The application of Goldstein's theory to the practical design of airscrews

Abstract

A recent paper on the Vortex theory of screw propellers, by Dr. S. Goldstein in the Proceedings of the Royal Society, contains a solution of the problem of the potential flow past a body consisting of a finite number of coaxial helicoids of infinite length but finite radius moving through a fluid with constant velocity. The results are applied to the case of an ideal airscrew having a finite number of blades and a particular distribution of circulation along the blade for small values of the thrust. The present paper contains a summary of Goldstein's results, which are then applied to the airscrew problem by a method which leads to formulae differing from the standard formulae of the "Vortex theory" by the addition of a factor to the formulae for the components of inflow; the value of this factor may be obtained from a chart embodying the results of Goldstein's calculations. The formulae of the Vortex theory are developed simultaneously from first principles by au analogous method which differs somewhat from the method used by its originator and brings out clearly the close analogy with the Prandtl theory of a monoplane wing; they also represent the limit of the Goldstein formulae for the case of an infinite number of blades.