Si - Excellent observation.
IMHO, even if done using the most accurate measurements and using a consistent computational technique, sidecut radii numbers are at best only good to about plus or minus about 5%.
As mentioned earlier in this thread, determination of the exact position of the front and rear contact points (and ski width at these points) is always a bit of an issue, but, in principle, this can be done quite accurately for hard snow. There is a minor problem in that the contact points move slightly fore and aft as the ski is edged and flexed, but this is a fairly small effect.
A more significant problem pertaining to contact length is whether or not a particular mfgr does something incredibly stupid like simply uses the maximum tip and tail dimensions (and the fore-aft distance between them) for their computation, even if the widest points occur in the upturned portions of the ski.
In my opinion, (and as also stated earlier), the major problem in determining an accurate sidecut radius is that the sidecut curve is not exactly a part of a circle, and thus, when you try to fit a circle (ie, radius) to it, you get different results depending on what procedure you use.
I've tried a few different procedures and they all give different estimates for the sidecut radius. Below are some of the procedures I've tried:
1a) A single curve fit to a circle knowing the sidecut dimensions, contact length, but NOT knowing the exact location of the waist. In addition, use the standard small angle approximations. This is the procedure given in many sources (eg, Physics of Skiing), and is the one I use in my published spreadsheet,
1b) Same as 1a but not using the standard small angle approximations. This is pretty obscure, and I was surprised to find a website in Sweden that discusses this approach. The computations are significantly more difficult and probably not suitable for the average user.
2) A single curve fit to a circle knowing the sidecut dimensions, contact length, but knowing the exact fore-aft location of the waist.
3) Knowing the sidecut dimensions, contact length, and exact fore-aft position of the waist, estimate one radius for the fore-body of the ski, and another for the rear of the ski and average the two radii. The two radii are often surprisingly (several meters) different.
Basically, given the above differences, as well as the effects of snow compaction, the small degree of skarving present in even the best "carves", and the effects of flex on the actual turning radius, I personally take sidecut numbers with a proverbial grain of salt that is anywhere from 0.5 m to 1 m wide
If I'm really interested in getting an accurate comparison of some skis, I'll measure the skis myself and do the calculations for all the skis consistently by the same method (eg, my spreadsheet) instead of having to worry whether the mfgrs all used the same measurement and computation techniques. Even doing this, I'll mostly use the numbers I obtain to rank order the radii and get an idea of the spread in radii, and not take them as "Gospel".
Tom / PM