Optimizing Steady Turns for Gliding Trajectories

Abstract

Dubins planners provide minimum-length planar paths between waypoints for turning constrained vehicles. For a no-thrust or glider aircraft, Dubins paths have been extrapolated to three dimensions by augmenting the planar path with a constant flight-path angle in each path segment. Best-glide flight maximizes the horizontal distance traveled per unit altitude loss, but steeper flight-path angles result in a maximum heading change per unit altitude loss. This paper investigates combinations of bank and flight-path angles yielding maximum ranges for gliding Dubins trajectories. Starting from the extrema flight-path angles usually applied in the literature, it is shown that the maximum range along each flight radial from an initial point (that is, the footprint) is obtained at a maximum glidepath angle for a given turn radius. This result is applied in a novel three-dimensional maximum-range Dubins path. Three-dimensional Dubins examples with different heading constraints are presented. The impact of constraining solutions to a single pair of turning bank and flight-path angles is analyzed.