Flight trajectory optimization of a sailplane after rope break during an aerotow takeoff

A study was performed to obtain an optimized return trajectory for a sailplane after a rope break failure during an aerotow launch procedure. The performance of the sailplane was simulated using the equations of motion for quasi-steady flight in a timestepping routine based on published aerodynamic polar data. The flight trajectory was discretized into six distinct phases which simulated the sailplane taking off under normal aerotow and performing a series of turns after a rope break failure to land in the runway. A gradient-based interior point optimization algorithm was implemented to the simulated trajectory considering the glide velocity, bank angles, and runway offset angle to determine the minimum rope break altitude where a successful return could be theoretically produced. Two sailplane models, the SGS 1-26 and SGS 2-33, were considered. The minimum rope break altitudes resulted in 55 ft and 80 ft AGL at moderate bank angles for the SGS 1-26 and the SGS 2-33, respectively. The optimized trajectories were determined to be unsafe to practically fly due to turn recoveries occurring at low altitudes near the ground. Nevertheless, the theoretical rope break limits obtained provide an insight into feasible and safe trajectories that can be performed at lower failure altitudes than the commonly practiced decision altitude of 200 ft.