Scale dependence in hydrodynamic regime for jumping on water.

Momentum transfer from the water surface is strongly related to the dynamical scale and morphology of jumping animals. Here, we investigate the scale-dependent momentum transfer of various jumping organisms and engineered systems at an air-water interface. A simplified analytical model for calculating the maximum momentum transfer identifies an intermediate dynamical scale region highly disadvantageous for jumping on water. The Weber number of the systems should be designed far from 1 to achieve high jumping performance on water. We design a relatively large water-jumping robot in the drag-dominant scale range, having a high Weber number, for maximum jumping height and distance. The jumping robot, around 10 times larger than water striders, has a take-off speed of 3.6 m/s facilitated by drag-based propulsion, which is the highest value reported thus far. The scale-dependent hydrodynamics of water jumpers provides a useful framework for understanding nature and robotic system interacting with the water surface.