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Some comments on centrifugal and centripetal forces

post #1 of 53
Thread Starter 
The subject of centrifugal and centripetal forces (and their distinction) is at the heart of all ski or boarding turns, and must eventually arise in any deep technical discussion. It has recently done so in the WaistSteering thread by Gary Dranow: http://forums.epicski.com/showthread.php?t=28471&page=10&pp=20

Some of the participants in that thread have sent me private messages asking me to help them understand these concepts, while other participants have made serious errors in what they have said about the physics of these forces. This thread is in response to the above.

There are a huge number of discussions of centrifugal and centripetal forces available both in classical physics/mechanics texts, on the Internet, as well as even here on Epic, e.g.:

http://forums.epicski.com/showpost.php?p=185567&postcount=132
http://forums.epicski.com/showpost.php?p=86591&postcount=144
http://forums.epicski.com/showpost.php?p=86592&postcount=145
http://forums.epicski.com/showthread.php?t=8461&highlight=centrifugal+centri petal
http://forums.epicski.com/showpost.php?p=100752&postcount=55

Unfortunately, the subject of centrifugal and centripetal forces is not “obvious”, and to really understand it requires a significant amount of traditional academic study. Because of this, I can not attempt to give a full discussion of the subject, just make a few, hopefully relevant comments.

Unfortunately, with altogether too much regularity, someone will not want to make this effort, yet still believe they know all about this subject and write as if they are an expert. For example, the first link in the above list is to some posts in the infamous “Get off those edges” thread by DaSlider. Rick/Fastman and I tried hard to explain the basics to this guy, but he was more interested in debating than getting to a true technical understanding. This led to a highly contentious thread, tremendously frustrating for both Rick and I, given the amount of time we put in. I have absolutely no interest in a repeat of that experience.

That said, here's a short summary of centrifugal and centripetal forces:

  1. Centrifugal force is the force the skis exert on the snow. It's what causes the snow to be indented sideways by your skis in the apex of a high G turn.
    -
  2. Centripetal force is the force that the snow exerts on your skis. It's what causes your skis to deviate from a straight line path when they are appropriately edged, weighted, etc.
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  3. It is absolutely fundamental and critically important to realize that these two forces are acting on totally different bodies - one acts on the snow, one acts on the skis. Thus, they must never be considered simultaneously in any analysis. If you want to understand the motion of the skis, you look at the sum of the forces and torques acting on them, ie, #2 plus the forces and torques your legs exert on the skis.
    -
  4. If you want to understand the effect of the skis on the snow, you look at the forces acting on it, ie, #1
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  5. Forces can only cancel in any reasonable sense of the term if they are being exerted on the same object, and at the same point on that object.
    -
  6. Because centrifugal and centripetal forces truly act on different objects, these two forces NEVER "cancel". It is as much nonsense to say centrifugal forces cancel centripetal forces as it would be to say that the force my chair is exerting on my butt cancels the force your butt exerts on your chair, even though we weigh the same. The numbers may happen to be the same, but that’s irrelevant – they are different objects under consideration.
    -
  7. In any one analysis or line of reasoning, because of #3-#6, above, while appealing, it will be ultimately misleading and often lead to incorrect conclusions if someone discusses centrifugal forces acting on one part of a skier’s body, while simultaneously trying to mix into the discussion, centripetal forces acting on some other part of the skier’s body.
    -
  8. If you need to figure out what forces are acting on different parts of a skier’s body, and how the forces are affecting the motion of those parts separately, you have to be extremely precise in your analysis. You have to separate and clearly define the parts of the body that you want to consider, and then do extremely good bookkeeping on the various force diagrams that you get. This is quite difficult to do, and I applaud folks like Rick and Bob Barnes who do such a great job explaining this to non-technical skiers / racers.

    In a typical engineering or physics curriculum, typically, we wouldn’t introduce a student to the analysis of the dynamics of multiple, connected objects until a student has had one full year of university level calculus and physics, plus one more semester of a specialized “statics” course (or physics equivalent). Even with this preparation, the traditional 2nd year course in Analytical Mechanics / Dynamics often is very hard for students, and all too frequently causes students who had intended to go into this area to switch to a different major.

    Even worse, without the use of force diagrams and equations in a text-based internet forum such as this, with rare exceptions, attempts at such a multi-body dynamics analysis are often incorrect.
    -
  9. The issue of “frames of reference” often comes up, along with questions about the “reality” of these two forces. This is one of the most complicated aspects of the understanding of these forces. It was discussed at some length in some of the Epicski threads referenced above.
    -
  10. A summary of this discussion is that both centrifugal and centripetal forces are as real as any other force. The snow “really” gets pushed to the side by the centrifugal force from the skier pushing on it, just as the skier’s path “really” gets turned into an arc by the force of the snow on the skis, ie, the centripetal force.
    -
  11. My recommendation is that if all possible, do your analysis in a stationary frame of reference, ie, looking at the skier from the edge of the trail. If possible, it will generally be the easiest way to correct answers.
    -
  12. However, thoughtful, advanced skiers such as those in Gary and Rick’s thread are interested in what they feel as they ski through high G turns. Thus, we have to deal with the difficulties of doing a correct dynamics analysis from the point of view of the skier/racer in the middle of a turn (ie, in an accelerating frame of reference). I’m not going to say much more about this, other than unfortunately, there are many subtle complications and one must be very careful to do this correctly.
Anyway, I don’t expect a lot of interest in such a technical topic, but I hope the above comments provides some insight and help to those of you that have sent me private messages about this subject both recently as well as in the past.

Cheers,

Tom / PM

PS - I am in the middle of intensive preparations for the fall semsester (lots of changes going on at school), so I probably won't be able to respond to messages in this thread as quickly as I would like, but I'll try to keep checking in as often as possible.
post #2 of 53
Tom,

Physics was always my true favorite subject (not sure why I didn't just follow my natural interests in my academic pursuits) and so I actually appreciate and enjoy your comments here independent of skiing.

With that said I am not sure I agree that I totally agree with your comment:

Quote:
Unfortunately, the subject of centrifugal and centripetal forces is not “obvious”, and to really understand it requires a significant amount of traditional academic study.

In order to explain these forces and try to give someone a simple perceptual basis for understanding them I would rely on the approach that these "forces" are simply a result of Newton's first and third laws of motion.

For centripetal force consider Newton's first law: An object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it. In my way of thinking centripetal force results from the external resistance to a body's continued straight line motion, i.e. the external force required to have a body deviate from its uniform motion. In skiing this is the force the snow exerts on the ski as you've said.

Similarly, centrifugal force is a direct consequence of Newton's third law of motion that: For every action there is an equal and opposite reaction, with the centrifugal force being the opposite and equal reaction to the centripetal force and vice versa. Again, as you've said, in skiing this is the force the ski exerts on the snow. While these forces act on different objects I think it's important to always remember that they are just the "reaction" of opposing forces from the third law.

Of course these laws only came about as a generalization of observations from him (and others?) who were able to recognize that such forces seemed to always be needed to be present in order to have a body deviate from straight line motion. So perhaps we need not refer to the laws at all but just our basic perceptions of bodies in motion.

Hope this provides a slightly different way to view things that helps to clarify rather than muddy the waters.
post #3 of 53
I'm no physicist, but I appreciate what you have added to PM's discussion. The notion of both being "opposite and equal" reactions to each other squares with my experience in skiing.
post #4 of 53

At the risk of being a called a pseudo intellectual...

Can we now discuss why centrifugal force is called a pseudo force?
post #5 of 53
Quote:
Originally Posted by therusty
Can we now discuss why centrifugal force is called a pseudo force?
Put on some slick britches and sit in the back of someone's car with leather seats. When they hang a tight corner at 60mph and you fly into the opposing door, did a phantom push you? However, when you hit the door, it's a pretty real force. Centrifugal forces don't act on the mass in motion they act on something else.

That's my lame explanation and I'm stickin' (get it) to it.
post #6 of 53
Quote:
Originally Posted by therusty
Can we now discuss why centrifugal force is called a pseudo force?
It starts with a body in motion traveling in a straight line. If there is no external force then nothing happens. In order to make it turn (accelerate in the sense of angular change) there must be an external (centripetal force applied). One interpretation of centrifugal force is the opposite but equal reaction (force) to the centripetal force, a true force.

However, another interpretaion is that there is a "centrifugal" force that pushes the rider in a car against across the seat and into the door. There is NO such force just a demonstrtion of inertia, i.e. the person naturally (according to Newton's first law) follows a straight path (unless there is adequate friction of the seat or seatbelt force) until the door applies adequate centripetal force to turn the person at the same rate as the car. When centrifugal is used in this fashion (as the force moving the person across the seat) it is called a pseudo force because no such force exists and what is observed is just the result of inertia, i.e. the first law.
post #7 of 53
We're almost there. Tom's description of centrifugal force is as a real force (if I read him right). How do we explain the discrepancy?
post #8 of 53
Gosh!

If I were trying to resolve forces, I would use vector diagrams and and know that if all the vectors didn't sum to zero, then there must be something "not at rest".
I know I can move a vector anywhere along it's direction without changing "the system" So pulling or pushing means nothing.

F=ma

Pushing or pulling, The ski Pushes on the snow due to the skiers inertia. Inertia, quantified as momentum.
The snow provides Resistance and with resistance to inertia, the skier can then travel an arc instead of a straight line. Just as if instantaniously suspended by a string.

Centrifugal or centripetal, forces left unopposed result in motion of the object being acted on. But we don't really need centrifugal forces, we already have inertia

There are only four vector directions that concern us. ( Our mass not our thoughts and ideas) Gravity and terra firma claim the verticle (even if covered with snow), inertia and indented snow swap authority over the horizontal. (Even these directions cross lines in the commotion of motion.)

Let's just leave centrifugal forces out of this ;-)

CalG

For reference: http://scienceworld.wolfram.com/physics/
post #9 of 53
Rusty

Tom's description is relatable, but flawed due to the introduction of a "duplicate" force.
Centrifugal force might be accepted as a special case of inertia. but who needs it.

foot pounds , pound feet, newton meters, joules, or watts. We have pleanty of names for stuff.

Do you know what I mean????


CalG
post #10 of 53
Quote:
Originally Posted by therusty
We're almost there. Tom's description of centrifugal force is as a real force (if I read him right). How do we explain the discrepancy?
I guess I would explain the discrepancy by saying that centrifugal force is a "real" force at the time it encounters centripetal force (ala hitting the car door). The "pseudo" part is the common misconception that there is a phantom force pushing or pulling the passenger through space before hitting the door.

As Si pointed out this is just the result of Newton's postulate that a body in motion will continue in a straight line until encountering a force that alters or stops the motion. In a round about way, the "phantom" force is whatever accelerated the mass in the first place, but it is a "residual force" when the passenger is flying across the seat.


.
post #11 of 53
Another description of "centrifugal force"

An outward-directed "fictitious force" exerted on a body when it moves azimuthally in a noninertial rotating reference frame. For example, a rider standing on a carousel feels himself "pulled" outward as the carousel spins around. Centrifugal force is a fictitious force because it is a by-product of measuring coordinates with respect to a rotating coordinate system as opposed to an actual "push or pull."

The centrifugal force on a body of mass m is given by (These didn't paste! Reference http://scienceworld.wolfram.com/phys...ugalForce.html)

where a is the centrifugal acceleration, v is the tangential velocity, r is the distance from the center of rotation and is the unit vector in the outward-pointing radial direction.
post #12 of 53
Quote:
I have absolutely no interest in a repeat of that experience.
Ahhh, c'mon man, we all live for non-sequitur arguments that never lead anywhere! Whatsamatter!

Great work, thanks for the help and deflection!!! The only question I have, when one feels they must use those terms in a discussion, how should the concept be presented in a simple expression?

MH
post #13 of 53
Quote:
Originally Posted by therusty
We're almost there. Tom's description of centrifugal force is as a real force (if I read him right). How do we explain the discrepancy?
If you define centrifugal force as the opposite and equal reaction (force) to cenripetal force (as Tom did) then it's a real force.

If you define centrifugal force as for example that which pushes the back seat occupant across the seat in a turning car then it is a pseudo or fictitious force as there is no force being applied to the person they are merely attempting to follow straight line travel (Newton's first law) in a (non-inirtial) reference frame (the car) that is turning.

So I don't think there's a discrepancy. Just 2 different definitions.
post #14 of 53
Sorry if I'm repeating myself, but I get "page cannot be displayed" when I click on the link.

I agree suggestion 11 is the simplest way for the physics challenged. Consider the motion of one defined body the skis say, or even simpler the the skier and skis as a single unit. Add all the forces vectorially (using directions) acting ON that body and you get it's acceleration from a = F/M. The key to keeping things straight is to consider ONLY the forces that act on that body.

Now as to what is a "real" force and what is a ficticious force? It depends on your point of veiw (point of reference?). Newtons first law states that a body will continue in motion in a straight line unless acted upon by an external force, and his second law yields F=ma. Most people understand this as a straight line drawn on the surface of the Earth, eg. a bowling ball going straight down a bowling alley. We start by having a "fixed" frame of reference that is "not moving". But the Earth is moving. For one thing, it is spinning. The bowling ball if allowed to travel far enough would actually seem to us, who have fixed our reference point to the spinning surface of the Earth, to be travelling in a curved path. The amount of curvature introduced by the spinning Earth on things is so small that it only comes into play at large scale, eg Global winds and currents, (Coriolis).

Ok, so you might say lets use the sun as our fixed frame of reference. It's moving around galactic centre. The galaxie is moving. There is no absolute fixed frame of reference!

Here's a thought experiment. Imagine you and scientists live a sheltered life inside an elevator. Consider the motion of a ball being passed back and forth in a frictionless elevator. Start with the elevator " not moving" (referenced to the ground). F=ma says that it will move straight from person to another when thrown, except that gravity will cause it accelerate toward the floor. There has to be a force (gravity) acting on the ball causing it to accelerate toward the elevator floor.

Now what if the cable is broken and the emergency brakes fail: the elevator is in perpetual downwards acceleration. F=ma; the ball and the players both accelerate toward the Earth. But if we fix our "stationary" frame of reference to the elevator floor (and we are quite free to do so, as there is no "real" absolute non-moving frame of reference), it would seem to us that the motion of the ball is not accelerating (towards the floor). There is not net force acting on the ball! F=ma can only work if gravity does not exist (and if our scientists spent their entire lives in this falling elevator they would have no need of it), or if there is an other force acting on the ball in an upwards direction.

Now consider our elevator moving around a curved path as defined by a reference point fixed on a "non-moving" point on the surface of the Earth. We want to use F=ma : NO ACCELERATION for NO NET FORCE. If we use a frame of reference fixed on the ground, then it is Easy. The ball travels in a straight line, getting closer to the outside wall as the elevator follows the curve. If we wish to use a frame of reference fixed to the floor of the elevator, our ball will seem to accelerate towards the outside (of the curve) wall. If we want to use F=ma to explain the motion relative to the elevator floor we can do it by including a force acting on the ball that accelerates it towards the outside of the curve: a centrifugal force acting on the ball.

Newtons third law states that there is an equal and opposite reaction force (one that ACTS ON A DIFFERENT OBJECT). This force does not affect the motion of the object. In a frame of reference fixed to the hill, the reaction force to the centripetal force of the snow acting on the ski/skier ACTS ON THE SNOW. This reaction force, though it flees the centre, is not to be confused with the centrifugal force acting on the skier in a frame of reference fixed to the skis.
post #15 of 53

Centrifigul Force - why it's fake

Take a weight - put it on a rope and spin it over your head.

Centrifigul force is your belief that if you let go of the rope that the weight will move away from the center of the circle. You perceive and and imagine a outward pull on the rope. But if you release the rope, the weight will move tangentally to it's path in the circle exposing the apparent "outward" force was really not an outward pull at all.

This is why is referred to as a "fake" force.
post #16 of 53
Perhaps some may benefit by the simplification of making all observations and changes in the direction of motion. That is just speeding up or slowing down in a particular direction.

Bungee jumping! Oh! so "Two directional".

We don't often think of motion in the same direction as gravity as being centrifugal or centripetal. But it's all the same, kind of, just rotated ;-)
Linear acceleration, Easily likened to a tiny time and direction slice of angular motion. Changes in the direction and speed of travel due to the earth's gravity are familiar to us all.

Add to the complexity. Imagine moving at a steady speed down a slope that has undulations, up and down. Moving at a steady state in one direction and at the same time moving with variable velocity in another. Essential bump skiing and pressure management. four directions now!

That brings us to the fifth and sixth directions! (not dimensions, just directions. dimension with plus and minus signs)
Up and Down, left and right, in and out. That pretty much covers it. Mix 'em and match 'em, Sum 'em with vectors. Call them whatever, just don't confuse anyone.

Does everyone "know" that changing direction IS acceleration? The moon is "accelerated" to describe it's path around the earth, even if it always takes the same 27.3 days to complete it's orbit.

I always liked those old Dynastar MV2's The equation for Acceleration!

CalG
post #17 of 53
Quote:
Originally Posted by John Mason
Take a weight - put it on a rope and spin it over your head.

Centrifigul force is your belief that if you let go of the rope that the weight will move away from the center of the circle. You perceive and and imagine a outward pull on the rope. But if you release the rope, the weight will move tangentally to it's path in the circle exposing the apparent "outward" force was really not an outward pull at all.

This is why is referred to as a "fake" force.
That's just utter rubbish. I can put a fish scale in line with that rope and it will read some non-zero value of force as I spin the weight around.

Now, just how much belief, perception and imagination do you think a fish scale has?

If a fish scale says there's a force there, then it's a real force in my book.

By the way, I've done this exact experiment for my kid many years ago, so I know it works.

YOT
post #18 of 53
This is the sort of fish scale I'm thinking about - http://media2.e-commedia.com/thumb.p...ackle/5392.jpg

YOT
post #19 of 53
PhysicsMan may wince at some of the posts above but most are pretty interesting.

In the Car examples mentioned (where a person appears to ‘slide to the side’ when the car turns) … if we assumed no seat friction, wouldn’t it be more appropriate to say that The Car Accelerated to the -other- side rather than the person moving? And therefore no centrifugal force was involved on the person?

In the Weight on a String example: Since the string is -attached- to the weight, centrifugal force would be involved and it’s quite busy tugging away on the string, right? But nothing is tugging on the person in the car seat example so centrifugal force is not acting on the person, right?

---
Much about skiing may be perceptual but I suspect that any Force Felt must be a Force that really does Exist regardless of philosophical perspective, though we must remain mindful of misused pharmaceuticals.

Ghost’s (and others) ‘Rotating frames of motion’ and the resulting appearance of curvilinear motion to a body moving in an otherwise ‘straight’ line is an interesting perspective. Smacks of that whole ‘Warped Space & Gravity’ thing. Can’t think of a way to use it in a ski lesson though. Maybe during a really big earthquake. Or a clinic after too many beers. Definite rotating frames of reference found that way.

.ma
post #20 of 53
The force measured by the fish scale is a centripetal force pulling the weight around in a circle, accelerating the weight in the direction of the centre of the circle.

Some people navigate by orientating a map with north on the top. Some people navigate by orientating a map so that their direction of travel coincides with the top of the map (so they move up the map as they move forwards). Most people understand physics problems best when they fix the frame of reference to the ground. Sometimes it MAY be simpler to fix the frame of reference to some other object that is moving with respect to the ground.

In the car example, YES it is better and easier for most people to say that the person is traveling straight and not being acted upon by any force, but if (for some reason) you want to think of the motion of the person with respect to the car seat and reference it to the car seat (i.e. attach your origin and x-y axis to the car), the description of the motion of that person (with respect to the car seat) is that as far as a person strapped in sees things inside the car, ignoring what is going on outside the car, the unstrapped person is accelerating toward the outside door. It is still possible to analyze things describing how things are moving compared to the car and use F=ma when doing this, but in order to do so when the car is accelerating (speeding up, slowing down, or turning), F=ma will only work out right if you include an extra force in your equations.

The rotating frame of reference could for example be a car going around a corner, or a skier traveling in a curve. You might want to analyze what your cm is doing compared to your outside ski for example.
post #21 of 53

Of course - but not what I was saying

Quote:
Originally Posted by YoungOldTimer
That's just utter rubbish. I can put a fish scale in line with that rope and it will read some non-zero value of force as I spin the weight around.

Now, just how much belief, perception and imagination do you think a fish scale has?

If a fish scale says there's a force there, then it's a real force in my book.

By the way, I've done this exact experiment for my kid many years ago, so I know it works.

YOT
You can "rubbish" my post all you want but I don't disagree with you at all. I have no disagreement with your fish scale at all. The faster you spin the more the force on the rope. Release the spinning object and it will go straight not out from the center.

http://www.infoplease.com/ce6/sci/A0811114.html

The last two sentences of that link describe better what I was trying to say. Most people mislabel and misuse the term centrifugal force is all I was pointing out.
post #22 of 53
Quote:
Originally Posted by John Mason
Release the spinning object and it will go straight not out from the center.
Your right about the direction the object will travel if the string is released, John. It will continue in the (approx ?) staight line direction it was traveling when the string was released. Anyone who's spent enough time on the side of a race course and has observed the direction racers who suddenly loose all edge purchase are ejected out of the course have substancial first hand knowledge of this principle. It's called the fall zone.

But that straight line of momentum does strive to direct a skiers line of travel farther away form the center of the circle. It's at a tangent to the radius, but it's still takes the skier farther away from center. That's why in real skiing CG force is felt as a lateral force perpendicular to the skis,,, because it has an outward to the intended direction of travel orientation.

QUESTION FOR PM, SI, CAL: Notice my use of (approx?). Did this because I'm not sure whether or not there's a lag effect with this. If the string is cut will the rock travel in the exact current direction of travel, or will there be a degree of lag between current direction ejection direction? I guess I'm asking if momentum plays catch up at all with change of direction.

I ask because the feeling when skiing is that there is a lag effect. Could just be an illusion created by focusing on the front of the ski leading the direction change, which would give a false sense of the actual current direction of travel.
post #23 of 53
Quote:
Originally Posted by Rick
QUESTION FOR PM, SI, CAL: Notice my use of (approx?). Did this because I'm not sure whether or not there's a lag effect with this. If the string is cut will the rock travel in the exact current direction of travel, or will there be a degree of lag between current direction ejection direction? I guess I'm asking if momentum plays catch up at all with change of direction.

I ask because the feeling when skiing is that there is a lag effect. Could just be an illusion created by focusing on the front of the ski leading the direction change, which would give a false sense of the actual current direction of travel.
There is no lag effect if the (centripetal) force is instantaneously removed. In the real world so there might be a transition period as the force is reduced rapidly, but not instantaneously, to 0. I suspect that the "lag effect" you refer to in skiing may be a human perceptual effect. If a skier has adequate centripetal force (snow pushing on ski) one moment and none the next the expectation of the force being there may perhaps delay the accurate perception of the new reality. This is only a working hypothesis, however, as I have no specific knowledge of any such perceptual lag. Hope that answers your question.
post #24 of 53
Thanks Si, it does answer my question. I think your perception hypothesis has merit, it would make sense. Your mind is skiing in the future so the mind is anticipating a directional orientation ahead of the reality.

Also what could happen in a progressive unloading situation is that as the centripetal force (muscular/skeletal resistance) is progressively released, momentum can start taking over and doing its thing to the body (tossing it over the skis) while the skis still have enough pressure on them to keep them in reverse camber and arcing. In essence the CM and the still arcing skis begin to part ways. Would that make sense Si?

As to the instantaneous release situation I'm envisioning the famous Herman fall in the Olympic DH where he went airborne for about a half a mile, spun around mid air, hit and bounce multiple times over multiple pop fences, got up and dusted himself off. His losing contact with the snow created a situation of instant release of centripetal force. There was no lag in his flight pattern that I could see.

Thanks again Si. This stuff is fun. Hmmmm,,,, I wonder what that says about me? :
post #25 of 53
I just thought of an example that might be good for some.

As you were (are still) a kid on a swing. When at the maximum height, forward or back, did you ever "fall into the center"? We used to call that "bumping". At any rate, it is an example of what happens when the forward inertia is lost. The "pull" to the outside is lost, the chain goes slack. you can "fall" to the inside. (No centripital forces are required on an object without momentum). Then, when your trajectory again reaches the limits of the chain. BUMP!

Well, it makes sense to me.

CalG
post #26 of 53
The swing: The faster you go the more force needed to make you follow the chain's radius. At the bottom you are going fastest and feel the most force against the seat. All of the gravity (pulling straight down) must also be overcome by the centripetal force of the chains at this point. Near the top, if you are swinging past the point of attachment of the chains to the swing's frame, as your velocity reaches 0, less centripetal force is needed, and as the attachment pointis below the swing's position, a component of gravity pulls concides with the radial direction so the chain has to pull less. At the top, once stopped no pull is required to keep you on your circular path, but gravity is still pulling you down it pulls you straight down in a chord to the original circular path and slakens the chain until you bump back to the circle.

Fall Zone. From the point of view of an outside observer with an origin on the ski hill the direction the ball travels is tangential to the curve. From the point of view of an observer moving along with his origin and axis system continuing to move in the circular path the ball would have traveled were it not released, the ball moves straight sideways. (edit: in this point of view, the ball is not moving until the string is cut; it is at position (0,0); the force on the string is balanced by centrifugal force)

It's all relative. The skier loosing it in a left turn moves in a straight line tangential to the curve he lost it on (no net force = no acceleration), and moves straight right from where he would be had he not lost it (centrifugal force = acceleration to the right).
post #27 of 53
Quote:
Originally Posted by Rick
Also what could happen in a progressive unloading situation is that as the centripetal force (muscular/skeletal resistance) is progressively released, momentum can start taking over and doing its thing to the body (tossing it over the skis) while the skis still have enough pressure on them to keep them in reverse camber and arcing. In essence the CM and the still arcing skis begin to part ways. Would that make sense Si?
Rick, I don't think is quite right. Remember that the centripetal force is applied by the snow onto the skis. It is trasmitted to the rest of the body (which can be modeled by the CM) through the force transmission or musculoskeletal "stacking" that a skier employs. The amount of pressure on the skis (centripetal force) is the same amount of centripetal force that is available to the body. If the body get's tossed over the skis it is because the centripetal force has not been transmitted properly from the skis due to a lack of appropriate force transmission through the body ("stacking").

Again I would hypothesize that the situation you describe may occur as a consequence of perception. As a skier feels a reducing pressure on the skis they may over compensate and reduce their "stacking" thus allowing the body's momentum to carry it forward beyond the skis. Also, as the ability to propery transmit forces from the skis upward is directly related to a skiers posture (fore/aft, angulation, inclination, etc.), there may be times when it becomes impossible for the skier to adequately transmit the centripetal forces exerted on the skis. In such a case the skier falls!
post #28 of 53
I think Si si right. The wave of releasing pressure moves up the legs at the speed of sound (in the medium), so the head is still circling due to release not having reached it for a (very small) fraction of a second.

Wether or not we can perceive that time is another question. Perception of time is very subjective. Some of us have had the flow of time change (without the aid of drugs); we've had time to think volumes in fractions of a second and moved in slow motion during high stress moments.

Have you ever looked at a digital watch and though it was stopped for a fraction of a second? It only seems to do that when you first look at it. It really is ticking away at a steady rate.
post #29 of 53
As I’m not a racer I’ve not experienced many unintentional high-speed turn failures. Still, I’ve had a number of turn failures doing medium radius turns in bump fields (an L3 task in the PNW). This occurs when a bump launches me higher than my inseam can accommodate for continued ski/snow contact.

I figure Rick’s description of ‘lag effect’ is real since the ‘lag’ is probably the time between actual edge release and ‘central perception’ that it has occurred. When my own edges suddenly release mid-turn I notice an upper-body delay even though my skies start going straight immediately. Because my body is loaded up and somewhat flexed overall there is a momentary period where I 'extend' with the skis that are abandoning me.

I don’t fully appreciate the level of calamity until I’ve no more leg/body extension to go with the skis as they go into the trees.

Somewhat like when hiking over thin spring snow - As the snow gives way and my feet plummet into a void, I extend rapidly for a moment with great confidence my feet will find support. It’s only when my upper body goes completely weightless that a committee of spatially aware neurons agree there’s a problem.

In a lost ski turn, there is a certain distance (forward) I need to travel before my legs reach their maximum extension and detect with certainty that there’s nothing there to support me any more. Crashing is still not inevitable - in fact, the crash detection system has just been triggered. Phase two is the cat-like-contortions one makes to reorient the feet to … somewhere good - prior to their next encounter with a supportive surface (be it snow, tree, snowboarder, etc).

All that said, I suspect the skis experience instantaneous direction change - it’s just that the amount of change we are able to detect requires a certain distance of forward travel to become apparent.

If my head and shoulders are still ‘circling’, it is because I’m accelerating my skis, boots and legs (a sizeable mass) into the direction of lost support, thus faking out the comittee for a brief perod of time. If this were not done (due to fully extended posture at moment of abandonment) there would be immediate full body commitment into the (instantaneous) turn tangent for everthing from ski to woolly ski cap.

.ma

PS: Figuring ski-things out is always fun for me and give me great ideas for experiments next season.
post #30 of 53
Michael,
I think you've got it. Your upper body is pushing your feet and lower legs further accelerating them out of the turn; the reaction force is pushing back on your upper body, continuing to provide the centripetal force to accelerate it in the curve.
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EpicSki › The Barking Bear Forums › Ski Training and Pro Forums › Ski Instruction & Coaching › Some comments on centrifugal and centripetal forces