Is the early wood the weak link to cause set?

[PatM]

Edge grain would be stiffer because it acts like vertical lams rather than  flat lams. The same way a baseball bat is struck on edge rather than the flat face.  Parallel bars for gymnastics used to be Ash with the rings oriented vertically rather than flat like a typical bow.

 This seems counter to what happened with Arvin's bow though.

  I think Maple appears better on average because it is very homogenous wood.

[Allyn T]

Pat you have any theories on why Arvin's bow took more set?

[Selfbowman]

Questions: 1 does the amount of early wood have a direct coalition in density when it comes to a float test? 60% late wood 40% early wood will float higher than say 70% late wood and 30% early wood?
2 : if we have more early wood in the bottom half of the limb will it lose strength in compression and if we have more early in the back half of the limb will we fail in tension?

3 would the best scenario be late ring on the back, then early ring , then late ring in the middle of the limb, then early ring , and last late ring on the belly? This will make the sheer the same in tension and compression? Yes or no?  The sheer leaning toward the tips in tension and leaning toward the handle in compression. 
4 all this happening in harmony and set being limited to very little

Thanks Alan and the rest of you guys input on what is causing this nagging problem called set.

[mmattockx]

So rock maple looks like it's kicking osages butt

Not really, it is just stiffer. That is not necessarily a desirable characteristic in a bow wood. What is wanted is a very high ratio of strength to stiffness. This lets you bend the wood farther before it will fail (or take set). The reason osage is a better bow wood than maple is it will have a higher strength than maple while being lower stiffness. Yew also has this characteristic.


Mark

[Selfbowman]

Pat I  tend to agree on you edge grain theory being more stiff but it could fail sooner due to not having a continuous late ring in tension.

[PatM]

Pat you have any theories on why Arvin's bow took more set?

 
   I would think decreased total latewood on the belly is the cause.   If it was a left a correspondingly increased width it may have offset that.

[RyanY]

Alan, could you describe the relationship between these measures? I see different terms used a lot but haven’t seen it in the context of having specific numbers.

[willie]

Does wood in a bow even follow Hookes Law? or is it bent to far for that? (I think I know what I am talking about)

I think it does until the last few inches of draw.  Below is a stress strain diagram for wood. the droop at the top of the curves is where set occurs and the wood is said to be undergoing plastic deformation. the lack of a well defined yield point is typical of wood. Wood testing reports often use the term "proportional limit" to describe the offset from the linear or elastic part of the graph described by Hookes Law.  Wood is also said to be viscoelastic.
https://en.wikipedia.org/wiki/Viscoelasticity
We see this behavior when initial unstrung set is reduced by resting the bow for a while.

[avcase]

Alan, could you describe the relationship between these measures? I see different terms used a lot but haven’t seen it in the context of having specific numbers.

Right now, I am measuring the Elastic Modulus of these different materials.  This indicates how the material resists deformation under a load.  For example, I came up with a number averaging 2.18 msi for edge grain osage. This is 2.18 million pounds per square inch. What does this mean?  Picture a cube of this edge grain osage that is 1” wide by 1” tall, by 1” deep. Now imagine pulling opposite sides of this cube to stretch it. Let’s assume this osage cube is magic and will not break no matter how much force is used to stretch it. It will take 2.18 million pounds to stretch this cube enough to double its length to 2” long.  Of course the wood will break before this happens, but it might be able to stretch almost 1% before breaking.  1% stretch = .01” with this cube. The amount of force required to stretch this cube 0.01” is 2.18 X .01 = 21,800 pounds!

A material with a higher elastic modulus number is stiffer than a material with a lower number.  Here is another way to look at what this number means. Let’s say we make two identical bows in every way except the material that the bow is made with. Bow #1 is made with this edge grain osage with a 2.18 msi elastic modulus.  Bow #2 is made from the water buffalo horn with a 0.85 msi elastic modulus.  This means the osage used in bow #1 is just over 2-1/2 times as stiff as the horn used in bow #2.  So if bow #1 happened to have a 50 pound draw weight at 28” draw. The draw weight of an identical bow #2 made from horn will be (0.85/2.18)*50# = 19.5#.

I hope this helps.

Alan

[RyanY]

Thanks Alan. That was very helpful.

As far as it applies to bows, if a wood is stiffer/less stiff than other woods then to make a bow of the same draw weight as another wood you would need to adjust the "width" proportionally to the other woods elastic modulus? Using your example with the two bows, would making the horn 2.5x wider help it equal the draw weight of the osage bow?

I'm guessing a different measurement is needed to assess if woods will bend to the different degrees before set.

[avcase]

RyanY,
Yes, you got it.

There is a second material property that you hint at in your last paragraph which drives the design of the bows. This is the maximum bending stress that the material can handle before it takes on significant set or permanent damage, and I am working on that next.  It may require trying a few things, but the basic process is adding increasing bending loads until the sample doesn’t quite snap back to its original shape once the load is removed. This will give a yield stress value for the wood.  If this is known, than we can really start to have some fun.

There are a couple of things that can complicate this. One possible issue is that pesky viscoelastic behavior that Willie posted about earlier.  This is where a material takes a temporary set or relaxes under load, but it gradually recovers after a short time with no apparent permanent damage. I think the horn will be most affected by this. The other issue is finding a best method to measure and model this viscoelastic effect. The wood samples will show some of this also. It may turn out that it is best to stay below the stress levels before there is any significant viscoelastic behavior because this contributes to hysteresis losses.

Alan

[PatM]

I would think it would make more sense to narrow and thicken the  theoretical horn bow.

[avcase]

Questions: 1 does the amount of early wood have a direct coalition in density when it comes to a float test? 60% late wood 40% early wood will float higher than say 70% late wood and 30% early wood?
2 : if we have more early wood in the bottom half of the limb will it lose strength in compression and if we have more early in the back half of the limb will we fail in tension?

3 would the best scenario be late ring on the back, then early ring , then late ring in the middle of the limb, then early ring , and last late ring on the belly? This will make the sheer the same in tension and compression? Yes or no?  The sheer leaning toward the tips in tension and leaning toward the handle in compression. 
4 all this happening in harmony and set being limited to very little

Thanks Alan and the rest of you guys input on what is causing this nagging problem called set.

Arvin,
Question 1:
Yes, more early wood means lower density, so you might notice a difference in a float test. However, I was surprised at how little the mix of early and late growth rings affected the density of these samples.

Question 2:
I hope we can learn more about early and late wood with this little research project. I see early wood reducing the elastic modulus or stiffness in these tests, but I haven’t measured the impact on strength yet. This will show if it just means the bow with more early wood needs to be just a little wider in order to achieve equivalent performance of a bow of higher late wood content. I think a higher late wood content will always be better because the material will have more uniform properties, but it is just a guess.

Question 3:
It seems like it might be best to end with a solid late wood ring on the belly, but it depends on how elastic the early wood is. It also may depend on tensile versus compression properties. If the early wood is very elastic, then it might not matter much.

Question 4:
Harmony is good.

[RyanY]

Thanks for your hard work and explanations with this Alan. It is greatly appreciated.

If a wood is able to bend further than other woods before taking set, would it be fair to say that it is storing more energy for the same amount of mass? My thinking is that these bows could be narrower and thicker to achieve the same draw weight.

[avcase]

Thanks for your hard work and explanations with this Alan. It is greatly appreciated.

If a wood is able to bend further than other woods before taking set, would it be fair to say that it is storing more energy for the same amount of mass? My thinking is that these bows could be narrower and thicker to achieve the same draw weight.

Yes, you are on the right track. The amount of energy that a material can store in bending is a product of the elastic modulus and amount of strain or deformation it can handle before taking a set.  It can be taken a step further by throwing in the density in order to get a property that rates materials as ft-lb of energy per ounce of material.

Alan