The definitive science on bow design was done back in the 1930s by Paul Klosteg and Clarence Hickman. It's all in "Archery, the Technical Side." It's kind of overwhelming math and physics at times, for me at least. But we're just reinventing the bow when we try to sort it out from scratch.
Klopsteg was a brilliant engineer who did secret and very technically advanced work for the U.S. during WWII. He was also an avid archer and bowhunter. He did lots of experimenting with arrows, bows, accuracy and related issues.
Get the book if you can.
Jim Davis