Fastman - As usual, another great, thoughtful post.
FASTMAN:From reading these responses it seems we are commenting on two different concepts. I believe (correct me if I am wrong) Nolo and arcadie are commenting on this statement: "Change the edge angle without changing the angle of the lower leg off of vertical..." , and Physics man and I are commenting on this statement: "Change the edge angle without changing the angle of the CM off of vertical..."
Fastman, you nailed it. You are absolutely correct about this difference. This sort of misunderstanding is a prime example of the terminology issue I keep coming back to. Here are four of us, all of whom know one heck of a lot about skiing, and we even have all the time in the world to get to the bottom of an issue like this, and *still* there are misunderstandings like this. This is precisely why I started the thread on definitions. The vagueness and inconsistencies in the most commonly used ones are causing a lot of people to waste an awful lot of time.
FASTMAN:...I think all four of us would agree with nolo and arcadie comment on the statement they were referring to, the area of contention is on the statement PM and I were referring to. As I know what I am saying is unquestionably correct, my suspicion is we are focusing on different issues...
Almost, but not quite. Fastman and I would indeed agree totally, except that we are making slightly but critically different initial assumptions, and hence are led to conclusions that are appropriate in different situations.
Central to Fastman's argument is his assumption that, "...Now, if that in-balance skier increases his edge angle a few things happen. Immediately his turn radius decreases, and this causes M to increase and thus the R angle to increase...".
In other words, Fastman is assuming a turn with a big carving component, and hence, there is a direct and strong link between the edge angle and turn radius (and hence momentum forces). I am not making this assumption because I am thinking about other skiing situations. For example, (a) standing still or (b) being able to traverse in a perfectly straight line (even on shaped skis) at different edge angles by introducing appropriate (small) amounts of skidding into the traverse.
In each of the two situations that I just mentioned, there is no M force at all (since you are not turning), and hence, no linkage whatsoever between the angle of the R vector (it always is exactly equal to the gravity vector) and edge angle. Without this linkage, you can vary your edge angle all you want and not have to move your CM angle one degree away from vertical.
The reason for the difference between our fundamental assumptions is obvious. Carved turns are the tools of racers and Fastman comes from this background. Hence, in the turns that are important to him, the above linkage is a big effect, and his conclusion is correct.
Not coming from this background, I was thinking about all the other things tht non-racers do on skis, e.g., stop, go slow, skid, skarve, pivot, etc., all involving small or zero momentum forces.
Thus, I would argue that in general, one can often vary the edge angle without changing the angle of the CM from vertical, but, as Fastman correctly pointed out, this ability is restricted in carved turns.
Tom / PM
PS - Mr. T. - Dude - I'm truly sorry, man. I know it was painful, but it just had to be done.
PS#2 (added in edit) - For the record, what Fastman and I are discussing is not an "either-or" thing. There is obviously a continuum between the extremes (ie, no momentum forces vs. lots of momentum forces), and a corresponding continuum in the constraint placed on the mechanics of the skier. Specifically, in low (but non-zero) G turns, your CM to vertical angle has to adjust itself (exactly as Fastman described) to changes in edge angle, but much less than it would for the same change in edge angle in hi-G turns.
PS#3 (added in edit) - Although it hasn't been said explicitly, I think its important to point out that the "momentum forces" that Fastman and I refer to include not only the usual centrifugal forces, but also linear decelerating forces (eg, resulting from a hockey stop).[ July 04, 2003, 08:36 PM: Message edited by: PhysicsMan ]