Del, your drawing seems to have been done with a bias of preponderance to fail. Is this due to your experience, or just theory? If you'd have drawn one you were determined would succeed, as they often do, I suspect it would/should look different.
If we were to assume, as you did, that an arc/portion of a cylinder presented 'angles' by interceding with compressive forces, we would have to assume there were an infinite number of them, each at different angles, because it's a force vector interceding a portion of a cylinder(of identical material btw), and often an oblique arc/cylinder, which also helps dissipate the force in other vectors as well.
But I'm not even sure I buy all that 'angle stuff'. If the glue joint is properly done, it's at least as strong as the wood itself... and if the wood for the patch is carefully chosen from the same species and/or actual tree and ring and grain bias, then just-as-gradually-tillered and taught to resist the forces of compression as the balance of the limb was, the forces transfer into and through the patch, along the same lines as they did anywhere else in the limb. No problem. This hypothesis aligns itself more with what I've experienced in actual results. It's not a piece of polished titanium we're putting in there.
Hey, I like physics as much as the next guy, I'm just telling you guys it has worked really well for me... and is relatively quick and easy, compared to grinding the belly off one or both limbs and adding a lam, or replacing an entire limb, and reshaping and retillering the bow.
