Flight trajectory optimization of sailplane after rope break

A study was performed to characterize an optimum return trajectory for a sailplane after a rope-break failure during an aerotow launch procedure. The performance of an SGS 1-26E sailplane was simulated using the equations of motion for quasi-steady flight in a time-stepping routine and published aerodynamic polar data. A gradient-based optimization algorithm was implemented using the simulated trajectory considering the glide velocity, bank angles, and runway offset angle to determine the minimum rope-break altitude from which a successful return could be theoretically produced. The SGS 1-26E sailplane was used in a flight-test campaign for empirical turn modeling and validation of the performance simulation. The minimum altitude where a return trajectory and downwind runway landing could be successfully completed after a rope-break event was observed to be 76.4 ft above ground level. A headwind and crosswind presence was observed to decrease the minimum rope-break altitude with increasing wind velocity up to a critical value, after which rope-break altitudes began to increase. These minimum rope-break altitudes serve as a theoretical indication that safe trajectories can be performed at lower failure altitudes than the commonly practiced decision altitude of 200 ft for certain wind conditions.