Computing an Aircraft's Gliding Range and Minimal Return Altitude in Presence of Obstacles and Wind

In the event of a total loss of thrust, a pilot must identify a reachable landing site and subsequently execute a forced landing. To do so, they must estimate which region on the ground can be reached safely in gliding flight. We call this the gliding reachable region (GRR). To compute the GRR, we employ an optimal control formulation aiming to reach a point in space while minimizing altitude loss. A simplified model of the aircraft's dynamics is used, where the effect of turns is neglected. The resulting equations are discretized on a grid and solved numerically. Our algorithm for computing the GRR is fast enough to run in real time during flight, it accounts for ground obstacles and wind, and for each point in the GRR it outputs the path to reach it with minimal loss of altitude. A related problem is estimating the minimal altitude an aircraft needs in order to glide to a given airfield in the presence of obstacles. This information enables pilots to plan routes that always have an airport within gliding distance. We formalize this problem using an optimal control formulation based on the same aircraft dynamics model. The resulting equations are solved with a second algorithm that outputs the minimal re-entry altitude and the paths to reach the airfield from any position while avoiding obstacles. The algorithms we develop are based on the Ordered Upwind Method and the Fast Marching Method.