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# Geometrical analysis of ski tracks - Page 4

PhysicsMan,

May I kindly request to work on a specific and simply data that will make sense to many of the colleagues out here. What really is and should be more interesting for any coach is what can be applied to almost any racer regardless of physical build, skill and weight. The question should really be when, where and how much the forces will change on a skier as the slope will increase the steepness, assuming the turn radius remains the same. It is far easier to overcome gravity on a medium hill than on a steep slope which will cause us to stand longer on the edge within a turn. So would it not be interesting to know at what point in a turn on a specific steepness is the influence of the forces at peak level? How far will it shift when it gets steeper or more flat, or simply does it even change at all?
This data will or should tell you far more about an approach and tight line within the gates and what is faster.
All the percentages on how much the outside ski needs to be weight versus the inside ski and when to change to the next outside ski is really completely situation dependent and just too vague. Besides it changes from skier to skier partially because of difference in skill or simply personal preference.
Thanks for your consideration.

MfG.
BigE, does this help?
Is there a link to PM's spreadsheet on the wiki?  I can't find one, and the one from the thread is dead.
Thanks Martin.  That's very interesting from the technology point of view.
However, It's too much data for my purposes at the moment.
• I am going to get my GS skis out and draw on to the wall the shapes they make for a range of edge angles .  Then I'm going to make cut-outs in cardboard and calculate radius of turn for each edge angle.
• Then, I'm going to define where the acceleration goes from Linear to rotational.
• Many ski teachers theorise that the maximum speed down the hill must be in the fall-line.
Looking at lemaster and Gurshman stop-motion work and it's obvious it's the slowest point on the track is through the fall-line, however it's the point of max aceleration of the change of direction.
The linear acceleration down the hill in the GS comes in the glide after the turn is finished.  (I'm assuming there's sufficient space between the gates in this.)
I think this is a crucial point.  This is where the control of line comes.
This is the difference between piste performance turns and GS turns.  The GS turn at the vertex is relatively short radius - just a couple of metres at most.
Sorry to all who already knew this.  I knew it too, I just never thought about it.
I also saw the other huge thread on snowheads, but as usual, all calculations seem to make a big assumption that skiers in gates go from one to the next in a big circle.
Thanks to all for contributions.
D
Apologies, BigE -- that was one of my early wikis that I forgot to go back and fix -- will do so today.

In the meantime, here's the link to the Physicsman's spreadsheet
Nolo, thanks, but that's not it.

That's the ski radius sidecut calculator.

The spreadsheet that is supposed to be in this thread is the one where you enter the width of tracks and space between your legs and the spreadsheet spits out drawings of the tracks and graphs of edge angles.
Darn. I'll look around some more tomorrow. I have it somewhere.
I hope you find it. That was an excellent spreadsheet.
Thanks to dchan, the spreadsheet is now appended to the Geometry of Ski Tracks wiki.

I am a HS Math teacher attempting to inspire my class prior to Xmas break.  We just finished sinusoidal modeling with the usual models of a Ferris wheel, daylight hours, AC, tides, predator/prey.  I still have a few students who are not buying into the content asking the usual, "when will I ever use this?"  They could also use a review of parabolic modeling prior to midterms in Jan.  I came across your thread and thought this would make a great activity.  I was thinking of bringing in my 20+ year old skis as well as some new parabolic designs and giving a brief overview of how ski products have changed over the last 2+ decades and how that relates to the skiing industry.  Then I thought I would use some of your data and give students the zeros (centerline) and min/max values (gates) and ask them to represent a left/right turn sequence as a sinusoidal function or as a piecewise quadratic function.  They could then discuss which path is more efficient (what does efficient mean to them?) as well as which model was easier to create and which model would be easier to manipulate.  I am trying to promote the field of engineering especially to the females.  Many of these students think they want to major in engineering when they have no hands-on experience . . . or students with great mechanical hands-on skills don't believe they are smart enough to major in the field.  Also, I have students who will not be going on to college who have plans to become HVAC apprentices who don't believe this material will benefit them.  I need some inspiration!  Do you have any suggestions for how I can implement this activity for HS seniors?  They have TI-83/84s at their disposal and I have a projector and Smartboard in my room.  Thanks!!!!!!

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