One of my favorite applications for the mass theory is when making ELBS. I believe with the heavier war bows the mass comes out a bit too high and needs some adjustment but never the less it still reflects the relationship between design, wood density and tiller shape. An ELB is unique in several ways when compared to an american longbow. First of all we need to mainatin a 5/8 ratio of thickness to width. We need to have at least a slighlty round belly, the bows are usually but not always longer than the American counterpart and they are expected to at least slightly bend through the handle.
If a bow is 72" long or 68" long we need to maintain at least a minimal amount of width in the bow to guarantee lateral stability and no twisting of the limbs. The challenge starts here when making bows for target shooters in the 50# and below range. A 50#@28', 72" bow with a circular tiller should way about 15 oz when finished. If you were to take a hickory backed ipe and build it to ELB demesions and expect to hit mass weight you would only be 3/4" wide and very unstable in the outer limbs. If you were to build that bow to floor tiller using minimum stable demensions you might end up about 1.125 wide and around 26oz to 28 oz.
The way we solve this problem using the mass principle is to simply raise the projected weight by changing the tiller shape and working areas of the bow. The other solution is to use lighter woods allowing for a more circular tiller shape. By adding a 16", 1/2 bending center section and stiffening the outer 8" of outer limb the mass projection goes up to about 23oz which should be no problem bringing the floor tillered un refined 26 oz stave down to.
I have found knowing how much mass forces me to adjust the design or materials to optimize a design based on materials used.
