Bow thickness

[DC]

Math not being my strong point I'll ask. If doubling the thickness of a bow increases the draw weight 8 times how much thicker do I have to make it to just double the draw weight?

[Pat B]

I never consider thickness but tiller to the weight I'm aiming for. I start tillering from about 5/8" to 3/4".
Math has never been my strong point.

[bradsmith2010]

just a little,,,

[peacefullymadewarbows]

Oh boy I've been wanting to know this formula for a while too. I'll be watching for a precise answer. I've never been able to find an answer even searching through here. I tried to look into the physics of a beam but for someone not educated in that field I could not make a straightforward answer. Is it linear or algorithmic progression of thickness to draw weight addition? The world may never know.

[bradsmith2010]

1 8th ?

[DC]

I was just on my walk and started wondering(wandering comes in a few years) how thick to make the levers on my Molle. My grandaughter just figured it out for me. For us normal people if you want to double the weigh multiply the original thickness by 1.25992. For you math people I think this is all of it.

[Pat B]

You do have to consider the stability of the very narrow tips(lever) so they don't pull to one side or the other when under stress.

[avcase]

You got it. This only works if the bending stresses do not exceed the proportional limit of your materials however.  The bending stresses also go up by the same ratio if the rest of the dimensions of the bow remain the same and the bowis drawn the same amount.  If these bending stresses exceed the material limits then this will result in some set, so the actual increase in draw weight will probably end up something less than double.

Alan

[sleek]

I reckoned 1.25 based on if twice is 8 and you want 2, two is 1/4 of 8. So the answer must be .25 extra. So, 1.25

[peacefullymadewarbows]

Your grand daughter should have charged for that equation haha. Thank you very much for posting that. It will help tremendously in planning out new bow dimensions based off of previous ones from same wood/tree.

[bradsmith2010]

Wow

[NonBacked]

Don –

Give your granddaughter a pat-on-the-back! She did a great job “deciphering” our wood beam-mechanics dilemma! If we convert her formula to a generic equation, it allows us to adjust the desired draw weight (theatrically) “up” or “down”.

T = Original Thickness
D = Original Draw Weight
P = Preferred Draw Weight
M = P/D = Draw Weight Multiplier
Y = (M)-3 = Thickness Multiplier
N = T x Y = New Thickness
   
Example 1: Increase the Draw Weight      

T = 0.50”   
D = 30 lb. 
P = 45 lb
M = 45/30 = 1.5
Y = (1.5)-3 = 1.44      
N = 0.5 x 1.44 = 0.72”

Example 2: Decrease the Draw Weight

T = 0.50”   
D = 60 lb. 
P = 45 lb
M = 45/60 = 0.75
Y = (0.75)-3 = 0.91      
N = 0.5 x 0.91 = 0.46”

Just wondering and wandering, neither limb length nor limb width enter into the equation.
H

[High-Desert]

I reckoned 1.25 based on if twice is 8 and you want 2, two is 1/4 of 8. So the answer must be .25 extra. So, 1.25

Sleek, 2 being a quarter of 8 is just a coincidence that matches up. It’s just the cube root of whatever multiple of poundage increase. So three times draw weight would (cube root of 3) be 1.442 time as thick.

 It may be a way of estimating rough out if you are making a bow out of your typical weight range, giving you a starting place. Would be worth an experiment

[sleek]

I reckoned 1.25 based on if twice is 8 and you want 2, two is 1/4 of 8. So the answer must be .25 extra. So, 1.25

Sleek, 2 being a quarter of 8 is just a coincidence that matches up. It’s just the cube root of whatever multiple of poundage increase. So three times draw weight would (cube root of 3) be 1.442 time as thick.

 It may be a way of estimating rough out if you are making a bow out of your typical weight range, giving you a starting place. Would be worth an experiment

Wont be the first time i was right on accident.

[sleek]

Using the example of 3 times, you take 3÷8 then add your 1 and you get 1.375 times thickness to make it 3Xs stronger. Carry that logic to 4 times, which is half of 8, the answers should be 1.5. 4÷8+1=1.5. To make the bow 4 times stronger, you need tlit 1.5 times thicker. It works out all the way to 8 times stronger, 8÷8+1=2. So, i think that proves the equation to be true. Its just a simpmified version of what DCs granddaughter came up with. Good on her btw. Most kids dont think that way.