Minimum‐time turn trajectories to fly‐to points

The existence of a (global) optimal control u* is established which ensures the execution of a constant‐altitude, minimum‐time flight trajectory to a specified fly‐to point, given the aircraft maximum performance turn radius and the wind speed W and direction tHw. Fast, accurate numerical procedures based on elementary geometry and the solution of a fixed‐point equation are derived for the calculation of u* and the associated optimal trajectory (x*, y*). An example is given and the application of these results to the real‐time solution of the case where the aircraft roll rate is also incorporated into the flight dynamics is discussed.