Variational approach to the problem of optimal propeller design

The aim of this paper is to evaluate the theoretical efficiency of optimal propellers by means of a variational approach; non classical propellers are included in the analysis. A solution to the optimum rotor problem, in the context of propeller vortex theory, was given by Goldstein in 1929; in this paper, a variational formulation of the optimum rotor problem is proposed. The formulation consists into finding a class of functions (the circulation along the blade axis) for which the thrust and drag momentum functionals are well defined; in this class, the functional is proved to be strictly convex and, thus, the global minimum exists and is unique. Some configurations are analysed using the Ritz method: classical straight blade, parabolic blade, elliptical blade; single and multiple blade propellers are compared.