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# Getting pushed around on snow

I sorta promised to write this in another thread so I guess I hav’ta. I don’t think I have ever written this whole thing out. I’ve shared it with some people on hill in different ways but on hill and on paper are two different things.

My first online meeting with Bob Barnes was many years ago when the PSIA forum was a worthwhile place to post and it consisted of a weeks worth of exchanges on the subject of centrifugal force. Bob used the term and I objected because I don’t believe in it. I decided that I wanted a model of the forces I experience when skiing the didn’t involve the concept of centrifugal force. Well I came up with one and you’re going to get it ready or not.

I started with the idea that I wanted to be able to move myself where I wanted to go on the hill. Next I thought about the forces that would be needed to move the mass of my body from point A to point B. Gravity is a constant to me. It causes me to progress down the hill and has a very little effect on the forces I feel if I never fight against it. What I needed was a force to propel my body from right to left and from left to right as I skied. In my exchange with Bob way back when I referred to the force I felt under my feet and commented that rather than feeling it as a force to fight against I felt it as a force to use to push myself around the hill to get where I wanted to go. I have used the idea of a force pushing up on the foot effectively over the years to improve peoples skiing. So why not explain that model in terms of Newtonian physics.

I have a mass (my body) moving across a slick slanted surface. Gravity is going to act to pull my body down the hill, i’ll let it. I want to reverse my direction of travel and go back the other way. Newton says that a mass will continue moving in the same direction unless a force is applied to it. Well I have a force pushing up on the soles of my feet so if I line up my mass I can use some portion of the at force to push against my body and first slow and stop its movement across the slope and then accelerate it back the other way. Newton liked to conserve momentum so applying a force to the moving body produced a curved path.

So I have a body moving down the hill and back and forth across the hill in a series of curves. I can even control how fast I progress down the hill by using the force under my feet to oppose the force of gravity and move me up the hill. Now all I have to do come up with a source for the force I feel under my feet. Well, I do have skis on so maybe its the skis that push up on the boots that pushes up on my soles. An edged ski pressured in the center will want to follow a curved path along the snow, the ski following the path will generate a force pushing in toward the center point of the arc. So there is a force pushing up on the bottom of my feet and I can transfer that force through my legs and apply it to my center of mass and change the path my COM is following.

So, I can control the arced path that the COM is following by using the force under my feet and I can control the path of my feet by my use of the ski. I can set up these two paths to cross and I get my feet on the other side of my body where I can use the force under my feet to push me back the other way.

Now here’s the Epic part of looking at skiing like this. When I experience the forces of a turn they aren’t something I am resisting as I fight to not go that way but something that is propelling me “over there where I want to go".

Well, that didn’t take so long after all and I’m sure that I made it so clear that there will be no questions of comments to reply to so I think I’ll plan on going skiing tomorrow,

Yd

[ November 09, 2003, 10:10 AM: Message edited by: Ydnar ]
Sounds like a pretty fine model to me. I've got no serious gripes with it. (...at least at the level of detail you outlined thusfar.)

Basically, it seems like you consistently look at the forces acting ON the skier, and have a good intuitive understanding of how to manipulate them to move you where you want to go.

Since any correct dynamics model considers either (a) the forces on a moving object, or (b) the forces that the moving object exerts on its surroundings, and shouldn't mix the two types of forces, your very reasonable and very common preference is to use with method (a). Thus, there is absolutely no need to bring centrifugal force into your model.

My only concern in your entire post is with your statement about centrifugal forces, "...Bob used the term and I objected because I don’t believe in it." You presently have no need for this concept and will continue to have no need for this concept if you are consistent and always stick with your present model, (a) - forces *on* the skier.

However, the concept of centrifugal forces becomes essential when you analyze a situation using model (b) instead of (a). For example, when you spin a can of water around on the end of a string, what do you call the force that the string is obviously exerting on your hand, trying to pull it outward? This is a radially outward force that can be measured with a little spring scale put in line with the spring. Its as real as any other force in the universe.

The big difference between this situation and your analysis of the skier is that you are used to analyzing the force making the skier (or can of water) move in an arc, whereas, sometimes its way more convenient to consider the force that the arcing skier (can of water) is exerting on the snow (twirler's hand).

I do assume that you are happy with "centripetal" as the name to hang on forces which cause something to go in a circle, since that's what you pretty much are doing in your model.

Other than that, go skiing. I wish I could.

Tom / PM

PS - BTW, after your comment about going skiing tmmrw, I looked at the location given at the bottom of your post. Didn't you used to live in NJ last season? Am I confusing you with someone else? Have you moved? Permanently?

PS (a day later) - Ignore the previous "PS". It was late. I was confusing Ydnar with Yuki.

[ November 10, 2003, 10:59 PM: Message edited by: PhysicsMan ]
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