100% Carve

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

Dave Mac wrote: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.

Thats exactly what I worked on during my season in Soldeu. Although I did alternate between Euclidian and Bacchanalian Space!!!

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.

rainmaker wrote:
Am not expert by the way, and I never read that article referenced by some dude earlier
And again, I am not an expert.

If you want to refer to a post by another forum member, it's useful to use their Forum name. It's on their post.

I actually believe 100% carve would be fastest way but is unachievable as you are constrained by your skis shape. Whenever you want to turn sharper than ski radius you are forced to bring in an element of pivot or skid. This is why on a nice wide run a strong skier can 100% carve, picking up massive speed as they go. Unfortunately having to maintain maximum attainable speed and navigate gates requires compromise (unless you were to change skiis between gates) and different elements of steering. This is what makes watching racers so exciting, blend of massive power and commitment as they do their stuff.