I find some of this fairly complicated and decoupled from the actual skiing... especially the COM/BOS references.
Here's the quick physics of a turn on groomed hard snow, using a shaped ski with camber - how the "push" appears and how this relates to technique.
centripetal force
the ski/snow interaction creates the centripetal force, along the entire ski, which bends the ski if the skier opposes that from the boot mounting point. A weak interaction like in a skid will create a weak force and a strong interaction (carving, hockey stop) will create a strong force.
As an aside: a stiff ski will dig the tip deeper and keep it engaged at higher speeds, while also requiring a larger force to bend the ski in the first place.
When the ski is engaged, the forces are balanced and there is no movement towards the "outside"... there is just circular motion of the skis. For a rough model, we can disregard snow compaction underfoot and other such small issues.
Z turns or C turns
Here's the thousand dollar question: are we discussing Z turns, i.e. skidding to an edge set or C turns? Let's take the C turn model, i.e. carving where the forces are balanced.
The initial state is one where the skier is gliding on a flat ski across the slope, so there is lateral momentum across and down the slope.
engagement
the trickiest part of the turn is the top of the turn, the high C, where engagement happens. From a lateral force of zero when the skis are flat in transition, we tip the skis on edge. As the edge angle increases, so does the centripetal force CP, if the skier maintains the ski edge engaged.
As the ski edges and engages, the CP increases. As the CP increases, the ski bends. As the ski bends, it turns.
In terms of technique - some are tempted to push into the ski here and try to bend it by pushing into it, that's a bad idea if you're looking for high performance... as JFB puts it "relax as you engage" or "don't give pressure to the mountain". the best skiers maintain just enough pressure to keep the edge engaged.
apex
However, the initial state was one with lateral momentum. When the skis are approaching the apex, the momentum will compound with the CP. Gravity also starts to add up. Just past the apex, the pressure is maximum, assuming the skier is resisting it (with a long leg). In JFB's words: "receive pressure from the mountain".
deflection and release
How does the lateral impulse to deflect gets created? First look at what's being created:
a) resisting this maximum force will compress and tense the body and bend the ski, peaking right under the apex
b) the circular motion has momentum at this point, pointing across and down the slope
When the ski is engaged, the forces are balanced and there is no movement towards the "outside"... there is just circular motion of the skis. If the skier does not do anything, there will be no deflection, as the ski will complete a circle, go up the hill and the hips just scribe their own little circle.
If we release at this point, a) will generate "rebound" which is back up the hill and across the hill and b) will slingshot the boots and skis across and down.
The question is:
x) has the skier generated enough a) and b) to be able to flex to release or does the skier need to add to the current forces by pushing and hopping to get off the edges?
y) can the skier use b) to impulse the body across the slope?
x) is the big discriminator: if the skier hops out of the turn, he or she will not engage the skis in the next high C, unless the turns are slow enough and big enough.
As always, most beginners can carve clean big arcs on green runs. What discriminates an expert is the ability to carve small arcs on a black run!
middle of the boot
We did not need to discuss COM/BOS at all so far and we were able to describe roughly everything, with the simple assumption that the skier will stay in the middle of the boot and only control tipping and untipping (and whatever else is needed to maintain contact and stay in balance, like flexing and extending of the legs etc)
Fore/aft are optimizations of this model - as noted multiple times in the past few threads, the shaped skis can be carved reasonably from the middle, at a lower level of performance.
clean carving
I think by now all are convinced that there can be 100% carved turns. Easily demonstrated by doing large arcs on a green. The harder and faster it gets, the harder it is to maintain the clean carving.
one foot or two feet
Pressuring one foot vs two feet is not relevant for this rough model, although the body's weight will create more CP via one single foot engaged as opposed to two (distributing the body's weight will reduce the CP in half on each leg and this will reduce the ski bend, especially at the top of the turn)
Also, since the inside leg cannot be long through the arc (at any decent angles), putting any supplemental pressure on it will result in increased tiredness, as this leg is not stacked, but bent and thus "extra" weight on it requires significant muscle action. You can see why racers avoid that, especially as they pull 3g in the middle of a GS turn. if they put 50% of weight on the inside ski, for equal ski bend it's like doing a squat with 150% of the body weight - if they put even just 20% of that on the inside foot, it would mean doing a full squat with 0.6 x body weight, in every turn... which would be completely unnecessary
it's late, so I'll end here. I will expand on this later and dive into the current WC technique and why it's simply the effective solution to the physics of skiing.
