Thin Airfoil Theory Calculator
A cambered airfoil with α_L0 = −2° at 5° angle of attack gives a section lift coefficient of 0.767636; on a wing of aspect ratio 8 it falls to about 0.61.
Symmetric airfoils 0°; cambered airfoils negative, e.g. −2° for NACA 2412.
0.767635897862506
Full answer, then cut to fewer decimals (not rounded):
- 0.767635897862506
- 0.76763589786250
- 0.7676358978625
- 0.767635897862
- 0.76763589786
- 0.7676358978
- 0.767635897
- 0.76763589
- 0.7676358
- 0.767635
- 0.76763
- 0.7676
- 0.767
- 0.76
- 0.7
- Finite-wing lift slope a = a₀/(1 + a₀/πeAR)
- 5.026548246 per rad
- Finite-wing slope
- 0.0877298169 per degree
- Wing lift coefficient C_L
- 0.6141087183
- Induced drag coefficient C_L²/(πeAR)
- 0.01500550674
- Circulation Γ = ½Vc c_l (Kutta–Joukowski)
- 28.78634617 m²/s
- Centre of pressure (symmetric airfoil)
- 25 % chord
Step-by-step solution
- c_l = 2π(α − α_L0) = 2π × (5° − (-2°)) × π/180 = 0.7676358979
- a = 2π ÷ (1 + 2π/(πeAR)) = 5.026548246 per rad
- C_L = a(α − α_L0) = 0.6141087183
Thin Airfoil Theory Formula
c_l = 2π(α − α_L0), a = a₀/(1 + a₀/(πeAR))
Kutta–Joukowski L′ = ρV∞Γ, so Γ = ½V∞ c c_l
Worked Example
A cambered airfoil (α_L0 = −2°) at 5° on a wing of aspect ratio 8:
- c_l = 2π(α − α_L0) = 2π × (5° − (-2°)) × π/180 = 0.7676358979
- a = 2π ÷ (1 + 2π/(πeAR)) = 5.026548246 per rad
- C_L = a(α − α_L0) = 0.6141087183
Finite-wing slope: 0.0877298169 per degree · Wing lift coefficient C_L: 0.6141087183 · Induced drag coefficient C_L²/(πeAR): 0.01500550674 · Circulation Γ = ½Vc c_l (Kutta–Joukowski): 28.78634617 m²/s · Centre of pressure (symmetric airfoil): 25 % chord
GATE tip
Symmetric airfoils have α_L0 = 0 and the aerodynamic centre and centre of pressure at quarter chord. Cambered airfoils keep the aerodynamic centre at c/4 but the centre of pressure moves with α.
More Aerodynamics Calculators
-
Induced Drag Calculator
C_Di = C_L² / (π e AR)
AR = b²/S; elliptic loading e = 1, induced angle αᵢ = C_L/(πAR)
Example: A wing at C_L = 0.6 with aspect ratio 8 and elliptic loading: Induced drag coefficient C_Di = 0.0143239.
-
Boundary Layer Calculator
Laminar: δ = 5x/√Reₓ, c_f = 0.664/√Reₓ
δ* = 1.7208x/√Reₓ, θ = 0.664x/√Reₓ; turbulent δ = 0.37x/Reₓ^0.2, c_f = 0.0592/Reₓ^0.2
Example: Air at 10 m/s, 0.5 m from the leading edge (ν = 1.46 × 10⁻⁵ m²/s): Boundary-layer thickness δ = 4.272 mm.
-
Pitot Tube Calculator
V = √(2(p₀ − p)/ρ)
subsonic M = √((2/(γ−1))[(p₀/p)^((γ−1)/γ) − 1]); supersonic: Rayleigh formula p₀₂/p₁(M₁)
Example: A low-speed pitot reading 1000 Pa dynamic pressure in sea-level air: Airspeed V = 40.4061 m/s.
Frequently asked questions
Where does 2π come from?
Thin airfoil theory models the airfoil as a vortex sheet satisfying the Kutta condition; the result is a lift slope of 2π per radian, about 0.11 per degree.
Why is the finite-wing slope lower?
Downwash reduces the effective angle of attack. The slope tends to 2π only as aspect ratio becomes infinite.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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Scientific Converters. (2026, October 15). Thin Airfoil Theory Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/thin-airfoil-calculator/
IEEE
Scientific Converters, "Thin Airfoil Theory Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/thin-airfoil-calculator/