or Connect
New Posts  All Forums:Forum Nav:

Get off those edges. - Page 2

Quote:
 Originally Posted by BigE But the turning mechanisms are entirely different. The skate does not carve like a ski at all. The rocker on a skate allows the skater to rock forwards and backwards, and while doing so, rotate. It also allows the skater to pivot the skate, since the tip and tail of the blade are not in contact with the ice. Turning on skates is not like skiing -- it's remarkably different.
BigE, thanks for your enlightening email - I hasten to add, I make no claim to be an expert on ice-skating technique! I was merely theorising and postulating, based on the "feel" of what happens when I change direction (rather ineptly) during a "beginner league" ice-hockey game!
But I have a follow-up question: if the turning mechanism on skates is purely rotary, how does a skater initiate that rotation?
Quote:
 Originally Posted by Rick Are you sure Tom? With no tipping rotating wheels don't naturally turn. When tipped they do. I see the resultant turning of a rolling wheel when it's tipped being due to differing circumferences of the contact area.
And maybe due to the flatening of the wheel surface some, the contact occurs ahead of the wheel's axis of rotation which whould have a tendancy to pull the wheel in a new direction. The distance from the initial contact to the axis being less than the full radius of the wheel in it's new tipped circumferance. Add leg/hip rotation and you have turn shaping I guess.

I don't blade, but I find it interesting that they would go to such great lengths to invent virtual edges on something round that obviously has no edges. Later, Ric.
RicB, I don't think the wheel edge terminology is anything more than an attempt at an analogy with skis and iceskates.

If you watch a penny roll it tends to tilt and it consequently turns. What is wrong with the simpler suggestion that the shift of the skater's CofG pulls the wheels to the inside the resultant of which is a change of direction, probably by gradual rotation of the skate. I don't find the shifting contact patch convincing and as for the differential radii, doesn't a smaller wheel just turn faster?
I inline skate enough to know that the "turning forces" created by tipping the skates are not enough to turn a skate. You need rotation. Period. The link provided by comprex is a joke, in my opinion. The link talks about a 5-foot radius turn, which is all but impossible to do on most skates without serious rotation.

Here is a little experiment: take a new skate (4-5 wheels), tip it and roll it along the floor. Does it turn? Will it turn if you put a lot of pressure on it? Of course not !!! Let's not invent physics here.
agreed TomB, the cabbage patch turning theory is pretty far fetched, but doesn't a bike turn by leaning into a bend and doesn't the penny rolling also do the same thing? I agree that rotation plays its part, but not outright, the skate is rotated to follow the tendency of the tipped skate to turn (new physics; copyright pending).
The bike turns because the front wheel turns. Leaning alone won't make it turn to any appreciable amount. The penny is even more simple. When it starts leaning gravity will pull it down and forward rotation guarantees that it will start a turn. Put 2-3 pennies in-line (like a skate) and they won't turn when leaning. Right?
Unfortunately, I am still up to my ears in alligators with work, so I don’t have the time to compose a long message (or find somewhere on the net where someone already has analyzed these phenomena), but with respect to skate wheels, rolling coins and the like, different physical phenomena dominate in the various instances of rolling wheels, so you simply can not use the example of rolling coins to explain how a rollerskate turns.

For example, in the case of a rolling coin, gyroscopic phenomena dominate. As the coin slows down, its path starts to curve, and the coin tips over (aka, “banks”) at exactly the angle necessary to match the angle of the net centrifugal plus gravitational forces acting on its center of mass, just the way a skier in powder can bank his/her turns without angulation.

When you attach a human to tiny wheels (ie, a skater), gyroscopic phenomena become completely negligible compared to the forces and torques that the person exerts on the skate wheel(s) that are in contact with the ground. In other words, the “rotary” input from the skater becomes dominant.

When you put a human on big wheels (ie, a bicycle), the angular momenta involved increase like the square of the radius of the wheel, and gyroscopic phenomena once again dominate. The rolling coin is more closely related to how a bicycle (with human attached) turns, but that is a two wheeled device, not one, and introduces yet another set of constraints on the motion.

The material on rolling objects is great fun, and there are lots of incredibly interesting pages on the web devoted to bikes, coins, gyroscopic phenomena, etc., but to be honest, how they relate to carving skis seems weak.

The question of whether a ski with only a tiny length of edge in contact with hard snow can carve is essentially the same question as asking whether a ski like the Spatula with its reverse sidecut (ie, wider in the middle), and permanent reverse camber can carve. Fortunately, there is experimental evidence about this: Everyone who has ever gotten on a pair of Spatulas has said that they are impossible to carve with on packed surfaces – they are manageable on such surfaces, but only by classical skidded ski techniques.

The theoretical side of the discussion is a bit more difficult. Since we are assuming that there is only an infinitesimally short length of edge in contact with the hard snow surface, there is absolutely no meaning to the question whether or not all points along the edge pass over the same point in the snow because the rest of the ski isn’t touching the snow. Similarly, there is no meaning to the question of whether or not the track left by such a ski is of minimum width because again, only one point along the edge is in contact with the snow, so no matter what path the ski takes (eg, even an abrupt right angle turn), the width of the contact path will always be negligibly small.

With a ski like the Spatula, one can, of course use rotary motion to ensure that the ski is always pointed in the direction that it is moving, but this is hardly a suitable definition of carving since if these two directions are off by even tens of degrees, it hardly matters with respect to one’s progress down the hill. In this sense, a Spatula-like ski will handle much more like an ice skate or in-line roller skate with lots of rocker (ie, only one wheel in contact with the ground at any one time if you are near fore-aft balanced).

Skis with little sidecut or excess longitudinal softness will act much like the Spatula on hard snow because there isn’t enough force pressing into the surface at the tip and tail of the ski to have any significant effect on its path. The skier’s weight is concentrated on a short length of edge directly underfoot, just like with the Spatula. Thus, I would say that for such skis, they can’t carve any more than the Spatula can carve on hard snow. Just like with the Spatula, using rotary input, you can point them in the direction your CM is moving, but it hardly gains you anything. You certainly don’t feel that wonderful RR-tracks like sensation of a truly carving ski.

Gotta run.

Tom / PM
PM wrote: 'As the coin slows down, its path starts to curve, and the coin tips over (aka, “banks”) at exactly the angle necessary to match the angle of the net centrifugal plus gravitational forces acting on its center of mass,'

I think it is the other way; it starts to curve because it is falling over as it slows and the gyroscopic effect lessens, so the tipping does cause the turn.
daslider,

A quick question going back to the original topic. Which is more important in determining the amount of reverse camber of a ski the amount of sidecut paired with the degree of tipping or the pressure applied to the ski?

yd
Yd,

I'm not sure I can answer that, the various factors you have seperated are interdependent. The amount of reverse camber is effected by the pressure which itself results from the turning forces which are initiated by the skitips turning across the skiers momentum vector, the tipping of the ski causing the tips to engage assisted by the sidecut!
Quote:
 Originally Posted by daslider Yd, I'm not sure I can answer that, the various factors you have seperated are interdependent. The amount of reverse camber is effected by the pressure which itself results from the turning forces which are initiated by the skitips turning across the skiers momentum vector, the tipping of the ski causing the tips to engage assisted by the sidecut!

Hang on - why does everyone say have to tip skis to engage edges....

I was taught they engage when I pronate (ie pronation gives grip to ski) .... the tipping comes when i want to choose path I travel
Quote:
 Originally Posted by daslider RicB, I don't think the wheel edge terminology is anything more than an attempt at an analogy with skis and iceskates. If you watch a penny roll it tends to tilt and it consequently turns. What is wrong with the simpler suggestion that the shift of the skater's CofG pulls the wheels to the inside the resultant of which is a change of direction, probably by gradual rotation of the skate. I don't find the shifting contact patch convincing and as for the differential radii, doesn't a smaller wheel just turn faster?
Sure a smaller wheel turns faster, but what happens when a single wheel has a contact point that has an area from compression that has in it different ridiuses at the same time? Isn't there more going on here than simple inclination and leg rotation? What are the mechanics of the contact point?

Daslider, there is nothing wrong with any suggestion, but that doesn't make any of them right, including mine. Even if they sound good. What appears to be happening is not always what is really happening.

As far as the penny analogy goes, it would be a different thing if the blade wheels were hard like a penny. The penny has inertia and gravity, and in sports like blading and skiing we introduce a third force, centripetal force, our movements. This is viable only because of the contact point, either through surface compression or wheel compression. Like I said I don't blade, so I'm just having some fun thinking about this. Later, Ric.
Thanks PM. I just read your post. Follows what I was thinking, but much clearer.

Yd, without pressure, tipping and sidecut become meaningless.

Daslider, we always have pressure on our skis if we are on planet earth don't we? Unless we take air, and then it's only temporary. Though we do create more pressure by our movements through the action of tipping and it's effect on the ski's sidecut. Again, just having fun with the topic.

Disski, Your use of pronation is just moving the center of Mass to bear over the edge, it doesn't create the pressure, it controls where the pressure is focused, put simply. Later, Ric.
Quote:
 Originally Posted by ydnar A quick question going back to the original topic. Which is more important in determining the amount of reverse camber of a ski the amount of sidecut paired with the degree of tipping or the pressure applied to the ski?
For the answer to this question appropriate to hard snow conditions, grab a modern ski with deep sidecut and lay it down on a hardwood floor, and tip it up on edge by some known, fixed ammt (say 45 deg). Get your eyes down at floor level, and look at the gap between the ski edge and the floor. At the tip and tail, the edge will be touching the floor, but in the center of the ski, the edge will be above the floor by some distance.

Next, press down on the center of the ski with say 5 or 10 lbs of force. Now, the edge in the center of the ski will be touching the floor, and if you look carefully down the length of the ski from an end (a helper is useful here), you will see that the ski is actually in reverse camber. Now, put all your weight on the center of the ski (while maintaining the 45 deg angle). The ammt of reverse camber didn't increase one iota, did it? The center is "bottomed out" and can't go anywhere. Now, imagine doing the same experiment on a frictionless, extremely hard and flat icy surface with the ski possibly moving, either sideways in a skid, or forward. Even in these conditions, more downward force at the center of the ski will not make the ski go into more reverse camber.

On the other hand, increase the edging angle up to (say) 80 degrees, and notice that the degree of reverse camber when "bottomed out" increases by a large factor, but that the downward force needed to "bottom them out" still is quite modest (ie, much less than half of your weight for most skis).

Finally, dig out an old pair of skis with little sidecut and re-do the entire procedure described above. You will see that the ammt of reverse camber for these skis at the same edging angle is less, and exactly as in the case of the more deeply sidecut skis, dramatically increases with edging angle, and can't be increased by adding more downward force once they have a minimal force on them.

The above hard snow scenario is one of the limiting cases for ski behavior considered by ski designers, and pretty well describes how the camber of your skis will change in real-world hard snow conditions.

For the opposite case of extremely soft snow, it's more difficult to construct an equally easy and obvious demonstration of the flex behavior of a ski. When your wife is looking the other way, one can put the skis on something like a deep soft mattress, but measuring deflections, keeping the downward force and edge angles constant, etc. all becomes more difficult. In any case, in the soft snow limit, it should obvious that increasing the pressure will continuously increase the ammt of reverse camber - the center of the ski never "bottoms out". Increasing the width of the tip and tail (while holding the pressure and longitudinal stiffness constant) will cause the tip and tail to float higher and increase the degree of reverse camber, just like in the hard snow case. OTOH, increasing the edge angle (while holding constant the flex, sidecut and applied downward force) will have much less of an effect on the ammt of reverse camber. (Don't forget that in real powder turns, centrifugal force is generated and the downward force that the skier applies to the ski increases).

Quote:
 Originally Posted by daslider ...I think it is the other way; it starts to curve because it is falling over as it slows and the gyroscopic effect lessens, so the tipping does cause the turn...
It's a chicken-and-egg thing. As in many things in physics, you can look at it either way - they happen simultaneously.

HTH,

Tom / PM
All I know is that when I carve, I have two trenches in parallel. I don't know how bases can cause that kind of gouge.
Quote:
 Originally Posted by disski Hang on - why does everyone say have to tip skis to engage edges....I was taught they engage when I pronate (ie pronation gives grip to ski) .... the tipping comes when i want to choose path I travel
When you want to analyze the mechanical behavior of a system (in this case, skier + skis), by far, the best way is to break it apart into smaller pieces, each of which can be analyzed more easily and more completely, and then you see how they act on each other once you understand the isolated behavior of each piece.

Trying to understand a complicated mechanical system all at once, in its entirety, is doomed to at best generate qualitative discussion with a fuzzy final understanding, with "which came first, the chicken or the egg" paradoxes seeming to abound and never be resolved.

In the case of skiing, to deeply understand what's going on in the combined system, you first must consider the skier and the skis separately.

There are only a very limited number of truly distinct and elementary things that a skier can do to a ski:
1) You can change its angle with respect to the snow (measured with respect to each of the three axes);
2) You can apply force to the center of the ski (measured with respect to each of the three axes); and,
3) You can apply torque to the center of the ski (measured with respect to each of the three axes);

When you talk about pronating, you are talking about an action that is internal to the skier (not the ski), but which causes a combination of the three effects listed above to happen to the ski. The major effect will be to tip the ski up on edge, but as RicB pointed out, weight shifts (ie, forces and torques) also occur. This thread has been concerned with first understanding the behavior of the ski itself, and then, once this is done, adding in the skier.

This is why the people in this thread have been talking about ski tipping, and not about skier actions such as pronation that the skier has to execute to generate tipping (either by itself or in combination with other physical phenomena).

HTH,

Tom / PM
Good job all. Nice explanations PM.

For our next act we'll explain to Daslider that the earth is not square.

FASTMAN
Quote:
 Originally Posted by Ron All I know is that when I carve, I have two trenches in parallel. I don't know how bases can cause that kind of gouge.
In a low-G, long radius RR-track turn, you are absolutely correct that the snow is pushing upwards on BOTH the bases of your skis and on their edges. This situation is just one corner of a square up at (say) 45 degrees, being pulled through the snow. The snow pushes on both sides of the square that are in contact with it. Your bases leave one side of each trench, the sides of your skis leave the other side of each trench.

However, as the G-force increases in tight, high speed carved turns, a much larger fraction of the downward force is carried by the bases of the edged skis as compared to their sides. This is because in this situation, the net force that the skier is exerting on the skis (ie, the combination of gravity plus the outward centrifugal force) is over at an angle.

Tom / PM
PM

Chicken and egg quandries are necessarily circular a-b-a-b etc. I don't see that a rolling coin running straight follows such a pattern. Fate/chance/circumstance determines that it tips to one side or the other (equivalent to the skier's intent to turn) and what follows after that is a linear progression which I would argue follows from the tipping and in no way could be alternated as with egg/chicken scenarios. To suggest it turns and then tips to compensate is allowing it an agency it simply does not have; if it turns first, it falls over like coins on the dashboard when you hit a bend.

The static model of the ski's deflection imo has limits. When a ski is moving it can change its shape by moving into the grove that the tip is making and when the skiers momentum is added to further bendi/leverage the ski, it is behaving irrespective of its sidecut. Sidecut certainly plays a part in initiating this process but merely looking at the limits of sideways displacement statically on a hard floor does not tell it all - this is actually an example of the dangers of not looking 'in the round' which has to be done as well as breaking down into components.

Ron, think of the grooves as small embankments like on a racetrack bend (Travolta in Grease?)- the edge may help cut them, but it is the base pushing against the 'wall' that holds you in the turn.

Fastman, as fellow skiers, can we at least agree that the earth is flat, but, thankfully, just not all of it?
daSlider - Have you ever seen the experiment where a kid's toy gyroscope is suspended (axis of rotation horizontal) by a string from a post outside of the gyro cage, but on the axis of rotation. What amazes most people about this demonstration is that the gyro, even though it is being supported at a point well to the side of its center of mass does not fall. This is the usual gyroscopic effect.

What most people don't pay much attention to in this demo is that the axis of the gyro slowly starts to turn in a horizontal plane without the axis of the gyro noticeably dipping. This is the phenomena of gyroscopic precession. The same thing can happen to a rolling coin if it encounters a microscopic irregularity in the surface off to one side of the coin's center line (as I attempt to show below):
.

......-----
......|...|
......|...|
......|...|
......|...|
......|...|
......|...|
......-----
------^-------------------
.

This is exactly the situation that made the demonstration gyroscope precess. As in the case of the gyro, the axis of rotation of the coin will rotate in the horizontal plane. In other words, the path of the coin will start to deflect from a straight line without the coin initially tipping over at all. Obviously, as soon as it attempts to deflect from a straight line path, centrifugal forces will come into play and the coin will tip over to regain dynamic equilibrium.

This is the explicit reason why I said that the process could go either way: it could either start with the coin tipping and then turning, or with the coin turning and then tipping. As I said earlier, while interesting, coins are not good models for skis, and being personally short of time, I would prefer not to spend any more time on rolling coins than we have already expended.

.
Tom / PM
.

PS - Sorry about all the dots in the above graphic - just ignore them. The editor keeps removing all my blank spaces and messing up the figure unless I fill everything with some non-blank character.
We agree that the coin's passage is effected by some chance that starts a chain of events. I liken this to the skier's intent to go one way or the other. You are suggesting that the chance event causes a turn and then the coin compensates by tipping so as to conserve dynamic equilibrium. We can observe that it fails to do this and once its straight path is so unsettled, it goes into a spiral path and eventually falls over, suggesting the equilibrium it really seeks is to lie down flat and still!

You also suggest it could in fact be the other way around although you said " It's a chicken-and-egg thing. As in many things in physics, you can look at it either way - they happen simultaneously." 'Simultaneously' didn't ring true to me, but you changed this to which happens first is unimportant, either turn or tip will have the same outcome.

Curiously the skier has just this choice between the tip and the turn which quite neatly encapsulates modern ski method over the older attempts to change the skis' steering angle by rotation, but there is a choice involved. I'm not quite so sure the coin's fate is not rather more linearly determined, a deflection doesn't become an arc until there is progressive tipping involved, i.e. the tip instigates the process, otherwise the deflection is more like that of a billiard ball, such a non-tipped deflection would tend to topple it over but I can see that you have more important considerations for now!
Quote:
 Originally Posted by PhysicsMan For the answer to this question appropriate to hard snow conditions, grab a modern ski with deep sidecut and lay it down on a hardwood floor, and tip it up on edge by some known, fixed ammt (say 45 deg). Get your eyes down at floor level, and look at the gap between the ski edge and the floor. At the tip and tail, the edge will be touching the floor, but in the center of the ski, the edge will be above the floor by some distance. Next, press down on the center of the ski with say 5 or 10 lbs of force. Now, the edge in the center of the ski will be touching the floor, and if you look carefully down the length of the ski from an end (a helper is useful here), you will see that the ski is actually in reverse camber. Now, put all your weight on the center of the ski (while maintaining the 45 deg angle). The ammt of reverse camber didn't increase one iota, did it? The center is "bottomed out" and can't go anywhere. Now, imagine doing the same experiment on a frictionless, extremely hard and flat icy surface with the ski possibly moving, either sideways in a skid, or forward. Even in these conditions, more downward force at the center of the ski will not make the ski go into more reverse camber.
In theory, the above is all true. In practice, no surface that we ever ski on is infinitely hard. If you go and look at the racing line on the Hahnenkamm or the Birds of Prey after the race, even the hardest, slickest ice has tracks left in it from the skiers' edges. Therefore, IMHO, extra downward force actually does serve a purpose. Why else would those racers spend all that time squatting weights in the gym?
Quote:
 Originally Posted by Martin Bell I have a follow-up question: if the turning mechanism on skates is purely rotary, how does a skater initiate that rotation?
They rock forward onto the curved part, and rotate... You could rotate while rocking forwards as well....
A final thought on this coin (I really should be elsewhere trying to earn a few)...

An event that 'turns' the coin would deflect it onto a new straight path, but to set it into a curved path would require a series of such events such as an embankment or rail would do. Doesn't this suggest that the initial event actually wobbles the coin and the resulting tip is what produces the turn as it progressively tilts into a spiral path and falls so that it is a case of the tip causing the turn and not vice versa?
Quote:
 Originally Posted by Martin Bell In theory, the above is all true. In practice, no surface that we ever ski on is infinitely hard. If you go and look at the racing line on the Hahnenkamm or the Birds of Prey after the race, even the hardest, slickest ice has tracks left in it from the skiers' edges. Therefore, IMHO, extra downward force actually does serve a purpose. Why else would those racers spend all that time squatting weights in the gym?
That is why I described the hard snow scenario as "one of the limiting cases for ski behavior considered by ski designers". In my next paragraph, I described the opposite limiting case, extremely soft snow. All real-world situations (such as those that you mentioned) obviously fall in between these two extremes.

Your question as to whether extremely strong racers can get significantly more reverse camber in the hardest, slickest ice is interesting.

It can be answered by looking at the depths of their individual tracks (ie, not the overall rut left by the pack) in such a surface. One can derive a formula for the semi-hard snow case that tells you how much a given amount of extra reverse camber will tighten up their carves over the infinitely hard surface limit. The result of this formula is that if the maximum reverse camber at some edge angle in the infinitely hard limit is (say) 2 cm, and this generates an arc of radius (say) 10 meters, an extra 2 mm of reverse camber obtained by digging into the snow will decrease the carving radius by about 10% (ie, down to 9 meters). Look at the depth of the individual tracks in these hardest real-world situations that you mentioned, and you will be able to make a reasonable estimate as to how much extra the racers can tighten up the turn over the infinitely hard snow case.

Of course, there is another benefit to pressuring the ski on extremely hard snow. A small amout of indentation into the snow (ie, extra reverse camber) might not be enough to tighten up the arc substantially, but it may be all that is needed (even if only a mm or two) to give them purchase and prevent sideway slipping out of their carves on the ice.

Tom / PM
Interesting, PM, thanks for that formula. I had not realised that the radius could be decreased that significantly.
The question was asked: Can a highly muscled world cup skier apply more pressure to a carving ski than Flabby Fred the weekend skiing accountant?

Surprised? It's not as strange as it sounds. You have to understand the origin of the pressure applied to the ski. Only two elements play a role in this equation, gravity and centrifugal force (or momentum). Those two forces combine to produce a resultant force that acts to pressure the ski. The magnitude of that force is ever changing throughout the turn, depending on the speed, radius of the turn (as dictated by edge angle, sidecut, and snow integrity) and orientation to the falline.

But there is also a constant in the equation that also plays a role: SKIER MASS. I'm not talking about a Sunday morning slopeside service, I'm referring to the weight of the skier. The size of the resultant force of gravity and momentum is dictated by the size of the skier. For any turn of specific speed and shape the heavier the skier the larger the resultant force will be. You can demonstrate this to yourself by comparing the greater force you feel directed to your ski when carving turns with a heavy pack on your back.

It makes no difference if the weight is composed of muscle or fat, if Flabby Fred and Mister Muscle both weigh 200 lbs. they will both exert the same amount of pressure on the ski. Extra muscle does not allow one to apply extra pressure against a ski because there is no opposite platform (such as a ceiling over head) from which to brace against and push.

All extra muscle does is help in resisting, over multiple turns, the resultant forces (gravity and momentum) that are created during each turn which attempt to drive the skiers body into the ground, and allow the skier to combat the greater forces that result from employing high edge angles for smaller radius turns. In other words they can run a tighter line, and/or do more of them in succession.

Finally, to explode another myth. Mega muscle mass is not a pre requisite to making world cup style, high edge angle turns. There are some comparatively petite women in racing that make some pretty wicked high angle turns. Their secret is in the structural alignment they employ. They depend more on the force resistance potential afforded from an efficient body position than on brute strength. This is a technical reality at the disposal of all mortal recreational skiers.

FASTMAN

PS: If your interested in learning more about resultant force vectors, how they're created, how they're directed, and how the act on the center of mass, PhysicsMan and I did a very detailed thread on this topic a short while back. Ask Tom where to find it, recall betrays me.
Quote:
 Originally Posted by RicB Disski, Your use of pronation is just moving the center of Mass to bear over the edge, it doesn't create the pressure, it controls where the pressure is focused, put simply. Later, Ric.
know that - I have been told way too many times to edge FIRST then weight the engaged edge.... especially on ice when I tend to want to get weight fast onto the new outside ski(I know not to but damn it is tempting)

It just confuses me that everyone needs to TIP to engage edges... pronation feels so much more twist than tip to my feet... & I can do the physiotherapist's exercise with rubber bands while sitting down with minimal pressure & I am still pronating....I can see the foot change shape even....

& I know my ski edge engages when I do it in ski boots... (unless I only THINK I do the same movement)
Quote:
 Originally Posted by PhysicsMan When you want to analyze the mechanical behavior of a system (in this case, skier + skis), by far, the best way is to break it apart into smaller pieces, each of which can be analyzed more easily and more completely, and then you see how they act on each other once you understand the isolated behavior of each piece. Trying to understand a complicated mechanical system all at once, in its entirety, is doomed to at best generate qualitative discussion with a fuzzy final understanding, with "which came first, the chicken or the egg" paradoxes seeming to abound and never be resolved. In the case of skiing, to deeply understand what's going on in the combined system, you first must consider the skier and the skis separately. There are only a very limited number of truly distinct and elementary things that a skier can do to a ski: 1) You can change its angle with respect to the snow (measured with respect to each of the three axes); 2) You can apply force to the center of the ski (measured with respect to each of the three axes); and, 3) You can apply torque to the center of the ski (measured with respect to each of the three axes); When you talk about pronating, you are talking about an action that is internal to the skier (not the ski), but which causes a combination of the three effects listed above to happen to the ski. The major effect will be to tip the ski up on edge, but as RicB pointed out, weight shifts (ie, forces and torques) also occur. This thread has been concerned with first understanding the behavior of the ski itself, and then, once this is done, adding in the skier. This is why the people in this thread have been talking about ski tipping, and not about skier actions such as pronation that the skier has to execute to generate tipping (either by itself or in combination with other physical phenomena). HTH, Tom / PM
But I feel a lot more rotation than TIPPING when I engage the ski edge by pronation.... the pronated leg & foot rotate into the hill somewhat - the tipping does not feel large compared to that rotation....

The ski tip engages as it is TURNED into the hill... while also tilting a small amount

On ice if I stand HARD & try to angulate with my knees I WILL SLIDE(at least a little)... I MUST pronate first to allow that ski edge to start to cut into the slope(like a knife) rather than slide over (like a vegetable peeler or paring kinife scraping carrots)
Fastman