I was thinking that, wizardgoat. Taking a careful look at the fresh cut edges of the bow blank I found two places where the grain hooked, and I've finally decided this piece is a no-go for me. Bowandarrow473 I think you were right to question me on this one -- thanks, one more lesson learned here.
Bubby, I believe what you said about all being possible. But of course, the rub is, is the board good enough to pull it off -- especially without backing.
I think a board has to be absolutely perfect for an unbacked flat sawn bow in ash. I think now that good vertical grain (quarter sawn) blank would be easier to find, and the ring runout wouldn't have been a problem unless much more severe.
When you think about it, a bow with vertical ring orientation always creates runout at the edges of the bow, since the bow limbs taper. But as long as the grain is reasonably straight and parellel to the bow, bending is always going to be perpendicular to the rings, so they aren't subjected to shear the way they would have been if flat to the back.
Diagonal ring orientation is going to be a somewhere in between.
I looked for a quarter sawn board in my stack, found a couple, but those both were spoiled by one or two worm holes. So I'm going to give up on ash from this particular tree, for now. I'll wait until I cut a better one, and I'll keep in mind the need for quarter sawing, next time when cutting it up.
The birch looks good so far, and I still have a nice birch stave with the back on, so I'll keep on with that.