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thin-airfoil-section-theorylisted

Use when you must compute the section lift and the quarter-chord pitching moment of a thin cambered airfoil from its camber line: decompose the camber slope into the glauert-sine-series coefficients A0, A1 and A2 by trapezoid quadrature over the theta transform x = (1 - cos(theta))/2, then recover the zero-lift angle alpha_L0, the section lift coefficient cl = 2*pi*(alpha - alpha_L0), the quarter-chord pitching-moment coefficient cm_c4 = (pi/4)*(A2 - A1) and the center-of-pressure location x_cp/c = 1/4 - cm_c4/cl, for a NACA 4-digit mean line, a polynomial camber line or sampled camber stations. Produces the closed-form analytic section aerodynamics that anchor the numerical panel and viscous section tools. Trigger: glauert coefficients, zero lift angle, section pitching moment, camber line analysis, thin airfoil section.
ashfordeOU/aero-agent-skills · ★ 0 · AI & Automation · score 78
Install: claude install-skill ashfordeOU/aero-agent-skills
# Thin Airfoil Section Theory (aerodynamics/airfoil/thin-airfoil-section-theory) Use when you must turn a thin airfoil's camber line into its analytic section aerodynamics: the Glauert sine-series coefficients of the camber slope, the zero-lift angle, the section lift curve and the quarter-chord pitching moment. This leaf computes the closed-form thin-airfoil solution in pure stdlib Python, with trapezoid quadrature used only for the Fourier integrals over the theta transform. It pairs with aerodynamics/airfoil/airfoil-geometry, which produces the mean camber line ordinates and slope consumed here (both leaves can be cross-checked on the same NACA 2412 camber line), and it supplies the analytic anchor that the numerical and viscous section layers beneath it verify against. Section coefficients are derived here from the camber line; the finite-wing slope leaf aerodynamics/drag-polars/lift-curve-slope instead consumes alpha_zero and the section slope as given inputs for its aspect-ratio and sweep corrections, so it is the complement, not the duplicate. ## Domain quick reference - Glauert theta transform: x = (1 - cos(theta))/2 maps the chord x in [0, 1] onto theta in [0, pi], clustering stations at the leading edge where the camber slope varies fastest. All integrals run over this theta grid. - Camber slope input routes: NACA 4-digit mean line (m, p) with dz/dx = (2m/p^2)(p - x) for x <= p and dz/dx = (2m/(1-p)^2)(p - x) for x >= p (zero at x = p, matching the airfoi