Yes It's Davey again.
Hi Noodler. It was an old post wasn't it? But side-cut radius limited turns is still a current myth people choose to believe.
Hi Ghost
The theory that you can't carve a ski tighter than the sidecut radius is not correct in my humble opinion.
What your paper template model theory is proving is that if you park and ride a ski on a static circular arc, you get limited. But that's no surprise, is it?
If you are working the ski like an expert and get a cos of (for instance) 84 Degrees - well you are talking rTurn of one-tenth of the rSidecut even by your cos formula, but it is not as simple as that. It isn't a circular arc. It's a net effect of the combination of ever-decreasing circles.
I'm attempting to show by observation that the parabolic track carved in the GS Course by a skilled racer can allow them to carve perfect tracks that have a progressively Decreasing radius up until the shortest radius at the apex. Then the tight radius progressively increases again - allowing the linear speed to increase.
Illustration
Look at these GS race railtracks below. (skis are 21m rSidecut)
- First-off it isn't a circle.
- Second, it's tight. Looks like about 1.5m to me.
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There is no way that the minimum radius seen here is limited by the ski. If you load up the ski from tip through middle through tail on an ever-increasing edge-angle, you can carve clean tight parabolic arcs of an ellipse. See below.
You see: The simplistic calculations are for angular acceleration of zero. i.e. a circular arc. Make a parabola with a constant (nonzero) angular acceleration (Means angular velocity (rate of change of direction) is speeding up and slowing down), and you arrive at a tight apex radius like in the image below.
I have spent years trying to understand what the coaches have been trying to teach me. I've discovered that they are regurgitating error-based theory that they haven't worked through.
Going back to first principles with the Classical Newtonian mechanics is a revelation. This is where the racers get their slingshot out of the gate. It won't work when you make plain semicircles.
Cheers, and happy carving!
Edited by Davey - 11/5/09 at 3:29pm