
how the long-range orders are stabilized.
We have studied this problem by taking into account
the orbital degree of freedom of $t_{2g}$ electrons,
because V$^{3+}$ cation has two $d$ electrons in threefold $t_{2g}$ levels.
\cite{Tsunetsugu2003,Motome2004}
The important point is the spatial anisotropy of the $t_{2g}$ orbitals.
In the edge-sharing configuration of VO$_6$ octahedra,
the most relevant contribution in the hopping integrals
is given by the overlap between the same orbitals lying in the same plane,
that is, the so-called $\sigma$ bond.
We derived an effective spin-orbital coupled model
in the strong correlation limit
with considering only the $\sigma$-bond contribution
in the perturbation for the multiorbital Hubbard model.
We found that the effective model shows the strong anisotropy
(three-state Potts type) in the orbital intersite interactions.
This strong anisotropy plays a crucial role
in the keen competition between spin and orbital, and
finally reduces the frustration.
That is, the degeneracy is lifted in the orbital sector first,
with accompanied by the tetragonal lattice distortion.
This explains well the structural transition at $T_{\rm c1}$ in experiments.
\cite{Motome2004}
The mechanism of the magnetic transition at $T_{\rm c2}$ is also interesting.
In the orbital ordered state, $d_{xy}$ orbital is singly occupied
at every V site.
On the other hand,
$d_{yz}$ and $d_{zx}$ orbitals are occupied in the staggered way
in the $z$ direction.
The uniform occupation of $d_{xy}$ orbitals leads to
a large enhancement of the AF spin correlation
along one-dimensional (1D) chains lying in the $xy$ planes.
Thus, the magnetic frustration is partially lifted by the orbital ordering.
However, the relative angles of the staggered moments
between different $xy$ chains
are not yet determined because of the pyrochlore structure.
We proposed that the third-neighbor spin exchange $J_3'$ as well as
thermal and/or quantum fluctuations can lift the remaining degeneracy
and establish the 3D magnetic long-range order.
\cite{Tsunetsugu2003,Motome2004}
The 3D magnetic ordering pattern is hence determined
by the way of stacking the 1D AF $xy$ chains in the $z$ direction,
and strongly depends on the sign of $J_3'$.
When $J_3'$ is AF as in our effective model,
the spin configuration is up-up-down-down-...
(four-times period) along the $yz$ and $zx$ chains
as shown in Fig.~\ref{fig:1} (a).
This pattern is consistent with the neutron scattering results
by Niziol
\cite{Niziol1973}
and Lee {\it et al}.
\cite{Lee2004}
On the other hand, if we suppose the ferromagnetic $J_3'$,
the primitive unit cell (four-site tetrahedra) corresponds to
the magnetic unit cell, and
hence a different spin configuration may be obtained;
up-down-up-down-... in the $yz$ (or $zx$) chains and ferromagnetic in the others
as shown in Fig.~\ref{fig:1} (b).
However, we note that
it is rather difficult to obtain the ferromagnetic $J_3'$
by the perturbation for the multiorbital Hubbard model and
that the latter spin ordering may lead to further lowering of
lattice symmetry through the spin-lattice coupling.
Thus, theoretical predictions depend on
the sign of the small energy scale $J_{3}'$,
but the spin configuration in Fig.~\ref{fig:1} (a) is the most likely
within our theoretical model.
The point to be stressed is that the small coupling $J_3'$
becomes crucial only when the frustration is reduced by the orbital ordering.
\begin{figure}
\centerline{\includegraphics[width=120mm]{fig1.eps}}
\caption{
Magnetic ordering structure predicted in the effective
spin-orbital coupled model for vanadium spinels with
(a) antiferromagnetic $J_3'$ and (b) ferromagnetic $J_3'$.
}
\label{fig:1}
\end{figure}
\subsection{Titanium pyroxenes}
\label{sec:Ti-pyroxene}
Titanium pyroxenes $A$TiSi$_2$O$_6$ ($A$=Na or Li) are
another typical compounds with edge-sharing octahedra
where the orbital degree of freedom may play a crucial role.
These materials have quasi 1D structure in which
the octahedra share their edges alternatively to form zig-zag chains.
Due to this peculiar structure, threefold $t_{2g}$ levels split into
a lower doublet and a higher singlet.
Ti$^{3+}$ cation has one $d$ electron in the lower twofold levels.
The compounds show a phase transition at $T_{\rm c} \simeq 200$K
where the magnetic susceptibility suddenly drops and
the lattice structure is dimerized along the 1D zig-zag chains.
\cite{Isobe2002,Ninomiya2003}
The temperature dependence of the magnetic susceptibility
as well as the estimate of the spin gap compared to $T_{\rm c}$ suggests that
the transition cannot be understood by the usual spin-Peierls mechanism.
\cite{Isobe2002}
We have considered the mechanism of this peculiar transition
by taking account of the twofold orbital degeneracy explicitly.
As in the case of V spinels,
the spatial anisotropy of the $t_{2g}$ orbitals and
the edge-sharing geometry play an important role,
resulting the Ising-type orbital interaction
in the effective spin-orbital model.
We found that the model exhibits two different ground states;
one is the spin-dimer and orbital-ferro state and
the other is the spin-ferro and orbital-antiferro state.
The transition between them can be controlled by
the Hund's-rule coupling $J_{\rm H}$ and/or the external magnetic field $h$.
For the realistic values of parameters,
the ground state is the former one.
The obtained temperature dependence of the magnetic susceptibility explains
the experimental result semiquantitatively.
\cite{Hikihara2004}
Let us focus on the spin-orbital phase competition
in the parameter space of $J_{\rm H}$ and/or $h$.
A schematic phase diagram is shown in Fig.~\ref{fig:2}.
In the multicritical regime
(the hatched area in Fig.~\ref{fig:2}),
the competition becomes conspicuous;
both spin and orbital correlations are suppressed as the temperature decreases.
This severe competition suppresses $T_{\rm c}$
in the multicritical regime, and
enables us to see effects of the competition
more clearly above $T_{\rm c}$.
The details will be reported elsewhere.
\cite{HikiharaPREPRINT}
In order to observe the intrinsic effects of the spin-orbital competition,
it is desired to realize an experimental situation
in the vicinity of the multicritical point.
\begin{figure}
\centerline{\includegraphics[width=110mm]{fig2.eps}}
\caption{
Schematic multicritical phase diagram of the effective
spin-orbital model for titanium pyroxenes.
The hatched area shows the multicritical competing regime.
}
\label{fig:2}
\end{figure}
\section{Interplay between spin and lattice: Chromium spinels}
\label{sec:Cr-spinel}
Chromium spinels $A$Cr$_2$O$_4$ with nonmagnetic $A$ cations
show only one phase transition
\cite{Kino1971}
in contrast to the two transitions in V spinels in Sec.~\ref{sec:V-spinel}
nevertheless the lattice structures are isomorphic.
The difference is in the orbital state:
Because Cr$^{3+}$ has three $d$ electrons in threefold $t_{2g}$ orbitals,
the orbital degree of freedom is inactive in Cr spinels.
At the transition temperature, an AF spin ordering occurs simultaneously
with the structural change from cubic to tetragonal.
The origin of this transition has been discussed in terms of
the spin Jahn-Teller mechanism;
the geometrical frustration is reduced
by the lattice distortion which gains the magnetic exchange energy.
\cite{Yamashita2000,Tchernyshyov2002}
Very recently, the compounds with $A$=Hg or Cd are found to exhibit
the half-magnetization plateau, which is unusually stable,
under the external magnetic field.
\cite{Ueda2005,UedaUNPUBLISHED}
This plateau phenomenon has been also discussed
by using the AF Heisenberg model with the spin-lattice coupling.
\cite{Penc2004}
The plateau is well reproduced by the mean-field results
in the ground state for finite spin-lattice couplings.
Following this idea, we have extensively studied
finite-temperature properties of
the spin-lattice coupled model on the pyrochlore lattice
under the magnetic field
by using the Monte Carlo simulation.
We found that the half-magnetization plateau remains robust
at finite temperatures, and that
the temperature dependence of the magnetization curve is
favorably compared with the experimental results.
\cite{MotomePREPRINT}
We also found that the plateau phase is induced
by thermal fluctuations even in the absence of the spin-lattice coupling.
The details of the results and the comparison with the experimental results
will be reported elsewhere.
\cite{MotomePREPARATION}
\section*{Acknowledgements}
Y.M. would like to thank D.I. Khomskii and S.-H. Lee for stimulating discussions.
This work is supported by a Grant-in-Aid and NAREGI
from the Ministry of Education, Science, Sports, and Culture of Japan, and
the Hungarian OTKA Grant No. T038162 and the JSPS-HAS joint project.
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