airfoil-aerodynamics

name	airfoil-aerodynamics
description	Airfoil aerodynamics — lift and drag, thin airfoil theory, NACA sections, angle of attack, stall, Cl vs α curves, boundary layer, induced drag, finite wing theory, Prandtl lifting line.
metadata	{"priority":7,"promptSignals":{"phrases":["airfoil","aerofoil","NACA","lift coefficient","angle of attack","stall","thin airfoil","Cl","Cd"],"minScore":3}}

Airfoil Aerodynamics — Complete Skill

Airfoil Geometry (NACA 4-Digit)

NACA XYZZ: X = max camber/c ×100%, Y = location of max camber /c ×10, ZZ = max thickness/c ×100% NACA 2412: 2% camber at 40% chord, 12% thick NACA 0012: symmetric (zero camber), 12% thick

Lift curve slope (thin airfoil theory): dC_L/dα = 2π per radian = 0.1097 per degree (theoretical; experimental ≈ 0.1 per degree for symmetric)

Thin Airfoil Theory

Cambered Airfoil (2D, Incompressible)

C_L = 2π(α - α_L0) α_L0 = zero-lift angle (negative for cambered airfoils) For NACA 4-digit: α_L0 ≈ -2πε/chord_factor (ε = max camber ratio)

Pitching moment about quarter-chord: C_M,c/4 = -π/2 × (camber terms) = constant with α (aero center at c/4 for thin airfoil) Aero center = point where C_M is independent of α = 25% chord (subsonic, thin)

NACA Airfoil Data

Typical Performance (Re = 3×10⁶)

NACA 0012: C_L,max ≈ 1.52 at α = 16°; C_D0 ≈ 0.006; stall abrupt NACA 4412: C_L,max ≈ 1.65; α_L0 ≈ -4°; better stall behavior NACA 2412: C_L,max ≈ 1.55; C_D,min ≈ 0.006; α_L0 ≈ -2.1° NACA 23012: C_L,max ≈ 1.72; low C_M; used in wing sections

High-lift devices: Plain flap (20°): ΔC_L ≈ 0.3; flap camber only Split flap (40°): ΔC_L ≈ 0.5 Fowler flap (30°): ΔC_L ≈ 1.0-1.5 (area increase + camber) Slat + Fowler: ΔC_L ≈ 2.0-3.0 (landing configuration)

Drag Polar

C_D = C_D0 + C_L² / (π e AR) (total drag = profile + induced) C_D0 = zero-lift drag (parasite) e = Oswald span efficiency factor (0.7-0.95 for wings) AR = b²/S = aspect ratio (b = span, S = wing area)

Induced drag: C_Di = C_L² / (π e AR) Minimum at C_L,opt = √(π e AR C_D0) (best L/D condition) (L/D)_max = √(π e AR / (4 C_D0))

Finite Wing — Prandtl Lifting Line

Downwash angle: ε = C_L / (π AR e) [rad] Effective angle of attack: α_eff = α - ε (local AoA reduced by downwash) Induced drag coefficient: C_Di = C_L² / (π e AR)

For elliptic lift distribution: e = 1.0 (maximum efficiency, uniform downwash) Rectangular wing (AR=6): e ≈ 0.85-0.92

3D correction to lift curve slope: a = a₀ / (1 + a₀/(π e AR)) where a₀ = 2D slope (2π), a = 3D slope For AR=8: a ≈ 2π/(1 + 2π/(π × 0.9 × 8)) = 0.083 per degree

Stall and High α

Cl_max: depends on airfoil, Re, surface roughness Leading-edge stall (thin, sharp): abrupt Trailing-edge stall (thick, round): gradual Critical Re: stall behavior changes significantly below Re = 500,000 (laminar bubble)

Glauert compressibility correction (subsonic, M < 0.7): C_L = C_L,incomp / √(1-M²) (Prandtl-Glauert rule) Valid for M < 0.7; breaks down near critical Mach M_cr where flow first reaches M=1 locally

Output

Provide: C_L and C_D at given α [—], (L/D) ratio, α_stall [°], α_L0 [°], induced drag C_Di, Oswald efficiency e, lift curve slope a [/°], zero-lift angle for NACA designation.