Get off those edges.

Fastman,

Ric is right on in what he is saying. If it feels like your feet are being pushed into the snow by centrifugal force it seems to be human nature to feel that if you lose the grip you need to resist that force then you will be suddenly traveling in the direction that you sense the force pulling you in. Same type of thing happens when you ask someone to twirl a weight on a string around their head and release it at a target in front of them. Most will release when they feel the pull pointing at the target which will result in the weight flying off at a right angle to the line to the target. This is why I sometimes say I don't believe in centrifugal force because the outcome that my senses expect and the actual outcome in the real world aren't the same. Its also why I look at skiing as a problem of a body in motion and how that body accelerates in realtion to the forces acting on it and how I can create the forces needed to move that body where I want it to go. I just like the idea of going where I want to go, a positive attitude if you will, rather than resisting going where I don't want to go which is more of a negative attitude to what is going on.

yd

Not true, Physicsman is going skiing this weekend - on grass!
By the way, PM, I'm not the only one who suggests that grass skis are turned using movements similar to carving on snow; someone far more qualified than me, the 10 times World Champion Christian Balek from Austria, makes the same claim:
http://www.grasski.com/application/common.php

PM, the "caterpillar track" design, like Balek's, or these Japanese companies'
http://www.grass-ski.or.jp/jgsa-j06.htm
is the only type used in grass ski competitions, and definitely the one I would recommend for someone who is an accomplished skier on snow. If you used that type of grass ski on asphalt you would damage it.
The wheeled variety pictured on that French site is really more of an oversized inline skate - may be better for asphalt, but won't give you anything like the same grip on turf. (I don't know what they have for rentals at Bryce.)
For more of an idea of the technique, go to this link
http://www.grasski.com/application/action.php
and scroll down the page for some video clips.
If you enjoy the sport, and feel really brave, you could go on a grass skiing vacation, here:
http://www.skifed.ir/history4.asp

Grass skiing is a fun sport and a pretty similar sensation to snow skiing, but the main drawback, if you get involved in regular competitions, is the cleaning, maintenance and lubrication of the skis - a real pain in the arse!
One final tip: when moving, never, ever, touch your grass skis together!

ydnar,

I'd agree in a stactic sitution. However there are additional sensory inputs when skiing that your not considering. When skiing the mind not only senses the lateral centrifugal force acting upon it, it also senses the forward motion it's under and factors in the influence of the momentum of that forward motion in determining the line of ejection upon loss of edge hold.

Also remember that the line of ejection will vary depending on the location of the skier along the path of the arc. There are two forces acting on a skier during a turn, centrifugal force (call it momentum if you wish) and gravity. The direction gravity works in relation to momentum varies as the turn progresses. The mind has a handle on that also, and includes it in it's ejection direction calculations. No one expects to eject up hill if they lose edge grip at the top of a turn, but they do expect to eject down the slope at the bottom of a turn if they lose edge grip. They would be right in both instances.

The mind is a magnificent on board super computer that makes these calculations very well for us. It should not be underestimated.

FASTMAN

Fastman

the funny thing about these ideas that you insist are so way off the mark is the amount of agreement which this thread has mustered.

Thinking of carving only as something on a 2D surface with edges can make the concept of carving in softer snows in 3D more difficult to grasp. You can carve whipped cream.

Sidecuts assist carving considerably but are not fundamental - carving can happen without them. Too much emphasis on them may distract from more important things.

Centrifugal forces can easily be misunderstood.

My other point about balance, or rather imbalance, will live on for another day as when most people think about it, the essence of ski turning is achieving stability through imbalance (the shot-away leg or whatever metaphor you choose is not uncommon here).

I think ydnar's last post says a great deal more than many of the more analytical approaches some of which I have been trying to dust off, if not entirely debunk. That is a great post yd.

IMHO, when we're skiing dynamically through deep powder, especially with old moguls beneath the surface, we're in a permanent state of imbalance with occasional corrections thrown in. An analogy might be the "pogo stick" - it's virtually impossible to balance on it when stationary, but much easier when you're bouncing.

Err ... I think what I actually said, "when I get a chance", but thanks for the good natured prodding - I can always use it.

It actually does sound like fun and I think I will try it. Usually I drive within an hour or so of Bryce to visit family a couple of times per summer, and will probably incorporate grass skiing into one of those jaunts. My intention is to start out on terrain suitable for sub-walking speeds.

A few more questions, Martin ...

a) In practice, what sort of turn radius can you achieve at very low speeds; and,

b) If that radius isn't short enough for comfort, is it hard to tighten up the turn radius by doing 1000 steps, using diverging skating steps, etc.?

c) Besides the obvious difference of irregular terrain, what would you say are the main technique differences between grass skating and conventional in-line skating. (maybe we should start up a separate thread for this if this side topic takes off).

Tom / PM

a) maybe 30m, 40m - it's one of the real problems of the sport, you can't really tighten the radius until you achieve fairly high edge angle, and doing that is easier with a bit of speed.
b)No problem, you'll see expert grass skiers using steps if they want to make their way down slowly, eg. to the start of a training course.
c)Very few differences - the grass skis don't come around as quickly as in-line skates. And in grass ski racing it's considered poor technique to lift a ski off the ground at any time - because the "belt" slows down and must be re-accelerated when the ski regains contact with the ground, which grass skiers think costs kinetic energy.

Don't know whether it's worth starting up a thread - grass skiing is a very minority sport, and I doubt there's even anyone on this forum who's tried it.

No wonder he is egging me on to try grass skiing ...

A few min ago, I got to wondering who this obviously knowledgable fellow, Martin Bell, actually is, so I decided to see if there was any info in his published profile on Epic. Putting aside his Olympic and other skiing honors, from http://www.skimartinbell.com/ I now see:

...Martin represented Great Britain in grass skiing at the 1986 European Championships at Butser Hill, Hampshire, the 1987 World Championships in Japan, the 1997 World Championships in Switzerland, and the 1999 World Championships in Austria. His best grass skiing performance was 10th in GS at the 1999 Worlds...
.
No wonder he is egging me on to try grass skiing, and no wonder he received several very warm greetings when he joined Epic a month or so ago. Man, am I out of the loop ... :

Err... a belated but heartfelt welcome, Martin!




Tom / PM

That's not funny, it's sad.



To respond to this I'll repeat an earlier post of mine:

My whipped cream analogy was sensory based. In theory I fully support your position that carving, by your definition, can be done through fluff, mush or slush, as well as on hard packed. However, in execution the sensations are so polar they almost scream to be recognized as individual entities.

When I carve on hard packed snow I'm immersed in feelings of control, balance, platform consistency and strength, line precision, track cleanness, efficiency, economy of energy. It's reminiscent of driving a highly refined sports car through a series of S turns. I feel like I'm locked in the arc and in complete control.

When I carve through deep snow I feel a contrasting loss of precision. The sensation of snow contact is vague and the platform the ski compacts and rides is inconsistent and unreliable. Build too much force and it breaks away, it lacks integrity. This creates an environment in which the turn radius is susceptible to sudden unintended changes, and constant adjustments must be made to compensate for this inconsistent medium. Snow is being plowed and displaced which requires balance adjustments that disallow true through the foot balance platforms to be consistently maintained. In contrast to the hard snow sports car feeling, this is more reminiscent of driving a tractor through a muddy field.

While a tractor can be driven skillfully through a mucky field it will never feel like my lotus on dry pavement.




Sure you can daslider, I spent 30 years carving turns on pre shape skis in race courses all over North America and Europe. The difference is simply in the available range of turn radius the skis can produce (thank god for those differences), and the body positions required to be in balance while doing so. All the fundimentals of carving remain the same.





It's really not as complicated as you try to make out. There is a force that acts on the body which attempts to drive the skier out of the arc. We coin that force "centrifugal", and it must be counteracted by moving our CM inside and down to put ourself in a position to resist (balance) this force. It's really a basic and easy concept to understand.

Centrifugal force is really just the momentum of a body moving along an arc. No, the angle of that momentum is not 90 degrees to the arc, but the essential effect is felt as a lateral force and we must create an opposing lateral force to combat (balance) it.

Evidence of the existance and influence of this centrifugal force is found in the severely inclinated positions seen in racers making high speed, high edge angle carved turns. If an opposing force (centrifugal) did not truly exist then maintaining dynamic balance in these positions would be impossible. In simple terminology, the skier would fall on his/her butt.



Praise the lord.

FASTMAN

Fastman,

Try this idea. A skier making a highspeed carve is inclinated not to resist the force trying to throw them out of the turn but to better line up the force vector that is driving them into the turn. If they don't line thiings up properly then they must use muscular strength to transmit this force to their center of mass, this is inefficent. The skier doesn't fall on their butt for the same reason a sprinter doesn't fall on their face when they come out of the blocks, acceleration.

One of the reasons that I use this view of the forces of skiing is because it explaines how I can go from traveling 30 miles an hour in one direction to thirty miles an hour in the opposite direction in a second or two. Thinking in terms of centrifugal force just can't account for this fact.

yd

Are you saying the centrifugal force can't account for this, but centripetal force can (ie, are you attempting to indirectly point out someone's error in nomenclature or a simple mis-statement)
.
OR
.
are you saying that the magnitude of the centripetal force isn't large enough to account for the change in transverse velocity from +30 to -30 mph?

If it's the latter, you are wrong. Any kid who got more than a C in his first semester freshman physics course would not only agree with this, but also be able to calculate how much force was involved in the turn if given the duration (or speed) and the radius of the turn.

Tom / PM

Bob Barnes's feeling on centripetal & centrifugal in 2001

Ydnar's most recent post in this thread triggered my memory of a very similar discussion that he and Bob Barnes got into a few years ago, and with the help of the search function, I found it:

It turns out that Da man hath already spoken on this exact subject three years ago. Take a look at page 8 of the thread, http://forums.epicski.com/showthread.php?t=7776&page=8&pp=20&highlight=centr ifugal .

Scroll down about 15% of the page to Bob's posts dated November 10th, 2001, 02:18 PM, and November 10th, 2001, 02:49 PM.

Sorry folks, but Fastman, Bob and I are all of one mind on this subject:

Centrifugal = the force the skis exert on the snow in a turn
Centripetal = the force the snow exerts on the skis in a turn
Both are real forces to their respective observers.

Bob is probably sitting back in his old rocking chair in Maine, smiling & watching from the sidelines while we duke it out all over again.

Tom / PM

PS - Ydnar, I seem to recall that you and Bob got into quite a debate over the centrifugal / centripetal thing even prior to the Nov 2001 thread, but I can't seem to find that thread.

PS#2 - daSlider - Say, why don't you start a nice hearty round of discussion on unweighting and rebound as your next accomplishment?

Fastman

you may or may not understand centrifugal force despite your skiing experience. That is not really the point; your own established competence may not require you a complete technical understanding. There is enough evidence here to support my own experience that relative novices are having their chances of reaching your level jeapordised by inappropriate technical explanations. If you are happy with the 'follow me, do as I do and don't ask too many questions' style of teaching, well that's fine. It has worked for many.

Allow me one last stab at this centrifugal business, something I wrote earlier: "If you lean against a door it either leans back (so to speak) and holds you, or it opens, or breaks down, and you fall through. People take this analogy into centrifugal forces and assume that if the snow stopped pushing back and you broke out of your turn, you would head off pretty well where your legs were pointing, i.e. radially to the arc. Well you dont!!!"

A less statically positioned analysis would eliminate this myth and I concur with Ydnar in his more dynamic approach.

Something you wrote I had trouble understanding, please would you explain:"On hard snow I belief what happens is that as edge angle is added the ski tip is forced carve the ski into a new bend because pressure on the skis center has it locked into a high integrity cut platform that does not allow for lateral displacement. The tip carving in to the bend the ski needs to assume to regain stability is the only option it has. "

It's that last sentence I can't make any sense of. thanks.

Martin Bell

I agree that really variable snows hide hazzards that can be destabilising, like bumps under powder, but that is not the same thing as the basic imbalance that a very stable carved turn has to have. Imbalance and stability do go together. Your hidden bumps were probably skiid with the necessary imbalance and moments of instability, but not overall, you lived to tell the tale? It always amazes me how the body can react to such challenges and maintain overall stability.

This thread may all be semantics, but the moment good exponents try and teach skiing with innappropriate explanations it assumes some importance. How does the novice react to "...skiing is all about balance, now dive down that hill over your supporting platform and inside the line of your new outside ski..."

Rick, it's an imperfect world, and I certainly am not perfect, but I don't think I got my students fear's and reactions wrong. Peoples interpretation of the effect they feel and their sensory inputs are personal. Don't forget the mind body connection. It's like the difference between having a disease and/or having an illness. A person can have either one by itself or both together. You can treat a disease without knowing the person, but you can only treat an illness by knowing the person. Teaching skiing is no different. It's not my job to make my students illness fit the definition of a disease, it's my job to help my students cure themselves.

This is the great benefit teaching skiing has had on me. It has pushed my learning in so many new directions, and had such a profound impact on my personal journey in life, with such benefit to other areas of my life. everytime I open up my blinders a little more I can see more. Funny how that works. This is directed at myself not anyone else.

As far as teaching goes, if were to list one of my strongest strengths I would list making connections with my students at the top. Most of my return student are very smart people. PHDs, Doctors, Teachers, Businesspersons, ect. Cappable of exspressing themselves very well. We connect, we deal with the fundamentals of skiing, and we have fun as we all learn.

What a great job! Later, Ric.

PM, I have a few simple questions I would like you to clear up for me if you can. This takes us back to Dobbs and her book on Newton where she says that Newton replaced cetrifugal force with inertia and centripetal force, the mirror image of centrifugal force. She quotes him in pricipia as recognizing the illusory nature of centrifugal force, and goes on to say that modern physisists still treat it as illusory in nature. Is she correct in this, and if so, could you please reconcile this with your learned position? I'm in the position right now where I have to take one or the other as being wrong. This confuses me. Later, Ric.

Tom,

Of the two restatments of my comment it is the first that comes closest to what I was trying to say. I want to understand just what it is that moves me around on the hill. Gravity accounts for my motion down the hill but to my mind (from position of an outside observer) there has to be a force to account for my radical change in transverse motion. I also have to account for the fact that my down the hill motion must go from +30 when pointing straight down the fall line to 0 when I am moving at a right angle to the fall line which means that there must be a force acting counter to gravity. I can explain all this if there is a force vector pushing up on the bottom of my feet and I can line up the force with my CoM and shear it (I hope that's the right term) in different ways to accelerate my body in the ways I want. I can't account for these accelerations with a centrifugal force model and the idea that the snow is pushing back because Max's demons only push back as hard as they are pushed on. Hope this makes things clearer.

My and Bob's first cyber meeting took place on the old PSIA web site. The high point of that exchange was when Bob pointed out that from the skiers viewpoint the skier was motionless and the world was doing the moving. I responded that it would be very interesting to explain to the patroller that I was just standing there on my skis minding my own business when a tree rushed up and smacked me for no reason. We were the twin geeks arguing about who's viewpoint was correct. Mine was of course!!

yd

Coriolis Effect

PM, am I right in thinking that centrifugal force would not appear quite identical to gravity in the frame of reference of astronauts in Bob Barnes' rotating space station, because the Coriolis Effect would come into play? This would imply that centrifugal force does have a slightly different nature to other forces; objects wouldn't experience perfect straight-line acceleration as they would under a simple straight-line force. (Of course, I believe the Coriolis Effect exists on Earth too, in a very mild form - it causes the "trade winds".)

By the way, yes I have indeed made many turns on grass skis in competitions over the years. I'm not sure if all or any of them were strictly carved (by your mechanical definition). The ones in the mud in the slalom in Japan in 87 definitely weren't!

yd

I really like the way you and RicB are taking this discussion and I note that in the archive B.Barnes concludes that centrifugal force is probably best left out of skiing discussions because of these confusions, so the field is not as clearly cut as PM would have us believe. I do think inertia and momentum are more easily grasped concepts than forces.

Gravity is like the motor that gives the skier movement to play with. Once moving the skier has momentum which tends to take him as directly down the hill as possible, (he is said to have inertia which resists change). Turning is all about deflecting that momentum and controlling it as the skier wishes, but in doing so the skier has to overcome this 'directly down the hill as possible' tendency (he has to overcome inertia). He chooses his path by deflecting off the snow rather than sliding over it, but harnessing his own momentum just as billiard balls glance off each other. In managing his turn he is managing this succession of tiny glancing blows or deflections in a positive way to get to where he wants to go. He consequently aligns himself to deal with these upcoming deflections. In a very real sense he has to be ahead of himself. The next deflection is more important than the one he is making now.

In contrast, the centrifugal model is always looking at 'now' which in a dynamic situation is already history.

Fastman....let's not get crabby. I don't profess to be the brightest guy in the world, however, could SOME of the fault for any misunderstanding possibly lie in what you wrote?

As I alluded to, I remembered you writing something some time ago that I read with skepticism. I found it via the search function.

Here it is;

"A racer/skier can vary carved turn radius. As others have already said a ski is not limited to one carving radius. Turns can be carved at any variation between a straight line and the minimum radius limit of the skis sidecut.

How? Simple, edge angle. When a ski is put on edge (when no pressure is being applied) the center of the ski loses contact with the snow because of the sidecut. The larger the sidecut the larger the space between the snow and the edge. When pressure is then applied to the ski it will bend until the middle of the ski makes contact with the snow. The resulting bend in the ski is what is responsible for the specific shape of the carved turn, the more bend the tighter (smaller radius) the resulting turn.

So the key is to controlling the shape of the carve is to control the amount of bend in the ski. How do we do that? Again, in principle, easy. The higher we put a ski on edge, the more space between the snow and the center of the ski occurs, so the more the ski must be bent to reestablish edge contact with the snow. Also as the edge angle is increased the direction of bend becomes more horizontal (parallel to the snow) so the ski must bend more before the edge finds a base of support on the snow.

To summarize, increasing edge angle does two things that affect turn shape; it increases the amount of space under the center of the ski, and it changes the angle of bend. Both of these tighten the arc."

When you say, "The higher we put a ski on edge, the more space between the snow and the center of the ski occurs, so the more the ski must be bent to reestablish edge contact with the snow.", I have to take what you wrote on face and assume you believe a tipped ski produces an actual gap between the waist of the ski and the snow.

In your credit card demonstration this week you say a similar thing when you wrote, "The first factor, the amount the edge rises of the surface as a ski is tipped, is the reason a shape ski provides a smaller turn radius: it rises more when it's tipped.", and this again leads me to believe yo are suggesting....as you wrote, a tipped ski rises.

I'm not trying to be confrontational.

Is it your opinion that tipping a ski creates a ski with a midsection that rises?

Are you suggesting the creation of a space between the snow and the center of the ski?

Lastly, how can a shaped ski "carve" a straight line? For the sake of this discussion I guess I would discount any counter-rotational forces.

If you are I'm simply disagreeing.

I also want to add my compliments to all for a lively summer discussion.

Rusty

this is a good point, but I doubt Mr Fast expected this explanation to be taken absolutely literally - afterall even if there isn't any actual gap at the midpoint, a sidecut is still bound to lessen the contact and therefore increase the possibility of deflection in the ski. What really bends a ski is the fact that you stand on the middle of it!

I tend to think of this gap 'effect' as useful during initiation, but once the ski is carving the changes that occur are surely led from the front, by what the tipping-tips are doing? I see the midbody following into and leveraging the turn rather than setting it (I think Fastman is saying the midbody somehow forces the tips to turn; "The tip carving in to the bend the ski needs to assume to regain stability is the only option it has".)

Hey ho, nights are now drawing in...

Rusty, my apology was not sarcastic or "crabby", it was sincere. I didn't realize your level of understanding by your original question and I "dumbed down" my answer to much.

Now, moving on. The answers you seek are in my previous post to you, and the previous post of mine that you pasted here shows no inconsistency with what I've said in this thread.

Reconsider to following 2 pastes from above, the first from my latest response to you, and the second from your copy of my post in an earlier thread:

1) But as you point out it explains why a ski bends, but not clearly how it achieves that bend. Let me be clear, I TOTALLY AGREE WITH YOU, the ski does not actually rise off the snow. Saying that offers a clear picture of ski design function for new carvers, but it does not address the on snow reality.

In real life the pressure on the ski does not allow the center to lift and laterally displace, just as you suggest. On hard snow I belief what happens is that as edge angle is added the ski tip is forced carve the ski into a new bend because pressure on the skis center has it locked into a high integrity cut platform that does not allow for lateral displacement. The tip carving in to the bend the ski needs to assume to regain stability is the only option it has.

2) When a ski is put on edge (when no pressure is being applied) the center of the ski loses contact with the snow because of the sidecut.
-------------

Notice the qualifier in statement number 2 from the prior thread, "when no pressure is being applied". That qualifier acknowledges that in real skiing situations it works a little different, and that this is just the K.I.S.S. explanation.


I think it's obvious that I agree, as I said so in my previous post, that when skiing the center of the ski does not actually rise off the snow when the ski is tipped. I also explained why I explain it that way to new carvers, but to repeat, explaining the mechanics of sidecut and how and why a ski carves a turn is much easier and understandable if approached in this manner. It's the same reason your credit card demo works so well.

So to answer your questions (again):

1) Is it your opinion that tipping a ski creates a ski with a midsection that rises?

ANSWER: If tipped up by hand while sitting unweighted on the kitchen table, YES. If tipped while skiing, NO.

2) Are you suggesting the creation of a space between the snow and the center of the ski?

ANSWER: Same answer.

3) Lastly, how can a shaped ski "carve" a straight line? For the sake of this discussion I guess I would discount any counter-rotational forces

ANSWER: What? Did I say it could? Don't remember saying that. Guess it depends on your definition of carve. Kind of like Bill Clinton's definition of "IS".

Daslider, I do believe we're on the same wavelength here.

Your right in one respect with this statement ydnar, the inclination is executed with the intent to direct the resultant force vector (direction of force acting on a body, as measured by the cumulative effect of all individual forces acting on that body) from the skiers CM (center of mass) to the inside edge of the outside ski (the primary point of balance).

The problem is that this position may simultaneously serve to dismiss your position that centrifugal force does not exist. When a body is at rest the only significant force acting on it will be gravity. In this instance the resultant force vector will be 90 degrees to the ground, and the CM needs to be located directly vertical above the desired balance point.

The severely inclinated body position you refer to (as seen in high speed race turns) indicates a resultant force vector that has been severely tipped toward horizontal. This indicates another force has come into play, that combined with the force of gravity, has served to change its angle in relation to the ground. Some choose to call that force "centrifugal force", some call it "momentum", but the evidence of its existence is in the angle of the resultant force vector you identify.






Totally agree!

FASTMAN

Fastman,

I've still not managed to communicate my view point to you so let me try in a little different way. Your force vector is pointing from the CoM to the edge of the ski my force vector is pointing from the edge of the ski to the CoM. My force vector accounts for the accelerations that my body undergoes. I don't see how your force vector accounts for this acceleration. One thing that I find very interesting is that even though we look at the force vectors as working in opposite directions we fully agree on the positions/movements that we need to assume/make to deal with them.

To ramble on a bit because I have nothing better to do right now. Most people take the viewpoint that the pressure they are feeling under their feet is from them pushing down on the soles of their feet because the only experience they have with pressure under their feet is standing on their feet where the pressure is obviously caused by the weight of their body pushing down on their feet. From this experience it is only logical for them to interpret any pressure they feel under their feet as caused by their mass pushing on their feet. This makes it very difficult for many skiers to experience skiing as the sensation of being pushed around by your feet or 'powered flight on a snowcovered surface' as I like to think of it.

Just thinking about this is making me drool. I got to go get a napkin,

yd

It was in the same post quoted above that you wrote, "A racer/skier can vary carved turn radius. As others have already said a ski is not limited to one carving radius. Turns can be carved at any variation between a straight line and the minimum radius limit of the skis sidecut."

In fairness you didn't say a "racer/skier" was on a shaped ski although I suppose even the DH skis of the past had "shape"

I appreciate the response.

I think the manner you have described HOW a ski turns is a good one INCLUDING the theoretical "rise".

It merely threw me when taken literally.

OK, I see where you got that. What I tried to convey in that statement was the concept that by adjusting edge angle any shape turn could be produced, from infinitely large to the theoretical minimum limits of the sidecut.

I thought I had excluded a straight line by using the term "between", but I can see where it could have been misunderstood. And,,,,,, in rereading I see I did make a mistake. By using "between" I not only excluded a straight line, I also excluded "the minimum radius limit of the skis sidecut", which of course should be included.

Finally, to beat you's all to the punch. The minimum radius limit of a particular sidecut is not a fixed number, it's dependant on many factors, some of which are speed of travel, snow hardness, and skier mass.

FASTMAN

One dimension I think you guys have ignored in regard to turn radius versatility is Taper Angle.

In addition to all the other variables you all have mentioned I have found the less taper angle in a skis sidecut the less veratile the ski is in turn shape. In other words the wider the tail compared to the tip the less turn shapes (turn Radii) seem to be available. The narrower the tail compared to the tip the more turn shape can be varied.

Any comments are welcome!
over & out!
1

ydnar, I believe in your vector as much as I believe in mine.

They're both present, they have to be, it's the law of opposing forces. Momentum and gravity push the skier into the ground at an angle they determine by the cumulative affect of their individual magnitudes, and the ground pushes back with the exact same force, and in the exact opposite direction.

Physics man offered us a great example/explanation of this that is worth reposting:

Fastman,

Still no cigar. I'm not talking about the reaction force of the snow. The reaction force of the snow is simply the electro-magnetic force of a solid that among other things keeps us from sinking into the ground under the force of gravity. When you look at the system from the centrifugal force angle then you do need to the reaction force to balance the pushing force of the body in motion. But if the two forces are equal but oposite then there can be no net acceleration and it is my observation that the body is constantly being accelerated when we ski and accelerated in directions that can't be accounted for by gravity. So there must be a force that is not balanced by any other force to account for this acceleration.

How do you account for the net 60 mph of transverse acceleration in my example and the vertical accelerations that take us from 30 to 0 in the last half of the turn and then from 0 to 30 in the first half of the turn.

This is damn complicated ain't it,

yd