The Physics of Figure Skating

[FigureSpins]

There are quite a few sites on the internet that address figure skating and the physics involved in the sport.

Here is one site that was new to me:

http://btc.montana.edu/olympics/physbio/biomechanics/bio-intro.html
http://btc.montana.edu/olympics/physbio/biomechanics/cam-intro.html

This one does a good job of highlighting horizontal and vertical displacement on jumps:
http://btc.montana.edu/olympics/physbio/biomechanics/pm01.html

[Isk8NYC]

Here is a good powerpoint on "The Mathematics of Figure Skating" from a calculus class. 
Well, the graphics (can't go wrong with Peanuts) are really good, along with the text.  The rest is greek to me, lol.

http://pusdmail.pleasanton.k12.ca.us/~bdixon/calculus/projects/Ice_Skating.ppt

[Bill_S]

The other adult figure skater at my university rink is a nuclear physicist. Just for fun, she put together a "Physics of Figure Skating" presentation that she's given at a number of physics conferences. I know she's presented it at several venues around the country and perhaps outside the US since she travels a lot.

I do wish she had it posted online somewhere for everyone to see. The presentation examines some of the principles of a skate blade's glide as well as the dynamics of jumps, spins and even stroking. There are some interesting conclusions given in her presentation.

Maybe I can convince her to publish it online.

[FigureSpins]

That would be wonderful, Bill.  I'd love to see her presentation.

Found this page about Spin Physics:
"The Physics of Everyday Stuff"  http://www.bsharp.org/physics/spins

This one analyzes a Death Spiral as well as jump basics:
"The Physics Of Figure Skating" http://www.real-world-physics-problems.com/physics-of-figure-skating.html

[Bill_S]

That would be wonderful, Bill.  I'd love to see her presentation.

I asked her, but she's concerned about the images contained in her talk. Some are copyrighted, so she's unable to freely distribute the material on the web.

That's really too bad since it has great information in it.

[Query]

This is all lots of fun, though I'm sure it leaves out forum members who think physics is evil or confusing.

I'll add a few sample ideas.

I was thinking a lot about the physics edges and creating and dumping angular momentum, in connection with blade shapes and skate sharpening. Remarkably small shifts in weight and blade shape can have tremendous effects on initiating and checking turns, spins and jumps, as well as preserving speed and glide.

It is unstable for a center of rotation (note that surface contact constrains the axis of rotation to be at right angles to the ice surface, which is not the effective vertical created by the vector sum of gravitational and various inertial forces) to be ahead of the center of lateral resistance.

Consider how unstable a weather vane is when it has the point of major resistance temporally upwind of the center of rotation is unstable. It will turn so that the part of the vane with the largest resistance is downwind.

Proper use of these principles helps initiate turns, and checks them. Like a skateboarder who pushes down one part of the board to the surface to initiate a turn.  Or the classic bootlegger's turn, where you use the car's emergency brakes (which only brake the front wheels) to create and control a rapid turn, or various forms of wheely [sp?] on bikes. 3 turns and brackets follow similar principles.

It helps explains why a parabolic blades should in theory be better at both initiating and checking turns, spins and jumps, but only if you use them right. The ends of the blade have more resistance, so placing your weight and contact right makes it easier to control angular momentum. Tapered blades only make sense if you restrict yourself to forward-to-backward turns.

There are a lot of trade-offs on things like side honing - i.e., it should cause some things to work better, some worse.

When you edge a blade, you are tilting the rocker a bit into the horizontal plane, and thereby effectively creating a curved blade that want to turn. That also shortens the length in contact - though parabolic blades paradoxically lengthen the contact area.

It is also amazing how the tiny amount of lateral resistance on a blade created by friction on the side of the blade towards which you are edged can make 3-turns so much easier to initiate (but harder to check, because you have more angular momentum to rapidly dump) than brackets.

Edge shape actually has very complicated physics. Plus, there are a lot of trade-offs.

One thing that is very hard for me to understand is that some blade shape differences that are around 1/1000 inch make a huge difference in the blade/ice interaction and how I skate. It's fun to play with subtle sharpening changes.

But there is no obvious way to model anything physically, when people aren't certain how the underlying blade/ice physics works. People try to use intuitions derived from fluid dynamics (e.g., boats, aircraft), which probably don't apply very well.

Another physics issue is understanding the ways you transfer angular momentum from one body part to another. For example, people often swing legs or arms to temporarily hold the angular momentum being accumulated by an edge. When the swing stops, angular momentum is put back into the main body, and the rotation occurs.

For some reason, judges hate some forms of momentum transfer. If you swing your arms around to create a turn, test judges (especially for dance and moves) will mark you poorly. They like more subtle motions. But many of the best freestyle skaters begin some rotations with up stretched hands, transfer it to the arms, and then to the torso - and use this very unsubtle technique to win national and international competitions.

Again, tension without internal motion (e.g., pulling back a shoulder to initiate or check a turn) should have essentially no effect on the external motions of the body (standard physics theorem) - but it does. In part it reduces vibration and flopping around, which wastes energy. It seems to have huge effects it shouldn't have. Perhaps when we pull a shoulder back a few thousandths of an inch, it transfers a bit of angular momentum at the beginning and end of the pull, which is enough to initiate and check turns. Those displacements are so small, it seems implausible. Yet - what else could it be?

The physics of falling are also interesting. You have to dissipate the energy and momentum in a way that spreads it over a large portion of the body. This creates pressure and sheer waves, fluid motions, and compressions and tensions in many different body components. Some materials within the body are good at taking forces in very specific directions. Bone takes compression well (as long as it is altered slowly), sheer not so well, but fractures quite easily under tension, including that generated by torsion and bending. Muscles and ligaments take tension quite well along the fibers, not so well if it tends to split fibers apart, and have problems taking sheer and compression. People probably often destroy Achilles tendons precisely because the tendon isn't designed to take the compression and sheer forces the back of a freestyle boot imposes.

Body design is based and developmentally adapts and changes around the idea of compensating for the specific weaknesses and strengths of the component materials. It is not designed perfectly, in engineering terms - perhaps ligaments and muscles should pass through bones, so their tension is balanced against bone compression, for maximum strength. Plus, humans and animals don't take advantage of materials and structures that developed for other biological creatures (E.g., wood, Chitin, silicates), nor do they use steel or aluminum.

Consider the ways in which stiffness is created. If you want a lightweight composite material stiffness, you do the same thing - balance compression of something that mostly resists compression against tension of something that mostly resists stretching. For this to work, both materials must have substantial intra-laminar sheer strength, and they must be held together by an adhesive or sewn fibers that provide substantial inter-laminar sheer strength. This is used in composite material hockey and speed skates, as well as composite kayaks, canoes, and ultralight aircraft. The component layers do not have to be stiff or dense - they are only stiff when adhered or sewn together. In theory, you can create (non-isotropic) stiffness in selective directions, by controlling the directions in which the forces are balanced. E.g., it is possible to create boots that have a lot of sideways resistance, but are quite flexible for ankle point and flex, though I'm not sure anyone does that.

But stiffness in traditional leather boots is often achieved in a much less efficient fashion. The material is quite dense, and is saturated by adhesives that make the entire material rigid. This makes for a heavy boot, and it is very difficult to give it selective direction stiffness. I believe properly designed composite boots could have an overwhelming performance advantage over traditional leather boots.

Anyway, I hope you all enjoy playing with physics ideas.

[FigureSpins]

What are you talking about? No one's being "left out" in this discussion. 
There are kernels of information and technique tips in every link.

Back on topic:

This page has a nice summary of the physics of landing jumps:

http://iceskatingresources.org/PhysicsOfFigureSkating.html

To land, the skater extends (opens up) their arms and free leg in the same manner as exiting a spin on the ice. If the skater fails to control the angular momentum prior to landing, the skaters may land hard on the toe on a deep arc. A wide swinging free leg can cause a loss of control, free leg touching down or immediately stepping out of the landing. Ideally the the curve of the landing edge can be on the same arc established on the take-off, allowing the skater to control the angular momentum gained in the jump.

This is cool: Science Projects about Figure Skating that includes dizziness!
http://www.sciencebuddies.org/science-fair-projects/project_ideas/HumBio_p012.shtml

Continuing in that vein is a PBS online episode about spinning and dizziness:
http://pbskids.org/dragonflytv/show/iceskating.html
(Nice video! Love the zamboni trying to run them over!)

[sarahspins]

This is cool: Science Projects about Figure Skating that includes dizziness!
http://www.sciencebuddies.org/science-fair-projects/project_ideas/HumBio_p012.shtml

Continuing in that vein is a PBS online episode about spinning and dizziness:
http://pbskids.org/dragonflytv/show/iceskating.html
(Nice video! Love the zamboni trying to run them over!)

That really was a cute video.. I liked at the end that they wanted to "unwind" their brains by spinning the other way

[Isk8NYC]

That really was a cute video.. I liked at the end that they wanted to "unwind" their brains by spinning the other way

I have my students do that during lessons, so they don't stagger around the ice.  I tell them to "spin the other way" or "shake your brains [head]."  Either works fine in clearing the dizziness.

[Query]

The dizziness thing is a bit O.T., but...

Wow! The kids on the video loved getting dizzy!

Interesting that they understood controlled experiments well enough to try all the cases.

I have been working on spins a lot with my coach. Just want to be able to spin smoothly, on center, on a clean backwards edge, without drifting. After all these years trying, that isn't much to ask...  Thought I was finally mostly over the dizziness, but the coach managed to make me spin a little faster, and the dizziness came back.

I can't spin nearly as fast as the kids in the video. I rock forward and back. Maybe my head is getting shaken up. Or perhaps dizziness relates to my tendency towards motion sickness.

Like the kids, I get much more dizzy if I spin with eyes closed. Odd. When I flew on board an experimental aircraft in stormy weather, closing my eyes helped with motion sickness. So did laying down, when I could. I'll have to check whether I get dizzy in butt spins...

Unlike the kids, looking up makes me more dizzy.

Unwinding: coaches say spinning in alternate directions is confusing and wastes time, but it helps my dizziness a fair bit.

[MadMac]

Unwinding: coaches say spinning in alternate directions is confusing and wastes time, but it helps my dizziness a fair bit.

On the contrary, spinning in the opposite direction is worth big points in competition. Not to mention how much it helps ones overall skating and balances the body from all that one-sided activity. Well worth spending time on.

[Isk8NYC]

Another informative video - this one about the physics of jumping and spinning from a Sports Medicine perspective.

http://www.youtube.com/watch?v=oBsPvgS-6rE

Tried the office chair spin experiment - it's cool. You have to settle your weight over the spin spot, but then you can feel the pull in - stretch out speed differential.

[Query]

I don't see any sports medicine in the video, but it's reasonably well explained review of well known physics. Too bad they didn't use a spin example with more leg swing, to emphasize that component of angular momentum.

They also left leg momentum out of the rotating chair sit experiment. If she started the legs straight, than brought them in, she might have been really dizzy!

(Unless the chair fell over.)

In some of the 2011 Skate America pair skating examples, I noticed a man throwing a lady into the air while she is horizontal. She rotates about the horizontal axis, stops rotating, and is caught again. At least in the examples I looked at, she stores pretty much all her angular momentum in leg motions - her torso, that he is holding, doesn't rotate perceptibly at all until after he releases her, nor does she do much with her arms before release - the exact analog of when a figure skater doesn't start to rotate until they are off the ice in a freestyle jump, but stores a lot of the momentum in the leg. The main must be pushing with one arm much harder than the other to give the lady that angular momentum, but his arms stay symmetric - very cool.

A lot of the appeal of skating is when something like that looks impossible - torso starts to rotate mid-air - but skaters do it anyway. On the other hand, most land dance jumps, so I'm told, start rotating on the floor before take-off. Boring. I'm not sure how the difference evolved, but it is interesting that it did.

A Harlick boot maker mentioned to me that a prominent recent Olympic medalist loved heavy boots because it allowed said skater to store more momentum (linear, angular or both?) in the leg swing, and thereby get more revolutions. No doubt you have to be a very good and strong skater to be able to control and use that much weight. In today's world, where most skaters want lighter boots, it also shows that you can't create a single skate design that pleases everyone.

Can you imagine a dancer asking for heavy weight ballet slippers?

[Isk8NYC]

Found this on YouTube

https://www.youtube.com/watch?v=qd4CVvItJlo

[Query]

I LIKE it. No doubt one can debate a few of the things he says. But the videos are cool.

[FigureSpins]

Everyday Einstein -- explains spinning and jumping physics concepts

https://tunein.com/radio/Everyday-Einstein-p1045997/?topicId=119948823

[Query]

I suppose we really don't care what kind of boundary layers make ice skating possible. Maybe the only thing that matters to us is that ice is slippery.

Anyway, it's hard to imagine any immediately practical application of this for skaters, so I'm putting it in the "non-skating discussions" forum, but studies of the properties of the ice/air/blade boundary layers continue to be made:

The physics of ice skating

which summarizes a much more technical article in Physics Review X:

Nanorheology of Interfacial Water during Ice Gliding

(click on here to see the whole article)

I admit I haven't tried to read the second article. It would take a while, and I'd have to look a lot of things up. And it probably wouldn't affect the way we skate.

[Isk8NYC]

Topics merged

[Bill_S]

I found this YouTube video about the physics of slippery ice. Professionally produced, with the narrator sometimes taking to the ice on skates.

https://www.youtube.com/watch?v=yjSf7Yh9UZc

[Query]

It's a great, very understandable video! Of course it leaves more questions unanswered than answered.

I remain convinced that part of the reason so many questions remain unanswered is that no one is willing to pump the kind of money into studying the physics of ice skating as they are into, say, turbulent flow of water around naval ships, because it isn't seen as a major issue for national security, or for major league commercial applications. (Which isn't to say that turbulent flow is all that well explained or even quantified, in spite of all the studies, AFAIK.)

OTOH, that means that fairly ordinary people, without a lot of money, may be able to do "important" experiments.

The article I just cited tried to make it appear relevant to a larger market - saying that what they were studying could have relevance to the development of better lubricated surfaces. But it's always going to be a hard sell. It also is discussing a later generation (maybe a couple generations) of theory than the video.

I'm not even sure how you would study this issue if you had the money. You could tag atoms isotopically - but there aren't all that many isotopes of oxygen and hydrogen to use, and they have somewhat different chemical and physical properties (especially for hydrogen) than each other. Radiation scattering experiments leave a lot of ambiguities, and would be hard to do to pick up the ice/metal interface with a scattering experiment. Atomic force microscopes would mean something other than the air or skate blade would be in contact with the surface, and could only detect the external surface. Even if you just try to model it with computers, there are some open questions of how things work in quantum physics.

But I like that it points out that ice is far more slippery than water, so the presence of a "water layer" or "quasi-liquid layer" may not explain everything. The molecules that move around must be less well bonded to surrounding layers than water molecules are to each other. The mention the recently cited article makes about other studies that appeared to show the existence of bi-molecular-thick-layers, which are internally bonded, but not much to each other, might partly explain that.

I guess when you are dealing at an atomic scale, things can get very complicated. Even at a substantially larger scale, someone I know who works for Intel Corp. recently told me that each new generation of electronic chips, that lets you do things with smaller components and less power consumption, now takes years to develop (he works a couple generations ahead of the consumer market devices), because it is very hard to make them reliable. Also it is hard to observe the devices in detail, because they are so small. And they have a fair bit of money to work with, unlike the people who study the physics of ice skating.