# Toy cars, scaling model helps scientists understand how tires drive over sand

## "Think of bulldozers, excavators, all these things that need to manipulate and move granular material around," researcher Ken Kamrin said. "These aren’t really optimized."

Lab tests proved newly developed math equations can be used to accurately scale the physics of wheel models driving across sand. Photo by MIT

May 31 (UPI) -- Thanks to a new scaling law, scientists can study the physics of tires traveling across sand by analyzing toy car models.

Researchers used scaling laws to study air flow across airplane wings, testing miniature jets in wind tunnels, but this is the first time scaling laws have been developed for studying sand as a transportation medium.

The findings -- published in the journal Physical Review E -- could help engineers design superior bulldozers and tanks, or even a more efficient Mars rover.

"I'm excited that this could be a new tool we can use to design rovers for Mars," Ken Kamrin, an associate professor of mechanical engineering at MIT, said in a news release. "If we had a simulant of Martian soil in the lab, we could do experiments with a wheel shape that we want to test, and then use this scaling law to, with more accuracy, be able to tell you if that wheel would get stuck on Mars."

To scale air flow models, physicists look to scaleable equations that describe how air behaves -- specifically how it acts on an air foil at varying speeds. Similarly, researchers at MIT focused on arithmetic describing granular flow. The resistive force theory includes several equations that describe the resistive force acted on a moving object by a granular medium.

"RFT is not going to predict how sand moves or distributes stress," Kamrin said. "Its sole purpose is to tell how much force is needed to move an object of an arbitrary shape, in a certain direction, through sand."

Kamrin and his colleagues simplified RFT equations by removing dimensions, or units, from the inputs, allowing them to create a scaling law from the theory.

"For example, 'meters' is not a natural length -- it's something we invented," Kamrin said. "If we get rid of all these units, we will be left with the meat, some truth to the system."

To test their scaling law, researchers 3D-printed a large and small version of two wheel shapes, lug and cylindrical, and drove them across a bed of sand in the lab. Lug wheels are designed to dig out pockets of sand as they drive, preventing slippage, while cylindrical wheels move more smoothly across the sands surface, preventing sinkage.

Researchers tested the different wheels at various speeds and under various amounts of weight, and then used their scaling law to see if the miniature models could be used to predict the performance of the larger models.

"Our data followed the predictions," Kamrin said. "The small tests predicted the big tests, to a quantitative degree. We validated many times over the accuracy of the scaling law."