Originally Posted by narc
A higher edge angle = tighter radius
Absolutely true, but consider two cases:
Case 1: A 27-meter radius ski that carves a ~23-meter turn at an edge angle of 45 degrees
Case 2: A 33-meter radius ski that carves the same 23-meter turn at an edge angle of ~60 degrees
In either case the lateral acceleration at any given speed will be exactly the same, because they're carving exactly the same turn. That's what I meant when I said that edge angle in and of itself doesn't determine lateral acceleration.
Now imagine that you're going 15 meters/sec (about 30 mph) and you make a 23-meter turn entirely on the outside ski. In either case the lateral acceleration will be 15^2/23 = 9.8 m/sec^2, which just so happens to be exactly 1G. This means that your center of mass will have to be exactly as far "inside" of the ski as it is above the snow for you to be in balance. For example, if your CM is 30" above the snow, then it would also have to be 30" inside of the outside/carving ski to be in balance.
Now comes the fun part. In the case of the 27-meter ski, the edge angle and the CM->ski angle are both 45 degrees, so in this case there's basically only one way to carve the turn in balance: Lean your entire body in by 45 degrees (i.e. full-body inclination; I'm ignoring the fact that the inside of your outside ski isn't exactly centered under your CM to keep things simple).
In the case of the 33-meter ski, you have to somehow raise the ski on edge by 60 degrees while still keeping your center of mass 45 degrees to the inside. The way you would do that is by using some combination of knee and hip angulation, since both of those increase the edge angle by more than they increase the CM->ski angle.
That's why racers use a "comma shape" body profile on straighter skis (i.e. lots of angulation, not so much inclination), and "stacked skeletal alignment" (the opposite) on curvier ones.
Now consider what happens if you get caught "outside", meaning that your CM is either too high or not far enough inside of the carving edge. In the case of the 33-meter ski you can simply release your knee and/or hips (i.e. use less angulation) and the ski will straighten out. In the case of the 27-meter ski above the only thing you can do is skid, since you're already using 100% inclination. If the ski is ultra-sharp with 6 deg of side bevel then it's more likely you'll get "high centered" and crash horribly (http://www.youtube.com/watch?v=Win0irOcLps). This is actually the somewhat valid insight at the heart of the FIS' argument that longer-radius GS skis are safer. I don't agree with the extremes to which they've taken it - 27 m skis are plenty safe in real GS courses on real snow IMO. I actually did agree with the previous increase from 21m to 27m, though.