Revisiting the combinatorics of lifting line and 2D vortex lattice theory

摘要

This work revisits analyses of lifting line theory by A.R. Collar from 1958, bringing to bear some modern tools and techniques. The 2D vortex lattice model is also considered. Interesting combinatorial properties and simplified expressions for terms are presented, a simplified proof of model convergence shown, extension of the convergence properties to elliptical and arbitrary wing planforms is demonstrated, and approximations provided. An alternative proof of the optimality of constant downwash is presented. Modern automated theorem proving techniques are employed in confirming the combinatorial results.