Kasey Wagoner is an assistant professor of physics at NC State who is interested in the oldest light in the universe – the cosmic microwave background – as well as the physics of sports, including Olympic sports. He wrote this piece examining the physics of figure skating jumps. You can also read his explanation of the dynamic kickoff in football. You can find more information, including calculations and python code, on his Substack (https://substack.com/@kaseywagoner).
If you’re one of the millions of people who look forward to the Winter Olympics, you’re likely excited about watching figure skaters move gracefully across the ice. The way they glide is simultaneously beautiful and jawdropping.
The exciting crescendo of every routine comes when the skater performs one of their jumps. You’ve probably noticed that over time the number of revolutions that a skater can make in a single jump has slowly progressed upward. When I was a kid, on most jumps skaters would complete two revolutions (e.g., a double lutz), with only the most advanced skaters attempting the likes of a triple lutz. Contrast that with this year where you’re likely to see multiple skaters land quadruple jumps. So what’s happening here – what does it take to do an extra revolution on a jump?
The short answer is that to do a jump with an extra revolution requires significant practice to refine technique and a surprisingly large amount of extra strength. But let’s use the lens of physics to get a better understanding of this, and maybe we will even learn something fundamental about the cosmos along the way!
In order to do as many revolutions as possible within one jump, a skater needs to do two things, spin fast and leap high. Let’s explore the physics of both of these things that are paramount to success.
To spin fast during the jump, skaters work hard well before taking off. In the lead up to the jump, skaters push on the ice in a particular way to start spinning. In this process skaters provide as much rotational momentum as possible. Before jumping,the skaters’ arms and free leg will be spread wide. During the transition into the jump, skaters will quickly bring their arms and legs close to their body. During this transition the amount of rotational momentum remains the same, but how it’s distributed changes.
To understand this let’s use an analogy. You can think of this rotational momentum as the money skaters have to make the successful jump possible. Imagine you have a $10 bill, but you want to buy a soda from a vending machine. The $10 bill is effectively useless, but if you can convert the $10 bill into 10 $1 bills, you will have the same amount of money, but now it’s in a form that will help you accomplish your goal. Skaters are doing the same calculation, but with a slightly different goal in mind. As they bring their limbs closer to their torso, they are maintaining the same amount of rotational momentum, but they are converting most of it from a useless form (resistance to rotation) into a useful form (rotational speed). In this conversion, they are able to get themself spinning much faster, making it more likely that they will complete their desired number of revolutions.
Skaters have long capitalized on their physics knowledge to improve their ability to spin quickly. The real advancements that have unlocked the quadruple jump come from the leaping high aspect of a jump. In order for a typical, well practiced skater who can spin at about 300 revolutions per minute, to execute a triple jump they must jump just over 17 inches high. But to make it to that fourth revolution, they must jump over 30 inches off the ice. Anyone versed in vertical jumps will recognize that going from 17 inches to 30 inches is no easy feat, but the question is just how much harder is it? For skaters to make three revolutions they need to push off the ice with a force of 440 pounds, but to make the fourth revolution would require them increasing that to over 550 pounds. The thing that makes this extra jump incredibly challenging is that anything short of 550 pounds leads to a disappointing – and perhaps dream-shattering – fall.
It’s likely that if you’re watching the winter games you already appreciate the strength, skill and beauty of these athletes. But if you haven’t stopped to really think about just how impressive it is, we hope that this article has helped your jaw drop even farther as you watch the next successful lutz.
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