Modern Adaptation of Prandtl's Classic Lifting-Line Theory

The classical solution to Prandtl's well-known lifting-line theory applies only to a single lifting surface with no sweep and no dihedral. However, Prandtl's original model of a finite lifting surface has much broader applicability. A general numerical lifting-line method based on Prandtl's model is presented. Whereas classical lifting-line theory is based on applying the two-dimensional Kutta-Joukowski law to a three-dimensional flow, the present method is based on a fully three-dimensional vortex lifting law. The method can be used for systems of lifting surfaces with arbitrary camber, sweep, and dihedral. The accuracy realized from this method is shown to be comparable to that obtained from numerical panel methods and inviscid computational fluid dynamics solutions, but at a small fraction of the computational cost