Messages posted by : rainmaker
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Brucie has the right idea.
First one typo, Calculus of Manifolds, is known in its simpler forms (and it is not simple) as Calculus of Variations. Yes, while the basic Brachistochrone Curve solution is based on a frictionless surface, it is valid for surfaces with friction too, but introduction of friction creates many other complications, basically everything leads to fluid dynamical system like pde's and so small variations can lead to big changes in the solution. Also, the solution is deeper and holds even when there is an initial velocity different from zero. Point I was trying to contribute in this discussion was simple: (a) straight line representing shortest distance down a slope is NOT the fastest way (b) world class and other good racers know that, and find that cycloidal path, friction and all, not always perfect but they know, that is what they train for, and that is how they find the "thin line". (c) there is a reason when one watches racers closely, depending on the race, i.e. GS, vs Downhill vs. Slalom and all that, you can see where they turn high and early, and in other cases turn very late using pivot transitions etc. Am not expert by the way, and I never read that article referenced by some dude earlier but now I have, and I thank you for it, good piece for sure. Not all correct, but not a bad effort, since the entire enterprise is an inexact, hard to define problem. And again, I am not an expert. |
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Actually, the fastest path for an object subject to gravitational forces on an incline is defined by the Cycloid curve, and this problem is called finding the Brachistochrone Curve. It is solved using methods called the Calculus of Manifolds (i.e. in engineering and at a more basic level called Calculus of Manifolds). That is why the "thin line" between gates is not the straight line but the brachistochrone curve, which is a particular cycloid. Great skiers know how to find that from training, instinct and they just "got" it!
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The snow looks so good, when did you folks go? And also it does not look uber-difficult, so intermediates could ski it. Food for thought for next time. Another thing, is there a map you could post which gives a reader some orientation where you are say relative to WB. Excellent filming, and the snow is so good.
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on ski chatter: fyi
http://www.j2ski.com/ski-chat-forum/posts/list/12584.page |
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Last time he was on this forum, I think he was 7 years old. This time because of conditions, i.e. tons of snow but hardly any fresh, the 9 days straight we skied was more touring, than handling serious gnar, because even the uber-experts were not going there as snow had hardened into spring thaw and hence falls were likely of high consequence. Anyway, do not miss the world's highest meltdown at 7300ft ! Note video is 10mins but gives you an idea about WB. Young man skiing is now 9 years old.
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