Head-, tail- and crosswind effects on the maximum range of powered sailplanes with retractable engine

The effects of a constant head-, tail- or crosswind on the maximum range which powered sailplanes with a retractable engine can achieve are treated. The maximum-range flight of this type of vehicle has periodic properties because there are alternating flight phases where the engine is extended or retracted. Optimization of this flight mode which is known as sawtooth flight is a periodic optimal control problem where the best operating conditions of the powered and gliding phase have to be determined. Saw-tooth flight enables a significant increase in the maximum range when compared with the best steady-state cruise. It is shown that wind conditions (head-, tail- or crosswind) have a considerable influence on the achievable maximum range. Solutions of the periodic optimal flight problem were obtained using an efficient optimization method and applying a realistic mathematical model for describing the motion of the vehicle as well as the procedure for extending and retracting the engine.