Originally Posted by LiquidFeet
I'd like to compare what really happens when I try it, to what physics predicts should happen in an uncluttered world when only the ankles bend.
That's part of the problem, LiquidFeet--it is not an "uncluttered world." One particularly important variable is the amount of edge angle and edge engagement involved when you make your "forward movement." Are the edges gripping somewhat--skidding, as opposed to just slipping--when you sideslip? If so, the part of the edge that receives the most pressure will "drag" more than the part with less pressure. Another variable involves your starting point--where were you, fore-and-aft, when you started, before you flexed your ankles and moved more forward? And how extensive is the forward movement you're envisioning? Finally, in the first (turning) and third (traversing) scenarios, are your skis railed out carving (not really possible if they're traversing in a straight line, unless they have no sidecut), or are they skidding to some degree? How much? And what about snow conditions?
As far as Jesinstr's objection that flexing (bending, dorsiflexing) the ankles does not necessarily move your center of mass forward, if you are clear--as you were--that flexing the ankles is the only thing you do, then of course, your CM does move forward (relative to your feet)--and somewhat down at the same time. Interestingly, the more flexed they were before you started flexing them more, the more the resulting movement of your CM is down; the more upright (shins vertical) at the start, the more flexing your ankles moves your CM forward. Jesinstr--note that in your example of dropping lower, you are doing more than just flexing your ankles--you are also involving your knees, hips, and probably spine and arms. So I have to agree with LiquidFeet's premise that flexing your ankles--and only your ankles--moves your CM forward relative to your feet. This is a small point, though, because LF did specify that your ankle movement does move your CM forward, so even if you involve other joints, you must end up forward according to her instructions.
Anyway, it's still not that clear and "uncluttered" what happens to your skis when you do this, LF. Take the edges, the snow, and everything else out of the picture for a moment--in fact, go ahead out on the grass, or inside on your floor in bare feet. Starting "fore-aft neutral," with pressure along your whole foot (ball to heel), dorsiflex ("bend") your ankles, keeping your feet flat on the floor, such that you end up somewhat more "forward" and balanced over the balls of your feet. Pay close attention. You'll notice that the first thing that happens as you begin to flex your ankles is that pressure moves back onto your heels, as your forefoot gets "lighter" on the floor. This causes you to then "topple" forward, which results in the pressure moving forward on your feet, especially as you "catch" yourself and stop the forward movement. So that flexing of your ankles first shifts pressure back, momentarily, and then shifts it forward strongly, and then finally ends up somewhat forward as a result of your CM being more forward (relative to your feet) than it was before.
All this is academic, probably, because I think that your objective is pretty clear--what do your skis do once you have moved the balance point forward along their length, in the three different scenarios of your questions? Right? If so, then assuming that the skis are not completely flat on the snow, which is a fair assumption at least in your first (turning) and third (traversing) scenarios, imagine a simpler situation. Instead of flexing your ankles, imagine that we just put heavy weights on the tips of your skis, as you stayed centered. Can you picture the added "drag" from those weighted tips with their edges engaged, as the skis skid sideways, causing the tails to skid more than the tips? (Jamt will probably find fault with this simplification--rightly so--because it eliminates some of the torque effects that result from keeping the "weight" attached to the skis at the bindings even when we lean forward--which actually adds to the tendency of the tails to wash out.) Just flexing your ankles would cause the same thing--adding pressure to the tips--while also lightening the tails--even bending the skis and lifting the tails right off the snow if you move far enough forward. The tips would grip more, and the tails would slip more, causing your whole body (because you specified "doing nothing else," so it could not twist in any joint) and skis to rotate. In the turning scenario, you already have some rotational ("angular") momentum of your body just due to the turn itself, so when you lighten your tails and they break loose, you could find yourself quickly "spinning out." The same thing would happen in scenario 2 (straight sideslip), unless your skis were perfectly flat on the snow, which is not very likely. Even if they were, there would still be a little more resistance--friction--from the more-weighted tips on the snow, causing torque that would cause you to rotate, tails down the hill.
So that's my take on "the theory," with a few assumptions added to your "do nothing else." I suspect that by "do nothing else," you are particularly implying "don't rotate or counter-rotate your body" as you flex your ankles forward--and that is, indeed, critical to your experiment. At the same time, it's pretty hard to avoid entirely. And really, I suggest that even if you could eliminate all "body english" in the experiment, it would lose relevance to actual skiing, because these movements are so integral to real skiing.
One final very important point: As I mentioned before, the laws of physics do not cause gravity to pull the more heavily weighted end of your skis down the hill faster, as some people may assume would happen. Yes, the gravitational force ("weight") is proportional to the amount of mass (by definition--weight is mass X the gravitational constant), so the more mass, the more force. But more mass means also more inertia (resistance to change of motion), so ultimately, a boulder and a pebble will fall from a height at the same rate (in a vacuum, eliminating air resistance--which is another variable that could have "cluttering" significance in your experiment!).
You know the difference between theory and reality, of course. It's that In theory, there is no difference, but In reality, sometimes there is!