Originally Posted by Max_501
As long as the skis are edged they will will finish the turn. The do not stop turning until they go flat.
This is not quite true. They will stop carving even when they still are somewhat edged, and the radius of curvature of the turn will likely increase noticeably at this point.
The reason is that even at very low speeds, when the edging angle of skis becomes less than the critical angle (look up old posts by Bob Barnes and myself on this), they can't possibly stay on the little shelf in the snow that the edges are trying to make for themselves. This means that carving is no longer an option and some skidding must occur.
The importance of any such skidding (eg, the width of the track in the snow) depends on the angle between the direction the skis are pointed and the direction they are moving at this point in the turn. This important angle has been given various names including the yaw angle, the crabbing angle, the "angle of attack", and most recently, Rick's (Fastman's) recently coined term, the "angle of divergence".
If the skier is skilled and has anticipated this transition from carving to skidding, and his intent is to have a smooth, low drag transition, his skis will already be pointed in the direction they should be traveling at this point in the turn, namely, crossing under the body. Thus, the lack of carving during the low edge angle phase on either side of the transition can be extremely difficult to detect, let alone be a concern. In fact, if the path of the skier's COM and the path of his skis cross at a sufficiently large angle at the transition, the duration of this low edge angle phase can be very short, and the tracks will appear to go from one set of edges to the other within in a ski length or two.
At higher speeds, if the skier is still in a turn at the moment just before his edge angles goes below critical, there is some centrifugal force trying to make the skis go radially outward away from the center of that turn. Thus, the minimum angle required to keep the edges carving is larger than the critical angle discussed above in the low-G case by a value approximately equal to the arctangent of the radial g-force. Thus if the skier is in a "1-G" turn on the flats, his skis better be edged by more than 45 degrees if s/he wants to continue to have his edges "stay on the shelf" and carve.
Here's another, more complicated example: If s/he is making a 1-G turn on a 20 degree hill and is moving across the fall line at 45 degrees while pulling 1-G, roughly speaking, the low G contribution to the critical edge angle will be about 10 degrees (ie, about half of 20). The additional contribution to the critical edge angle because of the centrifugal force will be 45 degrees ( = arctan of one G). Thus, to continue to carve, his actual edge angle must be greater than (approx) 10 deg PLUS 45 deg, or 55 deg.
If the skier's actual edge angle is less than this value, say, because he has begun to decrease it as he is approaching transition, then the skis can not possibly continue to carve. As in the low-G case, in a high-G case, whether or not the loss of carving at this (earlier) moment has any effect on the skis path over the snow depends on how well the skier has anticipated this happening. If s/he didn't anticipated it well, there will be a glitch in the tracks and intentional rotary input in the old sense (around an axis perpendicular to the snow) will likely be employed to point the skis in the desired direction, to set new edges, etc.
Also, it should be noted that even after the skis are at such low edging angles that they can no longer carve, there can still be a large difference between the sideways drag forces on the tips and on the tails. How much of a difference, of course depends on various factors such as the crabbing angle, fore/aft pressuring and forcing the tips into the snow by torque around an axis perpendicular to the plane of the base of the edged ski.
Once no longer carving, any sideways drag force differential between tips and tails will cause the skis to rotate (around an axis perpendicular to the snow surface and through the midpoint of the ski). This is a drag-induced pivoting of the skis not directly caused by pivoting muscular input provided by the skier.
Whether or not the path of the COM of the skier is curved once skidding begins depends on the angle between the instantaneous direction of travel of the skier's COM, and the direction of the net drag force vector acting on the skis. If the net drag force is directly opposite the direction of travel, and passes through the COM (when viewed from above, perpendicular to the snow surface), the skier will be making a pure braking move with no tendancy to deflect his path from a straight line, ie, either a hockey stop or a pure sideslip. If there is an angle or offset between the two directions, the skidded path can become curved. Note, this is the reason that zero forward velocity sideslips can be made straight down the fall line with the skis either perpendicular to the fall line or at an angle other than 90 degrees.
Tom / PM