Primitive Archer
Main Discussion Area => Bows => Topic started by: DC on February 22, 2018, 02:05:09 pm
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This didn't seem to fit in the other two threads. Is there a way to test backing? Just bend it as much as it's going to bend? More?
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That's what I do Don. I grab it and bend it slightly beyond where it would be on a bow. I cant replicate the stresses, but if the backing wont bend that far on its own it wont get used by me. I got a sweet plank of 1/4 sawn shagbark from a friend. I was excited and planned on getting at least (24) 40" slats. I cut out 3-4 of them and gave one a test. I barely got it moving and it popped. Hmmmm? I grabbed the next few and the same results surfaced. I stopped sawing it up for backer slats and just use it for accents on tip over lays and grip build ups now.
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I think to test a backing you would want to bend it around a radius abouty 100 times its thickness. If it is .125 thick you would move the decimal point to the right 2 places and that would be your approx radius to test it two. So for .125 you would need about a 12" radius. Not 100% positive but I think this would give you a pretty good idea.
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Tests are probably useful to week out junk, but even if the piece passes the test, it's not under tension as is it will be on the bow...
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That seemed very tight but I tried it with one of my strips and it did it no problem. Thanks guys.
Jim, that's true but this will help with a measure of confidence.
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Jim, if you draw it to an equivalent radius it will be under similar stresses. We can't duplicate what the belly wood is without gluing them together.
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That's what I do Don. I grab it and bend it slightly beyond where it would be on a bow. I cant replicate the stresses, but if the backing wont bend that far on its own it wont get used by me. I got a sweet plank of 1/4 sawn shagbark from a friend. I was excited and planned on getting at least (24) 40" slats. I cut out 3-4 of them and gave one a test. I barely got it moving and it popped. Hmmmm? I grabbed the next few and the same results surfaced. I stopped sawing it up for backer slats and just use it for accents on tip over lays and grip build ups now.
That's a tragic tale, man. :(
Whatever we do to test them, I'm going to plug stock selection. You have to know what you are looking for, and not settle.
I know you all know, but that is step one, for sure.
I also stop and re-evaluate the grain/board each time I cut. Some planing or trimming might be in order.
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When you have a parallel slat and you bend it, you are putting most of the stress in the middle and not like you do with a bow. Even the best backing strip will eventually break if you abuse it.
I don't bother with bend testing, just inspect for pin knots, grain irregularities, and the straightness of grain especially on the edges of the slat. Reject those with defects for a backing. They might be useful for a core lam, rather than going broken into the waste bin.
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A token flex or two seems like reasonable insurance for not getting surprised after you glue it up.
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Without a doubt, Pat. To parlay on my above story. The fella that gave me that wonderful plank had a few bows blow up before I could tell him what was up. So, IMO it works and isn't a bad idea to at least try it before you spend all that time. I never knew why it was junk. It was cut healthy, stored properly and had exquisite grain.
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Jim, if you draw it to an equivalent radius it will be under similar stresses. We can't duplicate what the belly wood is without gluing them together.
Nope. Half the thickness will be in tension half in compression. And at that, both forces are concentrated near the surface where they act--something like 90% of the force within 10% of the thickness. When glued up, the force is concentrated in the outer 10% of the full thickness, which means the backing is taking nearly all of the tension.
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Jim, if you draw it to an equivalent radius it will be under similar stresses. We can't duplicate what the belly wood is without gluing them together.
Nope. Half the thickness will be in tension half in compression. And at that, both forces are concentrated near the surface where they act--something like 90% of the force within 10% of the thickness. When glued up, the force is concentrated in the outer 10% of the full thickness, which means the backing is taking nearly all of the tension.
I agree, the back is taking all the tension but not stretching much, forcing almost all of the movement into the compression side, I would guess that the top 20% or less is taking all the tension forces.
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Nope. Half the thickness will be in tension half in compression. And at that, both forces are concentrated near the surface where they act--something like 90% of the force within 10% of the thickness. When glued up, the force is concentrated in the outer 10% of the full thickness, which means the backing is taking nearly all of the tension.
I suspect that in both cases the outer 10% of the backing will be under the same amount of stress
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Nope. Half the thickness will be in tension half in compression. And at that, both forces are concentrated near the surface where they act--something like 90% of the force within 10% of the thickness. When glued up, the force is concentrated in the outer 10% of the full thickness, which means the backing is taking nearly all of the tension.
I suspect that in both cases the outer 10% of the backing will be under the same amount of stress
Perhaps, but in the glued up bow, all of the backing is in tension.
On another note, at a given radius, a thinner strip is under much less stress. That's why a thinner limb can bend farther without set. So bending that thin strip of backing by itself is of little use as a test.
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Jim, that is why when you give it a bend test the radius has to be relative to the thickness. If a 1/4 inch thick you bend on a 25" radius, on 1/2 thick you bend on a 50 inch radius, then they will be under the same stress.
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Steve, in principle, I agree, but I don't think the ratio is right. Since bending strength increases as the cube of the thickness.
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The thing is, you can bend it or not bend it. Bending will uncover bad grain that you can't see so that's a good thing. Not bending won't uncover anything. I'll bend it.
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Jim, I believe what you're referring to is that the second moment of area of a rectangular cross section is proportional to the cube of its thickness. This second moment of area is the letter 'I' in the attached beam bending equation. Thus, for a given force applied to the end of the beam (e.g. string pulling on bow limb tip), the resultant tip deflection is inversely proportional to the cube of the beam thickness. For a given force, doubling the thickness cuts the deflection to 1/8th; halving the thickness multiplies the deflection by 8.
The maximum stress in the beam does not follow this cubic relationship, however, and is in fact approximately linear, as Steve suggests. For a linear material -- which wood essentially is as long as its not taking set -- the stress is proportional to the strain. If you take a strip of material of thickness T and bend it around a radius R, the resultant maximum strain S (i.e. elongation and compression at the outer and inner surface) is approximately:
S = T / (2*R+T)
Now, since stress and strain are proportional, the ratio of stresses for two different bent strips will be equal to the ratio of strains.
So say I have two strips of material: my bow of expected thickness T1 and my experimental backing strip of thickness T2. From experience I know my bow will experience maximum bend radius R1. The question is: what radius must I bend my experimental backing strip on its own to feel confident it can survive the stresses it will experience as a backing in the bent bow? Setting the maximum strains equal, we need to solve for R2 in the equation:
T1 / (2*R1+T1) = T2 / (2*R2+T2)
The result is R2 = T2/T1 * R1
In other words, the necessary bend radius is indeed linearly proportional to the ratio of the thicknesses.
So if I expect my bow limb to be 1/2" thick and bend to a 36 inch radius, then a 1/8" backing strip will need to survive a bend radius of:
R2 = (1/8")/(1/2") * 36" = 9"
This analysis of course depends on the backing material being the same stiffness as the rest of the bow, which for hickory-backed maple or bamboo-backed ipe is not an unreasonable assumption. If the backing is stiffer than the belly wood, then the neutral plane will shift toward the back, subjecting the backing to less elongation and the belly to more compression. So if your experimental backing is stiffer than your belly wood, it doesn't need to survive as tight of a test bend. If your belly wood is stiffer than your backing, then your backing will need to survive a tighter test bend.
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Jim, think about it this way. Anytime you create a circle or radius with something you will have an inside and outside diameter. With wood we want the inside and out side diameter to be within 1% of each other or less. Regardless of thickness. So a 1/8" thick piece of wood need to create a radius that will be no more than 1% different than the outside measurement.