Originally Posted by Yury
ok, thanks, that gives me an idea.
in essense i am trying to ballpark the added value of a parabolic ski.
you need to remember that a modern ski with a 20M radius is measured when laying on a flat surface, so it can't actually carve a turn that big. And I don't know the math (we need to ask PhysicsMan), but I would suspect that if you take a ski with a big sidecut (small radius) and put it on edge and reversed the camber the same amount as an old ski, the realized turn radius reduction may not be 1:1 between the two. To try to explain this better, if you took a ski with a 20M radius and reversed the camber by bending the deck of the ski to a radius of 20M (the same way you put a ski tail on the floor, hold the tip and push on the middle of the ski to reverse the camber), and you took a ski with a 70M radius and reversed the camber the same amount and put both skis at a 45 degree angle to the surface, if for example, the 20M radius ski now had an effective arc of 7M (just about 1/3 the original), would the 70M radius ski have an effective radius of 23.3M or would it be more?
If the size of the arc is reduced at a greater rate for a ski with a smaller radius, then that increases the benefit of the increased sidecut more than just the difference of the radii of the two skis.