Is the early wood the weak link to cause set?

[avcase]

Updated table with gemsbok horn properties added. I was surprised how the density and elastic modulus is almost identical to the white water buffalo horn.

[mmattockx]

I would think it would make more sense to narrow and thicken the  theoretical horn bow.

My thinking is that these bows could be narrower and thicker to achieve the same draw weight.

Yes and yes. This is what make yew, ERC and the other junipers good bow wood. They can tolerate a fairly high amount of strain and let you make a narrower, thicker bow that performs very well.

Since we are on this, has anyone ever determined if narrower/thicker is more efficient than wider/thinner when it comes to bow limbs?

EDIT - I forgot to mention that I think a thicker/narrower limb should be more efficient but have not seen anything about that.


Mark

[PatM]

"Thicker is quicker"   is the saying . If the wood can take it.   

[mmattockx]

"Thicker is quicker"   is the saying . If the wood can take it.

This makes sense to me. When designing for maximum performance (in most anything) you almost always want to stress your materials to the maximum they can take so you are using as little material as possible to do the job. In a bow that means designing so the bend is the maximum the wood can take, then setting the width to get your desired draw weight at that bend.


Mark

[lonbow]

Thank you for the tests, avcase! It´s much apprechiated!

Let´s assume there would be a wood that doesn´t take set, no matter how much it is bent. A bow made out of this material could have a very deep cross section (it must still be a bit wider than deep so it doesn´t twist). The deepest possible cross section would make the lightest bow for sure, which might be very advantageous especially for accelerating light arrows.

But in reality, the amount of strain a wood can take is limited. I think there is an optimal cross section for every combination of bow design and the wood being used. The optimum will be the highest possible cross section where the set is still low.

lonbow

[avcase]

I ran a load-deflection curve on the Osage Edge Grain sample #1, and thought that this was starting to hint at some pretty cool data that is more applicable to us who build bows. 

First, a quick description of the procedure that I used. I placed the sample in the bending fixture and lightly flexed it a few times before setting the zero point on the dial indicator. Next, I applied a weight for three seconds and recorded how much the sample deflected. I then removed the weight and watched to see if the needle on the dial returned to zero. I then repeated this procedure with increasing weight. Part way through this process, the needle would immediately return a few thousandths of an inch above zero, and it would then slowly return to zero over a few seconds.  As the load increased even more, this offset increased. On the last two measurements with the highest weights applied, the deflection didn’t recover completely. Several minutes later, this still hasn’t recovered, indicating some more permanent set has already taken place. It isn’t much, just a few thousandth.

You can see this by comparing the curves on this graph.  The Orange line shows the maximum total deflection versus applied weight. The blue line subtracts the short term recovery immediately after the load was removed. What this is starting to show is increasing hysteresis in the sample as the stress is increased.  This is starting to get a little more interesting!

[Badger]

Interesting, what is also important is the recovery that takes place on the first fraction of a second, anything that happens after the arrow leaves the bow is what we are concerned with. Hysteresis is time sensitive, the heavier the arrow the slower the limbs and less hysteresis.   I like the test you are doing, it clearly demonstrates what we are looking for hear.

[Badger]

 What if you attached something like a needle to the end of the test piece and photographed it say 1/4 of a second after release? Have the needle lined up like a dial.

[avcase]

Steve,
I can take video of the test fixture so you can watch the dial as increasing loads are applied and quickly removed. It pretty clearly shows what happens and is precise.

Most bows are under about the same stress as I got to in this graph just sitting braced. I stopped at a bending stress of around 7500 psi (0.35% strain). I only held it at this level for about three seconds before letting it down, although I did this multiple times at each load. If I held a tape measure on the bow Arvin was measuring a few pages back, 0.35% strain would show the bow back stretching nearly 1/4”, and belly compressing by about the same amount.  If I go back and continue this graph to about double this stress level, then it would show very clearly the short and long term effects for a typical bow.  This will give three lines. One line showing the total deflection under load, a second line subtracting the short term hysteresis, and a third line subtracting out only the long term set.  What I love to see is a clear point on this graph where there the set and hysteresis losses balances against the design compromises necessary to keep the stresses in check.

The long term set reduces the capacity of the wood to store energy in bending.

The short term hysteresis just eats up energy that would otherwise go to the arrow.

Alan

[Selfbowman]

You are smart!!!

[RyanY]

Alan, you mention that the lengthening and shortening in tension and compression would be the same in Arvin’s bow but I think we normally assume that with wood being stronger in tension that the back does not stretch as much. Or perhaps my thinking is wrong and the back does stretch as much but is not under as much strain as the belly (not sure if that’s the correct use of strain/how close it is to breaking?). It would make sense to me that the back and belly experience set at different rates due to the differences in tension and compression. If trapping can equalize these forces and increase the degree of bend before taking set then my thought is that it would force the narrow back to stretch further and could result in a slightly thicker bow for the same draw weight. Bit off topic from the early wood discussion but just a thought.

[Allyn T]

Ryan The way I understand it is not that the back stretches less but that it handles tension stress better than the belly handles compression stress so trapping the back doesn't make the back stretch further It instead makes the same amount of stress take place on less wood

[Allyn T]

If you picture two men one stronger and one weaker picking up a beam if they both hold one end the weaker man will give out first. Trapping the back is like having the stronger man move his grip up further so that he is supporting more of the weight of the beam

[Selfbowman]

So if we had a sample with more early wood on one side could we start with early wood side up test and then flip the sample and retest to find out the difference. We could trap accordingly.

[RyanY]

Ryan The way I understand it is not that the back stretches less but that it handles tension stress better than the belly handles compression stress so trapping the back doesn't make the back stretch further It instead makes the same amount of stress take place on less wood

That’s where I’m wondering if I am misunderstanding the properties of wood. My understanding is that wood can’t stretch as much as it can compress just purely from a length standpoint before failure. I guess failure can be measured differently also as a tension failure is likely a full on breakage of the fibers versus a slower crushing in compression.