Methods for Computing Minimum-Time Paths in Strong Winds

This paper describes methods for computing minimum-time flight paths at high altitudes in the presence of strong horizontal winds. The first method shows how to calculate nonlinear feedback ("dynamic programming") solutions for minimum-time flight paths. To do this the Zermelo Problem for arbitrary winds is extended from a flat-Earth model to a spherical Earth model as a two-state problem (latitude and longitude) with one control (heading angle). Many minimum-time paths are calculated backward from New York's John F. Kennedy International Airport and San Francisco International Airport to points in the continental United States. Then the optimal heading angle and the minimum-time can be found by interpolation given the current latitude and longitude using an interpolant created by Delaunay triangulation. The second method, derived in prior work, is based on an analytical neighboring optimal control solution that computes neighboring optimal heading commands as a function of the winds along a nominal flight path. As an example, minimum-time paths to New York and San Francisco are determined for the actual jet stream winds on 14 February 2001 at 36 kft.