Stress and performance

[Aussie Yeoman]

  Aussie, 1st of all I wanted to publicly thank you for converting the mass formula to an excel spreadsheet for me many years ago.
 
  As for a bend test, I was never able to convert a bend test to usable information that I could apply to making a bow. I think if you could lay out the method for doing this, if it is not too complicated it would be a huge step in making higher performing bows. I came out with several tests that were useful in comparing wood but I was never able to directly apply it to a design. Hopefully you can send us in the right direction here.

Most welcome Badger, a pleasure and an honour to help out.

Laying out the method can be easy to understand, but it isn't necessarily something I can cover thoroughly in a short space. Fortunately though a few years ago I did lay out the method, from plank of wood to engineered bow here: https://ozbow.net/phpBB3/viewtopic.php?f=34&t=5450 it might take a while to read through but I tried hard to make it accessible.

the answer to your question is yes,, no graph or formula needed, just make the two bows and see for yourself,, its that easy

BradSmith, if by this you mean that it's easy to show that a short bow will be inherently more stressed than a longer one, then no that isn't a fair demonstration of the hypothesis. All you will demonstrate is that a more stressed bow takes more set than a less stressed bow. The reason is without common metrics and methodology, there's no way to control for the amount of experienced stress in the bending bow. By this I don't mean that the stress is uncontrollable, but that you can't be sure that the stress in the two bows is the same.

An aluminium rod and a dowel feel cold and tepid, respectively, when you pick them up in your workshop. But the reality is that if you measured them scientifically, they would actually be the same temperature. Observational studies are not always reliable reflections of physical phenomena.

The amount of plastic deformation (permanent set) a piece of wood (a bow) takes is dependent on the maximum amount of stress the wood is subject to during bending. More working stress = more set. Less working stress = less set. This is completely independent of draw length, draw weight or bow length.

We've all made short bows that took little set and long bows that took more. It has less to do with the length than it does with the stress as a proportion of the elastic limit of that piece of wood. The shorter bow with less set experienced a smaller proportion of its potential stress, and the longer one with more set was caused to endure a larger proportion of its potential stress.

On the weekend I'll bring together a few different theoretical bows with dimensions and if people wish they can make their own according to the dimensions. I'll do a short Mollegabet, a medium pyramid bow, and a longer D bow.

[bradsmith2010]

Aussie thank you so much for the details and explanation,, I just ment if you build the two bows,, alot of your answers will be revealed,,,

[Aussie Yeoman]

Oh, I see. Orrighty then.

Okay, so I pulled some stats and calculated some dimensions. These dimensions are for a sample of timber tested by Tim Baker many years ago. The design stress should result in a set of about 1.5". For what it's worth, the modulus of elasticity of this piece of timber was 16,415 MPa and the working strain is 0.085%.

64" pyramid bow (8" rigid centre not included - "Dist" = "dist from fade")
50# @ 28"
Dist_____Thck___Wdth
0.00_____0.47____1.58
4.67_____0.47____1.40
9.34_____0.47____1.18
14.02____0.47____0.92
18.69____0.47____0.63
23.36____0.47____0.55
28.03____0.47____0.47


71" bendy handle longbow
60# @ 28"
Dist_____Thck_____Wdth
0.00_____0.80_____0.87
3.94_____0.80_____0.86
7.87_____0.77_____0.84
11.81____0.73_____0.82
15.75____0.69_____0.80
19.69____0.62_____0.79
23.62____0.54_____0.77
27.56____0.48_____0.69
31.50____0.41_____0.54
35.43____0.36_____0.39

63" Modern Mollegabet
50# @ 28"
Dist_____Thck_____Wdth
0.00_____0.89____1.02
1.57_____0.78____1.00
3.15_____0.67____1.04
6.30_____0.56____1.05
9.45_____0.54____1.05
12.60____0.52____1.00
15.75____0.54____0.77
18.90____0.61____0.49
22.05____0.64____0.34
25.20____0.64____0.23
28.35____0.59____0.19
31.50____0.55____0.14

I've tried to upload a picture that overlays the drawn shapes of the longbow and the molly. My relationship with forum interfaces is often a fraught and tenuous one, though.

*EDIT*

Aha! It worked! For funzies, I also uploaded a snip of my bow dimensions calculating spreadsheet.

[RyanY]

How much wider would those designs have to be for 0.1” set?

[Aussie Yeoman]

The short answer is "quite a bit, but I'm not sure".

It would take some re-figuring. I might have some time tomorrow.

The thing is though that reducing strain means making it wider and thinner. Going in this direction increases the mass per unit of stiffness. So while you might have less set (no set), the performance will suffer by virtue of more of the stored energy being required to accelerate the limbs.

[bradsmith2010]

thats a very good point Aussie, I have made bows with little set ,, but shot slow,, to much mass,,

[sleek]

The short answer is "quite a bit, but I'm not sure".

It would take some re-figuring. I might have some time tomorrow.

The thing is though that reducing strain means making it wider and thinner. Going in this direction increases the mass per unit of stiffness. So while you might have less set (no set), the performance will suffer by virtue of more of the stored energy being required to accelerate the limbs.

the 63 inch Molly needs to be almost twice it's width.

[Aussie Yeoman]

I suppose you are quite right, on average. I tried to pick a timber that would be common in the US (almost none here), and I guess I picked a truly exceptional sample.

I'll run the numbers on some other samples and see if we get something more conventional. Closer to average.

[Aussie Yeoman]

Gonna conduct some necromancy on this old thread:

I found an old project where I followed the dimensions calculated and got pretty much exactly what I wanted. This was a pretty long Molly design, made from boo-backed ironbark. I calculated the dimensions and printed them out 1:1 as templates, then did the same with the projected tiller shape. It didn't take much tillering to get it to spec, and when it was done the draw weight/length were just what I wanted, the tiller shape matched the projection, and the dimensions were pretty much bang on. Just small fractions of an inch here and there.

[Aussie Yeoman]

Here's another one, in which I make a longbow from Maple, using an average of figures collected by others (Tim Baker's bend test data)

Because I didn't use figures from a sample from this very board, the set was a little higher than I'd have liked, but otherwise it turned out pretty much as designed:

https://ozbow.net/phpBB3/viewtopic.php?f=34&t=17080

[Selfbowman]

Guys you know I’ve built the same bow design for years because it works well for me.and yes by doing so I’ve played with moving mass to accommodate for set. I was told I was wasting my time. That made me laugh because I was still getting set. But that being said my bows have 1-1/2-3” of reflex in my he last ten inches of the limb. Causing more stress fade to mid limb. So I made that area wider and by adding the mass it cut down on set. If you use your calculations for n a straight limb bow it will be different from say my design. I don’t know how to estimate the added mass needed to prevent the set . Deflex in the handle can balance the stress load more evenly but that’s another can of worms. The more early draw the faster the bow. Think compound for a moment. This is why I think the farther the tips in front of the bow handle with the same set the faster the bow will be! That requires more width fades to mid limb. Short or long bow. Just an opinion.

[willie]

That requires more width fades to mid limb. Short or long bow. Just an opinion.

adding width to limit set certiany seems like you can get a good handle on how much extra width it takes to make your design shoot better.

does your width out of the handle run straight for a ways before you begin to taper? if so, have you changed the distance out the limb before the taper starts? or just go a little wider to the same point as before?

[Selfbowman]

Willie the best bow shots that I have gotten with broadhead arrows was with a straight taper bow 2-3/8” at fades to 1/4” at the tips. I have  taken it parallel for 9” then @18” 1-1/4 wide and then to narrow tips. All with the same reflex. This is with Osage . I think the parallel for nine inches is working better but still testing. On a 28” working limb  design it’s putting plenty of stress on the limbs especially the inner limbs. I am considering going to 2-3/4 at fades  . It might overbuild it though.

[Aussie Yeoman]

In Archery: The Tecnical Side Hickman showed that the ideal width profile for circular tiller is not straight line taper in width as we consider the classic 'pyramid' bow, but ever so slightly bulged near the flares/fades. I've found, when making pyramid bows with circular tiller, that running the limbs parallel width for 4-5 inches before tapering in straight lines to be a good-enough approximation for ease and speed of layout.

[mmattockx]

Badger also mentioned keeping width parallel out of the fades for 2-3" and I have used that as well. It does a great job of evening the stresses out right at the end of the fade into the working limb portion. There tends to be a bit of a stress concentration right at that point and a short parallel section smooths that out.

A second thing not mentioned yet is that the theoretical pyramid shape tapers to a sharp point at the nocks. Since this is impossible in reality the way around it is to layout the pyramid taper to a sharp point, then draw a short parallel width lever section from the nock to where it intercepts the pyramid taper. This can be as narrow as you think you can make it. On my last lam bow I think that lever is about 5/16" wide for something like 6". I was worried about that being fragile and maybe unstable but it has not proven to be so.

If you straight taper to the nocks with some width at the nock then it tends to overstress the middle of the limb a bit and you need to taper the thickness in the outer half of the limbs to balance that off.


Mark