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Lifting-Line Theory

Sequence of Expressions

Theorem

Let

\rho

be the fluid density,

\mathbf{V}_{\infty}

be the uniform free-stream velocity (magnitude

V

), and

C

be the airfoil contour. Define the circulation

\Gamma

around

C

as the line integral of the tangential component of the velocity

\mathbf{V}

relative to the free stream: \n

\Gamma = \oint_C \mathbf{V} \cdot d\mathbf{l}

\nThen, the lift force per unit span,

L'

, acting on the airfoil

C

is given by the Kutta-Joukowski Theorem:\n

L' = \rho V \Gamma