Between this thread and DC's string angle thread I had to do more looking at this.
Using Super Tiller I designed a basic flat pyramid bow. I chose this because it is what my current bow project is so I have all the dimensions at hand and it is as good of a flat bow design as there is in terms of performance and pleasant shooting characteristics. S65" NTN, 40lb@28", material is maple. The back profile is 2" wide out of the fades for 3", then a straight taper to 5/16" at the nocks. Limb thickness is constant out of the fades, 0.370" to get my draw weight and length (as predicted by Super Tiller). Brace height is 7.5", measured from the back of the bow (this is how Super Tiller geometry is set, nothing significant about it), which is more like 6" when measured conventionally from the belly side of the grip.
Once I had this bow analyzed I then made two more bows based on it. The back profiles are the same for all 3 bows, limb thickness is kept constant but was adjusted to get 40lb@28" for each bow. On one bow I recurved the outer 6" of the limb tips in a smooth arc to 2" forward of the handle. On the other bow I reflexed the entire limb out of the fades in a smooth arc to the same 2" forward of the handle.
I did not adjust the thickness taper to minimize stresses, which really needs to be done to maximize the recurved limb design. This is more a comparison of what happens when you take a simple flat bow and then either reflex it or flip the tips. The recurved version did not have big enough hooks to shorten the effective string length at brace, so it was very representative of many of the bows I see here. Here is a summary of the results. Excuse the funky formatting, the forum doesn't make that very user friendly. Note that the stresses are somewhat arbitrary and it is the changes between the designs that are important, not the absolute magnitude of the numbers.
Bow Version String Tension @ Brace (lb) Energy Stored (ft-lb) Energy Stored % Change Maximum Stress (psi) Max. Stress % Change
Flat 57.4 36.1 --- 22,009 ---
Recurved Tips 71.8 38.4 6.37 24,068 9.36
Reflexed Limb 63.4 37.2 3.05 23,923 8.70
IMO, the things to take away are that the recurved tips increase the early string tension, energy stored and stresses the most and that both recurving and reflexing increased the stresses more than they increased stored energy, which seems like a poor trade to me. I have done similar studies with R/D bows and they tend to increase energy stored more than stresses, so they would appear to be a better way to design a bow if you have the opportunity to do it that way from the start.
Mark