Stress and performance

[Aussie Yeoman]

Absolutely agree with you there. The taper profile needs to converge on a theoretical zero width tip, which in practicality has to have some width, as you mentioned.

This means that the limbs, of tillered perfectly symmetrically, probably won't be exactly the same thickness throughout, but need to taper ever so slightly in the last 1/4 of the limb or so.

I once made a bow with tips just under 1/4" wide. So narrow I cut a single nock in the back of each tip. That was for a Molly rather than a pyramid, but the theory holds.

In fact I think cutting a single nock on the back increases the stability because the point at which the string contacts the cross section of the limb is closer to the neutral plane.

That hypothesis could do with testing, if anyone could be bothered.

[mmattockx]

Absolutely agree with you there. The taper profile needs to converge on a theoretical zero width tip, which in practicality has to have some width, as you mentioned.

This means that the limbs, of tillered perfectly symmetrically, probably won't be exactly the same thickness throughout, but need to taper ever so slightly in the last 1/4 of the limb or so.

You are correct on needing to taper the outer limb thickness some if you straight taper to the nock width. You can keep the limbs constant thickness with a narrow lever to the nock, as shown here:







It is a bit hard to tell in the picture, but the end of the limb is parallel width for about the last 3.5" or so. It is 5/16" wide for that whole length. This lets the limb width taper follow the theoretical ideal that goes to a point at the nock, then transitions into a slightly stiff tip lever where the limb width goes below the 5/16" width. I added a tip wedge during layup to stiffen the tip a bit more and guarantee it was strong enough. This was the first time I had tried this and I was worried that the spindly narrow tip would be too fragile.


Mark

[Aussie Yeoman]

Good job on that one! That's quite the gnarly looking arrow pass design you have there. What was the draw weight/length on that one?

[mmattockx]

Good job on that one! That's quite the gnarly looking arrow pass design you have there. What was the draw weight/length on that one?

http://www.primitivearcher.com/smf/index.php/topic,70862.msg994666.html#msg994666


Mark

[Selfbowman]

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?

Willie if we overbuild the first three inches coming out of the fades but run parallel the limbs need to tapered in thickness ? If we overbuild in more overall width thru out the hole limb length but stay the same thickness could this be close to the same spreading the load. Extra mass in the first nine inches out of the fade has little effect on performance in my opinion. Again the added reflex in the last 9” of the limb is throwing a curve in the calculation. I think. Thats why I have been chasing the set with mass from bow to bow. Obviously I build by feel with mathematical measurements from the design in mind as I go. Not smart enough to do it any other way. 🤠🤠

[willie]

The thing is though that reducing strain means making it wider and thinner. Going in this direction increases the mass per unit of stiffness.

Aussie,
have you ever kept track of the grams/MPa of completed bows plotted against arrow speed ?

[Aussie Yeoman]

Do you mean grams of bow mass against the stiffness or stress of the timber against arrow speed? No, I haven't. Could be interesting though.

[willie]

Do you mean grams of bow mass against the stiffness or stress of the timber against arrow speed? No, I haven't. Could be interesting though.

grams of mass/MOE as determined by a bend test of the wood.
I guess you could calculate out the actual stress.........
but either way, you would need a bend test of the wood for the next bow to plan acordingly.

[Aussie Yeoman]

Oh! Yes, I have. When I've done bend tests in the past I've most usually also measured density.

Alas, all my data are on a computer that recently died and I've not yet tried to rescue them. But the data do exist.

[willie]

Arvin,
if you overbuilt the entire linb you would lower the actual stress throughout the entire limb, which might incur a mass penalty.  I dont think it matters if the first few inches coming out of the fades were thicker or wider so long as its stiffer.

Badger used to leave the inners on the stiffside as he tillered out, and brought the bend in towards the handle more if it looked like he was getting too much set too early. My guess is that near handle set is to be avoided more over set taking further out.  Perhaps he is reading along

[willie]

Oh! Yes, I have. When I've done bend tests in the past I've most usually also measured density.

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]

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

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]

So if we tiller a non perfect pyramid to look like a perfect one, the bow is not correctly tillered.

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.

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.

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]

So if we tiller a non perfect pyramid to look like a perfect one, the bow is not correctly tillered.

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.

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.

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

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.