Every so often I like to drive my self nuts looking for THE formula to calculate the radius of a ski. SnoCadX and BoardCrafter must use different formulas because if you input the same dimensions of a ski into each of the tools they give a different radius. So I searched the web and found a formula that Stockli published. It has a different formula giving a different radius. Plus when I used their formulas on a some of the skis the radius doesn't equal what they publish. Its not off my a couple CMs but by meters. And if anyone has the Excel spreadsheet that was on this site from years ago to calculate flex, it will give you a different radius but it's very close to SnoCadX. The spreadsheet uses geometry. Stockli uses algebra...
So I guess it depends on how the ski is designed determines how the radius is calculated since some skis are designed with multiple radi. I saw on Stocklis site the tip and tail lengths are calculated as a percentage of the length from the mid point to the tip and midpoint to the tail.
So if you're using a specific tool just go with what it tells you. Or drive yourself nuts
Here's the stockli formula. If you use the dims from the Race line of skis you'll see the formula doesn't give the same radius as what is published. So not sure what line of skis they use it for.
Calculating the Radius
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Re: Calculating the Radius
Don't get too hung up about the "radius" of a ski. The method you found that Atomic published is the same as how FIS requires the measurement to be made to determine the legality of using a particular ski in competition (gotta keep a level playing field). Do a search for the FIS Specifications for Alpine Competition Equipment and for ISO 6289. A new version of the FIS document is published every year as equipment requirements change. The "radius" that is calculated with this method is simply a constructed arc of constant curvature that passes through 3 chosen locations/points in space. The 3 points are those at the narrowest point of the ski (waist), and measuring from the waist to a location 90% of the distance from the waist to the tail, and at a location 80% the distance from the waist to the tip. The 90% and 80% measurement remove the effect of tip and tail treatments (ie curving the ski back in at the tip and tail) and the resulting calculated radius is one of the items that determines if a ski can be used for a particular racing discipline.
What actual geometry is used for the sidecut of the ski is arbitrary. It could be a a true radius as a segment of a circle, or a segment of any other conic section. It could be a spline function or any other smooth arcing "swoop". The only requirement per the FIS regulations is that it is that between the tip and tail measurement locations "continuously differentiable and monotone curved arch should remain sustained (for example, without a flex point between these two positions)."
The regs then go on to clarify:
"To achieve the requirement stated above the identification of the radius of the side cut must be as follows:
• at each point along the distance from bM (waist) to bHR (tail measurement) the width must be smaller than at bHR .
• at each point along the distance from bM (waist) to bVR (tip measurement) the width must be smaller than at bVR .
Should one of the criteria set out above not be fulfilled the related ski does not meet the specifications."
What actual geometry is used for the sidecut of the ski is arbitrary. It could be a a true radius as a segment of a circle, or a segment of any other conic section. It could be a spline function or any other smooth arcing "swoop". The only requirement per the FIS regulations is that it is that between the tip and tail measurement locations "continuously differentiable and monotone curved arch should remain sustained (for example, without a flex point between these two positions)."
The regs then go on to clarify:
"To achieve the requirement stated above the identification of the radius of the side cut must be as follows:
• at each point along the distance from bM (waist) to bHR (tail measurement) the width must be smaller than at bHR .
• at each point along the distance from bM (waist) to bVR (tip measurement) the width must be smaller than at bVR .
Should one of the criteria set out above not be fulfilled the related ski does not meet the specifications."

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Re: Calculating the Radius
Great info! And that clarifies the 80% and 90% calcs. I thought it was saying the tip and tail were 80% and 90% in length which would be pretty long for FIS Racing Ski.