I've roughed out the Hawthorn some more.
There isn't a straight bow in there without having the grain at weird angles or breaking out half way along a limb.
The solution, in theory, is to mark out two straight limbs and then bend the bow at the handle to line them up.
The fore and aft bend (reflex deflex, left pic) isn't a problem and is in a reasonably nice proportion already, I've left extra wood in the handle area so it can be narrow and deep.
The sideways bend is trickier, you can see from the second pic that the far limb is kicked off to the right.
Once the handle is slimmed down, steam and pressure should be able to bring them in line.
The bow is narrower than I'd hoped for, but at least the end grain is running in a reasonable direction.
There is still tons of hard work to do and the bandsaw has just about finished it's job (maybe it will help out on the handle a bit). To have got to this stage with hand tools would have been hard work.
I marked out the limbs in pic 1 by following the grain with a pencil. In the right pic I used a straight edge (an old metal carpet edging strip which is fairly flexible), I had to avoid splits and shakes and try to keep the end grain running in line with the back/belly of the bow.
This is the common and simplest grain alignment as the under bark surface can become the back of the bow.
You can also make a bow with the end grain running at 90 degrees e.g front to back if you are cutting a bow from a quarter sawn board.
You don't really want it at an ange, although I daresay, just about anything is possible.
Hmmm, just had a close look and the end grain at the other end isn't so good, it's at a bit of an angle and there's some grain run off on the far limb.
The Pic below shows what I mean.
The angle of the grain isn't too bad, my Yew longbow has a similar degree of twist. I think the wood in the top right of the pic is sapwood, I'll probably remove wood from the top edge to get down to the more even looking wood.
The next stage is working down the back of the bow with a spokeshave to try to get it somewhere near following a single growth ring. (I shoved the tip of the bow through the paper to give the camera something bigger to focus on and to help avoid the shot bleaching out)
I don't know! I've done a bit more this evening.
As I work it down, I'm hoping the grain will appear more orderly, but it's rather wayward.
Viewing on one edge the grain takes a sudden turn off twards the belly, but on the opposite edge it sweeps towards the back!
As it gets slimmer it feels lively, I think it wants to be a bow, but it could be just waiting to smash.
I shall keep my head well down when it's time to start pulling it back on the tiller!
Maybe it'll be a great bow, or maybe it'll beak in two and slap my face.
Sorry if I'm getting a bit fanciful here, but this one is a real tease!
I think I'll press on fast to see if it will work before I straighten it. If it blows up, I'll admit defeat and make a nice well behaved Ash pyramid style Ash bow with a nice bit of recurve on the tips.
The Hawthorn does feel like a good wood, but maybe this just isn't the right piece?