Figuring Out Figure Skating

How do Olympic figure skaters do triple axels and quadruple toe loops? It's all about angular momentum, vertical velocity, and conservation of angular momentum. NSF-funded sports scientist Deborah King, from the Department of Exercise and Sports Sciences at Ithaca College explains, using high-speed, high-resolution video of Olympic hopeful Rachael Flatt.

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LESTER HOLT, Anchor: Every four years, we watch the stakes for Olympic figure skaters get higher, as they try to increase rotation in the air with their triple axels and quadruple toe loops. How do they do that? It’s a scientific principle that we asked Olympic hopeful Rachael Flatt and Deborah King, a sports scientist funded by the National Science Foundation, to help explain.

HOLT: Figure skaters make it look so easy: leaping off the ice…rotating through the air…and landing in a graceful arc. But make no mistake about it: figure skating is one of the most demanding of all the events at the Winter Olympics. For 17-year-old Rachael Flatt, the demands of training for the Olympics have to compete with other demands.

RACHAEL FLATT, U.S Figure Skating Team: I basically head to the rink at around six o'clock. I ice skate from six thirty to seven fifteen. And then, um, I go to school from seven thirty until about twelve thirty. And then, um, basically from there I go straight back to the rink.

HOLT: When she’s on the ice, this AP Physics student might want to consider the science that goes into her every jump. To see this science in detail, Rachael agreed to train in front of a special high-speed camera called the Phantom Cam. It has the astonishing ability to capture her jumps at rates of up to 1500 frames per second.

RACHAEL FLATT: It's very cool watching myself on the phantom camera. You get to see every phase of the jump. And it's pretty incredible just to be able to see every aspect of it, you know, where exactly the placement of your arm is, and where my head is, you know, uh, just everything is really cool.

HOLT: We brought the footage to Deb King, a Professor of Sports Science at Ithaca College, and an advisor to United States Figure Skating.

DR. DEBORAH KING, Ithaca College: A figure skating jump is a really complicated skill that combines a lot of different motions in it. They need to really optimize a lot of different conditions in terms of speed, force, vertical velocity, um, generating angular momentum, and put it all together in a package - with just the right timing - to execute the skill.

HOLT: Deb watched the Phantom Cam footage to explain what Rachael needs to get height and speed in one of her jumps. The first factor is Angular Momentum.

DEBORAH KING: In figure skating, angular momentum determines how fast you are going to be able to rotate in a jump in the air. So when you do a spin, if you generate more angular momentum, you have the potential to spin faster.

HOLT: Going into her jump, Rachael generates angular momentum by pushing off the ice with her foot. Pushing off the ice also generates Vertical Velocity, which will help get Rachael high enough to do her spins.

DEBORAH KING: The vertical velocity comes from producing forces from their jump during takeoff. This is sort of where action/reaction comes into play. As they contract their muscles and very powerfully extend their leg, they are pushing down against the ice. The ice will create a force up on them, which gives them vertical velocity. And it's pretty much the laws of accelerated motion, or projectile motion: that the more velocity you have at takeoff - and this is vertical velocity - the more she can keep going fast, straight up, the higher she'll jump.

HOLT: When Rachael spins on the ice, she exploits a law of physics to rotate faster and faster – almost as if by magic. How does she increase her speed while she’s spinning? The answer lies in her arms. When Rachael first starts to spin with her arms extended, she rotates slowly. But as she pulls her arms in closer and closer, she starts to rotate faster and faster. Rachel’s following an important law of physics – the “Law of Conservation of Angular Momentum.” You can’t go to jail for breaking this law. In fact, you can’t break it at all.

DEBORAH KING: As you get a smaller body position, your speed goes up. If you get a bigger body position, your speed goes down. So they react in opposite directions.

HOLT: Back in her office, Deb King spins on an office chair to make the same point.

DEBORAH KING: What I'm going to do is, when I'm spinning, I'm going to go from a very open position to a tight position. You'll see my speed change. So let's give that a try. [She spins around on chair.] So this is pretty fast. Slower. Fast. Slow. Fast. And I'm going to keep going, and the only way to stop is when I’m going to put my foot down and grab the table. I'm really dizzy right now. [Laughs]

HOLT: If Rachael can keep her body straight, and hold her limbs in close, she’ll achieve a higher rate of speed. But it’s not as easy as it looks.

RACHAEL FLATT: It's hard to stay as straight as possible. With every force, you know, you’re basically being pulled out everywhere, um, so it's easier to stay in when you're crossed, with your hands and your legs. It just makes the jump more efficient.

HOLT: But no matter how much attention she pays to the science of her jump, Rachael’s road to the Olympics will depend on her making skating look effortless.

RACHAEL FLATT: You never know what's going to happen. The unexpected is, you know, it's amazing. [Laughs]

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Figure Skating