this quote from Badger is from another thread, but I have found his observations about wider limbs
interesting
I did some tests a few years ago on exceptionally wide osage bows. The results kind of disagreed with my own mass theory. I built several osage flat bows with stiff handles at about 2" wide to 2 1/4 inches wide. To my surprise the mass came in slightly lower than the 1 1/2" bows. I use to build all my 50# osage bows at about 1 1/8 wide to about 1 1/4 wide. I found I got less set when going wider and I also was adding mass but they were still better performers because of less set. When I bumped them up even wider I fully expected to see a substantial increase in mass but it didn't happen. The bows came out much thinner than I would have expected also. The only way this is possible is if at 1 1/2" wide I was still doing more damage to the wood than I thought I was.
Mass itself has very little to do with a bow in my opinion. Of course where mass is located is important, but mass is a function of, not a design feature of a bow.
Mass is only a biproduct of the bows width and thickness. Its width determines the stress it can take and its thickness determines how much it can bend before taking set. The combination of those two individual design parameters are what gives a bow its mass. Applied incorrectly, you can get a bow the correct mass bit not the correct draw weight the mass is supposed to give. The entire idea of chasing mass is not going to get anyone anywhere.
The stress of compression is spread out iver surface area, the stress of tension likewise. You need the correct surface area for the draw weight of the bow, and the correct thickness for the bend radius. The stresses are not distributed across the mass.
So the question is, how wide and long does a bow need to be to not take set. The formula I have been working on is an attempt to solve that issue.Im about 80% certain i have it figured out, but without more bows of many different wood species built, i wont be 100%. Its a simple formula The specific gravity is used along with the draw weight and from there you get how many sq inches of working limb you need. Soon as I know i am not putting out bad info, ill make a phone app that lets you put in your desired bow stats and it will tell you what you need to build.