Symmetrical Joukowsky airfoils in shear flow

Problem.The usual two-dimensional theory of airfoils assumes a uniform velocity for points far from the airfoil.There are many applications where this condition is not satisfied.For example near the ground there is a large vertical velocity gradient, and therefore a first approximation to the problem can be obtained by assuming a linear velocity distribution.This has, in fact, been done by H. v. Sanden1 in connection with 0. Lilienthal's experiments in natural wind.However, v. Sanden used a numerical method of integrating the differential equation and carried out the calculation only for a wedge-shaped body.Th. von Karman* suggested to the author to take up this problem again in order to develop a more complete theory.Hence in the * The author wishes to thank Dr. von Karmin for suggesting the problem and his kind interest during the course of the work.