Mt T thanks for taking on the issue. Here are some comments:
Piggyslayer, if you turn your bike to one side and you move your body in the opposite direction enough you can still go straight. It all depends on where the center of mass of the system bike + biker is.
Darn it, if I only new it is that simple I would not get all these bruises trying.
On inline skates, you do the same, if you can tip your skates and move your body in the opposite direction you can still go straight as well. However, it is a trickier thing to do for you do not have handlebars to help you with it.
NO you will NOT go straight, you will turn! And so will you on the bike just the radius on the bike will be bigger. This is the essence of my question: what is happening to cause the skate turning when tipped onto an edge.
If you'd like some sophisticated treatment on this part of mechanics, get yourself a copy of some advanced textbook in Physics at the master's level at least.
The relevant branch of science would be, I think, some branch of material?s science/continuum mechanics. This lies on crossroads of physics and mechanical engineering (closer to engineering) while continuum mechanics is more mathematized version of it. I do not think, a graduate physics textbooks would cover any of this. I my previous life I have done some of the math around continuum mechanics so this is how I know.
The hardness of the wheels also can contribute some to the turning radius.
I agree, and I think this is the essence of the parallel carved turn on inline skates or carvers. On a very high level the inline skate or carvers turn because the wheels are soft and get distorted around the contact area where they touch the pavement. The wheel partially reshapes itself to ?undo? the distortion and to a smaller extent parts of the contact area shift/move around.
This is how the turn happens but it is only hand waving explanation.
One could write easily a Master's thesis on the topic.
I think it can easily be a PhD thesis. I think some relevant work exist, not in textbooks, but is a part of the engineering study of motorcycle tires. Since tipping to one side or the other is how you ride a motorcycle engineers must have studied turning forces resulting from tire distortion due to the tipping action. I bet that whatever scientists/engineers have come up with is not much more than a finite element method to get some numerical assessments.
I guess I wrote the post to accentuate the fact that when we make our happy turns on skis we ride on top of easy to understand and comprehend physics (at least most of it), when we make our happy turns on inline skates or carvers we ride on top of a mystery.