Impact force reduction by consecutive water entry of spheres

TL;DR

This study experimentally investigates how consecutive water entries of spheres can reduce or increase impact forces, revealing the influence of cavity dynamics and timing, and introducing the Matryoshka number to classify regimes.

Contribution

It introduces the Matryoshka number to categorize impact regimes and demonstrates how cavity dynamics affect impact force reduction or increase.

Findings

Impact force on the second sphere can be reduced by up to 78%.

In one regime, impact force increases by over 400%.

The impact behavior depends on cavity evolution and timing.

Abstract

Free-falling objects impacting onto water pools experience a very high initial impact force, greatest at the moment when breaking through the free surface. Many have intuitively wondered whether throwing another object in front of an important object (like oneself) before impacting the water surface may reduce this high impact force. Here, we test this idea experimentally by allowing two spheres to consecutively enter the water and measuring the forces on the trailing sphere. We find that the impact acceleration reduction on the trailing sphere depends on the dynamics of the cavity created by the first sphere and the relative timing of the second sphere impact. These combined effects are captured by the non-dimensional `Matryoshka' number, which classifies the observed phenomena into four major regimes. In three of these regimes, we find that the impact acceleration on the second sphere is reduced by up to 78\% relative to impact on a quiescent water surface. Surprisingly, in one of the regimes, the force on the trailing sphere is dramatically increased by more than 400\% in the worst case observed. We explain how the various stages of cavity evolution result in the observed alterations in impact force in this multi-body water entry problem.