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Stress and performance
willie:
--- Quote from: Aussie Yeoman on May 17, 2024, 10:28:03 pm ---Oh! Yes, I have. When I've done bend tests in the past I've most usually also measured density.
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I was thinking of both sort of. deriving a mass/moe value and plotting it against some performance metric like arrowspeed
I guess if you have bend tests of the timber used in good performing bows and can still evaluate the working mass, it might be useful
Aussie Yeoman:
Ah yes I see where you're going.
I think the warmer rabbit hole would be working strain against mass compared to arrow speed. Yew, for example, has quite a low stiffness but can accommodate a prodigious amount of working strain.
sleek:
--- Quote from: mmattockx on May 16, 2024, 01:22:39 pm ---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
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You are hinting at something here but didn't explain all the way through. The perfect pyramid tiller looks like a circle. But we can't build a perfect pyramid for the reasons you described. So if we tiller a non perfect pyramid to look like a perfect one, the bow is not correctly tillered.
Since a pyramid bow is essentially a piked bow, you know that the tiller shifts when you pike the bow. The tips gain more leverage and get stiffer, which pushes the stress towards the inner limbs. You need longer parallels than what you said was suggested. You need about 7 inches per my experiences, as a little loss in length magnifies in stress as the distance increases. 7 inches is a rough number. There is a ratio to explore but I don't know it yet.
In short, it's my strong opinion a pyramid bow shouldn't actually be a pyramid, nor tillered like one. It should start out parallel, then straight taper to stiff tips. Tiller should be stiff tips, that lead to an ellipse. That will allow the short coming of what is possible to be compensated for vs what works on paper.
All that said, a well made pyramid bow will not fail you as Old Self bowman aka Arvin has proven time and time again.
mmattockx:
--- Quote from: sleek on May 21, 2024, 03:13:11 am ---So if we tiller a non perfect pyramid to look like a perfect one, the bow is not correctly tillered.
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You can't get the circular bend with constant limb thickness on a non-perfect pyramid, but you can if you tweak the thickness in the outer half of the limb. I don't know if that should be considered 'not correctly tillered' or not. The red oak lam bow I did with the lever tips was very close to circular tiller with the tips stiff, which to me is very close to an optimal arrangement of mass and strain. This is what Arvin keeps chasing and his bows have shown the results of those efforts.
I haven't found any need for more than the 2-3" parallel out of the fades, but I am sure the longer section you suggest will work fine if the thickness is tapered to suit.
--- Quote from: sleek on May 21, 2024, 03:13:11 am ---In short, it's my strong opinion a pyramid bow shouldn't actually be a pyramid, nor tillered like one. It should start out parallel, then straight taper to stiff tips.
--- End quote ---
Well, that certainly isn't a pyramid bow as you describe. It's basically an ASL and will need thickness taper and tiller to suit.
Mark
sleek:
--- Quote from: mmattockx on May 21, 2024, 12:57:59 pm ---
--- Quote from: sleek on May 21, 2024, 03:13:11 am ---So if we tiller a non perfect pyramid to look like a perfect one, the bow is not correctly tillered.
--- End quote ---
You can't get the circular bend with constant limb thickness on a non-perfect pyramid, but you can if you tweak the thickness in the outer half of the limb. I don't know if that should be considered 'not correctly tillered' or not. The red oak lam bow I did with the lever tips was very close to circular tiller with the tips stiff, which to me is very close to an optimal arrangement of mass and strain. This is what Arvin keeps chasing and his bows have shown the results of those efforts.
I haven't found any need for more than the 2-3" parallel out of the fades, but I am sure the longer section you suggest will work fine if the thickness is tapered to suit.
--- Quote from: sleek on May 21, 2024, 03:13:11 am ---In short, it's my strong opinion a pyramid bow shouldn't actually be a pyramid, nor tillered like one. It should start out parallel, then straight taper to stiff tips.
--- End quote ---
Well, that certainly isn't a pyramid bow as you describe. It's basically an ASL and will need thickness taper and tiller to suit.
Mark
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I agree. So, my point being that a perfect pyramid can not be built, so modifications must be made. In my opinion, these are the best ones to make. I will add, the 7 inches parallel is not a must. It's not even an accurate description of what's being done there. What's actually happening is the surface area is being increased therefore the amount of stress per square inch is reduced. You can just make the bow wider there and deal with the extra mass mid limb or taper it more agressive towards a straight taper.
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