I sense that there is another underlying question
yes George, there is something that I am trying to understand better. I will try to explain.
with all due respect to Mike, whom I quote below, I think that some of the "dictations" need qualification.
Tiller profile is dictated by the width profile of the limbs.
This is certainly true if a constant thickness taper is assumed. It is the physics or beam theory that he mentioned earlier.
Let's for the sake of a thought experiment, consider a pyramid bow that is almost tillered out. It has the desired circular profile that is considered correct for the width shape, and the assumed constant thickness. If I then thin the thickness of the mid to outer limbs, they will come around more into an elliptical shape considered "proper" for the straight limbed bow. Have I created set anywhere by doing this?
Or consider the opposite width profile, a straight limbed bow with the preferred stiffer inner limb. Will thinning that inner limb to make the overall appearance more circular create set? Only if I go too far and create a hinge. For the sake of examining tiller profiles, Lets assume that we can tiller either limb to any profile we want
The purpose of this "experiment" is to try to separate the out the reasons or (at least, suspicions), of whether one kind of tiller profile might outperform the other. There are two things that come to mind. The first being the mass distribution of the limb.
not because of tiller profile per se but because the limbs are long and therefore heavier and slower moving
Mike states the case for heavy arrows well, and others have mentioned similar logic. Heavy arrows are a joy to shoot, taming the vibrations of the limbs, and extracting efficiency from the bow. They can also be uninteresting.
Considering the case for light G.P.P arrows seems a bit trickier. Ignoring the weight distribution "dictated" by the back shape. (I know, that's a co-premise to what Mike actually said), Is there anything i
nherent in tiller shape it'self, or the way the limb "unwinds" and returns it's energy to the arrow, that can be ascertained? Performance of light arrows is not just raw speed, as Steve frequently points out, and creating a "sweet shooting" bow while shooting light arrows is of interest. Steves observations about simpler limb designs often out shooting more complex designs are keenly noted.
I do not actually expect that anyone can answer these questions definitively with facts and numbers, but we all have our intuitive ideas formed from experience, and I appreciate all the comments, ideas and even speculations of all.