Periodic optimal control for range maximization of powered sailplanes with retractable electric motor

The maximum-range flight of a powered sailplane with a retractable electric motor is treated as a periodic optimal control problem. The periodic nature of the maximum-range flight, known as saw-tooth mode, is due to the high drag when the motor is extended and the low drag when the motor is retracted. An optimization treatment based on energy considerations is performed to develop analytical solutions and to deepen the insight into the physical mechanism underlying the superiority of the saw-tooth mode. This is complemented by a treatment using a modeling based on point mass dynamics and an efficient optimization method to construct solutions for maximum-range saw-tooth flight. As a main result concerning the range performance, it is shown that the maximum range achievable with optimal saw-tooth flight is considerably larger than the greatest range possible with the best steady-state cruise.