Prandtl Lifting-Line Wing Circulation Calculator

Classical Aerodynamics: Calculate bound vortex circulation ($\Gamma_0$), downwash ($w_0$), induced angle of attack ($\alpha_i$), and 3D lift curve slope ($a$).

Wing Geometry & Flight State

Wingspan $b$ (m):

Wing Reference Area $S$ (m²):

Freestream Speed $V_\infty$ (m/s):

Air Density $\rho_\infty$ (kg/m³):

Airfoil Section Properties

Geometric Angle $\alpha$ (°):

2D Section Slope $a_0$ (/rad):

Zero-Lift Angle $\alpha_{L0}$ (°):

Circulation & Aerodynamic Performance

Total Lift Force ($L$)

-- N

Lift Coeff C_L: --

Peak Circulation ($\Gamma_0$)

-- m²/s

Aspect Ratio AR: --

Downwash Velocity ($w_0$)

-- m/s

Induced α_i: -- °

3D Lift Curve Slope ($a$)

-- /rad

In degrees: -- /°

Lifting-Line Insights:

• $a = \frac{a_0}{1 + a_0 / (\pi AR)}$: Finite wing tip vortices reduce effective angle of attack ($\alpha_{eff} = \alpha - \alpha_i$).

• Elliptic circulation $\Gamma(y) = \Gamma_0 \sqrt{1 - (2y/b)^2}$ produces uniform downwash $w_0 = \frac{\Gamma_0}{2b}$ across the span.

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Prandtl Lifting-Line Wing Circulation Calculator

Wing Geometry & Flight State

Airfoil Section Properties

Circulation & Aerodynamic Performance

Frequently Asked Questions