Frontiers Physics World  June 2021

Researchers unveil the physics of the skipping stone

Hop, skip and jump The physics of skipping stones could be used to understand how flying vehicles behave when they impact water upon landing. (Courtesy: Stewart Nimmo/CC BY-SA 4.0)

The physics that allows spinning flat stones to skip across the surface of water has been analysed by researchers in China. They used theoretical models and simple experiments to identify three key factors underlying the process, with their findings potentially leading to important insights into the dynamics of aircraft and spacecraft that land on water (Physics of Fluids 33 043316). 

By imparting the right combination of throwing angle, speed, and spin, a flat stone will bounce several times on water before sinking. In their study, Jie Tang at Southwest Jiaotong University and colleagues constructed a mathematical model of stone skipping, which incorporated two key effects. The first was the Magnus effect, whereby the trajectory of a rotating object in a fluid is deflected – an effect that footballers use to send a ball on a curved trajectory. The other was the gyro effect, in which a spinning object tends to maintain a steady axis of rotation and travel in a straight line.

To verify their model’s predictions, the team did a simple experiment involving a spinning aluminium disc that was fitted with a navigation module to measure its spin and trajectory during flight. Their set-up enabled a tight control over the disc’s speed, rate of spin and angle of approach to the water’s surface. Through a series of experiments, the team measured how variations in each of these values affected the disc’s skipping dynamics. The researchers conclude that the upward acceleration of the disc – determined by its velocity and angle of approach to the water – is critical. If it is over 4 g (four times the gravitational acceleration) the disc will skip. Yet at 3.8 g, the disc will instead “surf”, skimming along the water’s surface at an oscillating angle, but not bouncing.

Also important is how the gyro effect can guarantee the stability of the disc’s angle of approach to the water, creating more favourable conditions for continuous bouncing. For spin rates lower than 18 rotations per second, the Magnus effect dominates, and the disc will veer off to the left or right, depending on its direction of spin. Above this rate, the gyro effect dominates, and the disc will continue in a straight path.

Tang’s team hopes that the results could improve our understanding of how flying vehicles behave when impacting water upon landing. This could enable engineers to design better vehicles and flight paths: ensuring both minimal damage to valuable equipment, and better safety for passengers.

Sam Jarman