Originally Posted by 2-turn
OK, I'm a little late on this thread, but how about this simple explanation. If turn initiation is a braking motion, perhaps we're storing the lost kinetic energy in the ski, turning it into potential energy, and turning that potential energy back into kinetic energy at the end of the turn. It isn't creating energy, but reusing as close to the same amount of energy lost as possible...
Try pumping on a swing strung up with stretchy ropes. If the ropes have sufficient give, it's almost impossible because centrifugal force will move your center of mass away from the center of the turn (the support) at those moments you need to be forcing your CM up towards the support and thereby gaining extra angular velocity (at constant angular momentum, ie, m*v^2 / r is constant). Flex in the skis WILL return some of the energy you put into them, but pumping is extra, something different, on top of this.
Originally Posted by 2-turn
As far as Physicsman's analogy of the figure skater, that's bogus. The figure skater has a certain rotational momentum, when they bring their arms in, they are decreasing their rotational mass by bringing some of their mass closer to center, and therefore rotate faster. It has nothing to do with the subject at hand.
Sorry, but it does. Two comments:
1) There is indeed rotational angular momentium of a skier in a turn. Consider a skier at the apex of a pure carved arc. His or her path is close to a circle of a certain radius and there is a mass (the skier) traveling around that circle. That means that there is angular momemtum around the center of rotation. If you decrease radius of the turn by phyically moving your CM towards the center of the turn (ie, not changing the radius of curvature of the turn), then, by the conservation of angular momentum, your tangential velocity will increase, just like the pirouetting skater. At each transition, ie, where your angular momentum is zero, and so up-and-down motions won't change your angular momentium (ie, it will remain zero), if you let your CM settle back down a bit towards you skis, you will be set to repeat this movement over and over again. This is the simplest version of pumping.
2) Did you even glance at the peer-reviewed journal article I cited where they analyzed pumping on a swing in the rotational domain by making an analogy with what is essentially a figure skater pirouetting on a lazy susan constrained by a spiral (wind-up) spring. Even if you don't understand the math or physics behind their analysis, it should be obvious from the most casual read that one group of PhD's made a sufficiently accurate analogy between a swing and the rotational motion of a pirouetting skater that a second, completely independent group (the reviewers of the article) agreed completely. In actuality, what they were doing is trying to simplify the analysis of the swing to the analysis of something (conservation of angular momentum) that everyone can understand.
MichaelA nailed it correctly in his recent post where he pointed out (in simpler language) what I described above, e.g., it's not about storing energy in the skis, his comments on the limitations of the pumping technique due to our physical limitations, etc.
Jinx also has it correct in his edit about not recovering lost energy.
JamesK - The reason "pumping" doesn't work from a dead stop (ie, the situation you described) is exactly the same reason you can't pump a swing that is not already moving (at least a bit) - you need some initial angular momentum to build on.
Tom / PM