Neutral Energy Cycles for a Vehicle in Sinusoidal and Turbulent Vertical Gusts

Energy can be extracted from natural atmospheric motions, even those with no mean vertical speed component. This procedure is extensively exploited by birds. Natural wind fluctuations can be of the order of 2 m/s. For Unmanned Air Vehicles (UAVs) with flight speeds in the range of 10 m/s, or less than about five times natural wind fluctuations, there is potential for significant energy savings. A flight maneuver in which a vehicle “rides” atmospheric fluctuations so as to complete a cycle at the same speed and altitude as its initial state is defined as an energy neutral cycle. Such a process can be sustained indefinitely while the atmospheric conditions maintain. Neutral energy cycles are developed for a vehicle flying through a vertical gust of sinusoidal shape. Control laws for the lift vector are developed for neutral energy cycles by formulating the problem as a parametric optimization problem with realistic constraints. Results for neutral trajectories for different gust strengths and time periods are shown. Cases are given for control defined by: a locally variable active random input, a sinusoidal input and a sinusoidal input with linearized solution. Results show that the primary parameter for achieving a neutral energy is the magnitude of the maximum lift-to-drag ratio of the vehicle, that must be large. For example at a lift-to-drag ratio of 20, a vehicle can sustain energy neutral cruise in a gust of about 20% of the cruise speed with proper control inputs. An instrumented flight test vehicle of 2.0 m span and 0.48 kg mass has been designed and flown. Flight test results (not available to date) will be used to evaluate the estimates made here and to determine the differences from the analytical model in actual atmospheric conditions with practical constraints.