Primitive Archer
Main Discussion Area => Bows => Topic started by: DC on March 31, 2019, 03:34:26 pm
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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?
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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.
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just a little,,, :)
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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.
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1 8th ????
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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.
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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.
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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
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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
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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.
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Wow :NN
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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
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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
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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.
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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.
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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.
It may be close enough, all I was saying was that it wasn’t mathematically correct as far as where it derives from. Your method is much faster when you don’t have a calculator.
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Bending strength is proportional to the moment of inertia of a rectangular cross section. The moment of inertia formula of a rectangle is I = [(Width)x (Thickness)^3]/3. So it's a cubed root relationship.
Assuming you are keeping the width the same and you want to double the strength, take the cubed root of 2.
2X Stronger = 1.259x original thickness (your grand daughter is smart :) , I had to go to college for 5 years and I still don't know a lot of this, or better yet I forgot most of it)
3X = 1.442
4X= 1.587
8X= 2
The cubed root of 8 happens to be 2.
The length of the bow is not relevant in this discussion.
You can also use the % increase in moment of inertia to determine how much affect a few thousandths of an inch will have on it's bending strength.
See below. Increasing the thickness in this example by 0.010" will theoretically increase the strength by 6 %.
Width Thickness Inertia % increase
1.1 0.5 0.045833333
1.1 0.502 0.046385536 1.20554244
1.1 0.503 0.046663293 1.811562048
1.1 0.504 0.046942157 2.419996073
1.1 0.505 0.047222129 3.030849315
1.1 0.506 0.047503213 3.644126575
1.1 0.507 0.047785409 4.259832653
1.1 0.508 0.048068721 4.877972349
1.1 0.509 0.048353151 5.498550462
1.1 0.51 0.0486387 6.121571793
Don't get too carried away with this as there's assumptions that go into the formula. Rectangular cross section and uniform material are important to note. But it's good for approximations.
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easy to see where a little wood makes a big diifereence when it comes to tillering those last six inches.
Don
so just remove wood to lighten the tips until they the bending becomes perceptible?,
and why are there so many engineers types gather round this campfire tillering sticks like primitives?
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Closet cave men ;D ;D
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Two divided by eight
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***Disclaimer- none of these formulas will help you build better bows***
Building bows will help you build better bows :BB
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The fun part of all this is, none of this actually has anything to do with how strong the bow is at 28". Rather it has to do with how many inches of draw it takes for it to hit the calculated draw weight, assuming the draw weight, bow length and width doesnt change from the bow you based your calculations off of.
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D=F•E(L^2)/(( H^ 2)( W ))
Displacement at the noches of the bow
E modulous of elasticity
H thickness
W width
L length
F force applied to a noch in the horizontal component
With all other factors being constant, the displacement is inversely proportional to the square of thickness as in, D=Constant/H^2
Knowing this will not help you make a better bow with natural materials because the engineering properties of organic materials are highly variable. Even within the same tree E can very by quite a bit. Just go with experience.
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I think that is what i said first,, just a little,, )P( :D
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Even within the same tree E can very by quite a bit.
yes, and the elasticity also
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This is the thread I've been wanting for a long time. (lol) Agreed that each stave within a species can vary drastically but this is just very cool and allows one to ideally take an overweight bow with an already good tiller down more precisely to desired draw weight without changing tiller because you can use proportional change of limb thickness along the whole limb. Gotta make sure your calipers are in good shape though. ;) Wish I could have contributed more.
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I may have started this thread but I sure wouldn't use this information for other than the wildest ballpark estimates. I sure wouldn't count on it for determining the thickness of a primo yew stave. I asked because I was unsure if the levers on my Molle were going to be thick enough and double the thickness was just way to much so I wondered how much thicker it had to be to double the weight. I was pretty sure that would still be too thick but it would be a lot closer.
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I'm not disparaging anybody, because you are all both correct and helpful. Some of you guys really know your stuff. (And, I love you all, and I love this site). However, I am POSITIVE our friend DC a has been around long enough to already know a lot of what was said. He's just a guy who likes to learn through questions.
"I never consider thickness, but tiller to the weight I'm aiming for." Agreed, but you gotta start somewhere. I lose more bows "roughing out" than I do anywhere else.
"You do have to consider the stability of the very narrow tips(lever)." Indeed, but that's implicit to what he's asking. "If I narrow by this much HERE, how much thickness do I have to add so it bends the same (bad idea)? And how much do I need to add to make it bend less? How much to make it NOT bend? How much narrowing is too much?, etc.
"This only works if the bending stresses do not exceed the proportional limit of your materials however." Indeed. The main, constant, and universal consideration when making bows of wood. Bowyery 101.
"Just wondering and wandering, neither limb length nor limb width enter into the equation." Correct, but that's ok because the rule applies to any length or width. As a rule of thumb, with some experience, it can be applied to the proportions of any given bow.
"Knowing this will not help you make a better bow with natural materials because the engineering properties of organic materials are highly variable." I agree that making wooden bows by formula doesn't work well, but I think it DOES help me make better bows (along with a slew of other design principles).
It has helped me a lot. It helps make sure you have too much, rather than too little, material to work with. It also makes no sense to do work with scrapers and sandpaper that could be done with a plane or rasp, nor to leave dead weight where it isn't needed. It helps ME to realize what I can get away with, and when I really ought to stop.
Marc says: "Two divided by eight." I agree with this. The cubed root calculation is technically CLOSER, more accurate, but I generally use 25%, because, like Pat said, you still have to tiler the bow. It gives me plenty to work with later, but not so much that I get bored to death scraping.
This rule of thumb applies best to starting points, and helping one keep an eye on one's work as tiller progresses.
For instance, say I'm making a 66" elm Mollie. If I add 25% of the bending limb thickness to the outer limb, it will be stiffer, even though half as wide. If I fudge that up to 30%, I'm really in the clear, esp. since I know I will be messing some with the cross section of the lever. So, now I know I can fade-IN from thin to thick over the 2", have totally stiff levers during tillering, and arrive at tiller by working the thickness of the bending limb by TILLER, not measurement. Thinning there only increases the ratio, so when I'm done there, I still have enough material in the levers to tweak them down narrow, work the straight, and maybe reverse trap them a bit as I finish off, all while keeping the
"I may have started this thread but I sure wouldn't use this information for other than the wildest ballpark estimates." I think that's how that rule of thumb is best applied.
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I kind of applied this yesterday but... The working limbs are tapered both in width and thickness as are the levers. By the time I figured an average for each and divided the width of the working limb by the width of the lever and then worked out the thickness of the.... well by then it was obviously going to be a WAG.
But there is no such thing as useless knowledge, every little thing you learn about bows helps, even if you don't think it does. ;D
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I think DC got it right. I can tell you the length and width of of any bow in my collection. I cant tell you the thickness of any of them. Every one of them is just thin enough to bend properly. That is not meant to disparage anyone who may put more value in that component than myself. To each his own, but for me, the thickness is the product of my work. Incidental to everything else.
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Thickness for two otherwise identical bows will vary based on the woods density. You design a bow to be 40@28, then scrape until the density and thickness are the proper ratio. Id wager that if bows were measured in thickness and density, within a margin or error, consistant ratios would be found.