The "Convex-Combination Approach": a Geometric Approach to the Optimization of Sailplane Trajectories

Abstract

Three different problems encountered in the sport of soaring are discussed: First, as an introduction, the classical "MacCready problem" is reviewed; this is concerned with the determination of the best cruise speed between columns of rising air under cumulus clouds. Next, a new solution concept is presented for the "optimal dolphin soaring problem." This is the problem of determining the best (varying) speed through regions with varying vertical atmospheric velocities. Finally, some new ideas are discussed which make new solutions possible to the "optimal zigzagging problem," which is the problem of whether, and if so how, to make use of favorable regions with upward atmospheric velocities which are present aside of the track to be flown.