The physics behind figure skating’s most difficult jump

We may earn a commission from links on this page.

Nathan Chen is on the verge of becoming the best figure skater alive, if he can cope with the pressures of his first world championship at the senior level.

The stresses on the 17-year-old American are not just psychological. Nathan’s known for doing more quadruple jumps in a single program than any other figure skater in the world. But the moves are incredibly taxing on the human body. And everyone has their limits.

To land a quadruple jump, skaters have to take off with a huge amount of momentum, often propelling themselves upward by striking the ice with the toe pick. Skaters have to jump high in the air while spinning fast enough to make four revolutions in well under a second. Then they have to withstand momentary impact forces between eight and 10 times their body weight, stop rotating, land, and continue with their routine.

In January, Nathan became the only skater to manage five quadruple jumps in a single program, catapulting him to the forefront of a revolution overtaking the sport in recent years.

It’s no longer enough for male figure skaters to have honed a single quad; Nathan does four different quads of varying difficulty: three that use the toe pick—one where he switches direction upon jumping (the Lutz) and two (the toe loop and flip jump) where he spins similarly but launches from different feet (the toe loop and flip jump)—and one where he takes off from the inside of his left skate and lands on his right foot (the Salchow).

The high-risk elements pay off big when it comes to scoring: at the US Championship in January, he won by a ridiculous margin of 55 points. But they’re also incredibly hard to land: at the World Championships in April, he fell attempting to break his own record.

Figure skating wasn’t always like this.

Figure skating
Originally, figure skating was about carving specific shapes into the ice, as shown in this excerpt of a book written by Gilbert Fuchs, the first world-champion figure skater.
Image: University of Connecticut Digital Archive

While all athletic competitions have evolved over the past century, figure skating in particular has come a long way since 1896, when Gilbert Fuchs became the first world champion at carving specific “figures” into the ice.

The basic versions of modern figure skating jumps were invented around then—the Axel by Norwegian Axel Paulsen, the Salchow by Swede Ulrich Salchow, the loop by German Werner Rittberger.

As it evolved, figure skating became increasingly about power—the ability of skaters to do bigger and more impressive jumps. In 1952, American Dick Button successfully landed the first double Axel and triple jump. In 1978, Canadian Vern Taylor made that double Axel a triple, and in 1988, Canadian Kurt Browning managed the first-ever quadruple jump.

Now, though, evolution in figure skating is happening at a startlingly fast pace. American Evan Lysacek won the Olympic gold in 2010 without a single quad jump in his routine. His victory was controversial then, but would now be considered impossible. In 2011, American Brandon Mroz landed the first ever quad Lutz in competition. Last year, skaters debuted the first quadruple flip jumps and quadruple loops. In January, Nathan Chen landed all three in the same program. And other skaters aren’t far behind.

The key to the “quad revolution”—so many skaters suddenly getting so good at jumps once considered impossible—is that coaches have a much better idea of what a successful quad looks like, and how their athletes need to train to do them.

That’s thanks, at least in part, to biomechanical research that’s been underway for years, and provided countless coaches with insight into the physics of the movement.

Jim Richards, a kinesiology professor at the University of Delaware, has spent more than a decade studying the physics of figure skaters’ jumps and helping them improve their technique. In one research project, he set up 10 cameras at an ice-skating rink to film skaters as they attempted different jumps. Through motion capture technology, their movements were mapped onto computer models.

Jim Richards’ software uses computer models that shows a figure skater’s form in a quadruple Salchow attempt (gold) and how he should alter it to land successfully (silver). A coach would use this information to tell the athlete to tuck his arms more, to achieve higher rotational velocity.
Image: Jim Richards, University of Delaware

Then, using a program that accounts for athletes’ specific weight distribution, the computer created a virtual model of what it takes for a skater to do the jump successfully, based on some pretty simple physics: Angular momentum = moment of inertia x rotational velocity.

Angular momentum is basically the impetus an athlete gets from takeoff. It’s equal to the athlete’s moment of inertia (basically a measure of how far their body mass is spread out in space) multiplied by their rotational velocity (how fast they’re spinning). The more outstretched an athlete is, the slower he or she spins. So Richards’ computer’s most useful piece of advice: how and when athletes should contract their bodies to manage more revolutions.

Many of America’s top skaters have participated in the study, Richards says. “If they can optimize what they’re doing when they’re in the air, in the flight phase of the jump, then they can usually land the jump pretty easily.”

There’s no signal that skaters have reached their limit. The next jump skaters will conquer is the quadruple Axel—a forward-facing jump with four and a half rotations. And some coaches are  beginning to look even further ahead.

“There will be naysayers out there but there’s going to be some, my guess, male skater in the next however many years—it might be within two years,—that lands a quadruple Axel,” says Tom Zakrajsek, a figure skating coach who’s worked with US national champions for decades. “And once that happens, everybody’s going to look to quintuple rotation.”

Getting the angular velocity to add another revolution would be incredibly hard, and probably require athletes start with their bodies further outstretched, twist more on takeoff, and pull in tighter. But athletes can only contract their bodies so much, and quads already require a level of contraction that keeps all but the most narrow-framed skaters from the top levels of competition.

This is part of what’s kept women skaters from having a similar quad revolution. Where puberty tends to make male skaters stronger and better at jumping, female skaters get wider hips and chests, which slow them down. France’s Surya Bonaly attempted numerous quads in competition in the 1990s, though none of them were considered successful. In 2002, Japan’s Miki Ando landed a quad successfully, and she remains the only female figure skater to have done so, though other women have landed them in practice.

But on the men’s side of the sport, there’s no sign of things slowing down. With the sport’s continued evolution, though, has come more than a fair share of reticence: is spectacular jumping really what figure skating is about? For many ice-skating officials, the answer is no. That’s why some elements, like the backflip, are banned.

“Sport is always going in one direction—it must be stronger, faster, higher,” says International Skating Union vice president Alexander Lakernik. “The problem for me is that i wouldn’t like figure skating to consist only of jumps. Jumps are part of figure skating…but for me the main thing is the balance, is the program in which difficult elements are integrated.”

Nathan Chen’s quadruple Lutz is the most difficult in his program, even if his triple Axel tends to give him the most trouble.
Image: NBC, Michael Tabb

Scientists worry the obsession with difficult jumps is dangerous. Because skaters will practice jumps dozens of times a day, and always land on the same foot, they’re prone to getting microfractures that can cause major issues later on. And there’s been very little research into how spinning so fast and absorbing so many landings affects the joints.

Studies show up to one in five figure skaters end up with stress fractures each year. And while some coaches are trying to limit how many jumps their skaters do in practice, there’s no way to gauge the damage it’s causing without more, improved research.

“If we want skaters to be able to perform well, they need to not only know how to do the skills, they have to stay healthy, and knowing the loading on the body can help with them stay healthy,” says Deb King, a biomechanist at Ithaca University. “It can also help them with the training, in terms of strengthening and flexibility to prepare the body to do those tricks.”

“These are kids, these are people who are still developing physically,” says Richards. “And the impact when they land in the ice is very high, that we know. Think of yourself jumping off a chair and landing on one foot, and landing flat-footed. How many times can you do that in a row? That’s what these kids are doing, and they’re doing it anywhere between 50 and 100 times a day. As artistic and beautiful as these kids look on ice, and as graceful as they look on ice, it’s a brutal sport.”

April 3: This article was updated with results of the 2017 World Figure Skating Championships.

Correction: A previous version of this article quoted Jim Richards as stating that Nathan Chen had participated in a motion-capture research project. Richards followed up with Quartz to let us know he had misspoke.