Variational Analysis and Euler Equations of the Optimum Propeller Problem

The problem of the optimum propeller with straight blades was first solved by Goldstein; in this paper, a variational formulation is proposed in order to extend the solution to non-planar blades. First, we find a class of functions (the circulation along the blade axis) for which the thrust and the aerodynamic drag moment are well defined. In this class, the objective functional is proved to be strictly convex and then the global minimum exists and is unique. Then we determine the Euler equation in the case of a general blade and show that the numerical results are consistent with the Goldstein’s solution. Finally, some numerical results with the Ritz method are presented for optimum propeller blades