I might be in way over my head here, but based on my skiing and engineering experience, here are my thoughts:
1. The turning radius the skier experiences is determined by two things, the sidecut and how much the ski is flexed.
2. How much the ski is flexed when turning is again determined by the weight of the skier, snow conditions, speed etc. You can imagine that a heavier (or stronger) skier should be able to push the ski into a tighter turn than a lighter, weaker skier.
3. If a ski otherwise is constructed the same, a short ski is actually stiffer than a long ski.
So if you add all this up you can say that the sidecut is the same, but since the lighter skier on the shorter ski might not be able to flex the ski as much as a heavier skier on the longer ski, the turning radius the skier experiences could be similar.
You see, in this world there's two kinds of people, my friend: Those with loaded guns and those who dig. You dig.
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