Interesting ideas...but no.
A key concept in skiing is that the skis turn the skier.
At the apex, as you say lots of "turning" is occouring...why do you beleive that the steering angle is zero? In a purley carved turn, are you suggesting the ski ceases to be bent at apex? Surely you can see the flaw in your logic. Further in a more skidded turn, the ski being angled across your direction of travel is no different....again your statement seems baseless. You seem to be confusing the idea of diverging and converging paths of our COM and BOS vs. steering angle. Very different ideas. Both valid thou.
Steering angle explains how our COM is turned by our skis. It also demonstrates how turns have a turning component and a slowing component. At the extremes you can have 100% slowing and 0% steering (ie hockey stop), the other end of the spectrum you have 100%turning and 0% slowing (ie pure carved turn). Most turns we do fall in between these two extremes.
The diverging and converging of our BOS/COM is based on the assumption that the turn is happening, the idea then shows the relative paths of our BOS/COM but it does not explain what makes the turn happen.
Did not see you post before. I don't believe that the steering angle is zero at the apex, but with your definition it will be.
I am not the one confusing the COM and BOS paths. That was the whole reason for my post. To repeat, your defintion was "angle between the direction the ski is pointing and the direction of motion of the centre of mass". If you are carving the direction the ski is pointing and the BOS path is almost the same.
If you tie a nut in a string and swing it, what would be your steeering angle? What is your steering angle on ice-skates?
Do you see why none of the definitions discussed make sense?
Yes I saw all your posts and read them carefully....
Yes, if you are carving, the angle your ski tip is pointing and the path of your of COM is the closet aligned you can get. As written earlier in the pure carving sense the steering angle is 100% steering no slowling, so it is effecient of a turn as a possible. You actually seem to get this....so I am confused by your writing it makes no sense.
For your other questions....
Nut on a string. Interesting...honestly I dont know the answer to that one. But a nut on a string is not skiing, or really like anything else we do as people except maybe swing on a rope. Very different to skiing, so not sure your analogy is apt. The simple answer I suppose is the difference between the tanget to the arc and the arc itself, but the string really just makes this all come down to finite elements. Not really skiing, and definaltey not the type of detail we would go to when using the simple steering angle concept.
Ice skates: Well good question. I had to look this up. http://en.wikibooks.org/wiki/Wikijunior:How_Things_Work/Ice_Skates
But according to this, skates are not flat, they have a curve build in...
According to this, they work just like skis, or on a bike
Good question thou,...but ultimatley, if you read all of the above and beleive it...or not....somthing is making those skates turn....what do you think it is?