Bio-inspired energy-harvesting mechanisms and patterns of dynamic soaring.

Albatrosses can make use of the dynamic soaring technique extracting energy from the wind field to achieve large-scale movement without a flap, which stimulates interest in effortless flight with small unmanned aerial vehicles (UAVs). However, mechanisms of energy harvesting in terms of the energy transfer from the wind to the flyer (albatross or UAV) are still indeterminate and controversial when using different reference frames in previous studies. In this paper, the classical four-phase Rayleigh cycle, includes sequentially upwind climb, downwind turn, downwind dive and upwind turn, is introduced in analyses of energy gain with the albatross's equation of motions and the simulated trajectory in dynamic soaring. Analytical and numerical results indicate that the energy gain in the air-relative frame mostly originates from large wind gradients at lower part of the climb and dive, while the energy gain in the inertial frame comes from the lift vector inclined to the wind speed direction during the climb, dive and downwind turn at higher altitude. These two energy-gain mechanisms are not equivalent in terms of energy sources and reference frames but have to be simultaneously satisfied in terms of the energy-neutral dynamic soaring cycle. For each reference frame, energy-loss phases are necessary to connect energy-gain ones. Based on these four essential phases in dynamic soaring and the albatrosses' flight trajectory, different dynamic soaring patterns are schematically depicted and corresponding optimal trajectories are computed. The optimal dynamic soaring trajectories are classified into two closed patterns including 'O' shape and '8' shape, and four travelling patterns including 'Ω' shape, 'α' shape, 'C' shape and 'S' shape. The correlation among these patterns are analysed and discussed. The completeness of the classification for different patterns is confirmed by listing and summarising dynamic soaring trajectories shown in studies over the past decades.