Speed of cast vs draw weight?

[mmattockx]

  Your description  proves the error.    The belly shortens.

granted, the back does not stretch as much as the belly compresses when a bow is drawn, but if (roughly speaking), wood is twice as strong in tension than in compression, the back is still stretching 1/2 as much as the belly is being compressed.

In a one piece (not a lam bow with different woods) rectangular cross section limb the back stretches exactly as much as the belly compresses, until set occurs. While many woods are much stronger in tension than compression, they have the same MOE (ie - stiffness) in both compression and tension until the compression side begins to fail. Different cross sections such as a trapped shape or high crown back do not have equal amounts of strain at the back and belly surfaces, but that is a property of the cross section shape and not the wood.


Mark

[DC]

In a one piece (not a lam bow with different woods) rectangular cross section limb the back stretches exactly as much as the belly compresses, until set occurs. While many woods are much stronger in tension than compression, they have the same MOE (ie - stiffness) in both compression and tension until the compression side begins to fail. Different cross sections such as a trapped shape or high crown back do not have equal amounts of strain at the back and belly surfaces, but that is a property of the cross section shape and not the wood.
Mark

I'm having a tough time wrapping my head around this. Maybe I'm confusing strength with something. If the back is stronger than the belly doesn't that shift the neutral plane? And if the neutral plane is shifted doesn't that change the "strain ratio". It would put more or less pressure on the belly depending on which way the NP is shifted. Now I'm starting to doubt my understanding of which way the NP moves.

[Badger]

 D/C I agree with you that the strength of the back increases the neutral plane. Here is where I am not 100% clear, my understanding is that if a back resists bending and is stronger that the belly can be a bit thinner. But I admit to not having a real clear understanding of how tension actually affects the bow beyond personal experience and observations.

[DC]

If "stiffness" is a resistance to bending then what causes stiffness? Bending stretches the outside and compresses the inside. Does it do anything else? If not then the whole thing revolves around stretching and compressing the wood. This is then complicated by how fast the wood recovers which is hysteresis, I believe. All this would mean that these three things pretty well cover it. Where am I wrong?

[Badger]

If "stiffness" is a resistance to bending then what causes stiffness? Bending stretches the outside and compresses the inside. Does it do anything else? If not then the whole thing revolves around stretching and compressing the wood. This is then complicated by how fast the wood recovers which is hysteresis, I believe. All this would mean that these three things pretty well cover it. Where am I wrong?

  You see it exactly as I do and that is why I am still unclear on it. If the back does not stretch at all then the neutral plane would be right under the back. If you took very exact measurement and bent a piece of wood into a complete circle then compared the inside and outside diameters to what it was straight I guess we would know exactly what was going on. My guess is that there is a very small amount of stretch, say a strong wood might stretch .1% and a weak wood might stretch .2%. I just pulled those numbers out of my head.

[Badger]

  One thing I do know for sure is that wood has very little hysteresis before it has taken set. Not much different than fiberglass.

[DC]

  One thing I do know for sure is that wood has very little hysteresis before it has taken set. Not much different than fiberglass.

I wonder what is happening at a microscopic level to cause this. I would think that a wood would have less after it was damaged. Like a new piece of rope is stiff and then softens up as you use it.

[Badger]

  One thing I do know for sure is that wood has very little hysteresis before it has taken set. Not much different than fiberglass.

I wonder what is happening at a microscopic level to cause this. I would think that a wood would have less after it was damaged. Like a new piece of rope is stiff and then softens up as you use it.

  In a perfect world your bow would have no memory of ever being bent. It would be like cutting a bow out to size and then shooting it with no change from how you cut it out.

[willie]

In a one piece (not a lam bow with different woods) rectangular cross section limb the back stretches exactly as much as the belly compresses, until set occurs. While many woods are much stronger in tension than compression, they have the same MOE (ie - stiffness) in both compression and tension until the compression side begins to fail.

thanks for correcting me on that, I guess the back stores as much energy as the belly, if not more.

Maybe I'm confusing strength with something

strength and stiffness are often confused with each other. The commonly cited "wood is twice as strong in tension" phrase most likely comes from a table  from The Mechanical Properties of Wood, by S J Record,  1914  reproduced below.  If one cares to read the paragraph above the table, in this link, https://www.gutenberg.org/files/12299/12299-h/12299-h.htm#I_01. some of the terminology used in discussions about wood strength and stiffness is discussed.

[mmattockx]

I'm having a tough time wrapping my head around this. Maybe I'm confusing strength with something. If the back is stronger than the belly doesn't that shift the neutral plane?

You are confusing strength and stiffness. Stiffness is how much the material deflects in response to a load. Strength is the maximum load the material can take before failing. In a same wood bow the back and the belly have the same stiffness, so they deflect equal amounts in response to the load of bending as the bow is drawn. But the wood is weaker in compression, meaning it will fail at a lower load, so the belly will fail before the back does. This shows up as set.

The confusion with strength and stiffness comes because bowyers will say a stiffer limb is 'stronger'. On an engineering basis that is incorrect terminology but is used all over the archery world and it clouds the distinction between the two.

You are correct that a materials stiffness mismatch will shift the neutral axis. This is why the above only applies to a bow made from one homogeneous piece of wood. Lam bows made with different woods in the various layers will not follow this rule because the different woods will have different MOE's and that will shift the neutral axis towards the stiffer wood.


Mark

[PatM]

But if the wood does not provide enough resistance for the back to be stretched by, why would it stretch?

 The wood nay be the same material but each side is given a different task.

   When wood is cranked in two  by tension, what is the linear increase before breaking? 

[willie]

But if the wood does not provide enough resistance for the back to be stretched by, why would it stretch?

It does provide enough resistance, up to the point the belly starts to take set (fail). A belly that has reached this point becomes weaker in terms of stiffness, and then (as as you already know), a hinge happens fast.

When wood is cranked in two  by tension, what is the linear increase before breaking? the actual distance?

assuming a 1/2 inch thick limb bent into a 24" radius (at the neutral plane), and the bow is about to break, then the back is at a radius of 24.25", and the belly is at a radius of 23.75".

 
3.142 x 2 x 23.75 = 149.3
3.142 x 2 x 24.25 = 152.4

if your limb is a 1/4 circle then
152.4/4 = 38.1
149.3 /4= 37.3

or about .80 difference or .4"  more than the length of the resting limb.

[PatM]

I mean cranked in two linearly as it is in the machine.

[DC]

I'm having a tough time wrapping my head around this. Maybe I'm confusing strength with something. If the back is stronger than the belly doesn't that shift the neutral plane?

You are confusing strength and stiffness. Stiffness is how much the material deflects in response to a load. Strength is the maximum load the material can take before failing. In a same wood bow the back and the belly have the same stiffness, so they deflect equal amounts in response to the load of bending as the bow is drawn. But the wood is weaker in compression, meaning it will fail at a lower load, so the belly will fail before the back does. This shows up as set.

The confusion with strength and stiffness comes because bowyers will say a stiffer limb is 'stronger'. On an engineering basis that is incorrect terminology but is used all over the archery world and it clouds the distinction between the two.

You are correct that a materials stiffness mismatch will shift the neutral axis. This is why the above only applies to a bow made from one homogeneous piece of wood. Lam bows made with different woods in the various layers will not follow this rule because the different woods will have different MOE's and that will shift the neutral axis towards the stiffer wood.


Mark

Is stiffness in any direction? In the Wood Database they show MOE as a bending force. Is strength then just stiffness(or any test) carried to destruction?

[willie]

I mean cranked in two linearly as it is in the machine.

it probably does not matter how the wood is stressed. bending or pure tension. the machine samples are double tapered, and the tested crossection is not very long, but if it were 36"  long, then it could stretch 7/16" before breaking   (approximating from the above example)