Originally Posted by BigE
I think a couple things go on with the model. It's ONLY capable of laying down carves -- no skids, no redirection. As far I as understnad, the only thing that is creating the different curvatures is tipping angle. So, if you too are laying down railroad tracks and using ONLY tipping to do it, your tracks will be very very similar to those of the model. I can't see it any other way.
Originally Posted by Helluva
Interestingly BigE, ask yourself this: Can railroad tracks be made by only tipping? At low edge angles I think the response would be a solid "yes." However, at high edge angles, where this error seems to be occurring (and as PM pointed out) I think it is safe to say that the tracks are formed by more than just tipping... although if it were possible to do such a thing (only use tipping) you may end up in some contorted position at the apex when using high edge angles - unfortunately I don't think the mechanics of the human body will allow it...
BigE / Helluva – My analysis is much “dumber” (ie, no assumptions) than either of you could possible believe.
(... at least as evidenced by your posts above...)
Until the very final step is performed (ie, attempting to convert L & R radii of curvature into L & R edge angles), no assumption is made about length or sidecut of the skis, nothing assumed about the boots or anything further up the kinetic chain, nothing about forces or torques acting on the skis, etc.
Until that final step, all the model does is make sure:
a)The path of the inside ski always clears the gates
b)The spacing between the ski paths conforms to the triangle diagrams that Helluva has posted.
c)The edging angle in those diagrams smoothly goes from zero degrees at the transitions to the maximum value specified by the user (at the apices); and,
d)The average cross hill position of the L&R tracks always follows a sinusoidal curve.
Once the unique pair (ie, L&R) of tracks is established which meets the above criteria, the model then calculates the radii of curvature of those tracks at each point in the turn.
Until this point, the model doesn’t care if the skier had to stand on his head, had to do a break-dancing move on the snow, or had to wave Harry Potter’s magic wand to meet constraints (a) – (d), above. It simply says that if these constraints are met, THEN: “Here’s the tracks that must have been laid down, and here’s the location and radius of curvature at each point along each track”.
This lack of assumptions about what is causing the skis to move to meet the constraints is true all the way up to 89.999 degrees edging angle. The complete disregard for what physical actions had to be performed to meet the above constraints is what makes the model so “dumb”, but it is also exactly what makes it so powerful and general.
The final step in the spreadsheet is an attempt to convert the instantaneous L&R radii of curvature into individual edging angles for (a) pure carving, (b) on skis of a specified sidecut radius, (c) on hard snow, (d) tipping only, etc. etc. I regard the main result of my model as the graphs showing the position and radius of curvature of the tracks, but I decided to throw in this final step almost an afterthought to give users some idea of the real edge angles (and differences between them) that might be encountered. As I said in an earlier post, once all the things associated with a physical mechanism to lay down the tracks are thrown into the model (ie, carving, sidecut, blah, blah), then anything that follows is much more debatable / suspect than what I regard as the main, least disputable output of the model, ie, the track geometry -- the graphs of L&R radii of curvature as a function of position in the turn.
Tom / PM