PatM:
Sinew is much less stiff than wood and stretches several time farther, so making bow thickness double by using sinew instead of wood raises draw weight by about 4 times instead of 8, and does so safely, where wood would break.
Yes, glue-soaked cotton is as heavy or heavier than bow wood. It's likely not the perfect elevator. one of it's purposes was to save sinew. Elevating the sinew was the goal, and being essentially neutral in tension or compression, it did that without the complications a wood core would bring--using a wood core would be essentially the same as starting with a thicker bow.
Mark:
Yes, balsa, or similar, might be better. Sheer forces develop in the limb; if back and belly can slip and relieve the strain it seems this would create large hysteresis and reduce stored energy [more study needed], if so then the trick will be to find a material stiff enough to resist slippage/deformation but be as light as possible.
I recently whipped some hide glue into a foamy froth; when it dried it was about .10 specific gravity and quite rigid. Some versions of that might be the ideal elevator. Experiments needed.
George:
The sinew on Inuit cable bows and similar was not highly elevated and not of large enough diameter to raise draw weight as in this case. And possibly the sheer-slippage situation too. Their ingenuity went simply into getting a working bow at all, from no apparent makings. If they'd had decent wood they likely would't have bothered with sinew.
gfugal:
Yes, once made silk cable-backed bows, the cable elevated with the nodes. A couple of problems with that: Since the cable is uniform in diameter it stretches most near the grip, essentially dead weight at the outer limb. This also meant that energy was mostly stored in the near grip sinew.
DC: Cork and related is well worth trying. It might surrender to the sheer forces, but only one way to know.
Stick bender:
Crowning the sinew means that only the top of the crown is highly stressed, sinew below that having progressively more mass per work done. And the hardest working crown-top portion would be a relatively small amount of sinew, unable to store near the energy of a rectangular section of equally high sinew. Typically such designs only gain a few extra pounds over the wood itself, the maid point of the sinew being to keep the bow from breaking.
But this is all in-progress thinking.
Tim