100% Carve

Smart,,interesting skiers on this site !

Also soooooo, helpful !

Pavel

Pavel,

Next time we are at SR, I'll get some video of you so all can see the true meaning of "smooth & graceful" !

Trencher, the slow motion is a great teaching aide!

Now only if winter would stick around a few more days.....

Mike

MIKE,

Noticed those Atomics in your picture !

I thought you had graduated to a "better" ski ?

Rumors are that you are really "carving" on a new pair of,,,,,,,!!!!

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!

Doesn't the Brachistochrone Curve assume no friction? In skiing, consideration of the loss of energy due to the interaction of skis and snow, and also the need to time weighting and unweighting might require a different course. Not that I know anything about physics (really) :lol:

Trencher wrote:Doesn't the Brachistochrone Curve assume no friction? In skiing, consideration of the loss of energy due to the interaction of skis and snow, and also the need to time weighting and unweighting might require a different course. Not that I know anything about physics (really) :lol:

Yes, the Brachistochrone Curve does assume no friction.

Moreover, the theory only applies from an an initial point of zero velocity, hence Rainmaker can be taken to be partly correct, (allowing for the friction error), but is only true from an initial start point of zero velocity.

Hence, assuming an impossible but theoretical frictionless ski, the theory only holds for a single turn, when starting from an initial point with zero velocity.

I thought everyone knew that?

On the other hand, Rainmaker is spot on with Calculus of Manifolds methodolgy ~ this being employed within Euclidian Space Theory. It is better treated with differentiable manifolds ~ these are embedded within Euclidian Space, and are at a level that can be understood by many.
Moreover, a differentiable manifold is a topological manifold. In addition, it is more common to define Euclidean space using Cartesian coordinates, eminently suitable for describing ski turns in a geometrical situation.
So, well done Rainmaker on that one.

I'd like to be there when you explain all that to Silvan Zurbriggen!



I suspect Rainmaker came across this http://quantum.u-aizu.ac.jp/Magazine/Slalom_en.htm