Poisson Effect Versus Neutral Plane - A Theory

[tom sawyer]

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.

[duffontap]

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

[tom sawyer]

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.

[tom sawyer]

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.

[SimonUK]

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&current=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.

[duffontap]

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

[Justin Snyder]

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

[duffontap]

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

[marvin]

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.

[DCM]

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.

[tom sawyer]

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. 

[duffontap]

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

[DCM]

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.

[marvin]

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.

[marvin]

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.