Having seen dozens of B2B SaaS (Software-as-a-Service) ventures growing, I have also seen lots of different organizational structures. Some failed, many were adjusted after a while, and very few have been a success from the beginning. Despite of its importance, there is little literature with a specialized focus on B2B software start-ups. Therefore, I want to give venture- as well as non-venture-backed founders some insights into what I have learnt being part of the start-up ecosystem for more than 10 years.

I exclude any aspects of leadership styles as well as micro organizational working cultures, as these aspects would require a separate blog post. Nevertheless, I am highly convinced that depending on the functional departments a close cross-department working approach with clear roles and responsibilities is and will be successful. This may be in a matrix or a network or a pure hierarchical organization. Moreover, I will not dive too much into detail regarding single departments, e.g. the sales department. I would like to focus on key personas I consider crucial in scaling and growing a B2B SaaS start-up as well as their functional responsibilities related to each other.

Some preliminary remarks

I assume (for the purpose of illustration) that a B2B SaaS venture is initially founded by three very complementary founders. I present four organizational charts depending on financing stage and number of employees (pre-financing, c. 25 FTEs, c. 50 FTEs, and c. 125+ FTEs). Another assumption is that the company scales and sufficient funding is available in order to “pre-finance” organizational structuring as well as hiring excellent people. This is the reason why you take on venture capital, right?

I see different levels of responsibility in a growing B2B SaaS company. These levels are structured from top to bottom, i.e. with a growing number of employees the skill set of each level will change:

- MD Level: this level consists of the operating management board, including all founders and/or managing directors. The MDs are jointly responsible for the success of the company. Nevertheless, with a growing team, clear responsibilities should be assigned. A MD must have very good skills in terms of leadership and motivation. Moreover, a hands-on mentality and a generalist approach to solve problems, i.e. out-of-the-box thinking, are needed.

- VP Level: a VP of a certain department needs profound experience in the respective professional area s/he is responsible for. Moreover s/he must have a network of potential team members, experience in recruitment and, above all, leadership skills in order to coordinate teams of 25+, with up to 7–8 direct reports.

- Director Level: a director has already gained leadership skills in a designated professional area before. S/he is responsible for teams of up to 10 team members, including team leads.

- Team Lead Level: a team leader supervises 2–3 people. You even sometimes recruit a team lead without having an actual team in place yet. Leadership experience is often limited. Team members with great potential are often promoted to team leads.

- Team Members: team members are employees with no leadership or any disciplinary guidance role. They are experts at what they are doing. Nevertheless, it is important to foster their skills in leadership in order to be able to promote them to team lead eventually.

According to my experience, founders hire really good additional managers too late. With a stable and predictable business model, the team might grow exponentially. This represents a huge challenge in terms of leadership and corporate culture. One VP sales might be able to handle 5 people, but suddenly struggles to set up structures and lead 25+ people. Therefore, rather spend 1€ more on an experienced leader that can also manage a team in years’ time.

B2B SaaS Org Chart: before initial investment

If you start your own start-up, it is often hard to distribute certain roles and responsibilities among the founding team. Founders are often generalist people trying to be involved in almost everything related to their venture. Nevertheless, it is important to implement certain responsibilities from the beginning. Not to hold people responsible, but to empower them to make decisions and take actions fast, which is crucial in a dynamic environment like a start-up. A similar approach applies to the first team members. The following separation into three functional roles has proven to be successful for a B2B SaaS venture before any initial financing means: sales & marketing (including customer success, which can be often neglected in the very beginning with no customers at place), product and tech (i.e. software development and product design as well as management), and processes including administration tasks like accounting and legal responsibilities.

B2B SaaS Org Chart: ~25 FTE

After a first seed investment, the founders have the chance to extend the team and create new positions. With three founders you need first team leads managing the operational teams within the three functional areas. These team leads can be either promoted from the initial existing team members or by new external sources. Founders often fear to demotivate existing employees if they recruit a new “boss” for them. Therefore, they often promote the team members to team leads without challenging their social leadership skills. With regard to this topic there is no right or wrong. However, always think about if the team member you want to promote is also capable of managing double or triple amount of people compared to current status quo. Some might argue that three founders can manage 25 FTEs on their own. They definitely can if the company stays at a level of 25 FTEs. But with a high growth B2B SaaS venture, you always need to be one step ahead.

Moreover, with more people onboard and first customers acquired, the founder’s workload increases drastically. This is why I always recommend hiring a so-called “Venture Manager” with the first funding round of EUR 1m+. So, what does a venture manager do and what does the profile look like? A venture manager supports the founders with all extraordinary sophisticated projects, e.g. implementing a CRM tool, or one-off intense tasks, e.g. recruitment of several new team members after a new financing round. S/he has a minimum of 4–5 years of work experience in a dynamic environment where s/he had to manage different task at the same time. They often used to work for consulting companies and have an MBA or equivalent business related education. With an expanding venture, sh/e has the chance to grow into a COO type of role in 5 years — provided that the leadership skills develop accordingly.

B2B SaaS Org Chart: ~50 FTE

When approaching 50 FTEs, you can really call your start-up a company. However, there are more and more tasks that you as a founding partner cannot manage alone anymore. And often your “personal best friend”, the venture manager reaches his limitations as well. It is time to recruit really good people on the VP level who gained experiences on how to scale, grow and lead large groups and departments in larger organizations. As mentioned above, founders often hire too junior people. The reasons for this are various. I experienced that they mainly want to save money or might have a problem with an “employee” earning more money than themselves. However, I can tell you this fact is totally normal. You are and should be incentivized by your shareholding — not your monthly salary. At this stage, it also often happens that one founder either does not fit anymore into the MD leadership role or s/he does not feel comfortable with mainly managing and recruiting people instead of doing operational tasks, which s/he did the years before. This is also normal. Realizing this and acting accordingly by stepping into a different role within the company and hiring a new MD shows great self-reflection and strength. It is super important that the founder team always challenges each other with the question: are we still the right people for the upcoming tasks?

With 50 FTEs on board, it is also the right time to hire an experienced HR manager. The profile should concentrate on recruitment and employee retention — not administrative tasks like payroll accounting. A former head hunter with experience in employee branding and career path development turned out to be a perfect match (at least 4+ years relevant work experience).

At this stage, the customer structure normally becomes more and more complex. Moreover, internal budgets should be assigned to the VPs and designated departments. Therefore, we recommend hiring a designated finance manager. S/he should have gained prior experience in accounting, controlling, and business intelligence (at least 5+ years of relevant work experience).

On the founder / MD level, the roles and responsibilities shall move into three classical C-level roles, namely Chief Revenue Officer (CRO), Chief Technology Officer (CTO) and Chief Operating Officer (COO including the financing responsibility).

B2B SaaS Org Chart: ~125+ FTE

Until now, scaling the company and setting up the organizational structure was an easy step (I know this is the perspective of an outside investor, our founders would definitely see that differently 😊 ). When you are approaching the “100 FTE sound barrier”, things are really getting complicated and cost efficiency often drops. There are many reasons for this inefficiency. With a larger organization, you increase overhead costs. Moreover, performance measures and processes are just about to be implemented at all levels and functional departments — so lack of performance is still not uncovered.

With more than 100 FTEs you should have reached the EUR 10m+ ARR run-rate level. Provided that you still have nice revenue growth rates, you will be facing the decision if you go for another large investment round of EUR 25m+ or steer the company towards break-even and plan a decent exit process in a year or so. No matter what you decide for, you should look at the US market. Series C and beyond financing rounds are often done by US VCs. Looking at the exit channels for B2B SaaS companies, the US market also plays a dominant role. Therefore, you need to have a strong CFO that can lead large financing or exit processes. The profile sounds simple, but it is not very easy to find. S/he should have at least 8+ years relevant experience as a CFO in a high-growth company. Knowing VC financing processes is mandatory. However, s/he must also be a great people manager as it makes lots of sense that s/he is also responsible for the HR department. When it comes to the US market, a clear CEO role should be in place. S/he is very often one of the founders, but sometimes, it is also an external MD who represents the company as CEO. This is the time when founders and MDs must decide who best represents the company.

Apart from C-level management, several VP and director level positions will be successively added. I would like to point out two positions in particular. The director BI and director implementation. The first one is crucial in order to determine and control capital efficiency. A director BI offers important insights into KPIs und unit economics for the CFO as well as the CRO. The director implementation analyzes how to automate with software tools processes, selects the right tools and implements these ones in the designated departments. Why do you need a designated position for this? I have seen many large companies having many diverse “island software solutions” in different departments with no interconnection between whatsoever. This increases overhead costs, reduces data and information transparency between departments, and decreases efficiency.

The positions within the illustration above in light blue are optional, i.e. depending on the nature of the B2B business, its customers, different offices, legal structure, capabilities of the team members etc. they can be relevant at this stage or might become later.

My five main learnings

So, how do you get to a successful 125+ FTE B2B SaaS company? These are my top five recommendations for founders who want to scale and structure their organization:

1. Take your time for recruitment! Set up decent processes and do not make premature decisions. Rather reject once a good candidate than hiring once a bad one. This is why you should hire an experienced recruitment manager rather sooner than later. On the other hand: if you hired someone who turns out to not be the right fit, give him a chance to improve. If this does not work out, let him go as soon as possible. Unfortunately, a high growth company has no time to educate people who turn out to be too junior for the position held.

2. Successful CEOs are always recruiting. No matter if you are on holidays or on a customer conference. Always think about your organization and what talents you might need now and in the future. Most CEOs consider 50%+ of their time as people management tasks including recruitment.

3. Never save money on a perfect candidate, just because s/he seems to be too experienced or senior for the current position. Think at least 12–18 months ahead!

4. Don’t feel weak or concerned about your company if you delegate tasks. You will not and cannot be any more on top of all things that happen within your firm. With the right recruitment process in place, you will hire the right people! A venture manager might be a good start.

5. Be flexible! There are some best-practices regarding organizational structures. Nevertheless, if you have met a great candidate for your company and there is no position currently available, hire him regardless — you will find a spot where s/he will contribute to the success of your firm. Great candidates can do much more than is written in their CVs.

As always, I am happy to receive comments and questions on this very relevant topic via alex@senovo.vc.


How Long Do You Have To Sign A Severance Agreement

While most companies offer a compensation agreement, they are not always obliged to do so; Laws may vary from state to state. The employer must not give workers 45 days to make a decision, seven days of revocation or a study link. Instead, the employer may want to take the ADEA risk to take the title risk VII by trying to meet only the general and voluntary standard and have the document signed sooner rather than later without right of retraction. If you are over 40, if you extend a comparison offer, the rules are very simple. They have rights under the Older Workers Benefit Protection Act (OWBPA) passed by Congress in 1990. Under this law, any sacked employee over the age of 40 who is offered a redundancy contract must have at least 21 days to review the offer. The federal unemployment compensation program provides temporary financial support to the unemployed. However, you must have lost the job without fault, and this is governed by state law. Taxable benefits typically last about 26 weeks, but a state can extend them if unemployment is high. Make sure your employer does not meet your entitle to this benefit.

If you are offering severance pay to a laid-off employee, it is advisable to give the employee some time to ask if he or she accepts. Finally, the employee generally waives important rights (such as the right to sue the company) in exchange for severance pay. If the individual is given time to review the offer, the company can demonstrate that an agreement has not been imposed or forced if necessary. But how much time to think about? Employers should ensure that workers have time to check whether they are signing a redundancy contract that varies with the age of the workers. This special legal requirement must be met to ensure that the release of the rights of the Age Discrimination in Employment Act (ADEA) as amended by the Protection of Older Workers Act (OWBPA) is enforceable. The agreement should contain specific information on all the terms of your separation, including: If you are laid off from your job, it is just as important to negotiate your path as it is to negotiate on your way in. Since a former employer probably has an interest in making the process as civil as possible and maintaining a reputation for good employment, you often have some leeway to negotiate. The CARES Act, which came into effect in March 2020, provides unemployment insurance (IU) to Americans affected by the new coronavirus pandemic, for example, quarantined or their reduced hours. The legislation also made part-time and self-employed benefits available to part-time and self-employed workers.

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Densetsu no Yuusha no Densetsu (Dub)

Watch Densetsu no Yuusha no Densetsu full episodes online English dub. Other tiles DenYuDen, DenYuuDen, Densetsu no Yusha no Densetsu, LOLH. Synopsis: “Alpha Stigma” are known to be eyes that can analyze all types of magic. However, they are more infamously known as cursed eyes that can only bring destruction and death to others. Ryner Lute, a talented mage and also an Alpha Stigma bearer, was once a student of the Roland Empire’s Magician Academy, an elite school dedicated to training magicians for military purposes. However, after many of his classmates died in a war, he makes an oath to make the nation a more orderly and peaceful place, with fellow survivor and best friend, Sion Astal. Now that Sion is the the king of Roland, he orders Ryner to search for useful relics that will aid the nation. Together with Ferris Eris, a beautiful and highly skilled swordswoman, Ryner goes on a journey to search for relics of legendary heroes from the past, and also uncover the secrets behind his cursed eyes.
More info: Myanimelist, Wikipedia

Genres: , , , ,

Views: 1,771 views

4 years anime editor experience.


What’s your real estate income? – The MTV Guide

The median monthly income for those earning between $40,000 and $60,000 per year is $1,636.

This is roughly double the median income of the bottom 40 percent of earners in the US, and almost $6,000 less than the median of the top 1 percent.

The median yearly income for the top 0.01 percent of Americans is $11.2 million, according to data compiled by the Economic Policy Institute, which advocates for a more equitable and sustainable economy.

The average annual income of Americans living in metropolitan areas is roughly $75,000.

However, the average income in the suburbs is only $30,000, while the median is $60.

The richest 5 percent of the population earned nearly $2 million last year, while those in the bottom 50 percent earned just $1.6 million, the data shows.

The median monthly household income in Los Angeles, the nation’s second-most expensive city, was $1 million.

It’s the highest income of any major metropolitan area in the United States.

In San Francisco, median income was $852, while in New York, the fourth-most costly city in the country, median monthly earnings were $1 to $2,000 lower than the national average.

In Seattle, median household income was slightly higher at $1 billion, while New York City was the only other big city in America with an income below $1 trillion.

While the US is the wealthiest country in the world, the gap between the middle and the top is growing rapidly.

The middle is growing at an even faster pace than the top one percent, according the data.

The top one-tenth of one percent of US households earned about $5.7 trillion in 2016, according data compiled from the Bureau of Labor Statistics.

The top 1.1 percent of households earned $9.7 billion last year.

That’s almost four times the income of all the bottom 90 percent of American households combined, according TOI.


npm Community Forum (Archive)

The npm community forum has been discontinued.

To discuss usage of npm, visit the GitHub Support Community.

There needs to be a way to denote OS-specific dependencies

Currently, the only real way you can have OS-specific dependencies is to list it in optionalDependencies and on that particular OS, run npm install dep@semver. For a concrete example of the issues this causes, Chokidar, although it doesn’t mandate it, heavily implies the need for .

Could there be something like a platformDependencies field, with keys being valid process.platform values and values being the list of dependencies? Also, a supportedPlatforms field would be nice to warn users installing it for all platforms when your module only works on certain platforms. (This warning would only be suppressed if either your supportedPlatforms is a subset or equal to theirs or it’s located in a matching platformDependencies field. It’d be generated across all platforms so it’s less likely to get missed.) And to save it to a platform in your package.json, you could use --save-platform platform/--save-platform-dev platform.

Concerning supportedPlatforms, I believe os already does that.

Yeah, I noticed that after I posted this…

I’m working on an RFC for something a bit more flexible.


Jul 192021

Jon-Emile S. Kenny MD [@heart_lung]

-Richard Feynman

Heat-related illness is a very common form of environmental injury. Like many insults, it may be modelled by ‘diathesis-stress.’ In other words, heat-related illness materializes at the cross-roads of inherent patient characteristics [e.g., age, co-morbidities, genotype, that is, one’s diathesis] and external stress [e.g., ambient temperature, humidity, exertion]. Thus, those with multiple, chronic co-morbidities, the elderly and children may be more susceptible because they are less able to dissipate heat and maintain oral hydration.

Ultimately, heat-related illness evolves as the body accrues positive heat balance as a function of the law of energy conservation. While the body has multiple thermoregulatory, homeostatic mechanisms to maintain constant internal temperature, these can be overwhelmed leading to many of the common, non-specific symptoms of heat-related illness: malaise, nausea, dizziness, irritability. With heat exhaustion, this is uncommonly accompanied by an internal temperature more than 40 degrees Celsius, but may be significantly higher in heatstroke – as considered later.

But how, specifically, does the body amass positive heat balance?  What are the compensatory mechanisms to maintain neutral heat balance?  How does heat-related illness [e.g., heat exhaustion and heatstroke] evolve and what are some of the cardiovascular consequences?

Energy and temperature

First, the average tissue specific heat is 3.47 kilojoule per kilogram x degree Celsius. What does this mean? This piece of physiological trivia helps us relate the amount of heat energy absorbed by the body to the average rise in body tissue temperature – how ‘heat energy’ is measured clinically. So, if the amount of heat energy and the mass of tissue are both known, then we can calculate the rise in temperature.

What’s an example of heat energy experienced by the body? If an 85 kg human were to run the pace of a 6-minute mile for 30 minutes, this person would burn about 700 Calories or 167 kilojoules [i.e., 1 Calorie = 4.2 kJ]. So, if all 167 kJ were absorbed by this running human, without any heat dissipation, then average body temperature would rise by 0.7 degrees Celsius [e.g., 36.3 to 37.0 Celsius or 97.3 to 98.6 degrees Fahrenheit] based on the average tissue specific heat noted above.

The aforementioned example also underscores the difference between total metabolic rate and metabolic heat production in the body. The amount of heat production can be determined by taking the entire metabolic rate and subtracting from it the external work performed. Interestingly, the human body is quite inefficient at performing external work, so the vast majority [i.e., greater than 80%] of the total metabolic rate is elaborated as metabolic heat. In fact, running approaches 0% external efficiency! Thus, in the example above, the rise in total metabolic rate with running is expressed almost entirely as metabolic heat.

Heat exchange

As above, while metabolic heat energy is elaborated into the body with rising metabolic rate, the body has a number of mechanisms by which heat energy is dissipated into the atmosphere; this prevents heat storage and maintains constant body temperature.

If we abbreviate heat storage as S, then it can be expressed as a balance between the addition of heat as per above [i.e., metabolic rate, less external work] and the subtraction of heat by dry transfer, evaporative heat transfer [e.g., sweating] and heat lost via respiration.

S = [(Metabolic rate – external work) – (transferdry + transferevaporative + transferrespiratory)]

If S is zero, then there is balanced heat exchange and body temperature is constant.  At resting room temperature, metabolic heat production is dissipated primarily by dry heat transfer.  However, in the example of the running individual above, roughly 167 kJ over 30 minutes of heat is added – assuming most of the metabolic rate is converted to metabolic heat [i.e., low external work efficiency]. If heat transfer processes cannot dissipate those 167 kJ over the same time period, then S > 0, and the patient is moving towards heat exhaustion and heatstroke.  Note that all of the above terms are expressed in energy over time [e.g., Watts] and with respect to the body. How might this equation explain the development of heat-related illnesses, that is, S > zero?

Dry transfer

Dry transfer has 3 basic components: conduction, convection and radiation. Thinking about how this equation explains the evolution of heat exhaustion requires conceptualizing negative heat transfer, that is, mechanisms that increase S above zero.

Conductive heat transfer occurs by direct contact; therefore, negative conductive heat transfer is an uncommon cause of heat-related illness unless a person is found down on a hot surface [e.g., asphalt]. Convection is heat transfer by liquid moving over a surface. For a human, it is proportional to the temperature gradient between the atmosphere and the skin or clothing surface as well as the velocity of the liquid [e.g., air] moving heat away. Negative convective heat transfer [i.e., rising S above], therefore, occurs when there is little air movement, when the ambient temperature is greater than or equal to the skin or clothing surface temperature and when homeostatic mechanisms prevent the skin from warming.  Because the gradient is relative to outer clothing temperature, heavy, insulated materials block convective losses and raise the risk of heat storage over time.

Finally, radiant heat transfer is an electromagnetic energy transfer between warm and cool bodies. Solar radiation is the most common form of radiant heat exposure that raises S. Like convection, this transfer is proportional to the gradient between the mean, ambient radiant temperature and the body surface. Note that humans are also a source of radiant heat, which can be visualized with infrared technology.

Evaporative Transfer

Heat transfer by evaporation is driven by the gradient between ambient humidity and the surface of the skin [e.g., sweating].  Evaporative transfer is therefore related to body surface area and the fraction of the area that is covered in sweat – normally this is about 6% but can increase to 85% in non-acclimatized individuals.  Evaporative transfer also has a convective component and is a relatively inefficient means of heat transfer despite being capable of eliminating roughly 140 – 150 kJ per hour under optimal conditions.  Sweating is usually engaged once dry losses cannot keep pace with heat production.  Sweating is clearly an adaptive mechanism meant to push S downwards and negative evaporative loss [i.e., condensation on the skin] would contribute to heat-related illness only in special conditions such as a steam room.

Respiratory transfer

Heat transfer via respiration is a special mechanism made up of both dry and evaporative transfer described above. The convective component relates to the specific heat capacity of the inspired gas and the minute ventilation moving said gas in and out of the respiratory tree; therefore, minute ventilation plays some role in total body heat transfer with the atmosphere. Similarly, evaporative, respiratory heat transfer occurs as a function of minute ventilation and the humidity difference between the inspired gas and the upper airways.  As above, respiratory heat transfer normally pushes S downwards and clinical scenarios in which respiratory transfer contributes to heat-related illness would require very hot and humid external conditions interacting with high minute ventilation.

Why first principles?

On first blush, the heat balance equation described above appears unnecessarily complicated for clinical medicine.  Nevertheless, thinking about heat transfer with an objective framework of independent and dependent variables conceptualizes patients at risk for heat-related illness and especially prevention and treatment.  In other words, how does the clinician lessen heat storage over time [i.e., S < 0] in patients with heat exhaustion and heatstroke?

Dr. Kenny is the cofounder and Chief Medical Officer of Flosonics Medical; he also the creator and author of a free hemodynamic curriculum at heart-lung.org. Download his free textbook.

Heat-Related Illness & First Principles


Question: What Is A Secondary Function?

What are the two primary of basic functions of money?

What is primary and secondary deposit?

Which is the most important function of management?

PlanningComplexities, Uncertain Events of Future Introduction: Planning is the most important function of management. The other functions of management start with it. In fact planning decides the objective of the management. It also decides the method of achieving those objectives.

What is primary and secondary function?

What is secondary money?

What are the 3 roles of money?

What are the two main functions of banks?

All banks have to perform two major primary functions namely:Accepting of deposits.Granting of loans and advances.

What are the 5 principles of management?

What are the two primary functions of a commercial bank?

The two primary characteristics of a commercial bank are lending and borrowing. The bank receives the deposits and gives money to various projects to earn interest (profit).

What is secondary function of bank?

Secondary Functions of Commercial Banks A bank acts as an agent to its customers for various services like: Collecting bills, draft, cheques, etc. Paying the insurance premium, rent, loan installments, etc. Working as a representative of a customer for purchasing or redeeming securities, etc. in the stock exchange.

What are secondary money functions?

2. What are the 5 Functions of Money? The 5 functions of money are a measure of value, an exchange medium, store of value, transfer of value, the standard of deferred payments.

What are the primary and secondary functions of banks?

Accepting deposits and Advancing loans can be termed as Primary functions of bank, while the secondary functions of the bank include (1) Agency Services and (2) General Utility Services. As we mentioned, one of the most important function of the Commercial Banks is to accept deposits.

What are the two primary or basic function of money?

What are the 7 functions of management?

What are the advantages of secondary market?

The benefits of secondary market trading are:It offers investors to make good gains in a shorter period.The stock price in these markets helps in evaluating a company effectively.For an investor, the ease of selling and buying in these markets ensures liquidity.More items…

What is the other name of secondary market?

The secondary market, also called the aftermarket and follow on public offering, is the financial market in which previously issued financial instruments such as stock, bonds, options, and futures are bought and sold. … After the initial issuance, investors can purchase from other investors in the secondary market.

What are primary functions?

Primary function means a major activity for which a building or facility is intended. … Primary function means a function that is frequently used and as such constitutes an essential function for which the Software is purchased e.g. Collecting, Analyzing, and Loading data, and running Standard Reports.

What are the secondary functions of management?

The management process consists of four primary functions that managers must perform: planning, organizing, leading, and controlling. Secondary function management. Four Functions of Management: Planning, Organizing, Leading & Controlling.

What are the two essential functions of a bank?

The two essential functions of banks in the economy are accepting deposits and granting advances or lending loans.

What are examples of secondary markets?


Section 01: Aggregate Demand

As discussed in the previous lesson, the accumulation expenditures version is a useful tool in determining the equilibrium level of output in the economy. It does have a significant fregulation, however: the aggregate expenditures model does not take right into account the impact of the price level on accumulation output. The Aggregate Demand also Curve (AD) represents, in that sense, an also even more correct design of accumulation output, bereason it shows the various amounts of products and also solutions which residential consumers (C), businesses (I), the federal government (G), and also foreign buyers (NX) jointly will certainly desire at each possible price level. Let’s start by reflecting the partnership between the accumulation expenditures version and also the AD curve.

You are watching: According to the real-balance effect, an increase in the price level

In the graph below, we present the conventional aggregate expenditures curve at 3 different price levels. When prices are high (P1), Consumption is low; as prices loss to P2 and also P3, Consumption rises. As the Consumption function shifts upward as a result of the falling prices, the equilibrium level of GDP goes up from GDP1 to GDP3. This is illustrated in the ADVERTISEMENT frame as a downward sloping AD curve.

Why does it make feeling for the AD curve to slope downward and to the right? We will certainly indicate three various rationales for the downward sloped curve: the genuine balances effect, the interest price impact, and also the international purchases result.

The Real Balances Effect

“Real balances” refers to the purchase power of a offered amount of money in circulation. We make the assumption that at any given allude in time, tright here is a fixed amount of money in circulation. At better price levels, the money in circulation deserve to purchase fewer items. Think of the easy of example of having actually $1,000 in circulation and the average price of the products and services in the economy being $10. A complete of 100 items could be purchased under these conditions. If the average price level were to rise to $20 per item, then the $1,000 in circulation would certainly just enable us to purchase 50 items. At higher prices, the money in circulation will certainly spreview over fewer goods. When prices fall, the purchasing power of the money in circulation goes up, and also civilization deserve to buy even more items and also solutions. This connection between prices and the amount of goods and also solutions that deserve to be purchased via a offered money supply is dubbed the genuine balances impact. It justifies our depiction of the ADVERTISEMENT curve as a downward sloping curve.

The Interest Rate Effect

The interemainder price result explains affect that the price level has actually on interest prices, and also thus on certain components of AD. When the price level goes up, world need more money to transact their day-to-day purchases. As such, higher prices bring about a boost in the demand also for money. With a resolved amount of money in circulation, increasing the demand for money will certainly reason the interest price to go up. Think of how you would behave actually if you were running a financial institution and also the demand also for money raised. You would try to encourage additional civilization to deposit money into the bank, and also at the exact same time discourage human being from coming into the bank to demand also money. The means to execute both all at once would certainly be to increase the interemainder price. As interemainder rates go up, investment demand also and specific interest-rate sensitive usage purchases will fall. Thus, boosts in the price cause boosts the interemainder rate, which reduces the demand also for both Consumption and also Investment, and also hence actual output. The interest price impact is therefore an additional justification for the downward sloping AD curve.

The Foregime Purchases Effect

Domestic prices also have an affect on Net Exports (NX) via what is referred to as the foreign purchases result. When US prices climb loved one to human being prices, foreigners buy fewer US products and Americans buy more international goods, so NX loss. Due to the fact that NX are component of AD, this contributes to an inverse partnership in between the price level and the demand also for our actual residential output. The oppowebsite is likewise true. The international purchases impact contributes to our dispute for why the AD is downward sloping.

Anything that alters the price level triggers these three effects and also is represented by motion alengthy a provided AD curve. Tright here are other components that affect aggregate demand also besides the price level, and these components are described as factors of ADVERTISEMENT. When these various other determinants adjust, they cause a shift in the entire ADVERTISEMENT curve and are periodically dubbed accumulation demand shifters. These accumulation demand also shifters include anypoint that will certainly affect the levels of Consumption, Investment, Government Spfinishing, or Net Exports OTHER THAN alters in the price level. Let’s think about each consequently.

Section 02: Aggregate Demand also Shifters

The graph below illustprices what a adjust in a determinant of aggregate demand also will perform to the position of the accumulation demand curve. As we take into consideration each of the determinants remember that those components that reason a rise in ADVERTISEMENT will certainly transition the curve outward and also to the appropriate and also those factors that reason a decrease in ADVERTISEMENT will certainly shift the curve inward and to the left.

Changes in Consumption unpertained to a adjust in the price

There are numerous components that might boost or decrease usage that are unregarded transforms in the price level. For instance, boosts in consumer wide range would certainly rise usage at each price level and would certainly be illustrated by a rightward transition in AD. Decreases in consumer wealth would have actually the oppowebsite impact. Increases in customer indebtedness would certainly decrease usage and change the aggregate demand also curve to the left, while decreases in indebtedness would have actually the opposite impact. Increases in taxes will decrease consumption (and transition the ADVERTISEMENT curve to the left) while decreases in taxes will certainly increase consumption and also change the AD curve to the right. Consumer expectations about the future of the economic climate have the right to have actually a solid impact on consumptions. Optimism around the economy will boost consumption and also transition the ADVERTISEMENT curve to the ideal, while widespreview pessimism dampens consumer spending and also shifts the AD curve to the left. You have the right to most likely think of various other components that will shift the AD curve bereason they affect intake independent of the price level.

Changes in Investment unrelated to a adjust in the price

There are numerous determinants unregarded transforms in the price level that might increase or decrease Investment and thereby transition the AD curve. For circumstances, any type of readjust in the interest rate not lugged around by a change in the price level would adjust the level of investment in the economic situation, and shift the AD curve. Increases in the interest price will certainly reduce investment demand; decreases in the interemainder price will increase investment demand. Company taxes have the right to be structured to either encourage investment (moving the ADVERTISEMENT to the right) or discourage investment (moving AD to the left). Technological renovations in an market could make old tools obsolete and also stimulate investment, moving AD to the ideal. Finally, prefer the impact of expectations on consumers, optimism (or pessimism) on the part of company owners have the right to bring about boosts (or decreases) in investment task and also transition the ADVERTISEMENT curve to the right (or left).

Changes in Government Spfinishing unpertained to a change in the price

The political process will certainly occasionally bring about increases or decreases in the level of federal government spending. Increases in government spending will certainly shift the AD curve to the right; decreases in federal government spfinishing will transition the ADVERTISEMENT curve to the left.

Changes in Net Exports unpertained to changes in the price

Tright here are 2 important determinants unconcerned the price level that can increase or decrease the level of Net Exports and also thereby transition the ADVERTISEMENT Curve. The initially hregarding carry out via changes in nationwide revenue awide. As income abroad grows loved one to revenue in the United States, foreigners are able to buy US commodities more conveniently and also Americans have the right to afford fewer international products. Net exports will certainly go up, changing the ADVERTISEMENT curve to the best. If incomes abroad autumn family member to income in the US, the AD curve will certainly change left due to a decrease in net exports. The second element hregarding carry out via exchange rates, or the relative worth of our money to the money of a trading partner. As an example, let’s say that it takes 90 Japanese Yen to buy one US dollar. If the worth of the yen relative to the dollar changes so that it takes 100 Yen to buy one US dollar, this will decrease the amount that Japanese citizens will buy in the US, and also boost the amount that US citizens deserve to buy in Japan. This readjust in the exadjust price will certainly reason net exports to autumn and the AD curve to transition to the left. If the Japanese Yen were to appreciate family member to the dollar, net exports would certainly increase and also the ADVERTISEMENT curve would shift to the appropriate.

Rerevolve to the course in I-Discover and also complete the task that corresponds with this material.

Section 03: Aggregate Supply

Aggregate Supply (AS) is a curve reflecting the level of genuine residential output easily accessible at each possible price level. Typically AS is shown via an inexplicable looking graph prefer the one presented listed below. There is a specific reason for why the AS has this strange form. The AS curve have the right to be separated right into three distinct arrays referred to as the Keynesian Range, the Intermediate Range, and the Classical Range. The various ranges depict three various states in which the economic climate might find itself. The 3 says of the economy have the right to all be assumed of in relation to what is referred to as the full-employment level of output, labeled Qf in the graph below. We will now comment on each of the three arrays of the AS.

In the Keynesian variety of AS, we are at outputs which are dramatically below Qf. This horizontal range indicates an economic situation in major recession or depression. Remember that Keynes created his General Theory during the heights of the Great Depression, so the selection of AS that is linked via his name synchronizes to such an economic situation. Assume that you were running a manufacturing facility during a major recession through high joblessness, and also you decided that you would like to rise output. You realize that, to increase output, you are going to have to employ more inputs, mainly even more labor—yet, a comparable dispute can be made about high joblessness of any of the other determinants of production. You go to the factory door, open it, and uncover countless unemployed workers standing in line, wanting to occupational at your manufacturing facility. How a lot would certainly you have to pay them to obtain them to go to occupational for you? Certainly, you would certainly not have to pay them more than the going wage price in the market, right? Basically, you could hire as many kind of unemployed resources as you would certainly like without bidding up wages and prices, because of the extensive joblessness. The horizontal or Keynesian AS illustrates the principle of the economy being able to boost real output through no increase in the price level in the time of periods of high joblessness. This range of the AS curve is also sometimes described as the Brief Run AS curve.

In the Classical Range of AS, we are at or very close to the full-employment level of output. This variety is named after the Classical Economists who assumed that the economic situation, in the lengthy run, would certainly constantly attain complete employment. The Classical AS curve is periodically called the Long Run AS curve. Assume again that you are running a factory, only this time, the economic situation is at full-employment. Let’s say aobtain that you desire to boost output, and that in order to execute so you have to rise the number of workers at your manufacturing facility. You go to the manufacturing facility door and also open it to find nobody waiting in line. Tright here does not show up to be anyone looking for a job bereason everyone already has one! In order to hire added workers, you go to other employers’ workers, and ask them to leave their job to work-related for you. How much are you going to have to pay these employees to acquire them to perform that? Most most likely you will need to pay them more than they are currently making. As you bid up wages in the labor market to tempt added workers, prices in the economic climate will certainly also climb, bereason currently it prices even more to create your product. That added expense is passed to the consumer in the develop of higher prices, to the degree feasible. Attempts to boost output in the Classical Range leads to higher price levels in the economy yet what around actual GDP? Does it actually increase? Well, your output may go up, however the output of the factory wbelow your brand-new workers offered to work will certainly go dvery own, so the all at once output in the economy stays the exact same at Qf.

In the Intermediate Range, we are at output levels that are listed below complete employment, but not so much listed below as to constitute a deep recession or depression. In this range, increasing output is possible, but only at the cost of climbing prices. While that Keynesian Range is a rare short-run occurrence, and also the Classical Range is the long-run secure state of the economic climate, the Intermediate Range is most likely wbelow we discover ourselves many frequently in the economic climate.

Depending on the state of the economy, any type of attempt to adjust the output of the economy will relocate us along a given AS curve. Tright here are determinants that affect accumulation supply, illustratable by moving the AS curve—these components are described as determinants of AS. When these other determinants adjust, they reason a transition in the entire AS curve and are periodically referred to as accumulation supply shifters. These aggregate supply shifters include Changes in Resource Prices, Changes in Resource Productivity, Company Taxes and also Subsidies, and also Government Regulations. Let’s consider each in turn.

Section 04: Determinants of Aggregate Supply

The graph listed below illustrates what a change in a determinant of accumulation supply will carry out to the place of the accumulation supply curve. As we take into consideration each of the components remember that those determinants that cause a boost in AS will certainly change the curve outward and also to the best and also those factors that cause a decrease in AS will change the curve upward and also to the left.

Changes in Input Prices

Anypoint that reasons input prices to climb will certainly decrease AS and also change the AS curve to the left. Anything that causes input prices to fall will rise AS and transition the AS curve to the appropriate. For instance, if a specific input into the production procedure is easily obtainable from residential providers, it will generally be cheaper, holding all else consistent (cet. par.). If for no various other factor, transport expenses of moving a domestic resource to a domestic producer will certainly be less than moving the the same reresource from a international supplier. That does not also take right into account the problems of acquiring a foreign reresource such as duties and also tariffs, political or social instability abroad, or various other international disruptions. Anvarious other element that can affect input prices would certainly be the market power of the suppliers of the reresource. The even more competition in the supply of a source, the cheaper that reresource will certainly be, cet. par. If the reresource is gave by a monopolist or a cartel (think OPEC oil), the price of that reresource will certainly be greater than if the resource is supplied by an extra competitive industry (think corn-developed ethanol).

Changes in Productivity

Independent of its price, anything that provides resources more fertile will increase AS and also transition the AS curve to the right; anypoint that renders sources much less abundant will decrease AS and also transition the AS curve to the left. If workers come to be more fertile because of investments in physical or humale resources, the economy will certainly have the ability to create even more and also the AS curve will change to the appropriate. If employees come to be much less fertile bereason of outmoded devices, inadequate training, or too much union interference in their worklocation, the economic situation will be much less fertile, and also the AS curve will shift to the left.

Business Taxes and Subsidies

In brief, organization taxes increase the expense of manufacturing and shift the AS curve to the left; subsidies decrease the expense of production and also transition the AS curve to the best.

Government Regulations

Government regulations also affect the prices of production. Increasing federal government regulations provides it more expensive to develop the nation’s output and also shifts the AS curve to the left; reducing government regulations lessens the burden of company and also shifts the AS curve to the best.

Rerotate to the course in I-Find Out and finish the activity that synchronizes through this product.

Section 05: Equilibrium

What does the equilibrium in between ADVERTISEMENT and also AS determine? The Price Level in the economic situation and the Real Output (GDP) of the economic climate. Equilibrium is illustrated below as the interarea between AD and AS.

Section 06: Shifts in the AD Curve

Let’s testimonial every one of the feasible impacts on the price level and the level of actual GDP from a shift in the ADVERTISEMENT curve. An rise in the AD in the Keynesian Range of AS will boost Real Output, but leave the Price Level the same; a decrease in ADVERTISEMENT in the Keynesian Range of the AS will certainly decrease Real Output but leave the Price Level the very same.

An increase in AD in the Intermediate Range of AS will increase Real Output and boost the Price Level; a decrease in AD in the Intermediate Range of AS will decrease Real Output and decrease the Price Level. Notice that in the intermediate variety, there is a tradeoff in between two of the key financial variables that concern US citizens: Inflation and Unemployment. Typically, we would certainly choose both inflation and also unemployment to be low. In the intermediate range, yet, if we rise AD, inflation will go up as unemployment falls (notice that if genuine GDP is going up, unemployment is going down: in order to rise GDP, you need to hire even more workers). On the other hand, if we decrease ADVERTISEMENT, inflation will certainly autumn but joblessness will rise. Tbelow is no means to all at once decrease inflation and decrease unemployment utilizing demand side shifts.

An increase in ADVERTISEMENT in the Classical Range of AS will certainly leave Real Output unchanged, however will certainly increase the Price Level. A decrease in ADVERTISEMENT in the Classical Range of ADVERTISEMENT will leave Real Output unchanged, yet will certainly lower the Price Level.

See more: 13 Reasons Why Season 1 Episode 1 Watch Online 123Movies, 13 Reasons Why

The price boosts that outcome from rises in ADVERTISEMENT are examples of Demand-Pull Inflation

Do you think that decreases in ADVERTISEMENT have precisely the opposite impacts as the increases? Usually they perform, but tbelow is a possibility of inversatility downward of prices as a result of the “ratchet impact.” In business economics, the ratchet impact says that while prices are quick to boost, they are extremely slow to autumn. Why carry out you think that prices would certainly go up extremely conveniently yet autumn just slowly? Part of the answer hregarding do via the truth that it actually prices businesses money to adjust their prices (think of printing new catalogs, printing brand-new menus, recoding prices in a computer and also on scanners, or sfinishing a worker out to readjust the prices on a marquee). It is worth it to the company to incur this cost as soon as the price is going up, but once the price is going dvery own they are unconvinced to take on the price of transforming prices!

Section 07: Shifts in Aggregate Supply

A decrease in AS will certainly increase the Price Level and decrease Real Output. An rise in AS will certainly alleviate the Price Level and increase Real Output. The inflation that is associated with a decrease in the AS is called Cost-Push Inflation. Throughout the 1970s, a selection of components shifted the AS curve to the left. The high inflation that was combined with a stagnant economic situation (low levels of output and also high unemployment) offered climb to the term Stagflation.

When Ronald Reagan was chosen President in 1980, the inflation rate was 13.5% and also the joblessness rate was 7.5%. Reagan employed supply side policies that were designed to shift the AS curve to the best and also mitigate both inflation and also unemployment concurrently. Only by supply side plans have the right to you decrease both inflation and also unemployment at the exact same time. By the time that Reagan left office eight years later, the inflation rate in the economic climate was 4.1% and also the joblessness price of 5.3%.


Do barbell rows help with pull ups?

Do rows help with pull-ups?

Bent-over dumbbell rows

This exercise works your upper back and bicep, two areas that will help to lift you up into a pullup.

Are barbell rows or pull-ups better?

You can also do an inverted row, where you lie on your back, grab a bar above you and pull your chest up to the bar. Rows work your latissimus dorsi more than pull-ups. Out of all of the row variations, the inverted row works your latissimus dorsi the most.

Are rows easier than pull ups?

Pull-Ups are one of the best exercises for building a strong back. They develop your lats and are a great measure of strength. They include Single-Arm Rows and Inverted Rows, which develop the major back muscles—your lats, traps and rhomboids. …

Are Bent-over rows better than deadlifts?

Where deadlifts mostly target the muscles in your lower body and lower back, bent-over barbell rows target several muscles in your upper back. It also targets two muscles in your arm, the brachialis and brachioradialis of the biceps, and the pectoralis major in your chest. …

Are barbell rows worth it?

The barbell row is a fundamental exercise that will pack serious meat onto your back — and it does more than that, too. It also helps bulletproof your shoulders, building the back muscle needed to prevent your shoulders from rolling forward when you stand up, a common issue for lifters who bench press often.

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Are rows enough for biceps?

In contrast to lat pulldowns, rows don’t seem to work your biceps as well as curls do. The bicep thickness increased by 11.06% in the arms that had trained dumbbell curls, but only by about half (5.16%) in the arms that had trained dumbbell rows.

Do inverted rows build muscle?

Inverted rows are an excellent addition to a full-body workout. Overall, they can improve upper body strength and grip strength, recruit the glutes and hamstrings, and give your biceps a boost.


How to edit a remote agreement

Once you have filled out your remote agreement, it will be sent to the customer to sign ( to see how to complete a remote agreement, click here). The agreement will then be sitting in your list of accounts. To find the list of your accounts simply go to the administration tab at the top of the page and select either all agreements or remote agreements.

Here, you will see a list of all of the agreements that you have. If an agreement has been sent to a customer and has not yet been signed, the status will be awaiting signature and you will be able to amend it should you need to. So, if the customer receives the agreement and wants to change a payment date or start date, you can go into the agreement and make changes.

Click on the edit entry box and it will bring up all of the details of the customer's agreement. You can then simply change the detail that needs changing.

Now you just need to scroll to the bottom of the page and click on update.

That will update the agreement. If an agreement has already been signed, it cannot be amended. So if a customer needs to make a change, it is important that they do so before signing.


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Democrats: Show Russian collusion, or shut up

Show collusion between Trump, or people associated with his campaign, and the Russians, or shut the heck up.

The "Russian Investigation" is a sham.  The nightly news reporting of said investigation is a sham.

We, Republicans generally, and Trump, specifically, have allowed the Democrats and the media (but I repeat myself) to conflate two issues.  One: Russians attempted to, or were successful in, influencing the election.  Two: Said influence involved active collusion among Trump, his surrogates, and Vladimir Putin.

The intelligence community has presented all parties (Democrats and Republicans alike) with intelligence that Russia worked to influence the 2016 election.  What that intelligence included, specifically, is anybody's guess, as much of it has been kept within the investigatory bodies.  No one is surprised that Russia has geopolitical interests in influencing the direction of its most prominent adversary, the United States.

Where the narrative goes off the rails, and has traveled much (much) farther than should have been allowed, is that Donald Trump or his surrogates were actively working with Putin, or Russia, to elevate Trump to the presidency as a form of quid pro quo.  Set aside for a moment that, in an infamous "hot mic" moment, Barack Obama told Russian president Dmitri Medvedev that "after my election, I'll have more flexibility," and also set aside that, as secretary of state, Hillary Clinton signed off on a uranium deal with Russia, as money was being donated to the Clinton Foundation.

The media were seemingly incurious about our "involvement with Russia" during these incidences, but now they are bending over backward to infer that Donald Trump worked with Russia to gain him the American presidency.  Nothing – let me repeat: nothing – has been presented to show collusion between Donald Trump and the Russians.

You want to investigate Russia's influence in American politics?  Knock yourself out.  If you find methods they're using to affect the outcome of elections, by all means, close those doors.

But, and here's the kicker, if you haven't found evidence, even after "incidentally collecting intelligence" from Trump and his transition team that he, or his surrogates, colluded with Russia to gain him the presidency, close down that portion of the investigation.  Our president deserves the opportunity to govern without a sham assertion being made about his complicity in Vladimir Putin's geopolitical activities.

Donald Trump should demand evidence implicating his complicity.  He and the duplicitous GOP have allowed this sham to go on for far too long.

Show collusion, or STHU!


Dynamics of Atmospheric Flight

Dynamics of Atmospheric Flight

by Bernard Etkin

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Geared toward upper-level undergrads, graduate students, and practicing engineers, this comprehensive treatment of the dynamics of atmospheric flight focuses especially on the stability and control of airplanes. An extensive set of numerical examples covers STOL airplanes, subsonic jet transports, hypersonic flight, stability augmentation, and wind and density gradients.
The equations of motion receive a very full treatment, including the effects of the curvature and rotation of the Earth and distortional motion. Complete chapters are given to human pilots and handling qualities and to flight in turbulence, with numerical examples for a jet transport. Small-perturbation equations for longitudinal and lateral motion appear in convenient matrix forms, both in time-domain and Laplace transforms, dimensional and nondimensional.

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Product Details

ISBN-13: 9780486445229
Publisher: Dover Publications
Publication date: 09/20/2005
Series: Dover Books on Aeronautical Engineering
Pages: 608

Read an Excerpt

Dynamics of Atmospheric Flight

By Bernard Etkin

Dover Publications, Inc.

Copyright © 2000 Bernard Etkin
All rights reserved.
ISBN: 978-0-486-14165-7

This book is about the motion of vehicles that fly in the atmosphere. As such it belongs to the branch of engineering science called applied mechanics. The three italicized words above warrant further discussion. To begin with fly—the dictionary definition is not very restrictive, although it implies motion through the air, the earliest application being of course to birds. However, we also say "a stone flies" or "an arrow flies," so the notion of sustention (lift) is not necessarily implied. Even the atmospheric medium is lost in "the flight of angels." We propose as a logical scientific definition that flying be defined as motion through a fluid medium or empty space. Thus a satellite "flies" through space and a submarine "flies" through the water. Note that a dirigible in the air and a submarine in the water are the same from a mechanical standpoint—the weight in each instance is balanced by buoyancy. They are simply separated by three orders of magnitude in density. By vehicle is meant any flying object that is made up of an arbitrary system of deformable bodies that are somehow joined together. To illustrate with some examples: (1) A rifle bullet is the simplest kind, which can be thought of as a single ideally-rigid body. (2) A jet transport is a more complicated vehicle, comprising a main elastic body (the airframe and all the parts attached to it), rotating subsystems (the jet engines), articulated subsystems (the aerodynamic controls) and fluid subsystems (fuel in tanks). (3) An astronaut attached to his orbiting spacecraft by a long flexible cable is a further complex example of the general kind of system we are concerned with. Note that by the above definition a vehicle does not necessarily have to carry goods or passengers, although it usually does. The logic of the definitions is simply that the underlying engineering science is common to all these examples, and the methods of formulating and solving problems concerning the motion are fundamentally the same.

As is usual with definitions, we can find examples that don't fit very well. There are special cases of motion at an interface which we may or may not include in flying—for example, surface ships, hydrofoil craft and aircushion vehicles. In this connection it is worth noting that developments of hydrofoils and ACV's are frequently associated with the Aerospace industry. The main difference between these cases, and those of "true" flight, is that the latter is essentially three-dimensional, whereas the interface vehicles mentioned (as well as cars, trains, etc.) move approximately in a two-dimensional field. The underlying principles and methods are still the same however, with certain modifications in detail being needed to treat these "surface" vehicles.

Now having defined vehicles and flying, we go on to look more carefully at what we mean by motion. It is convenient to subdivide it into several parts:

Gross Motion:

(i) Trajectory of the vehicle mass center.

(ii) "Attitude" motion, or rotations of the vehicle "as a whole."

Fine Motion:

(i) Relative motion of rotating or articulated sub-systems, such as engines, gyroscopes, or aerodynamic control surfaces.

(ii) Distortional motion of deformable structures, such as wing bending and twisting.

(iii) Liquid sloshing.

This subdivision is helpful both from the standpoint of the technical problems associated with the different motions, and of the formulation of their analysis. It is surely self-evident that studies of these motions must be central to the design and operation of aircraft, spacecraft, rockets, missiles, etc. To be able to formulate and solve the relevant problems, we must draw on several basic disciplines from engineering science. The relationships are shown on Fig. 1.1. It is quite evident from this figure that the practicing flight dynamicist requires intensive training in several branches of engineering science, and a broad outlook insofar as the practical ramifications of his work are concerned.

In the classes of vehicles, in the types of motions, and in the medium of flight, this book treats a restricted set of all possible cases. Its emphasis is on the flight of airplanes in the atmosphere. The general equations derived, and the methods of solution presented, are however readily modified and extended to treat the other situations that are embraced by the general problem.

All the fundamental science and mathematics needed to develop this subject existed in the literature by the time the Wright brothers flew. Newton, and other giants of the 18th and 19th centuries, such as Bernoulli, Euler, Lagrange, and Laplace, provided the building blocks in solid mechanics, fluid mechanics, and mathematics. The needed applications to aeronautics were made mostly after 1900 by workers in many countries, of whom special reference should be made to the Wright brothers, G. H. Bryan, F. W. Lanchester, J. C. Hunsaker, H. B. Glauert, B. M. Jones, and S. B. Gates. These pioneers introduced and extended the basis for analysis and experiment that underlies all modern practice. This body of knowledge is well documented in several texts of that period, e.g. ref. 1.4. Concurrently, principally in the USA and Britain, a large body of aerodynamic data was accumulated, serving as a basis for practical design.

Newton's laws of motion provide the connection between environmental forces and resulting motion for all but relativistic and quantum-dynamical processes, including all of "ordinary" and much of celestial mechanics. What then distinguishes flight dynamics from other branches of applied mechanics? Primarily it is the special nature of the force fields with which we have to be concerned, the absence of the kinematical constraints central to machines and mechanisms, and the nature of the control systems used in flight. The external force fields may be identified as follows:

"Strong" fields:

(i) Gravity

(ii) Aerodynamic

(iii) Buoyancy

"Weak" fields:

(iv) Magnetic

(v) Solar radiation

We should observe that two of these fields, aerodynamic and solar radiation, produce important heat transfer to the vehicle in addition to momentum transfer (force). Sometimes we cannot separate the thermal and mechanical problems (ref. 1.5). Of these fields only the strong ones are of interest for atmospheric and oceanic flight, the weak fields being important only in space. It should be remarked that even in atmospheric flight the gravity force can not always be approximated as a constant vector in an inertial frame. Rotations associated with Earth curvature, and the inverse square law, become important in certain cases of high-speed and high-altitude flight (Chapters 5 and 9).

The prediction and measurement of aerodynamic forces is the principal distinguishing feature of flight dynamics. The size of this task is illustrated by Fig. 1.2, which shows the enormous range of variables that need to be considered in connection with wings alone. To be added, of course, are the complications of propulsion systems (propellers, jets, rockets) and of compound geometries (wing + body + tail).

As remarked above, Newton's laws state the connection between force and motion. The commonest problem consists of finding the motion when the laws for the forces are given (all the numerical examples given in this book are of this kind). However we must be aware of certain important variations:

1. Inverse problems of first kind—the system and the motion are given and the forces have to be calculated.

2. Inverse problem of the second kind—the forces and the motion are given and the system constants have to be found.

3. Mixed problems—the unknowns are a mixture of variables from the force, system, and motion.

Examples of these inverse and mixed problems often turn up in research, when one is trying to deduce aerodynamic forces from the observed motion of a vehicle in flight or of a model in a wind tunnel. Another example is the deduction of harmonics of the Earth's gravity field from observed perturbations of satellite orbits. These problems are closely related to the "plant identification" or "parameter identification" problem that is of great current interest in system theory. (Inverse problems were treated in Chapter 11 of Dynamics of Flight—Stability and Control, but are omitted here.)

The main types of flight dynamics problem that occur in engineering practice are:

1. Calculation of "performance" quantities, such as speed, height, range, and fuel consumption.

2. Calculation of trajectories, such as launch, reentry, orbital and landing.

3. Stability of motion.

4. Response of vehicle to control actuation and to propulsive changes.

5. Response to atmospheric turbulence, and how to control it.

6. Aeroelastic oscillations (flutter).

7. Assessment of human-pilot/machine combination (handling qualities).

It takes little imagination to appreciate that, in view of the many vehicle types that have to be dealt with, a number of subspecialties exist within the ranks of flight dynamicists, related to some extent to the above problem categories. In the context of the modern aerospace industry these problems are seldom simple or routine. On the contrary they present great challenges in analysis, computation, and experiment.

The tools used by flight dynamicists to solve the design and operational problems of vehicles may be grouped under three headings:

The analytical tools are essentially the same as those used in other branches of mechanics. Applied mathematics is the analyst's handmaiden (and sometimes proves to be such a charmer that she seduces him away from flight dynamics). One important branch of applied mathematics is what is now known as system theory, including stochastic processes and optimization. It has become a central tool for analysts. Another aspect of this subject that has received a great deal of attention in recent years is stability theory, sparked by the rediscovery in the English-speaking world of the 19th century work of Lyapunov. At least insofar as manned flight vehicles are concerned, vehicle stability per se is not as important as one might suppose. It is neither a necessary nor a sufficient condition for successful controlled flight. Good airplanes have had slightly unstable modes in some part of their flight regime, and on the other hand, a completely stable vehicle may have quite unacceptable handling qualities. It isperformance criteria that really matter, so to expend a great deal of analytical and computational effort on finding stability boundaries of nonlinear and time-varying systems may not be really worthwhile. On the other hand, the computation of stability of small disturbances from a steady state, i.e. the linear eigenvalue problem that is normally part of the system study, is very useful indeed, and may well provide enough information about stability from a practical standpoint.

On the computation side, the most important fact is that the availability of machine computation has revolutionized practice in this subject over the past ten years. Problems of system performance, system design, and optimization that could not have been tackled at all a dozen years ago are now handled on a more or less routine basis.

The experimental tools of the flight dynamicist are generally unique to this field. First, there are those that are used to find the aerodynamic inputs. Wind tunnels and shock tubes that cover most of the spectrum of atmospheric flight are now available in the major aerodynamic laboratories of the world. In addition to fixed laboratory equipment, there are aeroballistic ranges for dynamic investigations, as well as rocket-boosted and gun-launched free-flight model techniques. Hand in hand with the development of these general facilities has gone that of a myriad of sensors and instruments, mainly electronic, for measuring forces, pressures, temperatures, acceleration, angular velocity, etc.

Second, we must mention the flight simulator as an experimental tool used directly by the flight dynamicist. In it he studies mainly the matching of the man to the machine. This is an essential step for radically new flight situations, e.g. space capsule reentry, or transition of a tilt-wing VTOL airplane from hovering to forward speed. The ability of the pilot to control the vehicle must be assured long before the prototype stage. This cannot yet be done without test, although limited progress in this direction is being made through studies of mathematical models of human pilots. The prewar Link trainer, a rudimentary device, has evolved today into a highly complex, highly sophisticated apparatus. Special simulators, built for most new major aircraft types, provide both efficient means for pilot training, and a research tool for studying flying qualities of vehicles and dynamics of human pilots.

Analytical tools

This chapter contains a summary of the principal analytical tools that are used in the formulation and solution of problems of flight mechanics. Much of the content will be familiar to readers with a strong mathematical background, and they should make short work of it.

The topics treated are vector/matrix algebra, Laplace and Fourier transforms, random process theory, and machine computation. This selection is a reflection of current needs in research and industry. The vector/matrix formalism has been adopted as a principal mathematical tool because it provides a single powerful framework that serves for all of kinematics, dynamics, and system theory, and because it is at the same time a most suitable way of organizing analysis for digital computation. The treatment is intended to be of an expository and summary nature, rather than rigorous, although some derivations are included. The student who wishes to pursue any of the topics in greater detail should consult the bibliography.

As has already been remarked, this book is written largely in the language of matrix algebra. Since this subject is now so well covered in undergraduate mathematics courses and in numerous text books, (2.1, 2.11) we make only a few observations here.

Excerpted from Dynamics of Atmospheric Flight by Bernard Etkin. Copyright © 2000 Bernard Etkin. Excerpted by permission of Dover Publications, Inc..

Table of Contents

1. Introduction
2. Analytical Tools
3. System Theory
4. Reference Frames and Transformations
5. General Equations of Unsteady Motion
6. Longitudinal Aerodynamic Characteristics—Part 1
7. Longitudinal Aerodynamic Characteristics—Part 2
8. Lateral Aerodynamic Characteristics
9. Stability of Steady Flight
10. Response to Actuation of the Controls (Open Loop)
11. Closed-Loop Control
12. Human Pilots and Handling Qualities
13. Flight in a Turbulent Atmosphere

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The shore of the Bay of Fundy in front of our home in Port Maitland, NS

Anxiety vs Fear
Norma and I are completing Day 10 of our 14 day Canadian Government imposed self-isolation/quarantine since we came back from Florida. For us, an important part of keeping sane, and keeping Finn, our Brittany, sane as well, are daily walks. We aren’t allowed here to go to parks or other public areas until our 14 days are up – and even then many public places are simply closed.
One of our normal walks, then, has become going from our house along the highway in front of the house (not a busy road by most places’ standards) and then down a short dirt road to the shore. The entire walk is about a kilometer and a half each way, and there is marsh grass and beach at the end which entertains Finn immensely.
The shore also has a calming effect, we find. Watching the gulls circling and the waves lapping is very soothing, and the sounds of the shore are therapeutic. The Provincial Government has closed the public beach just to our south, to avoid any crowds at the parking lot, and so we just stood on the northern edge of our property, where I got the image and took it all in.
I listened to a CBC news interview, a day or two ago, with a psychologist I know, and he reminded us of the difference between anxiety and fear. Anxiety, an apprehension of a real or imagined future threat, he said makes people withdraw and try to shy away or minimize the thing causing the anxiety. Even if there is some reason to be anxious. This kind of response leads folks to do things that aren’t really helpful. Things like withdrawal or denial or giving in to an overwhelming sense of dread.
Fear, on the other hand, is a human emotion that comes as the result of our feeling in danger. Fear is faced not by withdrawal, but by courage. Courage to confront the thing causing the fear, and a collective action to overcome it.
Instead of being anxious and listening to all the doomsday news in our home, isolated but trapped, Norma and I have decided to confront the fear, and do what we feel is a better antidote – go outside and note that there is still beauty and wonder in nature. It works for us.
And, Finn approves.