That doesn't negate the fact that a heavier skier is at an advantage should they be skiing against someone with roughly the same technical competence.
Agreed, the "all things being equal" argument. My only point is that in the real world all things aren't equal, and that skiers will, consciously or subconsciously, employ different ways of steering their skis when the travel along cat tracks. It is this which accounts for most of the difference in speed, and consideration of other, physical or equipment, factors will be of less importance by at least an order of magnitude.
Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
altis wrote:
The summary is in the last equatio:
A = g*sin(theta) - mu*g*cos(theta) - (Cd*Ap*rho*V^2)/(2*m)
A = acceleratio of skier
g*sin(theta) = acceleratio due to gravity
mu*g*cos(theta) = loss of acceleratio due to snow friction
(Cd*Ap*rho*V^2)/(2*m) = loss of acceleratio due to air drag
Notice that 'm' (= mass of skier) only appears in the last term - and then in the bottom line.
From this we can say that most of the acceleratio of the skier is independant of mass. However, the loss due to wind drag gets smaller with increased mass. Therefore the heavier skier will go faster - slightly.
You trying to tell us something?
Well, the person's real but it's just a made up name, see?
Well, the person's real but it's just a made up name, see?
altis, I think your last sentence echoes what I've been trying to say
Thanks to all who have helped answer my query. I think that the final answer that makes most sense to me is...
Quote:
From this we can say that most of the acceleration of the skier is independent of mass. However, the loss due to wind drag gets smaller with increased mass. Therefore the heavier skier will go faster - slightly.
I note that several of you brought out the old chestnut about the increased pressure of skates on ice causes and increase in temperature and consequently a thin layer of water upon which the skis slide. Recently, I read a long discussion of this and it proved that the rise in temperature caused by the weight of the skates was far too small to melt any ice and the actual answer was that the top layer of ice molecules fail to bond effectively to the ice below. Effectively providing a layer of tiny ball bearings upon which the skate slides. I assume the same logic applies to skis on snow.
So..... more pies and a decent tuck seem to be the answer. 52mph top speed last year (NOT on a cat track!). I'll let you all know what effect the increased pie consumption has in a couple of weeks time
I note that several of you brought out the old chestnut about the increased pressure of skates on ice causes and increase in temperature and consequently a thin layer of water upon which the skis slide. Recently, I read a long discussion of this and it proved that the rise in temperature caused by the weight of the skates was far too small to melt any ice and the actual answer was that the top layer of ice molecules fail to bond effectively to the ice below. Effectively providing a layer of tiny ball bearings upon which the skate slides. I assume the same logic applies to skis on snow.
It maybe old but that chestnut is applicable to skiing. Put a substance under pressure and it heats up. You don't have to apply a lot of pressure to snow to achieve this. Ice skates and ice may be a different story.
Then you can post your own questions or snow reports...
Then you can post your own questions or snow reports...
I recall a similar discussion a couple of years ago where it was concluded that, other things being equal., a heavy but small skier would schuss faster than any other build. This seems to be what Altis' equation says.
Sometimes it's good to be dense.
After all it is free
After all it is free
Zero-G, Nope, I think I'm happy to stick my neck out on this one and say that I'm sure that pressure melting doesn't make sense. Consider this...
"So, ice melts when you apply pressure, but the effect is very small. You need to apply a pressure 121 times that of the atmosphere (1.22 MPa, to be specific) to lower the melting temperature by just one degree Celsius. Now how does this apply to ice skaters? In his explanatory text, chemist Kevin Lehmann of the University of Virginia tells us to assume in ice skater weighing 75 kg and the skate’s width to be 3 mm and its length 200 mm. “One can calculate that the entire gravitational force exerted on the area of one skate is only a pressure of about 12 atmospheres"
So that's how it applies to ice skaters. However, let's assume that ice skates have a surface area of 600mm X 2 = 1200mm sq. Skis have a surface area of approx 432,000mm sq. (1800 X 120 X 2). That means that when the skis are running flat they exert 1/360th of the pressure that skis exert. So, if skates can raise the melting point by 0.1 degree, then it seem to follow that skis would raise the warming temperature by 0.0003 degrees.
You could argue that friction melting plays a more important role, but all the articles I have looked at suggest the effect is still minimal.
Thoughts?
You'll get to see more forums and be part of the best ski club on the net.
You'll get to see more forums and be part of the best ski club on the net.
foxtrotzulu, you're assuming the same amount of pressure is required to produce the same melt rate of solid ice as that of loosely packed snowflakes. If you factor in the difference, I'd be interested to see the results.
Ski the Net with snowHeads
Ski the Net with snowHeads
foxtrotzulu wrote:
1. So, ice melts when you apply pressure, but the effect is very small.
2. You need to apply a pressure 121 times that of the atmosphere (1.22 MPa, to be specific) to lower the melting temperature by just one degree Celsius. Now how does this apply to ice skaters?
Thoughts?
1 and 2 are entirely different. In 1 you are increasing the temp by applying a small amount of pressure. In 2 you are decreasing the melting point by applying a massive amount of pressure.
The original Bang Goes the Theory programme had much more in it but is no longer available. At least that clip shows the highlights.
And love to help out and answer questions and of course, read each other's snow reports.
And love to help out and answer questions and of course, read each other's snow reports.
I think we over-complicating - this is simply Newton's law in action.
The force required to accelerate (or decelarate) an object is proportional to its mass, in the formula Force = Mass x Acceleration (f=ma).
In this case, if both skiers start the cat track at the same velocity, the force required to slow down the heavier skier is greater than the force required to slow down the lighter skier. The force in this case being all types of friction, be it wind resistance or friction on the base of skis.
So, someone twice the wieight would require twice the force to slow down at the same rate.
My guess is that the friction (force) experienced by the heavier skier is not proportionately higher than that of a lighter skier - this may be because typically they have longer ski, or simply there is not a straight line relationship between the mass and the friction (skis being relatively smooth things).
So the heavier skier slows down less quickly than the lighter skier (and therefore goes further and appears quicker).
As an analogy, imagine a heavy curling stone on ice and a similarly shaped (and similarly smooth) object made of polystyrene. Which will be going more quickly half way down the rink, and whcih will stop first, if they start at the same speed.
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
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
Zero-G,
Quote:
you're assuming the same amount of pressure is required to produce the same melt rate of solid ice as that of loosely packed snowflakes. If you factor in the difference, I'd be interested to see the results.
Yes, I'm assuming it is the same. As they are both molecules of frozen water I don't see what difference there is. I could be wrong, but I don't think so. Put it another way, the energy required to raise 1Kg of snow by 1 degree is probably the same as to raise 1kg of ice by 1 degree. Actually, I have just looked it up... the specific heat capacity of snow IS the same as water ice.
Thornyhill, You may have a point that 1 and 2 are different, although I can't help feeling that is more a result of the explanation than reality. However, you did misquote slightly. In 1 the effect is small, not the added pressure. In 2, the effect is also very small.
You know it makes sense.
You know it makes sense.
rg1, I think you are right, although this may not account for the fact that I seem to experience the same effect when going from a standing start. Perhaps there is no such thing as a standing start? By the same token would a heavy skier and light skier also accelerate at the same rate down a steep slope? I assume by your logic that they would not and the heavier skier would accelerate faster. Makes sense to me.
Otherwise you'll just go on seeing the one name:
Otherwise you'll just go on seeing the one name:
altis, OK, I'll bow to the BBC's greater knowledge which suggests that friction heating is the answer to why skis slide. But I am still a little dubious. There is a lot of debate out there that suggests otherwise, and I am deeply sceptical of the claim that a skier is generating 300 Watts of energy (which is automatically transferred into heat energy at the base of the skis.)
Poster: A snowHead
Poster: A snowHead
foxtrotzulu wrote:
Thornyhill, You may have a point that 1 and 2 are different, although I can't help feeling that is more a result of the explanation than reality. However, you did misquote slightly. In 1 the effect is small, not the added pressure. In 2, the effect is also very small.
You aren't trying to apply enough pressure to decrease the freezing point, which is the premise of the article you quoted. True, the article correctly states that the pressure required would be far in excess of the pressure available.
What you are actually doing is applying a small amount of pressure which will increase the temperature. The pressure doesn't need to be anywhere near as great to have more a substantial effect on the temp. Much easier to demonstrate with gases than liquids and solids (Boyles Law - p1v1/t1=p2v2/t2) but the same principles apply, although not in direct proportion.
Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
Quote:
Boyles Law - p1v1/t1=p2v2/t2
Technically, that expresses Boyle's Law and Charles's Law combined.
Well, the person's real but it's just a made up name, see?
Well, the person's real but it's just a made up name, see?
foxtrotzulu,
Yes, the heavier skier will accelerate down a steeper slope faster than a light one for the same reason - the friction experienced does not increase proportionately to the mass of the skier (skis being relatively smooth or low friction (which may well be due to melting....)).
As an example, if we have two skiers, on the same slope and same skis, one of whom is twice the mass of the other.
The heavier skier requires twice the net force to accelerate at the same rate as the lighter skier.
Let's assume that the friction rises at only half the rate of increase in mass. Gravitational force is proportional to the mass of the two objects (in this case the person and the Earth, so the difference is just the mass of the person) - obviously the actual propulsive force depends on the angle of the slope, but since both skiers are on the same slope I am just calling this gravity.
For the smaller skier, in simple terms, the net force is gravity - friction, acceleration is therefore = (gravity - friction)/mass of light skier
For the heavier skier the force is 2 x gravity - 1.5 x friction and acceleration is (2 x gravity - 1.5 x friction)/2 x mass of light skier, or (gravity - 0.75 friction)/mass of light skier
So in this case, acceleration of the heavier skier is faster by 0.25 x friction/mass of light skier
Simples....
All this of course rests on the assertion that the friction does not rise in proportion to the mass, which feels correct, but I'll let the real scientists get into why that would be....
The physics is getting beyond me now, so I'll have to ask someone with more ability than me to do the maths. (please note the 's' in maths!).
Assume a 75kg skier whose weight is spread evenly over an area of 4320cm sq (see guestimates above). This equates to 0.17 Newtons/cm sq. Who can calculate the temperature increase on snow (specific heat capacity of 2090 Joules/Kg per degree Kelvin).
I appreciate that a skiers weight is never spread evenly over that entire area, but let's work this one out and then guess at a 50% loading for a slow flat schuss.
Anyone bored enough to try and work this one out?
Anyway, snowHeads is much more fun if you do.
Anyway, snowHeads is much more fun if you do.
rg1, I think you have nailed my original question. Thank you. See if you can help with the supplementary question of why skis slide in the first place. Is it:
1. Friction melting that causes a film of water to act as a lubricant.
2. Pressure melting that causes a film.......
3. 'surface melting', that has nothing to do with melting as we usually know it. You'll need to look it up!
4. A trail of low friction pie crumbs left by the snowhead in front.
5. All of the above.
The short of it is, those of us who are lightweights have no chance of beating the pants off the heavyweights but we'll certainly give it a good go!
Then you can post your own questions or snow reports...
Then you can post your own questions or snow reports...
foxtrotzulu,
Now you are getting into areas way above my pay grade. The simple answer that I like is that skis are relatively smooth things and snow is a relatively smooth surface, so friction between them is relatively low, and therefore skis slide quite easily.... But I am sure this is way too simplistic, and some better explanation involving pie crumbs is much more likely....
After all it is free
After all it is free
Quote:
skis are relatively smooth things and snow is a relatively smooth surface
I've just heard the BBC tell me that snow is pretty HIGH friction stuff, so no idea where that leaves us.
Interestingly, I have just learned that skis don't work when the temperature falls to -40C. Maybe the pie crumbs freeze too hard?
You'll get to see more forums and be part of the best ski club on the net.
You'll get to see more forums and be part of the best ski club on the net.
foxtrotzulu wrote:
Interestingly, I have just learned that skis don't work when the temperature falls to -40C. Maybe the pie crumbs freeze too hard?
Maybe you aren't heavy enough to cause the pressure increase required to melt it then? Solution? More pies
Ski the Net with snowHeads
Ski the Net with snowHeads
More importantly was Galile OK with his name change?
snowHeads are a friendly bunch.
snowHeads are a friendly bunch.
Axsman,
Quote:
More importantly was Galile OK with his name change?
Absolutely priceless!!
On a related matter, can I just apologise to ALL snowheads for propagating such an incredibly dull thread as this when you could all have been having far more fun discussing Wayneo's name change.
And love to help out and answer questions and of course, read each other's snow reports.
And love to help out and answer questions and of course, read each other's snow reports.
Wind
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
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
abc wrote:
Wind
That would depend on the legume content of the pie surely?
You know it makes sense.
You know it makes sense.
foxtrotzulu wrote:
Axsman,
Quote:
More importantly was Galile OK with his name change?
Absolutely priceless!!
On a related matter, can I just apologise to ALL snowheads for propagating such an incredibly dull thread as this when you could all have been having far more fun discussing Wayneo's name change.
Apology accepted. Try not to do it again.
Otherwise you'll just go on seeing the one name:
Otherwise you'll just go on seeing the one name:
foxtrotzulu wrote:
The physics is getting beyond me now, so I'll have to ask someone with more ability than me to do the maths. (please note the 's' in maths!).
That's because people are totally over-complicated things by introducing all the MINOR factors while discounting the major one as "can't make that much a difference". It can.
They were mentioned quite early in the thread. Wind resistance!
If you look at those formula quoted, there're 1 term to speed up and 2 terms to slow down. If there's no air (no 2nd term), the masses would cancel out and 2 skiers of different mass would accelerate at the same rate (which is exactly what happens in vacuum). So the RELATIVE value of air resistance to mass induced acceleration is the most significant difference.
What we all consider "slow" speed while skiing is actually quite fast, even at a cat track. Ever come upon someone who crashed right in front of you? You quickly realize you have extremely short time to get around the stationary object! People who had clocked their speed reported about 10-15mph even on flat bits of cat tracks. At that speed, wind resistance is significant. Ever notice how any loose clothing flap around even on cat tracks?
Keep in mind it doesn't take a huge amount of difference in acceleration rate to produced a much bigger difference in speed, because the acceleration is cumulative. And the distance traveled is also cumulative of speed. So a tiny bit of acceleration would result in a heavier skier traveling faster and faster, and arriving at the end of the cat track quite noticeably ahead of the lighter skier. And the longer the cat track, the bigger the difference.
A lot of the other factor mention, such as the snow melting rate or what not, would be entirely over-shadowed by the quality of the wax job and the small variation of ski length/width.
For a lighter skier (I'm one), I tuck if I need to keep the speed up. By reducing my frontal area, I can pass heavier skier standing upright.
Poster: A snowHead
Poster: A snowHead
As a mechanical engineer, I've explained this quite a few times. Simply put:
The force (gravity) acting down the hill is proportional to mass (F = m x g sin(theta))
The air resistance is proportional to surface area (F = 0.5 x p x A x V^2 x Cd)
Now, if you take 2 people of similar proportions but different "sizes", then m is proportional to the cube of the person's "size", whereas surface area is only proportional to the square.
Bigger people therefore have less air resistance relative to their mass, hence they go faster.
A bit of a simplification, but gets my point across...
Obviously A snowHead isn't a real person
Obviously A snowHead isn't a real person
Now if only we had a physics lecturer familiar with the works of Galile.
Well, the person's real but it's just a made up name, see?
Well, the person's real but it's just a made up name, see?
Aerodynamics, and ski angle count for the difference. ice temp, air pressure, and lunar tides count for bug all.
So, aerodynamics (and pies) are the definitive answer. But..... did we ever sort out why skis slide in the first place. Search the interweb and you'll come up with any number of contradictory answers. Maybe I should pm Wayne and ask him. He's bound to know.
Anyway, snowHeads is much more fun if you do.
Anyway, snowHeads is much more fun if you do.
foxtrotzulu wrote:
So, aerodynamics (and pies) are the definitive answer.
foxtrotzulu, You might get him to pop back and put in a brief appearance, sort of like a ....... cameo
Then you can post your own questions or snow reports...
Then you can post your own questions or snow reports...
Quote:
sort of like a ....... cameo
It's taken me an entire day, but I got this in the end. Very good! Brav'o'!
After all it is free
After all it is free
Although not skiing i think this video demonstrates the impact of weight on speed down a slope (although there could be an explanation based on circumference or some such) with the heavier tyre being the fastest http://youtube.com/v/-vj0ld8rCEs
You'll get to see more forums and be part of the best ski club on the net.
You'll get to see more forums and be part of the best ski club on the net.
The F1 tyre really shows the significance of air resistance.
FAQ
Poster: A snowHead
