On the existence of optimum propellers

Abstract

For most problems in hydrodynamics we have by experience sufficient information about the existence of a solution. In fact hydrodynamic problems usually reduce to the solution of a boundary value problem or of an integral equation of some well known type. In section 5.6 however we discussed already the nonexistence of an optimum propeller of a class of rotating screw propellers for which the rotational velocity was left free. This phenomenon becomes more complicated in the case of unsteady propulsion where the base motion or the added motion or both can have an infinite number of degrees of freedom. As we mentioned in the preface the nonexistence of an optimum motion of a class of propellers, does not mean that there are no propulsive systems with a high efficiency in that class. It only states that it is not possible by using some algorithm to find a propulsive system of which the efficiency is better than or equal to the efficiency of any other system of the class.