Barnes, J., "Semi-Empirical Vortex Step Method for the Lift and Induced Drag Loading of 2D or 3D Wings," SAE Technical Paper 975559, 1997, doi:10.4271/975559.
The familiar “vortex step” method for calculating the lift slope, spanwise distribution of lift, and aerodynamic center position is reviewed and enhanced to more accurately locate the wing aerodynamic center and to accommodate arbitrary spanwise variations of sweep, chord, twist, camber, flaps, and dihedral. Lifting and downwash line position and shape are adjusted to account for semi-empirical effects of planform and airfoil properties. Vector and matrix methods are then applied to solve for the spanwise distribution of lift normal to the spar, or for the required twist to obtain a prescribed loading. For induced drag, an “apparent downwash” method is proposed to reveal the negative induced drag of winglets. Then, predicted 2D and 3D wing characteristics are compared to test data. Finally, the methods are applied to the design and analysis of unique wing configurations.