On the Existence of Optimum Propulsion

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 5.7 however we discussed already the non-existence of an optimum propeller of a class of screw propellers for which the rotational velocity was left free. This phenomenon becomes more complicated in the case of unsteady propulsion where for a given base motion the added motion can have an infinite number of degrees of freedom. As we mentioned in the Preface of this book, the non-existence of an optimum motion for 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.