Wave-Slope Soaring of the Brown Pelican
We theoretically assess the energy savings associated with wave-slope soaring of the brown pelican over near-shoaling ocean surface waves. The steady, constant altitude flight of a pelican is analyzed as a control. The airflow induced by a passing wave, or the “wave-induced wind,” is theoretically analyzed for shallow water solitary waves. These waves are assumed to be well described by the KdV equation. We use potential flow theory to describe the wave- induced wind. Using a regular expansion of the Stokes stream function and the Green’s function for Laplace in 2D with Dirichlet boundary conditions, we obtain integral expressions for the horizontal and vertical components of the wave-induced wind in a frame of reference moving with the wave. The theory results in expressions wherein provided with the amplitude and period of an incoming swell, horizontal and vertical components of the wave-induced wind in a frame of reference moving with the wave are produced. Wave-slope soaring flight is analyzed over near-shoaling solitary waves on size scales corresponding to wind swell, with amplitude of 1m and period of 10s. We find an upper bound benefit of 57.6% decrease in required mechanical power output as compared with flight out of ground effect and 52.4% benefit as compared with standard ground effect flight. The theory in this work define sufficient evidence that wave- slope soaring could become a viable strategy for energy efficient flight of unmanned autonomous vehicles (UAVs).