concept

Zermelo navigation problem

The classical problem posed by Ernst Zermelo in 1931: find the minimum-time path for a craft of limited own-speed crossing a moving current or wind field. The answer is almost never a straight line — the optimal heading must keep changing, sometimes aiming well away from the destination in order to catch a favourable stream first. The degenerate case is the most interesting one: as own-speed goes to zero the craft loses all horizontal steering authority, and the entire art of navigation collapses into a single decision — WHICH moving layer to sit in, and letting that layer do the carrying.