Drag reduction and locomotory power in dolphins: Gray's paradox revealed.

Abstract

For 88 years, biologists and engineers have sought to understand the hydrodynamics enabling dolphins to swim at speeds seemingly beyond their energetic capabilities, a phenomenon known as Gray's paradox. Hydromechanical models calculating the drag of swimming dolphins estimated power requirements for sustained high-speed swimming, which were physiologically impossible. Using an uncrewed aerial vehicle, we calculated the total power of free-ranging dusky dolphins (Lagenorhynchus obscurus) at speeds from 0.9 to 6.9 m s-1, deriving drag coefficients (Cd) and drag. Our results showed that the Cd decreased exponentially with speed, reducing drag by up to 89% at speeds >2 m s-1, with an additional 17% reduction during porpoising (>4.0 m s-1). At 6.9 m s-1, drag was 32 N, with a power of 15.8 W kg-1, nearly identical to the mass-specific allometric prediction for the maximum aerobic capacity of other mammals and physiologically possible. The Cd at speeds >2.5 m s-1 indicated reduced turbulence in the boundary layer around the dolphin's body, thereby reducing drag. The ability of dusky dolphins to swim at sustained high speeds resulted from an exponential decrease in Cd, which was further reduced by porpoising, thereby explaining the low drag and locomotory power that resolved Gray's paradox.