SUMMARYThis paper presents optimal patterns of glider dynamic soaring utilizing wind gradients. A set of threedimensional 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.

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SUMMARYThis paper studies optimal powered dynamic soaring flights of unmanned aerial vehicles (UAVs) that utilize low-altitude wind gradients for reducing fuel consumptions. Three-dimensional point-mass UAV equations of motion are used, and linear wind gradients are assumed. Fundamental UAV performance parameters are identified through the normalization of the equations of motion. In particular, a single wind condition parameter is defined that represents the combined effect of air density, UAV wing loading, and wind gradient slope on UAV flight. An optimal control problem is first used to determine bounds on wind conditions over which optimal powered dynamic soaring is meaningful. Then, powered UAV dynamic soaring flights through wind gradients are formulated as non-linear optimal control problems. For a jetengined UAV, performance indices are selected to minimize the average thrust required per cycle of powered dynamic soaring that employs either variable or constant thrust. For a propeller-driven UAV, in comparison, performance indices are selected to minimize the average power required per cycle of powered dynamic soaring with either variable or constant power. All problem formulations are subject to UAV equations of motion, UAV operational constraints, proper initial conditions, and terminal conditions that enforce a periodic flight. These optimal control problems are converted into parameter optimization with a collocation method and solved numerically using the parameter optimization software NPSOL. Analytical gradient expressions are derived for the numerical solution process. Extensive numerical solutions are obtained for a wide range of wind conditions and UAV performance parameters. Results reveal basic features of powered dynamic soaring flights through linear wind gradients.