Michael, what you're talking about is exactly what my skid angle refers to. Now you're seeing why I adopted a different term. Steering angle is harbored with definitions that just don't work for what I'm trying to describe.
LeMaster talks not only about steering angles under foot, but also about steering angles within various parts of the ski, including both tail and forebody. Those were the other reference points I spoke of earlier. So yes, by his description a carving ski has a built in steering angle. It's not zero. Skid angle would be 0.
You're right, the length of the ski alters the steering angle, even when the shape of the turn is exactly the same. Quite confusing indeed. Ski length has no effect on skid angle when carving. With skid angle carving is 0, period.
Interesting too, he has a term he uses for the steering angle created solely via the sidecut of the ski. He calls it the "local steering angle". It harbors the same peculiarity you just recognized. A longer ski with the exact same sidecut radius will have a larger local steering angle. Two skis that will produce the same turn shape, but have different local steering angles.
Well since my earlier questions are too difficult how about answering these:
How does your "skid angle" concept help us understand skiing?
Does it allow us to measure somthing?
(I think it wont allow any meaningful measure, because in reality the ski is almost always bent somewhat, and that bend has a huge effect...so "skid angle" cannot dictate turn shape, or anything else really...except maybe for amount of breaking being applied, but I again I cant really see the value in measuring it, nor how you would do it while standing on the hill doing D&C, or even with video do to the various angles and distortions etc.)
Does it provide insight into how skis work?
Does it provide insight into the tradeoffs between various ski techniques?
Does it explain forces we feel in a turn?
The steering angle concept does all of that......."skid angle"....seems to be lacking still. But I would be pleased if you could prove me wrong.