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Researchers investigate physics of stone skipping

Splash Lab study has implications for water toys, naval crafts, basic physics understanding

When it comes to skipping stones, kids know to look for the perfect rock. But according to a team of researchers from the School of Engineering, the Naval Undersea Warfare Center in Newport and Utah State University, it is elastic balls that they should be after.

In a paper published Feb. 4, the team of researchers offered new insights into the fluid-solid interactions that send “skipping stones” and balls jumping across water surfaces. 

The result could have implications on anything from pool toys to water skis to inflatable boats for the navy, but the main purpose behind the project was the “advancement of scientific understanding,” said Allan Bower, professor of engineering  and member of the research team behind the paper.

In the case of this experiment — part of which took place at Utah State University’s “Splash Lab”, which is run by Tadd Truscott — the scientific understanding came with a hearty dose of fun. “It’s definitely the most fun thing I’ve ever done academically,” said Jesse Belden, researcher at the Naval Undersea Warfare Center and another author of the paper.

“There is something about skipping stones that has always intrigued people,” he added.

Though the physics of skipping stones across water has long been studied, it “turns out nobody has looked at how squishy objects bounce off water surfaces,” Bower said.

The team found that elastic balls “automatically adopt a favorable shape” when they impact the water, deforming into the flattened discs that rock-skippers know to look for, Bower said. The water then pushes back on the ball and sends it into the next skip — or, in the team’s experiments, the next 60 skips. 

Hydrodynamic forces — more generally known as lift, the mechanism responsible for airplane flight — cause this phenomenon, Bower said. The ball exerts a downward force on the water, and — per Newton’s laws — the fluid pushes back.

Bower explained that this force is very different from the surface tension that enables insects to walk on water, but similar to basilisk lizards running across and seaplanes landing on water surfaces.

The team constructed the balls from a silicone rubber called “Dragon Skin,” produced by a company called Smooth-On and available to anyone online, said Michael Jandron, another researcher at the Naval Undersea Warfare Center. The team then used launchers to project the balls at specific velocities and angles and recorded the trajectories using high-speed cameras.

The team was especially curious about how the elasticity of the material would affect the ball’s deformation and ability to skip. By changing the stiffness, radii and density of the balls, the researchers found that “softer is always better for skipping,” Bower said.

Belden and Jandron, who study fluid dynamics, worked with Bower, an expert in solid dynamics, to create a computer model that could extrapolate further results — for example, to test a 10-foot diameter ball, Jandron said.

The team “had a great collaboration,” Belden said. “We had (a) couple students, professors and research scientists. Everybody had different strengths, and all were integral in resolving the problem.”

But Bower was quick to point out that one does not have to take high-speed images of rocks to have fun experimenting. “Anything you pick up is so cool,” he said as he started spinning one of the small, scientific contraptions on his desk. “There should be a class on what’s cool, though that might not look good for the resume.”


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