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# Physics of Friction

Something has always seemed somewhat inconsistant about the fact that longer skis are faster than shorter skis - given that more surface area is in contact with the snow. When you look into it you run across that puzzling fact that friction increases with pressure between two surfaces - but not with surface area. Finally they have an interesting new theory about this, check it out at: http://www.sciam.com/news/092001/2.html
VERRRRRRRRY INTERESTING! [img]smile.gif[/img]
If my skis have cracks in the bottoms maybe I should send them back. Are you sure the cracks are self healing?
I don't know, maybe you ought to put bandaids on the bottoms of them just in case . . . and then race me for \$. :
Hey Todd -

Thanks for the link. Tribology (the study of friction) has been the ugly duckling of physics until about 10 years ago, when people began to be able to simulate the interactions of large enough groups of atoms using supercomputers. Lots of that work is now paying off, not only in tribology, but in other areas (eg, biotech) where the interaction between two surfaces (or one surface and a single molecule) is of critical importance.

With respect to the somewhat unexpected observation that long skis go faster, in spite of having more area in contact with the snow, there are lots of friction mechanisms at work when you are skiing, and understanding what makes a ski "go fast" must consider the contributions of all of them.

For example, here is one friction mechanism (applicable to skiing) for which the frictional force clearly decreases with decreasing pressure (pounds per square inch). This is in contrast to the usual "Coulombic" friction from high school physics (and mentioned in the article) which is independent of pressure and depends only on total force (pounds).

In soft snow, as a ski passes over a given area, it must continually compact the new snow that is passing under it. To do this, the ski has to do mechanical work on the snow, or equivalently, the ski must give up some of its energy to the snow. This is sometimes called "compaction drag" and is one of the many friction mechanisms acting on the ski.

A ski carrying the same load, but with a larger surface area, doesn't have to compact the snow as deeply, and doesn't give up as much energy.

On the other hand, such a ski has a more snow under it and thus needs to compact a larger quantity of snow than a smaller ski, so this would tend to actually increase the compaction drag. It turns out these two effects do partially cancel, but because the compaction depth is a nonlinear function of the pressure, the overall compaction drag still winds up decreasing with increasing area for a constant total weight.

There are lots of other fine points like what happens on firmer snow, and whether a long thin ski of the same area as a short fat ski experiences the same drag, but the take home message is that this is just one example of friction that (counter to most people's intuition) actually gets less with larger objects!

Tom / PM

PS - You knew I'd get sucked in and respond, now didn't you? [img]smile.gif[/img]
It's the same reason that longer sail boat hulls are inherently faster than shorter ones. That's my third grade interpretation of PM's Doctorate level explanation.

How humbling... [img]redface.gif[/img]
Hey, I *counted* on you getting sucked in! Helps fill out my knowledge, thanks.
So size DOES matter??????
Sometimes I just can't resist! [img]tongue.gif[/img]
Lisamarie: "So size DOES matter??????"

Absolutely! But, if you are interested in a really comprehensive understanding of this subject, the physics of the angle of the dangle must also be understood and factored in.

Tom / PM
Hey Physiscs man,

In regards to the longer skiis being faster, does'nt the answer have more to do with Pinheads answer. When the ski is "gliding" across snow, isn't really more of a fluid dymanics question than a static or sliding friction problem? Ultimately it's problably all the same thing - at least when you get beyond undergrad physics - but it I seem to recall issues of laminar flow, and fluid drag etc, that explained why longer hulled boats were faster (given a certain range of parameters - obviously a short boat with a bigger engine is faster). :
fudman - I'm still in time-cruch mode, so this is going to have to be a very terse answer, but you brought up some interesting points and obviously know some physics, so I wanted to respond to them.

First, since the gap between the solid surface of the ski and the snow is very thin, a few tens of microns at most, there is no possibility for turbulent fluid flow - everything is laminar. To see this, look at the formula you have for Reynolds number and notice that the Reynolds number decreases strongly with decreasing gap size. I haven't calculated it recently, but I would guess that its probably less than 10^-3.

With respect to you question of "isn't it all fluid dynamics", unfortunately, the answer is "no". There are a whole host of differenct drag mechanisms at work on a ski., and only two (if I remember correctly) involve the fluid layer. I listed some of these mechanisms in a previous post, but a much more complete story can be found in the classic book, "The Physics of Skiing - Skiing at the Triple Point" (available from Amazon and many other places).

Finally, there is a major difference between fluid flow in skiing and boating. The major difference is the one I mentioned above: the Reynolds number for skiing is based on a scale length of a few tens of microns. The scale length for a boat is based on its length, a few tens of meters!!!

The second difference is that the flow in skiing is "internal" flow - flow inside of solid boundaries. The fluid flow in boating is "external" flow - ie, around the boundaries of a solid object. In this latter case, the flow has to come back together after it passes the object (ie, re-attach) if the flow drag is to be minimal. This impacts the optimal shape of the aft half of the boat, but doesn't enter into the physics of skiing at all.

Gotta run - hope this helped.

Tom / PM
All this talk about, friction, dangle angles, bigger is better, and fluid dynamics is making my head swim. Do we get extra credit by reading these threads? Is this really about skiing, or apres-ski?

sorry, carry on,

Jim
Look, nerds like me need something to pass the time until skiing starts. [img]redface.gif[/img]

Tom / PM
Hmmmmmmmm.... putting a bump in the rug makes it easier to drag the carpet across the floor....Ok, but if I put a 100 pound trunk on the rug it becomes more difficult, but haven't I put more pressure between the two surfaces, and therefore friction should reduce and the carpet moves easier,.... not it doesn't !

Movement from one place to another is dominated by the most resistent medium. The more surface area on the snow, the greater the melting, creating that very thin but temporary layer of water, which has less friction than snow in it's unmelted state. Everyone notices that on very very cold days, the skis don't move across the snow so well, there is more friction because the snow doesn't melt so easily unless of course you are on ice and then it doesn't matter much, or you use the right wax......Oh, I get it, this is why "NotWax" works so well...or is it ???!!!!!!! The more we know the more questions that need to be answered.
There is more to the extra drag you feel on cold days with fresh snow. The snow crystals are also sharper and directly 'grab' the ski bases more. This is one of the reasons you want harder wax's on colder/fresher snow.
Something else to ponder.

We now have these wonderful shaped skis, that becasue of that shape and use of materials we can ski just as well up to 20 cm shorter than the traditional "pencil" shaped skis.

While edge length "effectiveness," seems to be about the same, [ again due to the shape of the ski, and the actual amount of "usable/effective" edge on the snow is about the same or greater ] is the surface area on the snow also about the same ? I am not sure.

So the next group of questions come to mind.

Other than flotation in powder, crud, and/or slushy spring like conditions, does surface area mean that much in terms of ski performance ?

Is surface area only a means to create regidity between the shaped edges, provide a platform for mounting the bindings, and acts only as an efficient medium to separate the snow from the skier who basically is skiing from edge to edge?

What is the inter relationship between a ski's surface area and effectiveness of edges on the snow ? Can these concepts [ if in fact they are correct concepts ] be separated ? If not, how are they linked ?

Ok... Physics man your input now again, if you have time, please. And Bob Barnes, I bet you have some really useful knowledge on this as well. Todd, since you started this thread, let's hear from you as well.
Except in the softer snow conditions you mentioned - I do wonder how much surface area affects overall performance. Some of my favorite skis are my Elan X-Techs - very unusual skis that are very shaped but narrower at their widest point than the narrowest point of any other skis I've ever seen (except XC skating skis). They are lightening fast in the gate, and of course the narrowness of them means they are the fastest skis edge to edge I've ever experienced. Because they are so narrow they have an integrated 30mm lifter on them so that you don't boot out all the time, for increased leverage, and its angled out so that at the top of the lifter there is enough room for a binding to mount since otherwise the ski is too narrow for any binding.
> Wink:
> Other than flotation in powder, crud,
> and/or slushy spring like conditions, does
> surface area mean that much in terms of
> ski performance?

> Is surface area only a means to create
> regidity between the shaped edges, provide
> a platform for mounting the bindings, and
> acts only as an efficient medium to
> separate the snow from the skier who
> basically is skiing from edge to edge?

> What is the inter relationship between a
> ski's surface area and effectiveness of
> edges on the snow ? Can these concepts
> [ if in fact they are correct concepts ]
> be separated? If not, how are they linked?

Wink, these are a very neat bunch of questions, and its pretty obvious that no one has definitive answers to all of them, but here's what I know.

First, there is the "simple" answer to your first question. Lets assume that the length of the ski is held fixed, and lets assume a normal flush base (ie, not like the catamaran example of the next paragraph). In this case, surface area directly translates into width, and everyone knows the major differences in performance between skis with 65 mm vs. 90 mm waists. For example, (a) when put on edge, fats try to torque themselves flatter more than narrower skis; (b) fats are slower edge-to-edge (ie, you have to move your knee more to achive a given edge angle); (c) if the snow is at all soft, fats reduce compaction and plowing drag dramatically, etc.

However, given your second question, I think you are thinking about something much more interesting. In particular, I think that the ultimate extrapolation of your 2nd question is that your are essentially asking (a) how a ski built with an extremely narrow waist (approaching zero waist width) might work, or (b), how a ski built like a catamaran with no solid base between the edges might work.

Todd gave the answer to (a), namely, even with a very narrow waist, there is enough load bearing area in the tip and tail to allow them to have enough float to perform reasonably well in all but very soft snow.

Unfortunately, we already know the answer to design (b): It would simply act just like a ski with a absurdly concave base (aka, a seriously "railed" ski). Even on very hard snow, such a ski is extremely twitchy when absolutely flat, and when edged, it locks into a carve with absolutely no skidding possible.

A solid base flush with the edges serves to smooth out transitions from one edge to the other, and permits some degree of skidding, however modest, which I would argue is essential to all skiers.

Thus, I think that the part of the ski between the edges does much more than serve as a place to mount the bindings (grin).

Tom / PM
>>Thus, I think that the part of the ski between the edges does much more than serve as a place to mount the bindings (grin).<<

I would be suprised to find a skier that *doesn't* think the same!
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