Trad Gang
Main Boards => The Bowyer's Bench => Topic started by: inksoup on October 06, 2015, 05:23:00 AM
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it is closely related to MOE and MOR values of woods.
MOE is modulus of elasticity: this number should be as low as possible. low value means wood can be easily bended.
MOR is modulus of rupture: this value should be as high a s possible. high value means wood can NOT be broken easily.
so the formula:
Bow Index = (MOR / MOE)*1000
(multiply with 1000 since the division number will not be easy to read :) )
Example:
osage orange:
MOR: 18,650
MOE: 1,689,000
(18650 / 1689000 )*1000 = 11,042036708 ~ 11.05
any value between 9 - 13 is ok for the bow.
so...
for the bow wood choosing this information can give you an idea.
up to here i summarized from http://www.wood-database.com/wood-articles/bow-woods/
now My Theory for the laminated wood bows...
each of the lamination level should be calculated as in the formula and take the percentage of the wood on the bow and sum them up.
let see:
so as an example i will use this http://tradgang.com/noncgi/ultimatebb.php?ubb=get_topic;f=125;t=013128
it is ipe and hickory. i do not know which ipe and which hickory so i just used more common ones.
so ipe bow index with the formula is 8.01
hickory bow index with the formula is 9.35
assume that 75% ipe, 25% hickory used
8.01*0.75 + 9.35*0.25 = 9.01
so this combination is just ok for the bow making.
so friends... go and grab your calculator and start some math... :D because both math and bow making are fun!
have fun...
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Very nice!
thanks!
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Dang it Ink, now I have a headache! :confused:
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hahahaha crittergetter... get a beer yourself, then you will start feeling better :D
there some more variables in laminated bows that i was planning to put in the formula but i guess that will do the job for a while....
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Thanks but bowmaking is more fun than math. :)
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OMG I can't believe I just deleted all that! I'll try again in pieces.
Those who don't like math should close their eyes.
OK, first of all, I'm going to discuss calculating energy storage per unit mass in woods. The premise being that the best bow woods store the most energy with the least weight. This may not be the only concern, but this is in my opinion the most critical factor.
First lets see what variables we have to use. From wood database we can obtain:
MOR - Modulus of Rupture; a measure of strain at failure. units of force per unit cross sectional area.
MOE - Modulus of Elasticity; a measure of the stiffness on a material in the region of elastic deformation
Density - measure of mass per unit volume, SG is normalized to the density of water.
OK so before we go farther, let me mention that wood is not a simple engineering material for the following reasons at least:
1)non-isotropic (mechanical properties depend on the orientation of the material)
2)wood exhibits significant creep and stress relaxation
3)wood deforms plastically before failing, therefore MOR is always measured after the wood has taken maximum set!
We will use the following assumptions:
1)all data from wood database is taken in the longitudinal axis(along the grain)
2)quasi-static; creep and stress relaxation are ignored
3)MOR is proportional to stress at the elastic limit (shown as proportionality limit in the stress strain curve below). In other words, higher MOR always means higher stress at the elastic limit. Elastic limit and proportionality limit are not identical but close enough for this discussion.
With these assumptions we can make a ******qualitative estimate of energy storage *******
So what has Ink calculated with MOR/MOE? well given the assumptions I have made, Ink has basically estimated (only qualitatively, not quantitatively) the strain at the elastic limit.
So what do we need to calculate or rather estimate? We need to estimate the energy stored by the wood during elastic deformation. The energy is stored is roughly 1/2 (stress at the elastic limit) * (Strain at the elastic limit).
Since we already said that MOR/MOE is roughly the strain at the elastic limit, and that MOR is an estimator of stress at the elastic limit, the equation for estimated energy storage is :
Energy = 1/2 (MOR/MOE)*(MOR)
since our estimate is only qualitative (only for comparison between woods) we can ignore the 1/2.
Therefore:
Energy ~ (MOR/MOE)*MOR
to get Energy/mass ~(MOR/MOE)*(MOR)*(1/density)
so there it is ...
Where does this fall short? Well MOR may not be a proportional estimator of the stress at the elastic limit. It's probably lose enough that it will give you some info, but may not be accurate enough to determine the better of two woods which rate very closely.
Stress strain curve to be added momentarily.
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(http://i1212.photobucket.com/albums/cc450/Benjaminklein/Mobile%20Uploads/IMG_0150.jpg) (http://s1212.photobucket.com/user/Benjaminklein/media/Mobile%20Uploads/IMG_0150.jpg.html)
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I got it, or-- Think I'll have a double Mojito. :)
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I'm just gonna stick wif Osage:)
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Wow, if I was still a drinking man it would take at least 3 vodka gimlets to get through this. And I still wouldn't understand it.
Guess I'm stuck with the old math: Osage=Good. ;)
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Ya beat me to it, Roy.
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I just have one question
It is possible to synthesize excited bromide in an argon matrix ? :cool:
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I do it all the time, Mark.. :)
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Littleben's occupation is a Mad Scientist
:biglaugh:
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The real problem I see is that all wood no matter what species varies so much from piece to piece that trying to nail down and give specific values to MOE, MOR, stress, strain etc isn't really going to give you meaningful numbers at the end. Too many givens!
A simply bend test will tell you all you need to know about any potential bow wood....granted you need to have a piece to test but still ;)
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X'2 Mike.. Sometimes even the best looking piece of Osage has given me a loud cracking surprise on the tillering tree:)
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Originally posted by mikkekeswick:
The real problem I see is that all wood no matter what species varies so much from piece to piece that trying to nail down and give specific values to MOE, MOR, stress, strain etc isn't really going to give you meaningful numbers...
Yup.
It's easy for us engineering types to overthink these things. Just read some I my older posts.
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Never met an engineer I trusted... :) Had one here a couple years ago to help me with my first glass takedown build. He had it between his ears, and talked a good game plan, but couldn't transfer it to his hands. I ended up trashing that bow.
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I think Mike and Dave both make good points. And I wouldn't waste my time to determine a chart of "bow index". Also, the simple fact that Steve Gardner's mass formula works suggests that most wood is pretty close in terms of energy storage per mass. So my guess is if we bothered to calculate them all out, they'd all be remarkably close.
I do think, however, that there is meaningful information you can take from the empirical data we can get our hands on.
An example, let's say i built a bamboo backed osage 1.25" wide, and 62" long. The bow turned out well, and I liked it. I have a piece of clean yew and I want to make a bow of basically the same length and design and weight as I did with the osage, but using my nice new piece of pacific yew.
I would log onto TG and say, hey mike, how wide should my awesome yew bow be? Since no one has bend tested my osage or my yew, we're basically just going on people's experience. And probably if 10 people responded I would get 4-5 different answers.
I could alternatively log onto wood database and I could see that osage and yew end about the same amount before breaking, and osage is about 20% stiffer than yew.
So I could just start building the yew bow 20% wider than my osage bow which would be 1.5" wide.
Is it perfect? No. But there's definately meaningful information to be taken.
Osage and Yew are also well known, so what do I do when I wanna build a bow with a shedua belly? I've got to start somewhere, and there may be no one to ask.
So bottom line, if you can bend test ... Great, but if you've got nothing to spare, better to start from the wood database data than a total guess.
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Originally posted by canopyboy:
It's easy for engineering types to overthink these things.
Holy Crap! :scared: Did our resident engineer just say this?!?!?!?!? :laughing:
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Ah but there you go Ben the yew shouldn't be wider it should be thicker than the osage.....
Numbers are all well and good for ballpark guesses but....you've got to know how to apply them!!!
A bend test can be done on a matchstick sized piece if necessary....obviously bigger is better though!
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John, I believe ole canopygirl has gone as far as forgetting to renew her engineering license... :)
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I'm an Engineer but actively avoid getting too technically specific with building bows. Wood is too variable a material, besides which, I love the art of it and Engineering is work. I make bows to get away from work!
In Australia we don't have a long tradition of bow timbers so in many ways, we're still learning what can be used and what can't, and in what way. I'm still looking for that native timber that can be used for a good backing... The science helps work a few things out though.
I tend to think of MoE as a measure of how thick the limb needs to be and how quickly it will develop loading. Lower the better, or if it's above 18ish, it needs a real good Bulk Mod.
MoCrushing/Bulk Mod is my measure of how good the timber is in compression, usually on the belly. Higher the better but you can get away with low values if the MoE is low too, like Elm, as long as it's not backed with something crazy like bamboo or glass.
MoR is for tension and there's too many variables for it to be a good measure, in my opinion. Grain orientation is essential, and I've no idea what the grain was like on the test pieces they took the numbers from.
I guess it's all about matching appropriate backing and belly materials, like Maple/Walnut, Osage/Bamboo, Hickory/Yew. The closer these properties are matched, the 'sweeter' or more efficient your bow will be. I wrote a bunch of engineering notes down on the subject and posted them on another forum, PM me if anyone is interested.
Not sure what the policy is on posting out of forum, but there's an awesome thread on using maths in making bows here - http://www.ozbow.net/phpBB3/viewtopic.php?f=34&t=5450 - Yeoman has done a lot of work and has been real successful. If you're inclined, the thread is long but well worth a read.
Neil
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Ahoy all,
Another Aussie bowyer here. In fact, I wrote that post Nezwin linked to above.
It's true that we're essentially still in the pioneering stage of exploring the potential of Australian timbers for making bows here. The list grows constantly, but from a relatively small base.
Let me just say early on that I'm not an engineer, and I nearly flunked maths in high school.
Let me also say that of course I recognise that there are thousands of bowyers who do not conduct bend tests or make bows by numbers. And they make very good bows. But there are also some of us who have gone down the engineering route, I think for the benefit of the bowmaking community.
Many years ago, in an effort to better understand bow design and to maximise my use of Australian timbers, I forced myself to learn the engineering of cantilevers (because a bow is just two cantilevers joined at their origins), and also learned how to conduct bend tests.
I learned quite a lot about wood, as it related to bowmaking. I learned that the published MoR of any timber is only indicative of its merits for making a bow in the same way the speedometer in a car is indicative of how quickly it will accelerate.
For bowmaking purposes the MoR is not terribly helpful, because although the MoR is a measure of bending stress; it is the bending stress at which the wood fails. The stresses in a working, effective bow are far below the rupture stress. In addition to this, how wood will respond to bending stresses leading up to that rupture point differ wildly by species and growing conditions, among other things.
Published data for timbers are rarely helpful for definitive (as opposed to indicative) guidance on making a bow. This is because two samples of the same species can have wildly different properties (like up to 20% in extreme cases), and the features we as bowmakers want is not generally tested, never mind published.
In my mind the best way to use the numbers to make a bow is to conduct a bend test of a sample of wood from the stave that will be used to make the bow. This will most reliably indicate the properties of the very wood inside the stave that you'll make a bow from.
What qualities are important? The strain the wood can withstand before it takes an acceptable amount of set; and, the stiffness of the timber when it reaches that amount of set.
When a bow is drawn 28 inches, its tips will move about 14. If about one inch of set is acceptable, then a set equal to 8% of deflection is about right. So when I'm bend testing, I look for that deflection that causes the sample to take 8% of the deflection in set. Then I also take the corresponding stiffness.
Strain, for those that might not know, is the percentage of lengthening or shortening due to tension or compression under load. Happily, multiplying the stiffness by the strain will give you the bending stress at that same load.
A wood that can tolerate a large amount of strain at the 8% set can make a thicker bow than a timber that cannot tolerate as much strain.
A wood that is very stiff can make a narrower bow than a wood that is not as stiff.
Yew does not make an excellent bow wood because its MoE is low. Far from it. Willow has a similar MoE. Yew makes an exceptional bow wood because it can withstand a monumental amount of strain before taking the 8% set. This means it can be much thicker than other woods. Being thicker, it does not have to be as wide as other woods of the same stiffness.
Incidentally, the wood database gives an MoE for Yew of 9.31 GPa. Some of our Australian woods are about 24 GPa, and they make exceptional bows too. Not because their MoE is high, but because their allowable strain is favourable.
I could go on and on about how the mechanical properties of wood interact and influence the suitability of wood for bows, but I have prattled on a bit too long already, methinks, so I should leave it there for now.
Cheers,
Dave
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Another thing that I don't see used anywhere near enough is trapping. Making the limbs cross section a trapezoid. A large number of the woods we use are quite a lot stronger in tension than they are in compression at a given bend. By making the back narrower (or indeed the belly for the opposite)you can 'even out' these properties and get a low set great shooting bow from woods that a lot of people are down on. Eg. red oak people are always saying its not so great and a beginners wood - narrow the back around 30 - 35% and boy does it shine. Similar results can be had with a whole load of different woods. Again a simple bend test with a small piece of the stave you are using can show you which way to go.