Jumping dynamics of aquatic animals.

Jumping out of water is a phenomenon exhibited by a variety of aquatic and semi-aquatic animals. Yet, there is no common groundwork that clarifies the physical constraints required to jump out of water. In this study, we elucidate the physical conditions required for an animal to jump out of water. More than 100 jumps are analysed over five taxonomic groups. By balancing the power produced by animals with drag-induced dissipation, we expect that maximum jumping height, H, scales with body length, L, as H/ L ∼ L-1/3 ∼ Fr2, where the Froude number, Fr, is a ratio of inertia to gravity. To identify jumping regimes, simplified experiments are conducted by shooting axisymmetric bodies through the water surface. Here, we see a transition in which partial exits scale as H/ L ∼ Fr and complete exits scale as H/ L ∼ Fr2. A bioinspired robotic flapping mechanism was designed to mimic the fast motion of impulsive jumping animals. When exiting water, the robot carries a large volume of fluid referred to as an entrained mass. A theoretical model is developed to predict the jumping height of various water-exiting bodies, which shows that the mass of the entrained fluid relative to the mass of the body limits the maximum jumping height. We conclude that the lack of entrained fluid allows animals to reach extraordinary heights compared to our water-exiting robots.