Range Maximization by Saw-Tooth Mode Optimization for Motor Gliders with Retractable Engines

Abstract

The range maximization of a motor glider with a retractable engine is treated as a periodic optimal control problem.  The periodicity of the optimal range flight, known as saw-tooth mode, is due to cycles that consist of alternating climbing phases with the engine extended and gliding phases with the engine retracted.  It is shown that the maximum range of the optimal saw-tooth flight mode is considerably larger than the greatest range achievable with the best steady-state cruise.  The time histories of the state and control variables are determined as well as the optimal altitude interval of the maximum-range saw-tooth flight mode.  Further, results on the achievable range are presented for saw-tooth cycles with altitude intervals that differ from the optimal value.  An efficient optimization method is applied to solve the periodic optimal control problem, using realistic models of the motor-glider dynamics and of the procedure for extending and retracting the engine.