ecopus/transport-wings-500

Transport Wings 500

A dataset of procedurally generated, aircraft-style wings built from fixed airfoil cross-sections with associated polars. Each row includes planform geometry (spanwise stations, chord, twist), airfoil perimeter coordinates, derived metrics (S, AR, MAC, Clmax, Cdmin, (L/D)max, Cla, α0L), and a 3D preview image (render_png).

This dataset is intended for training agents to design wings conditioned on objective (min Cd / max Cl / max Cl/Cd) and chosen airfoil.

How the 500 Wing Samples Are Generated

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

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1) Inputs & Reproducibility

• Airfoil geometry: Each airfoil file contains two columns $x,yx,\; y$ forming a closed perimeter ordered TE → upper → LE → lower → TE.
  • On load, $xx$ is normalized to $[0,1][0,1]$; the perimeter is rotated so the first point is closest to the trailing edge $1,01,0$ and the upper surface comes first.
• Polars (optional): QBlade/XFOIL exports with $\alpha ,C_l,C_d,C_m\backslash alpha,\; C\_l,\; C\_d,\; C\_m$.
  • Files are matched to airfoils by flexible filename heuristics.
  • Polars are parsed (3–4 numeric columns), deduplicated in $\alpha \backslash alpha$, and sorted by $\alpha \backslash alpha$.
• Random seed: We use np.random.default_rng(42) so all 500 wings are reproducible bit-for-bit.

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

We use 20 stations (indices or 'slices') along the half-span:

$$\text{Dis}[j]=y_j=\frac{j-1}{19}s,j=\mathrm{1..20.}\backslash text\{Dis\}[j]\; =\; y\_j\; =\; \backslash frac\{j-1\}\{19\}\backslash ;\; s,\backslash quad\; j=1..20.$$

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3) Chord Distribution: Schrenk’s Approximation

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

• Linear (trapezoid) chord:

$$c_{\text{trap}}(y)=c_{\text{root}}+(c_{\text{tip}}-c_{\text{root}})\frac{y}{s}\mathrm{.}c\_\{\backslash text\{trap\}\}(y)\; =\; c\_\{\backslash text\{root\}\}\; +\; (c\_\{\backslash text\{tip\}\}\; -\; c\_\{\backslash text\{root\}\})\backslash ,\backslash frac\{y\}\{s\}.$$

• Elliptic surrogate:

$$c_{\text{ell}}(y)=c_{\text{root}}\sqrt{1-{\left(\frac{y}{s}\right)}^2}\mathrm{.}c\_\{\backslash text\{ell\}\}(y)\; =\; c\_\{\backslash text\{root\}\}\backslash sqrt\{1\; -\; \backslash left(\backslash frac\{y\}\{s\}\backslash right)^2\}.$$

• Schrenk chord at each station:

$$c(y)=\frac{1}{2}[c_{\text{trap}}(y)+c_{\text{ell}}(y)]\mathrm{.}c(y)\; =\; \backslash tfrac\{1\}\{2\}\backslash left[c\_\{\backslash text\{trap\}\}(y)\; +\; c\_\{\backslash text\{ell\}\}(y)\backslash right].$$

A small clamp prevents pathological tips for extreme tapers:

$$c(y)\leftarrow \max \text{\hspace{0.17em}⁣}(c(y),0.25\cdot {\min }_y{c}_{\text{trap}}(y))\mathrm{.}c(y)\; \backslash leftarrow\; \backslash max\backslash !\backslash big(c(y),\backslash ;0.25\backslash cdot\backslash min\backslash nolimits\_y\; c\_\{\backslash text\{trap\}\}(y)\backslash big).$$

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

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4) Twist (Washout) Distribution

With sampled endpoints $i_{\text{root}}i\_\{\backslash text\{root\}\}$ and $i_{\text{tip}}i\_\{\backslash text\{tip\}\}$, define a linear twist:

$$\text{Twi}[j]=i_{\text{root}}+(i_{\text{tip}}-i_{\text{root}})\frac{y_j}{s},j=\mathrm{1..20.}\backslash text\{Twi\}[j]\; =\; i\_\{\backslash text\{root\}\}\; +\; \backslash big(i\_\{\backslash text\{tip\}\}\; -\; i\_\{\backslash text\{root\}\}\backslash big)\backslash frac\{y\_j\}\{s\},\backslash quad\; j=1..20.$$

Then set $\text{Twi}[1]=0^{\circ }\backslash text\{Twi\}[1]=0^\{\backslash circ\}$ (root plane hinge).

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5) Lofting the 3D Wing for Previews

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

1. Shift section to pivot origin: $x_c=\bar{x}-0.25x\_c\; =\; \backslash bar\{x\}\; -\; 0.25$.
2. Scale to local chord $c_{j}c\_j$ (inches): $X_s=x_c{c}_j,Y_s=\bar{y}{c}_{j}X\_s\; =\; x\_c\backslash ,c\_j,\backslash ;\; Y\_s\; =\; \backslash bar\{y\}\backslash ,c\_j$.
3. Rotate by ${\theta }_j=\text{Twi}[j]\cdot \pi \mathrm{/}180\backslash theta\_j=\backslash text\{Twi\}[j]\backslash cdot\backslash pi/180$:

4. Spanwise coordinate for the whole perimeter at station $jj$: $S=y_{j}S=y\_j$ (inches).

The arrays $S,Y,ZS,\; Y,\; Z$ generate a fast wireframe 3D PNG used as the dataset’s render_png field.

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6) Planform Integrals & Derived Metrics

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

• Wing area (full wing):

$$S_{\frac{1}{2}}={\int }_0^{s}c(y)dy\approx \mathrm{trapz}(\text{Dis},\text{Cho})[{\text{in}}^2],S_{\text{full}}=2S_{\frac{1}{2}}\mathrm{.}S\_\{\backslash tfrac\{1\}\{2\}\}\; =\; \backslash int\_0^s\; c(y)\backslash ,dy\; \backslash ;\backslash approx\backslash ;\; \backslash operatorname\{trapz\}(\backslash text\{Dis\},\backslash text\{Cho\})\backslash quad\; [\backslash text\{in\}^2],\; \backslash qquad\; S\_\{\backslash text\{full\}\}\; =\; 2\backslash ,S\_\{\backslash tfrac\{1\}\{2\}\}.$$

Convert: $S_{{\text{full (m}}^2)}=S_{\text{full}}\cdot (0.0254{)}^{2}S\_\{\backslash text\{full\; (m\}^2)\}\; =\; S\_\{\backslash text\{full\}\}\backslash cdot(0.0254)^2$.

• Mean Aerodynamic Chord (full wing):

$$\text{MAC}=\frac{2}{S_{\text{full}}}{\int }_{-s}^{s}c(y{)}^{2}dy=\frac{4}{S_{\text{full}}}{\int }_0^{s}c(y{)}^{2}dy\mathrm{.}\backslash text\{MAC\}\; =\; \backslash frac\{2\}\{S\_\{\backslash text\{full\}\}\}\; \backslash int\_\{-s\}^\{s\}\; c(y)^2\backslash ,dy\; =\; \backslash frac\{4\}\{S\_\{\backslash text\{full\}\}\}\; \backslash int\_0^s\; c(y)^2\backslash ,dy.$$

We integrate on the half-span (inches), then convert MAC to meters.

• Aspect Ratio (full span $b=2s\cdot 0.0254b=2s\backslash cdot\; 0.0254$ meters):

$$\text{AR}=\frac{b^2}{S_{{\text{full (m}}^2)}}\mathrm{.}\backslash text\{AR\}\; =\; \backslash frac\{b^2\}\{S\_\{\backslash text\{full\; (m\}^2)\}\}.$$

• Polar-derived metrics (if a polar is found):
  • $C_{l,\max }=\max C_{l}C\_\{l,\backslash max\}=\backslash max\; C\_l$ at ${\alpha }_{C_{l,\max }}\backslash alpha\_\{C\_\{l,\backslash max\}\}$.
  • $C_{d,\min }=\min C_{d}C\_\{d,\backslash min\}=\backslash min\; C\_d$ at ${\alpha }_{C_{d,\min }}\backslash alpha\_\{C\_\{d,\backslash min\}\}$.
  • $(L\mathrm{/}D{)}_{\max }=\max (C_l\mathrm{/}{C}_d)(L/D)\_\{\backslash max\}\; =\; \backslash max(C\_l/C\_d)$ at ${\alpha }_{(L\mathrm{/}D{)}_{\max }}\backslash alpha\_\{(L/D)\_\{\backslash max\}\}$.
  • Small-angle lift slope and zero-lift angle (linear fit on $\alpha \in [-5^{\circ },5^{\circ }]\backslash alpha\backslash in[-5^\{\backslash circ\},5^\{\backslash circ\}]$):

$$C_l\approx m{\alpha }_{\text{deg}}+b\Rightarrow C_{l_{\alpha }}[\text{per rad}]=m\cdot \frac{180}{\pi },{\alpha }_{0L}{[}^{\circ }]=-\frac{b}{m}\mathrm{.}C\_l\; \backslash approx\; m\backslash ,\backslash alpha\_\backslash text\{deg\}\; +\; b\; \backslash ;\backslash Rightarrow\backslash ;\; C\_\{l\_\backslash alpha\}\backslash ;[\backslash text\{per\; rad\}]\; =\; m\backslash cdot\; \backslash frac\{180\}\{\backslash pi\},\; \backslash quad\; \backslash alpha\_\{0L\}\backslash ;[^\{\backslash circ\}]\; =\; -\backslash frac\{b\}\{m\}.$$

• 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.

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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.

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8) Image Preview Column

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

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

This renders directly in the Hugging Face Dataset viewer.

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9) Why These Look Like Transport Wings

• Aspect ratio typically in the 7–11 range (after area settles) due to sampled spans/cords.
• Taper $0.25\to 0.500.25\backslash to\; 0.50$ and washout $-6^{\circ }\to -2^{\circ }-6^\{\backslash circ\}\backslash to\; -2^\{\backslash circ\}$ 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.

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10) Worked Example (Representative Draw)

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

Mid-span chord $y=50y=50$ in:

$$c_{\text{trap}}(50)=30+(10.5-30)\cdot 0.5=20.25\text{ in},c_{\text{ell}}(50)=30\sqrt{1-{0.5}^2}\approx 25.98\text{ in},c\_\{\backslash text\{trap\}\}(50)\; =\; 30\; +\; (10.5-30)\backslash cdot\; 0.5\; =\; 20.25\backslash text\{\; in\},\backslash quad\; c\_\{\backslash text\{ell\}\}(50)\; =\; 30\backslash sqrt\{1-0.5^2\}\; \backslash approx\; 25.98\backslash text\{\; in\},$$

$$c(50)\approx \frac{1}{2}(20.25+25.98)\approx 23.11\text{ in}\mathrm{.}c(50)\; \backslash approx\; \backslash tfrac\{1\}\{2\}(20.25+25.98)\; \backslash approx\; 23.11\backslash text\{\; in\}.$$

If $S_{\text{full}}\approx 5000{\text{in}}^2\Rightarrow S_{\text{full}}\approx 3.226{\text{m}}^{2}S\_\{\backslash text\{full\}\}\; \backslash approx\; 5000\backslash ;\backslash text\{in\}^2\; \backslash Rightarrow\; S\_\{\backslash text\{full\}\}\; \backslash approx\; 3.226\backslash ;\backslash text\{m\}^2$ and full span $b=200b=200$ in $=5.08=5.08$ m, then:

$$\text{AR}=\frac{b^2}{S}\approx \frac{(5.08{)}^2}{3.226}\approx \mathrm{8.0.}\backslash text\{AR\}\; =\; \backslash frac\{b^2\}\{S\}\; \backslash approx\; \backslash frac\{(5.08)^2\}\{3.226\}\; \backslash approx\; 8.0.$$

MAC comes from the $c(y{)}^{2}c(y)^2$ integral and is often in the $0.3\text{–}0.50.3\backslash text\{–\}0.5$ m range here.

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11) What Makes Each of the 500 Unique?

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

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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.