 Poster: A snowHead
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GrahamN, Cheeky 
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Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
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GrahamN,
Quite right about the equation! I changed it.... I did actually use the right one in the little sums that I did!
Mike Lawrie and Rob,
The force is the centripetal force. You are right that gravity will tend so slow you once you reach the bottom of the circle (180 deg point). However, whether the overall effect is slower depends on the centripetal force. The centripetal force is mv^2/r (as I and others have eluded to previously). The component of gravity down the slope is gravity x sin (slope inclination). So if the centripetal force happens to be greater than the gravitational component, you will be able to accelerate up the hill, even though gravity is acting against you. This was the basis of the last post I made, assuming the system simple, on a 30degree slope and on a circular radius of 20m, one would need to be travelling at in excess of about 35kph at the bottom of the circle, in order to accelerate back up the hill. I know it sounds complex, but what you need to accept is that while gravity is constant (roughly!), the centripetal force varies with both speed and circular radius.
I am not even going to start into the loading and friction discussion.... while all previous is day to day stuff, going beyond it would need me to think!
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Well, the person's real but it's just a made up name, see?
Well, the person's real but it's just a made up name, see?
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| buns wrote: |
| So if the centripetal force happens to be greater than the gravitational component, you will be able to accelerate up the hill, even though gravity is acting against you! |
Accelerate in the sense of your velocity vector changing direction rather than magnitude (speed). The speed only comes from gravity and obviously bleeds away as you begin to turn uphill.
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buns, you can only accelerate up the hill if you are adding another force to the equation. ie releasing stored energy in the ski/board or (arguably) changing the radius of the turn. once this force/energy is exhausted you're coasting and decelerating. You're looking at a very brief interval (1 sec?) of accel.
Of course you could just have got your pole stuck in a passing snowmobile pilot 
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Anyway, snowHeads is much more fun if you do.
Anyway, snowHeads is much more fun if you do.
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Masque, you've just illustrated my point, I think. Physicists like buns have a different definition of 'accelerate' than lay people. Thus, to a physicist, an object moving in a circle at a constant speed is accelerating - towards the centre of the circle.
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| buns wrote: |
Mike Lawrie and Rob,
The force is the centripetal force. |
As I understand centripetal force, it acts on the skier by the snow "pushing against" the skis towards the centre of the arc that the skier is following. This force is exactly equal and opposite to the force that the ski exerts against the snow (ie Newton's Third Law). Therefore, there is no net force on the skier, so accelerating (in the sense of gaining speed) up the hill is impossible? Any acceleration must be due to an external force such as gravity or the rebound effect of skis (although I find it difficult to believe that this is large enough to overcome gravity pulling the skier down the slope.
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| laundryman wrote: |
| Masque, you've just illustrated my point, I think. Physicists like buns have a different definition of 'accelerate' than lay people. Thus, to a physicist, an object moving in a circle at a constant speed is accelerating - towards the centre of the circle. |
Exactly, though i hasten to point out that the physics definition is correct!
It is very hard to argue this point further, I cant really get any more basic. I just need to think of an example else you all wont believe me! You probably wont accept that if zero overall force exists, a circular path isnt possible... so that would mean that if the acceleration due to centripetal was countered to zero, it actuall wouldnt be possible to carve at all....
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buns, I think from the above postings most of us have at sufficient O ( or was it A ) level physics to understand that dv/dt is not the same thing as ds/dt, or for that matter as d(theta)/dt! I also think that we are agreed that ds/dt (or d(theta)/dt ) ceases to increase at the 180° point?
Since Newton seems unable to explain why 70% of skiers get out of their depth, maybe Einstein can help?
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| Mike Lawrie wrote: |
buns,
Since Newton seems unable to explain why 70% of skiers get out of their depth, maybe Einstein can help? |
Maybe why sH end up talking about the same things time and time again?
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snowHeads are a friendly bunch.
snowHeads are a friendly bunch.
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And love to help out and answer questions and of course, read each other's snow reports.
And love to help out and answer questions and of course, read each other's snow reports.
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| buns wrote: |
| Exactly, though i hasten to point out that the physics definition is correct! |
Of course! 
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You know it makes sense.
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Otherwise you'll just go on seeing the one name:
Otherwise you'll just go on seeing the one name:
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saxabar, judging from what is being claimed in this thread it's not unreasonable to expect skiers to reach relativistic speeds on carving skis, especially when skiing uphill, so the question was not entirely frivolous
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Poster: A snowHead
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| Mike Lawrie wrote: |
buns I also think that we are agreed that ds/dt (or d(theta)/dt ) ceases to increase at the 180° point?
Since Newton seems unable to explain why 70% of skiers get out of their depth, maybe Einstein can help? |
Actually no. I believe that it is possible for ds/dt (s being speed not displacement of course) to increase even when a skier has an uphill component. I refer back to previous discussion comparing centripetal and gravitational accelerations.
To those who argue that the centripetal is balanced out by another force (centrifugal presumably), consider this: What is the difference between a body at constant velocity in a straight line and a body at the same speed on a circular path? Answer, the circular is experiencing a force perpendicular to its tangential motion. If that force were balanced out, there would be no net force, so what would be forcing the body into circular motion?
Also, if what I said is wrong, this would mean that not only would a carve be unable to give scalar acceleration up the hill, but it also would mean that a carve would not accelerate your down the hill (the two are complimentary). This would mean that the very maximum speed achievable would be directly down the slope. Thus if you carve, you can never better this speed, but you will travel further. Hence a carve would ALWAYS result in it taking LONGER to get down a hill.
Adam
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Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
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buns, as far as I'm informed the principle of conservation of energy applies. That is: nothing in - nothing out. If the overall speed of the system is to increase while going uphill then something must be adding energy to the system. Where is that energy coming from?
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This would mean that the very maximum speed achievable would be directly down the slope. Thus if you carve, you can never better this speed, but you will travel further. Hence a carve would ALWAYS result in it taking LONGER to get down a hill.
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I think that pretty much sums it up! The fastes way down the hill is...wait for it... straight down the hill.
If this goes on much longer then I'm going to open another bottle of wine.
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Well, the person's real but it's just a made up name, see?
Well, the person's real but it's just a made up name, see?
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buns, you're getting yourself confused here - you need to consider the vector sum of your gravitational and centripetal components, as they are generally acting in different directions.
Quick summary (of the world according to GrahamN anyway)
1) ds/dt (tangential) cannot increase if the motion has an uphill component (unless we get into the loading/slingshot/skating/jumping arguments).
2) centripetal force acts perpendicular to the tangential direction and so has NO effect on tangential speed - but provides the radial acceleration (F = ma), used to change the body's direction.
3) reducing the radius of the turn does NOT change the tangential speed (conservation of energy), but gets you round the corner sooner (increasing angular velocity with reduction in moment of inertia - conservation of angular momentum)
4) Maximum tangential acceleration is when pointing down the fall line, and is g x sin(angle of slope) (less any resistance due to snow/air friction - these exactly balance the gravitational acceleration if the skier is travelling "maxed out")
5) Maximum speed if travelling in a curved path (again ignoring friction) is the point in the curve furthest down the hill (maximum conversion of potential to kinetic energy) - if in a circular carved path this will be when travelling perpendicular to the fall line. (In the presence of friction you will be slowing down as you travel, so max speed will be somewhere between the fall line and the perpendicular to it)
6) Maximum force in your legs (not that it's actually of any real significance in this argument) will actually be at the bottom of a circular curve, as a) you are going fastest so the force required to provided the centripetal acceleration is greatest and b) you also have to overcome gravity attempting to pull you downhill.
7) I do think is would be possible to get an additional net overall velocity component in the desired direction by a series of short carved turns with repeated jump/skate type bodily movements down the slope, as in the discussion I had with Masque on slaloming the tail of his board (or stern sculling a boat). Here the skier/rider is putting extra energy into the system, over and above the loss of potential energy by virtual of altitude change) by repeatedly working to change the distance between his body and the the ski/board (energy = integral of force over distance through which it is exerted).
Note that when you are accelerating under gravity at the max you feel the least force in your legs - as the weight you feel is the residual force opposing your natural acceleration due to gravity required to stop you piling into the ground (the extreme case of this is caternary flights used for weightlessness simulations in astronaut training - or jumping off a cliff, although in the latter case payback time is generally a bit sooner).
I have to say I think the term "180° point" is confusing - 180° from what? I'm also finding it more and more difficult to buy SimonN's example of the carving skier getting to the bottom of the slope at the same time as the straightliner (unless he's doing what I mentioned in the last summary point). It's certainly the case that if this is true the carver could beat the straightliner by stopping turning some way up the slope, pointing straight down and using their extra kinetic energy (speed) to overtake the straightliner (as in the waterskier/boat case). But Simon's stated that the straightliner can't be beaten, only equalled - so he's in a logical contradiction there!
(do we qualify for Epic obsessives points yet  )
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I am not breaking conservation, the energy will remain constant. I am not saying that it is possible to do a complete circle and end up faster than you started.
I ask again, how does a body do circular motion without a force applied to it. If you tell me how, i will accept I am wrong and you should write a paper telling the scientific community how very wrong they have been!
The fastest way down the hill isnt the best example actually....
Have a look at http://www.mcasco.com/p1cmot.html
Look at the 3rd diagram, it illustrates the inherent acceleration in circular motion.... the world as we know it just doesnt work without this concept
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Anyway, snowHeads is much more fun if you do.
Anyway, snowHeads is much more fun if you do.
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buns, I don't think either I or Mike are disagreeing with your circular motion descriptions, just the conclusion you draw at the end of it when you try combining it with gravity (the point I think you make your error). In that link of yours the closest analogy is the pendulum - and as you know (from your A-level mechanics) the point at which the pendulum bob is moving fastest is at the bottom of its swing, and it's slowing down from the moment it starts rising.
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I am considering vectors Graham. At the bottom of the carve, the centripetal acts directly up the slope, so it is thus in direct opposition to the gravity component down the slope (g x sin (slope angle)).
I think im going to give up, this is probably a question of definition now..... there are just far too darned many ideas on the table and we are missing the most vital part of any physics problem..... a diagram!
Have a good night guys and irrelevant of what has gone on, please accept the acceleration inherent within a circular path! 
Adam
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OK buns, what you actually seem to be calculating is the force perpendicular to the ski during the turn, and so the force that the snow is required to exert on the ski to avoid sideslipping. In your example above (35.656kph , 20m radius, 30degree slope) you will have 1G along the slope if that condition applies when you are turning up the slope (F = mv^2/r + mgsin(inclination)). If you are turning down the slope, i.e. currently turning across the hill from initially travelling uphill the force towards the centre of the turn is F = mv^2/r - mgsin(inclination), so you will actually have zero G sideways, so this actually describes the radius of turn you would make if on perfectly slick ice and had zero sideways grip at all. The basic point you are getting confused about here is that the mv^2/r term is centripetal (which I accept you're clear about), i.e. radial - and so has no effect on tangential speed (which I don't think you are clear about). And I repeat - neither Mike nor I are suggesting any "balancing force" to the centripetal force, and we agree that it's that that provides the radial acceleration - it's just that that is provided by pressure of snow against ski, rather than anything to do with gravitational force (except in that slick ice example above), which may just add to or subtract from the amount of force the snow is required to provide. (The full equation for radial force required to keep the ski moving in its arc is F = mv^2/r + m.g.sin(slope inclination).sin(angle of ski from fallline))
The actual equation for the accelerating force on the ski in its direction of travel (in the absence of friction/elasticity effects) is F = m.g.sin(slope inclination).cos(angle of ski to fallline). At the bottom of the turn the cos term is zero and there is no accelerating effect on the ski IN ITS DIRECTION OF TRAVEL - irrespective of turn radius. As the ski turns up the fall-line the cos term goes negative and the ski starts slowing down.
(NB my angles are 90degrees less than Mike's: 0 is pointing directly down slope, 90degrees is pointing across slope at bottom of arc, turning up it)
Is there anything in that summary post with which you disagree?
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It's Ok graham, i have worked out where the contradiction is coming from..... Im still working on Simon's assertions earlier, so have been working on an acceleration up the hill. So I apologise, I did not mean that the overal speed can increase while travelling up the hill. I have been speaking of the velocity component up the hill.... this probably clarifies alot since everyone can relate to it. At the bottom of a carve you have no velocity component up the hill. You can prove to yourself (by trying it), that you can then carve to a point higher on the hill than this bottom position. So if follows that you must have experienced a net acceleration up the hill.
All agreed?
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You'll get to see more forums and be part of the best ski club on the net.
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buns, yup.
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| buns wrote: |
| ... I did not mean that the overal speed can increase while travelling up the hill. I have been speaking of the velocity component up the hill.... |
Which is pretty well what I said a while back:
| Quote: |
| Accelerate in the sense of your velocity vector changing direction rather than magnitude (speed). The speed only comes from gravity and obviously bleeds away as you begin to turn uphill. |
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snowHeads are a friendly bunch.
snowHeads are a friendly bunch.
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3 AM! ... 
As far as I can see, all the calculations above rely on a fixed mass of the object (skis & skier). This is patently untrue in practice, it is a dynamic variable and when a skier sinks into the turn he is absorbing energy in the direction of travel before the turn (gravity if you like), to return to the water-skier allegory, when he pushes to complete the turn he's applying force at a tangent to the direction of travel so even if you're still carving the turn, you will accelerate. It's all to do with the skiers ability to conserve energy increasing potential mass and releasing it into the correct place on the ski and at the right time in the turn. Without that there's no acceleration.
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And love to help out and answer questions and of course, read each other's snow reports.
And love to help out and answer questions and of course, read each other's snow reports.
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| Masque wrote: |
| As far as I can see, all the calculations above rely on a fixed mass of the object (skis & skier). |
Correct
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| This is patently untrue in practice |
..and that is a patenetly untrue statement (unless you take such a hairy turn you cr@p yourself half way through.
Those calculations were attempting to sort out the knots buns was tying himself in.
It's possible to put additional work into the system, to provide some additional acceleration, and an increased final velocity as we've both agreed above. I'm not at all convinced you can get acceleration by this mechanism along the length of the ski at any given point in the turn though - just across it, in a direction the ski eventually turns into. I think your waterskiing example here though is very wide of the mark.
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| Without that there's no acceleration. |
Agreed.
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| GrahamN wrote: |
| I'm not at all convinced you can get acceleration by this mechanism along the length of the ski at any given point in the turn though - just across it, in a direction the ski eventually turns into. |
I suspect you can, once you take into account what we blissfully ignore - friction. The action of putting the skis on their edges reduces friction, like a hot knife through butter!
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You know it makes sense.
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laundryman, don't believe that. Friction is always a decelerant (unless the thing you are sliding over is initially moving faster than you are - not the case here), but reducing friction will reduce the amount of deceleration, so you will then more freely experience any acceleration due to gravity (or whatever), so you will come out faster than you otherwise would have done.
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Otherwise you'll just go on seeing the one name:
Otherwise you'll just go on seeing the one name:
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Poster: A snowHead
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GrahamN, that's exactly what I meant - we're in complete agreement!
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Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
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| Quote: |
the centripetal is balanced out by another force (centrifugal presumably),
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Centrifugal effect but no centrifugal force, being pedantic
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Well, the person's real but it's just a made up name, see?
Well, the person's real but it's just a made up name, see?
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You need to Login to know who's really who.
You need to Login to know who's really who.
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Mike Lawrie, from early on this thread:
"The only criterion that you really should apply is: If I do this run, and I take a tumble, am I going to hurt myself or kill myself. "
NO - it should be am I going to hurt or kill anyone else
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Anyway, snowHeads is much more fun if you do.
Anyway, snowHeads is much more fun if you do.
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slikedges, If you take that model we wouldn't be able to walk let alone jump. Why does everyone assume that the skier is an inert mass bolted to a solid object?
OK I'll make it easy . . . why does a park swing work? ... we are engines that can control inertial masses to add to the equation and if you add energy to a static model in the right place it WILL accelerate beyond the restriction of drag.
It's the skiers ability that must determine both drag/friction and energy input dynamic.
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There is no such thing as centrifugal force! GRRRRRR 
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Masque, there would be no problem hopping, skipping or jumping, because what happens in a water-ski or drag lift model cannot be usefully related to those activities. I didn't say that there is no way of accelerating a ski using dynamic movement and the elasticity of the ski. In fact anyone who is carving turns is likely to be doing it, as the ski must rebound some time, and if standing properly on your skis, at least some of that energy must be propelling you in a downhill direction. Of course, this acceleration will never make up (in the downhill direction) for being out of the fall-line in the first place.
Here's something I posted a while back. A skier's timely dynamic contribution will help take best advantage of the ski's charateristics.
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You'll get to see more forums and be part of the best ski club on the net.
You'll get to see more forums and be part of the best ski club on the net.
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slikedges, I don't think that any of us have a real conflict in this, it's probably more an issue of 'what's the problem we're arguing about?' Obviously any body in a stable linear track down the fall line is just that ... stable, there's little that the pilot can do other than add or absorb energy in one vertical dimension ... like a swing or a skate-park half-pipe and that's what ski jumpers use to gain extra distance. Their acceleration is gained in that brief period of their leg extension before they leave the jump surface. To early and it's wasted, too late and they're pushing against air.
In our case it seems that the physicists amongst us are making the analogy that we're all just dead weights on the end of a virtual string.
If a ski (or board for that matter) is set into a track by a controlled carve, then additional energy can be added by using the latent energy in the body's musculature and in excess of what already exists in the mass, vector, gravity, friction equation. It's my postulation that maximum acceleration is achieved while the skier is moving relatively slowly and at a shallow angle to the fall line where human reactions are able to influence ballistics.
All this ignores the energy storage potential in a ski or board ... and that manifestly effects the timeline...
duck and cover
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easiski,
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Mike Lawrie, from early on this thread:
"The only criterion that you really should apply is: If I do this run, and I take a tumble, am I going to hurt myself or kill myself. "
NO - it should be am I going to hurt or kill anyone else
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My God, yes, I remember, that's what the thread was about...
But in answer to your answer, and just to do something I have not done for a while, I disagree
The thread is not about whether you get 70% of other skiers out of their depth ( which may well be the case, but not the one that's being argued here), but whether you get yourself out of your depth. I contend that on normal pistes with decent grippy snow you are unlikely to up in a situation where you are likely to hurt yourself and hence end up in serious trouble, so you should always push the envelope a bit 
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FAQ
. Except about the water-skier 