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# Ski Radius Calculator

K = measured length of straight line between tip and tail
H = sidecut height (depth)

R = ((K*K)/(H*8) + (H/2))

How:
I took a long staight aluminium beam and used that for measuring when ski was updside down on the table redy for waxing.
Do have a wall:
Tie your ski stopper up. Place your ski on the floor, bottom down, and press it against a straight wall. Measure how many mm there is between skis edge and the wall and whats the distance between were your tip and tail touches the wall. Remember edges on bottom, not top of ski.

My new 161cm Head iSL RD r=11,5 measures:
K = 1,46m (146cm)
H = 0,022m (22mm)
R = ((1,46*1,46)/(0,022*8))+(0,022/2) = 12,12m
There is a slight difference of 0,62m. Something like 5% bigger r.

My sons 130cm Elan r=10m measures:
K = 1,16m
H = 0,019m
R = 8,86m
Here the difference is much more 1,14m. In % that is about 11% less.

My 180cm Olin powder and back country skiis measures:
K = 1,635m
H = 0,015m
R = 22,28m

Calculate your own ski radius or send me your measurements K and H and Ill do it for you free of charge. Post here some of your results and lets see how far off manufacturers figures are. Offcourse this is just a mathematical formula based on a true arch. A ski is allways cut unevenly to give it other properties as well.
Why don´t you use the preciser variation of the FIS method:
contact legth squared divided by: 20x (tip width + tail width - 2x waist width)
To get most precise results you need not the official tip width (which is often the ski´s maximum width outside of the contact) but the real width in contact points, especially when dealing with a hard-snow ski (little or practically no penetration into the snow surface).
Are you measuring between the widest part of the tip and tail, or the overall length of the ski? And you should be measuring the actual (curved) length of the ski, not the chord length.

Also, even if you're measuring from the wide part of the tip to the wide part of the tail, you're introducing inaccuracies. The natural parabolic arc of the ski has stopped and turned inward before you reach that part. The "actual" tip width if you continued the same parabola would be wider than the actual ski tip.

Seems like a better idea would be to have someone stand on the ski while it's on the floor and measure the distance between the point on the ski where it looks like it starts curving back towards itself on the tip and tail. Obviously this is going to be relatively inaccurate. Can't you just ask the manufacturer?

### try this one

Or try this spreadsheet by Tom, (Physicsman)

other calculators
Looks like PhysicsMan uses a "fudge factor" that seems to closely approximate the inaccuracies, which seems to work quite well.
[nevermind, used the wrong measurement for H)

Hm, if I plug the measurements for my Volant Souls into this formula I get a radius of about 7 or 8 meters..
A few thoughts:

I believe the original poster's method is almost the same checkracer mentions. The only difference is that the original poster added h/2, which is more correct, though the difference is obviously minor. Half the sidecut depth is something in the range of 10 millimeters, and the radius is in the range of 15 meters.

The actual FIS version is different, and -- as far as I understand it -- less accurate. It uses the actual waist to tip length and actual waist to tail length (rather than just the overall length), but it arbitrarily uses the point 80% of the way from the waist to the tip (and 90% of the way from the waist to the tail) as the place to measure width.

The original poster is using "unwound," rather than chord length, because he says to "press it against a straight wall," thus flattening the camber out. At least I think that's what he meant.

Another, perhaps mind-numbing, thread:

http://forums.epicski.com/showthread.php?t=17913
If you're so inclined, you could use this:

R = Sqrt [ (Df^2/2Lf + Lf/2 + Dr^2/2Lr + Lr/2) / (Df/Lf + Dr/Lr)^2 + (-Df/Lf * (Df^2/2Lf + Lf/2 + Dr^2/2Lr + Lr/2) / (Df/Lf + Dr/Lr) + Df^2/2Lf + Lf/2)^2 ]

Making it a tad easier to read and caculate:

Ix = (Df^2/2Lf + Lf/2 + Dr^2/2Lr + Lr/2) / (Df/Lf + Dr/Lr)
Iy = -Df/Lf * Ix + Df^2/2Lf + Lf/2
R = Sqrt (Ix^2 + Iy^2)

Where
R = radius
Df = Depth of sidecut in front = 1/2 of (width of widest point toward tip - width of waist)
Dr = Depth of sidecut to the rear
Lf = Length of front, i.e. distance from waist to widest point toward tip
Df = Length of rear

There's no built-in correction for units, so you need to use the same units all the way through (that is you can't use millimeters for width, centimeters for length and wind up with the radius in meters ... )
jonnythan - what are your Volant Souls mearuements? Yes, you are right, the tail and the tip does flatten out a bit. Left my skiis at the ski-school today so I must make new measurements tomorrow.

If I use physicsmans formula for my Heads I get 11,4m. My formula gives 12,2m and the factory r=11,5m. Looks like physicsmans formula gives the manufacturing r allmost exactly.
yeeps!

Pass the asprin!! My head hurts:
Quote:
 Originally Posted by tdk6 jonnythan - what are your Volant Souls mearuements? Yes, you are right, the tail and the tip does flatten out a bit. Left my skiis at the ski-school today so I must make new measurements tomorrow. If I use physicsmans formula for my Heads I get 11,4m. My formula gives 12,2m and the factory r=11,5m. Looks like physicsmans formula gives the manufacturing r allmost exactly.
That's what I would expect. My going all the way to the widest part of the tip, I'd expect you to overestimate the angle of the sidecut slightly. To get it accurate, you'd either need a fudge factor or to measure to a point closer to the middle than the widest part of the tip.
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