Scale dependence in hydrodynamic regime for jumping on water

Inspired by semi-aquatic animals, such as water striders and fisher spiders, that can exhibit a unique locomotion mechanism involving jumping on water, the authors find the scale dependency of water jumping performance and verify it with a theoretical model and robots with improved jumping performance. 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.

Automated summary

Inspired by semi-aquatic animals, the authors investigate the scale dependency of water jumping performance and verify it through experiments with robots. They find that momentum transfer from the water surface is strongly related to the dynamical scale and morphology of jumping animals. A simplified analytical model is used to calculate the maximum momentum transfer and identifies an intermediate dynamical scale region that is highly disadvantageous for jumping on water. The study also presents a large water-jumping robot that achieves the highest reported take-off speed using drag-based propulsion.