Bob noted and understood.
I can see that the original was steam-bent from a single piece. I don't have the equipment to do that. I have also noticed that others have made this from 1/4" strips that could be easily bent and glued together around a form.
But I am going to give my "composite" bow a go first. If it doesn't work out, then I will probably hand it over to a shop that can steam-bend one. But since I already have this wood, I want to take the low-budget route first.
The main horizontal section will be strong as it travels with the grain. It's the vertical pieces that go across the grain that would be weak. Since I don't have enough thickness anyway to cut from a single piece, I will make it from a layered "sandwich" of pieces.
The vertical sections will be a composite of wood in two different grain directions. Between that and copious wood glue, it should make it much stronger than if I just cut it from a single piece of wood.
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