Optimal patterns of glider dynamic soaring

Abstract

Abstract This paper presents optimal patterns of glider dynamic soaring utilizing wind gradients. A set of three‐dimensional point‐mass equations of motion is used and basic glider performance parameters are identified through normalizations of these equations. In particular, a single parameter is defined that represents the combined effects of air density, glider wing loading, and wind gradient slope. Glider dynamic soaring flights are formulated as non‐linear optimal control problems and three performance indices are considered. In the first formulation, the completion time of one cycle of dynamic soaring is minimized subject to glider equations of motion, limitations on glider flights, and appropriate terminal constraints that enforce a periodic dynamic soaring flight. In the second formulation, the final altitude after one cycle of dynamic soaring is maximized subject to similar constraints. In the third formulation, the least required wind gradient slope that can sustain an energy‐neutral dynamic soaring flight is determined. Different terminal constraints are used to produce basic, travelling, and loiter dynamic soaring patterns. These optimal control problems are converted into parameter optimization via a collocation approach and solved numerically with the software NPSOL. Different patterns of glider dynamic soaring are compared in terms of cycle completion time and altitude‐increasing capability. Effects of wind gradient slope and wind profile non‐linearity on dynamic soaring patterns are examined. Copyright © 2004 John Wiley & Sons, Ltd.