Ski Coaching

My fellow coach Dave Tapley reported to me that one or two skiing blogs have recently been filled with (largely rubbish) posts from well-meaning but clearly confused instructors. The kind who can ski well no doubt, but who's comprehension of skiing is shall we say rather shallowly based.

The discussion hinges on whether or not "parallel" skiing is actually possible. Dave quoted his own observation that when you are "carving" perfectly you can inspect your skis' tracks and they look to be perfectly parallel. However, they are not drawing the same radius arcs (part-circles).

So, After some thought I wrote to a pupil and friend of mine,  physicist Tony York. Here is the e-mail like what I wrote.

Let's say we have a skier effecting an arc, a perfectly "carved" arc - an arc during which both skis slide perfectly (no skid) -and let's say that his skis are parallel to one another all the way round that arc.

For this to happen, the inner ski must perforce travel a shorter distance than the outer ski.  For this to happen without skidding, the inner ski must either, tilt more, or bend more, or a combination of both. Were this not to be the case, they would necessarily be describing segments of arcs of non-concentric circles.

To bend more it would need to be receiving greater centripetal force, which we know would be very unstable for the skier, so optimally no more than 50% of the force should be being resisted by the inner ski. Unless - I wonder - being nearer to the circle's centre it inevitably receives more force ? ?

Even in this scenario, the inner ski must be tilted slightly more than the outer ski, or it would skid. This is because were it to be tilted to the same degree it would be describing a circle of the same diameter as the outer, but in a different location - they would not be concentric; and if you draw this out on a piece of paper it becomes obvious that the two circles must cross (twice) which thereby denies the "parallel" requirement of this experiment.

Now, there is plenty enough bio-mechanical movement in the hips and ankles to permit this variation, but here a little confusion arises in my mind ( which is rather unusual  -  because usually there is a lot of confusion in my mind; I must do this again!).

There will be one aggregate centre of mass for the skier, supported against the centripetal force by two platforms.  Here then is where my confusion arises.

Where, precisely is the centripetal force's own centre of origin? Or is this a daft question?  Is there, for example, just one centre of centripetal force, or since there are two platforms, are there also two centres of this force? After considering this I feel there must be two, because each ski (platform) is resisting a force, and I feel that this necessitates having two forces, coming from two slightly different directions. This being the case, then there are two reasons for the inner ski to tilt more - 1) in order to present a platform at 90 degrees to the force, and 2) in order to enable the ski to slide perfectly around a circle of smaller radius.

But if this is so, then if you followed the directional lines of these forces (or this force) from whence do they emanate? Is it for example on the snow's surface? Or precisely at the interface between the platform and supporting surface? Or - does it emanate from somewhere else, underground? And if so, how far away/down?

I think it must be at the interface only, which is where the force and the resistance meet. Am I right? After all ( I conjecture) unless there is resistance, there will be no centripetal force - in effect they are one and the same???? Without the one, you cannot have the other.

Bob

PS - It's just occurred to me that the bend in the ski is created at least in part by a force from ahead of it, acting on the shovel through a couple between the shovel and the ski's centre. The shorter the radius of the circle being followed for any given tangential speed, wouldn't the force be inevitably greater? So might we not get more bend anyway even though the skier's mass was being equally distributed between the two skis?

Tony, after considerable cogitation answered as follows, and I'm very grateful to him.

OK, (he said) here are my thoughts so far:
 
Since the skis are going round curves of different radii, and are therefore travelling at different speeds, it is mathematically easier to say they are both moving with the same angular velocity (ie they would both take the same time to complete a full circle).  The expression for the force is then mw²r (m is mass, w is angular velocity, r is radius).  Because r is greater for the outside ski, there will be more force, which is what the skier needs, in order to be stable.
 
So far so good - but then how do the skis provide this force?  If the outer one is producing more of the centripetal force, and they are both at the same angle, it will bend more, making it impossible for both skis to be "carving", as the inner one is following a tighter curve.  If the inner one is tilted more, perhaps it could be describing a tighter arc, but be bent less, consistent with it producing less force.  I should stop now while I'm ahead, but I have a horrible feeling that if you look at a still photo of a racer in a turn, the outside ski is tilted more! (Yes, but you'll usually see that the inner ski is all but "floating" and is not actually carving, even though that's what they would like. Bob)
 
The bending of the ski is a result of the snow pushing against it, but that won't be simple either.  Even in the simplest imaginable scenario of the same force from the snow against each cm of the ski, the front of the ski will have more bending moment, as it is longer than the tail.  Whether this leads to more actual bending depends on the stiffness of the ski, which varies along the ski in a very complex manner, I would imagine.
 
As implicit in last para, as far as the ski is concerned the force comes from the snow immediately in contact with it, but that snow is in turn supported by the snow beneath it, which is in turn supported by the ground beneath it.  This is of course why the skier sinks deeper into powder before there is enough force generated to support him/her.
 
I don't think the idea of a "centre of centripetal force" is useful.  The vector sum of all the forces from both skis must pass through the centre of mass of the skier and be directed towards the centre of the circle in which he/she is travelling.  One also needs to be careful in talking about reaction forces.  This vector sum is effectively a single force acting on the skier.  There is no sense in which the skier is in equilibrium; he/she is being continually accelerated towards the centre of the circle.
 
God knows how ski designers do the business, & God knows how any of us can actually get the skis to do what we want (sometimes).  I should probably stick to making furniture or high energy nuclear physics; that would be simpler. 

I am very grateful to Tony for his observations, and if anyone wants to join in, then please do so; it won't make anybody's skiing any better, but it keeps the old grey matter from atrophying any more quickly than is necessary! And it sure as Hell beats "doing turns!"

Bob Valentine Trueman

Sounds a little impolite that - "watch your language" but it was just to get your attention, and to illustrate that the words you choose will have very different effects on your reader, or listener.

Human beings are tribal, and a feature of all tribes is that they have a language which is exclusive to them, and often is designed to be exclusive of non-members.

A good example of this is the street language of adolescents - all that "I'm like, Doh!" stuff; and "radical man", and much more that I can neither comprehend nor remember.

Of interest to me is the ski instructor tribe. This tribe also has a language of its own, which is readily bought into especially by younger trainees and instructors, and those new to the activity. Its use is one of the ways that a great many ski teachers can help themselves to feel that they are a part of the group.

Unfortunately, an unintended side effect is that your client, your pupil, is excluded in the process, because (s)he is not privy to the secret meanings attached to the words and phrases.

Let me give you an example - take the word "edge". This is one of the commonest words in the ski instructor's lexicon, and one of the least efficacious. It is often employed in totally meaningless phrases dreamt up by the marketing departments of the manufacturers of skis. A classic example is the "this ski is faster edge-to-edge than that ski".

What in Heaven's name is this supposed to convey? Here is a short list of some of the things it does not define :-

1. It doesn't define what an "edge" is, in this context.

2. It doesn't define when a ski is on an "edge" and when it isn't.

3. It in no way illustrates what is required to get the ski to move from one edge to another, nor why it is perceived to take less time to do this than on any other ski.

I could go on, but I'll leave it there.

Does it perhaps mean, "this ski is easy to get to change direction"? And if that is what is intended to be conveyed, why not say so? Because that wouldn't be tribal, exclusive, and sound "cool" would it?

One of the essential precepts of Neuro Linguistic Programming, with respect to communication, is that the only mechanism humans have for conveying ideas from one mind to another's mind, is words.

The process goes something like this - I formulate an idea in my mind; I then have to search for words - and a structure for those words - which within the framework of my experience, I believe expresses my idea.

I then utter those words, which are picked up by my intended recipient, who first of all runs those words through a kind of database in his/her mind and via some form of cross referencing retrieves their meanings for those words, which when assembled in the order that I gave them, builds an idea in their mind.

During this process there are manifold opportunities for omissions, distortions, and deletions. You can see, I'm sure, that the chances of the two ideas being congruent are minimal indeed, even at the best of times. The potential for misunderstandings is so huge that it is a wonder any of us can communicate at all with anyone else. Perhaps we don't!

N.L.P. tells us that words are merely labels for experiences. For example when I see a colour, which I know as blue, I give it the label "blue". You also have a label called "blue" and you apply it to the colour which you have become accustomed to apply this label to. But is the colour you see, the colour that I am seeing? We can never know. The colour that you are seeing, when I see it, I perhaps give the label "red" to.

I might be seeing the colour which you call "red" but I have become accustomed to labelling it "blue". I saw an hilarious example of this once, when I met a gun dog trainer who had trained his dog to do the opposite of every instruction he gave him. When he said "sit" it stood up; when he said "away" it came back; and so on. The instructions were the same, but their labels were reversed, to the watching throng "sit" meant one thing, but to the dog, another.

Now let's just revisit that word "edge". If you are ski instructor, then you know perfectly well what you mean by "edge", and the idea doesn't bother you at all; in fact as an instructor and excellent skier you might even like it. But how many other people like edges? Not many.

To most people, edges are narrow, sharp, unpleasant, easy to fall off, and associated with knives and things; altogether to be avoided. And here are you telling them to "get an early edge"; "get the ski on the edge" (without you will note, advising them on what to do to achieve this).

What I'm saying is this - if you want to communicate with others, and especially with pupils who are not members of  your tribe - pay attention to their likely experience of skiing; to their possible perceptions about the labels you use; and do your best to keep the jargon out of it.

Bob Valentine Trueman

www.bobski.com / www.blogstoday.co.uk (Search for Limits to Growth)