Datasets:

ecopus
/

transport-wings-500

This document explains how the Python pipeline creates the 500 aircraft‑style wings in your dataset—what varies, what’s fixed, and the exact math behind the values stored.

1) Inputs & Reproducibility

Airfoil geometry: Each airfoil file contains two columns ((x, y)) forming a closed perimeter ordered TE → upper → LE → lower → TE.
- On load, (x) is normalized to ([0,1]); the perimeter is rotated so the first point is closest to the trailing edge ((1,0)) and the upper surface comes first.
Polars (optional): QBlade/XFOIL exports with (\alpha, C_l, C_d, C_m).
- Files are matched to airfoils by flexible filename heuristics.
- Polars are parsed (3–4 numeric columns), deduplicated in (\alpha), and sorted by (\alpha).
Random seed: We use np.random.default_rng(42) so all 500 wings are reproducible bit‑for‑bit.

2) Per‑Wing Planform Sampling (What Varies)

We generate 500 wings. Airfoils are cycled round‑robin (≈50 wings per foil). For each wing we sample:

Half‑span (s) (inches):
(s \sim \mathcal{U}[60,;120]).
Root chord (c_{\text{root}}) (inches):
(c_{\text{root}} \sim \mathcal{U}[18,;36]).
Taper ratio (\lambda):
(\lambda \sim \mathcal{U}[0.25,;0.50]), so (c_{\text{tip}}=\lambda,c_{\text{root}}).
Twist endpoints (washout) (degrees):
(i_{\text{root}} \sim \mathcal{U}[0,;2]), (i_{\text{tip}} \sim \mathcal{U}[-6,;-2]).
- The final twist distribution is linear from root to tip; then we pin the very first station to 0° so the wing “hinges” at the root plane (legacy convention).

We use 20 stations along the half‑span: [ \text{Dis}[j] = y_j = \frac{j-1}{19}; s,\quad j=1..20. ]

3) Chord Distribution: Schrenk’s Approximation

We blend a trapezoid with an ellipse to approximate an elliptical lift distribution:

Linear (trapezoid) chord: [ c_{\text{trap}}(y) = c_{\text{root}} + (c_{\text{tip}} - c_{\text{root}}),\frac{y}{s}. ]
Elliptic surrogate: [ c_{\text{ell}}(y) = c_{\text{root}}\sqrt{1 - \left(\frac{y}{s}\right)^2}. ]
Schrenk chord at each station: [ c(y) = \tfrac{1}{2}\left[c_{\text{trap}}(y) + c_{\text{ell}}(y)\right]. ]

A small clamp prevents pathological tips for extreme tapers: [ c(y) \leftarrow \max!\big(c(y),;0.25\cdot\min\nolimits_y c_{\text{trap}}(y)\big). ]

This yields the Cho vector (inches) over the 20 stations.

4) Twist (Washout) Distribution

With sampled endpoints (i_{\text{root}}) and (i_{\text{tip}}), define a linear twist: [ \text{Twi}[j] = i_{\text{root}} + \big(i_{\text{tip}} - i_{\text{root}}\big)\frac{y_j}{s},\quad j=1..20. ] Then set (\text{Twi}[1]=0^\circ) (root plane hinge).

5) Lofting the 3D Wing for Previews

Given the normalized perimeter ((\bar{x},\bar{y})) (TE→upper→LE→lower→TE), we scale and twist each section about the quarter‑chord (x_{\text{pivot}}=0.25):

Shift section to pivot origin: (x_c = \bar{x} - 0.25).
Scale to local chord (c_j) (inches): (X_s = x_c,c_j,; Y_s = \bar{y},c_j).
Rotate by (\theta_j=\text{Twi}[j]\cdot\pi/180): [ \begin{bmatrix} Y \ Z \end{bmatrix} = \begin{bmatrix} \cos\theta_j & -\sin\theta_j \ \sin\theta_j & \cos\theta_j \end{bmatrix} \begin{bmatrix} X_s \ Y_s \end{bmatrix}. ]
Spanwise coordinate for the whole perimeter at station (j): (S=y_j) (inches).

The arrays (S, Y, Z) generate a fast wireframe 3D PNG used as the dataset’s render_png field.

6) Planform Integrals & Derived Metrics

Treat Dis/Cho as samples over the half‑span ([0,s]) in inches. We integrate with the trapezoidal rule, then convert to SI for storage.

Wing area (full wing): [ S_{\tfrac{1}{2}} = \int_0^s c(y),dy ;\approx; \operatorname{trapz}(\text{Dis},\text{Cho})\quad [\text{in}^2], \qquad S_{\text{full}} = 2,S_{\tfrac{1}{2}}. ] Convert: (S_{\text{full (m}^2)} = S_{\text{full}}\cdot(0.0254)^2).
Mean Aerodynamic Chord (full wing): [ \text{MAC} = \frac{2}{S_{\text{full}}} \int_{-s}^{s} c(y)^2,dy = \frac{4}{S_{\text{full}}} \int_0^s c(y)^2,dy. ] We integrate on the half‑span (inches), then convert MAC to meters.
Aspect Ratio (full span (b=2s\cdot 0.0254) meters): [ \text{AR} = \frac{b^2}{S_{\text{full (m}^2)}}. ]
Polar‑derived metrics (if a polar is found):
- (C_{l,\max}=\max C_l) at (\alpha_{C_{l,\max}}).
- (C_{d,\min}=\min C_d) at (\alpha_{C_{d,\min}}).
- ((L/D){\max} = \max(C_l/C_d)) at (\alpha{(L/D)_{\max}}).
- Small‑angle lift slope and zero‑lift angle (linear fit on (\alpha\in[-5^\circ,5^\circ])): [ C_l \approx m,\alpha_{\deg} + b ;\Rightarrow; C_{l_\alpha};[\text{per rad}] = m\cdot \frac{180}{\pi}, \quad \alpha_{0L};[^\circ] = -\frac{b}{m}. ]
- Also stored as objective‑style scores:
  - score_min_cd = min(C_d)
  - score_max_cl = max(C_l)
  - score_max_ld = max(C_l/C_d)

If a polar is not found, these fields are NaN; geometry is still fully populated.

7) Station Count & Units

Stations: always 20 over the half‑span (keeps compatibility with legacy builders).
Units: dataset stores SI (dis_m, chord_m, span_m, area_m2, mac_m). Inches are used internally during generation for readability and then converted.

8) Image Preview Column

Each wing includes a 3D wireframe PNG (render_png) created from the lofted (S,Y,Z) arrays:

Section loops at every station,
~14 spanwise polylines to suggest the surface,
Isometric view (elev (20^\circ), azim (35^\circ)),
Title string with span, root/tip chords, and taper.

This renders directly in the Hugging Face Dataset viewer.

9) Why These Look Like Transport Wings

Aspect ratio typically in the 7–11 range (after area settles) due to sampled spans/cords.
Taper (0.25\to 0.50) and washout (-6^\circ\to -2^\circ) are characteristic of transport wings aimed at cruise efficiency and benign stall.
Quarter‑chord pivot is the standard torsion axis.
Schrenk chord smooths the planform compared to pure linear taper, approximating more elliptical loading.

10) Worked Example (Representative Draw)

Let (s=100) in, (c_{\text{root}}=30) in, (\lambda=0.35 \Rightarrow c_{\text{tip}}=10.5) in, stations=20.
Twist endpoints: (i_{\text{root}}=1.0^\circ), (i_{\text{tip}}=-4.0^\circ), then (\text{Twi}[1]=0^\circ).

Mid‑span chord (y=50) in: [ c_{\text{trap}}(50) = 30 + (10.5-30)\cdot 0.5 = 20.25\text{ in},\quad c_{\text{ell}}(50) = 30\sqrt{1-0.5^2} \approx 25.98\text{ in}, ] [ c(50) \approx \tfrac{1}{2}(20.25+25.98) \approx 23.11\text{ in}. ]

If (S_{\text{full}} \approx 5000;\text{in}^2 \Rightarrow S_{\text{full}} \approx 3.226;\text{m}^2) and full span (b=200) in (=5.08) m, then: [ \text{AR} = \frac{b^2}{S} \approx \frac{(5.08)^2}{3.226} \approx 8.0. ]

MAC comes from the (c(y)^2) integral and is often in the (0.3\text{–}0.5) m range here.

11) What Makes Each of the 500 Unique?

Airfoil choice (≈50 samples per foil) → geometry & polar behavior differ.
Planform: each wing draws a new ((s,;c_{\text{root}},;\lambda)) → different area, AR, MAC.
Twist: each wing draws ((i_{\text{root}}, i_{\text{tip}})) → different load tendency.
Performance summaries: objective‑style scores ((\min C_d), (\max C_l), (\max C_l/C_d)) and the (\alpha) at which they occur differ per wing.

Notes for Objective‑Conditioned Training

To bias toward a given objective at training time:

Condition on objective ∈ {min Cd, max Cl, max Cl/Cd} and airfoil (name or perimeter).
Use the scalar scores as targets (e.g., regress score_min_cd) or form ranking pairs within the same airfoil.
Optionally post‑select the top‑k wings per airfoil by the chosen objective as exemplar targets.