DC's post got me on to this train of thought. I have to say, I still have a lot of questions about backings, mostly because guys I know make fine bows are doing things I don't get, or even wouldn't agree are correct. Here is what I THINK I know.
The main purpose of the back of a bow, unless sinew or cable backed, is to hold the bow together. "A bow is a bow until it's back breaks." Everything else is secondary.
Uninterrupted fibers from a single ring, either under the bark, or "chased" are best. A sawn wood backing seeks to replicate this strength, by the nature of the wood specie chosen and our selection and milling of the grain. We back staves that otherwise could not stand on their own, and to improve their profile.
Do we all agree so far?
Now, Baker originally said that a backing too thick for the belly wood could overpower the belly, and listed a bunch of ratios for hickory + other woods. He also extolled the rectangular cross section. I still see this idea touted a lot, and I don't buy it at face value. Baker later issued a correction, saying backings should be NARROWED by trapping rather than thinned, to match their bellies. He offered a bamboo-backed red oak as an example, the bamboo surface being barely over half as wide as the belly. I know I have had a good handful of very successful bows that ended up half backing and half belly. I have likewise made good tri-lams with "tough wood/light wood/strong wood" combos, the belly slat being less than half the total thickness.
We know most woods are tough to break, but stretch very little before breaking. I.E. A hickory backing may perhaps be stronger than maple, but both will break if stretched their length + 2%, give or take. Some woods are weak in tension, thus we see very few poplar-backed osage bows, right? Commonly chosen backing woods are proven to be tension strong. Hickory may be stronger than maple, but maple is stronger than average.....
So, all that said, I truly believe that backed bows FAIL for exactly the same reasons self bows fail: I guess a backing could overpower the belly, but far more often I have either had a backing fail from a FLAW (as do selfbow backs), or I had a belly fail because I expected too much of it....... I.E. I'm back to TBB basics, DESIGN IS KING!
It's a sloppy sample, because backed bows are often profiled by Perry reflex or whatever, but what I mean is the back still has to not blow, and the belly still has to take the compression, or it'll take set. WIDTH, length, profile, and thickness are still key, more so than the specie of the backing.
If I take a 2" wide elm stave, plane down the back, and back it with hickory, maple, or white oak, I have essentially done nothing as far as I can tell. Perhaps I have added a little bit of weight. Tillered in, ALL of those woods will "hold" an elm belly, and all will stretch a similarly tiny amount. All will ask the same amount of compression of the belly, and all those bows could be tillered to similar draw weights at the same width and essentially the same thickness. Plane down a 1-1/2" wide osage stave, and the story is the same, unless you tiller toward a very high draw weight.
So, I'm thinking the question is "will the backing hold the stiffness of the belly" whether that comes from thickness or a stiffer belly wood. I haven't done it, but I know an elm backing would hold a black locust belly, ASSUMING the width, thickness, and (by extension) the draw weight is appropriate, as well as a pristine BL back would have. I expect maple is slightly less tension strong than elm or hickory, but not so much it won't hold the locust. MAYBE a hickory back could be trapped more (or an elm back more crowned) than maple, but its probably a tiny difference. Maybe a 1-1/2" wide locust belly should have a lower targeted final draw weight, than a 1-7/8" BL belly slat, but that would be true of a self bow, too.
If I try to make a 100 lb maple-backed locust only 1-3/8" wide, well, I better tiller better than I ever have in my life. If I back a fir 2 x 2 with maple and try to tiller THAT to 100 lbs, even worse. BUT that has little to do with the backing. It's more about width, belly wood, and design.
Anyway, I could be wrong here and there, but I don't buy that backings overpower bellies. It's more likely that we back marginal staves or even marginal designs. I don't think thickness of the backing kills bellies, I think stiffness of the belly does. I do think trapped AND crowned backs are a fine strategy, assuming there is enough strength there to hold the bow. I also think different woods used as backings act about the same and interact with the belly about the same, except it may take more to break a hickory back than a maple back. Finally, It seems backings are not as strong as pristine wood, but, unless flawed, or badly designed, are plenty strong. Likewise, I have to assume a truly perfect maple backing would be better than a sketch hickory backing.
I'm leaving bamboo out for now.