Here are some pictures to clarify what i mean. What would be the maximum drawweight before i need to add a backing? I can't imagine that a grain that's diagonal trough the board doesn't matter at higher drawweights.
There are two kinds of things people refer to as 'Grain". One is the growth rings. The other is the radial grain. If you let a log sit out, you will see little splits develop in the ends, These splits will extend out from the center of the log like spokes of a wheel. You can split a log along these lines, and as long as it follows that radial grain, the back will be ALMOST as strong as an intact growth ring, because the fibers are separated, not cut across. In fact, if you follow the fibers, any angle is ok, but you MUST follow the fibers.
You can make horrendously powerful bows from boards, without backings, as long as the back follows those fibers. This is why only one board in 50-100 will make a bow. How strong a bow you can make depends on design, and quality of the board, not on raw draw weight. Any bow will break iff made too strong.
So, with the board bow, sans intact growth ring or backing, make it as strong as you want. *BUT* do so by making it wider. If a perfect stave of hickory with an intact growth ring will make a 50 lb bow 1-3/4" wide, then the same wood, quartersawn into a board stave, will make a similar-tiller bow 2" wide at the same poundage. And it will make a 70 lb bow if made LONGER or WIDER.