Primitive Archer
Main Discussion Area => Bows => Topic started by: tom sawyer on June 07, 2007, 04:03:08 pm
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Recently, Tim Baker reported on a couple of simple experiments he did to demonstrate the practical significance of something we were talking about on another site, namely the Poisson Effect. I thought I'd share them and throw out a theory on what was going on.
First, let me briefly summarize the Poisson Effect. When something is stretched it gets narrower, and when something is compressed it gets wider. This goes for wood. When you bend a bow limb, the back tries to get narrower at the same time the belly is trying to get wider. The result is that the limb edges curl towards the back. So a rectangular cross section when unbraced, becomes something of a "smile" at full draw. The effect is more pronounced with a wider limb. Tim bent a piece of wood with rectangular cross section, and showed the curl was visible to the naked eye using a shadow cast across the limb. So right there, I think the wheels must have been turning in his head about his absolute insistence that a rectangular cross-section is superior.
Second, he took the piee of wood and cut off the inner edges so make a "v" shaped belly (leaving the back flat). When he bent this he saw the the edges of the limb now curled down towards the belly, opposite the direction of the Poisson Effect. He didn't speculate about why this was, but I think he reallized this was a significant observation. I've thought about this and have an explanation that helps me answer a question I've posed to myself before. Namely, how does a neutral plane behave when a limb cross-section isn't symmetrical?
A neutral plane (NP) is that imaginary line where half the limb mass is on one side, half on the other. Its a plane, which means it has to be flat right? But an assymmetrical cross-section is not going to have a flat NP. And yet I think it wants to be flat, and when you bend the limb it tries to get that way. So if you design a cross-section that has a "smile" (rounder belly than back) or a "frown" (flatter belly than back), when you bend that limb it is going to try and move to straighten this situation out. How much, depends no how far from flat the NP is to begin with and how far you bend the limb.
Taken together, I think its possible to make the NP "frown" just enough (by rounding belly slightly more than back) to counter the effect of the Poisson Effect, which would mean no net change in the cross-sectional shape during the draw. I would suppose that this is the true "best" cross-section for equal distribution of forces across a bow limb.
What do you think?
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Why would this matter, and how would exactly negating the Poisson Effect have any advantage you ask?
If there is no net movement in the cross-sectoin, then there is less energy lost to returning this mass to its initial position. Increased effiency would be the result. And the two counter-acting forces, would presumably produce slightly greater stored energy in the limb. Granted, these increases would probably be small.
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A neutral plane (NP) is that imaginary line where half the limb mass is on one side, half on the other.
The neutrality of the plane refers to the zero-tension, zero-compression position within the limb and not the equal division of mass. Unless there were a perfect balance of tension and compression strength in a stave, the NP wouldn't correspond to the physical center, or mass center of the limb.
Also, I would think that this position would 'warp' its way though a character stave rather than being a flat plane but I could be wrong.
J. D. Duff
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Lennie, I will have to reread this a few times for it to totally sink in but I think I get the gist. ??? Let me throw in a monkey wrench...for woods that are weaker in compression, wouldn't a belly that has more curvature than the back suffer excessive strain down the center of the belly(crown) especially if the back is also crowned? Would this be a good candidate for trapezoidal cross section? :-\ Pat
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Lennie,
Would Tim say that the rectangular section still has the energy-storage advantage even if it is more subject to the poison effect? I do think you're onto something.
J. D.
By the way, if you make my head explode, the blood is on your hands. ;D
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Interesting Lennie. I would be interested to see you put this into practical use.
I think you may be reading into it a little. I think it is wood being crushed between the back and the belly. If the energy is too great for the back it explodes. If the energy is to great for the belly it frets. The energy on the bow that does neither is stored in the wood in the center of the bow, and tries to escape out the sides. Because it is being pushed toward the belly it pushes the belly wood out more. The belly wood being pushed out is still trying to escape out the belly, so it curls toward the belly and outside edge. By rounding it will not have a straight edge where the human eye can see the movement. Just my thoughts. Justin
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For me it's simpler than that. The bow with a v cross section frowns because it has no belly at the sides to stop them curling towards the belly. After all, you're stretching the back and it wants to be as short as possible.
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JD and Pat, for a selfbow the position of the NP coincides with the center of mass. A single material has only one elasticity, so it stretches and compresses equally well. The "strength in compression" and "strength in tension" numbers (which are different for a given material) have nothing to do with the neutral plane, they only refer to when the back or belly will break. When you say "a wood is stronger in tension than compression", it doesn't mean the back is doing more work than the belly.
With a crowned back, you'd make your belly either flat or slightly roudned but not as much as the back. That would make the cross section "frown", and it would go away and be flat at full draw. Theoretically.
Using different materials in one limb, like a bamboo backing that is less elastic than wood, shifts the NP towards the backjing but it doesn't change the fact that the NP is not planar and wants to get that way. Come to think of it, theres a good reason to try and keep the cross-seciotn from "smilling" or frowning on a bamboo-backed bow, because this could lead to splintering when the backing gets mashed together by the Poisson Effect.
Can't you feel your head getting bigger?
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JD and Pat, for a selfbow the position of the NP coincides with the center of mass. A single material has only one elasticity, so it stretches and compresses equally well. The "strength in compression" and "strength in tension" numbers (which are different for a given material) have nothing to do with the neutral plane, they only refer to when the back or belly will break. When you say "a wood is stronger in tension than compression", it doesn't mean the back is doing more work than the belly.
As I understand it:
1. Wood is not completely homogeneous (consider Yew with sapwood or Osage with wide variety of latewood ring widths).
2. The same piece of wood does respond differently to compression and tension stresses.
J. D. Duff
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Lennie, couple of ways you could look at it, the tension or work you are putting into the string and being transferred to the limb is causing this effect, wouldn't the reverse affect just transfer the energy back to the arrow when you rleased the string?
The other possible way to look at it is also the reason I prefer slightly oval shaped limbs, is that when the affect starts to take place it is simply amatter of the wood kind of giving up and folding, using more mass in the limb than you actually need for the same amount of work. I find I can control mass better on oval shaped limbs than flat limbs, the poisen affect may be a reason for this. Steve
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Damn, I'll be reading and rereading all night! ::) Takes my pea brain a long time to absorb and comprehend. Give me a few days and I'll get back to you. ;D
This is interesting and I actually think I understand ::) what you(or Tim) are saying...but I still have to think about it for a while. Pat
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Steve, I agree that rounding edges minimizes the consequences of the Poisson effect since there is less mass moving out there. As for the bend transferring energy back, whenever you move something it has to be moved back so the Poisson bend going back uses a bit of energy. If it didn't move at all, you wouldn't be wasting any energy. I don't know if this is why your rounded-edge bows do better, it might also be better aerodynamics of the limb.
JD, a yew bow with sapwood back would be an exception. And wood isn't perfectly homogeneous, but it is reasonably so. Most bows have a fairly smooth thickness taper as judged by the feathering of rings on the belly. If density were all over the place, you wouldn't see this. And wood does respond differently to compresion and tension, but that doesn't mean it produces more spring power on the tension side than the compression side. Elasticity is elasticity, whether you stretch or compress. A metal spring is as hard to stretch as it is to compress, even though the metal might break in tension before compression.
Simon, you might be correct in your description but the back side wants to be skinnier so I would have predicted that the sides would still curl up. In fact I would have thought they'd curl up farther since there's no belly wood preventing movement. It seems to me that all the parts of the limb are trying to get to a place where there is eual mass on both the tension and compressoin sides. Hence the idea of the NP wanting to be flat (in a 2-D sense).
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Lennie,
The NP refers to a "place" where the tension and compression forces are theoretically equal correct?
So if I take a perfectly rectangluar cross section your saying that the NP is physicaly/geographicly positioned dead center because I have the same amount of wood(mass) doing tension work as compression work?
If I remove material(mass) from either side of the original location of the nuetral plane then I have a situation where more wood(mass) is doing more tension or compression which would have to shift the physical/geographical location of the NP correct?
Looking for clarification before I jump in and reveal my ignorance further :)
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Simon, you might be correct in your description but the back side wants to be skinnier so I would have predicted that the sides would still curl up. In fact I would have thought they'd curl up farther since there's no belly wood preventing movement. It seems to me that all the parts of the limb are trying to get to a place where there is eual mass on both the tension and compressoin sides. Hence the idea of the NP wanting to be flat (in a 2-D sense).
I think it's wrong to say that the neutral plane 'wants' to be any particular shape. It is what it is, depending on what the wood immediately around it wants to do.
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Sorry, just to clarify what I mean on my first post. I was saying that the stretched back wants to be shorter - it does this, not by being skinnier, but by 'cutting the corner' on the curve you produce by bending the bow. i.e. it tries to form a less severe curve. But I see your point... generally things do get skinnier when stretched.
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Simon, its doing the opposite. The edges curved down towards the belly. If it was cutting a corner, it would have lagged behind like a standard Poisson Effect does. And yes, I shouldn't use that terminology, but how would I describe the idea that a non-symmetric cross-section will change shape in order to become more symmetrical with respect to a plane down the middle of the limb? Its an idea that is tough for me to express any other way.
Marvin, yes the NP is going to be right in the center of the limb. Measure from back tobelly at any spot on a selfbow limb, the halfway point is where the NP lies. Connect all the dots and you get a line across the limb tht runs roughly in the center of mass. Connect all the lines and you have a plane, although If the cross-section is symmetrical, then line is straight. If the cross-sectoin is assymmetrical, the line isn't straight. I'm theorizing that a non-symmetrical cross-section tries to bend into more of a symmetrical position when bent. If you remove mass, you have to measure again and draw a new NP line.
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A neutral plane (NP) is that imaginary line where half the limb mass is on one side, half on the other.
'Neutral plane' does not mean 'middle line,' or center of mass. It means wood that is neither compression wood, nor tension wood but is 'neutral.' For the neutral plane to fall on the geographical center of the bow, or the mass center you would need:
1. 100% homogeneous material.
2. 100% rectangular section.
Since 0% of bows fit that category, the definition you give above has a corresponding 0% application. I'm only harping on this because you are proposing a confusing and misleading definition. 'Neutral' wood is where it is--that is going to vary with section, substance, etc.
I agree that you can say it is very close to center on self bows with rectangular sections but that is not a definition of 'neutral plane.'
J. D. Duff
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It does equate to center of mass of a selfbow, because it takes x amount of wood to store a given amount of energy in tension or compression. And equal amounts of energy is stored in tension and compression in a selfbow.
Just because a cross-section isn't perfectly rectangular, doesn't mean there is no neutral plane. There very well is a place in the interior of every limb that is under neither tension nor compression, and where shear is greatest. Measure the length of the back of an unstrung bow, and the belly. The distances should be the same, assuming not a lot of set. Now measure the length of the back and belly at full draw. The back is longer, and the belly is the same distance shorter. Stretching equals compressing.
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Take any cross-sectoin, and draw a line across that give you euqal mass of wood on either side. That is one way to estimate the position of the neutral plane. But if you put dots along with center in between edges, the line won't be straight but stil you'll have equal amounts of wood on either side. My contention, is that this is more like where the actual neutral plane lies, since each little area of the back is working against its corresponding place on the belly. Sure there's some evening out, but not that much. If there was, then the crowned area of a limb wouldn't be under more stress since it would get shared around. Each little area is its own entity, which makes the neutral plane funky shaped. I simply think the explanation of Tim's second observation is explained by thinking of the NP this way, and that there are forces working to restore some degree of symmetry to the cross section and by extension, to the NP.
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Here's what I mean by the edges of the back trying to 'cut the corner' of the bent v shaped bow:
http://s166.photobucket.com/albums/u118/simon2468/?action=view¤t=scan1.jpg
The edges of the back can reduce the amount they have to stretch by trying to get nearer the string. Obviously there is a slight conflict of interest because as you say, it also wants to get skinnier so there must be some tension across the back from left to right.
I guess the net forces at work make frowning the least stressful position for the back to be in.
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It does equate to center of mass of a selfbow, because it takes x amount of wood to store a given amount of energy in tension or compression. And equal amounts of energy is stored in tension and compression in a selfbow.
According to that theory, you couldn't underbuild or overbuild a bow. We know that you can store more or less energy in the same amount of wood by changing its configuration (ie section).
Just because a cross-section isn't perfectly rectangular, doesn't mean there is no neutral plane. There very well is a place in the interior of every limb that is under neither tension nor compression, and where shear is greatest.
I didn't say there was no NP. Of course it's there. I said you defined it wrong by calling it a predictable, measurable, geographical position rather than the correct definition you just gave ('under neither tension or compression, and where the shear is greatest').
Measure the length of the back of an unstrung bow, and the belly. The distances should be the same, assuming not a lot of set. Now measure the length of the back and belly at full draw. The back is longer, and the belly is the same distance shorter. Stretching equals compressing.
Have you tested this or is it theoretical?
J. D. Duff
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The neutral plane is a bad term. It is not a plane (nor does it want to be) unless the bow is symmetrical. It is also not the center of mass unless the wood, homogeneous or not. It is the point where the wood on the back pushing toward the belly, and the wood on the belly pushing toward the back neutralize each other with equal force. The piece of wood would have to have exactly the same tension strength as compression. Think of it like this: Take a 600# sumo wrestler and a 200# sumo wrestler and put them in a ring. If the 200# wrestler is pushes back the same as he is being pushed, the neutral plane is between them and offset by 400# of mass. It is the neutral plane because it is not pushing either way. It is not flat, it follows the contour of the bodies. Justin
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Lennie,
I'm sorry if I'm creating confusion by harping on this. My main point was that this is not a correct definition of neutral plane:
A neutral plane (NP) is that imaginary line where half the limb mass is on one side, half on the other.
And this is the correct definition:
There very well is a place in the interior of every limb that is under neither tension nor compression, and where shear is greatest.
Justin,
I think you are right that the term 'plane' is misleading. Neutral 'fibers,' or 'zone,' might cause less confusion if we're getting technical with our definitions.
J. D. Duff
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Lennie, I wasn't agreeing with you just trying to make sure I understood what you were trying to say :)
I'm thinking about your comments and feel that discussing both the NP and the Poisson effect at the same time is creating additional confusion. I'm going to make some simple assumptions for a moment to try and get clarity on this discussion.
Imagine a limb with a rectangular/equal cross section. Let's assume that the NP is in the physical center of this limb equal distances from the belly and back.(I'm not yet convinced that this is true and want to explore that point further but not now)
According to the Poisson effect if the back and all fibers from the back right up to but just before the NP are all in tension to some degree then that section of the limb wants to narrow as it's being stretched. The belly and all the fibers from the belly right up to but just before the NP are all in compression and want to widen as it's being crushed.
What is the significance of this? In my opinion not much. It really just boils down to finding out how much "wood" you need to deal with either the tension or compression forces. If your particular wood specimen happens to be very strong in tension then you know you can get away with less "wood" in the back area then what your using in the belly without having a failure. Witness the common practice of "trapping" or creating a trapezoidal cross section in limbs. Why would you want to do this? What's the benefit? Mass reduction is the answer. The less mass in the limb the faster is will shoot an arrow because it's not wasting energy moving any more extra mass then needed thus leaving more energy to be transfered to the arrow.
Optimising the cross section of a limb is about balancing those opposing forces of tension and compression. What Tim Baker observed was predictable behavior based on the Poisson effect. Can that effect be manipulated to any benefit by changing the shape of the limbs cross section? Maybe.
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Stimulating conversation. Thanks Lennie.
Without too much consideration, and no research, I would speculate the amount of compression or tension a particular area of limb section sees is relative to the degree of bend, it's width and thickness and not it's physical properties. A wood's maximum capacity for tension and compression is not the same as it's tendancy for same under bending stress. I think this has been posted already, perhaps elsewhere, as Lennie did the Johnny Appleseed thing with this topic all over the net.
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Justin, I think you are confusing the strength and elasticity terms. Just because wood is stronger in tension, does not mean the back is the 400lb wrestler. The wood has one elasticity, also known as stiffness. This stiffness is the same whether you stretch or compress it. Maybe I'm not understanding your point though, I'll think on it some more.
Marvin, I didn't say it was all that significant. But the Poisson Effect and possibly this other business I am describing is there and I'm simply pointing out that there are stresses on a bow limb that we don't always think about. Its kind of hard to measure things like cross-section of a bow at full draw, so we tend not to think there is anything going on.
Will you make a better bow, knowing these stresses exist? Heck I don't know. I do think it changes the argument for rectangular cross-section just a bit. That subject has been debated pretty heatedly in the recent past.
I agree that "plane" is misleading, in that it implies a flat 3D surface. Since the limb bends, the plane is curved. What I am not positive about, is whether the NP (neutral place?) is flat in 2 dimensions or is whatever shape is dictated by the cross-section.
Simon, I see what you're saying, it could be that this is the explanation. What would you call that? The edge is obviously moving to the point of least stress, and it is doing so in spite of the Poisson Effect tendency. So it must be stronger than this effect. I think it is possible to make a cross-section where there is no net movement.
This must be simple stuff to a physicist who has studied bending and the like. We aren't discovering some unknown property here.
Mims I felt like I needed to post everywhere, to get a few responses. I actually got more good input than I expected.
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Lennie,
I'm glad you brought this whole discussion up. Is this basically what you have in mind?:
If some of the muscle energy used to draw the bow is absorbed by the NP trying to straighten itself out, bows which are less affected by the poisson effect will transfer more stored energy to the arrow.
I wasn't trying to get off-topic by talking about a strict definition of the NP. I thought a correct understanding was necessary deal logically with your theory.
J. D. Duff
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Lennie,
Each site has it's on character(s). ;-) Not critisizing, just noticing. But I deplore naming things, "Baker effect", "Perry reflex", etc. As you've pointed out, there's little or nothing new in this game. Just a pet-peeve.
Was Paleo the recent heated debate. I may have missed it.
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Good, thought provoking stuff Lennie. A refreshing discussion.
"Will you make a better bow, knowing these stresses exist? Heck I don't know. I do think it changes the argument for rectangular cross-section just a bit. That subject has been debated pretty heatedly in the recent past."
I think your right. My experience was that although it may be theoretically a superior cross section shape it did not have as much of a real world effect as other limb design factors. I've made radiused bellied, lenticular like cross section limbs that performed much better then my best rectangular cross section.
"I agree that "plane" is misleading, in that it implies a flat 3D surface. Since the limb bends, the plane is curved. What I am not positive about, is whether the NP (neutral place?) is flat in 2 dimensions or is whatever shape is dictated by the cross-section."
Now I understand better what you're talking about and exploring. Very interesting question. I would think the NP would NOT be flat in cross sections where at any given point in the cross sections width there is more wood either side of the physical center regardless of the poisson effect.
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David, I think it was paleoplanet that he's referring to.
I really appreciate folks like Lennie and David and a few others who discuss/explore the more technical aspects of primitive archery and look forward to seeing more threads like this one.
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Mims, you never know which site is going to provide the most interesting discussion. PP tends to have engineers weighing in and they are the ones who would contribute a lot to this discussion, but none really have over there. And Baker has been oddly silent as well. He's probably rueing the fact that he posted his results, I suspect he might write about this one day. I do think my discussins of the Possion Effect got him thinking and caused him to do the experiment in the first place. thats the great thing about Tim, he goes and measures stuff. I need to do more of that. The LW discussion is really good, and I posted a bit of this on a related thread on radiused vs flat bellies and got a stellar reponse from a guy named Ken. I asked if I could post his reply other places.
This place has had the best overall discussion though. Very enjoyable. And I am the first to say that my ideas are not necessariy correct, which is why I try them out on people.
I shouldn't have said "recently" argued, I was referring to Baker and Torges' exchanges several years ago. But it comes up from time to time and people always have their favorite. You know they both work pretty well though.
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I shouldn't have said "recently" argued, I was referring to Baker and Torges' exchanges several years ago. But it comes up from time to time and people always have their favorite. You know they both work pretty well though.
Is that exchange available to read?
J. D.
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Not that I know of, and to be honest I heard about it second-hand as I wasn't into traditional archery back when it ocurred.
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I know there were some pointed comments in the TBM column that became Hunting the Osage Bow. I would love to see an actual exchange though.
J. D.
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Lennie,
Each site has it's on character(s). ;-) Not critisizing, just noticing. But I deplore naming things, "Baker effect", "Perry reflex", etc. As you've pointed out, there's little or nothing new in this game. Just a pet-peeve.
David, I used to feel the same way but have grown to like it now, if an individual simply makes something popular, explains it, or invents it, I don't mind seeing their name on it,
What does bug me is that if the ideas were all ready popularized or somehow credit was robbed from a known individual who deserved some recognition. I have yet to see anything new in bowyering since I have been involved, at best I have seen a better understanding of existing principles start to fall into place. The main reason I like the use of names is for easy identification and uniform understanding of a procedure. I also think it encourages and recognizes bowyers who have gone one step beyond in their homework. I know of only a handful of procedures that would fall into this category. Steve
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Would someone please explain Poisson Effect to me. Maybe that would help. When I build a self bow I let the wood tell me what it wants to be. Usually the theoretically aspects don't even enter my head. Pat
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Pat,
Take a rectangular pice of foam rubber and bend it in an arc. The back will cup and narrow and the belly will crown and widen. I think.
J. D. Duff
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Pat,
The real scientific types will probably cringe at my explanation but essentially the Poisson effect describes the tendency of materials to narrow when stretched or put under tension and conversely widen when compressed.
It's a fancy mathematical way of describing material distorting it's shape when stretched or compressed. :)
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Lennie, if you want some really technical discussion from engineer types you should post this at the flight archery site.
http://www.flightarchery.com/forum
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Thanks Josh and Marvin. That I can understand. ;D Pat
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Justin, I think you are confusing the strength and elasticity terms. Just because wood is stronger in tension, does not mean the back is the 400lb wrestler. The wood has one elasticity, also known as stiffness. This stiffness is the same whether you stretch or compress it. Maybe I'm not understanding your point though, I'll think on it some more.
If the wood does not stretch, bud does compress the neutral plane will shift toward the back. If it stretches bud don't compress it shifts to the belly. Some woods don't compress better and some stretch better. That is why we use different woods for bellies and backings on a laminated bow. Justin
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What do you mean by "better"? Stretching and compressing are both aspects of elasticity. Within elastic limits, a particular piece of wood will produce equal amounts of tension and compression work. Your "better", is how much stress it can handle before it breaks.
I'm sure this "bending opposite Poisson effect" is explained by simple engineering terms, but if Baker turns out to have been the first one to apply this to bows and actually explains it to us, then it'd be about like Perry and his reflex method. What'll really tickle me though, is to see him admit that the purely rectangular cross section isn't necessarily such a cut-and-dried best bet. I'm not holding my breath of course.
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Lennie, I tend to treat all woods as if they are equal in tension and compression when laying out a bow, but the fact is they are not, it becomes evident as you build the bow and get further into the tillering. It is very common for hickory and black locust both to be stronger in tension than compression. I think for general purposes most of the time it is safe to assume they are pretty close to equal. When a stav is pretty well equaly matched in it's tension and compression properties you will be rewarded with a very low set bow with low mass. If you know ahead of time they are not well matched you can compensate in the design. Steve
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Lennie,
The following is an attempt to describe how I see it. I could be wrong as I haven't performed a test on anything. I am not as noble or helpful as Tim Baker in that respect. I'm trying to work on that. At any rate:
A rope has high tension resistance and no compression resistance, while a stack of unmortared bricks has high compression resistance but almost no tension resistance. Every piece of wood will have similar qualities to varying degrees.
I don't think elasticity is the same thing as bend strength. Elasticity is the ability of the wood to bend or deform without being damaged. Bend strength is the tension resistance + compression resistance.
Example: Locust can be stretched without damage further than it can be compressed, while juniper can be compressed without damage further than it can be stretched.
If a selfbow finds that it is easier to stretch a little more and compress a little less, this will move the NP.
J. D. Duff
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l give up trying to convince you guys.
Ok one more time. :P
Yes locust can be stretched farther without breaking than it can be compressed. That is what strength in (compression/tension) tells you.
But it takes exactly as much energy to compress BL 1mm, as it takes to stretch BL 1mm. That is what elasticity tells you. There is no such thing as elasticity in tension or elasticity in compression. Elasticity is another word for stiffness.
I can think of a case where a selfbow doesn't have its NP right in the center of mass of the cros-section. That would be when it shows some set, which is generally due to a slight (you hope) plastic deformation of the belly wood. Now you've damaged your belly wood a bit and its properties are now slightly different. Its a bit compressed, probably a little stiffer now since it has a slightly higher density.
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Here's a quote from an engineer guy named Ken, he is a wise person. "Wise" being defined as someone who agrees with my point of view on the subject.
"The neutral plain may indeed be trying to flatten out and this could be expected with a triangular belly since by flattening of the neutral plane you would have the back and belly both curving down and the effective distance from the neutral axis (not surface) would get smaller and thus reduce the absolute amount of stress (and strain) on the limb. This also has the effect of reducing the Moment of Inertia which slightly raises the Stress level. The equilibrium point you are witnessing is the lowest energy state for the circumstances."
"The thing to remember is that stress and strain go hand in hand. In order to be stressed X amount, the material must strain Y amount. If this can't happen then the material will try to compensate by whatever means necessary so that it reaches the lowest energy state possible for the situation. With materials (solid or laminate), a combination of shear flow and deformation occurs until equilibrium is established or failure occurs. Poisson's ratio is an expression of the relationship between stress and strain and is indicative of how the material will reach the lowest energy state."
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Lennie, strength in compression or tension only refers to its resistance to bending, has no relation to it's elasticity. You have a modulus of elasticity and a modulus or rupture that refer more to those thngs. Steve
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OK we don't have to agree on what the terms mean, to think about what is going on in a limb. Regardless of where the NP lies in a limb, all the wood within that limb is trying to be as close to it as possible so that stress is minimized. It strains to get there, as evidenced by Baker's observation #2 (the triangular cross-section).
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But it takes exactly as much energy to compress BL 1mm, as it takes to stretch BL 1mm. That is what elasticity tells you. There is no such thing as elasticity in tension or elasticity in compression. Elasticity is another word for stiffness.
Did you even read my last post? ??? We're talking about the same thing--I'm just (respectfully) disagreeing with you.
1. It takes different amounts of energy to stretch a material than it does to compress it. This is true for every substance on earth. Why would any substance respond to opposite forces in exactly the same way?
2. If there is no such thing as elasticity in compression and tension, Perry and Baker are mistaken in much of their thinking.
e-las-tic
adjective
capable of returning to its original length, shape, etc., after being stretched, deformed, compressed, or expanded: an elastic waistband; elastic fiber.
J. D. Duff
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I thought I read it. And now I've reread it.
Elasticity also equates to stiffness. If something is less elastic, it is more stiff. Just words on the ends of the same measurement.
Modulus of elasticity is actually more properly modulus of stiffness, because higher is actually stiffer. Its a measure of how much energy it takes to bend a board in a particular direction. More energy means stiffer board.
I'm not trying to get you peeved about this. We should just agree to disagree. The observation made isn't dependent on exactly where the NP is in the limb. You just need to know that the wood strains to get to the lowest energy state which is the closest to the NP. I think that explains the observation quite nicely. It and the Poisson Effect, are things we should consider when we discuss the merits of bow limb cross-sectoins.
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Well.....I'm with you fella's......Delmer
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Koan--I laughed my head off! You are a brilliant man.
J. D. Duff
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Simon, I see what you're saying, it could be that this is the explanation. What would you call that? The edge is obviously moving to the point of least stress, and it is doing so in spite of the Poisson Effect tendency. So it must be stronger than this effect. I think it is possible to make a cross-section where there is no net movement.
It's a good point. If the back isn't alowed to curl in either direction, it implies it must be under greater stress. Therefore it might be harder to pull and store more energy. You've reduced the weight of the bow by removing wood from the sides of the belly = faster bow.
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Lennie,
I'm sorry, but I have to take the weekend off to work on my personal dwelling. In the mean time I will take a class on physics so I can disagree with you with greater confidence. ;D
J. D.
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Man you guys are making my head ache ???
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If there is no net movement in the cross-sectoin, then there is less energy lost to returning this mass to its initial position. Increased effiency would be the result. And the two counter-acting forces, would presumably produce slightly greater stored energy in the limb. Granted, these increases would probably be small.
I've been reading this over at PP and here. If this theory pans out, then the increases in efficiency would be small (as you said). My initial thoughts are that the increases would be so small so as to have no measurable affect on the efficiency of the bow whatosever. But I'm not saying for certain that is the case.
Fascinating theory, and I look foward to seeing Tim, Tom Sawyer, and Ken work this out.
My basic working theory on bows is to go symetrical. If the back is flat, then the belly is flat. If the back is crowned, then the belly matches the crown, and so forth. Extremes in either way (high arched D bows, super flat bellies on crowned selfbows, etc) make me nervous. Work with the wood and try not to impose.
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Agree whit all you guys said even if I didn't understand a word ::) (had to stop readyng on page 3 :o :o
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Wow ! Learn sometin' every day ! Didn't realize "herpatology an poisson" had anything ta do with neutral plane ! ;D ;D...bob
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Simon, I see what you're saying, it could be that this is the explanation. What would you call that?
Oh it's got to be the 'Sawyer effect' if it doesn't have a name already :)
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JD, hope your weekend was as nice as mine. The wife and I went to Cloverdale on Saturday and shot the Trad Nationals, then went to the wild game potluck that evening. Very nice time, saw a lot of nice people including Pappy from here at PA. He was up to his usual, making snakey bows and helping anyone that stopped by his camp. I beat the wife on the course, but she was the only one who hit the aerial target game they were running.
I remember now where I read about the info pertaining to this argument. It was in Archery: The Technical Side by Hickman and Klopsteg. Unfortunately I only have a xerox copy and I can't locate it at the moment. I did Google a site using "bend moment neutral plane":
http://hsc.csu.edu.au/engineering_studies/civil_structures/bending/bending_stress.html
I quote a section of the page:
"The geometric centre of a two-dimensional area is known as the centroid. In relation to beams the centroid will be the geometric centre of the cross-sectional shape of the beam. It is significant because the neutral plane, discussed above, will pass through the centroid of the beam. When considering a rectangular beam, the centroid is simply found by joining the diagonals but becomes more complex for composite shapes."
They are talking about a beam with a symmetrical cross-section, of an isotropic material that is supported on both ends and bent in the middle. This is close to what we have with a bow limb. You can argue that a piece of wood is not isotropic but I think it is reasonably so if the piece is clear and straight. Consider that you can make a backed board bow from any orientation of wood (plain, rift or quartersawn) ands you don't have to orient a plainsawn board so the outer side is to the back. To me that is proof that wood is a reasonably isotropic material. In any case, mull this over. I know how you guys are thinking, I used to believe this until I read otherwise. Its confusing because you would think that "stronger in tension than compression" means it stores more energy in tension than compression. Thats not the case as I hope I've shown now.
Simon, I have nothing to do with this stuff, other than bringing it up for consideration within the context of our application. Tim made an interesting observation, and Ken described what was going on. All I'm doing is passing it along because I think it is interesting.
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A summary of where I'm at with this:
1) The Poisson effect causes some stress in the bow limb that results in a strain that pushes the edgs of the limb upwards.
2) Assymmetry of limb cross section causes other types of stresses that cause limb wood to strain to get to a point of least stress, which is nearest the neutral plane. This movement can actually counter-act the Poisson Effect if the particular symmetry forces wood to move in the direction opposite this effect.
3) Assymmetry of cross-section can also be caused by assymmetrical material combinations, as in backed bows. This moves the neutral plane to somewhere other than geometrical center (centroid). The wood in the limb still strains in order to find the least stressful point.
4) Forced reflex glueups of backed bows with assymmetrical cross-sections, are about as complicated as it gets when it comes to trying to understand all the stresses in the limbs.
Thank goodness you don't have to udnerstand it to use it. But I do think those who would champion a particualr cross-section, have a lot more to consider than meets the eye.
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Update.
Some guys on another site wrestled me down and twisted me arm behind my back until I admitted that wood can have slightly different MOEs in tension versus compression. So I now have to admit that the NP may not always be at the geometrical center of the bow. I did get them to agree that the strength values have nothing to do with NP though, that the poundage is coming from the stiffness aspect which is represented by MOE.
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Uhhhg. Me put little stick on string attached to big stick. Me pull back, me let go. Little stick fly away. This good. Me happy. Uhhhg.
Lennie, not make me think more. Makes head hurt. Uhhhg. ;D
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So easy a caveman can do it ;D
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So we sort of agree that a V or D shaped belly might have a slight advantage over a rectangular one. There are plenty of D shaped designs aren't there? It's just a question of how pronounced the D should be. Any ideas Tom?
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I haven't even progressed as far as determining whther there IS such a thing as a superior cross-section. I'm just noting different stresses that are inherent to greater degrees in certain designs. Nothing I've been talking about, is necessarily pointing to any "best design". All it does is poke some little holes in the arguments of some people who dare to make those kinds of statements.
I've always been in the camp that thought either a mostly rectangular or mildly radiused design would work similarly. The latter having greater aesthetic appeal as well as being slightly easier to accomplish.
I kind of like the idea that you should sort of match the crown of your back, on your belly, maybe leaving the belly slightly flatter than the crown of the back. That puts the NP fairly near the center of the bow. It makes the back do more work which is good since the material is stronger in tension.
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My understanding from the discussion above is that you would need to remove just enough wood from the sides of the belly or back to stop the poisson effect happening. It might not be much wood at all. And the effect on performance might be tiny, but it's a very interesting idea.
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i think my brain is bleeding. me with hillbilly
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:D :D :D :D :D LOL......
Is this primitive archery or rocket science?.... ::)
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I think I was following this for a while, and then my head started hurting.. :P Then I remembered about the ACS-type section of <whisper>fibreglass limbs - what happens there, and my head went BANG ! :-\ Sorry about that not being primitive ;)
In my case, I feel that nature abhors a perfectly straight line, and also corners, however sharp. Stress of course loves corners, and the sharper the better! So I tend to make the limbs of the few bows which I have done, oval or lenticular in section, and all section transitions via smooth flowing lines. They just seem 'right' when handled and used. I cant explain it further than that, but I guess that for me, this is in the same mindset as 'doing what the wood asks', inasmuch as it is an imprecise science ;D
I need to make some more shavings, and soon.........
//Bob
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One of the things I love about primitive archery is that it is both simple and complex. You don't need to know anything about the science or technical aspects to make a good bow and have fun. Yet if you want you can jump into the deep end of the pool and explore the amazing physics behind what is going on with a bow and how different design elements effect it's behavior.
You can have it both ways. Pick your pleasure :)
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ACS-type section of <whisper>fibreglass limbs
//Bob
Bob,
I was thinking about an article I read in which fiberglass bows were forced into a hollow 'C' section. Such bows had far superior performance. I had thought for a which about hollowing-out a 'C' section bow to see what it acted like but it's too much work. Is that what you're talking about?
Tom,
Where else have you been talking about this? The PP site didn't have much.
J. D. Duff
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JD the thread at stickbow is probably the longest I've seen.
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Thanks a lot.
J. D.
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JD, yes the ACS limb cross-section is C-shaped. Supposedly it made the limb stiffer, sort of like an I-beam. I don't know whether the concave side was the back, or vice-versa.
I did find my copy of Archery the Technical Side.
A quote from page 34: "If a bow having a symmetrical cross-sectoin is all made from either heart or sap-wood, the elongation along the back of the bow will in general equal the compression along the belly. In such a bow there is a thin section located midway between the belly and back which is the neutral plane of bending."
This corroborates my position on where the neutral plane resides in a selfbow.
And page 38: "Lay out the shape of the cross-section on a heavy cardboard, using any convenient enlarged scale. Cut this cardboard section out with a pair of sheaars. Draw a line from the belly to the back which divides the section into two equal parts. Punch a small pin through the cardboard section on this line as such a position that the sectin will remain in balance on the pin for any position. After a number of trials you will find a point where the cardboard section may be rotated on the pin to any position, and at which, it will be in balance. This point is known as the center of gravity and is on the line corresponding to the plane of neutral bending."
This corroborates my position that the neutral plane is indeed a line at the center of gravity, meaning same amount of wood on either side of the line.
Interestingly, they are saying here that the neutral plane is a striaght line even when the cross-section is assymmetrical. So my idea that the neutral plane is curved, and is trying to straighten out, might not be correct.
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Very nice Lennie. I need to pick that up. If you scroll back to the earlier pages, my arguements were that 1) the 'midway point' may correspond with the NP but that is not what 'neutral plane' means and it is a definition with very limited application; 2) wood can respond differently to tension and compression forces. I spent the whole weekend imagining a way to test this and I have it figured out. I will try to test a couple samples to try to show that they can respond differently to the opposite forces but I may prove myself to be in error.
I think you would agree too that 'a thin section located midway' is not exactly explicit. I am willing to change my mind on the tension/compression elasticity if evidence gets in the way of my bowyer's intuition. I sure can take a lesson from Tim Baker and start testing theories on wood once in a while. :P
J. D. Duff
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I know what you mean.
We can easily test this hypothesis by measuring the back and belly length changes of a drawn bow or just a slat of wood long enough and bent far enough for a difference in length to be measured. IF the NP is in the middle, both changes will be equal.
By "we", I mean you of course.
And if you read that other thread, there is some data that shows at least some woods have different MOE in tension versus compression, so you are proved right already. I don't guess I mentioned that earlier. hehe And that other thread has some interesting new posts.
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I do not know if this is entirely relevant to the discussion, but my best attempt at the Ambush Bow Challenge was a bamboo-backed osage with horn belly that exploded, splitting the osage core EXACTLY DOWN THE MIDDLE of the osage core on the bottom limb. I do think that this combination at such a short length of 58" and 28" of draw and reflex-deflex design must have caused a tremendous sheer effect on the exact center of the wooden core. At least that is what my theory is of why it failed. I know that I was FROWNING, NOT SMILING, when it happened. Great discussion, though. I think in TBB they illustrate the Poisson effect by showing a rubber band bending and the edges curling up, do they not?
Dan Spier
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Sounds like the combination of horn and boo might be too much for a core, especially with a stress-concentrating design like a short R/D. I don't know if horn stretches more or less than boo, but it sounds like there was more shear than normal. Those things don't usually split down the center like that. I suppose you could determine that your NP was right in the center, thats doing it the hard way though.
A sinew-backed hornbow puts the NP much closer to the belly than bamboo would. It probably constrains the core much less too. The ancient bowyers probably tried the combination you used, and had the same results. You might have re-created an actual scene in an ancient bowyer's shop, complete with cursing and crying.
I'll look in the TBB, didn't remember Poisson being mentioned but its been a long time since I read those.
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bamboo is just the opposite from sinew which would normaly be used as a backing, bamboo doesnt like to stretch that much and horn doesnt like to compress that much, i guess it figured the tug of war was a draw so they split down the middle. Steve
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I now horn can take more compression stress than wood, but is it stiffer?
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I suppose you could determine that your NP was right in the center, thats doing it the hard way though.
Once again I think you are reading to much into this result. The only thing you can determine is that the weak spot was in the middle. Even if you did assume that the neutral plane was at the break, (which would be a huge assumption) it would not be the center of mass like hypothesized earlier. The horn is significantly heavier than the boo. Justin
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ACS-type section of <whisper>fibreglass limbs
//Bob
I was thinking about an article I read in which fiberglass bows were forced into a hollow 'C' section. Such bows had far superior performance. I had thought for a which about hollowing-out a 'C' section bow to see what it acted like but it's too much work. Is that what you're talking about?
Hi JD,
Yes, it is the curved section limbs that I was thinking about. The ones mentioned have a convex back, and a concave belly, although with a fair sized radius. The overall limb section is C-shaped. The claim is that the limbs are far lower in mass for the same draw weight, and hence they shoot more quickly for the same draw weight.
Considering these limbs with the Poisson effect is what made my brain fade :o
//Bob
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Justin, I wouldn't assume that a composite would still have its NP in the center of mass. It would only be the case if the horn and the boo had similar MOEs for their respective positions, correcting for thickness. The center of mass only equates to NP for single materials.
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Trying to picture this C shaped bow... If you made it out of wood, you might run the risk of frets on the tips of the C as that's where the compression would be concentrated. However, if the poisson effect flattens out the C as you bend the bow, you could avoid that. I guess it would have to be quite a shallow C shape.
I prefer the sawyer effect bow where the sides are thinner and there is no change in the cross sectional shape as you bend the bow. That way all the energy goes into stretching the back rather than making it skinnier.