An exact solution of the problem of designing an airfoil with a prescribed velocity distribution on the suction surface in a given uniform flow of an incompressible perfect liquid is obtained by replacing the boundary of the airfoil by vortices. By this device, a method of solution is developed, which is applicable both to isolated airfoils and to airfoils in cascade. The conformal transformation of the designed airfoil into a circle can then be obtained and the velocity distribution at any angle of attack computed. Numerical illustrations of the method are given for the airfoil in cascade.

By the assumption that the pressure-volume relation is linear, a method is given for computing the airfoil shape with a prescribed velocity distribution in a potential flow of a compressible nonviscous fluid.

If the prescribed velocity distribution is not theoretically attainable, the method gives a way of modifying the distribution so as to obtain a blade shape.

Includes the Committee's Technical reports no. 1-1058, reprinted in v. 1-37.