Originally Posted by majortato
I think in your 'theoretical world' where the skiers are exactly the same, and take the exact same line through a course (not possible btw, with different length skis...but we're being creative here), you can simplify this problem to a wax race straight line between a long and short ski then.
Let's make this really simple...the terrain is perfectly smooth and the snow is perfect and very hard. The skier experiences no fear and controls both skis exactly the same. So will the longer ski offer a higher top speed or accelerate faster? Short answer...No...they will be exactly the same. The extra surface area does not increase or decrease friction because the pressure is also spread out with larger surface area.
However...that is probably simplifying it to the point where it's useless to talk about. We've turned it into a physics 101 problem. In the real world, the answer is yes, the longer ski will be faster...even if you simplify it down to a wax race. A lot of factors come into play...some big ones are:
- more spread out pressure across larger surface area = ski won't dig into snow as much = less drag
- longer ski will glide over minor terrain inconsistencies much better = less drag
- longer ski has more inertia and will resist twisting = more stable = higher speed
What does this equate to in say a 1 minute drag race? Tough to say...it's very dependent on the conditions and pitch of the slope. I would guess a few seconds on average.
This seems like the best answer from a raw physics/glide perspective.
Theoretically, friction between two moving surfaces being pressed against each other is proportional to (pressure * surface area * velocity). If the weight pressing down on the skis stays the same, this product also stays the same as the surface area of the skis change. So for straightlining on a flat ski I wouldn't expect to see a significant difference between a longer and shorter ski.
However, the 'friction' on ski edges during a turn (on hard snow) is being applied to a hard metal surface lubricated with a thin layer of compressed water digging into snow/ice, so it may not be such a linear relationship. You need a different guy for that -- I can tell you a bit about semiconductors and MOSFETs, but not fluid dynamics.
If you just care about straight line top speed I suspect that wind resistance dominates, since that is roughly proportional to (cross-sectional area * velocity^2). Probably the base/wax setup also matters more than the length per se.
In terms of a race course, in a 'speed'-type course (SG/DH) a longer ski will be more stable/controllable at speed, enabling the skier to take a more aggressive line. In a 'technical' course (SL/GS) at a certain point a longer ski will be slower, because you won't be able to take as tight a line between closely spaced gates at lower speeds. That will be a much, MUCH bigger factor than a tiny difference in drag on the edges.