Steve B:
I would say it's more important to get the inner limbs bending more on a short bow to reach draw length, because this contributes less to a shortening of tip-to-tip length as draw progresses. That's why holmgaar/molly designs do well at short lengths.
Where more aggressively elliptical tiller (that is, bends more near the tips) is beneficial is in longer bows. Say I have an order for a bow that for whatever reason, HAD to be 90 inches long but only 28" draw. What I would do is make the tiller so aggressively elliptical that it would almost appear I put two 28" normal limbs on a barely bending handle 34 inches long.
Others,
I'm not sure if the question was answered sufficiently, so here's some more fat to chew:
For a beam of uniform thickness to bend with equal stress along its length, it must taper in width in something very close to straight lines.
For a beam of uniform width to bend with equal stress along its length, the thickness must taper in a convex fashion, becoming more steeply tapered about 1/4 out from the tip.
We want a bow to bend with even stress as much as possible. Why is this? If a bow is bending to experience 10 units of stress everywhere except a 2" length of limb around midlimb, which experiences 7 units of stress, then that bit of limb likely has excess mass which slows the bow down. It also means the wood inside of that patch likely took more set, which projects to bigger set out at the tips.
Where you can afford to have less than equal stress is in the riser/handle/fade/flare area, as the amount of bend here (for flatbows most usually) is very low anyway, and usually takes no set.
Here's a design idea I just thought of: Think of a tiller shape you want to tiller. Some sort of ellipse. Start with a bow profile cut to pyramid design and tiller it to that desired tiller shape. What you will find is that the further out towards the tip you go, the more set it will have taken.
Now make another bow. But this time, using your first bow as a reference, make the profile a little wider wherever you see the set being too much. Just a little wider. You likely will still have a bow that has too much set in the outer half. So rinse and repeat.
Eventually, after a few tries, you will have empirically come to learn the perfect thickness taper and profile for that exact tiller shape you want.
Labour intensive, but an interesting exercise.
A bit more:
Strain is the percentage a beam's surface expands or contracts as a result of tension/compression. It is directly related to the radius of curvature the beam is bent to and the thickness of the beam. It can also be calculated by knowing the stiffness of the beam material, and the bending stress. A thick beam that bends a small amount might feel a great deal more strain than a thinner beam bent quite a bit further.
Theoretically, a properly tillered pyramid bow will not taper in straight lines, but will bulge slightly near the fades and taper to a zero-width at the tips. This is of course not possible in the real world and so there must be some width here. Adding width to a part of the beam increases bend resistance locally, meaning it becomes more stiff in proportion to the rest of the limb. As such, to make this section of limb less stiff, thickness must be reduced.
I've found lately that for a pyramid profile bow, the outer 1/3 to 1/2 of the limb need to be thinned slightly to achieve proper circular tiller.
A pyramid bow can be so narrow in the outer half because it is so thin in the inner half. Being thinner in the inner half, it bends further than the same part of a limb that has parallel width. The deflection here on the pyramid bow projects to a large displacement out at the tips, which means the outer half of the limbs can be of a cross section that bends less compared to the same section of limb in a bow with a parallel profile. It's kinda like a race between two cars. One has high acceleration and decides to coast along, while the other has lower rate of acceleration, but maintains it for longer.
Man it feels late. I'm just blabbering along now with no real point. Not even sure if, when I read this in the morning, it will make any sense.
Badger, I hope I'm not detracting all too much from your original intent...but I suspect I am.
Dave
