Thursday 22 August 2024

Boo Yew Ipe Flight ELB draw weight estimation

I'm trying to build a flight bow, but the belly lamination will be an Ipe slat which is 4.5 mm thick and this doesn't leave a lot of material for tillering. 
So I'm tillering it as Boo Yew stave and trying to estimate how the extra 4.5 mm of Ipe will increase the draw weight. Just for ease of calculation I'm assuming the Ipe will be the same as the Yew (it is stronger in compression, but I'm just trying to get an estimate.

Currently the bow is 40# @ 17.5" which correlates to 61.7 @ 27" draw (short draw flight bow).
Mid limb thickness is 16mm. 16 cubed is 4096 (stiffness being proportional to the cube of the thickness)

If I add 4.5mm to the thickness this gives 20.5 which when cubed is 8615.
8615/4096 = 2.1 so adding 4.5mm would give 2.1 times the draw weight! 129#
Hmm, looks like I need to take more off the belly before glue up.
Trying to calculate an appropriate draw weight and length without the Ipe to give the desired final result with the Ipe is beyond me, so it's down to the old successive approximation. Keep doing a bit and re-calculating.
BTW. Target draw weight is somewhere between 60 and 80#, so I have some margin to play with.

I've done some more work, but this is all rather guesswork. Adding 4.5 mm (I'm calling it 4 to allow for finishing) won't give the same effect at the tips as at mid limb. Say the tip is 12mm thick an extra 4mm is making it 33% thicker whereas near the grip where it is say 20mm thick it's only adding 20%. I s'pose taking the mid limb thickness isn't too bad.
I've currently got it drawing 19" at 35# with a 15mm thickness mid limb, which is giving a finished estimate of 101# . Still a bit high, if I can get the estimate down to below 90, I think I'll go for glue up.

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