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Poisson Effect Versus Neutral Plane - A Theory

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tom sawyer:
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?

tom sawyer:
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.

duffontap:

--- Quote from: tom sawyer on June 07, 2007, 04:03:08 pm ---A neutral plane (NP) is that imaginary line where half the limb mass is on one side, half on the other. 

--- End quote ---

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

Pat B:
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

duffontap:
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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