Spin-leap performance by cetaceans is influenced by moment of inertia

Cetaceans are capable of extraordinary locomotor behaviors in both water and air. Whales and dolphins can execute aerial leaps by swimming rapidly to the water surface to achieve an escape velocity. Previous research on spinner dolphins demonstrated the capability of leaping and completing multiple spins around their longitudinal axis with high angular velocities. This prior research suggested the slender body morphology of spinner dolphins together with the shapes and positions of their appendages allowed for rapid spins in the air. To test whether greater moments of inertia reduced spinning performance, videos and biologging data of cetaceans above and below the water surface were obtained. The principal factors affecting the number of aerial spins a cetacean can execute were moment of inertia and use of control surfaces for subsurface corkscrewing. For spinner dolphin, Pacific striped dolphin, bottlenose dolphin, minke whale and humpback whale, each with swim speeds of 6-7 m s-1, our model predicted that the number of aerial spins executable was 7, 2, 2, 0.76 and 1, respectively, which was consistent with observations. These data implied that the rate of subsurface corkscrewing was limited to 14.0, 6.8, 6.2, 2.2 and 0.75 rad s-1 for spinner dolphins, striped dolphins, bottlenose dolphins, minke whales and humpback whales, respectively. In our study, the moment of inertia of the cetaceans spanned a 21,000-fold range. The greater moments of inertia for the last four species produced large torques on control surfaces that limited subsurface corkscrewing motion and aerial maneuvers compared with spinner dolphins.