 Poster: A snowHead
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You can't accelerate uphill, no matter what method you use to steer your skis. The force you feel of the snow pushing against your skis as you carve across the fall line and up the hill, is equal (and opposite) to the force you use to push against the snow when steering your skis. There is no net force acting on you (if you disregard friction and gravity), therefore it is impossible to accelerate up the hill. The only force that can accelerate you is gravity, and that always pulls you down the hill. As DM said, it's just Newtonian physics at work, and his laws have proven to be fairly robust.
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Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
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| David Murdoch wrote: |
SimonN, gravity is a constant. It can't increase the g-force anywhere (gravitational waves notwithstanding).
"once you are at max speed in the fall line and are no longer accelerating, a correctly carved turn increases your speed".
I am afraid, no, not if what you mean is you can go faster.
If you are at max speed in the fall line and can't change your wax mid schuss, flatten your skis, attach a rocket pack, that is as fast as you are going to go. You will be at "terminal velocity". Turning can ONLY slow you down, although you might find that you accelerate in a sideways direction...
I am afraid those are just the sad realities of Newtonian physics. |
I haven't said that gravity increases g-force. I said g-forces are increased. However, isn't g- force a function of acceleration/deceleration and gravity? I am not a scientist so I cannot enter into a "Newtonian" discussion.
All I know for sure is that I have done the excersise I mentioned above and I will now repeat. We all set off down the fall line and one stays in the fall line while the others start carving. If you carve well enough, you can keep up with the person in the fall line. Now, assuming that the person in the fall line is staying at max volicity, that has to mean that the others are going faster than him/her, although the VMG is the same. I am told that you cannot exceed the VMG of somebody in the fall line, only equal it.
I know that this happens. So, at some point the carvers must accelerate. Please can somebody explain, in scientific terms, how and when this happens?
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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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| obelix67 wrote: |
| AxsMan, the leading you onto the wrong colour is how my mate got me onto a black run at my first day at verbier at new year. |
I hope you rewarded your mate with a suitable level of abuse when you got down to the bottom! I wasn't suggesting that it was a good thing to take anyone down a run that was well beyond their abilities, I guess that's part of being a good instructor - recognising what your pupil is really capable of and giving them the confidence and skills to extend their limits. Wheras scaring the cr@p out of your mates on a black run day one is just 'being a mate' 
GrahamN, (et al) firstly - great debate, fascinating and informative!
I have to admit admit that the whole physics of this speeding up by carving thing is way beyond my dimly remembered 'O' level standard. All I know for sure is that my main concern on a piste with any noticeable gradient is to shed speed through sliding turns and try very hard not to nose plant. Carving (for me) is purely for those big swoopy areas where I feel comfortable going faster than your average milk cart. I Still like the waterskiing analogy though, and from my turns driving the boat, I don't recall having to compensate for the pull from the skier, but it was a big boat with an inboard engine, and maybe there was just too much momentum and torque in the system to notice.
I also think that Kramer raised a good point - isn't gravity strictly acting on your body directly towards the ground, and the angle your ski makes with the slope of the hill tranlates this into forward (downhill) motion. in which case varying the angle, and decreasing the friction (by carving over on one edge) will affect your acceleration along the piste? (or is that another dumb question). 
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BTW, this still doesn't explain how a water skier can catch up the towing boat that mainatins a constant speed.
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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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SimonN, Good point, well made 
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You'll need to Register first of course.
You'll need to Register first of course.
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| SimonN wrote: |
| I know that this happens. So, at some point the carvers must accelerate. Please can somebody explain, in scientific terms, how and when this happens? |
A ski which is riding on its edges will have a lower frictional coefficient that a ski riding on the full width of its base (especially if it is badly/not waxed).
Having said that it might be theoretically possible for that reason, I don't think it does happen in reality. I did some race training last autumn and without doubt the fastest way down the piste was in a straight line. Even though I was trying to carve as well as possibly, with no skidded turns, there was no way that I could keep up with somebody who was just straight-lining it down the course.
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| SimonN wrote: |
| BTW, this still doesn't explain how a water skier can catch up the towing boat that mainatins a constant speed. |
But does ity explain that it's not possible to accelerate uphill?
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This thread seems to have got too technical for me so I thought that I would share with you my "instant" thought when I saw the thread title:
I only go out of my depth when I wear blades in really soft Powder.
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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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Nick L, or let go of the rope when waterskiing!
SimonN, the way that happens is as follows: the boat maintains a constant velocity down the course, the skier cuts across its path say at angle A away from the boat, so to maintain the boat's speed S in the down the course direction they have to be going through the water at S/cosA, so if travelling at 60 degrees to the boat they will be going along their path twice as fast as the boat is along its path. The skier then carves a turn to run parallel to the boat; this means the skier pushes against the water solely to change direction, does not gain speed during that turn (and will actually lose some through friction against the water), but that speed is carried through the turn as kinetic energy and the fact that the skier was travelling faster than the boat in the cut means they can now overtake the boat as they are going in the same direction (until they hit the jump and find someone has forgotten to turn on the water ). I maintain that the fundamental difference between the water and snow skier is that the waterskier can increase the tension in the rope at will as he increases the cut angle (within reason of course), whereas gravity can only exert a constant force.
AxsMan, your experience is almost certainly greater than mine (I'm only a beginner in the melted stuff), but when getting a few tows last summer I was told to not cut so hard as I was slowing the boat down!
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Centripetal force (what you experience due to circular motion) acts to the centre of the circle. If you start a carve when you are directly across the slope, the centripetal force acts down the slope. As you turn, it continues to act to the centre of your carve thus its component down the slope decreases. When you are directly pointing down the slope, the centripetal force has ZERO component down the hill. As you continue the carve, the component of centripetal force begins to act UP the hill and maximises as you return to a cross slope stance. If you integrate the centripetal force over this manoever, the result is zero.
This simply cannot be argued. If you do argue it, you are not grasping the simple physics behind it! Any departure from what I state above is due to an external perturbation.
It is true that your speed can be increased with a turn, but it is simply IMPOSSIBLE to use a turn to increase the downhill component. Any suggestion otherwise is in direct the laws of physics. And before you start saying that classical phyics has been shown not strictly correct, it is more than good enough for macroscopic calculations of this sort!
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snowHeads are a friendly bunch.
snowHeads are a friendly bunch.
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Without analysis of the water situation..... the rope is not rigid and the situation we are talking about is not a complete carve. I said that the total integrated force is zero when you complete a 'half' carve (effectively rotate by 180 degrees). With this waterski analogy, you only go through 90 degrees, so the net result of the centripetal force would no longer be zero, so the skier being able to out pace the boat is an acceptable observation.
Maybe it is worth pointing out that a snow skier carving can travel faster down the hill than a straight liner ON A LOCAL BASIS, but if you start to consider more than the 90 degree turn, this ceases to be true. I think this might almost work as an analogue for phase velocity compared to wave velocity....
GrahamN: you know your stuff, is it just a good memory or do you work in a related field?
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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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SimonN, regarding:
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| What I have stated is that, if due to a force acting through the skis you are accelerating, there is a period of time when the graviational forces of going up hill are not great enough to counteract that acceleration and therefore for a period, however, brief, you will accelerate up hill. |
I think you are confusing acceleration with velocity or something? Acceleration doesn't just happen - there needs to be a force causing it. In skiing, there are just three significant forces: 1) Gravity, which is what gives you all of your speed (when combined with normal force, which I will cover after) 2) Friction. When you turn, you are using friction to change directions. Friction is always acting opposite to the direction of motion, and is therefore always slowing you down. Air resistance is another type of friction, which is also going to always be opposite to the direction of motion. It is true that you can excellerate during normal carving, but this is only because the friction is less than the gravity. 3) Normal force, which is the force that reacts to gravity, and accelerates you in the direction perpendicular to the slope. Normal force + gravity give you your overall downhill acceleration.
Now, when you carve uphill: 1) Gravity works in the direction opposite to your motion, and thus slows you down 2) Friction (both air resistance and ski/snow friction) works in the direction opposite to your motion, and thus slows you down 3) Normal force works in the direction opposite to your motion, and thus slows you down.
Everything is accelerating you downhill - there is no force (save a rocketpack or something) that is acting to accelerate you uphill, and thus when carving uphill there is no way that you will be accelerating (in the sense of gaining speed), even for a moment.
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SimonN, it's quite simple a water skier can use the force created by pushing against the forward motion caused by the towing boat to generate speed, that doesn't happen when skiing, terminal velocity is finite exactly as it is when water skiing.
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You know it makes sense.
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OK. So how does Newtonian physics explain the fact that 70% of skiers go out of their depth?
As I found out on a foggy piste in Austria recently Newton got it mostly right. At least my orthopod doctor thinks so 
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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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Fine reply, Mike 
So, now I have had a bit of time to think, lets have a look at Newton to see what he says. He stated that F=ma So, from that we learn that the acceration is a function of mass and the force applied to it. Now, when going down the fall line, the mass is your body weight and the force is gravity. Now, unless I am mistaken, a change in direction along a new trejectory results in an increase in g-force. If a 10 stone person is experiences 2 g's, their body weight would read 20 stone on a set of scales. In our case, it would be through the ski. So the mass, as experienced by the ski, has increased. Therefore you get acceleration. This means you can ski faster if you change direction from the fall line.
I think (or is it just hope) that ponder agrees that, so long as you remain in a substantially downhill direction, you can accelerate in a turn. The question then becomes whether you can accelerate going up hill. Now, I agree that substatially you cannot, but that is not what I argued. I suggest that if you can accelerate in a turn, if you could keep the forces going until your skiing was (very) slightly up hill. Now, so long as the accelerating force remained stronger than the gravitational force, then (theoretically) its possible. At some point there is a cross over between acceleration, max speed and slowing down. I remain to be unconvinced that cross over point is where you start to go up hill (rather like my arguement!).
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Poster: A snowHead
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I've been following this thread with some bemusement, as theories offered seem to have been disagreeing with my basic teaching (as offered many years ago). Could someone please explain how it is possible to accelerate uphill (against the force of gravity) without external forces? Basic teaching (as per quite a few years ago) tells me that anyone who says this is possible is talking complete codswallop.
Puzzled,
Alastair
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Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
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SimonN,
You can accelerate, yes meaning you can get faster. However, your speed down the hill (resloved to being a pure downhill component) cannot be greater than a straight down the hill line (unless you invoke an external force). So assuming only gravity and circular (carving) motions, the most rapid way down a hill is directly down it.
To the latter point, that is complex because it depends on the slope, the radius of carve and the velocity. The sums would be that
g x sin (angle of slope inclination) = v^2/r
Just as an idea, assume the slope 30 degrees, the radius 20m and gravity 10m/s^2. This would require a speed of about 35kmph to balance gravity at the centripetal force maxiumum (i.e. when going straight across the slope). When you actually start to point up the slope, the speed required will increase accordingly. It would follow that, on a true carve, there will be a minumum speed at which you must first enter the carve, else you will never meet the criteria outlined.
That may all sound reasonably acceptable, but there is a sticking point. Say you were on the flat, the gravitational component is now zero so in theory you need zero speed. So you will see that, as the inclination angle decreases, the sums start to fail. This is not because they are wrong, rather there are additional influences. Given the zero inclination situation, it indicates that these other influences make it even harder to attain a state where your centripetal force (due to the carve) can be greater than the opposing gravitational component.
So theoretically (!!!! friction is never wise to ignore!!!!!) it may be possible, up to a point, to gain speed while going up hill, but it will be totally impossible to continue to do so anywhere near as would be necessary to complete a loop. There are also factors I do not know to include.... like the carve radius as a function of speed. For all I know, a factor such as this may totally negate the possibility.
Alastair,
Circular motion could be defined by the fact that a body following such a path, will experience a force to the centre of the trajectory. At the bottom of the trajectory, the force will be directly upwards. At any point in the lower hemisphere, there will be a component of that force acting upwards. If this force were in excess of the gravitational component, there could be an increase of speed against gravity. You should of course note that the longer you work against gravity, the less the centripetal component and the less chance that you can actually gain speed against gravity. Apologies if this is overly complex, I rarely have to explain to anyone less than undergrad physicists!
Adam
Last edited by Obviously A snowHead isn't a real person on Sat 28-01-06 18:25; edited 1 time in total
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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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I'm out. Brain hurts too much, have to concentrate on helping people at the out of hours centre. 
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You need to Login to know who's really who.
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| Kramer wrote: |
| I'm out. Brain hurts too much, have to concentrate on helping people at the out of hours centre. |
Well im on holidays, I didnt expect to have to do physics for another week yet!
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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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OK. I think I follow which isn't bad for somebody who last did physics at school 30 years ago! I think we are agreeing on the following.
1. A turn can lead to an increase in speed.
2. Theoretically, you can gain speed while going up hill but that would be (very) short lived. I totally agree that there would never be a time you could complete a loop
Then it gets a little hazy. I would agree that the max VMG down a hill is achieved going straight down but I think that what has been said is that a higher speed can be achieved by accelerating using a turn. However, because of the extra distance skied it is not possible to achieve a higher max VMG down the slope than going straight down.
However, I am sure we can all agree on one thing and that is that it is a great deal more fun trying to carve a perfect turn and getting max VMG than talking about it theoretically 
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You'll need to Register first of course.
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buns, if we consider the case of a skier carving in circles on a flat piste on completely frictionless snow in a vacuum ( Ok, I don't want to be there ) then he will be experiencing constant acceleration by virtue of the fact that anyone moving in a circle is constantly changing their velocity since velocity is a vector and he is constanly changing direction... However he will not be changing his speed over the ground, or the rate at which he sweeps out the arc of the circle, and he will continue to go round and round for ever 
If we tip the surface on which the skier is standing then he will be experiencing additional acceleration due to gravity such that starting at the highest point of the circle he will start to increase his speed (i.e the rate at which he sweeps out the arc). The maximum accelerating force will apply at the point where the component of g force along the slope is greatest, i.e at the 90° point ( big surprise, that's when he's pointing straight down the hill ), at the 180° point the force along the slope will be at right angles to his direction of motion and will no longer cause an increase in speed, so the point of maximum speed is at the bottom of the slope. The instant he crosses over the 180° point the force due to gravity wil decelerate him again, max deceleration is at 270° and he will come to a standstill, or back to his original speed at 360°.
So how can he be increasing his speed when going up the slope
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| buns wrote: |
| So theoretically (!!!! friction is never wise to ignore!!!!!) it may be possible, up to a point, to gain speed while going up hill |
So what force is being applied to this skier to enable him to accelerate while going up hill?
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Have you built into your equations the effect of the gradual loading of the skis above and into the fall-line, and the pressure being released as you come out of the fall-line? This is how the racer keeps his speed and accelerates out of turns. Could the loading of the skis followed by the release of pressure as gravity and centrifugal forces balance out leaving the fall-line theoretically mean that the acceleration effect was maintained for an extremely short period of time even if the gradient is very slightly uphill? Obviously if the skis are still loaded as you exit the fall-line the deceleration effect would be marked, with increased force exerted by the snow, but if you've timed it right with the upward movement 'lifting' you sufficiently as you exit the fall-line, would this compensate for gravity/friction for a split second?
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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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Going back to the water skier overtaking the boat analogy
The arguments put forward ignore the single most important factor in the equation, the person on the skis.
If you ski across the back of the boat at constant speed and do a constant radius turn you willl maintain a constant speed and not catch up the boat. What the water skier does is the same as the ice skater does in a spin which is change the turn radius. As radius of turn reduces, speed increases (Newtonian physics again I'm afraid) so its quite possible to gain enough speed to overtake the boat for a short peroid.
Can you accelerate up hill on ski. While doing a constant radius turn - no, if you work the skis and reduce the turn radius - maybe but only while you're actively altering the radius which is preety short lived.
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rich, I'm glad someone got there in the end
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snowHeads are a friendly bunch.
snowHeads are a friendly bunch.
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rich, now that makes sense and definitely ties in with what I was trying to say about the effect of loading the skis during the turn.
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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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PG, if the loading and unloading of the skis during the turn were a totally passive affair then there would be no overall net gain, what you would gain coming out of one turn, you would lose going into the next, but generally with a good skier I think that it is more active, with the skier working the skis, and so putting extra energy into the system, which may come out as increased speed.
BTW to everyone else, AFAIK it is possible to do a 360 degree loop on a slope, it's just very difficult.
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Kramer, you can see the effect of increased speed with a race trained skier, they will alter their stance during a turn to generate acceleration. Slalom skiers use this technique a lot, they 'jet' their skis by getting over the tails as they exit the turn.
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You know it makes sense.
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The minimum energy put into the system produces the maximum speed. The maximum speed is achieved on the shortest possible line - the straight-line schuss down the fall-line. Any deviation from the fall-line reduces speed.
Not sure if that's relevant to your point, Kramer, so I'm sorry if that was a red run herring.
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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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David Goldsmith, As David points out when you use your mass to put energy into the tails of the skis, that energy can be released in a through a decreasing radius turn and give acceleration beyond that of the simple gravity/fall line/friction equation. Being able to do it consciously and in control is another matter.
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Poster: A snowHead
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David@traxvax, I use that technique sometimes. Not intentionally, but I do use it!
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Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
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I've been unsure for a while how useful it is to keep going with this ( ), although for the saddoes (like me) here it's still fun, but there are a few errors that need clearing up.
| Masque wrote: |
| rich, I'm glad someone got there in the end |
. I'm sorry but rich is wrong on almost all points of detail there.
1) In the water-skier's case it's not the radius of turn that governs their speed but their angle of travel relative to the boat. As an extreme case, give them an infinitely long rope, point them at 60 degrees from the direction of the boat's travel and they will travel at twice the boat's speed, with an infinite turn radius. The constraint on the motion is that the distance from the skier to the boat is constant (the rope length), so the equation I gave above (Fri 17:27) is actually only correct for when the distance of the skier to the boat along the boat's direction of travel is constant, a good approximation for when the skier is directly behind the boat (or has that infintely long rope). If the skier then makes a sudden carved turn to point in the same direction of the boat they will catch the boat up due to retaining their kinetic energy during the carved turn (in practice the radius of turn that would allow this to show up would be limited due to friction from the ater during the turn).
2) The tangential velocity (speed) of the peripheries of the ice skater in a spin does NOT increase as they pull in their arms; the angular velocity increases in direct proportion to the decrease in moment of inertia (so conserving angular momentum - simple Newtonian mechanics ) so it looks as if they are going faster (as they are spinning at a higher frequency). In the extreme case of all the skater's mass at their peripheries (a reasonable approximation to the carving snow-skier) the moment of inertia changes in direct proportion to the radius of the spin, so the peripheral speed (angular velocity * radius) is constant. In the less extreme case, with only some of the skater/skiers mass being moved to the centre of the spin, the increase of angular velocity is less and so the peripheries actually slow down. You will feel a higher force though as the angular velocity increases as the centripetal force is 0.5 m x r x w**2. This then causes the argument that you accelerate through a changing radius turn, purely by virtue of the change of radius, to fail.
The equation in buns' post (Sat 03:50) is I'm afraid also wrong. If you want to go down this route you should have a '+' rather than a 'x' after the sin term; as it stands it is dimensionally incorrect (it has units of acceleration squared). This then gets over the problem you have on a flat piste - but I think it's a little complicated to cover both effects in the same equation. (buns, I'm a chemist by training, have spent my working life as a physicist and softie developing Magnetic Resonance systems, but was always quite keen on mechanics in 6th form maths....and have a pretty reasonable memory)
Mike Lawrie got to the simplification I was going to do for next - a turn on a flat piste. As he says, you will maintain a constant speed through a pure carved turn of whatever radius in the absence of friction (snow or air) - on simple conservation of energy arguments. This is the fundamental point in this discussion - the forces you undoubtedly experience during that turn, and are associated solely with the turn itself, are perpendicular to the ski, which are purely there to change the direction of travel, and have no effect at all on speed. The only forces you get along the direction of the ski - which are the only forces that will make you go faster or slower - are frictional, which will only slow you down.
Loading and unloading the skis - this is where we get back to the skating issue, and the cruical point here is relative motion between the ski and the skier. I've said this a couple of times before, but it probably requires a bit more explanation. I see the main way this works is that you can reduce the distance between your centre of mass and the ski as you enter the turn, just by virtue of the effect of gravity acting on your body mass into the slope - this will have no effect on your speed. You can then use the fact that during the turn your skis are pointing in a different direction to your eventual direction of travel out of the turn to give an extra push against the ski, over and above that you would need just to make the carved turn, to give you some extra momentum in your eventual desired direction of travel. So for a short period of time your body is moving faster than your skis. As you come out of the turn you then use that momentum gain to pull your skis to catch up with the rest of your body (so actually slowing your body slightly) to equalise your body and ski velocities. (This is a long winded way of saying you are effectively jumping in the new direction of travel).
Once again it has nothing to do with the actual mechanics of the ski's carved turn per se, and nothing to do with any gravitational or centripetal forces applying during the turn. Skating is effectively a series of these movemements - i.e. you push against each ski pointing alternately at angles either side of the direction of travel of your centre of mass (or if going around a corner keep on pushing away alternately on skates angled in the same direction of travel).
"Jetting" off the tails? Probably the same thing as I've just described, but just a bit later, so using the last bit of the ski angled across the direction of travel (?). Storing energy in the tails? The only way the ski will store energy by bending, and the only way for it to release is to push angainst something (typically) as it unbends, so for that to be useful it has to be while the ski is angled across the eventual direction of travel, as the unbend can not push the ski forward in its track. So I think this just allows a greater time window for you to get in the compression/release action. (This final bit is all a bit tentative).
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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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GrahamN, Going back to barely remembered school physics, is a carved turn a constant radius or can it be tightened through user input? It can on a board so that as the radius decreases (assuming no increase in friction) then the relative speed of the skier/boarder over the ground will increase. As for stored energy in the bent ski, it has to go somewhere, either by releasing from the snow and snapping straight in a skid or as the skier ceases the turn the energy is released into the ski track in the snow and adds to the forward momentum. The harder the snow surface the less energy will be lost if the ski remains in the track.
This could be a perceptual anomaly where the user's senses are being fooled and only embedded accelerometers on the skis will give an empirical proof one way or another but I know I can load the tail of my board while torquing its shape to increase the carve and get a very real and positive sense of acceleration to the point where the board can leave the ground. That's something we see slalom skiers do every week on Ski Sunday.
Don't water-skiers accelerate because they are travelling further (across the direction of the tow) along what's essentially a hypotenuse but at the end the pull in the turn to the tow direction they are decelarating to match the tow speed.
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You need to Login to know who's really who.
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This thread will be available as a 24-volume boxed set shortly.
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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 wrote: |
| is a carved turn a constant radius or can it be tightened through user input? |
It can be tightened by user input.
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| as the radius decreases (assuming no increase in friction) then the relative speed of the skier/boarder over the ground will increase. |
I don't believe it does, although the force required to make the turn will increase as the radius decreases (inverse square law). To avoid any confusion, the force on the ski is also completely different from that you would get from gravitational attraction (also an inverse square law) as e.g. a planet orbiting a star, in which case tangential speed does change as it executes an elliptical or parabolic path around the star.
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| the energy is released into the ski track in the snow and adds to the forward momentum. |
Don't see the mechanism for this (in a straight track), other than that I described in my previous post, but if anyone knows better....
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| I know I can load the tail of my board while torquing its shape to increase the carve and get a very real and positive sense of acceleration to the point where the board can leave the ground. |
I believe that's due to linked movements of your centre of mass wrt the board, as in the "skating/jumping" argument above. "Slaloming" the tail would giver you a forward component from alternate angled pushes, in the same way as stern sculling a dinghy/rowing boat.
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| Don't water-skiers accelerate because they are travelling further (across the direction of the tow) along what's essentially a hypotenuse |
yes, beacuse the boat constrains them to a constant velocity along the "adjacent edge" of the velocity triangle
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| but at the end the pull in the turn to the tow direction they are decelarating to match the tow speed. |
yes...by friction of water against the ski, rather than anything to do with the turn itself. If you turn slowly into the boat's track friction will scrub your speed so you don't overtake the boat. A slalom waterskier will lose speed making a sharp turn with a high carve angle (with an unavoidable large amount of spray and "skid", completing it pointing back across the other way across the stern of boat) around the buoy then pick up speed again as they are on the next "tack".
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GrahamN, I think we're pretty much on the same wavelength and I'm the first to say my maths is inadequate but I'm sure that there is a force vector direction equation that gives an acceleration component in an elliptical path that in most circumstances is negated by friction but here friction is markedly reduced ... I'll have to go dig later ... I've a vague memory of Aberdeen Uni doing something with skiing forces, don't know if it's applicable).
The latent energy in a bent ski has to go somewhere when it's released, whether it's absorbed and damped by the user's body or the user has the skill to direct it into the snow surface. I think it's more down to the ability of the skier to increase the potential energy into the ski and to control the release that makes the difference between acceleration which will only occur during that release and just a carved turn where the skier is a passenger rather than a pilot.
I'm sure I've read a bit of research on this but I can't find the mental index card, If it surfaces I'll dig up the reference.
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| GrahamN wrote: |
| I don't believe it does, although the force required to make the turn will increase as the radius decreases (inverse square law). |
Just inverse, not inverse square, relationship: F = m.v^2/r
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laundryman, of course...doh...clearly scrambled brains on the menu at that point (confusing myself with the v**2 or w**2 terms).
Masque, fairy doos. Sounds plausible, and may be a sort of continuous version of my essentially discrete argument above. The important thing is for the acceleration out of the ellipse to not be counteracted by some deceleration when loading up the tail. I'm pretty certain (and it sounds like you are too) that there can be no net acceleration if the skier is just a passenger in the carve.
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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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Every been glad that you never got involved 
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Frosty the Snowman, waiting for when we get onto whether this is more effective for the lighter or....erm....better built skier?
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