Optimum Design of Ducted Propellers

In design method of open propellers, the distribution of circulation that gives the highest propulsive efficiency was obtained by Goldstein by satisfying the requirement of ``Betz's condition'' in late 1920s. On the other hand, any theoretical optimum design method of ducted fan has not been developed yet though the use of ducted fans by UAV, VTOL, etc., has increased in recent years. We developed the design method that gives the distribution of circulations with highest efficiency in the configuration of ``ducted propeller.'' The key point of this design method is that it is mathematically proven that the solution obtained by this method is the unique global optimum solution. In addition, the optimized blades here had wide tip chord as expected.