Physics of Skating

In the "must read" philosophy section I mentioned how skating involves moving in arcs and circles. When you move in a circle you are accelerated toward the center of the circle. I already know what you're thinking. You're thinking if anything you are accelerated away from the center of the circle because you can feel yourself wanting to fly off...away from the center. But consider this. In order to keep skating in a circle you must constantly apply a push (from your skates) toward the center. That force acts along the radius of the arc and it points toward the center. It is applied by the ground pushing on your wheels! This is called centripital force and it produces a centripital acceleration pointing toward the center of the arc. And this centripital acceleration is the key to skating. Incidentally this is the same way planets stay revolving around the sun. The sun's gravity exerts a constant pull on the planets (toward the center) and their tangential velocities allow them to move around the sun without spiraling into the center.

If Issac Newton had skates he may well have figured out what Einstein did...that acceleration is equivalent to gravity. When you learn how to skate well you will learn how to ride the gravity waves created by your acceleration and ride them not unlike the way a surfer rides a wave. If you wanted to skate in a figure eight you would start off skating in a circular arc and after executing one full circle you would change the angle of your skate so that the force from the ground is pointing to a new center. At this point the angular momentum you possess from having made the first circle is redirected into the new one. This can be accomplished with the slightest amount of energy. The concept of redirecting your angular momentum is the key to efficient skating. When Apollo 13 suffered an explosion en route to the moon it would have required far too much energy to reverse its course and come back to the earth. The only solution was to continue their course to the moon and use the moon's gravity to sling shot the spacecraft around the moon. At that moment the ship would be pointing toward the earth and a fairly small amount of energy in the form of a short burn could be made to break free of the moon's gravity and send the rocket heading back to earth. I know it sounds a bit crazy but this is exactly what you will learn to do on your skates! You will add small amounts of energy to your already established momentum and redirect your body in the direction you want to go. This way your skating will be efficient and nearly effortless.

THE PHYSICS OF

SKATING IN A CIRCLE

This may be a basic high school physics problem but what is of interest to us now is to really think about what this equation means to us skaters.

First it is easy to prove that it is impossible to skate in a circle without leaning toward the center. You might think that you can keep your body vertical while executing a circle but in actuality you will not be able to skate in a circle without the ground applying that resultant force Rx. And Rx=m*g*tan (theta) so that if theta=0, tan(theta)=0 and so Rx=0...unless r=infinity (a straight line). When you first learn how to cross over or skate in a tight circle most people tend to shy away from leaning into the center of the arc. This is a very common fear. You will invariably bail out of the lean and when you bail out you lose your Rx force and are no longer able to skate in an arc. I still do this sometimes when I'm learing new tricks. It is a good idea to imagine someone skating along the outside of your arc and constantly pushing on your shoulder so as to force you to keep that banking angle. Try to keep the bank going.

Looking at these equations you can see that if you specify a V (tangential velocity) and an r (Radius of our circle) then theta and all other varibles can be determined. This equation is easily solved by a spreadsheet program like excel. I have done this and some results follow.

Here is one way to see the situation.

For a specific velocity say 10 ft/s we can vary the size of the radius and determine the bank angle and the reaction forces.

What do we see? As you try to skate in an ever tighter circle at the same speed you have to keep increasing your bank angle and the reaction force Rx gets bigger and bigger. It's interesting to look at the actual numbers. If you could skate at 10 ft/s in a 5 foot radius (that's pretty tight) your ankles would have to supply 106 lbs of force and you would have to bank at 32 degrees from the vertical.

As the radius increases to 50 feet you need only a slight bank angle and mere 10 lbs. of force.

Here I've kept the radius, r constant at 30 ft. As you can see as you increase your speed your bank angle increases as does the necessary reaction force, Rx.

Notice also that if you double your speed from 10 ft/s to 20 ft/s your bank angle and the reactiion force more than triples.

The most important thing to come away with in this discussion of the physics of skating is that the tighter your radius the more you have to lean and the greater force you must exert on the ground to hold the arc. Keep in mind that if you lean too much and you are required to exert too much of a reaction force there will come a point at which the friction between the skates and the ground just can't hold it any more. What will happen at that moment? Your skates will start to slip out from under you. But when your wheels are new and you have sharp skating skills it is remarkable how much force and how much bank you can achieve. The so called "edge" of your skate wheels can really hold tighter than you might imagine. This is when having softer wheels can be a blessing. Think of Olympic speed ice skaters. They bank so much that they can easily skim their hands over the ice. Think of motor-cross drivers. Their motorcycles bank so much their knees hit the ground.

When the ground is wet the friction is significantly reduced and holding the "edge" becomes very difficult. This can be a dangerous situation so be careful of wet surfaces. If you skate in streets be on guard for oil drips from cars. These can send you flying.

Try to get over your fear of leaning. The more you are able to lean the tighter arcs you will be able to skate. It's also not a particularly bad type of fall when you lose the edge skating in an arc. Since you are already leaning toward the ground you don't have as far to go before you hit. You can also sense when you're going to lose the "edge." Have fun and remember my friends, when Newton said F=ma you can follow that up with, and then there was light... and good skating!