Originally Posted by Jamt
In the plane of the slope the force on the ski is more or less perpendicular to its direction, because there is little friction in the fore-aft direction.
When carving the force is almost perpendicular to the direction of travel and hence there is little slowing down.
When we have a steering angle some of the force will be directed against the direction of travel and will hence slow you down more.
The tightness of the turn (of the CoM) in any give moment is given by the centripetal force and the speed:
r=mass x speed^2 / Force.
This mean that to tighten a turn you either have to slow down or increase the force.
Generally and a bit simplified we can say that more edging increases the force and more steering angle reduces the speed.
BTS point that doing both simultaneously is very difficult is spot on.
I'm primarily thinking of racing speeds. If we are going slow to start with it is possible to tighten the turn with steering, but it is not possible if you are going fast without slowing down first.
Jamt some really great points and clarifying physics as usual. Want to add to it, even in an arc'd turn there is some steering angle present, because the ski is bent. The force vector under the foot may be perpindicular but other parts of the ski are not. I think that's what you meant by "almost".
So going for a tighter arc should theoretically slow you down a bit, even without any brushing due to increased steering angle, not to mention it gets you out of the fall line sooner.
I didn't want to complicate the discussion with steering angle vs skid angle but maybe now is the time?
Even arcing skis are creating new steering angle as they go, continuously. But they are minimizing skid angle to zero.
In one sense, a perfect arc is a perfect amount of self steering that exacly matches the turn shape such that the tail doesn't skid. However edge lock provides some wiggle room so that we can arc without finding a "perfect" balance of steering angle pressures.
Brushing the skis means to avoid edge lock and achieve some skid angle in addition to steering angle.
Perhaps a perfect brushed carve is one where
the steering angle is continually generated at just the right amount to match the turn shape and skid angle such that the skid angle remains constant, ie.... The tails do not fan out nor straighten into edge lock.
IMHO this is more difficult then edge locked arcing because there is no wiggle room to find that perfect balance of self steering.
The equations that you and ghost brought in really clarify the matter. At speed or on steepness, you need more redirecting force for the steering angle to matter. While the steering angle determines the direction of that force, the intensity comes from edge angle.
At speed or on steeper inclines, more force: more edge angle will be needed.
Tipping more creates more steering angle by bending the ski, more redirection due to increased force. If brushing happens then you get all possible speed control factors happening together. You get high edge angle forces, a certain max sweet spot of steering angle, line choices that keep you out of the fall line, and minimal time with disengaged skis.
Active pivoting only happens on flat or disengaged skis. You might be able to push the heels of edged and engaged skis, but that is fundamentally different then rotary movements often discussed.
If you are constrained to slow speeds and easy runs then some kind of flat pivoty steered thing might work, but as jamt pointed out, step it up a notch and now you really need to embrace tip-centric movements and use the self steering properties of the skis to pivot the skis just the right amount for achieving tight, brushed turns that use all available factors to slow you. Otherwise at speed or on steeps you will end up with fast-slow-fast-slow skiing; with pivot entries followed by hard edge sets to slow you down.