Poisson Effect Versus Neutral Plane - A Theory

[tom sawyer]

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."

[Badger]

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

[tom sawyer]

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).

[duffontap]

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

[tom sawyer]

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.

[koan]

Well.....I'm with you fella's......Delmer

[duffontap]

Koan--I laughed my head off!  You are a brilliant man.

        J. D. Duff

[SimonUK]

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.

[duffontap]

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.   

        J. D.

[DanaM]

Man you guys are making my head ache

[shamus]

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.
 

[NOMADIC PIRATE]

Agree whit all you guys said even if I didn't understand a word (had to stop readyng on page 3

[Coo-wah-chobee]

 Wow ! Learn sometin' every day ! Didn't realize "herpatology an poisson" had anything ta do with neutral plane ! ...bob

[SimonUK]

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 

[tom sawyer]

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.