I picked 45 degrees because I thought that in the manner I've always understood and explained balance it would make things easier. If balance exists with the CM on a 45 degree rise line from the ski base it means that magnitude of the horizontal force of momentum (centrifugal force) acting on our CM is equal to the magnitude of the vertical force of gravity. When such a state of equal vertical and horizontal forces exist, the resultant force vector acts on the CM at a 45 degree angle.
By making it 45 degrees I assumed all I'd have to do would be determine what radius turn at 30 mph would produce a centrifugal force equal to 32fps2.
Thanks for the formula for centripetal acceleration. That may be the formula I was missing for calculating the centrifugal force levels. I assume it works for the opposite side of the force picture relationship (centripetal/centrifugal) as both exist in a state of harmonic opposition.
I'm still sure something is wrong here. I wonder if reducing the Gravity component to 22 because of the pivoted tip may have something to do with it. Here's my thinking. The force of gravity always carries the pure potential of 32fps2. The resultant acceleration will only be diminished if a resistant force opposes it, in this case the ground. But,,, if we are in a state of balance there is no tipping/acceleration occurring, only the potential exists and acts on the CM. 32 pushing down from gravity, 32 pushing laterally from momentum, and we have a resultant state of force equilibrium in which the resultant force pushes directly into the snow under the ski, and the snow pushes directly back.
What do you think? Under that scenario we would have velocity2 (1936 fps)/r = 32 fps2. Result would be a 60.5 ft radius, a little under 20 meters.
Hmmmm,,, still seems off to me. That's like putting a FIS legal GS ski on a 1 degree edge angle and running the arc that it would produce with the CM inclined at 45 degrees. Man, talk about reverse angulation! Sompin aint right here. We need some professional help.
Oh, and I caught a small mistake. About your time to complete a 180 degree, 85 ft radius turn, at 30mph. Distance covered would be 85(pi) at 44 fps, so actually it would be around 6 seconds.
I'm sure everyone is just captivated by this conversation.