OPTIMAL DOLPHIN SOARING AS A VARIATION PROBLEM

Abstract

In this paper we have solved the problem of minimum flight time in dynamic soaring by the application of calculus of variations. The sailplane ls assumed to go from one stationary flight condition to another continuously so that the polar equation is satisfied all the time along the course. Consequently all possible transients are ignored. The optimal airspeed policy is derived by applying a quadratic polar equation approximation. The application of the 'laminar bucket' approximation would lead to a cubic root expression of the optimal airspeed i. e. no difficulties would have arisen, if it had been applied. We, however, apply the quadratic polar equation approximation, because it can be fitted to a sailplane's polar data quite satisfactorily, and because the square root operation is more easily effected than the cubic root operation in manual numerical calculations. We treat the special case of slnusoldal lift variation and give two examples, the first of which clearly demonstrates the optimal dolphin motion.