Mechanical Properties of Wood for Building Bows and Arrows

[joachimM]

Likewise you see that with steel too. It doesn't make a very good bow material for two reasons, it's heavy and repeated bending ultimately leads to the weakening of the metal and it breaks.

The raw numbers disagree with that statement: spring steel has a relative stiffness (MoE divided by density) equal to that of bamboo (guadua, moso, ...), and will allow a tension strain of 1.5%, more than any wood.
This means that a bow made of spring steel with a mass of 400 g, and designed according to the mass principle, will cast an arrow at the same speed as a bamboo bow, all else being equal. It would just be ten times narrower, which would make it hard to shoot (but there are ways around this issue).


As for the repeated bending leading to breaks:
that's all about the "cycle rate to failure" (or mean cycles between failure), which has to do with design. Say a rope has a guaranteed breaking strength of 10 KN (it can statically bear a load of 1019 kg), that means it can at least sustain this load once.
When loaded statically with a lower mass, say 900 kg, its expected failure rate may only be after 100 loadings, at 800 kg maybe hundreds of times, and at 700 kg its failure rate may reach infinity. (the failure rate distribution is typically exponential)

That's the reason we need to shoot in a bow: if we can shoot it 500 times without breaking, chances are high the bow was built with a reasonable enough safety margin. We see this often in flight shooting, with strings made so thin that they break after a single shot.

So if your bow breaks (down) after some shooting, it just wasn't well made, or at least not made to last. It doesn't matter if it was made of spring steel or of osage...
A bow intended for 50# 28" may shoot thousands of arrows, but drawn once to 60# 31" it may have become junk (if not broken). So the cycle rate to failure may be 1 for 60#, and "infinity" for 50#...

[PatM]

The old Seefab steel bows were in fact very slim and painted to look like bamboo!

[Aussie Yeoman]

Badger,

I've given little to no thought to the arrow-suitability of wood. In bowmaking, the density of the timber doesn't matter anywhere near so much as with arrows. I suspect there's an ideal ratio of stiffness to density, because a timber that has 60% of the density but 80% of the stiffness of another heavier, stiffer timber is going to make a better arrow.

Nevertheless, here's a screenshot of some of the stiffest timbers. Alas there are no density data.

It seems there's been a lot of discussion since I last got online. There's much to discuss re: strain, stress and suitability of timber for backings, it seems!

[joachimM]

Interestingly, Joachim said in an earlier thread that flax "stacks". That might bear further investigation as it indicates some sort of work hardening might be occurring.

Flax stacks indeed a bit, meaning that the stress-strain curve is not a straight line, but a concave one: as the strain increases, the stress (load) increases more than expected.
When loaded slowly (not as in a bow!), it can withstand a strain of 2.4%. The first 1.5% of strain is pretty linear, after that it requires more force than expected from a fixed stress-strain ratio to strain it further.

Irrespective of this, in relation to wood, flax always seems to stack (same as hemp), in that it is about twice as strong in tension as wood, for the same mass of backing added. For the same volume of backing added (say a layer covering the bow's back, of 2 mm thick), it's about five times stronger than wood. Hence a thick enough layer of flax on the back of a bow will force the entire bow's wood into compression. A thin layer, or a narrower crowned strip ("trapped") won't.
When backing a bow with flax, you better opt for a wider than usual bow with thinner than usual limbs, otherwise you'll get excessive fretting. 

The reason for this strength is that flax's cellulose content (per mass unit) is nearly twice as high as in wood (85% compared to 45%), and cellulose is the molecule providing tension strength to wood (while lignin and other compounds provide compression).

Sisal, on the other hand, is much more forgiving than flax. Its MoE is a bit lower than that of bamboo, but it can sustain more elastic strain (>2%) and hence store more energy). It is therefore less likely to overpower a belly (but I have seen it cause a good deal of chrysalling on some bows too).

[Marc St Louis]

Mark, do you think the Bubinga would have done better with a thinner or narrower piece of bamboo?

I tried 2 different styles of bow with Bubinga, longbows with Bamboo and Maple backings and a Bamboo backed RD bow.  The Bamboo was thinned to my usual 1/8" thick in the middle tapering to 1/16" at the tips.  The longbows were perhaps 1 1/8" wide and the RD bow around 1 1/4" wide

[Jim Davis]

Aussie, no fault of yours, but the Osage numbers (as always) are the result testing green wood. If you had dry numbers to work with, Osage would be much higher in your list.

[Aussie Yeoman]

@ Jim Davis:

I have seen that, as exemplified in your short table, almost all woods are 3 to 4 times as strong in tension as compression, so all this talk of bamboo or hickory overpowering the belly wood is balderdash, in that almost any intact backing wood is stronger than almost any belly wood.

I would have to heartily disagree here. I backed some Ironbark (similar to Ipe) with reasonably good Elm, and the Elm was torn apart. The reason was the force used to bend the Ironbark produced massive stress, and so the strain packed on early, beyond the strain Elm could handle. Backing choice matters a great deal.

Aussie, no fault of yours, but the Osage numbers (as always) are the result testing green wood. If you had dry numbers to work with, Osage would be much higher in your list.

Alea culpa. Those numbers are from Tim Baker’s corpus of data. I have a few bits of Osage, which is now well seasoned. I should test it and add it to the database. If I ever got time.

@ PatM:

Sinew has a working strain of around 4%. Exceptional wood of around 1.1%. Many ‘good’ bow woods around 0.8%, and Willow is down there below 0.6%. No idea where carbon and glass sit.

Maybe but it takes different amounts of strain to get that stretch to happen.  So bamboo or Hickory is not going to budge when you try to stretch it over a piece of ERC.

Stretch is strain. Strain is the change in length due to compression or tension, given as a percentage.

but I think we are just putting numbers and trying to explain scientifically  what we already know.

Yes, we are doing exactly that. There is no harm in it, and in fact it can be very helpful. The same things have happened in engineering, medicine and the like and the world is a better place because of it.

@ gfugal:

Tim Baker showed this with his flax backed pine right? Flax is very ….. that it isn't rigid anymore. Styrofoam might do that, but even the most chrysaled wood still maintains some rigidity.

Interesting tidbit: in a beam of homogeneous material, the neutral plane is at half the depth. If you put a backing on with a higher stiffness than the belly, the neutral plane moves toward the back. Given that the surface stress/strain at the surface is equal to the cube of the distance from the neutral plane to the surface, you can quickly see how backing a wood of low stiffness with a material of high stiffness overpowers a belly: it dramatically increases the strain/stress at the belly.

This is why a belly and backing material should have at least vaguely similar stiffness. At the other extreme, see the experience backing Ironbark with Elm, above. Elm is terrific in tension, but only when matched with a belly material of similar stiffness.

Supposedly bone has a similar, if just slightly less, flexiblity as wood.

Depends on the bone. An adult femur is far less elastic than a rib, for example.

If we can learn more about tension qualities of the materiel's we work with, I think there is room for improvement.

It’s easy. Pick a timber with a higher working strain and similar stiffness to the belly material, then Perry Reflex the bow.

[joachimM]

greg, Patm,

Strain levels for
Raw glassfiber: 4.9%
Gordon high strength fiber lam (GC 70 ULZ): 3.3%
Carbon (gordon laminate GC 70 UCL): 1.4%, with a MoE of 151 GPa!

See the excel sheet i posted earlier

[PatM]

So my wording was not refined enough but those points are essentially accurate.

[willie]

Joachim

I do not question the specs you have posted for various fibers, but wish to know more about your thoughts when using them in bow building applications.

1. The strains  seem to be "safe" elongation, quite useful for comparing the relative qualities of filaments for use in applications where breaking strength is the primary concern. When used in a bow limb however, they seemed to be strained to a much lower degree. The limb thickness on my 60" modern materiel bow is about 6mm, indicating that a very stiff materiel working at lower levels of strain could be what makes the the modern materiel limbs more efficient? Do you think there a correlation between strain levels and hysteresis? Possibly a correlation that could help us when choosing natural materiels for higher efficiency?

2. In what application did you find the flax  to "stack"? Embedded in a matrix of glue? Spun into a yarn? I cannot think of any other natural (animal or vegetable) materiel that exhibits such behavior. Usually work hardening is associated with metals and synthetic crystalline materiel,  but then again, cellulose is said to crystalline also.

[Jim Davis]

Aussie Yeoman said"

I would have to heartily disagree here. I backed some Ironbark (similar to Ipe) with reasonably good Elm, and the Elm was torn apart. The reason was the force used to bend the Ironbark produced massive stress, and so the strain packed on early, beyond the strain Elm could handle. Backing choice matters a great deal.

My point was that even in a self bow, the back is going to be stronger than the belly, in all but a few woods, such as cherry.

[Badger]

   Willie, a few years back I worked out a test to identify hysteresis in wood bows. It proved beyond a doubt there is a direct correlation between hysteresis and strain levels. Once you get into the plastic range on a bow hysteresis starts increasing. I had no need to identify what the number was as long as I could identify at what point this started happening on a bow during the construction phase. As soon as it starts to loose draw weight simply because it was drawn a further distance then you are picking up hysteresis and most likely set. I started using a not set tillering technique which is really just a method of monitoring the condition of the wood as you tiller and my results improved dramatically.

[joachimM]

Joachim

1. The strains  seem to be "safe" elongation, quite useful for comparing the relative qualities of filaments for use in applications where breaking strength is the primary concern. When used in a bow limb however, they seemed to be strained to a much lower degree. The limb thickness on my 60" modern materiel bow is about 6mm, indicating that a very stiff materiel working at lower levels of strain could be what makes the the modern materiel limbs more efficient?

Do you think there a correlation between strain levels and hysteresis? Possibly a correlation that could help us when choosing natural materiels for higher efficiency?

2. In what application did you find the flax  to "stack"? Embedded in a matrix of glue? Spun into a yarn? I cannot think of any other natural (animal or vegetable) materiel that exhibits such behavior. Usually work hardening is associated with metals and synthetic crystalline materiel,  but then again, cellulose is said to crystalline also.

Excellent observations! Indeed, if the backing is very strong (like in glassfiber, but also in flax), limbs should be made thinner, in order for the belly to be capable of taking the compression. To have enough draw weight, we then need to widen the limbs in flax-wood bows. in GF bows, both the backing and the belly are stronger, while the wood core is merely the matrix on which the GF-epoxy matrix was glued to. It would be a good test to see how thin we can make well-performing flax-wood composites.
As for hysteresis: I'm sure less strain means less hysteresis. Hysteresis being the internal friction between components in a solid matrix. Less strain is less severe fiber friction. Temporary set is IMO nothing else than a slow rebound from hysteresis.

Stacking in flax: I did some tests with branch bows (as these are better in compression because of more juvenile wood), roughly tillered them to 30#, and then added a flax layer on top, 1 mm thick at most. These bows were a lot stronger, and when drawing them to 15" or so on the tillering tree, they sometimes exploded right away (dry spaghetti-like). My guess is that the flax was so strong that much more wood was forced into compression, leading to sudden hinges that led to overstraining of the back fibers.

[Aussie Yeoman]

Aussie, no fault of yours, but the Osage numbers (as always) are the result testing green wood. If you had dry numbers to work with, Osage would be much higher in your list.

Actually, having gone through the data, I don't think the test results were due to green wood. There are four samples in my database, all from either Woodbear or Tim Baker:
Osage 1: 15182 MPa
Osage 2: 14277 MPa
Osage 3: 14015 MPa
Osage 4: 12952 MPa

The results are more consistent than disparate samples within other species. Perhaps you think Osage should have placed higher because it is such an exceptional bow wood. As you will see below, it is not Osage's stiffness that makes it exceptional, but its working strain.

Below I've captured the 30 top woods for stiffness, and also the 30 top woods for working strain. You can see there are very few (red bold) that are common to both lists, but most all of them are favourite bow woods. Does this mean the mathematics/engineering is a fraud? No. It means that the combination of both is not as important. Personally, I think working strain is more important than stiffness, and certainly more important than some sort of ratio. Yew and Willow have a similar stiffness, for example; no one would doubt Yew's suitability as a Top Dog among bow woods.

[joachimM]

Aussie, no fault of yours, but the Osage numbers (as always) are the result testing green wood. If you had dry numbers to work with, Osage would be much higher in your list.

Perhaps you think Osage should have placed higher because it is such an exceptional bow wood. As you will see below, it is not Osage's stiffness that makes it exceptional, but its working strain.

Personally, I think working strain is more important than stiffness, and certainly more important than some sort of ratio. Yew and Willow have a similar stiffness, for example; no one would doubt Yew's suitability as a Top Dog among bow woods.

There is actually a trade-off between strain and stiffness: woods with high stiffness (MoE) endure little strain, and vice-versa. For arrows, we use the stiffest woods, which we know are also less ideal as bow woods (larch, port orford cedar, douglas fir, ...).
Bow woods which we generally consider as very good have low (relative) stiffness but sustain high strain levels (osage, yew, plum, ...). Idem with juvenile wood (branch / sapling bows!): this has lower MoE, but higher strain tolerance.

The ideal would be high stiffness and high strain tolerance. Glass fiber is right up there. cough cough. Within all natural materials, bamboo has the best trade-off: high MoE and high strain tolerance.

As for willow, it's unfair to compare it in this way to yew, as its density is only half that of yew. There's just less wood to be strained. That's why it's important to (as per the mass principle) to compare relative stiffness, the MoE divided by density. This allows to compare what a bow of the same mass would perform like. Most willows have a relative stiffness comparable to bamboo (but much lower density).
Still, white willow (Salix alba) is still a very poor bow wood for its density and stiffness, both in tension and compression.