Hi Fastman - It's great to see you posting on Epic again, and yup, for some reason, this discussion does seem strangely familiar.
Your posts have always been superbly clear, and your last one is no exception. I think I understand what’s really going on in this discussion about whether angulation helps one stay in balance. I think an analogy to a simpler situation will be useful.
Imagine you are driving a sports car with a manual transmission. You have two totally independent, separately adjustable controls available to set the speed of the car: (1) How much gas you give it; and, (2) What gear you are in. If I want to go 30 mph, I could do it in 1st gear with the engine at a fairly high RPM. I could also go 30 mph in 2nd at a more moderate RPM, or I could let the engine loaf along at low RPM in 3rd gear and still be going 30 mph. I don’t think anyone would ever argue that the gear shift lever is linked to the gas pedal.
On a flat road, fundamentally, it doesn’t really matter all that much which gear you pick. All three gears will let you roll along at 30 mph, so you might decide between them on the basis of something not related to speed. For example, if minimizing engine wear is a consideration, you would favor higher gears. If you are a sports car buff and like the sound of the engine/exhaust, you would probably keep it in a lower gear. If you just learning to drive a stick shift and don't know how to shift out of 1st, you can still drive, albeit in a more limited way. The gear and gas are still separately adjustable.
However, lets imagine you now are on a really hilly road, and you must maintain 30 to keep up with traffic. As you go up and down the hills, you will be forced to simultaneously adjust both the gas and gear because you won’t be able to go up steep hills in 3rd. Suddenly, the gas pedal and gear shift lever *must* be used in concert, and to an outside observer, it might seem like they aren’t independent. Well, they still are mechanically totally independent, but when you put a constraint on the problem (ie, "maintain 30 mph on a hilly road"), they have to be used together to achieve the desired goal.
I think that the usage of the two controls in the automotive example is quite analogous to usage of two controls in skiing: CM angle and degree of angulation. A speed constraint on the car is analogous to the speed and turn shape constraint on a ski racer.
Specifically, recreational skiers, like drivers without speed constraints, can go as fast or slow as they want, can make turns wherever and whenever they want, and they can randomly decide to skid or carve a particular turn. A lot of novice skiers don't know how to angulate, just like people learning to drive a stick shift don't yet know how to shift out of first gear. The novice skiers are always at zero angulation, and accept that all of their turns will be skidded. For the rec skiers described above, angulation remains an adjustment (ie, change in body shape) that can be manipulated (or kept constant at zero) totally independently of the things they need to do to keep their CM in the right place to remain in balance.
On the other hand, skiers who ski with an intent to go to specific places on the hill using a specific path (eg, more advanced recreational skiers, racers) do not as much freedom. For example, racers are solving a very tightly constrained problem, namely, maximizing their speed while following a preset line. As Fastman described, they have to simultaneously adjust their CM angle and degree of angulation together to meet their constraints, just like the driver on the hilly road has to simultaneously adjust the gas and gear to meet the constraint of keeping his speed constant.
The fact that racers (and other skiers with specific intent) have to adjust angulation simultaneously with CM moves does not mean that angulation adjustments are fundamental to staying in balance. It only means that angulation adjustments are needed to stay in balance when your line and speed are constrained. It’s still a physically separate movement from CM angle adjustments.
I hope that the above discussion has answered whether or not angulation is a balancing move. Another question that could be asked is if angulation is a "cause" or "effect"? I wouldn’t put the question that way. It's certainly not an "effect". Skiing doesn't force anyone to angulate. Maybe a better question would be "cause" (ie, input under the user's volitional control) versus "reaction", and I think this has been answered as well.
To summarize the discussion of whether angulation can be adjusted at will, in the case of unconstrained (ie, free skiing), I think its pretty obvious (see my arguments in the previous posts) that it can be adjusted independently and one can still stay in balance. Of course, the side effect of doing this is that you will wind up making different shaped turns. OTOH, constrain the turn shape and speed (eg, racing), and as Fastman pointed out, you *must* constrain angulation to follow the course AND stay in balance.
Clear as mud, eh?
Tom / PM[ January 16, 2004, 02:40 AM: Message edited by: PhysicsMan ]