Trajectory Generation Methods for a Turnback Maneuver After a Total Loss of Thrust During Takeoff

In the general aviation community, the “impossible turn” refers to a maneuver where—when there is a total loss of thrust during takeoff, the pilot immediately turns back and attempts to land on the departed runway. Most flight instructors advise against performing such a maneuver due to the risk of stalling and the fact that there may not be enough altitude to turn back. Despite the warning, pilots still attempt the maneuver—and there have been both tragic accidents and incredible survival stories. However, at airports with mountainous terrain or in urban areas, the turnback might be a preferred option compared to other alternatives. This fact drives ongoing research among the general aviation community. The community is developing a decision process on whether the maneuver should be attempted and also the specifics of how the maneuver should be flown. In this paper, we attempt to answer the question: Is it possible to automate the maneuver? Ween vision an onboard system showing whether the aircraft will be able to reach the runway. If the pilot chooses to turn back, the autopilot can be engaged, and the turnback will be flown autonomously. Alternatively, if the pilot chooses to fly the turnback manually, the system could be treated as a flight director. In other words, the system would output the command bars. The turnback problem is formulated as an optimal trajectory generation problem that minimizes altitude loss with terminal constraints on crossrange position and track angle. We first present the full nonlinear optimal control problem in order to gain initial insights of the maneuver. However, the computation time for the full problem is too slow to run in real time. We then propose two near-optimal algorithms with characteristics similar to the full optimal solution, yet the computation times are significantly faster, enabling the algorithms to be run in real time. The algorithms are based on concatenations of optimal segments. The algorithms consist of both offline and online trajectory computations. Nondimensional equations of motion were also employed in order to save both offline computation time and onboard storage space. We test both algorithms in the receding horizon manner and show that both algorithms are robust against changes in the initial conditions.