Originally Posted by Ghost
Two things are in play when you are skiing: you move the ski; the ski moves you.
You interact with the ski at the boot. The snow interacts with the ski all along the ski, including at the tip and tails.
Consider forces acting on the ski from the ski interacting with the snow. A ski tip 4 feet in front of you digging into the snow with a force of 50 lbs equates to 200 ft-lbs of torque acting at your ski - boot interface. The same force, 2 feet in front of the boot exerts half as much torque. A bigger ski acts on you like a bigger wrench.
Your cm 4 feet above the boot, decelerating with a force of 50 lbs will exert a torque at the boot binding interface of 200 ft-lbs. Your cm 3 feet above the boot, decelerating with a force of 50 lbs will exert a torque at the boot binding interface of 150 lbs. A taller skier acts on the ski like a bigger wrench.
Taller skiers don't need as much force to affect a long ski as shorter skiers do.
One of the cleanest teaching examples I've heard. And all correct. Only caveat IMO is that the ski is not an isolated system, but is contact (we hope) with the snow. If the snow is firm, as Ghost's example, most of these forces will rebound back into the system; the edges can push against something. So the example works. Have a feeling we should be thinking about all this as angular, since we're usually turning around an axis, but too lazy to reach for my physics text. Plenty of engineers here to work it out.
OTOH if you think about it, on ice a longer ski's also acting on the skier like a bigger wrench. Including his/her knees, muscles, etc. So a longer ski will require more energy to compensate against that torque. And in theory, if you turn the system on its head - linked lever arms beginning at the ski, forces aimed upward, a taller skier will have more torque operating on his/her knees and hips, for any length ski. So mixed blessing, being tall.
If the snow is soft, there's practically speaking very little rebound. So unclear if height is still relevant. Weight is, since in pow that's what flexes the ski and creates arc to turn.