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# Lightening - Page 2

Cgieb,

Right on the money. As I said somewhere this is a very exciting (and fast) way to ski.

This is also a very idealized turn and something I only put together occasionally. I'm quite happy if the first third of the arc is solidly engaging the edges so that I can use the skis to create the force needed to move me back across the hill in the middle third of the arc and then use the last third of the arc to manage things to ge back to neutral. This I can do fairly consistantly and is almost as much fun (and a lot less work).

Yd
Quote:
 Originally posted by Si:.... Cgeib, Switching my frame of reference from the previous post, what I'm saying (as Ric B and Yd have also said) a turn involves a building followed by a reduction of the centripetal turning force (note that the only the so-called centrifugal force is shown in the figure and that the centripetal force is of the same magnitude but in exactly opposite direction). That is, in order to start move away from "A" (slow down the acceleration toward A) in the figure there must be a reduction of the centripital turning force. I think this diagram has some significant shortcoming for this discusssion as it doesn't include the path of the skis nor the relative loading of each ski. Thus, I hesitate to talk about where this reduction of turning force occurs but I believe it is right at 5 or between 5 and 6....
SI,

Thanks for the clarification. I think I have a better idea what you're saying now, concerning centripetal force. In the quote I referenced in my prior post, you mentioned momentum, and it didn't make sense to me. Naturally, I'm just asking questions here to get a better understand as well, and I look forward to Ydnar's post concerning these forces.

[ November 05, 2003, 10:32 PM: Message edited by: cgeib ]
Si,

Man, we badly need to ski. I will give it one more shot and then declare you a non-believer!

There is no question that the centrifugal/centripetal force on the skis gradually decrease as the turn completes. But not because of lightening! The turn completes because the arc of the ski and the arc of the CM eventually intersect. This process gradually decreases the centrifugal/centripetal forces all the way to zero, since at transition the CM only has a perpendicular force on the ski with no centrifugal/centripetal component. The real disconnect here is that you think it takes "lightening" to get the skis back under you. I insist that in ideal turns that is an illusion. All you really have to do is to retract your legs to accommodate the converging paths of the skis and CM. And you only have to retract if you want to keep the CM at relatively constant distance from the ground. Otherwise you would be bobbing up and down through your turn. [img]smile.gif[/img]
Tom B,

First, retraction is lightening! (As far as that goes relaxation of the legs even without active flexion is lightening - at least that's how its ultimately used as a cue in the progression we have been discussing). I am not at all trying to argue about the semantics. I don't even use that particular "cue" in my own skiing (if anything I think about it in terms of retraction!). I have only used it here because we have been discussing lifting/tipping -> lightening/tipping as an effective progression towards high level skiing.

Second, I don't know what else to say but repeat that the arc is a consequence of forces acting on the ski/skier system not the other way around.

Third, I think you need to retract/lighten at some point in a turn no matter what. Turning in one direction, one leg is downhill and longer than the other. Going the other way, they reverse their lengths with the long one becoming shorter and shorter one becoming longer. To get between these you've got to retract/lighten.

If you want to discuss/clarify further I'd be happy to do it in email if not here.

You said "The real disconnect here is that you think it takes "lightening" to get the skis back under you." I actually think and have talked about "lightening" (leg muscle relaxation, leg flexation, leg retraction) being needed well before that to slow the separation of the CM and skis. This is where the end of one turn and beginning of another overlap from my point of view.

[ November 06, 2003, 11:24 AM: Message edited by: Si ]
Si: Second, I don't know what else to say but repeat that the arc is a consequence of forces acting on the ski/skier system not the other way around.

Ric B: Maybe we can say it this way, the arc of both the body and the ski are a result of the "systematic execution of actions" (websters definition of process) which harness and utilze the already existing force of gravity and our momentum.

TomB, if our actions create a turn, then don't our actions have to uncreate the turn. What is it we do, movement wise to uncreate the turn? We can give in to the forces we created, but then that requires an "action with intent, or movement with purpose" quoting someone I respect. We have to put the actions that are creating the turn in reverse with some action.

If something hasn't been explained to someone's satisfaction, does that make them a non believer?
Ric B,

I think we are now converging to very similar views! I should add that the "non-believer" statement was a only a joke. I consider Si a friend. So let me respond to some comments (these are my opinions only and may be completely incorrect):

Si: First, retraction is lightening
TomB: It is not a good idea to use them interchangeably. Why? Because retraction is the act of accommodating the skis to come back under you while maintaining constant ski-snow contact and lightening is the act of actually decreasing the ski-snow contact (the pressure on the ski) to compensate for a mistake (like the CM being too far inside the turn). This is an important point because it explains why lightening is sometimes required to compensate for real-world skiing.

Si: Second, I don't know what else to say but repeat that the arc is a consequence of forces acting on the ski/skier system not the other way around.
TomB: Fair enough. This is the old centrifugal/centripetal argument. No issues here, I understand your point.

Si: Third, I think you need to retract/lighten at some point in a turn no matter what
TomB: Not if you are willing to raise the CM at the end of the turn. Consider this: suppose that at the apex of the turn the skis are in the fall line, your CM is close to the ground and the outside leg is extended as far as possible (think racers). As the turn completes, the outside leg could stay relatively straight and you can gradually lengthen the inside leg until CM and skis "intersect". But then at the end of the turn you are standing too tall (kind of ridiculous). So you retract to keep the CM low. Again I prefer to use retract not lighten for the reasons give above.

Ric B: If our actions create a turn, then don't our actions have to uncreate the turn.
TomB: Well, yes, but it is the path taken by the CM that will ensure that the ideal turn terminates. However, if you park-and-ride the turn (CM and skis take the same arc) then one has to lighten skis or increase pressure on the skis to break the turn.

By the way, I normally would not get into such discussions, since I am far from qualified to do so. But the truth is that this thread helped me explain the difference between dynamic skiing and the park-and-ride style. I was always able to tell the difference between the two (visually), but could never really explain what are the mechanics required to avoid the latter.
Tom, I considered you a friend until you disgreed with me in a publice forum . Ric, comments like Tom calling me a disbeliever present a great example of the misinterpretation that can occur in a written exchange like this. It reminds me that I should try to assume the best intent in this forum and only think otherwise when someone has shown their true colors repeatedly.

TomB: It is not a good idea to use them interchangeably. Why? Because retraction is the act of accommodating the skis to come back under you while maintaining constant ski-snow contact and lightening is the act of actually decreasing the ski-snow contact (the pressure on the ski) to compensate for a mistake (like the CM being too far inside the turn). This is an important point because it explains why lightening is sometimes required to compensate for real-world skiing.

Si: Perhaps semantics is the crux of the matter here. I don't think there's any difference between these two definitions except the editorial comment: "to compensate for a mistake" attached to lightening. As you use it above, "accommodating" involves a decrease of the "pressure on the ski." Lightening as I have encountered its use by others (PMTS and otherwise) is ususally described with words like "relaxation of the muscles in the leg."

In essence I don't think our viewpoints are in much conflict. I would say that I think you are hung up on the idea that lightening (and even lifting) are corrective movements. I do not agree and in fact think that the concept of lightening is exactly what you do in "accommodating the skis to come back under you while maintaining constant ski-snow contact." I think it is important to note, however the constant ski-snow contact does not mean constant pressure (which is where lightning/retractionflexation come in) and furthermore in examining the range of "expert" turns the constant ski-snow contact is not even universally true (as a number of people have pointed out in describing the turns of the Mahres and as can be seen in some top racers at times).

Also, in terms of differences that remain, I think I understand the conceptual model you use as a basis for the point of view you are presenting. I think though, that while it is useful, it is also limiting because of its teleologic nature. I like Ric's definition: "the arc of both the body and the ski are a result of the "systematic execution of actions" (websters definition of process) which harness and utilze the already existing force of gravity and our momentum." An important point to note here is that this still includes the concept that the arc results from action vs. actions result from the arc.

A final note. Trying to desribe a turn where retraction/lightening or whatever is not used seems a bit detached from the discussion here - which from my reading was focused on 1) what high level idealized turns are about and 2) what are effective progressions to help a skier develop in that direction.

[ November 07, 2003, 10:00 AM: Message edited by: Si ]
Si said: In essence I don't think our viewpoints are in much conflict. I would say that I think you are hung up on the idea that lightening (and even lifting) are corrective movements. I do not agree and in fact think that the concept of lightening is exactly what you do in "accommodating the skis to come back under you while maintaining constant ski-snow contact."

If retraction and lightening mean the same thing we are in complete agreement. What we don't have is a word (action) to describe the situation where the ski-snow contact is not constant. Consider this:

Remember the Forces in Ski Turns diagram that Bob Barnes showed us? Although the 2 components (gravitational force and the centrifugal force) change through the turn, the resultant downward force on the ski (which is the vector sum of gravitational force and the centrifugal force) is always constant in the ideal turn. By constant I mean the magnitude is constant, not the direction. At the transition point the downward force = gravitational force.

But in everyday skiing this force does not have constant magnitude, since many times the skis are lighter and even completely off the snow at the end of a turn. What action causes the decrease in magnitude of the downward force? You will probably say it is too much retraction/lightening. Good enough for me. But I think it is fair to recognize that too much lightening/retraction is, in fact, a "corrective" move. It is an attempt to change the original path of the arcs taken by the skis and the CM.

==================

On a lighter note, are you coming to the Academy? I have enrolled in the Academy and booked flight and hotel, so unless disaster strikes, I will be there. We can pretend to ski ideal turns, while lightening, lifting and skidding all over Snowbird. [img]graemlins/thumbsup.gif[/img]

[ November 07, 2003, 12:53 PM: Message edited by: TomB ]
Yes Tom I think we have found agreement on very "ideal" turns! [img]smile.gif[/img]

But.... there are still some points you're making that still don't jive for me. As I said before Bob's Forces in Ski Turns diagram has substantial limits for purposed of the discusssion here on lightening as it doesn't deal with the loading on each individual ski. As I have said, in going from one direction to another one ski has to go from "more pressure to lighter pressure and the other goes in the opposite direction. I think we have been talking about and should continue to talk about (although I'm sure some would prefer we would just stop) what happens to each ski, both before and after, as we go through the transition point.

Another important point to me is that I wouldn't automatically classify what you've described with: "the skis are lighter and even completely off the snow" as a "corrective move." The amount of lightening, the rate that you lighten, and the timing of lightening (all a part of pressure management I believe) play a critical role in defining the nature of advanced skiing turns. I think the goal is to learn how to use lightening to vary the turns. I will agree, though, that a good turn involves smooth purposeful transition that produces the type of turn the skier is aiming for. The accomplished skier looks accomplished whether they are "carving" in the air or on the snow and displays the same kind of control, smoothness, and efficency in both exptremes.

Finally, no I will not be at the Academy. I will be getting "schooled" by Rendevous Mountain as I will be in JH for the gathering as well as a few days both before and after. And if I'm lucky I will be working on very uniform, sizeable leg retractions (no mere lightening I hope) in the steep and deep.

Edit: Of course I will do my best to make those retractions smooth and efficient

[ November 07, 2003, 02:02 PM: Message edited by: Si ]
Quote:
 Originally posted by TomB:Consider this: Remember the Forces in Ski Turns diagram that Bob Barnes showed us? Although the 2 components (gravitational force and the centrifugal force) change through the turn, the resultant downward force on the ski (which is the vector sum of gravitational force and the centrifugal force) is always constant in the ideal turn. By constant I mean the magnitude is constant, not the direction. At the transition point the downward force = gravitational force.
Is this some kind of new physics? Are you saying that as the centrepedal force of a turn builds up, gravitational forces decrease? Does this always happen, or is it only in ideal turns where the skier's speed approaches the speed of light?
In fact, the total forces acting on the skier increase as the turn develops. At some point, the skier releases the pressure (force) either by extending the uphill leg or relaxing the downhill leg. This reduction of pressure allows the CM to move out of the turn and across the path of the skis into the new turn, where the forces begin to build up again. And by the way, the downward force is always equal to the gravitational force (or more accurately the component of the gravitational force normal to the surface), unless the skier is actively increasing or decreasing pressure in that direction.

We all need to get out and ski more.

RR
Quote:
 Originally posted by TomB:...Consider this: Remember the Forces in Ski Turns diagram that Bob Barnes showed us? Although the 2 components (gravitational force and the centrifugal force) change through the turn, the resultant downward force on the ski (which is the vector sum of gravitational force and the centrifugal force) is always constant in the ideal turn. By constant I mean the magnitude is constant, not the direction. At the transition point the downward force = gravitational force...
No. The magnitude of the force does not generally stay constant. It may appear to do so if the forces due to acceleration are small compared to gravity, but when this is not the case, the net force can vary considerably. For example, consider the following two examples, (a) a flat and fast run with lots of G's compared to gravity:

(b) Steep and slow run with low-G's due to centrifugal and other acceleration forces:

These graphs were produced by a simulation I started to develop last night to address some of the isues raised in this thread. The parameters of the simulation are shown at the bottom of each image and include: slope angle, "wavelength" (ie, (say) distance between two successive LH traverses), over-the-snow-speed in mph, and "amplitude" (ie, how far to the left and right of center do the turns extend).

Gotta run. More later.

Tom / PM
Amazing diagrams, Tom/PM. It's amazing how sometimes mathematics and science mimic reality!

Thanks for putting that together. Now we have something to talk about!

Quote:
 At some point, the skier releases the pressure (force) either by extending the uphill leg or relaxing the downhill leg. This reduction of pressure allows the CM to move out of the turn and across the path of the skis into the new turn, where the forces begin to build up again.
Roland Rock--this point is the heart of the matter of this whole discussion, isn't it? I agree that extending the uphill leg or relaxing the downhill leg can accelerate the CM across the skis into the new turn (especially with a wider stance). But consider this question: how do bicyclists, unicyclists, monoskiers, "skwallers," snowboarders, and one-legged skiers (without outriggers or poles), all of whom lack the ability to "transfer weight" (change support foot), accomplish this "crossover"?

Therein lies the crux!

Best regards,
Bob Barnes

PS--what's a "skwaller," some may ask?
Quote:
quote:
At some point, the skier releases the pressure (force) either by extending the uphill leg or relaxing the downhill leg. This reduction of pressure allows the CM to move out of the turn and across the path of the skis into the new turn, where the forces begin to build up again.
Roland Rock--this point is the heart of the matter of this whole discussion, isn't it? I agree that extending the uphill leg or relaxing the downhill leg can accelerate the CM across the skis into the new turn (especially with a wider stance). But consider this question: how do bicyclists, unicyclists, monoskiers, "skwallers," snowboarders, and one-legged skiers (without outriggers or poles), all of whom lack the ability to "transfer weight" (change support foot), accomplish this "crossover"?
</font>[/quote]I was thinking about this conversation as I went through Ron LeMaster's web site last night. What I noticed is that, during the transition of these high-speed turns, the inside knee begins to angle downhill (thus releasing the edges) before there is a sign that the outside leg has reduced pressure. It seems to me that these world class skiers are releasing their uphill ski, directing their downhill ski into the new turn, and as a result have the new inside ski lightened.

I admit I may be seeing what I expect, but the order is telling, I think.

I find myself wondering: could I tun on just a skwaller?

ssh
Quote:
 Originally posted by Bob Barnes/Colorado:But consider this question: how do bicyclists, unicyclists, monoskiers, "skwallers," snowboarders, and one-legged skiers (without outriggers or poles), all of whom lack the ability to "transfer weight" (change support foot), accomplish this "crossover"? Therein lies the crux!
Bob, I don't think these really present a crux after thinking about it.

First I'd have to say that I'd throw out the bicycle analogy. It has a steering mechanism used to initiate turns that is not very similar to skiing. Additionally it has a 2 rounded compliant running surface with no edges. Unicylists don't have independent steering mechanism but are even more different in the running surface where there is a very short (almost point) contact and from what little I know pivoting is used quite a bit (I don't think we want to bring pivoting into this focused discussion and muddy the waters).

One legged skiers, snowboarders, monoskiers and skwallers all involve a single platform instead of two. Perhaps they are analogous to what in my own mind I refer to as 2 footed skiing where extension and retraction occur together (especially used in softer snow) but they do not have the same dynamics as someone on a two footed platform that can extend one leg while retracting the other.

So, I think we should focus on the specific cased at hand as these examples are interesting but all different enough in their dynamics that they would open up a much broader set of issues that I think will take us away from the question at hand.
Quote:
 Originally posted by ssh:I was thinking about this conversation as I went through Ron LeMaster's web site last night. What I noticed is that, during the transition of these high-speed turns, the inside knee begins to angle downhill (thus releasing the edges) before there is a sign that the outside leg has reduced pressure. It seems to me that these world class skiers are releasing their uphill ski, directing their downhill ski into the new turn, and as a result have the new inside ski lightened. I admit I may be seeing what I expect, but the order is telling, I think.
Like you ssh, I may be seeing what I expect. However, well before the inside knee (either old inside or outside knee which ever you meant) begins to angle downhill, the old outside leg is retracting and the old outside ski is reducing its edge angle (flattening/releasing).
OK Si--I maintain that it does not matter, but for the sake of argument, let's take the bicycle rider's hands off the bars, and not allow either the cyclist OR the unicyclist to tighten the radius of the turn by steering or pivoting, in order to create a "cross-under" move. Balance is critical, of course, but are they not still able to do it? Of course they are!

And the point remains that, while skiers are certainly ABLE to redirect their centers of mass by changing the support foot, the fact that snowboards, skwalls, and such can link turns at all suggests that they do not HAVE to. These "single-board" riders, of course, could also tighten the radius of their turns such that the board crosses under their CM, and they often DO. But they too do not NEED to, and indeed, when they do, it is for one of two reasons: either they are reacting skillfully to a need or desire to redirect their CM from the "ideal" sine wave path, or they are doing it to compensate for imbalance.

Pre-turning, counter-steering, "retraction turns" (both legs), and actively changing support foot (weight transfer/lift/lighten/etc.) are all important mechanisms for DISRUPTING the sine-wave flow of the CM, or recovering from imbalance. All are essential in the expert skier's repertoire. But none should be considered (or taught as) a fundamental or necessary movement!

Best regards,
Bob Barnes
Quote:
 Originally posted by Si:
quote:
Originally posted by ssh: I was thinking about this conversation as I went through Ron LeMaster's web site last night. What I noticed is that, during the transition of these high-speed turns, the inside knee begins to angle downhill (thus releasing the edges) before there is a sign that the outside leg has reduced pressure. It seems to me that these world class skiers are releasing their uphill ski, directing their downhill ski into the new turn, and as a result have the new inside ski lightened. I admit I may be seeing what I expect, but the order is telling, I think.
Like you ssh, I may be seeing what I expect. However, well before the inside knee (either old inside or outside knee which ever you meant) begins to angle downhill, the old outside leg is retracting and the old outside ski is reducing its edge angle (flattening/releasing).</font>[/quote]Si,

This is interesting for me! I hope you don't mind the detail of this post... I went back to see what you meant, and I think I can see it. I'd like to look specifically at schleper-lvlnd-gs-2-ws, which is the last photo montage in the index (far right).

In images 1 and 2, she seems balanced on both skis (to me), with slightly more weight on the outside ski.

In image 3, she has begun to roll her left knee downhill at a sharper angle than her right. Her right ski is still holding the line.

In image 4, her left ski is almost flat while her right ski is slightly edged but flattening. This reminds me of the old "A Frame" from my younger racing days.

In image 5, she's on both skis running almost flat. She is more upright in this frame than in the earlier one, so there has been no "retraction" of either leg but rather extension.

In image 6, she has extended her outside ski, but her insight leg angle is approximately the same as in the previous image.

By the time she gets to the panel in image 9, her left leg is extended almost as much as possible, while her left leg is drawn up under her.

The GS pictures of Maier show this, as well.

At least to my eyes! What am I missing?

ssh
What you are missing is that in a transition stance that wide, you are not going to be able to maintain equal edge angles. This allows for a slight redirection of the new outside ski, BTW.
No Black PMTS cert for Hermann this year.
Quote:
 Originally posted by milesb:What you are missing is that in a transition stance that wide, you are not going to be able to maintain equal edge angles. This allows for a slight redirection of the new outside ski, BTW. No Black PMTS cert for Hermann this year.
Milesb, help me a bit more?

I get that the transition stance is wide. That's part of the point. (One of the concepts that Ron discusses in his presentations is the reason for that width in the rest of the turn.) But, that doesn't change what's happening in terms of weight on each ski, does it?

Although his stance is wide, he could "lift" or "lighten", but that's not what he's doing. Right? Or wrong?

Hope you'll forgive my struggles, here!

ssh
Roland Rock, P.E.,

Thank you, you are right, I stand corrected. PhysicsMan already made it clear, but I rather ignored the g-force that can increases substantially beyond the gravitational force in turns.

I think I should have said that the magnitude of the resultant force >= gravitational force. Does that make more sense?

Si,

You are right about the fact that I am no longer concentrating on the pressure management between the 2 skis. We are now snowboarders!
TomB, sorry, I had to ask so I could understand what you really meant. Sometimes true meanings can be dequised.

Now TomB: Well, yes, but it is the path taken by the CM that will ensure that the ideal turn terminates. However, if you park-and-ride the turn (CM and skis take the same arc) then one has to lighten skis or increase pressure on the skis to break the turn.

Ric says: One thing that seems certain for me, and that is, if I don't exercise control (creating/uncreating) over the forces and consequently the path of my CoM, the forces will control it for me. How could I otherwise change the radius of my "Perfect Turn"(yikes) from one turn to the next. I think the Park and Ride syndrome is an example of giving up control and allowing the forces to ski us as opposed to control by constantly creating and harnessing the forces to our advantage. and yes I agree, this does require extra movements to regain control. Action with intent-movement with purpose, to me says I do only what's needed for my intent to be realized, but I always need to be doing something, no matter small. When I stop moving, I stop being in control.

PM, I don't have the math or computer skills you have, but this diagram still seems lacking to me. If I were to draw what I see in my minds eye, I would have opposing arrows, drawn perpendicular to the direction of travel,(our inertia), representing centripetal force and the resistance of the snow. They would show the amount of force and opposing resistance being created by their size drawn, and this would be in direction relation to the amount of change in direction of our CoM that is happening and the acceleration/deacceleration of going into and out of the fall line. And yes, I intentionaly left out centrifugal.
Quote:
 Action with intent-movement with purpose, to me says I do only what's needed for my intent to be realized, but I always need to be doing something, no matter small. When I stop moving, I stop being in control.
Well said, RicB, and an excellent description of the "park & ride" syndrome!

SSH--You are exactly right in your observations of Hermann Maier and other World Cup racers. Their wide stance ALLOWS them maximum ability to redirect their CM left and right by simply actively changing their support foot ("lifting," "lightening," stepping, or flexing one leg or extending the other). And the fact that they DON'T use these options any more than they have to is the point. Maximizing options, while minimizing the need to exploit them--that's the key to both versatility and efficiency!

Typically, those who suggest that active weight transfer should be a fundamental movement of turns, and an integral highlight of a teaching progression, also recommend a NARROW stance. The reasons are clear, aren't they? The narrower the stance, the less disruption of the CM when you actively change your support foot. The active weight transfer is an error as a rule, and a very narrow stance minimizes its consequences, while at the same time eliminating one of the greatest tools in the repertoire of the complete skier.

Ric B--I'm sure Tom/PM will speak for himself when he finds the time, but I'll suggest that his arrows (vectors) represent the RESULTANT force--the combination of all forces acting on the skier. They are virtually the same as the Resultant arrows in my diagrams, although surely far more accurate for the specific parameters of Tom's illustrations--turn shape, speed, and steepness.

Steep hill, lower speed means the relevant component of gravity is large throughout the turn, while centrifugal force is minimal (although it increases with speed). Shallow hill, high speed means the gravity vector is small throughout the turn, and centrifugal force is the primary factor. Tom's diagrams show the resultant of both, in both scenarios. My diagrams show the components AND the resultant, again in both scenarios.

Best regards,
Bob Barnes
Some thoughts of the sine waves from my hot tub. I see the sine waves as an outcome of perfect execution of the movements required for the perfect turn.

How does the unicylist achieve this? As a casual observer, I would say she achieves this through leveraging one part of the body against another, leveraging against their momentum, and utilizing the friction between the tire and the ground using pressure and/or resistance to the pedals and opposing pressure from one side to the unicycle to other using the pedals.

Have no time now, but I find this conversation very enlightening for myself. Later, Ric.
What I particularly like about Tom's diagrams is the "constant change" they illustrate--the continuous flow of motion, and the smooth, constantly varying forces the skier must deal with. The forces are in constant flux, resulting in (or causing, depending on your frame of reference) the smooth sine-wave turn shape. There is no identifiable moment when any significant disruption of the path of the CM occurs in these "ideal" turn shapes--there can't be!

Again, since real turns come in every shape possible, skiers DO need the ability redirect the CM--to CHANGE the "ideal" sine-wave turn shape. So none of these arguments should be construed as suggesting that active weight transfer, stepping, "lifting," and so on, along with (active) unweighting, pivoting, and twisting are bad moves in themselves. Only that a technique based on them as fundamentals lacks efficiency and compromises options. If you have to transfer weight to the uphill ski just to get into a turn, then what do you do when you have to get into it even more quickly, or into an even tighter turn?

Maximum efficiency in the "ideal" turn is fundamental. Maximum options to change that "ideal" turn shape and adapt to other than "ideal" conditions are what make the complete, versatile skier.

Best regards,
Bob
Quote:
 Originally posted by Ric B:...PM, I don't have the math or computer skills you have, but this diagram still seems lacking to me. If I were to draw what I see in my minds eye, I would have opposing arrows, drawn perpendicular to the direction of travel,(our inertia), representing centripetal force and the resistance of the snow. They would show the amount of force and opposing resistance being created by their size drawn, and this would be in direction relation to the amount of change in direction of our CoM that is happening and the acceleration/deacceleration of going into and out of the fall line. And yes, I intentionaly left out centrifugal.
You bring up a good point - one that is absolutely critical to an understanding of how dynamical situations are analyzed: In the good old F = ma equation, if you know where an object (the skier) is at every point in time, you also know exactly the acceleration that the object is undergoing, because "a" is just the second derivative of the (known) position as a function of time.

Earlier in this thread, someone suggested that skiers making a sine-wave path down the hill would be an interesting case. Once this assumption was made, the rest of the acceleration analysis is a slam dunk. Basically, we just turn the mathematical crank, and immediately can determine the acceleration (due to motion in our reference frame) that is acting on the skier at every point in time. Add in the acceleration due to gravity because the slope angle is not zero, and you have an exact value for the net acceleration of the object at every point along its path. Multiply these values by the mass, "m", and you have the net force acting on the body at every point along its path.

The previous paragraph was a long-winded version of Bob's response to the same question. My diagrams (exactly as do his), show the resultant, or net acceleration of the body, which is essentially the same as showing the net force acting on the body. I did not show the components that went into each of my "resultant" vectors because, as Bob suggested, I wanted to emphasize the flow and continuity and so, wanted to show the resultant vector at a lot of points. Including the two vectors that add together to make each resultant in my diagram would have hopelessly crowded the drawing. Besides, Bob's drawing (with fewer total number of points) already shows the components quite well.

The above analysis makes absolutely no attempt to say how this "net force" arises from the interactions between ski and the snow, just that IF the skier is doing what we said he is doing (ie, making sine-waves), then the net force is precisely and inarguably known.

On the other hand, RicB brought up a very interesting and important question, namely, the other side of the F=ma equation - How do we decompose this net force into the various physical mechanisms that actually create it. These mechanisms include the snow drag that was mentioned, but also include aerodynamic drag, forces exerted by the snow perpendicular to the base and edges, etc..

I didn't attempt to decompose the net force into the various physical interactions between the ski/skier and his environment which create these forces for a couple of important reasons:

1) It wasn't necessary for what I wanted to show (ie, which is exactly what BobB wanted to show by his illustration), namely, how the overall net force varies through a turn.

2) To decompose the net force into the various ski-snow interaction mechanisms, one would have to make a whole bunch of weak assumptions, none of which are fundamental or readily verifiable, and all of which depend in complicated ways on parameters applicable only to very specific skiing situations including pressure on the snow surface, type of snow surface, edge angle (if skidding when edged), angle of attack, speed, etc.

Put differently, I believe my diagram is complete as is (and shows what it is supposed to illustrate), but there is another, completely different diagram with lots of arrows on it that is not shown at all. The only relation between the two diagrams is that for corresponding points on each diagram, the vector sum of all the components in one diagram must be identical to the vector sum in the other diagram. In other words, the left side of F=ma has to equal the right side of F=ma at each point. What RicB suggested in his post (eg, adding drag and other vectors to the diagram I showed) is essentially putting these non-acceleration arrows in the wrong diagram. They go in the vector diagram for the other side of the equation (that I decided not to show).

I hope this further elaboration helped.

As I get time over the next few days, I am going to try to develop this model a bit further to specifically answer questions about the main subject of this thread, namely, the motion of the skier's center of mass across his skis.

Cheers,

Tom / PM

[ November 09, 2003, 12:04 AM: Message edited by: PhysicsMan ]
Quote:
 Originally posted by PhysicsMan:As I get time over the next few days, I am going to try to develop this model a bit further to specifically answer questions about the main subject of this thread, namely, the motion of the skier's center of mass across his skis.
PM, I, for one, am really looking forward to seeing that!!! Thanks for taking it on!

ssh
Thanks PM, and thanks BobB. I'm looking forward to the evolution of this thread.
Shhh:

"In image 3, she has begun to roll her left knee downhill at a sharper angle than her right. Her right ski is still holding the line.

In image 4, her left ski is almost flat while her right ski is slightly edged but flattening. This reminds me of the old "A Frame" from my younger racing days"

What I was getting at is that the rolling of the left knee downhill at a sharper angle could be an illusion. A "wedge" is unavoidable in a transition stance that wide, even if all you do is tip the old outside ski downhill. Bob Barnes explained this in the "perfect turns, illustrated" thread.
What a great explanation, Tom/PM!

Quote:
 I didn't attempt to decompose the net force into the various physical interactions between the ski/skier and his environment which create these forces for a couple of important reasons:
This speaks to the exact, and critical, difference between the physics of what absolutely must, by immutable natural laws, happen for any given turn, and the technique the skier must use to make those things happen. Tom's diagrams show what DOES happen, (at least for the given idealized parameters of the turns he's illustrated). The instructor's job is to understand HOW it happens, and what the skier needs to do to make it happen. It's also essential to understand what moves might actually prevent it from happening, even if they seem "right." And, it is important too for us to understand what moves we need to master in order to alter the shape of the "idealized" turn, and to deal with the inevitable, uncontrollable "other forces" that apply in the real world of skiing on mountains with inconsistent snow, varying steepness, gusts of wind, loss of balance, technical mistakes, and the individual whims of the skier.

While some might argue that the physics, and understanding the physics, doesn't matter (because we can't change them anyway), I think that knowing what MUST happen can very much help in determining what you SHOULD DO to make it happen. It can help instructors doing movement analysis, especially. Realizing that some observation you've made entails that some force had to have applied, the analysis may become the simple search for the source of the force. Maybe it wasn't obvious, and you didn't see it at first, but knowing that it had to be there can make even the subtlest of movements stand out.

Best regards,
Bob Barnes

[ November 09, 2003, 09:07 AM: Message edited by: Bob Barnes/Colorado ]
Quote:
 Originally posted by milesb:Shhh: "In image 3, she has begun to roll her left knee downhill at a sharper angle than her right. Her right ski is still holding the line. In image 4, her left ski is almost flat while her right ski is slightly edged but flattening. This reminds me of the old "A Frame" from my younger racing days" What I was getting at is that the rolling of the left knee downhill at a sharper angle could be an illusion. A "wedge" is unavoidable in a transition stance that wide, even if all you do is tip the old outside ski downhill. Bob Barnes explained this in the "perfect turns, illustrated" thread.
That's ssh to you, buddy! In case you're wondering, those are simply my initials (and my username for nearly 20 years on various systems!).

I don't think it's an illusion, though, since the relative angle of the ski on the snow changes. I am looking at the angle of flex of the knees, the angles of skis on snow, and the implications.

BTW, Ron also talks quite a bit about the "virtual bump" in his book and presentations, and this gives additional illustration to that sense of lightening (of both skis).

My 2 cents...
ssh
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