i agree with pat, there really isnt any way to know unless you are copying exactly one design. after making quite a few board bows out of 1x2's, i can roughly guess how thick i need it to be, but this is because im using the same limb width and taper. when you stray from that its really a tossup. if you narrow a limb you have to compensate by adding thickness, and vice-versa. the old adage of(a piece of wood twice as wide is twice as strong, whereas a piece of wood twice as thick is eight times as strong) usually plays a part in my estimates of a thickness needed, but i still start off with what i think is more than i need and work down.