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How does the NACA aerofoil math work?

asked by Tobias Schmidt · 2026-05-24
Standard NACA 4-digit formula, untouched since NASA TR-460 (1933). A 4-digit code like `2412` encodes:

- digit 1 = maximum camber, as a percentage of chord (here: 2%)
- digit 2 = position of maximum camber, in tenths of chord (here: 4 → 40%)
- digits 3–4 = maximum thickness, as a percentage of chord (here: 12%)

Thickness distribution: `yt(x) = 5·t·(0.2969·√x – 0.1260·x – 0.3516·x² + 0.2843·x³ – 0.1015·x⁴)`

Camber line: piecewise quadratic, switching at x = p (camber position).

Upper + lower surfaces = camber line ± (thickness rotated to camber tangent).

The generator samples 128 points along the chord, builds a closed contour, normalises it to your chord length, then hands it to the morph engine as the L profile (and the R profile too, if you didn't ask for a morph).

References: NACA Report 460 (Jacobs et al., 1933), or any modern RC-plane textbook.

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