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# Sidect calculator...what gives?

I can put a ski into 3 different sidecut calculators and get 3 different results, which is usually different than what is shown on the ski. We need a definitive calculator.
Which ones are you using?

p-mans has generally been pretty accurate when I toyed with it. Remember these are all approximations. At least the ones I know of...

Are you seeing massive divergence or +/- 5 or 10% ?
Quote:
 Originally Posted by Philpug I can put a ski into 3 different sidecut calculators and get 3 different results, which is usually different than what is shown on the ski. We need a definitive calculator.
The "definitive" formula used to be published with the alpine rules by USSA. I don't have any reason to believe it has changed.

Page two of this PDF

One reason you may get different results from what is marked on the ski is that dimensions marked on the ski are not always correct. Also there isn't any standard I know of for this measurement outside what is in this PDF and that I believe to be what FIS uses, so if a marketing d-bag decides 14m sounds better than 16m there isn't anything to stop him unless it is a race ski meant for use in competition.
Even the "definitive" USSA formula is nothing but a convention, and you can definitely question their definition of tip and tail lengths as a fixed percentage for all skis. Obviously that's not true for all skis nowadays. But it's one possible convention you can standardize on, even if not truly accurate.

If you want to do it absolutely right, you need to know the exact sidecut curve (ie, the equation for it) and then calculate the radius of curvature using Calculus. It's actually quite simple, but the problem is that nobody other than the ski designer will know that curve. But Phil, maybe you can get access to that info. In lieu of that, most formulas assume a cubic for the ski sidecut, which only requires tip, waist, and tail dimensions and the lengths between them. Where the formulas may differ is the definition of the lengths from tip to waist and waist to tail; they may only input a single length and then make assumptions like the USSA formula for tip/tail geometry.

When I get a chance, I will derive and scan the general formula. You can then make your own assumptions, or if you know the various lengths directly, then calculate R with no assumptions.
Tip & tail shape can make a huge difference. I would add a few CM to any race or race-like ski and subtract up to 10cm for twin tips.

If I do this, Physics-mans calculator is accurate and consistent with factory data.

Michael
OK, here's the most general formula for radius while still assuming a cubic fit:

http://hunter.pairsite.com/craig/Scan001.PDF

At a minimum, you need to know the width of tip, waist, and tail, and the distance from tip to waist and tail to waist. A simplification is given when those two distances are equal, and that's the same formula PM's calculator is based on, though he makes assumptions about tip/tail geometry (akin to, but not the same as the USSA formula).

Here's a spreadsheet with the general formula derived in my PDF:

I put a few example skis in there, with educated guesses for the various lengths. If you have actual measurements for the tip-waist and tail-waist lengths, then the calculation should be very realistic.
Here is another one that helps, but is still different... http://members.fortunecity.com/hhitme/skiradius.html
Quote:
 Originally Posted by skier219 Even the "definitive" USSA formula is nothing but a convention
Right, but it is the only convention that matters. (at least if you are a ski manufacturer and your stuff goes into an equipment tent)

Interestingly the FIS chooses not to publish that particular convention in the equipment rules. The FIS equipment rules leave a lot of things to the imagination. So it could be a different convention altogether they are actually using.
Quote:
 If you want to do it absolutely right, you need to know the exact sidecut curve (ie, the equation for it) and then calculate the radius of curvature using Calculus.
Even such a calculation must rely on convention to some extent AFAIK. It isn't going to be useful to calculate the radius of curvature at fifty different points along the ski using accurate info, as you still then have to come up with a single number to print for the sake of comparison. So somehow you must represent a mean RoC of sorts, and I don't know how you produce a meaningful, comparable result without some convention.

(or is there some real pretty result I'm unaware of? I know enough calculus to bury my head in the sand, and not much more.)
Garrett, I think calculating the RoC at the waist would make the most sense, but you are correct in noting that may itself be arbitrary. But I have no idea what kind of shapes are used for sidecuts these days; it's entirely possible that they are using a circular arc which would have a single RoC. It would be interesting to get some mold lines from a ski manufacturer and see what kind of shape is used.
No one really talks about it much with skis (at least not since back when VĂ¶lkl started marketing "3D" sidecuts in the late 90's) but snowboard marketing lit pretty commonly refers to different types of curves being applied to different boards in the line. With the extremely short radius most snowboards have, the differences in the shapes are probably more noticeable. Can't say I know enough about snowboarding to verify that suspicion.

It would be interesting to know more about the curves in use. I read a paper that said sidecuts were typically elliptic curves (which are special cubics, right?) but I don't know how accurate that was, and I can't remember where I read it now.
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