Originally Posted by Max_501
So, we've gotten to a point where it appears there is agreement that the turn shape (radius) varies throughout the turn. Is it possible to have both skis tracking so that at any given point in time they are on the same radius or is the inside ski always running a tighter radius (lets assume a carving ski)?
Not only can you do it both ways, but the difference in skier input required is so small, who cares?
Let me give you some numbers that will hopefully illustrate this.
Lets assume that both skis have a 10 meter sidecut radius, and at the apex of the turn, the outer ski is edged at 45 degrees relative to the snow. If all the conditions for perfect carving are true (eg, the snow is hard and perfectly smooth, the stiffness pattern of the ski is appropriate so that waist of the ski is bottomed out, but the tip is not folding, etc.etc.), then the theoretical carving radius of that ski will be cos(45)*10m, or 7.07 meters.
If we want the arcs of both skis to have a common center, we can ask how much difference in edge angle is needed for the engaged edge of the inner ski in the turn to track (say) 10 inches away from the engaged edge of the outer ski in the turn.
This is very easy to calculate using the same formula as above. If the edge angle for the inner ski is 47.0 degrees, ie, just two degrees more than the outer ski at 45.0 degrees, then the turn radii for the two skis will be different by a comfortable 9.88 inches. If we assume the knees of the skier are 2 feet above the edges, the skier will have to move his inner knee an extra 0.8 inches to the inside of the turn to generate the required 2.0 extra degrees of edging.
Of course, another option is for the skier to keep both edge angles at exactly 45.0 degrees so that the instantaneous radii are the same, but now, the instantaneous centers of the the two arcs would no longer be coincident, but rather, be separated by a distance exactly equal to the spacing between the skis. Obviously, any strategy intermediate between these two extremes would also allow the skis retain the 10 inch spacing around the apex of the turn.
As far as I am concerned, differences in edging of order 2 degrees are negligible for most real-world skiing situations. For example, there are probably edging differences between the two skis of order 2 degrees caused by differences in terrain undulations each ski encounters.
Next, lets see what happens as the skier moves past the apex towards the transition. As he does this, he/she will start to flatten both skis so they approach zero edge angle (ie, are flat) at the transition. To start, lets look at a point somewhat before the transition where the edge angle of the outer ski has been reduced to 20 degrees (to the snow). If the skier keeps the difference in edge angles at exactly 2.0 degrees, the theoretical difference in carved radii is now 5 inches, ie, the tracks of the two skis will start to get closer. Of course, if, the skier is hell-bent on keeping the center of the arc for each ski coincident, AND keeping them separated by 10 inches, with equal ease, he could decide to increase the difference in edge angles to the point where this would happen.
Obviously, at some point, as the edging angle continues to be reduced as transition is approached, the skis can no longer carve, and will be much more free to be slid easily towards or away from each other (while still parallel and still pointed in the direction they are moving). Thus, the skier is pretty much free to adjust their spacing, depending on exactly what spacing the skier likes to have at the transition.
This almost-flat ski mode continues through the transition and into the next turn until the edge angles once again increase and the skis start carving again.
Thus, to achieve a constant ski separation throughout a run, the skier has essentially an infinite number of options open to him, none of which require particularly large or strenuous movements. This is one of the reasons why I just can't get too excited about the issue of edge angles and centers of rotation for parallel ski tracks
Tom / PM