a sliding question

A snowHead

One for the physicists and mathematicians.....

If skiing down a very gentle slope at a constant speed and you change from skiing on 2 skis, to skiing on one ski will you (apart from looking daft) -

speed up, slow down or stay at the same speed ?

A snowHead

I'm neither a physicist or a mathemician, but if you want some empirical information, I do find that when I am running down a gentle slope (my home run) and the snow is rather sticky and slow I go faster on one leg. When that leg gets tired, I change. It's a good exercise! And personally I don't think I look daft, I think I look rather cool!

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Someone who knows the science will no doubt be along to explain.

Well, the person's real but it's just a made up name, see?

Now I am no physics guru, nor a mathmetician of note, but surely if sliding down a slope it will be at a rate of constant acceleration, as opposed to constant speed, once gravity is taken into account?

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Guvnor, I think friction between the skis and the snow and wind resistence would also play a major part, otherwise on a long enough slope you'd have skiers breaking the sound barrier!...so on a gentle slope I think you'd reach your terminal velocity pretty quickly....lifting one ski whould effectively reduce the friction between the snow and the skis by half...so you should go faster....I think ??

Anyway, snowHeads is much more fun if you do.

It will be constant speed once the force of gravity is balanced by wind resistance plus the friction of the ski on the snow. As to whether you go faster on one ski or two - it depends which causes most friction. I would suspect that could vary depending on the snow condition.

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Then you can post your own questions or snow reports...

i am assuming the slope angle does n't change, neither do the snow or wind conditions, one has reached a constant velocity because the force of gravity is balanced by air resistance and friction of the skis, but will then changing to one ski alter the friction and hence a change in speed, according to regular newtonian physics it should not as friction is not dependent on surface area, but people would argue it does.... i have no snow here to experiment with.... dammit.

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I agree with alex_heney. A further factor with wet piste snow is the "sucking" effect of water which I find I can reduce by putting the ski on edge, so reducing the area involved (so I imagine one ski would be faster in that case too).

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alex_heney, dry surface (kinetic) friction is not dependant on surface area, but on the pressure between the surfaces. I think larger area tyres are to do with managing the deforming forces, dispelling water, etc. I think larger brake pads are to do with heat management.

Anyway, that's all a red herring as the friction between ski and snow is modified/produced by the extremely thin surface of molten ice (water) between the ski and snow. And is thus well beyond my atrophied analytical skills.

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hsdee, There are too many variables for a definitive answer so all that can be said is 'possibly' it might also be true that you slow down Confused

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hsdee, any wway, I think you stay at the same speed. Unless it's so slushy that you get snow in the way. But I have no idea why. Just my experience. I suspect that the slowing effect on a gentle slope is more wind resistance than snow resistance.

You know it makes sense.

Friction is something you can only really measure, not calculate, so the only thing would be to do some experiments. Factors which might have an effect are:
- less snow-dynamic drag, cos you've only got one ski point digging through the snow instead of two
- less surface area in contact with snow, which means more downward pressure per square inch. I think that would tend to increase friction, as you have higher downward force, which in turn would build up more heat and melt more snow. I don't know whether that's a good thing or not.

Best thing to do is, from a standing start straightline down a slope and time it. Then do the same standing on one leg.

Otherwise you'll just go on seeing the one name:

thanks for your answers, it's a question that got me thinking, i am starting to think that it is a good excuse to do another winter season just to study this under different snow and temperature conditions....perhaps i could get some research funding....or perhaps i could write to the engineers at Atomic whom i hope would know.....

A snowHead

hsdee, speaking not as a physicist or mathematician (this time) but as a skier, I think in the conditions you cite you go faster on one ski than two, provided the piste is reasonably hard. I actually do this quite a lot, as these are the ideal conditions for practicing one footed skiing. When moving from two feet to one I normally end up catching the guy in front faster than previously. It may be related to where where you are balanced on your ski - on two skis move the balance very slightly aft so you are standing just on you heels rather than on the balls of the feet and you feel a definite acceleration. Putting the scientist's hat back on for a brief moment, I suspect that this may be due to the reduced pressure on the front of the ski allowing a smoother packing down and melting of the snow under the ski, so there's not so much of a blocking effect as the shovel suddenly forces itself into any loose snow, and the ski planes better. You of course pay for that in reduced control from the main part of the ski. Until you are very comfortable on one ski you will tend to stand more on your heel than in the middle of the foot.

(BTW I agree with midgetbiker regarding the friction/force question, and also suspect - based on virtually no evidence - that you'll go slower if the snow is soft enough for the ski to sink into it, say maybe more than a couple of cm).

The other benefit of one ski when you are making gentle turns on flattish snow (if you change ski at the transition, so always ski on the outer foot) is that you also get a bit of a skating action as you push off from one ski onto the other - and this makes a huge difference, as you are putting extra energy into the motion. Yes you can get that push when skiing two footed, but it's a much less natural action and you have to work fairly hard to get it smooth - and smoothness (i.e. preventing inadvertent edge sets) is the overriding effect above all these when trying to maintain skiing speed on flattish slopes.

Now...as for my consultancy fee... Wink

A snowHead

Well, the person's real but it's just a made up name, see?

Shallimus, in that case no - I'm doing a pretty simple direct lift of the spare foot and the gain in speed develops progressively over several 10s of metres. You'll see though that I do address that point in my third para.

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Ah, but I was referring to the 'on a down slope' scenario posited in the initial post. I have no further useful info to offer here re: skis as it has been some years since I used two planks, but on a board if I need to increase speed I make sure that I'm flat (i.e. not on an edge) which would indicate more surface area/less digging in equals more speed. I realise this was a skiing question, so I acknowledge that this may not be relevant. I think I remember going faster on one ski, but I'm not sure what the physics of that would be.

Anyway, snowHeads is much more fun if you do.

I would go along with GrahamN, but with a proviso.

I suspect most skiers wobble about a bit on one ski (yawing, rolling and pitching in nautical terms) which will slow down their straight line progress. If it were a reliable method of increasing speed, you would see racers doing it, rather than adopting a rock-solid, feet apart, two-ski tuck.

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I suspect most skiers wobble about a bit on two skis wink

With regard to racers, maybe there are lots of other reasons - aerodynamic, stability etc. - for not lifting a ski off the snow. It does not follow that it does not increase speed at "lower" speeds. (I'm not saying that it does, just expressing concern about the logic Toofy Grin

)

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Ok... done some experiements in the office.

Equipment:
2 identical pencils
4 'foldback' clips (the black ones with silvery arms you can 'fold back')
1 tiltable flat surface

Method:
Place clip flat (black) end down on a flat surface. Insert pencil through arms (it will probably be loose at this point.) Open out the arms so that the pencil is jammed in. adjust the position of the clip until the pencil balances like a see-saw.
Repeat with second pencil, this time using two clips, so that the pencil stands on two legs - this one should be easier to balance
Finally attach the fourth clip onto the first pencil, so that it doesn't touch the ground but still balances. This is two ensure that both sets of equipment weight the same.

Place on flat surface(with pencils parallel to slope to aid balance.) If neccessary for reasons of space on the back of your file they can be one above the other. Gradually tilt the slope and see which one slides first. Or whether the higher pencil catches up with the lower one. Repeat several times, switching the starting positions to remove potential bias.

Result:
The pencil with one 'ski' slid first and fastest 9 times out of 10

Conclusion:
On a flat surface, ignoring wind resistance (greater for skiers than pencils), and 'ploughing through the snow' requirements, skiing on one ski is faster.

Please *do* try this at home.

After all it is free

robcraine, productive day yesterday? snowHead

Lets see what an engineer could make out of it.

As far as friction is concerned it is a constant factor between the two materials between the sliding face. In this case one is snow and the other is the ski. No idea of what that is but my guess is it should around 0.1 as suggested by [url=http://www.newi.ac.uk/buckleyc/forces2.htm}this site[/url].

Thus a piste user sliding down a slope of say 1 vertical in 2 horizontal, which is tangent (1//2) or 26.56 degree then the driving force of him to move forward would be half of his body weight divided by the square root of 5 (due to 1 vertical against 2 horizontal slope and the diagonal being the square root of 5). The friction aginst his movement would be 0.1 times his body weight divided by the square root of 5. Therefore the piste user is able to ski because the net force available is (0.5-0.1) times the body mass divided by the square root of 5.

The above would imply skiing on one plank or two planks can hardy alter the physics of it.

The net force of (0.5-0.1) * body weight/(square root of 5) will allow the skier to go faster and faster until he reaches the terminal velocity in which the downward force is balanced by the resistances in the system, which I would expect the most significant component to be the wind. In other word the wind in front of him is a t zero velocity (in a windless situation) when he is traveling at a speed. The air therefore has to cushion him with a pressure equal or proportional to the square of the velocity divided by 2 times the gravitational acceleration. ( Wind pressure=velocity head )

On the practical side of it when a skier trying to to change position from two legs to one leg he has to move or un-weigh the body weight. In so doing he must turn slightly and deviate from a perfectly straight line which is the shortest route between any two points. Therefore the one-leg skiing must travel slightly more distance and so would be marginally slower to reach the same destination.

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one ski goes faster, fact.

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stab,

If this fact is based on the reduction of the contacting area then the same fact must apply to using a ski half the length too? Say using a child's skis.

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Yoda, I think your point agrees with mine.

You know it makes sense.

Otherwise you'll just go on seeing the one name:

on a board I'll go into a manual/wheelie through crud, probably the same effect, less contact area.

A snowHead

robcraine, nice protocol, sadly ruined by the fact that you;re playing with static rather than fluid resistance... wink

A snowHead

saikee, unfortunately skis on snow don't behave in line with classical friction theory.

Normal friction rules say the frictional force or retardation is proportional to the perpendicular force. The friction force is independent of the surface area and is constant.

Skis actually run on a film of water generated between ski and snow. The generation of the water film is dependent on contact pressure which brings in the area factor.

Switching to one leg from two will double the contact pressure, form a better water film, drop the friction coefficient and go faster.
Its also why modern skis go faster on edge than flat (line contact on an edge generates very high pressures).

Slush is another matter Puzzled

Well, the person's real but it's just a made up name, see?

rich,

The snow in different states of compaction would exhibit different sliding frictions I would have thought. The a film of water at the interface does hold water in dry power snow.

A higher pressure does cause the snow to melt easier though and so a film of water may be present in some cases when the speed is low. At a high speed the sliding friction may generate heat in assisting the melting of the snow.

Help!!

a sliding question

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