 Poster: A snowHead
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Sideshow_Bob, good point.
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Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
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| laundryman wrote: |
| Sideshow_Bob, good point. |
Agreed. I was pondering this too.
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Well, the person's real but it's just a made up name, see?
Well, the person's real but it's just a made up name, see?
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I've read through all this thread (and in the process I realised I forgot A LOT of maths - used to be good at it...  )
And I'm not an instructor either, so no credentials.
First of all: I'm firmly in the camp of "the differences are so small compared to the approximations of the model (snow not perfectly flat, carving not perfect, transition phase involves flat skis at some point) that it's extremely hard to say whether the legs / skis are doing identical or nearly identical things.
Here are some comments though:
It's clear from the various demonstrations put forward that the curves can't be parallel. I think it's a question of terminology - don't think V8 had a clear understanding of the definition of a parallel curve.
It seems however they can be identical, and there was a discussion on how this can be achieved without tipping the inside ski more and skiing bow-legged. Here I have a question. If you try actively to retract the inside leg so there's little inside tip lead, aren't you effectively pressuring the shovel more and allowing the ski to diverge slightly at the beginning of a turn, without needing to put a lot of weight on that inside ski? The ski will follow a shorter path than the outside one and would normally travel faster, but the skier can effectively slow it down since our legs are usually joined at the waist...(and, since the ski is already carving in the snow, slowing it down doesn't need to result in a skid, as long as the snow exerts enough force to keep the inside ski bent in its track).
That would avoid (a lot of) scissoring and also (I think) the need to tip the inside ski more. It might even feel / look like the skis are doing exactly the same thing - it's just that the weight distribution is central on the outside ski and forward on the inside one, so the inside one flexes more.
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| horizon wrote: |
It seems however they can be identical, and there was a discussion on how this can be achieved without tipping the inside ski more and skiing bow-legged. Here I have a question. If you try actively to retract the inside leg so there's little inside tip lead, aren't you effectively pressuring the shovel more and allowing the ski to diverge slightly at the beginning of a turn, without needing to put a lot of weight on that inside ski? The ski will follow a shorter path than the outside one and would normally travel faster, but the skier can effectively slow it down since our legs are usually joined at the waist...(and, since the ski is already carving in the snow, slowing it down doesn't need to result in a skid, as long as the snow exerts enough force to keep the inside ski bent in its track).
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Yes, I think that's quite feasible and has been discussed already at various points along the way. Ski bending does not come from weight transfer alone, so there's no reason why the inside ski cannot be bent more than the outer if it's being steered or more forward loaded. As you say, whether it skids or carves depends on how much grip there is available.
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Anyway, snowHeads is much more fun if you do.
Anyway, snowHeads is much more fun if you do.
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As a little thought experiment:
Fit a ski on your left foot
But instead of fitting a ski on your right foot, fix a small pointed stick to the base of your boot
Now ski a perfect right hand turn, so the single outside ski carves out a perfect partial circle.
While doing this keep your inside boot parallel to the outside and just let the stick mark a path in the snow. Remember there is no inside ski to take any load, so the stick is simply marking the trajectory of the inside boot.
So what are we left with? I would imagine a pair of perfectly parallel curved tracks, one produced by the outside ski and the other produced by the stick. A mathematical observer would note that the inside track made by the stick was of a smaller radius than the outer ski track.
So to me this implies that if there had been an inside ski attached as normal, there would have been forces naturally trying to make it follow the inside radius as dictated by the dominant outer ski track and the relative positioning of the skier's two boots. It is not inconceivable that this would lead to the inside ski bending to conform to it's geometrical constraints.
Thoughts on this please?
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| Quote: |
| Another simple fact that only V8 would disagree with. In fact he has implied that it would be virtually impossible to load the inside ski in such a way as to carve a tighter radius (which I disagree with), |
If you were to ski like this, think about what would happen to the outside ski as a consequence of bending the inside ski more.
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| veeeight wrote: |
| Quote: |
| Another simple fact that only V8 would disagree with. In fact he has implied that it would be virtually impossible to load the inside ski in such a way as to carve a tighter radius (which I disagree with), |
If you were to ski like this, think about what would happen to the outside ski as a consequence of bending the inside ski more. |
Can you give me a clue?
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| veeeight wrote: |
Caveat: You shouldn't really use WC montages to justify a position......this one's pretty nice:
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In my previous post I was deliberately talking about GS, and I used only GS montages. I noticed you showed a couple of examples from slalom, where there seems to be a different mechanism and you often see wider skis at transition than at the apex. (At a guess I would say this is a deliberate tactic to bring the outside ski closer to the gate and shorten the distance travelled.)
I agree that it is inaccurate to use one single montage to justify a position. However, when a particular phenomenon occurs time and time again, it may be used to support a hypothesis - which is all that was.
It is always difficult to analyse turns mathematically using montages. As Sideshow Bob mentioned regarding the above Kostelic montage, there may always be some pivoting that happens between two frames and is not captured.
However the mathematical fact remains:
Ski tracks can either be parallel or identical, but not simultaneously both.
Having that theoretical understanding is, I believe, a useful tool when watching skiers and studying their tracks. So therefore this thread, despite the length, has actually been of practical use.
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| uktrailmonster wrote: |
It is not inconceivable that this would lead to the inside ski bending to conform to it's geometrical constraints.
Thoughts on this please? |
On an infinitely hard surface, there are only two factors which limit how far the ski will bend: sidecut and edge angle.
This was very eloquently defined here:
http://forums.epicski.com/showpost.php?p=184808&postcount=7
(But on a softer surface, further bending of the ski is possible through snow compression.)
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Martin Bell,
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| Ski tracks can either be parallel or identical, but not simultaneously both. |
This is correct, with overwhelming proof having been supplied.
But what vexes me is how a certain young gentleman, in the face of this overwhelming, incontrovertible evidence, can still cling to the fallacy that identical radii (ski tracks, in this case) can be laid down in parallel!
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snowHeads are a friendly bunch.
snowHeads are a friendly bunch.
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| Martin Bell wrote: |
| uktrailmonster wrote: |
It is not inconceivable that this would lead to the inside ski bending to conform to it's geometrical constraints.
Thoughts on this please? |
On an infinitely hard surface, there are only two factors which limit how far the ski will bend: sidecut and edge angle.
This was very eloquently defined here:
http://forums.epicski.com/showpost.php?p=184808&postcount=7
(But on a softer surface, further bending of the ski is possible through snow compression.) |
I'm starting to think that's a slightly simplistic view of the real situation based only on bending resulting from the in-line boot pressure applied directly to the middle of the ski. For sure on an infinitely hard surface the bending from this loading would be limited by the surface. But if any kind of torque loading (steering) is induced, depending on the edge grip available, the ski may deform further due to the dynamic loading along the entire length of its edge. My thought experiment above was trying to show if there is likely to be an induced torque acting on the inside ski, simply from attempting to ski perfectly parallel turns with your feet at a fixed distance apart. I'm thinking there is because in that situation the inside ski will be naturally forced to follow a tighter radius. Whether it carves or skids to achieve it is another matter!
Obviously this only applies if we're leaving parallel non skidded tracks.
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And love to help out and answer questions and of course, read each other's snow reports.
And love to help out and answer questions and of course, read each other's snow reports.
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| PJSki wrote: |
| But what vexes me is how a certain young gentleman, in the face of this overwhelming, incontrovertible evidence, can still cling to the fallacy that identical radii (ski tracks, in this case) can be laid down in parallel! |
The simple answer would be that mathematically, I agree that circles are either parallel, or identical.
Skiing Reality, as trialled my my colleagues and myself, can show otherwise, depending on a whole host of other factors beyond a simplistic assumption based on circles.
For a start, in a series of ski turns, where do we ever ski a circle of constant radius?
(hint: In the USA, on highway cloverleaf intersections, they have a constant circle radius ramp on/off (and thats why they feel so awful to negoiate. In the UK, complex motorway slip roads do not hold a constant circle radius, but a spiral of increasing tightness and decreasing tightness).
Last edited by So if you're just off somewhere snowy come back and post a snow report of your own and we'll all love you very much  on Mon 21-04-08 19:07; edited 1 time in total
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You know it makes sense.
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And in that Fastman post linked to above at Epic, here's one of the clues that he drops that will help us here in this thread, regarding a higher loading on the outside ski, causing it to bend more and prescribe a sharper arc than the inner ski. One of the potential side effects of this is that it will counter (sic) to some extent the natural track divergence that occurs at the apex of the turn (if the skier is holding a constant stance width).
| Quote: |
| The pervasive tendency is for the outside ski to be carrying the heavier load and higher edge angle. This can be clearly seen in most of the montages you posted. These higher loads and angles in the outside ski cause it to naturally arc a sharper turn, as too can be seen in the montages. It will do that even with no supplemental rotary force being applied to it. |
Note that Fastman, like myself, talk about arcs, and not circles.
PS: time for me to go out and train some racers, so my presence will be sparse. I'm sure you'll miss me.
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Otherwise you'll just go on seeing the one name:
Otherwise you'll just go on seeing the one name:
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| uktrailmonster wrote: |
| veeeight wrote: |
| Quote: |
| Another simple fact that only V8 would disagree with. In fact he has implied that it would be virtually impossible to load the inside ski in such a way as to carve a tighter radius (which I disagree with), |
If you were to ski like this, think about what would happen to the outside ski as a consequence of bending the inside ski more. |
Can you give me a clue? |
I'm not ignoring you, but it might take me a litle time to find you a pictorial example, as this is seldom technique intent by skiers/racers. But I'm sure any of my colleagues will be able to supply the answer.
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Poster: A snowHead
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| veeeight wrote: |
The simple answer would be that mathematically, I agree that circles are either parallel, or identical.
Skiing Reality, as trialled my my colleagues and myself, can show otherwise, depending on a whole host of other factors beyond a simplistic assumption based on circles.
...
For a start, in a series of ski turns, where do we ever ski a circle of constant radius?
...
Note that Fastman, like myself, talk about arcs, and not circles. |
You've had it pointed out plenty of times that "parallel and identical" cannot apply to ANY pair of arcs.
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Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
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veeeight,
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The simple answer would be that mathematically, I agree that circles are either parallel, or identical.
Skiing Reality, as trialled my my colleagues and myself, can show otherwise, depending on a whole host of other factors beyond a simplistic assumption based on circles.
For a start, in a series of ski turns, where do we ever ski a circle of constant radius? |
Now you really are floundering. I can actually hear the sound of goal posts being dug up and dragged to a different (still wrong) location. It matters not one got, young man, whether the arcs are constant or otherwise, if they are to be defined as identical (which is how you defined them) they cannot be parallel. There has to be divergence and convergence, the existence of which (in your so called "perfect parallel" tracks) you have thus far denied.
Last edited by Obviously A snowHead isn't a real person on Mon 21-04-08 19:46; edited 1 time in total
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Well, the person's real but it's just a made up name, see?
Well, the person's real but it's just a made up name, see?
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| veeeight wrote: |
The simple answer would be that mathematically, I agree that circles are either parallel, or identical.
Skiing Reality, as trialled my my colleagues and myself, can show otherwise, depending on a whole host of other factors beyond a simplistic assumption based on circles.
For a start, in a series of ski turns, where do we ever ski a circle of constant radius?
(hint: In the USA, on highway cloverleaf intersections, they have a constant circle radius ramp on/off (and thats why they feel so awful to negoiate. In the UK, complex motorway slip roads do not hold a constant circle radius, but a spiral of increasing tightness and decreasing tightness). |
It's not just perfect circles that are either parallel or identical. It applies to any random curvature too. This has been fully explained to you on numerous occasions by several qualified people, but you still don't understand. I agree we don't tend to ski constant radius turns, although there's nothing to stop us from doing so in theory. Since you bring up motorway slip roads, you may also note that if they happen to have 2 lanes, the inside lane will be parallel but not identical.
You need to finally get the idea that 2 identical arcs cannot be parallel to each other, regardless of their curvature. Come on it's really easy to understand this simple point. Then you can relate better to what really must be happening to the skis. You seem completely hung up on this idea that both skis are independently tracking identical arcs and yet somehow do not diverge or converge. Can you really not see the paradox here?
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You need to Login to know who's really who.
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uktrailmonster,
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| Can you really not see the paradox here? |
I don't believe he'll ever admit he's wrong. But it's interesting watching him trying to bend reality until it fits his own argument.
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Anyway, snowHeads is much more fun if you do.
Anyway, snowHeads is much more fun if you do.
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uktrailmonster, PJSki, laundryman, He isn't going to change his mind. You are throwing your efforts at a black hole. No light is ever likely to escape. Just bookmark this thread to link to (along with the pole straps thread perhaps) next time there is a spurious claim of Ski Instructor Infallibility. 
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You'll need to Register first of course.
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| veeeight wrote: |
The simple answer would be that mathematically, I agree that circles are either parallel, or identical.
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Well I guess that's a start 
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April 20th:
| veeeight wrote: |
| Scissoring and Diverging are NOT part of carving/skiing, and the inside ski does NOT need to carve a tighter radius. |
April 21st:
| veeeight wrote: |
| the natural track divergence that occurs at the apex of the turn |
Well done veeeight, the ability to retain an open and flexible mind, and resist clinging to rigid dogma, is a sign of a good coach.
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veeeight,
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| (hint: In the USA, on highway cloverleaf intersections, they have a constant circle radius ramp on/off (and thats why they feel so awful to negoiate. In the UK, complex motorway slip roads do not hold a constant circle radius, but a spiral of increasing tightness and decreasing tightness). |
So, according to you, the innermost white line of an increasingly and decreasingly curving motorway slip road is identical in curvature to the uttermost one? And if it could be moved, while retaining its curve, it could be exactly overlaid on its parallel cousin?
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You'll get to see more forums and be part of the best ski club on the net.
You'll get to see more forums and be part of the best ski club on the net.
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veeeight, Ok let's pretend I believe you for a minute, so we can move on as you say. What's the next step in understanding what is really happening here?
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| veeeight wrote: |
| For a start, in a series of ski turns, where do we ever ski a circle of constant radius? |
| veeeight wrote: |
| Note that Fastman, like myself, talk about arcs, and not circles. |
May I respectfully remind you that this point was already covered, back on page 5 (ah, those long lost halcyon days...):
| Martin Bell wrote: |
By the way it may be difficult to really define a turn "radius", because according to "Physicsman", a carved turn is not a circle but a "sinusoidal curve", whatever the hell that is 
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snowHeads are a friendly bunch.
snowHeads are a friendly bunch.
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veeeight,
| Quote: |
| (hint: In the USA, on highway cloverleaf intersections, they have a constant circle radius ramp on/off (and thats why they feel so awful to negoiate. In the UK, complex motorway slip roads do not hold a constant circle radius, but a spiral of increasing tightness and decreasing tightness). |
Can you just state for the record, that the above 'hint' is being presented by you as your proof that two identical arcs can exist in parallel in this context?
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And love to help out and answer questions and of course, read each other's snow reports.
And love to help out and answer questions and of course, read each other's snow reports.
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Thanks for those links, very informative. Those are exactly the 2 explanations I am thinking about i.e. additional bending from changes in load distribution along the ski length due to torque inputs (either induced or applied) or the alternative diverging and converging skis. I'm sure both occur to a certain degree depending on what you are trying to achieve i.e. beat the clock or carve pretty tracks
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You know it makes sense.
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| uktrailmonster wrote: |
| What's the next step in understanding what is really happening here? |
Maybe the next step is to encourage instructors, coaches and examiners to move away from the pursuit of the "perfect" carved turn (parallel skis, parallel shins). It has been conclusively proven that there will always be some divergence (either of shins or skis), or some other "fudging" through steering/rotary movements. (And I personally think the "extra shovel bending through added cuff pressure" tactic is a bit of a limited application, because it will not work on hard surfaces.)
We should always be skeptical of those who insist on certain movement patterns purely on the basis of some dubious aesthetics.
Good skiing means effective skiing; instructors and coaches should focus more on teaching a wide range of skills which can be applied flexibly in different situations where required.
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Otherwise you'll just go on seeing the one name:
Otherwise you'll just go on seeing the one name:
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Martin Bell, well said as usual. Your thoughts mirror what i have concluded, we can get pretty close to perfect but only cause we fudge perfectly carves turns through effective use of all the skiing turning skills. THe Epic links were most interesting and what i take away from them is that for high performance skiing high edge angle is king.. Nothing new when you look at all the WC photos presented here. I am still interested to see what steering element is most important to actively keep that pesky inner ski tracking well. I thought shovel loading or torque could be the main culprit but am open to other ideas. Your thoughts tend to keep coming back to the skier having to cope with convergence or divergence to maintain arcs. do you recon scissoring or pivoting are the more prevelent action with SL or GS skis and turns as opposed to shovel loading?
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Poster: A snowHead
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I think a reference was provided to a mathematic proof that identical arcs cannot be parallel. However, the full paper was not online. I want to provide a rough proof. Ideally, there’d be some accompanying diagrams: I’ll try to add them later. In the meantime, anyone who’s remotely interested should probably “sketch along”.
First some facts, that I hope can be treated as axiomatic, about arcs. They are continuous functions and so are their derivatives. In other words, the gradient of an arc changes continuously. It also changes in the same direction. In other words, in a single arc, there are no points of inflection (“transitions”, in skiing parlance). Crucially, no two points have the same gradient on an arc.
Now some points about parallelism. For two arcs to be parallel, for any point on one arc, a line drawn normal (at right angles) to its tangent must intersect the other arc also normal to its tangent at that point (no lead/lag!) - and the length of all such lines must be equal (no divergence/convergence!). This is clearly true - only an illustrative example - for the diameters of concentric circles.
Now, take any arc and duplicate it. Displace it by (∆x, ∆y). Take any point (A) on the original arc. Draw a line from it, normal to its tangent until it intersects the duplicate arc at point B. It should be clear that this line between the arcs (AB) can only be normal to the arc gradient at B if ∆x and ∆y are in some fixed proportion. If they are in any other proportion, the curves cannot be parallel.
But suppose ∆x and ∆y are in that proportion: we have found one line that intersects the tangents to the two arcs at right angles in each case. B must also be the closest point on the second arc to A, considering that we if move in either direction along the second arc from A the change in gradient takes the second arc away from A. Now lets go back to A on the first arc and move some (any) distance along its arc to point C. We need to get to the equivalent point (D) on the duplicate arc, in order that the length of CD is equal to that of AB (given by ∆x and ∆y according to Pythagoras). CD is clearly parallel to AB, but it cannot be normal to the tangent of either arc at C and D, since the gradient at C and D MUST be different to that at A and B. So, identical arcs, displaced from one another, cannot be parallel along their lengths.
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Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
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So in the haste to reload bullets everyone has ignored Fastman's statement that the outside ski arcs a sharper turn than the inside?
| Fastman wrote: |
| The pervasive tendency is for the outside ski to be carrying the heavier load and higher edge angle. This can be clearly seen in most of the montages you posted. These higher loads and angles in the outside ski cause it to naturally arc a sharper turn, as too can be seen in the montages. It will do that even with no supplemental rotary force being applied to it. |
This point is quite crucial in understanding how you can actually approach a two parallel arcs in the apex of the turn......
And Martin Bell, whilst I'm conviced that diverging and converging tracks are made in the snow as a result of identical arcs (if you park and ride), I'm not yet convinced that anywhere in the world, any ski racer/coach/instructor would wish to pattern diverging skis.......... if you consider a turn that is not park and ride, but instead one which is worked through with dominant loading on the outside ski, both skis would track a course that is closer to parallel as a result of the outside ski bending a tighter radius than the inside ski.
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Well, the person's real but it's just a made up name, see?
Well, the person's real but it's just a made up name, see?
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skimottaret, please please please when you're looking at the WC montages, in the vast majority of cases, which ski is bent more?
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You need to Login to know who's really who.
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| veeeight wrote: |
So in the haste to reload bullets everyone has ignored Fastman's statement that the outside ski arcs a sharper turn than the inside?
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Only because it had already been covered a couple of pages ago:
| Martin Bell wrote: |
3. Or you can even carve tracks where the outer radius is smaller (because of greater weighting of the outside ski), in which case divergence/convergence, and/or inside ski steering, become even more necessary. |
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Anyway, snowHeads is much more fun if you do.
Anyway, snowHeads is much more fun if you do.
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| veeeight wrote: |
| if you consider a turn that is not park and ride, but instead one which is worked through with dominant loading on the outside ski, both skis would track a course that is closer to parallel as a result of the outside ski bending a tighter radius than the inside ski. |
Not really. I'm not sure if you fully understood the Fastman explanation. Here is the key part:
| Fastman wrote: |
| The inside ski lifting and diverging can be attributed to a needed manual redirection at the top of the turn to compensate for the straighter inside ski arc the racer knows will occur. |
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You'll need to Register first of course.
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| Martin Bell wrote: |
| uktrailmonster wrote: |
| What's the next step in understanding what is really happening here? |
Maybe the next step is to encourage instructors, coaches and examiners to move away from the pursuit of the "perfect" carved turn (parallel skis, parallel shins). It has been conclusively proven that there will always be some divergence (either of shins or skis), or some other "fudging" through steering/rotary movements. (And I personally think the "extra shovel bending through added cuff pressure" tactic is a bit of a limited application, because it will not work on hard surfaces.)
We should always be skeptical of those who insist on certain movement patterns purely on the basis of some dubious aesthetics.
Good skiing means effective skiing; instructors and coaches should focus more on teaching a wide range of skills which can be applied flexibly in different situations where required. |
Never mind that I don't understand either the maths or the physics of all this, I find it strange that I've been telling students for years that parallel isn't that important and that WC skiers are rarely actually parallel!! Dogma is a dangerous thing. (Now going off again).
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easiski,
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| easiski wrote: |
| I find it strange that I've been telling students for years that parallel isn't that important |
But do they believe you ?
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You'll get to see more forums and be part of the best ski club on the net.
You'll get to see more forums and be part of the best ski club on the net.
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easiski, quite (and how many of those WC SL turns are carved all the way through either )
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FAQ
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