  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.
