Theoretical Solutions for Finite-Span Wings of Arbitrary Shapes Using Velocity Singularities

This pa per presents a new method of solution for the nite-span wings of arbitrary shapes, which avoids thedifculties of the previous methods. This method uses velocity singularities in the Trefftz plane to derive the contributions in the solution of the circulation distribution caused by the changes in the spanwise variation of the wing chord and incidence. The new functions derived for these contributions contain both natural and forced smmetry and antisymmetry terms (which are absent in the previo us metho ds) and thus represent a correct mathematical modeling of the physicalproblems that lead to highly accurate theo retical solutions. The methodhas been validatedby comparison with thesolutions obtained by Rasmussen and Smithand Carafoli for rectangular and tapered wings of uniform incidence, and with the panel method results by Katz and Plotkin. Accura te and efcient theoretical solutio ns of aeronautical interest are then obtained for wings with asymmetric incidence distributionscaused by sy mmetric a nd antisymmetric de ections of apsand ailerons and for wings with curved leading and trailing edges and variable incidence, which are difcult to model in current panel methods