Sorry guys for the math...
I tried to give an answer to your question: how thin does the board need to be for it to bend (and make a bow). Since I don't know how much it draws at the given thickness, I tried to provide a way how to calculate the required thickness yourself.
I know that not all pieces of wood are the same, but to a large degree, there are constants on which to build. Otherwise we wouldn't all want to make osage bows instead of willow, and you could as well take a belly of douglas fir instead of ipe. Onebowonder gave a good account of the limits of maths in bow design. Within a single board, odds are high this math approach will yield useful results.
Let me try to make it simpler through a few well-know facts in archery:
As bow
width doubles, the draw weight doubles. Very logic and intuitive: you doubled the amount of bow, so the draw weight follows that ratio.
as the bow
thickness doubles, the draw weight is multiplied by eight (TBB vol 1: tillering, by Jim Hamm). This is much less intuitive.
So if you have a bow of draw weight 20#, a similar bow of twice the thickness would draw 160# at the same draw length (if the wood could stand the compression and tension at that thickness and draw length). This is because thickness and draw weight follow a cubic (power 3) relation.
doubling thickness: original thickness times 2. Draw weight is then 2*2*2=2
3=two to the power of three = 8 times more
Adding or removing a tiny bit of thickness has a large influence, and this is what makes tillering so critical: one pass too many with the rasp can make the difference between a 40# and a 60# bow.
Suppose you increase or decrease thickness not by double or half, but by some smaller degree, what is the expected draw weight?
You take the relative amount you increase or decrease in thickness, multiply by itself two times and multiply by the former draw weight.
To go from 1 cm thick at 30#, to 1.1 cm, you multiply by 1.1. Take this to the power 3 (1.1*1.1*1.1 = 1.33), and this number tells you how much the draw weight is expected to increase. So at 1.1 cm thick, all other things being equal, you end up with a draw weight of 30#*1.33=39.90#
You can also do the opposite: if you know the draw weight at some thickness but want another draw weight, how thick should the limb be?
(this was the initial question here, more or less).
Suppose the thickness is some value A and gives a draw weight of say 80#, how thick should I make it to get to my target draw weight of, say, 60#? Or for your ipe board: how thick should the belly plus backing be to get to your intended draw weight?
I added a very simple excel sheet that allows you to calculate this by giving current draw weight, current thickness, intended draw weight. The output is the required total thickness (ipe plus bamboo) for the intended draw weight.
For you imperialists, I even added a inch-decimal inch-cm conversion chart
So you can forget all i wrote above, and just enter the numbers in the excel sheet and see how the output (in red) changes. Since you will need to pre-tiller the ipe belly for best results, you might as well have an idea what a certain thickness of bamboo lam will do to the draw weight.
Hope it helps.
