Optimal Flight Paths for Soaring Flight

The problem of optimizing sailplane flight paths to achieve maximum cross-country speeds with zero net altitude loss is considered. A variational formulation is chosen that includes three modes of cross-country soaring: thermalling, essing, and straight dolphining. Optimal solutions are obtained numerically for various atmospheric vertical velocity distributions using quadratic approximations to the polars of two sailplanes representing current high performance Standard and Open Class designs. Implications of the solutions are discussed; especially the optimality of any one mode when more than one mode is possible and the advance knowledge of the atmosphere required in order to choose an optimal speeds-to-fly policy. Particularly important is the result that the maximum cross-country speed through an element of the atmosphere capable of sustaining straight dolphin flight is attained with a speeds-to-fly policy identical to that of some equivalent interthermal flight.