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The Physics of Figure Skating

Let’s break down some of the crucial elements behind figure skating's moves, like the loop, flip, salchow, axel, and lutz.

By
Sabrina Stierwalt, PhD,
February 12, 2018
Episode #273

image of a figure skater jumping in the airFigure skaters not only have to perform incredible feats of human strength and agility, but they also have to push the limits of what is humanly possible while making their movements look easy. Their motions appear graceful and smooth as they hurtle their bodies through the air with nothing but the hard ice below.

As spectators, we take for granted that a figure skating routine will involve multiple jumps which incorporate triple and even quadruple spins in a single jump. Nathan Chen has taken the title of Quad King as the first person to land five quadruple jumps in a single routine and will attempt to match this feat in the 2018 Winter Olympics. Although skaters like Chen can make their sport look easy, executing the perfect jump requires a precise combination of speed, force, vertical velocity, angular momentum, friction, and of course timing. Let’s break down some of these crucial pieces that go into the perfect loop, flip, salchow, axel, or lutz.

Vertical Velocity

A skater’s vertical velocity, or their speed upward into a jump, helps determine how high they can go. Their altitude in turn determines how much time they have in the air before they return back to the ground and thus how much time they have to execute a spin or spins. A skater achieves vertical velocity by extending their leg downward to push down on the ice. The ice in turn pushes back providing a force upward.

The vertical velocity needed to reach a certain height is the same for any skater but the force needed to reach that velocity depends on the size and weight of the skater as well as how long the force is applied to propel the skater upward. Stronger muscles are required to create stronger forces. Skaters typically launch themselves off the ice skaters around 10 miles per hour and reach heights anywhere between one and four feet.

Angular Momentum

Another fundamental physics principle on display in a figure skating jump is the law of conservation of angular momentum. The angular momentum of a skater is the product of their linear momentum and their angular velocity or their rotational speed. Angular momentum works similarly to linear momentum in that spinning (or moving) things like to keep spinning (or moving) until acted on by an outside force. In other words, a larger angular momentum allows a skater to spin faster in the air until she hits the ground.

You may have noticed that skaters tend to begin their jumps with their arms extended but while in the air they draw their arms in toward their body to minimize their size as much as possible. This is because angular momentum must always be conserved without that action from an outside force. If you have a spinning chair, you can try this for yourself at home. Pulling your arms in reduces your rotational inertia so your angular velocity must increase in order to balance out this reduction and ultimately conserve angular momentum. And just like the figure skaters, you can slow yourself down by extending your arms outward again.

Speed

The vertical velocity, angular momentum, and speed all contribute to the ultimate goal for a figure skater which is more time in the air—called hang time—to complete their spins. The laws of physics help us translate a skater’s jump height to time spent in the air. At four feet, skaters have a full second of hang time, but more typical jump heights of one to two feet leave only 0.5 and 0.7 seconds to perform their spins. For comparison, snowboarders and skiers tend to see hang times of as long as three seconds giving them much more time to work with.

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