Primitive Archer
Main Discussion Area => Bows => Topic started by: Ballasted_Bowyer on April 02, 2017, 12:05:10 am
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http://www.wood-database.com/wood-articles/bow-woods/
I have made a few bows with Ipe. They worked for a while but then split as I did not follow the growth ring. Recently I came into a huge piece of Moso and had another go at Ipe with a thick Moso bamboo backing. This bow has less than two inches set and pulls 61lbs at 28 inches. Also put the arrow deep into both layers of sheet rock between rooms. A hem, What I mean to be pointing out is that in spite of the fact that it seems to have worked, I would also say the limbs are HEAVY even though I used a pyramid style tiller all the way to narrow nocks. I looked up the MOE/MOR ratio on Ipe and it is decidedly worse than basically any other common bow wood in North America and on the far side from Yew or Osage. And yet, I have seen some reports on the inter-webs that the stuff is awesome for bows. Is it? Or perhaps with a good backing its just strong enough in compression to be forgiving? I guess, what I really want to know is if those who both shoot well and make good bows think its an excellent choice of material compared to other common woods excluding yew or osage?
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When using a backing you count both materials.
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Pat, Just to make sure I understand, In this case the Ipe having a higher MOE than Moso Bamboo, and they are at similar thickness most of the length of the bow, the bamboo is stretching more than the Ipe is compressing which masks its low index? I also noticed bamboo has a low index as well by the method shown in the link, but it is light for its MOE.
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I use boo backers the same on all bows, i get the boo about as thin as i can, almost a knife edge, epe is a very good bow wood, but some of the quality is declining
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I don't believe that bamboo will stretch much at all. I could be wrong of course but not many wood like natural fibers have much stretch to them. The bamboo does seem to stand up well to ipe as far as not fracturing.
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if bamboo has been shown to be a good combo with ipe, isn't it because of what stretching it does? If the work in an Ipe bow is all about compression, than we might as well back with steel (not really suggesting this) but just wondering if the back designs make more of a difference than we often give credit for? maybe not just what , but how much?
that database should definitely take a back seat to (some) of what you can read here at PA, IMO
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No. Bamboo doesn't stretch . That's what makes it a good backing for Ipe. It forces the wood belly to store energy in compresssion and the wood can take it.
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Bamboo is stiffer than ipe? I have a hard time believing that. According to the data ipe is stiffer than most bone. I think the reason bamboo is so good as a backing is because it can handle the stress put on it from the stiff belly. If it's on the back then its under tension. Tension is stretching by definition, it just doesn't stretch much (less than 1%) but it does for sure.
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From what i could gather https://www.guaduabamboo.com/guadua/comparing-mechanical-properties-of-bamboo-guadua-vs-moso the stiffness (MOE) of moso bamboo is around 8 Gpa. According to the wood database Ipe has a stiffness of 22 Gpa (approaching 3 times as stiff but not as quite). but the rupture point (MOR) for the bamboo is greater than 100 Mpa mybe 110 Mba. That's a bow index close to 13 which is higher than pretty much anywood. Much higher than th 8 of ipe. This means it can handle tension and bend (stretch) much further than most, particularily ipe, making it a great backing.
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The very outer portion of bamboo is extremely dense. That's the part that matters in this context because it's the only part used.
Tonkin is denser than Ipe.
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Personally i don't care about a data base, i know boo which is a grass, has fibers that run from end to end, is a pain to flatten by hand, and is a great backer material, and epe doesn't really like to bend and wants to return to its original shape as soon as possible, seems like a good combo. Once again most of those data bases were not made with the end result bows
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The very outer portion of bamboo is extremely dense. That's the part that matters in this context because it's the only part used.
Tonkin is denser than Ipe.
Looks like bamboo can very just as much or more than wood, depending on species. Since the post was originally about moso i looked that up. It is not stiffer, but maybe the outer portion may be? I haven't found data for that but i'll go off your word. I tried searching for Tonkin and it brought me to this paleo discussion http://paleoplanet69529.yuku.com/reply/387096/Different-bamboo-species. Aparently tonkin is very stiff! Greater than ipe with a MOE around 40 Gpa. This really surprised me. But moso may or may not be. Either way bamboo should be able to handle being the back more than ipe by its self. This was never being debated.
Bubby your right in that data won't make a bow for you. You can still make excellent bows with no data, the ancients did it all the time. Knowing and understanding the data however can't hurt things as long as your still out there building and not just theorizing. True that it might not be the best representation of the actual properties but its what we have to make conclusions.
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Moso definitely has a very low proportion of power fibers.You'd have to test that minimal portion separately.
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Tim Bakers bow woods list has info on more differant woods than most guys will ever use, i reference that when i have to
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Despite what people say:
bamboo does stretch in tension on the back of a bow... Just test it.
The bow index of the wood database only indicates that the "good woods" have a low MOE and a high MOR for its density. And preferrably both in tension and compression.
In an ideal world, we want bow woods with high MOE and high MOR: stiff woods that still bend very far. Bamboo species are in that category (have data for Moso and Guadua bamboo to back this statement), at least in tension. They are crap in compression (unless heavily toasted, and with the dense outer layer on the belly too, like in split cane fishing rods).
For real wood species, there's a trade-off between stiffness (MOE) and elasticity (MOR), the combination of which determines how much energy a wood can store in bending. Basically, there's pretty little variation among energy storage capacity among all wood species, because of this trade-off. That brings us back to the findings of Comstock and Baker in their archery books: any wood allows you to make a bow, you just have to adapt the design to the wood properties and your own (MC) conditions.
Low-stiffness woods (relative to their density!) are just easier to turn into bows (more tolerant to tiny mistakes) and are likely also more stable in their tiller towards MC changes.
So that's why we use bamboo as a backing. Ipe is very dense and stiff wood, with just above average compression properties for its density. This makes it a good partner for bamboo. Osage and yew are less stiff, but better in compression. Net energy storage capacity will be similar, but requiring a different design.
J
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Perhaps statements are being taken a little TOO literally..
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I have never claimed much knowledge on any woods as far as properties go. I tend to just go with what works.
I have found with Ipe and other dense woods that they can be successfully backed by much weaker woods like maple, red oak, white oak, hickory etc. It seems like most any decent wood can be used for a backing with anything. I also haven't found a positive correlation that states bamboo backs are faster than other backings. I will say that my fastest bows were bamboo backed but on the average I don't see any real difference. Bamboo was the most common backing I used for many years so it had a better chance of producing more stand outs. Lately I have been using a lot more white oak simply because I can easily find 1/4 sawn straight grained boards to use.
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Your right badger i don't think it makes a faster bow , it isn't a magic backer or anything, maple and w oak are great, but i do love the look of a boo backed bow😉
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Thanks for posting your exxperiences, Steve. Perhaps backing selection is on down the list some, well behind belly qualities.
Other than species selection for belly wood, what do you look for most in a particular piece of wood?
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One thing I definitely like about the bamboo ipe combo is a narrow limb.
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The "Bow Index" is sort of representative of bending strain the wood takes when tested to failure. It would make more sense if the author multiplied the ratio of MOR to MOE by 100 instead of 1000, because it would indicate percent strain, which is the percent the outer fibers are compressed or stretched on the tension side at failure.
Keeping track of material properties can be very useful to bow building as long as we are using the right ones. One problem with the Modulus of Rupture property is that the test sample is put under increasing load until failure. This pushes the wood past the point where permanent damage (set) starts. The maximum load just prior to where this damage begins is called the Elastic Limit, which is the maximum stress value which would be more useful for designing bows. Some woods can continue taking increasing load well past this elastic limit, which probably explains what is happening to some of the woods shown with a high index number.
Some types of wood fail almost immediately after this elastic limit is exceeded, and I believe Ipe commonly falls in this category. Much of the Ipe I have experience with will explode catastrophically if pushed a little past the point where it begins to take some set. Materials that fail soon after exceeding the elastic limit will generally rank lower on the "Bow Index" list. On the other hand, if we had the Elastic Limit property for all the woods on the database, and used it instead of the MOR to calculate a Bow Index value, then we would probably see Ipe rise toward the top of the list.
Alan
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That was a good post Allen, I have noticed with Cherry, ipe, some black locust and several tropicals that are highly prone to chysal that they fail shortly after set starts happening. these same woods usually score very well on the low hysterisis scale as well.
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Is there a lab or something that a person could send samples to for testing? That way a person could specify what tests and to what point kind of stuff. We would also know the history of the sample.
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Is there a lab or something that a person could send samples to for testing? That way a person could specify what tests and to what point kind of stuff. We would also know the history of the sample.
A really good post would be explaining the procedure to make a test sight at your house. I doubt it would be too elaborate. I have tried to figure out meaningful test procedures but never really got around to doing anything. The thing that puzzles me most is how to accurately identify the nuetral plane. This would tell you all you needed to know about tension and compression.
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I usually test a small sample from board or stave (for moe and mor and where it begins to take set)
Its a simple wood jig that I hang on my tiller tree, and take measurements with a plastic dial caliper
Steve -I have given some thought in the past, to how one could locate the neutral plane of a particular combo . But I cannot remember why I thought having that info would help, or how I could use it. How would you apply the info in your designs?
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The easiest way to do this test is to obtain a sample of known length, width, and thickness between two supports. Apply a force on the middle and measure the deflection with a dial indicator. Repeat for increasing weight until the sample starts to take some set. Plot the force-deflection to identify at what point the sample started to take some set and this will be enough information to calculate the Modulus of Elasticity and bending stress limit. I imagine a test station similar in appearance to a arrow spine tester.
The location of the neutral plane depends on shape of the cross section. It could be affected a little if there is a significant difference between the modulus of elasticity for compression versus tension, but not much. Heat treating the belly might shift the neutral plane toward the bow belly a bit. In a clear rectangular board, the neutral plane should be pretty close to the center. If you have a composite of equal proportions of a relatively low modulus wood like maple on the back and ipe on the belly, then the neutral plane will shift pretty significantly toward the belly.
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The easiest way to do this test is to obtain a sample of known length, width, and thickness between two supports. Apply a force on the middle and measure the deflection with a dial indicator. Repeat for increasing weight until the sample starts to take some set. Plot the force-deflection to identify at what point the sample started to take some set and this will be enough information to calculate the Modulus of Elasticity and bending stress limit. I imagine a test station similar in appearance to a arrow spine tester.
The location of the neutral plane depends on shape of the cross section. It could be affected a little if there is a significant difference between the modulus of elasticity for compression versus tension, but not much. Heat treating the belly might shift the neutral plane toward the bow belly a bit. In a clear rectangular board, the neutral plane should be pretty close to the center. If you have a composite of equal proportions of a relatively low modulus wood like maple on the back and ipe on the belly, then the neutral plane will shift pretty significantly toward the belly.
Allen, I have always been under the impression that most wood did very little stretching mostly compressing. So you are saying they compress and stretch just about equally?
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The easiest way to do this test is to obtain a sample of known length, width, and thickness between two supports. Apply a force on the middle and measure the deflection with a dial indicator. Repeat for increasing weight until the sample starts to take some set. Plot the force-deflection to identify at what point the sample started to take some set and this will be enough information to calculate the Modulus of Elasticity and bending stress limit. I imagine a test station similar in appearance to a arrow spine tester.
The location of the neutral plane depends on shape of the cross section. It could be affected a little if there is a significant difference between the modulus of elasticity for compression versus tension, but not much. Heat treating the belly might shift the neutral plane toward the bow belly a bit. In a clear rectangular board, the neutral plane should be pretty close to the center. If you have a composite of equal proportions of a relatively low modulus wood like maple on the back and ipe on the belly, then the neutral plane will shift pretty significantly toward the belly.
Allen, I have always been under the impression that most wood did very little stretching mostly compressing. So you are saying they compress and stretch just about equally?
In the sinew process topic we had a discussion similar to this. The problem with just doing a deflection bend is that it doesn't distinguish between tension and compression. Wood isn't quite as simple of a material as something like metal. It has two different MOE for tension and compression. This is due to the nature of wood. In tension, you have the cellulose in the cell walls resisting stretching. Cellulose is a fiber, and like any fiber, it handles tension better than compression (imagine compressing a rope, you don't get much). However, it's not just acting like a cord but also forms cell walls essentially making pockets. This pocketing effect gives it its compressive ability (imagine compressing a balloon). However, the compression stiffness is less than the resistance it has to stretching. Therefore the neutral plane is not in the middle, its closer to the back unless the wood is backed with a material that is stiffer. I think it was discussed that it lies around 1/3 from the back and 2/3rd from the belly.
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Compression stiffness data of wood parallel to the grain is hard to come by. I found some measurements that shows the tensile and compressive modulus of several samples of multiple species as being nearly identical. I found another document that indicated the compressive modulus was much lower than the tensile modulus, but the samples in this test were very low density woods and were so full of knots and grain swirls that I don't see how the test could be meaningful.
With modern composites, both tensile and compressive modulus is usually pretty close, but wood has a completely different structure.
If anyone finds any good test data comparing tensile and compressive modulus then please let me know!
Alan
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Alan
https://www.fpl.fs.fed.us/documnts/fplgtr/fplgtr113/ch04.pdf has many of the commonly cited values.
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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.
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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.
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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.
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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.
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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.
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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?
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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.)
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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.
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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.
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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).
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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.
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Don't forget to factor in knots etc. ;)
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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.
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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.
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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?
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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?
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I think what would happen is that we would calibrate a rating system that would place the wood in 1 of 5 classes. each class might amount to a 1/4" in width we might need for a given design. You could also resolve some issues regarding trapping for instance.
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I can see where knowing how a particular wood rates, would be helpful for trapping and limb cross section design.
You have lost me on the 1/4" width idea, though. Would you be kind enough to offer more detail?
thanks
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Willie, suppose you start off and say a class 1 wood should be built at 1 1/4 wide for 50# and 66" long. Every class lower add 1/4" to the bows width. Somethign to that effect, I had not previosly given it much thought.
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I love this thread
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As Alan Case put so well, the author should have multiplied by 100 instead of 1000 and that would have been %strain, which is a meaningful engineering measurement.
% strain at failure is not the best indicator of bow performance at all though because it ignores the force required to achieve the strain and it ignores mass.
IMO the best bow index would be MOR/MOE x MOR/density which is at least roughly proportional to energy storage per unit mass. That formula basically amounts to a rough estimation of the area under the stress strain curve divided by the density.
It's still not perfect because as Alan noted, the wood may have already exceeded the elastic limit at the strain value corresponding to MOR; and more importantly for comparing different woods, some may fail very near the elastic limit, and others may undergo significant plastic deformation before failure. Since this is not necessarily constant across all woods, it makes it very difficult to use this type of data for quantitative or even qualitative comparative analysis.
Ideally you would test a whole bunch of woods using a single protocol and plot and publish stress strain curves for all the samples. Then you could do a pretty good retrospective analysis to determine energy storage/unit mass. Anyone have access to an Instron and a lot of free time. Lol.
I would test all the species in compression, and tension separately to get the most comprehensive data. Three point bending, or four point bending wouldn't be my first choice personally.
Sorry for the technical rant, but that's my take.
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As Alan Case put so well, the author should have multiplied by 100 instead of 1000 and that would have been %strain, which is a meaningful engineering measurement.
% strain at failure is not the best indicator of bow performance at all though because it ignores the force required to achieve the strain and it ignores mass.
IMO the best bow index would be MOR/MOE x MOR/density which is at least roughly proportional to energy storage per unit mass. That formula basically amounts to a rough estimation of the area under the stress strain curve divided by the density.
It's still not perfect because as Alan noted, the wood may have already exceeded the elastic limit at the strain value corresponding to MOR; and more importantly for comparing different woods, some may fail very near the elastic limit, and others may undergo significant plastic deformation before failure. Since this is not necessarily constant across all woods, it makes it very difficult to use this type of data for quantitative or even qualitative comparative analysis.
Ideally you would test a whole bunch of woods using a single protocol and plot and publish stress strain curves for all the samples. Then you could do a pretty good retrospective analysis to determine energy storage/unit mass. Anyone have access to an Instron and a lot of free time. Lol.
I would test all the species in compression, and tension separately to get the most comprehensive data. Three point bending, or four point bending wouldn't be my first choice personally.
Sorry for the technical rant, but that's my take.
That's gorgeous. Why not replace mor with elastic limit in you model?
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No data on elastic limit is available. Like I said the best would be to have stress-strain curves for all the woods, then you could do quite a bit.