| Dynamic soaring in the atmospheric boundary layer of a vertical variation of horizontal winds over arbitrary terrain offers small unmanned aerial vehicle gliders the ability to greatly expand mission operations while also extending endurance. Wandering albatrosses and other oceanic birds have provided the original evidence of the ability to exploit vertical wind gradients through their long distance circumnavigation flights using periodic maneuvers with cycles of upwind, crosswind, and downwind phases orchestrated to extract sufficient energy from the environment to allow perpetual flight. Dynamic soaring analysis presents additional challenges to the established theories of aerodynamic flight dynamics, due to the presence of wind vector fields that can vary their magnitude and direction in spatial and temporal dimensions. Preserving a consistency with typical flight analysis including static soaring, an air-relative wind-aligned / wind-fixed reference frame is proposed for dynamic soaring analysis, in particular for the computation of kinetic energy. Novel contributions of this present work include a logical progression of seven heuristic assumptions leading to a singular conclusion regarding the appropriate usage of airspeed for kinetic energy computation. Also, a concept of fundamental equivalence between spatial and temporal gradients experienced by a flight vehicle is presented, including the mechanism by which both generate the same accelerating reference frame and apparent dynamic soaring thrust. A novel reverse kinematics simulation is introduced, built on a parametric trajectory definition and analysis via Frenet-Serret equations. A series of dynamic soaring steady-state scenarios are presented and used to amplify the spatial and temporal gradient equivalence concept. The familiar glider sink polar curve is used in two novel ways: first, the curve shift procedures typically employed to account for changes in glider weight for uniform wind flight are proposed as also applicable to account for the apparent weight change during dynamic frame acceleration; second, the sink polar curve is transformed into a sink polar surface representing a family of curves with the additional dimension of weight inflation ratio. These novel insights and observations are intended to provide a solid foundation for present and future dynamic soaring analysis across a spectrum of interdisciplinary research. |
