OPTIMAL FLIGHT STRATEGY IN A GIVEN SPACE-DISTRIBUTION OF LIFTS WITH MINIMUM AND MAXIMUM ALTITUDE CONSTRAINTS

Abstract

In recent years, several researchers have examined the various problems connected with the optimization of the flight strategy for a sailplane soaring cross-country. Some of the most significant work can be found in the references. From the point of view of the theorist in optimization, these problems have a perfectly well defined objective. Indeed, it is always the total time whjch must be minimized, either because the sailplane is involved in a contest or because, when lift is due to thermals alone, the useful time for distance flight is limited to the day time period during which the sun produces thermals. 0n the other hand, an aspect of the problem which does not seem to have been completely resolved at the present time, is the atmospheric model that should be used. Some attempts have been made to model the shape of a thermal. We shall assume concentrated lift. We shall see later that this assumption is justified in the framework of the problem that we are treating. Simple rules have been derived for finding the global optimal flight strategy in the case of unequally spaced lifts of variable strength taking into account altitude constraints. The assumption that the locations and strengths of the lift regions are known in advance makes the practical usefulness of the results questionable during an actual flight. However it is now possible to determine optimal flight strategies in a set of given situations that are often encountered during a f'light. The importance of giving due  consideration to the altitude constraints is evident. From various tests conducted by the authors in a conmunity of experienced competition pilots it appears that the rules given here are at best intuitively approximated. Improvements to the theory should take into account the size and structure of the thermals in order to allow for dolphin flight segments. This seems possible only if a numerical model is set up. It implies that no simple rules for optimality will be obtained in that case but that a catalog of optimal strategies in a given set of situations could be derived.