A method for determining the camber and twist of a surface to support a given distribution of lift

A graphical method is described for finding the shape (camber and twist) of an airfoil having an arbitrary distribution of lift. The method consists in replacing the lifting surface and its wake with an equivalent arrangement of vortices and in finding the associated vertical velocities. By a division of the vortex pattern into circular strips concentric about the downwash point instead of into the usual rectangular strips, the lifting surface is reduced for each downwash point to an equivalent loaded line for which the induced velocity is readily computed. The ratio of the vertical velocity to the stream velocity is the slope of the surface in the free-stream direction. As an illustration, the shape of the wing consistent with the pressure distribution derived from the two-dimensional theories is found for two wings: a straight elliptical wing and one with 30 degree sweepback. Application of the method to solve the reverse problem - finding the lift distribution over a given surface - is briefly discussed.