I apologize in advance for this being so long. Sometimes an adequate answer needs to be, and sometimes I just get long-winded.
This is more in regards to question #1.
The weighted string... I use it a lot, sometimes for laying out a bow, sometimes just to point out what work needs done BEFORE I'm able to lay out a bow. Sometimes I barely use it at all, and sometimes just on half of a stave. It depends on the stave. But I digress...
Let's look at laying out staves like the ones you mentioned in question #1, in fact, let's combine them. Let's layout a stave that is wider on one end than the other, and with some propeller and bow to the side. There are probably lots of ways to do it, but this is how I would likely approach it.
Let's assume the back of the stave reveals a continuous growth ring ready to be the bow's back. In order to get an idea of what you're dealing with, put the stave in a bench vice with the handle area level and the crown in that area, if any, straight up. If it's flat, make the stave level in the vice across its width too. Now lay the string down it and take note of each limb and its alignment with the handle area, and then the stave as a whole. This hypothetical stave of ours shows a moderate amount of propeller and the limbs bend to the side enough that the weighted string is off the handle area. The stave will need corrected with heat.
Find the center of width in the stave's handle area and mark it with a pencil. Now, follow the grain, precisely, from there out to each end of the stave. If the stave was split out, rather than sawn, it should roughly follow the stave's center, but don't count on that, follow it with your eyes, and trace it very carefully with a pencil. Check and recheck to be sure you've stayed on course. It's easier to see this in some staves than others, and the type of lighting can make a big difference. Sometimes I have to use an incandescent shop light, and sometimes I throw the door open, or take the stave outside. When done, this is the centerline, and from where you'll lay out the stave's preliminary width.... I know, you're thinking... but HOW do I draw the lines for the stave's sides.... wait for it... wait for it...
Since this stave will need heat correction to align the limbs with the handle and remove limb twist, you need to decide if you'll be able to do it with a heat gun or will need to steam the whole thing at once or in sections. On a stave such as this, one that needs long, full limb, or full length corrections, I like to use a 4" steam tube that heats the whole thing at once. So I would lay the stave out about 2" wide(or whatever works best for the stave), off of that 'grain centerline'. Since practically nothing is straight on this stave, I might make a bunch of 1" measurements off of both sides of the centerline and then basically connect the dots. Sometimes you can scribe line by running your finger down the outside edge of the split stave to connect the dots, sometimes only for short distances, and sometimes it's just too rough and uneven and you can't do that at all. In such cases I have used a little 'gauge block' of wood as a guide, cut to length so it's half the intended width of the bow, 1" in this case. Pencil point held against one end, and follow the 'grain centerline' with the other. I have also used a compass.... carefully following the 'grain centerline' with the compass point, while letting the pencil side of the compass draw your stave's edge as you travel down the limb.
Next, cut it out on the bandsaw while keeping the stave's back perpendicular to the blade/parallel to the saw's table. Since our stave has some propeller, this will require great attention and turning/leaning it slightly as it's fed into the saw.
Next I like to smooth up the sides a little with a sander or the smooth side of a Farrer's rasp, scraper, etc, just to remove the saw marks so I can scribe an accurate pencil line down the side, using a finger tip against the edge/corner of the stave's back, to layout the stave's thickness. For a flatbow, I make the sides about 3/4" thick from dips to 5/8" at the tips... careful to leave enough wood thickness in the handle and dip area as needed. Make sure the stave's back is protected with shellac. Steam for an hour or so, then clamp it to a caul when it comes out... a little reflexed perhaps... using clamps and shims to push the limbs sideways and down on the high side to align them and remove twist as needed. Plan ahead and have all of this stuff sitting right there waiting.
After it has cooled and been removed from the caul, put it back in the vice, scrape, sand, or use alcohol to remove the shellac or whatever you sealed the back with and also to remove any old pencil lines. Again, level the stave in the vice and lay the string across it. If you did a good job aligning things when it came out of the steamer, the string should be able to be roughly centered on the stave's ends while bisecting the handle. If you did a REALLY nice job, you can simply lay a pattern on it and trace it... OR without a pattern, mark the ends where the string rests, and where it bisects the handle, then connect the dots with a yardstick, then lay the bow out off of that centerline. But if there is still some bow, or wiggle to the grain, as in some character bows, you may have to again follow the grain from the handle to the tips, and layout the width off of that centerline. The important thing here is that the center of the tips and center of the handle are in alignment, so you may or may not have to 'fudge the grain' a little bit in the non-bending handle area, or make a minor adjustment with the heat gun later... like after a heavy floor tillering.
Backing up now a bit... If, on the other hand, its issues were minor enough to begin with that I thought I could remove them with a heat gun instead of steaming the whole thing, I would have used that 'grain centerline' to lay out the stave closer to it's final width dimensions, leaving the tips a bit wide to allow for some alignment options there, thin it enough to get to a heavy floor tiller, then heat correct with the heat gun.
Yes, tapering the limb width off of a crooked centerline can be a pain in the butt, sometimes you just have to make a bunch of measurements to indicate your width profile, and connect the dots. The more character the bow has, the more measurements I make.
Sometimes, like on the super snakey osage bow I'm making now, I divide the limbs into equal sections 2 or 3" long, and make width measurements off the centerline at each section, gradually reducing that measurement by 1/16", or whatever the math works out to be, writing the measurement in pencil at each section, then duplicating it on the other limb.... then connect the dots. Make any sense?
