Originally Posted by Highway Star
It is not physically possible to truely carve a turn larger than your sidecut radius, you are skidding and only partially carving. When you are carving a longer turn on a small radius ski, at close to but still smaller than the sidecut radius, it must be at a relatively low speed, because you will generate alot of centripetal force if you are going too fast.
It is possible, however, to carve a turn much smaller than your sidecut radius. This is why I don't really ski anything under a 20m sidecut - I can lean the ski over and bend it into smaller arcs. I find it pretty useless to be on a ski that stops carving effectively above 30 mph.
I agree with half of your synopsis. I have resisted the temptation to get ultra low radius skis for precisely the reason in your first paragraph. If I am carving on short radius skis, it will be at lower speeds, since my knees can't handle the high stresses of trying to carve at faster speeds.
Trying to carve SR turns at fast speeds will overpower the edge grip at best, or will damage my already messed up knees. IIRC, the force relationship is m*(v**2)/r. If I use 10 M radius vs 20 M, the force is doubled at the same velocity. To maintain the same force at 20 M as at 10 M, the velocity must be raised by the square root of 2.
eg. let v**2/r = V**2/R . r is the short radius and R is the long radius. In the example, R=2*r.
So, solve for V in terms of v: 2 * v**2/r = V**2/r or
V = sqr(2)*v. Which means you can ski about 1.4 times faster on a 20 M radius turn than on a 10 M radius turn before the same forces arise. (Or about 70% of the speed on a ten meter turn. That means, 40MPH on a 20M turn is equivalent to 28 MPH on a 10M turn. )
But this says only that at your max ability/desire to handle the load, you will be carving more slowly in a short radius turn than in a long radius turn. It says nothing at all about the relative merits between SR and LR skis.
Your second paragraph is correct too, but there is a slight implication that is not -- the implication that you'll actually be carving at the higher speed during the shorter radius turn. You will be carving to your ability to manage the force and the ability for the snowpack to maintain the carve at the given speed -- totally irrelevant wrt ski radius... FWIW, the formulas above only speak to the speed of the skier and turn radius, not the radius of the ski.
A bigger impact on LR skis in SR turns is the height of the edge angles that you need to develop to make the ski carve. Isn't turning 1/2 radius or the ski a 60 degree edge angle? There is a huge implication that the snow pack could handle such oblique forces, especially at speed. There is the other implication that your body can handle the load.
And forget totally about carving the really short turns on the LR skis.
Personally, I don't want to go less than 14/15 M, 'cuz I like to carve, but don't want to ski as slowly as I would have to when carving the ultra SR ski. I like the longer 18M especially. I ski alot on 21 M, 'cuz it's easier...
As to SR skis on LR turns, why does full-on edge engagement matter if the ski and skier are tracing out turns of the same radius? I say it does not. The only implications are in poor snow conditions, where the SR ski could be thrown. IMO, the metron gets around this by adding mass -- it's a tank, so it goes straight at high speeds without wobbling.