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Physicist analyzes ice skating

Henry Gens | Thursday, November 21, 2013

While Charlotte Elster’s day job is researching at the forefront of theoretical nuclear physics, her self-described “early day” job is figure skating. A physics professor at Ohio University, Elster gave a lecture Wednesday about the intersection of her two passions: the physics of ice skating.   

As a physicist, Elster began with the most fundamental aspect of ice skating: the ice itself. Specifically, she addressed some common misconceptions about the reason ice is slippery, the exact cause of which was not confirmed until the early 2000s with Scanning Tunneling Microscopy (STM).

“[In 1859] Michael Faraday postulated that a thin film of liquid covers the surface of the ice, even at temperatures well below freezing,” Elster said. “Michael

Faraday had no STM, and no high-tech equipment, so it’s amazing what he said. All of this was neglected.”

One of the reasons people believe liquid exists on the surface of the ice is because the pressure caused by the weight of a person concentrated on the skate blade causes the ice to melt, which turns out not to be the case, Elster said. The effect of this pressure on the temperature on the ice for a 50-kilogram person is only roughly 0.2 degrees Celsius.

Elster said frictional melting could be a potential explanation, but found that rough calculations could only produce a 2.1 degree Celsius change in the temperature of the ice, not enough to melt ice in rinks that are generally kept between minus-seven and minus-eight degrees Celsius.

The real cause of ice’s low frictional coefficient is the gradient of the crystalline structure of the individual molecules in a block of ice, Elster said. In the middle of the ice the same amount of material is present around an arbitrary crystal in the structure; whereas molecules toward the surface don’t have such a uniform environment and are looser. Macroscopic objects, such as skate blades, cannot cut through this microscopic layer to the more solid one, which is the cause of ice’s slipperiness, she said.

Elster said the skater has a different perspective on this phenomenon.

“If you put your entire skate perpendicular to the direction you want to go you can just push off this way,” Elster said. “So basically, your forward force is only your push force times sine of theta, so you don’t get everything. So this lies in the plane of the ice. You, as the skater, don’t want to lie in the plane of the ice. So, standing on the blade, you actually have another angle, namely the angle of the lean of your blade. If you’re 90 degrees, you’re just standing. Nothing happens.”

Forward force, and hence much of movement on the ice, is essentially a function of these two angles, she said.

“The interesting thing is that the mass of the skater never shows up,” Elster said. “That means that the little girl or the little boy and the 200-pound hockey player with all the gear have the same rules going.”

The next stages of movement, the turns and fancy footwork, involve lots of torque and angular momentum, Elster said.  

“You have a body box, which is your shoulder and your hips,” she said. “Ideally, if they stay straight you have a perfectly straight alignment. As soon as you twist, you create a torque.”

From the skater’s view, a large part of spins and footwork is the fine control of motion, making small circles and keeping near-perfect balance. From the physicist’s view, this makes it attractive to model as a rigid body problem, Elster said.  

After discussing turns and footwork, Elster did mathematical plots of projectile motion, examining different flight paths and times based on velocities and flight angle. She said ice skaters, regardless of initial velocity, angle and skill do not have a lot of time in the air.

“They are below one second in the air,” she said. “The time in the air is actually not that great, so you have to do a lot of stuff in that short time.”

As with spinning, the success of the jump depends on the smallest of physical details. Often, ice skaters will know if a jump will end poorly before they’re even in the air, she said.

“The point is, in the jumps you have to make perfectly sure that you always jump up straight so that your rotation is on an axis perpendicular to the ice,” Elster said. “If you rotate on an axis non-perpendicular to the ice, the chance is that you’ll land bad.”

She ended by talking about the most famous of all jumps in ice skating, the triple axel, and whether a quadruple axel is possible. Elster’s conclusion was that it probably was not possible because of the short airtime constraint, which, according to the physics, cannot be altered by anything in the jump itself.
“That’s what we do as physicists,” Elster said. “We put in numbers and check it out. If in doubt, find out.”

Contact Henry Gens at hgens@nd.edu