DC, I'm pretty sure this thread got a bit sidetracked a long time ago. XD That may be partially my fault. Sorry for that.
But because I'm afraid I was being confusing earlier, let me clarify what I was saying.
When I said, "But every extremely reflexed bow I've ever seen has had some form of recurve. If the tips aren't pointing away from the belly at brace (string contact), then they're pretty damn close to being in line with the string." Recurve may not have been the word I was looking for. I meant any concavity of the back/convexity of the belly at brace. In other words, the profile bending away from the direction the material is being pulled. I feel like there should be a word for this!
To illustrate:
So Ben, your bow (at the low brace in this pic) is an example of the sort of profile I was talking about being less stable originally, and this is what I meant by being in line with the string.
Looking at a different profile, bows with recurved tips will usually show both convex and concave sections of the back, like so:
And bows with a kink/siyahs/whatever have the concave sections too, whether working or not. All kinds of weird things are possible:
But all these bows have at least one area where the back is concave at brace. I'm suggesting that this concavity makes flips much more likely in reflexed bows. It decreases string angle at the ends, and gives initial twist more leverage to twist more, in a sense.
As opposed to:
There is no area of that back that is concave, every part of the limb is going in the direction that it's being pulled. And nowhere is the limb close to running along the string. Given reasonably wide limbs, I'd expect this bow to be in negligible danger of flipping, no matter how much tension the string is under. It's hard to picture these limbs twisting in a way necessary to flip.
I wanted to use "recurve" to describe this concept, but I guess that implies that it's near the tips and curvy. I think it would be useful if we had a general word for concavity of the back at brace. Anyone with me?