No one else seems to be offering any advice so I'll jump it.
(Terms and conditions apply, contestants must be 18 or over
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Make 'em deep (thick) enough not to bend and wide enough to remain stable and not flex sideways.
So I'd guess that means about as wide as the the thickness of the bow at the working section and say 2-3 times as thick as the working section.
Just bear in mind that stiffnes is proportional to the cube of the thickness and directly proportional to the width.
Sl for arguments sake the rigid bit is 1/3 the width of the working section it will be 1/3 as stiff. But if you make it twice as thick it will be 2x2x2 = 8times as stiff.
So overall that would be 8/3 times stiffer which is near as damn it to 3times stiffer than the bending section, bear in mind that there is less leverage close to the string.
So 1/3 the width twice the thickness should do it. But obviously better to go for a bit more and then remove the excess as far as you can hold your nerve.
Del