Figure skating physics for normal humans

Figure skating has a lot to do with physics, and here’s what we mean. Also, what’s the difference between all those figure-skating jumps?

Many of us have been enjoying the 2018 Winter Olympics in Pyongyang. All of the athletes there are pretty amazing, but the figure skaters stand out, especially if you’ve spent any time on the ice yourself. Their spins and jumps — especially their jumps — can be jaw-dropping to us mere mortals. Though few skaters are actually physicists themselves, they might as well be given their mastery of key principles of motion.

Though we may not be physicists ourselves, we can understand enough to appreciate some of the science behind their powerful and yet somehow elegant athleticism.

Spins

Spins are all about physics’ conservation of momentum, and though dazzling on their own, they’re also a critical element in skaters’ gravity-defying jumps. There are few physics concepts involved.

First, inertia. Newton’s first law states, “An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.” The degree to which an object resists the influence of such a force is its inertia. The moment of inertia in skating is the measurement of the distance the skater’s mass extends outward from the axis on which he or she is spinning. The further it is from the axis, the larger is its moment of inertia value.

Next, there’s momentum, the amount of force it would take to stop a moving object. And here’s the thing: Unless some outside force slows down the object, an object’s momentum is conserved, remaining constant.

In the case of a spinning object, or skater, the force is referred to as angular momentum. It’s the product of multiplying:

Let’s say — using simple numbers with no relation to the real world to make this easier to follow — that:

• an object’s mass had a moment of inertia value of 10 and you multiplied it by an angular velocity value of 100 to arrive at an angular momentum value of 1000.
• Now, you decrease the distance by which the mass extends outward from its rotational axis, thus reducing its moment of inertia value to 5. Since momentum is always conserved, we’d have to plug in a larger angular velocity to arrive at our angular momentum of 1000. We’d need to double the angular velocity, or the speed of the spin, to 200.
• And so, this is what a skater does by pulling in his or her arms close to the body: The moment of inertia goes down, and the angular velocity, or speed, goes up.

You can try this for yourself if your chair spins by holding your arms out as you rotate and then pulling them in close to your body to reduce your mass — your chair spins faster. Or just watch.

(NSF/Science360/NBC Learn)

This shrinking of a skaters’ moment of inertia during rotations is a big part of generating the requisite high speeds required for multiple spins during a jump, as well see.

Death Spirals

The trust pair skaters must share is almost hard to imagine given the death-defying throws and potentially head- and spine-cracking death spirals. To calculate force the male skater needs to exert to remain anchored to the pivot point in the death spiral is a lesson in physics all by itself, according to Real World Physics Problems. It starts with these values.

Canadians Jamie Sale and David Pelletier (Brian Bahr)

• mA is the center of Sale’s mass.
• mB is the center of Pelletier’s mass.
• M equals the mass of the system, or the pair, mA plus mB. Note that the purple dot represents its center.
• LA is the distance from the center of Sale’s mass to the center of the pair’s mass, M
• LB is the distance from the center of Pelletier’s mass to the center of the pair’s mass, M. It’s shorter than LA because Pelletier is heavier than Sale.
• P is the system’s pivot point, or center of rotation where the front tip of Pelletier’s blade is planted in the ice to keep from being moved by the couple’s centripetal (inward-moving) force.
• R is the radius of the circle traveled by the center of mass around P
• w is the rotation rate
• The pair can be considered as a single rigid body, and a new value we need is M’s centripetal acceleration, aC — the force with which M wants to push inward into the spiral, threatening to dislocate Pelletier’s skate anchored at P, in the current direction of the centripetal force. aC = w2R, that is, the rotation rate squared times the radius of the circle being traveled. With aC in hand, we can work out the force Pelletier would need to hold onto his toehold.

concept of Real World Physics Problems

Most of these labels are familiar except:

• aC is the centripetal acceleration of M. In keeping with Newton’s second law — it's calculated as ΣF = MaG. (ΣF is the sum of all of the forces affecting M.)
• Fp is the force entered by Pelletier’s blade into the ice at P to hold the pair in place.
• The formula is Fp = (MA + MB)w2R, or Pelletier’s force plus the center of his and sale’s mass, times the rotation rate squared times the radius. Whew.

All of which is to say the man in a death spiral needs to apply only slightly less than his body weight to stay put, and thus crouches down for optimal leverage as his other skate lays sideways on the ice and his partner turns around him.

Jumps, Quad and Otherwise

A good deal of the fun of watching Olympic figure skating comes from the astonishing jumps. For those of us not clear on what differentiates a lutz from an axel, here’s an explanation of what’s what.

There are six types of jumps, and they fall (poor choice of words there) into two broad categories, depending on the part of the skate from which the jump is launched. The number descriptors — quad, triple, etc. — refer to the number of rotations a skater makes while in the air.

Skaters don’t get super-high off the ground: Men tend to jump around 18 inches and women about 16 inches, according to Ithaca Collge sports science professor Deborah King. That’s compared to, say, a male basketball player who may reach 30 inches or a woman jumping upward around 24. (Hamidou Diallo has leaped over 44.50 inches!)

Interestingly, each skater gets pretty much the same amount of time in the air every time he or she jumps, so the number of spins is really about how quickly and effectively the skater can reduce the moment of inertia.

The leading skater when it comes to quadruple jumps these days is the U.S.’s Nathan Chen, who can quad the toe loop, loop, salchow, flip, and lutz. There’s some question if — and when — we’ll ever see a jumper hitting five spins in a jump. WIRED refers to the idea as “impossible, definitely bonkers.”

Toe jumps

These jumps begin with the skater pushing upward from the jagged front edge, or “toe pick,” of their skate.

Edge jumps

Skate blades actually have a groove called a “hollow” running their length, offering a skater two distinct edges — inner and outer — from which to jump. The front of the groove angles slightly inward toward the big toe, and its back outward toward the pinky toe. Jumping from an edge requires bending the knee and then propelling upward off the ice.

All of that having been said, there are the six types of jump — the examples below were compiled by Vox.

The Toe Loop

This toe jump begins with the skater moving backward on one foot’s outside edge, jumping from its toe pick, and landing the jump on the same edge of the same foot including the toe pick. Since he’s launching with the toe pick, he doesn’t need to bend his knee to push off.

Javier Fernández (NBC)

The Loop

The loop is much the same as the toe loop, but it’s strictly an edge jump: The bent knee reveals that the backward-moving skater is launching off that outside edge alone without the toe pick. He lands the same way.

Nathan Chen (San Jose Ice Network)

Salchow

The salchow’s another edge jump, from the inside edge of one foot and landing on the outside edge of the opposite foot.

Yuzuru Hanyu (NBC)

Flip

In the toe-jump flip, the skater goes backward into the jump on the inside edge of one foot, and user the other foot’s toe pick to jump. She lands on outside edge of the first foot.

Alina Zagitova (The Olympic Channel)

Lutz

This toe jump is similar to the flip, though the skater lands on the foot whose toe pick initiates the upward movement.

Nathan Chen (NBC)

Axel

This edge jump is the only jump that occurs going forward. It’s especially hard since it requires an extra half-rotation to position the skater to glide backward during landing. The skater jumps off from the outside edge of one foot and lands on the other foot's outside edge.

Yuna Kim (NBC)

Beyond Physics

While it’s easy to judge the value of a skater based on his or her athletic abilities, a skater’s technical score is just one half of the story, and there’s also an artistic judgment made. Of course, art is hard to quantify and for commentators to describe, so much of the focus remains on physical feats of skill.

It’s likely that the skaters themselves are aware of the physics behind what they do to varying degrees. For us, it’s fun to think about it, but in terms of the eye-popping performances at the Olympics and other top-line competitions, it might just as well be magic.

Related Articles
Videos

Safe spaces: Where should the line of censorship be drawn?

Surprising Science

A controversial theory claims past, present, and future exist at the same time

Culture & Religion

Six disastrous encounters with the world’s most hostile uncontacted tribe

Surprising Science

Why birds fly south for the winter—and more about bird migration

What do we see from watching birds move across the country?

E. Fleischer
Surprising Science
• A total of eight billion birds migrate across the U.S. in the fall.
• The birds who migrate to the tropics fair better than the birds who winter in the U.S.
• Conservationists can arguably use these numbers to encourage the development of better habitats in the U.S., especially if temperatures begin to vary in the south.

The migration of birds — and we didn't even used to know that birds migrated; we assumed they hibernated; the modern understanding of bird migration was established when a white stork landed in a German village with an arrow from Central Africa through its neck in 1822 — draws us in the direction of having an understanding of the world. A bird is here and then travels somewhere else. Where does it go? It's a variation on the poetic refrain from The Catcher in the Rye. Where do the ducks go? How many are out there? What might it encounter along the way?

While there is a yearly bird count conducted every Christmas by amateur bird watchers across the country done in conjunction with The Audubon Society, the Cornell Lab of Ornithology recently released the results of a study that actually go some way towards answering heretofore abstract questions: every fall, as per cloud computing and 143 weather radar stations, four billion birds migrate into the United States from Canada and four billion more head south to the tropics.

In other words: the birds who went three to four times further than the birds staying in the U.S. faired better than the birds who stayed in the U.S. Why?

Part of the answer could be very well be what you might hear from a conservationist — only with numbers to back it up: the U.S. isn't built for birds. As Ken Rosenberg, the other co-author of the study, notes: "Birds wintering in the U.S. may have more habitat disturbances and more buildings to crash into, and they might not be adapted for that."

The other option is that birds lay more offspring in the U.S. than those who fly south for the winter.

What does observing eight billion birds mean in practice? To give myself a counterpoint to those numbers, I drove out to the Joppa Flats Education Center in Northern Massachusetts. The Center is a building that sits at the entrance to the Parker River National Wildlife Refuge and overlooks the Merrimack River, which is what I climbed the stairs up to the observation deck to see.

Once there, I paused. I took a breath. I listened. I looked out into the distance. Tiny flecks Of Bonaparte's Gulls drew small white lines across the length of the river and the wave of the grass toward a nearby city. What appeared to be flecks of double-crested cormorants made their way to the sea. A telescope downstairs enabled me to watch small gull-like birds make their way along the edges of the river, quietly pecking away at food just beneath the surface of the water. This was the experience of watching maybe half a dozen birds over fifteen-to-twenty minutes, which only served to drive home the scale of birds studied.

How does alcohol affect your brain?

Explore how alcohol affects your brain, from the first sip at the bar to life-long drinking habits.

(Photo by Angie Garrett/Wikimedia Commons)
Mind & Brain
• Alcohol is the world's most popular drug and has been a part of human culture for at least 9,000 years.
• Alcohol's effects on the brain range from temporarily limiting mental activity to sustained brain damage, depending on levels consumed and frequency of use.
• Understanding how alcohol affects your brain can help you determine what drinking habits are best for you.
Keep reading Show less

Scientists sequence the genome of this threatened species

If you want to know what makes a Canadian lynx a Canadian lynx a team of DNA sequencers has figured that out.

Surprising Science
• A team at UMass Amherst recently sequenced the genome of the Canadian lynx.
• It's part of a project intending to sequence the genome of every vertebrate in the world.
• Conservationists interested in the Canadian lynx have a new tool to work with.

If you want to know what makes a Canadian lynx a Canadian lynx, I can now—as of this month—point you directly to the DNA of a Canadian lynx, and say, "That's what makes a lynx a lynx." The genome was sequenced by a team at UMass Amherst, and it's one of 15 animals whose genomes have been sequenced by the Vertebrate Genomes Project, whose stated goal is to sequence the genome of all 66,000 vertebrate species in the world.

Sequencing the genome of a particular species of an animal is important in terms of preserving genetic diversity. Future generations don't necessarily have to worry about our memory of the Canadian Lynx warping the way hearsay warped perception a long time ago.

Artwork: Guillaume le Clerc / Wikimedia Commons

13th-century fantastical depiction of an elephant.

It is easy to see how one can look at 66,000 genomic sequences stored away as being the analogous equivalent of the Svalbard Global Seed Vault. It is a potential tool for future conservationists.

But what are the practicalities of sequencing the genome of a lynx beyond engaging with broad bioethical questions? As the animal's habitat shrinks and Earth warms, the Canadian lynx is demonstrating less genetic diversity. Cross-breeding with bobcats in some portions of the lynx's habitat also represents a challenge to the lynx's genetic makeup. The two themselves are also linked: warming climates could drive Canadian lynxes to cross-breed with bobcats.

John Organ, chief of the U.S. Geological Survey's Cooperative Fish and Wildlife units, said to MassLive that the results of the sequencing "can help us look at land conservation strategies to help maintain lynx on the landscape."

What does DNA have to do with land conservation strategies? Consider the fact that the food found in a landscape, the toxins found in a landscape, or the exposure to drugs can have an impact on genetic activity. That potential change can be transmitted down the generative line. If you know exactly how a lynx's DNA is impacted by something, then the environment they occupy can be fine-tuned to meet the needs of the lynx and any other creature that happens to inhabit that particular portion of the earth.

Given that the Trump administration is considering withdrawing protection for the Canadian lynx, a move that caught scientists by surprise, it is worth having as much information on hand as possible for those who have an interest in preserving the health of this creature—all the way down to the building blocks of a lynx's life.