airfoil-geometrylisted

# NACA Airfoil Geometry (aerodynamics/airfoil/airfoil-geometry) Use when the task is classic NACA airfoil geometry: designation decode, thickness and camber formula computation, and derived geometric properties. ## Domain quick reference - NACA 4-digit MPXX: M = max camber in percent chord (m = M / 100), P = camber position in tenths chord (p = P / 10), XX = max thickness in percent chord (t = XX / 100). - Thickness half-ordinate (NACA Report 460; public domain): y_t = (t / 0.2) * (0.29690 * sqrt(x) - 0.12600 * x - 0.35160 * x^2 + 0.28430 * x^3 - 0.10150 * x^4). Max half-thickness t / 2 at x = 0.3; the polynomial leaves a small trailing-edge thickness (0.0105 * t) that is faired to a sharp edge in practice. - Mean camber line: for x <= p, y_c = (m / p^2) * (2 * p * x - x^2); for x >= p, y_c = (m / (1 - p)^2) * (1 - 2 * p + 2 * p * x - x^2). Slope dy_c / dx = (2 * m / p^2) * (p - x) for x <= p, and (2 * m / (1 - p)^2) * (p - x) for x >= p; zero at x = p. - Upper surface = y_c + y_t, lower surface = y_c - y_t. - Leading-edge radius: r_le = 1.1019 * t^2 (fraction of chord). - Enclosed section area per unit span: A = 2 * integral(y_t dx) = 0.68508 * t (chord^2); independent of camber. - NACA 5-digit: design cl = first digit * 0.15 (23012 -> 0.3), camber position = second digit * 5 percent chord (23012 -> 15 percent), thickness = last two digits percent. Mean line 230: m = 0.15, k1 = 15.957. Third digit 1 marks a reflexed mean line. - NACA 6-series: 65