Speed of cast vs draw weight?

[BrandonH]

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

There do seem to be differences in stiffness in the compressive vs tensile directions.  The first figure below shows tensile and compressive MOE data for a few species.  Therefore under a given load I would expect nearly double the strain on the belly side vs the back.  Please provide any additional info you have on the topic, this is interesting stuff.

http://support.sbcindustry.com/Archive/2010/june/Paper_096.pdf

[mmattockx]

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?

It depends on the material. Something that is isotropic (same properties in every direction) like steel will have the same stiffness in all directions. A composite like wood is not isotropic and will show different properties depending on how it is oriented in testing. In wood the two major directions are with the grain and cross grain.  For bows all the loads are with the grain and the properties need to be measured in that direction.

The MOE and modulus of rupture are in psi, which is force/unit area. It is the same units that stress and pressure are measured in. The units are not related to any particular type of loading, just the force/area.

A tensile test will give both MOE and ultimate strength. Below is a typical stress/strain chart from a tensile test of a ductile material like steel.



A test graph for wood will look similar, except that the yield strength point for wood is the modulus of rupture and the curve will drop right off when that point is reached as the sample fails. Wood does not have the long, gradual arc at the top that a ductile material does. The ultimate strength will be given by the stress reached at MOR and the MOE is the slope of the curve in the linear-elastic region.


Mark

[mmattockx]

There do seem to be differences in stiffness in the compressive vs tensile directions.  The first figure below shows tensile and compressive MOE data for a few species.  Therefore under a given load I would expect nearly double the strain on the belly side vs the back.  Please provide any additional info you have on the topic, this is interesting stuff.

That is interesting, it is the first test data I have seen that says the MOE is different for tension and compression in wood. I have downloaded the paper and will give it a read. That changes the behaviour of the limb substantially.


Mark

[willie]

Hi Brandon,

welcome to the discussion. Wood is interesting stuff, and reading thru the paper, I would like to point out a few things that caught my eye.

1. the moisture content of the tested lumber is typical for the construction industry but not for bows. Higher MC wood does not perform well in compression. Below is a generalized graph from the FPL that shows how tension and compression vary with MC.

2, those knots!!  It would be interesting to compare values obtained in the Korean study with tests performed on clear straight grained specimens of the same species.

Admittedly, the graph reflects "strength", rather than stiffness, but it is commonly observed wood is easier to bend when its green, so there may be some correleations.

[BrandonH]

It was the first data of the kind I had seen as well.  Prior to this discussion I had taken it as an assumption that the belly side experienced greater strain, but after that was questioned I realized I didn't really have good reason for my assumption.

Yes, there are many questions I have about the paper as well.  I know nothing about those species for one.  The MC of 8-12% didn't catch my eye however.  But I found that MOE data specific to directions parallel to the grain were hard to come by.  I had found one additional source, but didn't really like the 'dogbone' shaped samples used.  I'll include below if anyone is interested.  It shows tension/compression ratios greater than 1 (but nowhere near double) for all species where they used the same specimen for both tests. 

https://www.dora.lib4ri.ch/empa/islandora/object/empa%3A15782/datastream/PDF/Bachtiar-2018-Mechanical_behavior_of_walnut_%28Juglans-%28published_version%29.pdf

[willie]

Good find. I was intrigued by the first two graphs in that study. the top graph is tension, and the long high line is for the longitudinal direction.  In comparing it to the compression graph below, we see that the stress/strain line is relatively straight, right up until it breaks. A straight line is indicative of little or no set taking. The bend or flattening in the lower compression graph is set taking, ie where it is bending further, but it's not taking much more force to make it bend further.

[PatM]

As expected.  Wood is spongy but not ductile.

[mmattockx]

Therefore under a given load I would expect nearly double the strain on the belly side vs the back.

The neutral axis doesn't shift that far. In the paper they calculated that 57.7% of the cross section was in compression (using composite beam theory). That means the belly will see 15.4% higher strains than if the MOE was the same in both tension and compression.


Mark

[BrandonH]

Absolutely.  If the strain is double on belly side that does not mean the neutral axis will shift 1:1 proportionally toward the back.

The real question is how we use this info to build a better bow.  Matching laminations?  Sizing back lam?  Dimensions for trapping?

It's a shame there is not more data specific to this topic.  My vote is that someone here buys a tension testing machine and starts a database for us

[willie]

The real question is how we use this info to build a better bow.  Matching laminations?  Sizing back lam?  Dimensions for trapping?

pairing laminations of correct MOE and sizing thicknesses are both important. The benefits from trapping might have more to do with reducing limb mass. Trapping also has a down side of concentrating stress, putting more demands on material quality.

I believe testing for tension could be done in the shop without an expensive machine. Finding backings of various moe and also capable of exceptional strain may be worth the research for those trying to break records at the flight shoot, but when you consider the  difference between a self bow vs. a backed bow in the broadhead 50# class, which might be representative of bows close to what the average guy shoots, the difference in cast is less than 4%.

[Selfbowman]

I believe testing for tension could be done in the shop without an expensive machine. Finding backings of various moe and also capable of exceptional strain may be worth the research for those trying to break records at the flight shoot, but when you consider the  difference between a self bow vs. a backed bow in the broadhead 50# class, which might be representative of bows close to what the average guy shoots, the difference in cast is less than 4%.

if I get enough flights in broadhead that might be less than 4%. I’m going after some other records . Then Steve and others are showing up with some real good bows. Arvin

[mmattockx]

Absolutely.  If the strain is double on belly side that does not mean the neutral axis will shift 1:1 proportionally toward the back.

The paper shows the strain on the belly is not double, it is 15.4% more for the wood they were investigating.

The real question is how we use this info to build a better bow.  Matching laminations?  Sizing back lam?  Dimensions for trapping?

That is the big question. If our woods are indeed twice as stiff in tension as compression that does seem to indicate that trapping is a very good idea for most same wood bows.

I have been looking at Perry reflex and getting sorted to try some experiments. I had calculated that I could lower compressive strains by ~4% if done properly, but that was assuming MOE was constant. I now have to redo the calculations with a 2:1 ratio of MOE and see how that affects the results. Either way I am still going to try building a few Perry reflex lam bows to see how it works out.

It's a shame there is not more data specific to this topic.  My vote is that someone here buys a tension testing machine and starts a database for us

It is unfortunate we have so little data, it is hard to optimize a design when you are working without accurate material properties. You go first on the tensile tester and let me know how it works out. 


Mark

[PatM]

It seems like bowyers have already figured all this out but people are hopeful there's some magical other combination lurking out there.

  Pairing the most extreme examples  seems to still average out to the same end result when a bow is made properly.

[mmattockx]

It seems like bowyers have already figured all this out but people are hopeful there's some magical other combination lurking out there.

Pat,

My goal is not to find a magical combination (I don't think such a thing exists) but to be able to understand the mechanics of the bow limbs and materials in order to be able to design a bow on paper and build it with high assurance of getting what I want without building 100's of bows and building an empirical database. As an engineer it is normal to me to use math to define the world around me and allow me to design structures and machines that work the first time out of the box. This is fundamentally no different.

Bow making has room for everyone in it, from those that want to use basic hand tools and craftsmanship to reveal the bow inside a stave to those who want to make bows in a more precise fashion, through understanding of the physics involved. All of these approaches are legitimate in my opinion, it is really just different strokes for different folks.


Mark

[bradsmith2010]

you still have to build quite a few bows to develope the skill to execute the design,, I think,, maybe 100's
there is so much variation in the wood,, what ever approach you like,, and makes it fun for you,,or enjoyable,,is great,,
you can look at one of DC's or Marcs bows,,Badgers and many more,,,,,there is the design,, right in front of your eyes,, all the specs are there,, but to execute it, is a different story,, and so on,, getting the design on paper is like notating  a violin part from Mozart,, there it is,, but to play it,,