Asymptotic Solution to the Rayleigh Problem of Dynamic Soaring

TL;DR

This paper provides an analytical and numerical framework for understanding the optimal flight trajectories of albatrosses during dynamic soaring, revealing that in thin wind shears, small angle arcs are most efficient, challenging previous assumptions.

Contribution

It introduces a new analytical model for dynamic soaring that accounts for shear thickness, showing optimal trajectories differ from traditional views and aligning with GPS data.

Findings

Optimal trajectories in thin shears involve small angle arcs.

Albatrosses act like flying sailboats, maximizing efficiency crosswind.

The framework applies broadly to energy extraction in complex winds.

Abstract

Albatrosses can travel a thousand kilometers daily over the oceans. This feat is achieved through dynamic soaring, a non-flapping flight strategy where propulsive energy is extracted from horizontal wind shears. Dynamic soaring has been described as a sequence of half-turns connecting upwind climbs and downwind dives through the surface shear layer. We analytically and numerically investigate the aerodynamically optimal flight trajectory for varying shear thicknesses. Contrary to current thinking, but consistent with GPS recordings of flying albatrosses, in thin shears the optimal trajectory is composed of small angle arcs. Essentially, the albatross is a flying sailboat, sequentially acting as sail and keel, and most efficient when remaining crosswind. Our analysis constitutes a general framework for dynamic soaring, and more broadly energy extraction in complex winds.