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# Slow Skis - Page 2

Quote:
 Originally Posted by Betaracer There are no slow skis, just slow skiers. technique plays as large a roll on how skis glide than just the tune.

Agree technique is a big factor. Disagree that there are no slow skis. Wanna race? You get my wife's Beast 72's, I get her Beta skating skis (or about anything else that glides on snow).

Newf
Check this out physics of skiing page out: It's amazing!

the relevant equation is:

Vmax=sqrt(2mg(tan(theta-u)/Cd*Rho*A)

Where m= mass of skier,

g = force of gravity,

theta is slope angle, u is coefficient of kinetic friction

Rho is air density,

Cd is drag coeeficient, A is skier area

Vmax is max velocity.

So Vmax is directly proportional to the mass of the skier. meaning heavier = faster...
Cheers!
Quote:
 Originally Posted by very good site, perhaps you read what you wanted to read Skiers go faster: as the slope angle increases (sin theta increases with increasing slope angle)the mass of the skier increases for everything else the same, the bigger skier is faster Acting in the direction opposite to gravity is friction between the ski and the snow surface Skiers go slower, and kinetic friction is greater, when: the slope angle decreases (cos theta increases with decreasing slope angle)the mass of the skier increases for everything else the same, the bigger skier has greater friction Air resistance is also a big factor in determing the speed of a downhill skier:
123
But on the friction side, mass is multiplied by the coefficient of friction, which is much less than (one to two orders of magnitude less than) one.

Look at formula for Vmax, which Big E posted above (one error: there should be a close paren after "theta"). The only situation in which increasing m could possibly decrease Vmax is if tan(theta) is less than the coefficient of friction: however in that situation Vmax is undefined (or imaginary), since it is the square root of a negative number. Actually, it's zero ... this is just the situation in which the slope is flat enough and the snow sticky enough that you don't slide at all.
Quote:
 Originally Posted by Betaracer There are no slow skis, just slow skiers. technique plays as large a roll on how skis glide than just the tune.
If you're doing turns, technique is dominant over ski "speed" (indeed, other characteristics of the ski may be more important than its "speed"). Just running straight down the hill, the ski speed becomes considerably more important, though it depends on some other variables:

- The faster you're going, the more important a good tuck becomes (I guess getting into a tuck is part of "technique").

- The faster you're going, the more other wind-resistance issues become important, like baggy clothes vs. DH suit.

- If there are bumps or rolls, how the skier handles them can make a difference. At one extreme, if they're big enough that the skiers get significant air, technique may be determinative, if only because the person with bad technique will probably crash. Even small rolls matter, though: minor things like shifting weight fore-and-aft can matter, as well as having enough "looseness" to let the ski stay flat on the snow laterally.

I don't know that you can really put a percentage on "technique" vs. "ski" in any conditions, since you're really trying to describe a ratio between two different measurements, one of which (technique) has no meaningful scale of values.

A World Cup downhill racer will beat a person who's never skied before with any ski that will slide, if only because the other guy will probably fall within a few feet.

At speeds above, say, 40 mph, a person who tucks with his hands against his belly and his shoulders up will almost always be slower than someone who knows how to tuck.

If the two skiers both have a pretty good idea what they're doing, and they're not (i) going so fast that tiny differences in position hugely affect air resistance or (ii) going over bumps, the faster ski will win virtually every time.
Quote:
 Originally Posted by sjjohnston But on the friction side, mass is multiplied by the coefficient of friction, which is much less than (one to two orders of magnitude less than) one. Look at formula for Vmax, which Big E posted above (one error: there should be a close paren after "theta"). The only situation in which increasing m could possibly decrease Vmax is ...snip
You are right, I botched the copying. Sorry .

The top of the fraction is 2*m*g*(tan(theta)-u).

Vmax is bigger when: 2*M*g*(tan(theta)-u) > 2*m*g*(tan(theta)-u).

Divide both sides by 2*g*(tan(theta)-u) give Vmax bigger when M > m. So, all else being equal the heavy weight is faster.

Cheers!
Nobody has mentioned edges. Metal edges add a lot of friction. You will go faster if you have more of a bevel on your ski edges. ie \_______/ as opposed to |_________|.

Who was it that won one an early 20th century downhill races with brass edges on one side of his skis instead of steel, cause he figered out that all his icy turns were one way?
Basically, the frictional force is independent of area.

Do a google, there are lots of examples. Like this one:
http://www.nano-world.org/frictionmo...bung/?=lang=en
Cheers!
Quote:
 Originally Posted by BigE Basically, the frictional force is independent of area. Do a google, there are lots of examples. Like this one:http://www.nano-world.org/frictionmo...bung/?=lang=en Cheers!

"All experiments lead to the conclusion that friction is proportional to the real area of contact as intuitively expected."

Do you read that as friction being independent of area?
The key to understanding that quotation is one word: "All experiments lead to the conclusion that friction is proportional to the real area of contact." The whole point that Bowden and Tabor made (so far as I understand this, which may not be far) is that the real area of contact is what matters, and it (i) is not the same as the geometric area of the surfaces that are sliding against one another, (ii) is much, much smaller than the geometric area and (iii) varies depending on how hard the two surfaces are pressed together.

The reason the real area of contact is so small is that no surface (much less no two surfaces) are perfectly smooth, so they only contact at widely spaced points. As they are pressed together more firmly, they deform one another slightly, and the points of contact grow larger and more numerous.

That is why the Leonardo/Coulomb theory appears to work. Take a 2x4* that's a foot long and weighs X lbs. Place it with the wide side down on a table: it has a geometric contact area of 48 square inches, and there's X/48 lbs pushing down on each square inch. Place it with the narrow side down: it has a geometric contact area of only 24 square inches, but there's X/24 lbs pushing down on each square inch. As a result, the percentage of the geometric contact area that's "really" contact area increases. Indeed, it approximately doubles ... thereby making Leonardo and Coulomb approximately right.

Two caveats:

(1) This friction stuff is pretty complicated and specialized ... really too complicated and certainly too specialized for me. An interesting note is that most basic, human-scale mechanics was pretty well understood in the 19th century, but Bowden and Tabor didn't come up with their theory until 1950.

(2) I'm not sure how this relates to the topic in the thread. If the notion is that friction is independent of the length and width of the ski, Leonardo/Coulomb and Bowden/Tabor would seem to support that. However, the mechanics are significantly complicated, because the snow/ski interaction isn't just simple friction. For one thing, you've got one surface (snow, unless you're going really fast) that may be undergoing a phase change, and isn't completely a solid in any event. For another, you've got the issue of distributing the skier's weight over the length of the ski. For another, you've got the fact that, in the real world, the snow isn't flat on the big, marco level (i.e. it has bumps, which you don't need a microscope to see). All these give me at least the gut feeling that there's a good physical reason why a relatively long, but not relatively wide ski should be faster.

-----
* Okay ... for the detail-oriented carpenters: I know 2 x 4's don't measure 2" by 4" ... let's just say they do.
That is a really excellent post. Thank you for the clarification of "real" versus "geometric" contact area.
Oops. I guess I just read enough to see what I wanted to see.

Nonetheless, the relevance is to Ghosts post, that suggests that the 0 degree base bevel vs a say 1 degree base bevel will make a speed difference. I can't see that as being significant, since the normal force over the width and length of the edge contributes very little. Surely there is more effect on surface area, like tuck vs standing upright.

SJ: The Vmax formula does take all the varying slope angles into account, so that if the skier experiences different slopes, like bumps, then Vmax will change from the tan(theta) component,but will always be larger for the heavier skier.

A missing element is how much does the flex of the ski contribute to friction. I'll suggest that a fat boy on a soft as butter ski will be way slower that the same guy on a stiffer ski. And that may just be why the skiis in question are considered slow.

Cheers!
Hey, Guys - Unfortunately, I haven't been able to be very active on Epic lately, but I just happened to notice your thread. A few comments:

1) Read the chapter on friction in "The Physics of Skiing" ( http://www.amazon.com/exec/obidos/t...=glance&s=books ). There are many different energy dissipation mechanisms active simultaneously in skiing besides the ones you've been discussing. To make matters worse, all these mechanisms have different behaviors as a function of speed and as a function of skier weight. With some the effective "coefficient of friction" decreases with speed, with others it increases. Even though this book is getting pretty old, it does an *excellent* job of summarizing them. It's a "must read" for anyone discussing friction in skiing.

2) There have been lots of previous posts about friction and skiing both here on Epic and elsewhere. For example, take a look at:

a) http://forums.epicski.com/showthread.php?p=892, particularly, posts #5 & #20 in that thread titled, "Are Longer Skis Faster?".

b) Post #5 in http://forums.epicski.com/showthread...04&#post211504

Tom / PM
I think that if you add up all the area of your edges and compare the coeffts. of friction, you will see that it not insignificant.

What about electrostatic repulsion?
Clearly, it's the case that ski-to-snow friction is more complicated than the simple model implied by using a constant coefficient of friction.

However, it does seem to be the case -- both intuitively and on the basis of experience (if not controlled experiments) -- that on packed snow, moving in the ordinary range of speeds, down a slope, with someone weighing in the normal range of weights, the increase in friction as a result of increasing mass has much less effect (an order of magnitude or two) than does the increased force of gravity. Put another way: if you hold all the other variables that affect friction constant, there is a coefficient of friction that behaves pretty close to how the model predicts, and it's somewhere in the range of .01 to .1.

Certainly, it's not hard to come up with examples in other situations where that's not the case, e.g. put someone heavy on skis just short enough in snow just soft enough for him to "posthole" when a slightly lighter skier glides. But that's outside the range of situations I'm talking about.
Quote:
 Originally Posted by sjjohnston Certainly, it's not hard to come up with examples in other situations where that's not the case, e.g. put someone heavy on skis just short enough in snow just soft enough for him to "posthole" when a slightly lighter skier glides. But that's outside the range of situations I'm talking about.
So, in normal situations, mass is not that important in the system...and in extreme situations, it can be very important?

Thats what I've been intuitively thinking. You have a lot more substance and thought into this.
No, SJ is saying that in extreme situations, heavy skiers can be slower, but on typical resort conditions (groomed/hardsnow, on trail, sutiable equipment) they will be faster.

Provided of course, that the surface area of the skier is not so big that the drag slows them down!
Yeah, that pretty much what I was going for.
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