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# Centripetal Force How Does It Relate To Skiing?

I have looked up the definition of Centripetal Force but am having difficulty understanding how is relates to skiing. I believe it has something to do with the path of COM. Centrifugal Force, a result of inertia, is what keeps us from falling over as our legs extend laterally away from our bodies. Maybe I am on the wrong track. Is there a simple explanation?

There is no simple explanation.

Tek,

Yes, there is a simple explanation but generally people mess it up by using terms like centripetal and centrifugal force.

When skiing we are a body in motion. A body in motion will go in a straight line unless acted on some force. Gravity supplies us with a force to work with but it only accelerates us in one direction, down the hill. If we want to go left or right we have to use the fancy tools on our feet to generate a force to push us in the direction we want to go. Most skiers rely on the the reactive force of the earth, I push the earth to the left and the earth pushes me to the right. Being somewhat less massive than the earth I get moved strongly to the right and the earth barely moves to the left. There is also the force that the ski itself can generate. I use these forces to push my 'body in motion' where I want it to go.

fom

In a way they're really the same thing, seen from different viewpoints.

Suppose a ball is rolling down a hill and you want to make it change direction. You apply a force to it on one side, maybe you tie a string to it and anchor the string to the ground, and the ball's path curves as long as you maintain that force.

Same thing happens with you on the hill. In order for your path to curve, there needs to be a force pushing on the bottom of your skis toward the center of the turn. That force is called the centripetal force; the name comes from the from Latin words centrum ("center") and petere ("to seek"). It's the force that causes your mass to seek the center of the turn.

But while the ground is pushing on your skis, at the same time you feel as if you're pushing back against the ground with the same amount of force. It feels like you're pushing the ground away from the center of the turn, right? That's the centrifugal force, from the Latin centrum ("center") fugere ("to flee"). It's the force that feels like it's making you flee the center of the turn - the resistance that your body has to changing direction.

Does that help?

Edited by chilehed - 12/9/11 at 11:35am

Balance.

Quote:

Balance.

It relates to skiing in that it helps us understand lateral balance.  The greater the centripedal force the more we need to incline to maintain lateral balance.

The concept is important because it explains why one cannot ski effectivley in all situations with just inclination and must also be able to angulate.  The concept also explains why we "topple" to engage turns and gives insight into why so many struggle with arc to arc carving.

Further the concept also explains why strenght is so important for expert level skiing and why as the performance level increases we need such stiff ski boots to support out ankles.  Those centripedal forces can be very signficant.  WC skiers in GS pull upto 3G.

equal and opposite.

centripital and centrifugal are equal and opposite forces.  We can not have one without the other and they are equal.

Quote:
Originally Posted by bud heishman

centripital and centrifugal are equal and opposite forces.  We can not have one without the other and they are equal.

Ah!!! I see now, MASTER. Thank You

Quote:
Originally Posted by bud heishman

centripital and centrifugal are equal and opposite forces.  We can not have one without the other and they are equal.

Thanks. I believe I am seeing the light. Cheers

Too bad the links in the thread started by PhysicsMan, linked to above, no longer work. There were some excellent discussions there. I suspect that most of them still exist in the archives here. If I stumble across them, I'll post links--and perhaps try to repair the links in that thread.

For starters, though, here's another thread discussing centrifugal force (which, though "pseudo," IS just as real as centripetal force--believe it or fall): Centrifugal Force.

Best regards,
Bob Barnes

Quote:
Originally Posted by Bob Barnes

Too bad the links in the thread started by PhysicsMan, linked to above, no longer work. There were some excellent discussions there. I suspect that most of them still exist in the archives here. If I stumble across them, I'll post links--and perhaps try to repair the links in that thread.
For starters, though, here's another thread discussing centrifugal force (which, though "pseudo," IS just as real as centripetal force--believe it or fall): Centrifugal Force.
Best regards,
Bob Barnes

Just read through the link.  That was a fun thread.  And somehow it avoided devolving into the "yes it is!" "no it isn't" exchange that many other centripetal discussions have over the years.

Equal and opposite actions and reactions needs to be understood through the lens of an unbalanced sum of lateral force causing the skier to turn. Without that, the equal and opposite idea might imply an equal sum of forces that would result in straight line travel. Additionally, it's worth noting we are talking trajectories and changing them, not static balance standing still. I know it comes down to perspectives but I can't tell you how many mis-understandings occur when we forget we are not talking about static balance and standing still on the skis.

Edited by justanotherskipro - 12/11/11 at 11:24am

which comes first the chicken or the egg?

This discussion always gets rather confusing.  In physics theory there is "action/reaction".  So the idea is that if you push against a wall with your hand, the wall pushes back with equal force.  That is how academics talk about it.

But if you are the one standing there pushing with your hand on the wall, the sensation you feel is that the wall is just inmovable, you don't feel it actually pushing on you, the way you are pushing on it.  All of the control over the force is generated from you standing there and using your muscles and body weight to push against it, and it never moves.  It seems to kind of always push back with exactly the same amount of force to counteract your strenuous pushing so that the two pushes cancel each other out and the wall does not move.  The wall has structural forces and forces of friction, etc. that are holding it stable and pushing back at you with the same amount of force.

Anyway, back to skiing, the forces of gravity are pulling your COM down the hill and you have some momentum.  When you edge your skis and start to turn, what happens is that the momentum creates centrifugal force due to the arcing path your COM is making, while the momentum wants to keep carrying it on a straight line.  That is primarily the sensation that your COM feels in a turn as you ski and is primarily the force that requires you to inclinate.

However, just like pushing on the wall with your hand, your ski edges are engaged in the snow and create a "wall" so to speak that you are pushing against.  The centrifugal force derived from redirected momentum and gravity are the forces pushing against that wall.  The wall is pushing back with exactly equal amounts, due only to friction.  Friction force is a result of other forces.  In this case the primary forces are gravity and momentum causing centrifugal forces, and the "wall' is the centripetal force that pushes back with exactly the same amount, no more, no less.  You feel this in your BOS as your skis pushing towards the center of the turn.

The thing is, you can't create the centrifugal force without centripetal.  The only way the centrifugal force comes to be is because the "wall" is pushing back and deflects the skier on a curved path, while momentum and gravity continue to try to take it in a straight line.  They are equal forces and nobody is ever able to really show a clear way that one precedes the other, they both come into existence simultaneously, with equal force.

But in skiing, you focus on centrifugal forces when balancing your COM, and you think about centripetal forces when feeling with your feet.

Flaming statement (but not at all controversial and well understood in physics since the 18th Century): Centrifugal force is not a real force as in F = ma where a is the acceleration of the object in a non-accelerating frame of reference; only centripetal force is real, the other is a mathematical construct.

For some problems in mechanics, it is mathematically convenient to pick an accelerating frame of reference, like the carving skier, for their formulation. Only in this frame of reference, also known as non-inertial or d'Alambert frame of reference, does the concept of centrifugal force (also known as pseudo, or inertial, or d'Alambert force) arise and become useful. Evidently, it is not widely known to those never suffer from a course in advanced mechanics that one does not use, talk about, or consider both centripetal and centrifugal forces in the same mechanical formulation of whatever it is one is talking about. Pick a frame of reference, and one type of force will go out the window. Except in academia and esoteric circles, the d'Alabert frame of reference is rarely used. In most daily matters, like discussions in this forum, an inertial frame of reference is implied. In this case, centrifugal force is not conceptually helpful, let alone real. Centripetal force is the only thing. We need no stinking centrifugal force to talk about skiiing. Yes! Really!

Crossing the finished line in a completely flat area, Ted Ligety carves a circle at high speed to the cheers of spectators. How does centripetal force relate to his skiing? (I am picking a flat end zone to avoid dealing with gravity which unnecessarily complicates the issue here)

In order for Ted to move in a circle, the net force on him has to be F= m*v^2/r where v is his speed and r the radius of the circle. And this force on him is directed toward the center of the circle (not pushing him outward as some may be confused with the centrifugal force concept). This centripetal force arises from the resistance of the snow agaisnt the skis as Ted puts them on edge (or whatever he does to carve). If the resistance is less than the required centripetal F, he will slide out, not be able to maintain the arc which is the case for me whenever I ski faster on icy slope. There is no centrifugal force.

Still don't believe me? Look at the a in the often cited F= ma. It is a vector quantity, and the vector points to the center of the circle. There is no centrifugal force in the usual inertial frame of reference, strictly speaking. In the case of a satelite orbiting the earth, gravity provides the centripetal force to keep it in orbit at the right speed and altitude. Here, the snow pushing against the skis as a result of the skier doing something nifty.

Shit you guys know how to complicate a concept that for skiing's purposes is REALLY effing simple.

Edit for the sake of our readers: I posted this too soon.

Edited by HeluvaSkier - 12/13/11 at 8:35pm

Quote:
Shit you guys know how to complicate a concept that for skiing's purposes is REALLY effing simple.

Absolutely right . Differential equations have never bought any skier a good turn (unless he/she already knows how to turn).

But as long as we are having fun invoking frames of reference and Newton's laws (as done in the related thread linked by BB), it would be refreshing to do so with some rigor.

Quote:
Originally Posted by ChuckT

In most daily matters, like discussions in this forum, an inertial frame of reference is implied. In this case, centrifugal force is not conceptually helpful, let alone real. Centripetal force is the only thing. We need no stinking centrifugal force to talk about skiiing. Yes! Really!

Alas, ChuckT, much of what you say may be technically accurate, and you've identified the crux of the confusion when you warn of unknowingly mixing frames of reference. But I submit that you are dead wrong when you say that usually "an inertial frame of reference is implied" in everyday discussion.

To whit, consider the following not-unusual statements: "I floored the accelerator, and the telephone poles flew past in a blur...." "Hold your hands still" (advice to a skier). "Sit still!" (advice to a child squirming in the car seat). "Don't move, or I'll blow up the train." "Move your hips back." And so on.... What frames of reference are implied in these statements? Clearly in each of these, "still" is relative not to the surface of the earth, but to the "accelerated frame of reference" of the speaker or the person spoken to. When you tell a skier to "hold your head still," I certainly wouldn't expect that you mean to leave your head behind on the hill while the rest of your body schusses on down.

No, clearly, many common descriptions of motion, and especially technique, imply the skier's accelerated frame of reference. Movements of body parts are certainly simpler to describe relative to other body parts or to your center of mass than to the earth's surface. Obviously, too, it is the frame of reference from which you, the skier, experience your own skiing. It is from that frame of reference that we feel an absolutely real--not imaginary, not fake, not "apparent"--force pulling laterally toward the outside of every turn we make on skis. And it is that very real force that we "lean in" against to maintain balance in our turns. That force--no matter that it can also be explained accurately but quite differently from another frame of reference--is called centrifugal force, and whether your brain thinks it's "real" or not, your body knows all about it, and you have spent your lifetime learning to deal with it.

Yes, when you're explaining the forces that caused Ted Ligety to travel in a circle in the finish area, you imply that the finish area is "still" and it is Ligety that is moving and accelerating. From that perspective, the force that causes him to turn is clearly centripetal force--by definition--and centrifugal force has nothing to do with it. But if Ligety were to describe the event from his perspective, he might say something like "I pressed against the snow and inclined (leaned) in for balance against the forces trying to cause a skid and trying to pull me out of the turn." Both descriptions are accurate and true, and neither is any more or less "real" than the other. Both have their uses, depending on what you're trying to describe. But again, to describe the technique of skiing and the movements of all the body's various parts, it would be ploddingly complex and confusing to try to describe these movements relative to the earth--and very simple to describe them relative to other body parts. "Tip your shoulders to the right" is a whole lot more digestible for the average person than "as your center of mass moves in an arc to the west, move your shoulders in a slightly larger radius arc such that they end up somewhat to the east of your hips..." (or something to that effect--you get the idea). Just imagine if you were trying to describe the same technique on an artificial slope on an ocean liner traveling southwest at fifteen knots through the water in a 7 knot northerly current. And, of course, it is no more than a construct of convenience to imagine even the earth's surface as "stationary," as it spins about the earth's axis, as the earth travels in its orbit around the sun, as the sun travels through the galaxy, as the universe expands, ....

No, indeed, it is dangerous to assume that anyone "implies" any particular frame of reference when describing movement or technique, or that anyone would guess accurately what frame of reference you are implying when you describe the same. And that is really the point here. We do experience, and quite often describe, skiing from our own personal "me-centered" frame of reference. And from that frame of reference, it is centrifugal force that matters, rarely centripetal. The very concept of "balance" implies equilibrium--a balance of forces with no net resultant force. So, if we're "implying" an inertial frame of reference when describing ski technique, a balanced skier cannot turn (since turns involve acceleration, which results only from unbalanced net force). And a turning skier could not be in balance. Ski technique, from the skier's frame of reference, is largely simply a problem of maintaining balance as various changing forces push and pull in different directions on our bodies.

On some levels, I realize that it can sound a little weird to realize that we often describe motion relative to ourselves and the frame of reference that moves constantly with me--meaning that "I" am stationary (in that coordinate system) and the world revolves around me. (We all know that Vail instructors think that way, but I suggest that we all do, more than we may realize!) I can assure you that, from my perspective, I am "here"--always, and without exception. Any time you ask me where I am, my answer will be the same: "I am here." You may see me move around from your perspective, but as far as I am concerned, I am ALWAYS "right here." In that sense, I do not move--do not accelerate, do not turn, and so on--otherwise I would naturally end up somewhere other than "here." Since I do not accelerate within my (accelerated) frame of reference, the forces acting on me must counter and cancel each other out, leaving no net force. And because of that--and only because of that--I can accurately speak of being in balance! I lean (incline) right, then left, and move my feet forward and back beneath my center of mass, and so on, all in order to counter the constantly changing barrage of--very real--forces acting on me, and I describe those movements as "ski technique."

Again, our bodies "understand" this stuff thoroughly and simply, whether we can wrap our minds around it or not. It's only when we need to describe the motion and techniques of skiing (or anything else) that it becomes critical to establish--clearly and unambiguously--a frame of reference. And quite often, the most convenient, natural, and simple frame of reference is NOT the inertial frame of reference based on the earth's surface. It is the personal frame of reference of the skier, the "coordinate system" that moves with him wherever he goes. Massive confusion and disagreement--including questions like whether or not centrifugal force exists, and whether the feet move in circles (see discussions of "backpedaling") or always "forward," and so on--arises when we unintentionally or unknowingly mix frames of reference.

There is a phenomenon that we feel--and that we can easily measure--that pulls laterally relative to our bodies when we turn. We can describe it in many ways, from different frames of reference. But it is as real as it could be. If you think otherwise and try to turn without "leaning in" against it, you're up for a rude awakening. But your body knows all about it. And it has a name: it is called Centrifugal Force.

Best regards,
Bob Barnes

Wow, Bob.

Once again I am in awe of your writing abilities.

I agree with everything you said, but there is no way I could have explained it that well.

Hi Bob,

Although I agree with Heluva that this stuff is utterly unnecessarily complicated for skiing, I am having fun and so are you, it seems. Therefore I will contest the validity of your statements as a physicist.

Quote:
Originally Posted by Bob Barnes
But I submit that you are dead wrong when you say that usually "an inertial frame of reference is implied" in everyday discussion.
... And quite often, the most convenient, natural, and simple frame of reference is NOT the inertial frame of reference based on the earth's surface. It is the personal frame of reference of the skier, the "coordinate system" that moves with him wherever he goes. Massive confusion and disagreement--including questions like whether or not centrifugal force exists, and whether the feet move in circles (see discussions of "backpedaling") or always "forward," and so on--arises when we unintentionally or unknowingly mix frames of reference.
There is a phenomenon that we feel--and that we can easily measure--that pulls laterally relative to our bodies when we turn. We can describe it in many ways, from different frames of reference. But it is as real as it could be. If you think otherwise and try to turn without "leaning in" against it, you're up for a rude awakening. But your body knows all about it. And it has a name: it is called Centrifugal Force.

First, in everyday discussion, we cite F = ma, right? That assumes an inertial frame of reference, period. If the skier is the frame of reference, his speed and acceleration must be zero by definition and thus experiencing no force (certainly not true for Ligety). Of course I am using the strict definition of frame of reference as it is used in physics to formulate and solve equations of motion, not the poetic sense of perspective as used in daily talk. If we agree that we are talking about physics where some math is involved, I am dead right that by using Newton second law in its usual form above, we are implying an inertial frame of reference.  A non-inertial (or d'Alambert, to be fancy) frame of reference is a completely different type of frame of reference, not equivalent with an inertial one and must be used with proper math to avoid the "Ligety paradox" above.

Now, we lean when we turn on skis or on bikes because that position allows gravity (plus the action and reaction bits) to result in a net force that is exactly centripetal with the right magnitude to change our velocity (changing direction) along the arc of the turn. There is no Centrifugal Force pushing outward. If there were this force balancing the centripetal force (which can be easily illustrated with a force vector diagram), we would move in a straight line at a constant speed as Sir Isaac dictated 300 odd years ago. "Leaning in" is not to balance against the fictitious centrifugal force so as not to fall, but to provide the centripetal force (you actually let gravity take over by getting out of static balance, ie you would have a rude awakening if you were not moving, or moving too slowly for the amount of leaning) required for the turn. Without leaning, you wouldn't fall due to an unbalanced centrifugal force, you simply won't turn at high speed. (By "leaning" I simply mean getting your COM outside of your BOS to avoid a ski-related controversy) There is no real Centrifugal Force. That's why one terminology for this concept in physics is a "pseudo force".

Human perception is of course a different matter. When you floor the gas pedal in your high torque, high power sport car, the seat of course accelerates forward and pushes your body to give you the same acceleration. It may feel that you are pushed backward into the seat. But that backward pointing force is not real, exactly the same in nature as our famous centrifugal force. These are called "psuedo forces" by physicists because they are not real.

Whatever works to help skiers ski better is perfectly fine with me. Physicists don't typically win WC races. If they do, I bet \$10K of Romney's money that they don't think about this stuff in the start house.

Regards,

Chuck

Quote:
Originally Posted by mdf

Wow, Bob.

Once again I am in awe of your writing abilities.

I agree with everything you said, but there is no way I could have explained it that well.

Yes, Bob is a fantastic writer. I agree he gives a good and useful description of what a skier feels. But someone has said about skiing that "perception is not reality". Bob's accelerating self as frame of reference would not produce a real force (centrifugal) to balance a real force (centripetal) in the earth frame of reference. Let's not forget that motion is relative to a frame of reference but force is not. It doesn't matter what frame of reference you choose, the net force on an object is always the same. There is no real centrifugal force to balance centripetal force. It is a convenient concept in some situations, but should always be used with the understanding that it is an artificial construct. Grab a text book on physics. Heck, let me google it for you. Here comes the University of Virginia, Physics Department

http://phun.physics.virginia.edu/topics/centrifugal.html

Must be a new ski season, the dreaded math monster (physics) is loose again. While I agree with Chuck that without a sum of forces that laterally accelerates us we would go straight. The rest is interesting on some level but more often than not in a ski lesson a discussion of equal and opposite forces is superfluous, or worse it's like throwing up on the student's skis. They didn't ask for it and it's completely un-welcome.

Obviously the OP solicited a discussion of inward fleeing forces, so I don't see why we have to automatically include outward fleeing ones to help him understand how centripetal forces are related to skiing. Fatoldman gave us a simple straight forward answer. If you don't want to go straight you need to do something to cause the skis to turn. It can be inclining the body, it can be rolling the ankles (I know it's everting and inverting the foot), abducting the knee while flexing it, moving the hips towards the inside of the turn, or a combination of these movements.  Nowhere in those phrases did I use, or need to use, any reference to centrifugal forces. Or frames of reference. What's more when I tell a skier what I saw them do it isn't from an accelerated frame of reference, it's from my perspective. So I avoid mixing my frames of reference for the sake of simplicity and clarity.

Another though not being considered is even though I have an internal FoR, to avoid collisions and safely navigate down the ski run I have to leave that FoR behind. The trees don't come towards us, we move towards them and if we want to avoid hitting one we had better learn how to change the direction we are traveling. Same goes for driving or riding in a car. I'm not moving relative to the car but both of us are traveling down the street. I know that when I look out the windows. We might pass a sign, or that very same pole Bob mentioned but it is stationary and it is me who is moving past it. If it was the other way around explain a turn, it is a change of direction but from my accelerated perspective I can't change the direction I am traveling since I'm not traveling.

So Tek, I hope all of this helps you understand that to turn while riding a ski, you have to do something to create a lateral acceleration and that occurs as a consequence of an unbalanced sum of forces acting on your body and accelerating you into the turn.

Most of what I have to say has been said in the linked to threads, but I have to agree with Bob.  Long before I took high-school physics (wherein I learned about accelerating frames of reference), I discussed being "pushed" into the seat of a high-powered muscle car when the accelerator was floored, or being pushed against the door going around a corner.   The problem is, as Chuck says, mixing our frames of reference.  A little knowledge is a dangerous thing.  Folks try to apply Newton's laws within a fixed frame of reference and include the centrifugal force in that frame of reference.  A simple solution is for folks to stick to the fixed frame of reference when applying Newton's laws to explain things, and to remember that the equal but opposite forces act on different objects.  Only the forces acting on the ski/skier body affect that ski/skier's acceleration.  BTW, you can think as Ma as the rate of change of momentum if your mathematically inclined.

• Centripetal force is simply the name we give to the combination of forces that make you move in a curved path instead of a straight line.
• If you are schussing straight down the hill, there is (almost) no centripetal force involved (I am ignoring the tiny amounts arising from Earth's rotation, orbit, etc.)
• If you turn, then there is a centripetal force because you need a force to deviate an object from its naturally straight path.
• The centripetal force is toward the center of your circular path (if your path isn't an actually circle, you can approximate it by a series of different circles at each instant, like one of those French Curve plastic templates in drafting class).
• The amount of centripetal force needed to move you in a circle depends on: your mass m, your speed v, and the radius R of the circle. More mass => more force. Smaller radius => more force. Higher speed => lots more force, because it is actually the velocity squared that applies (v * v). The specific formula (as someone above also posted) is F = m * v^2 / R.
• The centripetal force is provided by a combination of gravity (toward the center of the Earth), the force of the surface against you (which is perpendicular to the tilted surface), and friction.
• In skiing the friction and perpendicular forces are somewhat complicated because, for example, a ski carving on edge in ice is actually pressing with its edge against a tiny groove in the ice which is tilted compared to the overall run's surface, and a ski in deep powder is pushing with its base on the snow that is just beyond it, and if you are skidding on groomed then sliding friction is helping you make the turn (and if that friction disappears because you hit a patch of ice you may suddenly start going straight and exit the circle dramatically, thus experiencing the so-called centrifugal force).

The good news is that you don't have to think about any of this consciously while skiing! Your body knows what to do, and modern skis are very good at helping you create and use subtle forces.

-Jeff, former physicist

Just out of curiosity, why would one need to know all this?

Quote:
Originally Posted by BillA

Just out of curiosity, why would one need to know all this?

One wouldn't. This stuff is just good, clean fun while waiting for the next ski trip. You can tell I'm a certified geek.

Quote:
Originally Posted by ChuckT

.............. You can tell I'm a certified geek.

Heh. Aren't we all.

Ghost, Bob, While I understand the idea of feeling the seat pressing harder against your rear end as the car accelerates, that isn't the only sensory information we would be experiencing at that moment. We would also see through the windows and what we would see would be us moving past the terrain outside of the car at an ever increasing speed. The only time we would experience that internal world without other sensory input would be if we closed our eyes as we stomped on the gas pedal. So even though we say we felt the seat pressing harder against our back, it is assumed it's because the car is accelerating, as in moving faster through the external world we would experience through our other senses. That in a nutshell is why it's so hard to talk about internal (accelerated) perspectives without including any reference to the world around us. Look at the phrase "Press against the boot tongues while making a turn", From an accelerated perspective is that even possible? So isn't the phrase asking the skier to do the impossible from that limited (internal) perspective? Have I mixed my perspectives in that phrase, or have I maintained an external perspective where it isn't impossible to accomplish that task? Do I tell a skier they need to feel more pressure against the tongue of the boot during a turn? Sometimes but even then it's defined as to when we are experiencing that pressure (while turning), as in moving through that external world. So the external world and an external frame of reference are rarely excluded from my feedback and advice. Especially when that advice starts with "here's what I saw". That definately defines the frame of reference as external to them. That doesn't mean I don't solicit feedback from the student that includes how it felt to perform a movement, I do that regularly. I just don't try to teach my lessons exclusively from that accelerated perspective.  BTW, I've worked with Bob and feel he is one of our sports brighter mind but in this instance I feel the importance of using "me" world perspectives to teach skiing is being overstated. We want people to experience what they are feeling ( through their sense of feel, and emotionally) but not to the point of excluding / ignoring their place relative to world around them.

Quote:
Originally Posted by BillA

Just out of curiosity, why would one need to know all this?

Because it is critical to understand ski technqiue and why things are, the way they are.  It explains why skiing is not just a "matter of opinion", why you cant just simply say "well the way I define it", it explains why there is a right and a wrong, and it shows why those who disregard established schools of thought and just make it up on their own will almost always get it wrong unless they too are armed with a solid understanding of physics and biomechanics.

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