Bow Woods (From A Mathematical Perspective)

by Eric Meier

Disclaimer: I am neither a bowyer/archer nor a materials scientist/engineer. The data and ideas presented in this article are by no means meant to be considered authoritative or precisely correlated to real-world situations. The purpose of the article is simply to foster imagination and exploration in the area of bow woods and what does/does not constitute a good bow wood.

Archery bows present a somewhat unique challenge in finding the right requirements for the best wood. In the simplest and crudest terms possible, the wood should be able to bend, but not break. With all of the data available on the Wood Database, there’s no single measurement that directly indicates a wood’s ability to bend easily without breaking. Instead, it is primarily a combination of two values: the wood’s modulus of elasticity (also known as MOE), and the modulus of rupture (also known as MOR).

Again, dealing in the simplest terms:

  1. The modulus of elasticity (MOE) measures how easily a wood will bend, (the higher the number, the more stubborn and stiff it will be).
  2. The modulus of rupture (MOR) measures how easily the wood will break, (the higher the numer, the harder it is to break or rupture).

In terms of looking at the raw mechanical data of woods, the best bow woods tend to be those that have a low MOE and a high MOR. (Stated another way, the best bow woods tend to be those that will bend easily, and not break.) It’s of little advantage if a given wood scores well in one area, and poorly in another (i.e., a very low MOE or a very high MOR). What is most important, regardless of how low the MOE may be, or how high the MOR may be, is the ratio of the MOE to the MOR; it must be easy to bend AND hard to break.

Given the rationale and requirements, an equation can be formed to roughly assess a wood’s suitability for bow use: (MOR/MOE) * 1000. (The added factor of 1000 is simply to bring the number to a more manageable size and avoid dealing with tiny .00xx decimal values.) For lack of a better term, this ratio will simply be referred to as the wood’s “Bow Index.”

Analyzing all the woods in the Wood Database for their Bow Index, the following results are obtained:

The Highest Bow Index:

Wood Species

Bow Index

Comments

Madagascar Rosewood (Dalbergia baronii)

Madagascar Rosewood

13.79

This number is somewhat misleading because data is taken from a several species in the Dalbergia genus, (D. baronii, D. greveana, D. madagascariensis, and D. monticola), so it may not reflect an accurate picture of any one particular species of the grouping that is referred to as “Madagascar Rosewood.”

Kiaat (Pterocarpus angolensis)

Muninga

11.81

Along with Madagascar Rosewood, Muninga represents another curiosity. On paper, it appears to rank right alongside other historically proven bow woods such as Yew and Osage Orange. Real-world results may differ.

English Yew (Taxus baccata)

European Yew

11.52

No MOE data could be located for European Yew (Taxus baccata), but the values for Pacific Yew (Taxus brevifolia) are so close to identical that they have been carried over and used for the European species. A slightly higher MOR puts European Yew ahead of Pacific Yew by a nose, though from a numerical standpoint they should be considered equivalent.

Osage Orange (Maclura pomifera)

Osage Orange

11.51

 

Given the great differences in density and overall strength between Yew and Osage Orange, it’s very interesting to note that the Bow Index of the two species comes out to nearly the same. Note that this is for the North American species, with Argentine Osage Orange only scoring an above-average Bow Index of 9.06.

Pacific Yew (Taxus brevifolia)

Pacific Yew

11.26

Guajayvi 10.90  Some have rumored that this wood also makes excellent baseball bats.
Tambootie  10.90
Chinaberry  10.85
Pear  10.68
Cebil  10.61
Mansonia  10.57
Turkey Oak 10.57
Makore 10.55
Movingui 10.52
Field Maple 10.42
African Blackwood 10.40
English Walnut 10.31
Alligator Juniper 10.31
Brazilwood 10.22

The Lowest Bow Index:

Wood Species

Bow Index

Comments

Grand Fir 5.71
Balsa 5.73
Basswood 5.96
Austrian Pine 5.96
Pacific Silver Fir 6.09
Nepalese Alder 6.17
Balsam Poplar 6.18
Eastern Cottonwood 6.20
Sitka Spruce 6.34
Balsam Fir 6.35
Bigtooth Aspen 6.36
Subalpine Fir 6.36
Yellow Poplar 6.39
Yellow Buckeye 6.41
Sumatran Pine 6.49
Norway Spruce 6.49
Tatajuba 6.52
White Fir 6.53
Jelutong 6.56

Are you an aspiring wood nerd?

The poster, Worldwide Woods, Ranked by Hardness, should be required reading for anyone enrolled in the school of wood nerdery. I have amassed over 500 wood species on a single poster, arranged into eight major geographic regions, with each wood sorted and ranked according to its Janka hardness. Each wood has been meticulously documented and photographed, listed with its Janka hardness value (in lbf) and geographic and global hardness rankings. Consider this: the venerable Red Oak (Quercus rubra) sits at only #33 in North America and #278 worldwide for hardness! Aspiring wood nerds be advised: your syllabus may be calling for Worldwide Woods as part of your next assignment!

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Albert rogers

I am impressed by the response to my test entry “cedar”. I have an excellent Virginia Juniper in my front yard, and I disdain the practice of calling it and the Thuja plicata “red cedars”

Nick B

So, in the event someone wanted to give a metal bow a try, I did a little digging with comments here and elsewhere to look at the viability of Grade V Titanium for bow making after seeing how springy it was in another application. Based on MOR/MOE, titanium is on the correct scale with a value around 8 or 9. Based on MOR/Density (suggested by some comments as more helpful), grade V titanium initially appears to have a .22 compared to .15 for Osage Orange (MPa/(kg/m^3)). Given this math, it seems reasonable to say that this treatment of titanium would… Read more »

Smoke14

Just from playing around in the yard I believe wild shrubs would make a good bow wood so I think i’ll make a full size bow to to see

Vincent

What about carambola wood? It s main to be flexible wood and strong

Nick R

Young’s modulus is determined by measuring short deflections under load. It is a constant which reflects a material’s inherent stiffness. Modulus of Rupture is measured at the final breaking point where the wood gives way under load regardless of the amount of bend before the breakage occurs. A bow needs to flex in a dramatic way, so while these two measurements are important, they can’t tell the whole story. A low stiffness wood like pear could be too brittle and woods with higher stiffness to breakage ratios like hickory and black locust could make excellent bows. Since stiffness is a… Read more »

Jill

Bornean ironwood is it good for bowmaking?

Tim

Here is the post with file :) After seeing all the comments about the different ways to calculate the bow wood index I combined the two for a better overview. The difficult part is that even tho the calculations are based on the physical properties of the wood, things like heartwood/sapwood, interlocked grain, great compression strenght or the addition of a rawhide backing could alter these numbers significantly, which would mean that the number as calculated are not a 100% accurate in real life. A great example of this is juniper, the MOR/MOE *1000 gives 10.31 which is not to… Read more »

wood.jpg
Petros

Hei i cant see the file anymore, can you send it to my email? ( I started a new project making a bow from willow tree) so iwould like to see if yoi have data for it :) )

Tim

The image

wood.png
Don Schroeder

What is more important than computing an index, for any wood, regardless of the method used, is the fact that within any species of tree the qualities of individual specimens can vary by 25% or more. (US Forest Service Lab) This basically means that the published numbers aren’t relevant to the resulting bow tillered from any billets, stave, or board just because the wood is labeled. Equally significant is that the published values are obtained by testing samples with very significant sectional deviations from the cross sections of tillered limbs regardless of the bow design. (For example: testing a sample… Read more »

Tim

Hi there, After seeing all the comments about the different ways to calculate the bow wood index I combined the two for a better overview. The difficult part is that even tho the calculations are based on the physical properties of the wood, things like heartwood/sapwood, interlocked grain, great compression strenght or the addition of a rawhide backing could alter these numbers significantly, which would mean that the number as calculated are not a 100% accurate in real life. A great example of this is juniper, the MOR/MOE *1000 gives 10.31 which is not to bad, the MOR^2/MOE/dried weight gives… Read more »

James

It is really hard to find good wood with the ability to bend easily without breaking. Thank you for your help.

Flamentic

MOR^2/MOE/dried weight
Higher result = lighter limbs for the same draw weight = faster and more efficient bow

Flamentic

Lower MOE makes shorter and more efficient or more reflexed and powerful bows
The MoR need to be squared because draw weight*length at failure give the maximum amount of energy the wood can absorb and the MoE is the ratio draw weight/draw length
https://en.m.wikipedia.org/wiki/Resilience_(materials_science)

Terry Davis

Thanks for all your hard work and effort that it took you to put this posting up for all of us that live the art of bow making. We are always looking for the best way to build our perfect bow and the data you have supplied is a valuable resource for us again koodoos to you and your hard work on this matter

Paul

Thank you for posting this – It always crosses my mind when looking at potential bow woods! Incidentally, rowan should feature high on the list too; at 11.61 it would be higher than osage and yew… Norway maple is quite high too, and black locust and hophornbeam (reputably good bow woods are very low…) Where I think the difficulty comes from is dealing with the different potential sizes/geometries of limbs. Perhaps the ‘bow index’ is best used for determining how good a wood is at having narrow/deeper limbs? Yew and Osage are the clear examples – their limbs can be… Read more »

Marc

Contrary to what some say a low MOE is in fact desirable in a bow-wood, those that deny this just don’t have a proper understanding of what MOE means. The ratio of MOE to MOR is as good a method as any I have seen of identifying good bow-wood and after more than 20 years of making bow I have seen many. I commend you on your efforts

Michael

Be specific as to what species of hickory. They aren’t all equal.

Jesse Morgan

Did you consider bamboo at all in writing this article?

James Davis

I am reposting my initial comment, because this page still presents its wrong approach to determining the value of bow wood. The page should be taken down because it is harmful to the investigation. : I have been making bows for more than 15 years. My experience and logic say you have the concept diametrically opposed what is desireable for the MOE. You say wood needs to be EASY to bend. Wrong. What is needed is wood that is HARD to bend and hard to break. That allows less wood to do the work. Less wood means less mass to… Read more »

James Davis

As far as the Argentine Osage is concerned, it was probably not known by those making bows during the centuries when wood was the most used bow material. Second, you should be aware that no data exists for DRY Osage orange. Either the Forest Products Laboratories didn’t run tests on dry Osage or the data never got recorded. I’m sure all your data is from the FPL. I have been in contact with them several times and they have no data for dry Osage and no plans to do any testing. If there are numbers for the Argentine Osage, that… Read more »

Thawed Cave Bear

FPS on release is pretty major…Yew and Bamboo both excel unless I’m mistaken. Also fiberglass (which sucks at most other refined details).

Thawed Cave Bear

It’s a grass. Yes. …How on earth does that matter in any way concerning how to back a bow?

bob

i live in norway what is the best wood here?

Thawed Cave Bear

English/Spanish (European) yew, followed extremely closely by the not-almost-extinct…yet ‘Pacific Yew’.
Others would argue osage, and several of the densest tropical woods–say, Ipe or heartwood. Hickory is ‘easy’, but is the most boring, poor-performance wood in the world next to self-backed pacific yew

Thawed Cave Bear

Do you have elm (wich elm’s traditional)? White ash is good, but regular ‘European Ash’ is better/tougher. And there’s white oak. You don’t have Oregon Oak…but the movement of many European beeches (better than west hemisphere) into Norway expands options. …Also the maples. And the oak comin north, also. Junipers, I assume you have a variety–you need a huge amount of wood. Applewood, pear, and also Laburnum. Various types of maples (Norway Maple is good). Welsh oak (if you can get it, decent, and European Holly isn’t bad–please don’t tell me they have English holly sometimes in the land of… Read more »

Thawed Cave Bear

Wych elm.

Chris Traub

Bob, my wife and I visited your incredibly beautiful country two years ago. We were only there for a day and two nights but we did Norway in a Nutshell and saw a lot of the country. I did not see a single yew tree, taxus baccata, but it does occur in Norway. I think that would be your best native wood, but, from what I’ve read, it’s illegal to cut yew in Norway!

Mario Cargol

What about cupressus macrocarpa? It’s got long straight pieces and the MoR/MoE relation is 10.39, looks nice.. I’ve readed that some have made nice bows laminating alaskan yellow cedar wich has a worse MoR/MoE relation.. I think i’ll try and tell what about it ;)

????

Stiffer is better in terms of strength resisting the draw, allowing higher poundage– yet at the same time, too stiff with too little MOR to resist the breakage means the limb would not bend that far before it broke, limiting draw length and reflex design. Finally this does not factor in density at all, where higher mass limbs rob cast, because the moment (physics) is further diverted from arrow to limb. In actuality, there is no good metric to say which wood is the best for all the bow designs in the world out there: – Some bows have shorter… Read more »

Thawed Cave Bear

Elasticity IS still important for short bows–for the arrows as well as the bow. But your point is taken.

-As for the point about more massive limbs….that’s why European Yew will always beat Osage by more than a nose, with faster, better casts and less wasted energy :)

Patrick King

Otzi, the 5000 year old ice man mummy found in Europe had two kinds of wood with him. He had Cornel and Verbinum. The pbs show (Nova) wasn’t clear on which type of wood was used for his bow and arrows and which was used as an axe handle.

Mario Cargol

I’ve seen a recent article wich said the axe’s wood was yew

Danny Campbell

Is black cherry a good bow wood

Thawed Cave Bear

Yes it is, if backed by something else. For much more detail, there’s an entry in ‘The Traditional Bowyer’s Bible’, which you can page through on google books.

Thawed Cave Bear

Yes and no. Can have truly great characteristics, but it’s unreliable. It fails easily and unpredictably. Chrysals for no reason you can think of. But people tell me it’s almost self-backed yew, sometimes. Treat it right (whatever that is…), if you give it a shot? That’s what the kids are saying, anyway.

Charles Elias SR

I have and odd question has anyone tried crepe myrtle as a bow wood

Thawed Cave Bear

I recall the name coming up, so I’m going to say yes, and that…it’s probably supobtimal, but possible to use. Mostly guessing.

Ben

This is an interesting article to get people talking about how mechanical properties relate to bow performance. There are several problems however. 1) the value the author has effectively calculated is (%strain at failure)x10. In other words the change in length of the material at failure(rupture). 2) it ignores the density of the wood. modulus of rupture is a measure of strain at failure. Strain is force/area. So this is only a relevant value for comparing two woods of identical mass since limb mass will determine performance and not limb cross sectional area. 3) it assumes that a wood which… Read more »

nicethugbert

A bow is a spring. How well does MOE describe a spring? An easily bent bow is a weak bow. Rubberbands bend easily. Stronger bows require more strength to bend then weaker bows. So, I doubt a low MOE would describe a good bow.

The MOE would be matched to the strength of the person using the bow to know if it the bow is too stiff for them to draw.

UrbanBowyer

The thing is, a bow with a high MOE and a medium MOR will be strong but will make a bow with a very shallow and wide cross-section which isn’t very aerodynamic. For example although Hickory does make great bows, it relies on its raw strength rather than an efficient transfer of energy. You commonly see hickory short-bows so the ends of the limbs won’t be too far away from the center line to create much drag and the bows tend to not be the highest poundage because the wood is so thin. Hickory is great for backing a bow… Read more »

Doug

The two post prominent Australian bowwoods seem to be Red Ironbark and Spotted Gum. Yet using this method they both rank very low (7.37 and 7.17 respectively).

My understanding has always been that high density, high MoR woods were most likely to make good bowwoods.

Steve

One thing that should be included in the calculation is the density of the wood. A low density would make the limbs of the bow quicker. The equation would be modified be dividing by the density.

Question: what is the source that supports a low modulus? For 2 identical bows, the one with the higher modulus would have a higher stored energy and draw weight at the same length of draw. If the same draw weight is desired, then the limbs could be made thinner and lighter with the higher modulus wood. This would result in quicker bow limbs.

Matt

I wonder if we could get the raw numbers for these? I would imagine you’d want a wood with neither a very high, nor very low Modulus of Elasticity, since a bow too easy to bend ends up with less power, yes?

Drew

I live on the West coast of Australia, and have been trying some local timbers in bow building with little success. Has anyone had any success with Australian timbers for bow building

Doug

Spotted Gum and Red Ironbark are the two premier aussie bowwoods I’ve heard of. For the most part you want high density, high MoR timbers.

Dan Goodwin

Can anyone tell me what is the best glue to laminate a wooden bow?

kj

Tightbond, epoxy, and hide glue all work fine, if applied properly.

Joseph E. Cunanan

I’m chopping down a Blackwood Acacia (Australian Acacia, Black Acacia, Myrtlewood?) Tree, and I’ve got a few projects lining up, one of which is a Recurve or Long Bow and the other is a Cross-Bow/Mini-Cross-Bow or three. My questions are how does this wood add up for use as a Bow. It seems to be up there with the best Hickory in terms of Strength, Rupture, Harness, Elasticity, and Crushing Ratios. But, it doesn’t show up anywhere as a Material for a Bow. Is it because I only checked the Top Ten Search Listings on Google. Or, because the Australians… Read more »

Bowmakerindo

Any kind of acacia will do the job

Michael David

This is perfect for what I was looking for! I have been looking for good wood to make bo’s and Jo’s from and I wanted something that would flex, but not break. Perfect.

D

Unfortunately, I have to agree for bows. Too low an MOE is not ideal. You need the wood to be able to take all the force without bending too much and then deliver it back into the arrow. If it bends too much you will lose force. But I’m no scientist.

However for my purposes this has been fabulous as this is exactly what I was looking for, thank you. I’m making something (it’s hard to explain) that requires exactly this: migh MOR/ low MOE. Imagine my joy!

Thank you very much.

Rob Wilkey

This is an awesome article, but I have to agree with James Davis. The best recurve bow I’ve ever shot (that was mostly wood) was carved in Hickory.

I think the real value to this article is showing woods that work well in tensioned setups.

A furniture design I’ve been working on required tensioned lengths of wood for the legs and armrests, and this article has helped me narrow down the list of woods available for this purpose.

Thanks!

Thawed Cave Bear

Ugh. Hickory. I’m glad it did something for you, but…it’s the short bus of bow-woods, for me–so often recommended in suboptimal circumstances because “hey, at least you won’t break a hickory bow!” In efficiency, power, subtlety it doesn’t compare to a bow-material that can send arrows down-range through compression, like a rebounding string. It’s just cheap, robust, carries tension and is stable–and is easily covered in fiberglass. Would you like to buy a still-wonderfully functional Hickory longbow?

Thawed Cave Bear

(Cough) -Just a personal feeling about it–I meant no offense.

jonathan

This is an interesting article. I agree with Eric regarding the ratio of MOR to MOE. Hickory is known to have an excellent MOR but it also has a very high MOE. That I believe explains its inferiority to osage or yew. Black locust has a slightly lower MOE than hickory but a similar MOR- again explaining its superiority. I have made bows from osage, muninga and chinaberry and of none of them took much set (plastic deformation). The only problem with just using this ratio is that it doesn’t take into account the fact that you still need the… Read more »

Steve

A true MOR is measuring the bending strength of the wood, so crush would be included in the value. There is a good article at ask dot com. That is unless you are asking about transverse crush (cross grain). That value is typically directly related to wood density. Balsa would be immediately discounted because the light grades would crush in the archer’s hand.

Thawed Cave Bear

What a useless response, devoted to demonstrating alleged technical knowledge that’s not useful without context!

Alex Wirtz

A very qualified yes to this: if you’re building laminate bows – not selfbows – you get a different result for the back wood (the part of the bow facing away from the archer, requiring strong tensile strength) and for the belly (where compression strength is most important). One of the reasons yew has the primacy it does in European bowmaking is that it is, in effect, a laminate itself – the sapwood and heartwood have quite different qualities. Hickory is inferior to practically nothing as a back wood (not sure how a hickory-only selfbow would work, though I’ve seen… Read more »

Eric Hauck

Eric,
Thank you for your efforts and work in providing these correlations of tests and data. For those of us who battle the obsession of bow-making all additional information and studies are always welcome.
Best Regards,
Eric

P.S. Your disclaimer “…to foster imagination and exploration” is appreciated but probably not necessary :)).

James Davis

I have been making bows for more than 15 years. My experience and logic say you have the concept diametrically opposed what is desireable for the MOE. What is needed is wood that is HARD to bend and hard to break. That allows less wood to do the work. Less wood means less mass to be put in motion by the energy stored in the bent bow, resulting in faster arrow flight. Black locust the hickories, white ash and others balance the force required to bend them quite well with the force required to break them. Perhaps a formula recognizing… Read more »

LEM

It seems to me that the best bow material for bow making is bamboo. I don’t know the MOE or MOR of the wood but it will flex and return to it’s original shape better than the ones I have made from hickory, hard maple and Pacific Yew. Granted, the grain of these species is sometimes erratic. Tonkin Bamboo is a good species partly because it can be gotten in larger diameters 3″ to 4″ or so and split to 2″ strips, flattened, and planed to thicknesses for laminating. Bamboo in general is straight grained wwhich is part of the… Read more »

rockyrgs

What poundage are the so. eastern bamboo self bows? do they shoot arrows or bamboo darts like their crossbows? Although their bows on the crossbows are 4′ Mountain Yard mahogany.
BTW HOWARD HILL never shot bows less than 110 lbs draw weight. the movie with Errol Flynn he used that 110lb draw weight bow and the guys that he shot in the chest had 1″ wood boards backed with 1/4″steel and they hated to get hit with those arrows! they were really knocked off their horses! H.H. loved the bamboo bows.

jim

you would have to change never to most of the time. i still have the pictures of howard hill shooting my fathers recurve bow. my fathers name was frank murphy and he was a skilled bowyer out of new york.
locally his diamond bow company was a favorite among many new york target shooters and hunters. the chance meeting of HH at a field archery event was one of his favorite memories.

Thawed Cave Bear

Not even during the Great Leap Forward? (42 million dead for no important reason)? The continued Cultural Revolution?
–I guess all the hundreds of millions of historical slave-owners must have been right, too! It’s too many to be wrong.
-Bamboo may be ‘straight grained’ but it simply doesn’t last as long as its partners in crime–great tensile strength, but it needs replacing before a battle’s over.
-It’s unlikely Howard Hill shot the bow-hunting sequences in Errol Flynn’s (thematically rich AND historically accurate) masterpiece. More likely, I’d expect he was, say, stunt choreographer, or an AD.

Bug eater 357

Hundreds of millions of slave owners?