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# Does weight matter?

Recently I was having a conversation with a fellow Masters racer who was once a World Cug luger in the seventies.

With his personal body weight in the 150 pound range, international rules allowed him to add a certain amount of weight to his sled so that the running blade would generate the same amount of water film on the ice as the heavier lugers.

Our conversation soon turned to skiing and we agreed that the speed of the ski and the type of plastic in the base as well as the waxing can play a dominant role in the amount of friction that the ski encounters.

But we were somewhat at odds in my assertion that on a shuss, with all other factors being equal, it would be a heavier skier who would achieve the faster speed.

My argument was based on the idea that while gravity generates the same downward force for an equal mass, the air resistance experienced by a heavier (and larger) skier was not as detrimental as the air resistance experienced by a lighter (and smaller) skier.

If you double the height, width, and depth of a skier, his/her body mass goes up by a factor of 8 (2 times 2 times 2).

But the frontal air resistance only goes up by a factor of 4, due to the doubling of the height and the width. The depth of the skier's body is much less a factor in the air resistance, like a semi-tractor hauling one trailer versus two on a flat highway at a constant speed.

We see similar cases in nature where having a larger mass is an advantage, like a whale which loses less heat energy per pound of body weight than a bird, due to the difference between body surface area and total mass.

So if one accepts this argument that a bigger skier will be able to shuss faster than a smaller skier, what is the legality and practicality of wearing a weight belt in a speed type ski race?

We know that the FIS limits the height of a race plate to protect the skier from injuring himself due to the negative consequences of being too high over one's skis.

But apart from the need for a ski racer who wears a weight belt to have stronger legs to compensate for the extra weight, are there any safety issues?
Quote:
 Originally Posted by montreal But we were somewhat at odds in my assertion that on a shuss, with all other factors being equal, it would be a heavier skier who would achieve the faster speed.
This appears generally to be true, in a schuss.

If there is friction to be overcome, and it's equal for the two bodies, the heavier body will accelerate more quickly. In this case, the friction isn't necessarily equal, but (as you note) the increased friction for the heavier skier should generally be minimal. This is true both with respect to the sliding friction (ski on snow) and air resistance. Actually, the frontal area of a heavier skier in a tuck barely increases at all (unless he's too fat to get into a tuck, which is an issue for some of us).

Quote:
 So if one accepts this argument that a bigger skier will be able to shuss faster than a smaller skier, what is the legality and practicality of wearing a weight belt in a speed type ski race?
In a straight schuss, the weights should help. In any race with (i) turns or (ii) jumps, the disadvantage of trying to turn and control the extra weight rapidly outweighs the advantage.

I don't believe there's any FIS rule against carrying weight in Alpine events. In speed skiing, I think there are limits on weights of poles, etc.

A minor aside:

Quote:
 gravity generates the same downward force for an equal mass
I'm not sure I follow this. The whole point is that the mass is not equal, isn't it? You are correct, of course, that if two skiers have the same mass (i.e. if they weigh the same) gravity will act on them with the same force.

If they don't, gravity produces the same acceleration (if they're falling straight down in a vaccum), but there's more force on the heavier skier.
Quote:
 Originally Posted by sjjohnston I'm not sure I follow this. The whole point is that the mass is not equal, isn't it? You are correct, of course, that if two skiers have the same mass (i.e. if they weigh the same) gravity will act on them with the same force. If they don't, gravity produces the same acceleration (if they're falling straight down in a vaccum), but there's more force on the heavier skier.
In my extreme exageration of comparing two people where one person has double the dimensions of the other person, thus 8 times the weight and volume, when both people are in an identical tuck positions, the frontal projection would be 4 times higher for the larger person compared to the smaller person. Imagine a 40 pound child next to a 320 pound footballer.

What I meant about mass and gravity is that gravity pulls downward with the same force for the same mass. A 1 gram feather on the moon would accelerate downward with the same speed as a 1 gram steel ball-bearing.

On earth, these two objects, which have the same mass would not fall at the same speed because of the greater air resistance on the feather.

Skiers often ski with backpacks which may exceed 10 pounds in weight. While this will raise the center of gravity and make turning a bit harder, I wonder if such skiers have noticed any difference in their speed on the flats and while accelerating.

I often wear a 5 pound ankle weight on each leg while doing the stairmaster in the gym in order to simulate the realistic weight of a ski+boot when I am climbing with skis on while off trail.

Weights worn while skiing need not necessarily be attached high on the body. They could be attached to the ski boot or to the shin, like rapid-gate shin protectors.

As far as how much weight a 150 pound person would have to add in order to gain an advantage? If a modest 10 pound weight would generate 2% more speed, then in a 60 second race, that extra second might move one up a few ranks in the score list.

If weight mattered, racers would use solid steel skis and lead boots. Or, more likely, FIS would have rules regarding weight of equipment like the luge federation has.
Numerous skiers have told me that heavier skiers have an advantage in the gates over light weight skiers. I simply don't buy this. Just look at the juniors skiing, weighing less than 100 lbs, and compare these light weight kids to us old folks with our American hamburger weights.

More weight does not mean faster acceleration. (Galileo did the numbers on this one - If you drop a bowling ball and a small ball bearing out the window of a tower, they hit the ground at the same time. If you roll them down an incline, same thing.) Weight does however mean more momentum, thus slower acceleration and slower braking (think 18 wheeler vs. Volkswagon bug), and more weight does require more strength (force) to master the forces once the body does get up to speed.
Quote:
 Originally Posted by LiquidFeet More weight does not mean faster acceleration.
It does if there's friction.

Quote:
 Weight does however mean more momentum, thus slower acceleration and slower braking ... more weight does require more strength (force) to master the forces once the body does get up to speed.
You've really said the same thing two different ways here. But yes, this is why carrying weight (in your hands, a belt, or your belly) is not necessarily an advantage except in a straight schuss (and not then, if it interferes with getting into a low tuck).

### Weight matters

In the real non-schussing world of racing heavier is better on some race courses, but then again heavier is worse on others. Good thing - How could someone like Rhalves ever beat those beefy Austrians otherwise?
The fastest pacesetter gal at our Mt. - #3 national PLAT 21-25 division

( http://www.nastar.com/index.jsp?page...&compid=120692)

...is about 5'3" and prob 115 lbs soaking wet.

Conversely, the fastest guy (#3 national PLAT 21-25) is a typical alpine science project 6'+ 200#+

http://www.nastar.com/index.jsp?page...&compid=549370er...
Quote:
 Originally Posted by LiquidFeet If you drop a bowling ball and a small ball bearing out the window of a tower, they hit the ground at the same time. If you roll them down an incline, same thing.) Weight does however mean more momentum, thus slower acceleration and slower braking (think 18 wheeler vs. Volkswagon bug), and more weight does require more strength (force) to master the forces once the body does get up to speed.
I agree with you. The bowling ball and small ball bearing should hit the ground at the same time as long as the density is identical because we know that a 1 pound styrofoam ball and a one pound baseball will not hit the ground at the same time due to the difference of density. Where the weight is identical between the balls but the density is different, then the volume and surface area must also be different and this explains the difference in air resistance.

But for my comparison of a 40 pound child skier next to a 320 pound adult skier, I must assume they have the same body density and you are correct in saying that they should travel at the same speed on skis.

In other words, if you throw these same two people out of an airplane with parachutes, during the freefall, they should both obtain the same terminal velocity.

So if one of these two skiers is faster than the other in a shuss, I accept that the difference in speed would have to be due to some other factor, like the way the weight is distributed over the surface area of the ski bottom and how the snow changes resistance as speed increases.

Thanks for correcting my Physics 101.
Quote:
 Originally Posted by Woodee In the real non-schussing world of racing heavier is better on some race courses, but then again heavier is worse on others. Good thing - How could someone like Rhalves ever beat those beefy Austrians otherwise?
On flat race cources like Wengen, we often hear about the racer (glider) who is better able to carry his speed across the flats. Do these gliders tend to be the heavy weights? I can't remember.

But when a small guy wins a major downhill, a lot of eyebrows get raised because many are conditioned to expect that only the big guys can win on downhill courses.

Is there a difference in the ratio of strength to weight as skiers get bigger?
Lets get to the REAL question. Two racers. Lets stipulate roughly equal skill. Both are 200 lbs. One is 5'8". One is 6'2". Who is faster in a chinese downhill?

In short, is fat faster than skinny? Any engineers want to weigh in on the physics / airodynamics of endo versus exo? Haha!
Quote:
 Originally Posted by montreal But for my comparison of a 40 pound child skier next to a 320 pound adult skier, I must assume they have the same body density and you are correct in saying that they should travel at the same speed on skis.
Nope. The 320 lb. adult would be faster.* For one thing, the assumption you feel compelled to make isn't accurate, but let's put that to the side.

The main issue is that the 320 lb adult doesn't have 8 times the frontal area.

Put the skis to one side, and consider they're jumping out of a plane and taking a "dive" position.

Terminal velocity = the square root of ( 2 m g / d a c), where: m = mass, g = acceleration of gravity, d = density of air, a = frontal area and c = coefficient of friction. If the kid and the adult are in the same place at the same time, and wearing similar clothes, g, d and c (and, of course, 2) can be treated as constants. Let's just invent a constant K = the square root of (2 g / d c). K is a positive number. So terminal velocity = K * the square root of (m / a). If the frontal area of the adult is less than 8 times that of the child, his terminal velocity will be higher.

Friction of the ski on the snow also plays a role, and also favors the heavier skier. I think we can take it as an observational reality that ski-snow friction scarcely increases with weight, i.e. that skis on snow are "slippery," which I think is part of the fundamental appeal of the sport.

And: just to reiterate what's been said already, so somebody doesn't feel compelled to point out that I've ignored it -- this is all just talking about a straight schuss in ordinary conditions. Once you've got to turn or go over jumps, other factors also become important, and pure weight both (i) becomes a negative factor to some degree and (ii) becomes lost against (or "outweighed by," if you will) the much more significant factor of exactly how the skier makes his or her turns, etc.

-----
*As long as various other variables are within particular ranges: e.g. the slope is steep enough to get up to a speed where air resistance becomes significant, they're not post-holing in their skis into 4 feet of unpacked snow, etc.
FWIW, there are conditions in which a heavier skier will schuss more slowly than a light skier -- deep snow. The heavier skier will sink in more deeply and be fighting the drag from the denser snow deeper in the snowpack, as well as the drag of snow going by his legs.

You've probably seen this lots of times -- overweight turons on skinny skis who didn't keep their speed up and flounder on the runouts on big powder days.

YOT

PS - Didn't see the footnote of the previous poster in which he mentioned postholing in 4 foot deep snow. Other than exceptions to the rule like those just mentioned, I agree with the previous poster that heavier is almost always faster in a schuss. Throw in some turns, and the heavy guys often wind up making "bottom-heavy" (in more ways than one ) turns with lots of speed scrubbing at the end of each turn. I know, because I'm one of them.
Quote:
 Originally Posted by montreal Do these gliders tend to be the heavy weights? I can't remember.
Yes.

Walchhofer, often mentioned as a good glider = 6'4" / 220. Deneriaz, that's really his one forte = 6'2" / 214. Rahlves, always considered handicapped by flats and helped by technical sections = 5'8" / 185.

Kildow, who cleans up on courses like Lake Louise = 5'10" / 175. Ludlow, who's scarcely mentioned without noting she's good on the steep and technical and slow on flats = 5'3" / 135. In her own words, speaking of the Olympic Super G: "factors beyond my own athleticism or controlâ€”such as body weight and fast skisâ€”played a particularly large role in the outcome of the race. Of course these things are involved in every ski race, but the flat, easy hill especially favored the big girls and the good gliders."
So if all this is true then say a 300lb bodybulider with excellent skiing skills should slay on a downhill, yes?

I dont know I would think that the minute difference that weight plays in favor of, also acts detrimentally with regard to more friction. I would think its a wash.

### anybody remember Franz Weber....

he was built a lot like the gov. of California and cleaned up on Speed events.. Not overly tall, but muscular. I raced with him on mt. hood 20 years ago, and his body build and strength had more to do with his speed down the course than pure weight. Put the anybody in a tuck on a steep hill and fear of death must be overcome by love of speed, or go home empty handed..
Quote:
 Originally Posted by sjjohnston If the frontal area of the adult is less than 8 times that of the child, his terminal velocity will be higher.

Yes, I assumed that the frontal area of the adult would only be 4 times that of the child.

So if you drop a 100 pound steel ball out of the airplane at the same time as a 1 pound steel ball, likewise it is the bigger ball that will accelerate faster and obtain a higher terminal velocity as well.

If true, you seem to support my original premise (which I then doubted) that the larger (and proportionally heavier) skier will ski faster than the smaller one, but strictly in a shuss and assuming that the role of friction between the ski and snow is low compared to the air resistance at high racing speeds.
Quote:
 Originally Posted by YoungOldTimer FWIW, there are conditions in which a heavier skier will schuss more slowly than a light skier -- deep snow. The heavier skier will sink in more deeply and be fighting the drag from the denser snow deeper in the snowpack, as well as the drag of snow going by his legs.
Actually, for my question, I was assuming that the friction between the ski and snow was negligable compared to the air resistance at high speed.

If gravity is pulling the skier down the hill with a force proportional to his mass, then the terminal velocity will be determined when the air resistance counter balances the downward force.

Does the larger and heaver skier achieve a higher terminal velocity than the smaller and lighter skier because the mass goes up proportionally with the cube of the person's height, but the air resistance only goes up proportionally only with the square of the person's height?

P.S. I experienced terminal velocity when I went 136 kph on the speed course at Les Arc in 1996 on 200 cm GS skis and no speed suit. I weighed 155 pounds at the time.
Quote:
 Originally Posted by Mudi he was built a lot like the gov. of California and cleaned up on Speed events.. Not overly tall, but muscular. I raced with him on mt. hood 20 years ago, and his body build and strength had more to do with his speed down the course than pure weight. Put the anybody in a tuck on a steep hill and fear of death must be overcome by love of speed, or go home empty handed..

He skis much faster than I ever have. He's got a nice web site at:

http://www.franzweber.com/franz_weber_biography.html

Even pics with the governor. They do look like they're built the same way.
I think we should all be drinking beer while discussing this*. Bottoms up!

I'm not sure your discussion of air resistance is accurate. That is, I'm not sure that a man that weighs 250 lbs can be considered as having twice the frontal cross section of a man who weighs 125 lbs. OK.. SpongeBob SquarePants maybe, but real people, no... I understand the point you're trying to make, but I think that the increase in force of gravity outweights the frictional loss due to air resistance and static & dynamic friction between the skis and snow.

Still, as others have pointed out above, for we mortals on our typical beer league courses skill plays a much larger role. That's most commonly how that guy in the the spandex suit (which is screaming for mercy 'cause he bought it when he was 30 lbs lighter..) with a huge beer gut can trash you; generally, it's not his weight.. he's just a better skier. And, lucky for you that the beer gut is there 'cause he'd trash you even worse if he dropped a few lbs. So, cheer up, accept it, and maybe even lessen future pain by buying him a big cheese & chili dog and an extra round at the end of the evening. When he says "Thanks!" simply reply, "No, thank YOU! Bottoms up! "

*then we can go on to Ford trucks vs Chevy trucks. (Actually, isn't the answer obvious for trucks? So, no discussion is needed...)
Quote:
 Originally Posted by BobHarwood I'm not sure your discussion of air resistance is accurate. That is, I'm not sure that a man that weighs 250 lbs can be considered as having twice the frontal cross section of a man who weighs 125 lbs.
I never wanted to compare a 250 lb. person to a 125 lb person.

I wanted to compare a 6 foot person to a 3 foot person so that I could conclude that the 6 footer had twice the height, twice the width, and twice the depth, thus 8 times the weight.

With twice the height and twice the width, the frontal presentation (air resistance) would only be 4 times as much, even in a tuck position.

I suggested that the terminal velocity of the 6 footer doing a shuss would be higher than for the 3 foot person.

I chose these exagerated numbers to keep the math simple assuming the body density and silhouette of these two people were identical, and the resistance between ski and snow was not an issue.

Maybe this is the perfect apres ski beer drinking discussion. But it started in ernest when my fellow Masters racer recalled the international rules that allowed him to add a weight to his luge and then we began to discuss how well our 155 pound bodies fare in speed events.
It seems like there's at least general agreement on the main stuff. Bob Harwood's points all seem about right, particularly the observation that guys with beer guts are better skiers ....
I dont buy it, I think that the only reason a heavier skier skis faster overall is because his mass prevents any skiing corrections from affecting his speed as much as the lighter skier. Objects in motion stay in motion unless acted upon by an outside force. Objects with more mass take more energy to slow down. Truck vs. car.

If all things are equal (mountain, gear, technique) the lighter skier would ski faster, less frontal area and less friction are the reasons.

If you got a perfectly smooth mountain and got a man that is 5'9" and weighs 175lbs and another that is 6' and weighs 220lbs, and all they had to do is tuck, no turns and no bumps on the trail, (its speed skiing in speed skiing heaven)....the smaller and lighter guy would win.

However if both men had the exact same exterior dimensions but one guy had a metal skeleton, like X-men's Wolverine making him weigh 100lbs more, he would be slower due to the additional friction, as fractional as it may be.
Well ... everybody can think what they want, but I suspect you're approximately alone in that belief (or at least in the minority). Of course, what any of us think about it doesn't affect anybody's actual speed, or anything else for that matter ....
xj guy-

the facts on the hill do not bear out your theory-

### bobsled analogy

2-man vs 4-man sleds: same or negligible frontal surface areas, weight differential seems to make the difference, but sled runners are not P-Tex, and the extra weight supposedly "melts" the ice and lowers frictional drag. Am I way off base comparing apples and oranges?
Quote:
 Originally Posted by mr book 2-man vs 4-man sleds: same or negligible frontal surface areas, weight differential seems to make the difference, but sled runners are not P-Tex, and the extra weight supposedly "melts" the ice and lowers frictional drag. Am I way off base comparing apples and oranges?

No, you're not way off base. The terminal velosity of the bobsleds will be determined by the contributions in resistance imposed by the frontal surface area and the sliding resistance of the runners. Like with the skier, I suspect that the air resistance plays a bigger role at terminal speed.

When I'm skiing at high speed, it is the force against my upper body from the air that I feel much more than the sensation that my skis are dragging. I don't have to lean backwards to compensate for sticky skis, I have to lean forward to compensate for the wind pressing against my upper body.

I must assume that when we are talking about two skiers of different weight, we are also talking about there being a relative difference in the frontal air resistance, unlike the two and four man bobsled.

The purpose of my original question was to discover what exponential relationship there is between the way the gravitational force changes and the way air resistance changes as skiers get larger.

I think that's a fair question to ask and unfortunately I still don't have a clear answer. Any scientists out there, or skydivers?
Quote:
 Originally Posted by oldtimer xj guy- the facts on the hill do not bear out your theory-
I know they dont, for three reasons:

1) there is no such thing as a perfect mountain with no bumps
2) You cannot find two skiers that are identically talented.
3) You can play with wax and make up for the heavier guys additional friction.

But if it were possible to make everything identical and controlled, say using a computer simulation, I am pretty sure that you would find that the lighter skier will win.
Quote:
 Originally Posted by XJguy But if it were possible to make everything identical and controlled, say using a computer simulation, I am pretty sure that you would find that the lighter skier will win.
Consider the following web page:

http://www.glenbrook.k12.il.us/GBSSC...aws/u2l3e.html

And the quote:

"the amount of air resistance depends upon the speed of the object. A falling object will continue to accelerate to higher speeds until they encounter an amount of air resistance which is equal to their weight. Since the 150-kg skydiver (as opposed to a 100-kg skydiver) weighs more (experiences a greater force of gravity), it will accelerate to higher speeds before reaching a terminal velocity. Thus, more massive objects fall faster than less massive objects because they are acted upon by a larger force of gravity; for this reason, they accelerate to higher speeds until the air resistance force equals the gravity force."

If we look at the related animation:

http://www.glenbrook.k12.il.us/GBSSC...wtlaws/sd.html

In this example, 100% of air resistance is assumed to be coming uniquely from the parachute and it is further assumed that both the heavy and the lighter skydivers are using the same diameter parachute.

But while the 150-kg skydiver weighs 50% more than the 100-kg skydiver, what if the larger parachute was slightly less than 50% of the diameter of the smaller parachute. Which skydiver would reach terminal velocity sooner and would their final terminal velocities be the same?
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