Bow wood order of merit

[yeoman]

I started typing this last night. I thought it would be about two pages worth. It's now four pages and still going, so I will post this essay in chunks to make it more easily digestible.

This has been knocking around in my head for a while now, and I felt I needed to get it written down before I confuse myself too much. I don't suppose that by the end of it many people will have come around to my way of thinking. That's fine. We're all in this for fun. Perhaps though, some will come to understand wood a little better, and make bows under some new light. Who knows? I'd appreciate any feedback.

We have in the past sought to discover a way to numerically communicate the value of any particular sample of wood, in such a way that it can be compared to the numerical value of another wood and placed in some sort of ascending or descending order.

Going by memory alone, I believe some of the suggestions have been some combination of:

MoE & MoR; and,
MoE, MoR & Density;

In any case there has usually been some mention of the MoE and MoR. This seems to make sense. The MoE is a measure of how stiff the wood is. That is: how resistant is this sample of wood to being bent? The same would seem to be true for MoR, which is a measure of how much pressure the sample can withstand before mechanically failing.

The MoR figure is a little bit of a false target though. When we read MoR numbers we learn the point at which the wood sample fails mechanically in a wood bending test. I've read recently that scientific bodies that test this kind of thing may measure multiple samples, but they also do the bend test all in one go in a machine that costs More than we'd all make in a year put together. The downside of this...actually there are a couple:

A wood sample may behave admirably when bent once or a small number of times, but will fail if bent many times; and,
These bend tests tell us nothing about the set-taking properties of the wood.

So the pressure experienced by a piece of wood in a bow is well below the wood's MoR. A few years ago I did quite a bit of bend testing and I found that of the better samples, a bending stress useful for bows was about 60% of the measured MoR (the MoR that I measured, not the published values).

So, I suppose there would be some merit in quoting the MoR of a wood, especially if that figure was measured in a bend test which subjected the sample to many bends similar to its potential use in a bow.

However not all woods are the same. Some woods will have the same MoE and MoR, but if subjected to the same bending force will take different amounts of set, because their capacity to resist plastic deformation is different between load=zero and load=mass. You might think of it this way: Two sports cars may have the same HP engine, with the same measured top speed. These two cars take off from the start line at their maximum rate of acceleration. At any point in time before they both reach maximum speed, the two cars may have different speeds because of any number of reasons.

Still with me? I hope so.

So what are we to do? Well, as the powers that be are not considerate enough to conduct bend tests in such a way that perfectly suit our needs, we may have to all be conducting our own bend tests. This is I think less of a problem than many think, and for people who like making bows, this can become quite exciting (really, it can ).

END PART ONE

*edited to add*

This development is not entirely my own invention. I was inspired down this path by Woodbear on the paleoplanet forums, who said he is most interested with a bow wood's working strain, with other statistics coming afterwards.

[yeoman]

If we all did just a small number of bend tests, and shared the data, soon we'd have a catalogue of dozens of woods to compare.

But wait, Dave, how do we compare them? Woods have different densities, and the MoE and MoR are BOTH variables, and can be all over the place.

I hear you, I hear you. I propose that for the time being we ignore the density of any particular wood. Elm has a density of about .6 that of water, while I've measured some Ironbark that was 1.3. Both make excellent bows. Also, as Steve Gardner has amply proven, the final mass of any given bow, if made to shoot efficiently, will have a very similar mass to a bow made to the same specs (length, tiller, draw weight/length) made from wood of different density. Why this is so is perhaps better discussed in its own thread.

So for now, let's leave density aside.

We need a way to determine a number which is applicable to a particular sample, but is also useful in comparing samples which possess different overall values. Fortunately we have this number, and is is the measure of strain. Bending stress is the pressure generated by bending a sample. Strain, on the other hand, is the percentage the surface of the sample is stretched or compressed at a particular bend. So, if a beam is experiencing 1% strain, its surfaces are being stretched/compressed 1% of the length measured at rest.

Still with me?

For those doing bend tests, strain is very easy to calculate. It is the bending stress (less than MoR) at a given load, divided by the stiffness (MoE value).

Just. You. Wait. Right. There. You earlier said that MoE and MoR might not be the way to go. What gives?

Just give me a few More minutes and I'll get to it.

If we divide MoE by MoR we'll get the strain at rupture. Not useful for us. If we divide a bending stress 60% of MoR by MoE, we're really only calculating an arbitrary number, and depending on the wood, we might be sailing very close to the wind, or (arguably) worse, not be getting the full potential from our wood. See below for more on this.

So what I propose is calculating the strain for that bend which causes the wood to take a set 8% of deflection. So if in the bend test the sample bends 100 mm, and after that takes 8 mm set, then that bending stress is used to calculate the strain. Why 8%? In a bow drawing 28 inches, the tips of the bow will move approximately 14 inches. Around 1 inch of set is acceptable for most straight-stave bowyers (when making selfbows...ignoring backed bows, bows with lots of reflex, recurves, heat treated reflex, etc), which happens to be about 8% of the tip deflection.

Woods which are traditionally known to be good for bows have had this strain (called 'working strain') measured and found to be:

Yew - 0.96%
Osage - 0.93%
Lemonwood: 0.89%
Ash - 0.75%
Hickory - 0.75%
Red Oak - 0.71%

Some not-so-great bow woods showed:

Fir - 0.55%
Spruce - 0.62%
Willow - 0.75% (More on this later)

Some wood that I have tested has shown the following figures:

Spotted Gum - 0.67%
(better) Spotted Gum - 0.72%
Ironbark - 0.63%
(better) ironbark - 0.77%
Blackbutt - 0.60%

So, from this list, it should be obvious that better bow woods have a higher allowable level of working strain.

But this is not the whole story. You will notice the willow has a working strain the same as Hickory. So what's the deal here? Well, it happens to be that the stiffness of the Willow was almost the same as some of the Yew tested.

What? Just as stiff as Yew? The king of all bow woods?

Yep.

END PART TWO

[bigbob]

This is a brilliant dissertation and one I am following keenly. Thanks.

[yeoman]

Cheers bigbob. At least one person will get some enjoyment out of it at least.

Dave

[bigbob]

I am quite certain quite a few others will be very interested in your information and musings as well.

[yeoman]

To continue our story with an annoying recap:

What? Just as stiff as Yew? The king of all bow woods?

Yep.

BUT the strain Willow can take before failing is faaaar less than Yew's heroic tolerance of strain. So while it is fairly easy to bend, it takes set much earlier than Yew. That's the beauty of Yew. Because it has such a high working strain, it can be made much thicker than most other woods, which means draw weight can be built up quicker, and with a narrower profile. It is in so many ways 'full of win'.

If we then look at some of the samples I tested. We see that for some of them, the working strain was reasonably low, compared to the MoRe usual bow-suspects. Yet I made quite good bows from these samples. How was this so? The answer is in the MoE. Although the working strain could be described as mediocre, the MoE was through the roof, which meant the wood's (in)capacity to endure strain was blown out of the water by sheer stiffness. With the right design, these woods still had potential. Not much good for deep sectioned ELB style bows, very stiff but low working strain woods work better for very long bows (which will likely be narrow and end up flattish-bellied) or wide flatbows. (Additionally, these woods really, really shine when perry reflexed with a lamination of bamboo. Absolute screamers. The reason for this is also a topic for another discussion.)

We're getting close to the end.

So what I propose is not a single number. More of a statement of quality which is made up of numbers. In two parts. It will look like this:

XX.YYYYY

END PART THREE

[yeoman]

edited to remove pictures in the wrong place

[little arrows]

Hi yeoman,

very interesting reading - may I ask a question - you can have MoE and MoR for green and air dried timber - is your thesis on air dried?

cheers
sue

[yeoman]

Of course you may ask a question. I welcome it.

It is possible to calculate MoE, MoR and working strain for green wood.

However, when we do bend tests, it is best to use wood in as close a condition as it will be when we use it to make the bow. If we measure the wood when green, and make the bow when seasoned, the mechanical properties will of course be different, and so the bow will behave very differently to that which we had originally intended.

Here's a couple of pictures to break up the monotony of all my words:

[little arrows]

so did you stand in the paddock and just wait to see if the cow actually moved......

I figured you'd do it on air dryed, as that is the material you are working in - wonder if kiln drying effects the structure at all - anyhoo - carry on.

cheers
sue

[yeoman]

I don't think it makes as much difference as we might worry about.

Kiln dried timber has been compared to air dried timber before and has been found to be not too terribly different.

The secret is to tickle the inside of the cow's nostril with a blade of grass. I imagine.

[greybeard]

Dave,

Are the values based on milled boards and if so have they all been milled in a similar fashion i.e. quarter sawn?

I believe that split bush billets would probably be superior in the various tests.

Daryl.

[yeoman]

So what I propose is not a single number. More of a statement of quality which is made up of numbers. It will look like this:

XX.YYYYY

The first two digits are the working strain of the wood. The last five are the MoE in MP, with a leading zero if the MoE is less than 10,000. So a Bay tree, with a working strain of 0.89% and an MoE of 9,231 MPa would have a figure of 89.09231, while Ash, with a working strain of 0.75% and MoE of 11,601 would have a figure of 75.11601. Simple, yes?

In this way, woods can be ordered according to what I believe to be the MoRe important value: the allowable working strain, but the figure also contains sufficient information to be able to compare woods which have a similar or equal working strain. For example, in the above listed wood stats, the Ash and the ‘better Spotted Gum’ both had similar allowable working strains. However, the Spotted Gum has a much higher stiffness, which means the bow’s volume will be much smaller for the same mass. So in a toss up between the two I would pick the Spotted Gum.

Ash: 75.11601
Spotted Gum: 72.20169
Willow: 75.08929

I included Willow here to once again show that although it has a similar capacity to withstand strain as both Ash and Spotted Gum, its stiffness is pitiful.

To really be of any use, this method of notation needs to rely on the results of bend tests done by bowyers or other wood nerds. I mentioned before how I had found a working stress of 60% of MoR to work well...for some woods that I personally had tested. If we apply that to all woods from published data, we get some very confusing results, such as:

Red Maple: 50.11000
Rock Elm: 55.11000
Pacific Yew: 70.9000
Hickory: 52.16000

Of these, only the Yew looks anywhere near promising, all of them seemingly second rate bow woods. Yet we know from practical experience that these woods make terrific bows, and we know from scientific experimentation that the figures for these woods are much More appealing.

Published data for Australian woods are even worse:

Ironbark: 47.17000
Spotted Gum: 39.23000
Sydney Blue Gum: 46.18000

So I don’t think we can simply run tables photocopied from Bootle through a calculator and instantly have a massive head start on our catalogue of wood-specs. It really needs to be done the hard way. Which is actually not all that hard.

I have gone into some detail as to how to do a bend test, found here:

http://www.ozbow.net/phpBB3/viewtopic.php?f=34&t=5450

It’s pretty easy to calculate once all the equations are put into a spreadsheet.

I can even do it for you. Below is a link to download the spreadsheet. It’s really simple. You only need to put numbers into green cells. If there is a tiny red triangle in the top right of the cell, hover your mouse over that cell to see the comment for it.

https://www.dropbox.com/s/rlxx2slb184i6 ... sheet.xlsx


END PART FOUR

[yeoman]

Hi Daryl,

As for the northern hemisphere woods, I cannot comment as to the way the timber was curated. I suspect at least some of them were milled boards.

Most of my tests were with milled boards. As to the cut of those boards, I cannot remember, but I do know I tried to pick boards with the straightest grain possible.

As for bush billets being superior to milled boards, I imagine this would mostly be the case where the board was not specifically chosen to have perfect grain orientation.

Dave

[rodlonq]

Gidday Dave,

Your post has been very interesting and informative. It is all heading towards a very valuable resource that could come together quite quickly if enough interested parties participate actively. Below are a few topics I'd like to open for discussion.

As you said earlier that a straight forward bend test and measurement of bending stress (MoR) at failure is not all that useful. Would you suggest that for each load applied, it could be applied several times (i.e. loading and unloading say 3 or 5 times at each load) before measuring the deflection and set. This will only add a little time but greater value to the measurements.

Do you think it is necessary to use comparative sample sizes (i.e similar ratio of length to Ixx or depth), or even a standard size sample (that may not always be available though). I realise that the math behind the analysis makes all things equal, however real samples may vary in exhibited properties (i.e very thin samples of ring porous woods may have only one summer growth ring present). Also it could be useful to add a comment to the spreadsheet that indicates if the sample is quarter sawn or plain sawn.

Is there much point in taking multiple measurements past the 8% set measurement? This could shorten the time taken and make the process more attractive to those collecting data.

Could you expand a bit on the significance of the R/T ratio in your spreadsheet? It reduces to 1/(2*strain). How do you use it to compare results.

Thanks for going to the great amount of effort you have presented here, it is not only interesting but inspiring to see your enthusiasm.

Cheers..... Rod

[yeoman]

Thanks for the encouragement Rod. I hope it helps some out there. Especially me, if other people are willing to do some bend tests!

To responds to your points:

As you said earlier that a straight forward bend test and measurement of bending stress (MoR) at failure is not all that useful. Would you suggest that for each load applied, it could be applied several times (i.e. loading and unloading say 3 or 5 times at each load) before measuring the deflection and set. This will only add a little time but greater value to the measurements.

Bending several times before measurement is a great idea. The finished bow will be bent hundreds, hopefully thousands of times, so it makes sense to measure the wood once it's been exercised a bit at the displacement you want to measure. More is obviously better, but maybe five or so bends would be sufficient, I imagine.

Do you think it is necessary to use comparative sample sizes (i.e similar ratio of length to Ixx or depth), or even a standard size sample (that may not always be available though). I realise that the math behind the analysis makes all things equal, however real samples may vary in exhibited properties (i.e very thin samples of ring porous woods may have only one summer growth ring present). Also it could be useful to add a comment to the spreadsheet that indicates if the sample is quarter sawn or plain sawn.

I think using a sample size appropriate for the wood, rather than a standard size for all would be best. In Tim Baker's standard bend test, all samples had to be 1/2" square. Owing to the stiffness of some of the Australian woods compared to Elm or Yew, this thickness poses some problems with regards to the 'resolution of measurement' if you will. When testing Ironbark, for example, I like a piece that's maybe 5 mm thick and 15-20 mm wide. It is that thin so that a given load makes for a large displacement (which makes accurate measurement easier), and it is that wide to still be able to give a credible amount of resistance. If 1/2" thick, it would start taking set very early and would be difficult to hold at displacement long enough to make good measurements. And like you say: a wood with very wide rings may need a thicker sample to encapsulate a ring or two.

I have ideas in my head for how the spreadsheet of all the values would look. A space to allow a record of grain orientation would be easy and worthwhile.

Is there much point in taking multiple measurements past the 8% set measurement? This could shorten the time taken and make the process more attractive to those collecting data.

I think there is. I always test to the snap, so that I can observe the various stages a sample goes through to the point of failure. You might find that to get to 10% set requires more strain in one wood than in another, and for the increase in set, the saving in mass by being able to make a narrower limb might be worth it.

But if time is sparse, then I'd maybe test to 12% set or so. Maybe 20%.

Could you expand a bit on the significance of the R/T ratio in your spreadsheet? It reduces to 1/(2*strain). How do you use it to compare results.

The R/T ratio is the ratio of radius of bend (R) to thickness (T) allowed to achieve a given stress/strain. In the bend test sheet I shared, I invented some values to simulate some hypothetical wood. This wood happens to have an R/T figure of 72. So what you do with the number is this: Say you want to make a pyramid bow in which when the limbs are bent, bend in perfect arcs and have an even radius (R) of 660 mm.

If R/T = 72, and we know R, the equation becomes 660/T = 72. To find out T, we multiply both sides by T and then divide both sides by 72, which gives us T=660/72. or 9.167. So for our pyramid bow, the thickness to give our desired strain for the known radius is 9.167 mm.

You're pretty close to the calculation for R/T. It is actually R/T = MoE/(2 x desired bending stress). Use that bending stress calculated in the bend test which generated the 8% set. I did it slightly differently, but I was trying something tricky.

Thanks for going to the great amount of effort you have presented here, it is not only interesting but inspiring to see your enthusiasm.

You're most welcome. It feels quite cathartic to get it all out!

Dave

[yeoman]

So, we're now onto the implementation phase.

I took some time today to compile a bunch of data from bend tests that have already been done, and put them into a spreadsheet that contains, I think, most of the information I think we could be interested in. Hopefully the file attaches.

Merit list.xls

(30.5 KiB) Downloaded 159 times

I have filtered all the information so if you're unfamiliar with Excel, you can click on any of the little down arrows in the column headings to sort by different criteria.

In the case of this spreadsheet, I have separated the XX.YYYYY into two columns. This is so that for data manipulation purposes, such as when someone wants to quickly find all woods with a working strain greater than 0.75%, but also an MoE greater than 15,000MPa. I still think that a great shorthand notation outside of Excel is the XX.YYYYY format. So just pretend there's a full stop between columns B and C, mmkay?

The very great majority of the tests were done by Tim Baker in his preparation of Design and Performance chapter in TBB1. A very few of my bend test results are in there. I have more, but are inaccessible at the moment. Even a cursory glance at the information reveals some very interesting points for consideration (to follow along at home, make sure column B is sorted from largest to smallest):

The very good Ironbark had a working strain very similar to Mulberry, Pecan and Walnut, which are all touted as being great bow woods, yet the Ironbark was up to three times stiffer, meaning a bow from this log would have been very slender for the same other specs as bows made from similar woods. Of note, the one longbow I have so far made from this log developed some light chrysals despite taking low set, and shoots just fine, regardless.

The Spotted Gum had a reasonably similar working strain to Ash, but was twice as stiff. So same as above. But, the thing to note is that the Ash has more bend-before-break in it than the Spotted Gum did. Which is to say the Ash went on after this strain to take more and more set before breaking, while the Spotted gum did not take a great deal more before failing. Enough for the suggested working strain to be safely within the realm of dependable, but the horizon was much closer.

The lesser Ironbark was better than a Hickory sample in both columns. But as with the Spotted Gum above, Hickory had more life after working strain was found. Hickory is famous for its very high tensile strength. Which means the belly is going to fail first, which is manifest in taking set, fretting, chrysalling, and not shattering or lifting splinters on the back.

The Blackbutt's placement in the lineup surprised me. I found it to be a little unpredictable and catastrophic in its coming asunder. Not like Hickory. So in a toss-up between the two, I think I would pick Hickory every time.

Playing around with this sheet for even a short time with even a little knowledge of what woods are used by our northern-Hemisphere bowyer colleagues, and having the experiences we have with Australian woods; I think one point becomes eminently clear: While these numbers are very helpful, digits on a page are not the whole story. These numbers will not tell you that although Hickory and Blackbutt have similar stiffness and working strain: Hickory's tensile strength is immensely higher and is extraordinarily hard to break while Blackbutt might for its own cantankerous reasons let go all of a sudden. The numbers will not tell you that Ironbark can be a bit of a sod to work with hand tools while apple is smooth and creamy like butter under a drawknife. The numbers give not a hint that Ironbark may make a perfectly well shooting bow but still develop small frets.

But regardless, I think that examination of these numbers will help in determining which woods are worth pursuing in bowyery, and which might be left aside. For example if I tested a wood that had numbers anything similar to Willow, I would put it aside as fast as I was able and not ever bother trying to bend again. If I did a bend test of a sample and found its working strain to be above 0.85%, I would rush back to the timber yard to buy as much of it as I could, especially if the MoE was above 14,000 MPa.

I'm not sure exactly what will come of all this writing I've done on this subject. I'd like to think that it might encourage some people (perhaps one or two would be a good outcome) to have a go at doing bend tests, and sharing the results to add to the compendium for the benefit of all. And me. Hopefully, in the future, when I talk about making a bow, and mentioning offhand that the wood had a merit value of 75.21000, people will know what I am on about.

I think the next step is in figuring out a way to tier the results further. A wood with a working strain of 0.89% but an MoE of only 11,000 MPa (so, 89.11000) is enormously preferably to a wood with a value of 65.24000. But a wood with a merit value of 89.24000 would likely negate the need for fiberglass and carbon fiber. I'm seeing through the fog of tiredness a graph of working stress against MoE, where any combination above a line is Good (and the further above, the Gooder it is), while below the line is unfavourable (and the lower it is, the unfavourabler it is). But that's a problem for another day. Maybe even some day soon.

Happy bowyering,

Dave

[Dennis La Varenne]

Dave,

Jeff told me that you were trying to contact me recently. You must have a bunch of old email addresses. My current email address is on the site if you want to PM me any time.

I think Jeff told you I was crook. I was. It came close to costing me my life twice in a short period as my sister reminds me, but I am on the mend very slowly.

However, I did read your post 'BOW WOOD ORDER OF MERIT', and I think it is excellent. Something like that is what I have been dreaming of for a long time. I just lacked the brains to work it out like you have. I am a bit slow mentally at present and it presents a bit of concentration which is a bit of effort presently, but I will keep at it, but so far, I cannot see any flaws in it.

I still think my listing using mostly Bootle's published data serves a purpose limited to those just starting who know little and are just at the stage of looking for a prospective suitable bow wood. But that is as far as it was meant to go. It was not and could never be as definitive as your technique, and, if as you (and I) hope, enough bowyers do enough bend testing and record their data, then my tables will become redundant.

By the way, I discovered that US Forest Service publication nearly 10 years ago, but it has obviously been revamped. Well worth having indeed.

Best regards and keep it up.

[yeoman]

Thanks Dennis, I'm glad you like the proposed notation.

But to be clear, I shouldn't get all the credit. Woodbear on Paleoplanet mentioned at some stage (perhaps more than once) that in considering the value of any one wood, he thinks the working strain is more important than the MoE or MoR.

Realising this was in fact true (Yew has an enormous working strain, yet has a very low MoE for example), I thought this would be the way to rate woods.

Then, I realised there were more variables in wood than would allow for only one number to reasonably represent a wood's merit for bows, especially when compared to many other woods which have several of their own variables. So, I thought to include the MoE as well as the working strain.

In this way, collated data can be tiered and sorted in two ways. First, woods can be compared for relative bow value by way of the working strain. Then, within woods that have the same or similar working strain, they can be compared in an absolute sense through the MoE.

But of course you are right about Bootle. In lieu of vast tables of data sourced from DIY bend tests, published data does of course have it's place, and value. I'm not suggesting we abandon Bootle. In fact I would love to get my hands on a copy of that work still.

Here's hoping more bowyers start doing some bend tests.

Dave

[Dennis La Varenne]

Dave,

Bootle is out in paperback and available from -

'The Mail Order Bookshop'
A Division of Skills Publishing P/L
PO Box 514 Hazelbrook NSW 2779
P: -2 4759 2844
E: administration@skillspublish.com.au
W: http://www.skillspublish.com.au

Mine cost me $82 including freight back in March 2012.

I do have the earlier hardcover, but the only real difference seems to be in the layout of this later edition and perhaps a few minor edits here and there.

Regards,

[rodlonq]

Bootle can also be bought from fishpond.com.au for about $72 delivered from memory.

Cheers.... Rod

[bigbob]

I am still following this with huge interest but may have a similar problem to Dennis. When confronted by a mass of data that needs to be studied and analyse I find my brain struggling to maintain its ability to collate. I am widely read and have a diverse array of interests of a cerebral nature but am becoming far more visually proficient rather than having to ingest info through print. This is probably just the start of senior onset dementia

[yeoman]

I suffer the same problem. Believe it or not, I really struggle especially with numbers and mathsy stuff. What I've written so far is an attempt to get into some sort of order the massive tangle of thoughts propagating in my mind over the last few weeks.

If any of what I've written is too convoluted, please do let me know and I'll try to re-explain with examples or illustrations.

[yeoman]

I did some more work with regards to strain and MoE, and how they are manifest in different bow designs.

I wanted to get some sort of idea as to what standards of wood properties were required for some given bow designs.

Of course, mathematically, it should be possible to make any design of bow from any wood. In reality, there are limitations. A bendy handle longbow may be far too wide to hold comfortably, and the arrow will have trouble paradoxing around the handle. Some flatbows will be ridiculously wide at a normal length, well outside the realm of what most would consider to be aesthetically pleasing.

So I 'made' four bows of different design. When I say 'made' I mean I put heaps of numbers into a spreadsheet and calculated widths and thicknesses. The four bows are as follows:

A - 66" bend through the handle longbow, 50lb @ 28", width at centre: 36 mm.
B - 62" pyramid bow with rigid handle, 50lb @ 28", width at widest part of fade: 50 mm.
C - 71" bend through the handle warbow, 100lb @ 28", width at centre: 40 mm.
D - 68" rigid handle flatbow, 50lb @ 28", width at widest part of fade: 50mm.

My goal was to discover that working strain required from a wood of X stiffness (MoE) which would cause the bow to have the given width for the given draw weight and length. I decided the draw weight at random, bu thought them to be nice round numbers. The widths I arbitrarily decided for the sake of the exercise as being what would 'reasonably be accepted'.

I only recorded data for eight different measures of MoE. I found this to be sufficient to plot reasonable graphs however and so am happy with that. The MoE values used (all being in Megapascals, MPa) were:

25,000
22,500
20,000
17,500
15,000
12,500
10,000
8,000

The way I did it was to plug the MoE into my bow design spreadsheet as a given, as well as the draw weight and length etc, then adjust the working strain up or down until the width was within 1 mm of the definitions, above.

I was quite surprised, in a way, by the results.



To do a bit of interpretive analysis of this graph:

* for any given bow design, a stiffer wood can have a lower working strain to make an acceptable bow
* as the stiffness decreases, the required working strain increases in an exponential manner.
* This was not intentional, and was the most surprising thing to be, but...the minimum working strain per unit of stiffness was essentially exactly the same for the warbow & pyramid bow, and also the same for the longbow & flatbow. Bizarre.

On reflection, I think the warbow could have done with being a couple of inches longer. Nevertheless, it still illustrates the principle.

So the result of all this seems to be that if you want to make a pyramid or warbow, woods which have a higher working strain are required. If the wood you have cannot withstand quite as much strain, then it is best to make a longbow that bends throughout its length, or a longer flatbow.

If the bowyer was desperate to make a warbow or pyramid bow from a wood with a lower than ideal working strain, then the solution is to make the bow longer. Or make a lower weight bow to stay within a reasonable width.

Now, this will not come as news to a great many bowyers. It isn't news for me. But I still found it interesting to run the numbers and see the trend on graphical form. Previously, I had no idea the trend was exponential.

As an aside, I tested some Rose Gum (Eucalyptus grandis) yesterday. Its bow wood merit number was 66.18328. The MoE I found on the internet was 17,000 MPa, so that was pretty close.

How does this sit on the graph I posted above? Well, it would seem that the working strain for the MoE is a little below the ideal dictated in the graph. The solution? Just add a few inches of length, or make a lower weight bow, or both. Not a problem, really. A 70 inch bendy handle longbow instead of 66 is not all that great an increase in length, but should be enough to allow the weight to come up without blowing out the width.

The piece I have though has very nice grain and colour, and I'd like to show it off. So I think this board will become a flatbow.

Dave

[bigbob]

I will have to print all your gleaning and just sit down and have a long intensive research on this info as i can see it will be immensely valuable if I can channel it along my corroded synapses and neurons.