Lifting-line theory

Summary

Lifting-line theory is Prandtl's model of a straight wing of finite span and large aspect ratio in an ideal fluid. The wing is replaced by a single vortex line along the span whose circulation varies, together with a sheet of trailing vortices shed behind it. The trailing vortices induce a downwash that lowers the effective angle of attack, and this leads to Prandtl's lifting-line equation for the circulation. The theory explains induced drag and shows that, among planar wings of given span and lift, an elliptic lift distribution gives the least induced drag.