In the Eastern Division, there used to be a card in the Creative Teaching Module for one of our exams where the student was an airline pilot. I always thought of this one as sort of a "gimme", so easy to teach. The fun thing though is that I really do think of the movements in skiing as being like those in flying a plane. It's pretty easy to see how edging/tipping = aileron/pushing the stick side to side, and how rotary/twisting of the feet is analogous to using the rudder. But the other control, pitch doesn't quite seem to match up with the skill of managing pressure in the fore/aft plane.
I will often use this analogy with a student, because I think it's pretty easy for everyone to see how an airplane turns first by rolling it's wings, not by pushing the tail out with rudder. I will ask my students to make sure that when they are "wings level", they resist the urge to throw the rudder over and point the skis down the hill. I even had that exam card come to life once with a husband and wife couple who work for an airline as 757 instructors. Totally fun lesson.
So anyway.... a few weeks ago, our mountain got several feet of snow. Now our mountain opens at 7:30 AM, and a powder day, there may just be a "soft opening" a bit before that. It only takes an hour or two to track out most of the mountain. My lesson that day started at 9AM. My client was a pretty good skier, and I've skied with him many times before in bumps, trees and what have you, but never in really deep snow where you could get a true 3D experience. So of course, we headed for the woods to find the goods, and they were good. Now we were skiing tight steep lines and I'm skiing it at a slow pace so I can keep my first-time powder skier in one piece. His question - how do you make such tight turns in the deep snow? I was on a stiff ski w a 40M turn radius, and I think it would be safe to say that the turns I was making had a radius somewhere less than 4M. How? Well, I think this is where that third control comes in, pulling back on the stick. After the wings have rolled into the turn/skis have begun edging, heel pressure, strong heel-pressure becomes a steering movement just like it does in an airplane. When that turn is over, the stick goes back to neutral, I roll into the next turn and then I pull back on the stick again to tighten the turn.
Without the question, I'm not sure that I had ever thought about how I do what I do in powder, just thought I'd share.