Poisson Effect Versus Neutral Plane - A Theory

[tom sawyer]

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.

[tom sawyer]

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.

[Hillbilly]

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. 

[DanaM]

So easy a caveman can do it

[SimonUK]

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?

[tom sawyer]

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.

[SimonUK]

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.

[jamie]

i think my brain is bleeding. me with hillbilly

[Ryano]

LOL......
Is this primitive archery or rocket science?....

[bobnewboy]

I think I was following this for a while, and then my head started hurting..   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 

I need to make some more shavings, and soon.........

//Bob

[marvin]

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

[duffontap]

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

[DCM]

JD the thread at stickbow is probably the longest I've seen.

[duffontap]

Thanks a lot.

    J. D.

[tom sawyer]

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.