Mechanical properties of Yew wood

[ultraviolent]

Hi everyone,

As part of my AS level physics coursework I’ve decided to produce a report on the physics behind why yew wood was used to create longbows. The problem I’m having is that because yew wood is no longer used in modern engineering so no reference books at my local university library or online material databases have any data on it (I know this as I’ve already spent 3+ hours at the university library and 2+ hours researching this online).

I have managed to obtain values for working strain, working stress, strain energy stored, density and energy stored (area under stress strain curve). Does anyone know of any materials that are comparable to yew wood so I can work back from the working stress/strain values and calculate the young's modulus of yew wood?

Or, even better, does anyone have any ideas as to where I can obtain data for this project? I'm sure that this data will be archived in a book somewhere, but I don’t have enough time to go looking for this. If anyone knows of a book that will certainly contain this data then I could purchase this or request it from my local university library.

Many thanks in advance,

James

 

[NateTG]

Or, even better, does anyone have any ideas as to where I can obtain data for this project? I'm sure that this data will be archived in a book somewhere, but I don’t have enough time to go looking for this. If anyone knows of a book that will certainly contain this data then I could purchase this or request it from my local university library.

There was an article in - I think it was - scientific american a while ago about historic bow making. I'm not sure if it had hard numbers on yew wood since it quickly moved from the self bow to compound laminate recurve bows (using horn and sinew as well as wood).

http://www.imlusa.com/Fractometer%20I-%20engl.pdf
Has information on (at least relative) strengths for Yew wood, and refers to a coupe of relatively recent publications in the biliography.

 

[Gokul43201]

I believe that woods show little, if any, plastic behavior. But you might want to find out the elastic limit or the yield point (which will be pretty close, though higher than the EL) for your specific type of wood. This is more relevant than the working stress, which is often calculated from some point in the plastic region of the stress-strain curve. If the plastic behavior is truly small, the working stress will serve as a pretty good approximation.

Sorry, I know of know no specific resources, but http://ocw.mit.edu/NR/rdonlyres/Materials-Science-and-Engineering/3-11Mechanics-of-MaterialsFall1999/1B957032-BE5D-4475-8CDE-6D29E9EB6502/0/ss.pdf has some numbers on yew, which you may already have.

Other possibly useful pages :
http://www.bowyersedge.com/reaction.html
http://www.medievalwoodworking.com/articles/wood.htm
http://www.geocities.com/tech_ed_2000/industrial/manufacturing/wood/wood.htm

There's also a neat comparison between different bow woods at the bottom of http://www.primitivearcher.com/articles/engelm.html .

 

[ultraviolent]

Thank you both for your prompt reply. NateTG, do you know how long ago that was? I've searched the Scientific American website and I can't seem to find any reference to that article.

Gokul43201 - the .pdf document that you gave me a link too is exactly what I’ve found before, just in many different academic articles. The materials database that comes on the course CD rom also contains that same data, but nothing extra. I can't see a way to obtain the Young's Modulus of the material or real stress strain values from the data in that article, can you?

Given that "Modulus of toughness is given by calculating the total area under the stress/strain curve up to the point of failure. It is the ability of a material to absorb energy during plastic deformation." there must be more data around somewhere, as that could not have been calculated without it. I wonder if any of the books listed at the end of that article in the bibliography contain any further data?

- James

 

[Gokul43201]

Gokul43201 - the .pdf document that you gave me a link too is exactly what I’ve found before, just in many different academic articles. The materials database that comes on the course CD rom also contains that same data, but nothing extra. I can't see a way to obtain the Young's Modulus of the material or real stress strain values from the data in that article, can you?

Given that "Modulus of toughness is given by calculating the total area under the stress/strain curve up to the point of failure. It is the ability of a material to absorb energy during plastic deformation." there must be more data around somewhere, as that could not have been calculated without it. I wonder if any of the books listed at the end of that article in the bibliography contain any further data?

- James

The ratio of max. stress to max. strain is often a reasonable approximation for the Youngs Modulus, depending on exactly how these quantities are defined.

In this case, I suspect that this approximation will be pretty good, because I believe that the maximum stress is pretty close to the elastic limit, and the maximum strain is the strain at this point.

Let me explain why I believe this is so. (see attached picture) Assuming the stress-strain curve is crudely as in the attached picture, there are two likely possibilities for the maximum strain. It's either B or C in the picture. The maximum stress will be some number pretty close to A. If the maximum strain is defined as C - the strain at failure - then the area of the rectangle whose sides are the max. stress and max. strain must be greater than or equal to the value of the Toughness.

But multiplying max. stress and max strain (divide by 100, to remove the percentage), gives 120*0.003 = 0.36 MJ/m^3. This is smaller than the given number, T = 0.5 MJ/m^3. The only way, the product can be smaller than the toughness is if the max. strain is in fact, B. In this case, it is not inconceivable that twice the blue are be smaller than the sum of the blue and red areas, and in fact, this would seem quite reasonable.

So, to summarize, I think the elastic modulus of might be, E = 120/0.003 = 40 GPa. However, this sounds a little on the high side...most other woods are between 6 and 20 GPa.

Now I'm not so sure anymore...just wasted a bunch of time, I guess. Sorry

 

[ultraviolent]

http://www.woodbin.com/ref/wood/yew_european.htm

"Moderately heavy and hard with medium strength, relatively low stiffness and shock resistance, excellent steam bending, good stability in service, and good decay resistance."

What you worked out seems to make sense, but seeing as Young's Modulus is a measure of stiffness, and all the info I can find about Yew wood says it has a low stiffness, I am now not really sure...

I'm starting to run out of ideas as to how I can proceed with this project. Does anyone know where I would be able to find working stress, working strain, stress and strain values for a similar wood? I could then use these to derive the ratio that is normally used to calculate working stress and working strain for wood and then work backwards to get real stress strain values for yew wood.

If not, I think I am going to need to change my project to something where I can obtain data for it.

- James

EDIT: I've just send the Institute of Physics, who produce the course CD rom that also contains the data discussed, an email asking for the original source of their data. This may be a long shot, but at least it's worth a try...

Also, here is the data that I currently have for the project.

http://www.revlis.co.uk/james/store/data.jpg

 

[ultraviolent]

Ah yeh... I've just spotted what could be the reason your calculations didn't work. The data on the course CD rom shows that the max strain of yew wood is 0.9%, but that pdf document shows it as 0.3%.

Going through your calculations again gives me a value of 1.08 MJ/m^2 for strain energy stored, which seems far too high, but a more appropiate value of 13.3 GPa for Young's Modulus.

Any ideas?

- James

 

[Gokul43201]

It would be hard to determine anything to the kind of accuracy that is required.

Here's another link that lists elastic properties of different woods (not yew, though) :
http://www.mmat.ubc.ca/courses/apsc278/lectures/Wood/Wood(fill%20in%20the%20blanks).pdf

 

[Artman]

Another link:

http://www.engin.swarthmore.edu/~jsarmie1/Design.html
and another:
A note on indian bow making
and another

http://www.abotech.com/Articles/Baugh01.htm

Steel has an elastic modulus of 30 million psi (pounds per square inch), hickory has an elastic modulus of 2.2 million psi, black locust has 2.1 million psi, and the measurements I have made on yew wood give a figure of 1.2 million psi.

http://www.abotech.com/Articles/Baugh01.htm

 

[ultraviolent]

Artman thank you so much!

Last little problem for you lot and then i'll be off

"To convert PSI to Pascals, first convert to millibars and then multiply by 100 since 1 millibar is 100 pascals."

1 Psi = 68.948 mB

130x10^6 x 68.948 = 8963240000 mB

1 millibar = 100 pascals

8963240000 mB x 100 = 8,963,240,000,000 Pa or 8.96 x 10^11 Pa

Why is this so high? If it was 8.96 x 10^9 Pa that would seem fine (9 GPa) but I just don’t understand this. Google also agrees with this value, see here

Why didn't they come up with SI units sooner?

- James

EDIT: Ooops, make that 8.3 x 10^11 Pascals. I read the value wrong off that website. I still don't understand why my value is so large though...

 

[Gokul43201]

I think you're still using the wrong number. Don't you want to use 1.2 * 10^6 psi * 68.948 mB/psi ?

 

[ultraviolent]

Argh, I think I was pretty tired last night when I did that! Thanks Gokul43201 and everyone else for your help

 

[ChrisHarvey]

I realized this is probably a little late now (AS coursework deadline was probably early January!) and I not sure how helpful this will be, but I'll say it anyway.

One of the reasons why yew wood was used to create longbows was that it is a natural composite. When you take a cross-section of a yew tree branch, trunk, you will see 2 different colours. Around the outside, there is a thin section of pale, yellowy wood, called sapwood. This stuff is really elastic, and good in tension. In the middle there is an orangey colour wood called heartwood. This is not very good in tension, but excellent in compression.

The Bowyers (bow makers) realized this and for this reason they would cut the wood so that the sapwood formed the back of the bow, and the heartwood formed the belly. Therefore when the bow was pulled, the back would be stretched, and the belly compressed. Each wood performs the function to which it is best suited. Because the wood occurred this way naturally, this removed the problems of glueing together different types of wood (with different mechanical properties), which is a tricky process, and given that ancient yew war bows were generally required to shoot only about 24 arrows a good long distance before being discarded, the effort was not really worth it. Also glues were expensive - the best for the job coming from places like Hungary (made from some cooked rare fish!).

Quote (from above): "I believe that woods show little, if any, plastic behavior."

Actually, in traditional archery there is a term - "Following the string". When a bow is pulled (especially non-composite bows), inevitably parts of the heartwood are stretched, because the bulk of the bow is made from belly wood and therefore there are parts of this wood which lie on the other side of the "0 extension" line of the bow. The heartwood doesn't stretch elastically much at all. Once the bow has been pulled, parts of the wood will go into their plastic region. If you were to plot a graph of stress vs strain you would find that the loading path is different to the unloading path, and the unstrung bow is now no longer straight, but bent. It has "followed the string". The area on this graph between the loading and unloading lines represents the loss in energy stored in the limbs of the bow due to the plastic extension of the limbs.

Obviously wood does stretch plastically. Anyone who has ever over-pulled a bow will vouch for the fact that (contrary to popular belief), the bow becomes easier to pull just before it fails (and explodes splinters everywhere!). This would correspond to the decreasing load for increasing extension sections of the stress-strain graph.

Calculations for bows will also be very approximate. I think you methods will be very very rough for several reasons (maybe something to discuss in your report):
- The ultimate strength of a bow is determined by the weakest part of the bow. A yew bow will have a variable area (due to the way it is made - you must 'follow the grain'). There are also knots, and other areas of weaknesses. Small fractures and also notches. As a result of these you will get stress concentration factors coming into play. The failure stress will be the average stress at the weakest point multiplied by its stress concentration factor (SCF). You could approximate this SCF by guessing at the geometry of this weakness and applying formulae, i.e. maybe a notch so deep at the edge or a minimum area, or maybe experimentally. Either way, coming up with the values is not really the point at AS, it is more to do with showing you have thought about all the factors involved, and how you MIGHT find them / use them.
- Also - Yew is a composite. You have 2 materials in this bow with different properties. You could use average properties (and discuss the validity of this), or you could do some more complicated mechanics using redundancy. i.e. each section could be modeled as a rod, with the same external forces applied to them. Mechanically, there are 'too many' rods for this structure to be 'statically determinate', i.e. 1 rod could do the job on its own.

On a non-mechanical note, you may like to add to your report that another reason why english bows were made from yew is due to factors such as material availability. The reasons english / welsh bows are long (and cumbersome) as opposed to short is that no known material was available to bowyers at the time which could stretch that much (i.e. store enough energy) without failing. In the east, they used sinew (a fibrous material made from animal bone) which was exceptionally elastic. They could use short bow backed with either thin sections of wood or bone, and just paste sinew on to it. By making the welsh bow longer, they could store more energy than a short one, without it snapping.

Hope all of that was of some help,
This is a subject that really interests me,
Chris

P.S. When I did my AS coursework 2 years ago I did a similar project to yours for 1 part, and for another part built a device to measure and plot on a computer stored limb energy in a bow over the draw. It was quite sucessfull

You may find it interesting to read "The traditional Bowyer's Bible". This covers an awful lot of ground on making bows and bow performance. Volume 1, chapter "Bow design and Performance" by Tim Baker would be very useful for this topic.

 

[ultraviolent]

Thanks Chris that was really interesting :)

A lot of that would have been good to include in my report, it's a pity you didn't reply before as I handed in my coursework last week.

If you're interested I’ll let you have a copy of my coursework. I found the whole project really fascinating.

- James

 

[greeny]

James,
I'm doing a materials presentation on yew wood in long bows for my physics coursework, do you think i would be able to get a copy of your report please? it would be extremely useful for me.
Thanks Will

 

[greeny]

OH yeah my e-mail address is greenw@stedwards.oxon.sch.uk - Thanks

 

[ComeDown194]

Hi I'm also doing a materials presentation on longbows - would i be able to get a copy of your work as well please? - My email address is:
ComeDown194@hotmail.com

 

[Chris Hillman]

Trying to recall an odd citation which might help...

I'm doing a materials presentation on yew wood in long bows for my physics coursework, do you think i would be able to get a copy of your report please? it would be extremely useful for me.

This is too late for James, but might it just might help greeny if the following rings a bell with your local university librarian: I feel sure that I've seen a book on naval architecture, probably English, probably from the early twentieth or late nineteenth centuries, which offered an extensive (but with various omissions due to the variety of sources used) table of physical properties of various woods including yew and ironwood. As I recall it included not only stuff like density but some mechanical properties. Sorry I can't remember anything more.

 

[alzadia]

I want to make a yew wood long bow, i need know one aproximate value for elastic limit and young modulus. Someone can help me¡¡¡ Can be: 10%=120MPa, 30% = 350MPa, 50% = 480MPa, 90% = 680 MPa.

 

[tomsmith91]

i don't know if this helps but i found this while reaserching for my coursework that i am currently doing it has the max stress, strain and modulus of toughness(i think this is the youngs modulus not sure) of yew

http://web.mit.edu/course/3/3.11/www/modules/ss.pdf

ive been looking for this stuff for a while now and i know how difficult it is so yay

by the way its figure 12 just 2 save you some time looking for it