Analytic solution of the thickness problem of a rectangular wing in steady subsonic flow

Abstract

An analytic solution of the thickness problem of a rectangular wing with parabolic airfoil section in three-dimensional flow is presented. The free-air solution is obtained by integrating the equation of the axial perturbation velocity. The Prandtl-Glauert rule can be used to derive the subsonic solution. Parts of the free-air solution are verified by taking the limit of the axial peturbation velocity on the model surface as the wing span goes to infinity. Pressure coefficients are studied for a selected wing geometry in the flow field. The solution of the thickness problem of a rectangular wing in a rectangular wind tunnel is derived using the free-air solution and the method of images.