I used red oak from Home Depot. Actually, I've made two 40" bows. The first 40 incher was from a piece of 1x2 red oak scrap I had laying around from some cabinet work. It was just going to be a practice piece.
The board had very close spaced grain (~1/8" between growth rings) with the growth rings parallel to the 1-1/2" width. I laid out the bow side profile on the 1-1/2" width...i.e. the back and belly of the limbs are the 3/4" wide part of the board and are perpendicular to the growth rings. Before you all chide me for doing this, read on....
The bow came out MUCH better than I expected...and did not require any iterative tillering.
It was broken by my 12 year old son's idiot friend not one hour after I had finished the string. He picked the bow up while no one was around and drew it till he snapped both limbs. That had to be farther than 17" draw as I had drawn it that far myself.
I could have punched that kid right out of his shoes! But, I also learned something studying the breaks.
For the second 40 incher and the 48 incher, I chose boards with the same grain structure as the first one. I had to sort through a bunch of boards to find some like this as most of them have the growth rings running diagonally through the thickness of the board.
I did not have to do any iterative tillering for these bows either...I just cut'em to predetermined widths and thicknesses, sanded them smooth, and they bent into proper circular arcs.
Here's why I think that happened.
Early and late season growth have a different modulus of elasticity (MOE) (i.e. stretching strength). Building bows the "usual" way creates shearing stress between the growth rings as the the two different materials stretch differently . That is why when growth rings run off the face of the back of the limb, it is a highly likely place for the limb to split.
By bending the wood normal to the growth rings, there is a consistant reaction to bending across the full thickness of the limb. That may well be why I got nice circular bends by just cutting to the predetermined dimensions based purely on bending moment calculations.
What do you guys think?
Beginner's luck...is always nice...