This has bugged me for a long time and I haven't been able to sort it out on my own. Why/how does sinew help a bow bend so much? I've read that sinew stretches something like six times as much as wood. If that's the case why doesn't the wood just break under the sinew?
To get back to the original question: Sinew CAN stretch 6 times as much, but that doesn't mean it does it on every bow and throughout the depth of the sinew layer.
Sinewed wood bows will stretch at the back maybe 2%, in extreme cases 2.5%.
If you would make sinew at the surface of a bow with a wooden belly stretch 5%, the belly would effectively fret and collapse.
Sinew will stretch to about 5% on Turkish sinew-wood-horn composites, but only at its surface. The first layer, which is glued to the wooden core, will be stretched less than 1% (as the wood core needs to be kept intact as well, it cannot stretch more than 1% at the most or it will break).
The reason sinew is so interesting has to do with the shift of the neutral plane that backings give to a bow.
Since wood is a bit stronger in tension than in compression, the neutral plane of a self bow is about 33% from the back of the bow: 1/3 of the wood works in tension, 2/3 work in compression.
The opposite backing of sinew is flax: it cannot stretch very far, and needs a lot of force to stretch a tiny bit. If you add a 1.5 mm layer of flax backing to a 30 pound bow, you'll get a 60 pound bow (but short-lived): Because the flax is so strong, all the tension is carried by the flax, and the neutral plane will shift to just under the flax. The entire wood thickness (nearly double of before) now needs to work in compression, with dramatic results: if you're lucky, it just frets all over the place and takes set, if you're not, it buckles at some point and leads to an explosive break of wood (and flax) (been there). Paper thin backings of flax can be interesting to protect a back with grain violations from breaking.
Since sinew is both very elastic (it can stretch far) and has a low modulus of elasticity (it starts to stretch under low forces already), you need a decent layer to make it really work. Add a dense wood to it as a belly, such as osage (with the extra plus that osage is superb in compression), and you have a belly that doesn't need to work extra hard. Add 3 mm of sinew to a 30 pound bow, and you'll get 45 pound bow or so, but the neutral plane will shift just a tiny bit towards the back, and for a now stronger bow, there's just a minute amount of extra belly depth needed (or the belly surface is compressed just a little bit more).
(Do consider the numbers given here as thought experiments, not as facts)
Moreover, sinew has the extra advantage of shrinking when drying, so it pre-loads the bow by pulling the belly into tension and the back into compression! When you brace the bow, you first need to overcome this extra force, and you get a higher string tension at brace. The belly isn't put under more strain because of this, its kind of a free ride offered by the reflexed sinew.
There's an extra advantage in dry conditions. Tension strength of wood peaks at 12% MC, and decreases at lower and higher MC. Compression strength of wood only gets higher at lower MC. That's why very dry selfbows break when MC drops too much: tillered for higher MC, the neutral plane shifts towards the belly at low MC, and the backs are overstrained when drawn.
Tension strength of sinew also gets higher at lower MC. So in dry climates, sinew and wood complement each other extremely well, as they keep pace. The same goes for horn, by the way. That's why horn bows are kept as dry as possible.
So to summarize, sinew doesn't protect the belly, but it doesn't require a lot of extra strain either from the belly relative to the extra draw weight it adds. And in dry climates, it effectively protects the back from breaking.
that's my 2ct
