As I've got some time let me try and tackle some of this... agian, my 10 cents... not laying down the law! ;-)
"i think the issue that we all make with this disucssion is one alluded to by Andy in his many blogs. We look at a bat as a static object and the graphs I posted earlier are doing something similar."
Nope, that's Andy confusing stuff (maybe :-)). The bat is a static object, it does not change its shape etc when you swing it. Regardless, we are talking about bat shape - or really mass distribution.
Andy's right, and its true that the system is dynamic and mass distribution etc can effect all of this, swing weight etc, but that's not what we are talking about here, we are talking about the mass distribution as an absolute driver of middle performance - any dynamic difference would need to be removed - i.e. balanced out so that can be disregarded, and we just look at the shape impact.
"As a static object, F=MA varies across the face of the bat according to those graphs if the bat is static and a ball is bounced against it."
Well it really just depends how you measure it, normally you will be looking at the centre of mass, which is one point of the bat surface, so no, it does not really change across the face of the bat.
"What we forget is that a bat is almost never used as a static object and is nearly always part of a dynamic system. When we play a defensive shot, generally, the ball doesn't go very far, regardless of the bat. That's the impact of concaved versus non-concaved."
True, but irrelevant to decision on bat shape I think... to test the effect of the bat shape, we could just keep the bat still and fire the ball in to the different parts, that would isolate the effect of bat shape.
"When we drive, cut, pull, etc, we are using the bat dynamically. At this point the static distribution of weight across the face plays much less of a part, hence why perimiter weighting can work as it is the "swing weight" or Moment of Inertia that is in play. "
Again true, but its a different thing, if the shape can allow you to swing the bat faster, then great, but we are talking about absolute middle performance as an effect of mass distribution, everything else must be ignored.
"In baseball, and a lot less in cricket, there have been many studies of the effects of MoI and essentially it boils down to more mass hits the ball further but a lower MoI increases the bat speed and can also allow more control of the bat."
Yes, that's just basic physics.
"Well it is my belief that one of the reasons that it's hard (but not impossible) to hit the ball a long way using the edges of the bat is that when you hit the edge, the bat twists. Back to this dynamic model again. Coming back to Ross's argument, the mass difference is minimal between thick and thin edges, so that while you may counter the twisting force with thicker edges, you don't counter it enough to make a difference."
Again this is true, in part, but again twisting effects is another issues, it not about the absolute middle performance, and while it might be relevant over all, it should not for part of this disscsion for the same reason as above.
"Ultimately, the model you need to use it much more complicated than we like to pretend and a combination of forces and pivots come into play."
No we jut need to ask a more focused question. In fact pivots and forces are irrelevant, you have to assume they are all the same, otherwise you can't make any comparisons with anything ever!
Any way, who cares! ;-)
Good stuff, all in the right spirit.