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Poisson Effect Versus Neutral Plane - A Theory
duffontap:
--- Quote from: tom sawyer on June 07, 2007, 06:46:24 pm ---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.
--- End quote ---
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).
--- Quote from: tom sawyer on June 07, 2007, 06:46:24 pm ---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.
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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').
--- Quote from: tom sawyer on June 07, 2007, 06:46:24 pm ---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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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:
--- 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.
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And this is the correct definition:
--- Quote from: tom sawyer on June 07, 2007, 06:46:24 pm ---There very well is a place in the interior of every limb that is under neither tension nor compression, and where shear is greatest.
--- End quote ---
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.
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