Bow Index vs Ipe

[gfugal]

Here's the topic. I thought it was sinew process but it was actually sinew question. http://www.primitivearcher.com/smf/index.php/topic,59835.30.html. I originally thought the neutral plan stayed in the middle untill that thread. TBB1 on pg 106 talkes a bit about it. Tim Baker Quotes research done by physicist Michael Bloxkoham which shows 94% of the tension work is done withon 30% of limb depth. Since that number is close to 100% then it should be pretty close to the neutral plane. I think that's why JoachimM said 1/3 from back and 2/3 from belly. Because one third would be 100% at 33.3% depth which is close to the geven data. Additionally Willie posted an research article about the subject. https://www.researchgate.net/profile/Rakesh_Gupta24/publication/258111089_Revisiting_the_neutral_axis_in_wood_beams/links/53d7f3c10cf2a19eee7fe792/Revisiting-the-neutral-axis-in-wood-beams.pdf if i remember correctly it showed the plane to be about 40% tension and 60% compression. That's a bit closer to center than before but still favoring the back. I'll have to read the article you just posted.

[gfugal]

The method you describe though is an excellent thing to do. Tim Baker did something similar in TBB1 for determining comparable stiffness, elasticity, tension/compression strength etc. I Would like to start doing this myself, I just don't know if I can make a 1/2 by 1/2  perfectly to 1/100th of an inch. This may be more valuable than any data. However, what it won't do is tell you the individual MOE for tension and compression or where the neutral plane is. We can only guess. What it does give is probably an average MOE between the too which might be more useful anyway, unless you wanted to figure out individual properties for composite laminates. 

[avcase]

Thank so for the link. That's a pretty fascinating method to actually visualize the way bending stresses form in a test sample.  So this paper points to a somewhat lower stiffness/Modulus of Elasticity in compression compared to tension.  I am also finding other research that doesn't find a significant difference in the Elastic modulus for tension Vs. compression.  For example, see "Evaluation of the Longitudinal Modulus of Elasticity in Wood Species for Structural Application" by Eduardo Chahud and multiple other authors.

I feel it is worth contacting the authors at Oregon State University to get their feedback in regards to our application. They may have had more experience with this method of analyzing the bending properties of wood since publication which may be helpful.

[willie]

I Would like to start doing this myself, I just don't know if I can make a 1/2 by 1/2  perfectly to 1/100th of an inch.

Greg, My samples are squared up on a table saw. I measure the thickness and widths of the samples, to the 100th, before entering the values into the spreadsheet. Excel does the math for the MOE,  MOR,  % strain etc.....

 The jig hangs on my bow scale.  Samples of approx. 3/8" x3/8" x 12" (between supports) typically are pulled to normal tiller tree working weights of 20-50 lbs. Working limb widths, lengths and set can be estimated from a few minutes testing with any sample, and "mystery wood" samples can be dried in a microwave and easily evaluated.

I agree that this sort of testing is best suited to self bows, where knowing the exact location of the neutral plane is not useful. 

[willie]

In response to Greg's  post concerning Neutral Plane locations, I made a quick sketch, that I hope shows how different stiffnesses, in tension and compression, can be seen graphically. This may be more useful to someone planning a composite limb or considering trapping. Neutral plane locations are simply matters of proportion.

Sketch 1 is a bow limb cross section
This would be for a wood that is considered to be of equal strength in tension as in compression. The neutral plane is shown in the center of the limb.

Sketch 2 is what is known as a "transformation". It would be what a limb, made from a wood that is twice as stiff in tension than compression, would look like, if drawn with consistent units of stiffness. The area above the neutral plane is the same as the area below, but because the width above is greater, the relative position of the NP has moved upward.

Sketch 3 is a limb cross section of a laminate or backed bow. lets assume that the backing is three times as strong as the belly.

Sketch 4 shows the laminate in it's tranformed state. That is, as if it was all the same wood. Once again, the area above the NA is equal to the area below, and the relative position of the NP is even higher.

Of course, the belly portion (that part below the axis) is getting thicker, and is at risk of being overpowered by the back.

Sketch 5 shows a hypothetical limb cross section with a rather extreme NA location. (Perhaps the bowyer wants to see what happens when he puts a 4x as stiff bamboo backing on some very soft wood? The detail to the right shows how the surface of the back will stretch approx 1/3 as much as the surface of the belly will compress. It's shown by the diagonal drawn through the  neutral axis.Once again, just a proportion, dictated by the differences between the stiffness of the two different materials.



One can see that not only the choice of materiel's is important, but also the relative thickness (and/or width in the case of trapping) of each wood in the composite is important.


 

[PatM]

I'm curious what these results will tell you from a bow building perspective. If you test a sample  will it  make you necessarily build a different bow?

Also knowing how much wood varies from one section of a tee to another can you expect a great deal of accuracy?

[gfugal]

I'm curious what these results will tell you from a bow building perspective. If you test a sample  will it  make you necessarily build a different bow?

Also knowing how much wood varies from one section of a tee to another can you expect a great deal of accuracy?

This is what Tim baker was doing. see pg 103 or something in TBB1. He would do these tests before he built the bow, therefore he could account for variations within the same species. depending on the results he would design the bow accordingly (thicker or thinner, wider, longer etc.)

[PatM]

I'm curious what these results will tell you from a bow building perspective. If you test a sample  will it  make you necessarily build a different bow?

Also knowing how much wood varies from one section of a tee to another can you expect a great deal of accuracy?

This is what Tim baker was doing. see pg 103 or something in TBB1. He would do these tests before he built the bow, therefore he could account for variations within the same species. depending on the results he would design the bow accordingly (thicker or thinner, wider, longer etc.)

Yes but the wood will still make a variety of designs.  I can't see how the tests will really tell you what to make.

[willie]

If you test a sample  will it  make you necessarily build a different bow?

yes, I can tiller for a lesser or greater weight given a stave width limitation, or make my working portions of the limbs longer or shorter if a specific weight goal is desired. The greatest advantage I find, is to be able to design to minimal set, one I know where set taking happens with a particular wood.

Also knowing how much wood varies from one section of a tee to another can you expect a great deal of accuracy?

I suppose that I could test a sample from each end of the stave if that was an issue. I usually do not do much work on my handle until I see how the limbs are bending, and if my tapers are consistent, and one limb shows to be stiffer, than I could put it down and say "I planned it all along, that way"

I can't see how the tests will really tell you what to make.

Not what to make so much, Pat. More how to make it.

[gfugal]

I'm curious what these results will tell you from a bow building perspective. If you test a sample  will it  make you necessarily build a different bow?

Also knowing how much wood varies from one section of a tee to another can you expect a great deal of accuracy?

This is what Tim baker was doing. see pg 103 or something in TBB1. He would do these tests before he built the bow, therefore he could account for variations within the same species. depending on the results he would design the bow accordingly (thicker or thinner, wider, longer etc.)

Yes but the wood will still make a variety of designs.  I can't see how the tests will really tell you what to make.

I guess it's a matter of definition. I'm going to say there's styles (English Long Bow, American Long Bow, Flat Bow, Recurve, Derfelx Reflex, etc.), and designs (the specific widths thickness and lengths within a style). I'm going to go out on a limb and say any wood could make most styles as long as its design is adjusted appropriately for the different properties. So yes, these tests won't change what type of bow you're planning on making, usually. However, they most definitely will affect your design. You wouldn't make a 1" inch wide unbacked flatbow with recurves out of ERC like you could expect Osage to do. Not unless you change some other factor (like making it wider, longer, less poundage, or back it). 

[gfugal]

So here's an idea that I think I read somewhere to figure out where the neutral plane is. It's basically like what you were saying Willie, but instead of placing them sideways Imagine placing it vertically. The idea is this.

You separate it into two sections for the different materials based on their cross-sectional thickness. Then you find the hypothetical middle of the sections by augmenting the stiffer material based off its proportion to the weaker one. This hypothetical middle I'm going to call the sectional plane. to do this you take the average between the top and bottom heights with the hypothetical augmentation. SP = (bottom+top)/2. After that, you can find the neutral plane by taking the average between the two sectional planes. NP = (SP2+SP1)/2.

In the first image, you have two blue sections of the same stiffness, you can see the sectional plane of each section labeled in gray. since they are the same stiffness neither one gets augmented. Therefore SP1 = (0.0"+0.2")/2 = 0.1", and  SP2 = (0.2"+0.4")/2 = 0.3".  Now to get the neutral plane you just take the average of those values. NP = (0.3"+0.1")/2 = 0.2". This is what we would expect for a simpler material like metal or fiberglass, dead center. for the sake of simplicity, we'll stick with materials that have the same compression MOE as Tension MOE.   

Now the second example is one with a backing material 3 times as stiff, but the cross-sectional thickness ratio of material one to material two is still the same. The sectional plane of the belly section is the same as the previous example. SP1 = (0.0"+0.2")/2 = 0.1". However to find the hypothetical sectional plane of the stiffer material we have to augment it. SP2 = (0.2"+0.8")/2 = 0.5". Notice this is outside the realm of the actual cross section. This "sectional plane" doesn't actually exist, its just there to help us calculate the neutral plane. So to find the neutral plane you just take the average between the two sectional plane values (0.1"+0.5")/2 = 0.3". This is in the realm of the real cross section, and its closer to the stiffer back like we would expect.

[PatM]

Don't forget to factor in knots etc. 

[Badger]

   If I took a pice of wood and carefully measured the length say 24" long, we would bend it over an arc that would allow for .5% changes in length. This would be about 1/8". Now if the inside was 1/16 shorter and the outside was 1/16 longer I wouyld say the nuetral plane was centered. If the length increases by 1/32 for the back and 3/32 for the compression side I would say the nuetral plane was about 2/3 toward the back. I honestly think this is more realistic but only a real test could verify that.

[Badger]

   Jig to measure this would not be hard to build. It would take a little precision. Simply build an arc, find the radius that will give you a .5% in length change using an exactly 24" test strip that is exactly 1/2" thick. You could use dial calipers to take exact measurements. This would give you an accurate nuetral plane and if you measured the pressure it took to bend the test strip it would give you an accurate stiffness guide.

[willie]

Steve,
I have often considered an experimental measurement such as you describe. In fact I have a metal drum that's perfect for clamping a test piece on, as soon as I can determine the thickness for the bend. The question I have is, what would I do with the information? I do not use NP location in any of my calcs, do you?