Estimate of loads during wing-vortex interactions by Munk's transverse-flow method

The inviscid, incompressible interaction of a wing with a vortex is studied by use of Munk's transverse-flow method. The method assumes that the loading on the wing is such that the local circulatory flow of the vortex is turned so that the wing and its vortex wake act as a barrier to the flow. This permits the analysis to be carried out by mapping the transverse flowfield into the flow about a circle to find the vorticity distribution in the wake. Closed-form expressions are then derived for the bound circulation in the wind and for the lift and rolling moment induced by the vortex on the encountering wing. Comparisons of the loads predicted by these relationships with those of vortex-lattice theory for a flat wing of a rectangular planform indicate that they accurately represent the various parameters when the aspect ratio of the encountering wing is less than about two. When flat rectangular wings of higher aspect ratios are considered, some sort of correction is needed. Examples are then presented to illustrate some applications of the results.