AbstractThe existence of a (global) optimal controlu* 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 speedWand direction tHw. Fast, accurate numerical procedures based on elementary geometry and the solution of a fixed‐point equation are derived for the calculation ofu* 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