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On how steep the slope can be. A bit of physics

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jbob, It's Phil Ingle in the Photo - Me behind the camera, and yes he is on a very solid belay - the hole beneath him is 100ft deep or more

snowball, Yes Phil is heading forward and up through the gap between the serac (big lump of ice) and the rock

We are on the Glacier de Bossons having just skied the Glacier Rond
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Idris, Only joking. It just reminded me of a few occasions when I have turned around to shout "watch us 'ere" code for I'm coming off, only to see to my dismay my mate taking a photo!
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Quote:
Oleksii
No I wasn't wrong, CoF above 1 means that the gravitation alone is not enough to slip the object, i.e.


It's really quite frightening to see how happy you are to expound on something you so clearly know next to nothing about. You're not a management consultant by trade are you? rolling eyes
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Wayne, I think you reached Mornington Crescent in that one. You lost me with the implied straddle at Cockfosters.
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Farley Goode wrote:
Wayne, I think you reached Mornington Crescent in that one. You lost me with the implied straddle at Cockfosters.


OK then - no maths this time Toofy Grin .

Why “stuff” slides down a slope is really quite simple.

1 All stuff is attracted to all other stuff so they tend to move towards each other

2 If one of the bits of stuff is the Earth and the other bit of stuff is on a slope, the 2nd bit of stuff can’t go in a straight line towards the earth (as it wants to), so it moves towards it in the most direct line it can find - downwards, along the slope.

Note. The “pull” between the stuff on the slope and the earth is the same strength in both directions, but (for various reasons) it takes more to get the earth moving upwards then the stuff on the slope to slide down.

2nd Note. As you are standing on the earth (your frame of reference) regardless of the strength of the pull between the stuff on the slope and the earth, you will perceive the sliding stuff moving down rather than the earth moving up towards it. (I think Bert would be happy with that explanation)

3 We can (using maths – not “math” as they say in the US, and whilst we’re on the subject, it’s garden not yard) work out what the angle of the slope needs to be for the sliding to start.

4 The basics are that the heaver the object on the slope is, and the less the slope angle is, the less it is likely that any sliding will occur. (we are not talking about perfectly smooth slopes or stuff here BTW)

5 There are a number of reasons for the stuff either sliding or not. Firstly the weight of the stuff on the slope (can’t be bothered to discuss the difference between mass and weight here – it’s too early in the morning) and secondly the slopes angle.

6 The reason these two are important is that the stuff on the slope really wants to go in a straight line towards the center of the earth but the slope is stopping it. The more weight (mass) something has, the more it wants to move but the harder it is to get it to start moving.

7 So there is a force (again, it’s too early in the morning to go into to details – so you’ll have to take my word for it) pulling the stuff directly downwards (in a straight line) towards the center of the earth and the strength of this force needs to be overcome before the stuff will move – you can call this force friction if you like.

8 Of course there is also a force pulling the stuff down the slope.

9 When the force pulling the stuff down the slope is stronger than the force (friction) pulling it in a straight line towards the center of the earth, then it will start to slide.

10 If we increase the angle of the slope, the amount of force (down the slope) is increased so the stuff starts to slide.

Next – avalanches.

Points to remember:
1 Most people (not all, but most) studying avalanches are the ones who couldn’t hack it in physics NehNeh so they ended up doing something else they could get a grant for. But they still have the self-image of a physicist (it better then someone who just plays with snowballs)

2 The vast majority of stuff going on inside an avalanche is not really physics (other than at a very small scale), it’s actually fluid dynamics.

3 It’s simpler the get a grant for a physic based project than for one on fluid dynamics. And, on the same point, most people have at least heard of physics but not of fluid dynamics; so websites and TV documentaries tend to use to term physics to explain what’s going.

4 Why avalanches slide down a slope is also quite simple. But people who get paid to look at them and explain them couldn’t say that, or they wouldn’t get another grant.

5 People who get paid the look at avalanches and explain them will go to great lengths to make them sound complex.

Back to avalanches:
1 Snow and ice will stick to other snow and ice (and other stuff) in totally different ways.

Note. The different between snow and ice is that snow is frozen gas (moisture) and ice is frozen liquid.

2 As ice bonds with other stuff it is very difficult for a force to overcome this bonding, so the ice tends to stay where it is.

3 Snow, on the other hand doesn’t bond, it links (that is all the flakes tend to jumble together and the branches become intertwined)

4 As the only things holding the snow together is the strength of the branches (if they break the bond is broken) it doesn’t take much force to move it and send it sliding down a slope.

5 Of course the combined linkages within the snowpack, with lots and lots of snowflake branches, is very strong – you can even walk on it without going straight through and snowboarders can sit on it.

6 The combined weight of the snowpack, pressing downwards increases the energy within it so the snow melts slightly. This causes the delicate flake branches to lose their shapes and so the same amount snow can be squashed into a smaller area (like when a piste basher goes over the piste). Another effect of the squashing is that the temporary thawing of the snow crystals increases the QLL (quasi liquid layer) on each flake and the liquid flows onto the next flake. It then refreezes and forms a bond (rather than just an entanglement) so the join between the flakes is stronger and some of the snow turns into ice.

Note. The energy isn’t really increased. You can think about it as the same amount of energy, but in a smaller area, so it has more of a localised effect.

7 This thawing and freezing can happen for lots of reasons, warm days followed by cold nights, compression by piste bashers, wind, moving shadows, etc.

8 The result is that you end up with a layer of bonded crystals (ice).

9 If more snow falls onto this ice the results will be that it acts as a blanket and stops the thawing and refreezing of the first layer.

10 So you end up with a layer of snow on top of layer of ice (the ice doesn’t have to be really solid, just more bonded than the snow on top of it) and you have an area of weakness within the snow pack.

11 This is all fine and good until something either introduces more force/energy to the snowpack (like a skier going over it) or more snow falling. Or the bonds could weaken, or....... well you ge tthe idea, and the whole lot will comes sliding down.

12 I’ll leave the rest for a snowologist (or whatever their calling themselves these days) to explain the fluid dynamics of the avalanches after it starts to move. Hey and they could get a grant for explain the transfer of energy between the moving particles and how this combines to ……. (no, stop there, I don’t need a grant)

Madeye-Smiley


Last edited by Anyway, snowHeads is much more fun if you do. on Sat 15-09-12 10:09; edited 1 time in total
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I love cod science on interwebs Happy
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davidof me to, but it’s as near as needed (for here wink ). Mind you, still trying to come up with something to prove beyond doubt that Almonds evolved specifically to make Christmas cakes taste horrid.
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Wayne wrote:
davidof me to, but it’s as near as needed (for here wink ). Mind you, still trying to come up with something to prove beyond doubt that Almonds evolved specifically to make Christmas cakes taste horrid.


It's something to do with the way the almond crystals form a stronger bond when a rolling pin is used to compress them to make marzipan.

Not unlike a piste basher on new snow wink
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Wayne, unfortunately I think you got a little muddled at about no.7. The force downward towards the centre of the earth is the weight of the object: ie mass under the influence of gravity (not friction, as you say). This can be simply resolved geometrically into a force perpendicular to the slope and another parallel to the slope. It is the latter which tries to slide the object down the slope and is opposed by friction, which is represented as parallel with the slope in the opposite direction.
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snowball, mechanics - love it

But reality bites

Best seen in the vertical flutings of powder which characterise South American peaks - see


http://youtube.com/v/xZTfXf4qvsE&feature=related

look at 5:28

These just seem to defy normal and simple explanation. Seldom seen in the Alps, but is a kind of anti-gravity, face-stuck powder. Weird stuff. Nightmare to climb.
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valais2, yes, absolutely. Fantastic stuff.

(I just cooked razor clams for the first time and my hands still smell of the sea)
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Let's face it

tan(45) = 1 is a mathematical equation describing the physics of an object sliding a slope. It is always true. The problem is how we interpret it.

According to the OP presentation when an object is about to slide down a slope the coefficient of friction between the slope and underside surface of the object is given as tan(angle of the slope). Therefore when the slope is 45 degree the mathematics tells us the coefficient of friction =1. This is theory.

For snow not sliding down like the snow particles that can be accumulated at an angle a lot steeper than 45 degree or even 90 degree vertical that is not sliding between two defined surfaces.

In actual sliding as we in skiing the snow is compressed and the sliding surface is the underside of a ski or a snowboard. The coefficient of friction between these two is about 0.1 to 0.14 according to this web page. which also quote the coefficient up to 1.76 between new and old layers of snow within 24 hours.

Whenever we ski, even in powder, the snow underneath the skis will be compacted at least momentarily by our body weight and should not be confused with the friction between snow particles.

I think when a ski slope is steeper than 35 degree the grooming machine may have difficulty in getting up safely. This has nothing to do with friction between the machine and the snow but with the slow breaking up to become a loose layer unable to transfer the machine weight deeper into the snow. In other word the snow fail internally by shear.

The steepest groomed piste in Austria is the Karakiri in Mayehofen that is sign-posted to have 78% or 38 degree. It can groom this piste only by attaching to a winch.

Extreme skiing is defined in USA for slopes steeper than 45 degree which are obviously ungroomed.

For paved road in UK the steepest gradient is 1 in 3 which is approximately 19 degree as OP had stated. (tan(19 degree)=0.344 or 1 in 2.9).

It is my personal belief that as human we never descend a slope as steep as in skiing in our daily life. Say if we walk in the fells and have to descend a steep gradient we would turn around using hand and and legs to climb down so visually we never have the experience of charging down such a steep slope unless we have a pair of skis or a snowboard. Thus in forward direction going down gradients significantly steeper than those in daily life remains the unique experience for those who ski or snowboard.

It is also rather unique when viewing some black runs from the top our standing position does not always afford a full view of the bottom so it is challenging for some to start a descend not knowing what is installed at the bottom. In many black runs the full view of the bottom is only visible after one has committed and entered the piste.
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valais2 wrote:

Best seen in the vertical flutings of powder which characterise South American peaks - see


http://youtube.com/v/xZTfXf4qvsE&feature=related

look at 5:28

These just seem to defy normal and simple explanation. Seldom seen in the Alps, but is a kind of anti-gravity, face-stuck powder. Weird stuff. Nightmare to climb.


Maybe similar conditions to Alaska (where I gather snow can be stable/safe to ski on steeper slopes than most places) - very wet, adhesive snow falls, which sticks to very steep slopes, and is then 'dried out' by dry winds which makes it nicer to ski?


Last edited by So if you're just off somewhere snowy come back and post a snow report of your own and we'll all love you very much on Sat 15-09-12 18:46; edited 1 time in total
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clarky999, .....you're right....you can see them in All I Can.....
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Wayne, correct me if I'm wrong but isn't fluid dynamics a branch of physics!?
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saikee wrote:
......It is my personal belief that as human we never descend a slope as steep as in skiing in our daily life. Say if we walk in the fells and have to descend a steep gradient we would turn around using hand and and legs to climb down so visually we never have the experience of charging down such a steep slope unless we have a pair of skis or a snowboard. Thus in forward direction going down gradients significantly steeper than those in daily life remains the unique experience for those who ski or snowboard......

Good post. I'd never considered that before but obvious when you think about it.
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Except for Aussie style abseiling. Twisted Evil
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snowball, well before 7.

Quote:

4 The basics are that the heaver the object on the slope is, and the less the slope angle is, the less it is likely that any sliding will occur. (we are not talking about perfectly smooth slopes or stuff here BTW)


Whatever a heaver object is. Perhaps the classic cannonball and feather scenario.
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I know nothing but Wayne has my vote. Don't rock his boat.
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Can't believe people still have problem with school lesson on friction.

If an object with W is placed on a slope at an angle theta. The weight of the object can be resolved into two components of

(1) a component parallel to the slope = W * sin(theta)
(2) a component perpendicular to the slope =W * cos(theta)

Frictional resistance against sliding down is defined = coefficient of friction * component of force acting perpendicular to the slope

Thus the frictional resistance = coefficient of friction * W * cos(theta)

If the object is about to slide down the two must equal to each other and so

W* sin(theta) =coefficient of friction * W * cos(theta)

The W cancels on both side and since sin(theta)/cos(theta)=tan(theta) we therefore have

coefficient of friction = tan (theta). Therefore if the angle were 45 degree and the object is liable to slide down if the coefficient of friction, between the object and the slope, is 1 or less. (because tan(45 degree) =1)

The removal of W in the above equation means the weight of the object does not control when the object will slide down and should be ignored in our discussion. If the object is heavier then once in motion it could develop a bigger impact when its larger potential energy is converted into a correspondingly bigger kinetic energy.

It is also interesting to point out ASCE-7 which has the national guideline for designing snow load on buildings has indicated roof steeper than 70 degree can expect undrifted snow to slide off whereas drifted snow can slide off on roof as flat as 26 degree according to this web page.
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Nickski wrote:
snowball, well before 7.

Quote:

4 The basics are that the heaver the object on the slope is, and the less the slope angle is, the less it is likely that any sliding will occur. (we are not talking about perfectly smooth slopes or stuff here BTW)


Whatever a heaver object is. Perhaps the classic cannonball and feather scenario.


Sorry if this is a bit rambling but I'm trying to work it out from first principals:

Hang on (geddit wink ) Don't talk about heavier in this example surely? A heavy object is only heavy as a result of it's mass and the effect of gravity on that mass (gravity makes it heavy). If an object is more massive (cannonball, skier, snowball, feather etc..) then it will need a smaller (lower? shallower?) slope angle before it's mass and the effect of gravity (it's weight) causes it to move down the slope (gradient) and I'm disregarding friction at the moment, which is a resistive force opposing the effects of gravity, any external force acting (pushing) on the cannonball or the feather and the minimum slope angle below which no mass will move. The classic Galilean thought experiment of dropping a cannonball and a feather connected by a string doesn't really apply in this scenario. It only really reveals that more massive bodies reach terminal velocity before less massive bodies.

If you take resistive friction away then a mass of snow moves down a slope of the same angle at the same rate as anything else of the same mass since, as far as I can recall, the 'force' of gravity to all intents and purposes acts equally at all points on the earth's surface (and I include on a mountainside as well as at sea level for the pedants amongst us). You also have to recognise that such masses are not acting as point sources but also as extended sources and hence there will be a minimum slope angle that will result in movement of the mass (inclining the slope by 1 or 2 degrees from the horizontal is unlikely to have any discernible effect on the movement of a snow mass but a slope inclination of say 10 degrees or more may cause a snow mass to move if it is of the right dimensions). So ignoring resistive forces the angle of slope that snow will stick to depends only on the mass of snow build up on that particular slope.

Now, introducing friction puts me on shaky ground but it seems to me that frictional forces will play a major part on whether a snow mass will move or not and that these frictional forces are multiparameter dependant (dimensions and mass of the snow, surface area and structure of the surface on which the snow sits (mountainside) temperature gradient at the boundary between the snow lower surface and rock face surface, ambient temperature and variation in temperature during the day. A variation in any of these parameters will alter the minimum slope angle that snow will stick to.

Gonna stop there coz my head hurts but as I say I've tried to work this out from first principals and would appreciate feedback on where I've gone wrong.

Toofy Grin
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saikee, Thanks for that it helps a lot but does this only apply in a gross system where the slope angles are constant and smooth? In a real world situation where slope gradients constantly change and mountainsides have crenellations and crevices, is it acceptable to ignore these variations in the angle of the face presented to the snow, any crevices, temperature boundary layers etc...?
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halfhand, your constant and smooth surface is actually on a smaller level full of crenelations and crevices contributing to friction so the question is merely one of scale. You can basically think of the things you mention affecting the coefficient of friction. Also with snow as it falls in layers there is a point where it's only 'in friction' with another layer. Interestingly the experimental data I linked earlier based on a small amount of snow being tilted before it slide does tally pretty well with reality.
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meh wrote:
Wayne, correct me if I'm wrong but isn't fluid dynamics a branch of physics!?


It certainly was when I did my degree (in Physics), though I was specialising in the physical oceanography/fluid dynamics side in my 3rd year. Given the length & complexity of the equations it was most definitely physics (and maths!). Mind you, this was quite a while ago now...

(hence why I am not contributing to the thread other than to say that even in the Alps snow most definitely still sticks on slopes at 45º !)
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What is the regulation angle of a chalet roof? I find it surprising sometimes to see how loaded they can be with snow.
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miranda,

Haven't they got little fence things stopping it from sliding off?
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musher, I want science, not little fence things!!

(I can't see any little fence things, so they must be very little).
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halfhand wrote:
If an object is more massive (cannonball, skier, snowball, feather etc..) then it will need a smaller (lower? shallower?) slope angle before it's mass and the effect of gravity (it's weight) causes it to move down the slope (gradient)and I'm disregarding friction at the moment,
No this is wrong, the mass makes no difference. If you ignore friction anything on any slope will slide, and at the same rate, and the weight has nothing to do with it.
Quote:
The classic Galilean thought experiment of dropping a cannonball and a feather connected by a string doesn't really apply in this scenario.
Yes it does, and it wasn't a thought experiment but an actual experiment using a solid cannon ball and a hollow iron ball of the same size rolling down an inclined plane. No string involved. The masses were sufficient that air resistance could be ignored
Quote:
It only really reveals that more massive bodies reach terminal velocity before less massive bodies.
I think you meant the "less" and "more" the other way round. But it is a property of air resistance in relation to mass, not just of mass. A metal sphere of the same weight as the feather will fall at almost the same rate as the cannon ball [but not quite, since the mass goes up in proportion to the cube of the diameter while the surface area (and air resistance) goes up in relation to the square].


Last edited by So if you're just off somewhere snowy come back and post a snow report of your own and we'll all love you very much on Sun 16-09-12 15:02; edited 8 times in total
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saikee Seems like a good summary: I thought of extending into the maths but would have had to check if my remembered maths from forty-something years ago was right. However:
saikee wrote:

The removal of W in the above equation means the weight of the object does not control when the object will slide down and should be ignored in our discussion.
From basic physics this seems right yet I'm not sure if it is right in practice in relation to real snow. When there is a weak layer in the snow (from, for example, a layer of hoar-frost crystals) and new snow falls on top, increasing the mass, it is generally considered that the snow is more likely to avalanche. - I'd be interested in your thoughts on this.
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snowball,

If there is a weak layer that becomes loose then this is no long the scenario of an object sliding a slope but prevented by the frictional resistance between the two surfaces.

Your scenario is exactly the problem of the steepest groomed piste in Austria. The grooming machine was not sliding down by overcoming the frictional resistance but the layer of snow supporting it has disintegrated and fails. This can happen like we skid off road on a pile of wet snow. In between the tyre and the snow there is a layer of water which we all know has next to nothing frictional resistance.

halfhand,

The friction of an object sliding a slope is an idealised condition. In a real world the coefficient of friction can change from patch to patch on the slope, say due to different compaction and moisture condition, and the angle can vary along the slope too. Nevertheless this is physical model with which we explain the nature's phenomenon. Not saying this is exact but it is the best formulation by human for understanding the physics of it.
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saikee, in almost all cases when dealing with objects on snow and the weight of snow on lower layers, the snow is being crushed and distorted so this seems to be the norm rather than the exception in practice. The creation of a brief lubricating layer of water due to the pressure of the ski is the norm. Skiers' tracks which don't set off an avalanche may cut the snowpack but subsequently help to secure the slope.
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snowball, with snow loading you have to think about the general structure of the snowpack. Typically what you need for a slab avalanche is a bed surface, a weak layer and then a layer above. The increased mass causes the weak layer to collapse fracturing the layer/layers above with the whole lot sliding down on the bed surface. So in this case what actually happens is the support of the rest of the snowpack is removed from slab "drastically reducing the coefficient of friction" for the slab. Basically we're doing the maths wrong at this point with this explanation as the coefficient of friction between the slab and the layers below was always at the point where it should slide but the forces involved from the rest of the snowpack were holding it in place.

This is the entire point behind all the various localised tests you can do, you're looking for how easily layers can slide over one another and in other tests how readily fractures will propagate.
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snowball,

I doubt if a film of water could be formed when in a momentary contact with skis on a piste.

In an average condition the piste will be groomed and previously ran over by a machine weighing 6 to 8 tonnes. Thus the base will be well compacted. Grooves are formed at the surface and the coefficient of friction is possibly at its lowest because the surface will be plane and not disturbed. Once skied on the slope will have piles of loose snow here and there and so will be less smooth to ski on.

In skiing powder snow could be seen spraying around the skis whenever we turn. Unless the snow is wet before we ski I would say water formation due to our weight is not the norm.

A coefficient of friction of between 0.1 and 0.15 has been quoted for the waxed skis with snow. This would correspond to a gradient of 5.8 to 8 degree and is in line with my experience when I reach a flat part of a run, say on San Bernardo #7 piste of La Rosiere/La Thuile or at the bottom end of Hidden Valley of Dolomites. Although there is still a gentle slope but we have to walk because the gradient is not skiable. Many green runs when I checked them with the contour maps are around 12 to 17 degrees so this friction theory of an object sliding down a slope does hold water from my observation.
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saikee wrote:


I doubt if a film of water could be formed when in a momentary contact with skis on a piste.

However this is what I have read a number of times in accounts of (for example) ski base preparation. The previous compaction of the snow is irrelevant (except in so far as it affects the amount of snow in actual contact with the ski).
Sometimes when the snow is extremely cold it becomes slightly sticky for the ski and I was told this was because the skier's weight becomes insufficient to melt that little lubricating layer.
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snowball,

I suppose when a full length of a ski, say 1.6m long, passing the same spot on the snow the friction and heat could have melt the snow a little which in turn could assist or lubricate the sliding action. This would be a by-product of the skiing action. Purely vertical compaction from the skier's body weight may also cause additional mechanical re-arrangement of the snow particles forcing some solids into a fluid state since energy would be absorbed.

So at a microscopic level water could be present between the skis and the snow.


Last edited by Anyway, snowHeads is much more fun if you do. on Sun 16-09-12 18:38; edited 1 time in total
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Yes, I think we are talking microscopic.
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