Analytical solutions for the actuator disk with variable radial distribution of load

Abstract

An analytical method somewhat analogous to finite wing theory has been developed which enables the flow induced by a linearized propeller actuator disk with variable radial distribution of load to be solved in closed form for the first time. Analytical solutions are given for various load distributions including the case of an arbitrary polynomial loading. As in finite wing theory, the case of elliptic loading is exceptionally simple and the induced velocities and stream function are simple expressions of elementary functions. Results are also given for a practical propeller load distribution with finite hub. The method can also be used to solve a wide range of analogous electromagnetic problems.