Lifting line theory

Lifting-line theory is Prandtl’s model of a finite wing or blade as a single bound vortex of spanwise-varying circulation Gamma(y), shedding a trailing vortex sheet whose downwash reduces the effective angle of attack. The Kutta-Joukowski relation L’ = rho U Gamma gives local lift, and the integro-differential lifting-line equation links circulation to induced angle. It predicts induced drag scaling as C_L^2 / (pi AR e) and the loss of lift slope with aspect ratio. In ship work it is the classical basis for propeller blade design, treating each blade as a radially loaded lifting line before lifting-surface and panel refinements.