Dense woods and width/torsional stiffness

[DC]

Dense woods take less wood to make a bow, right? So for the same DW a dense bow can be narrower and thinner than a a light wood bow. On a highly reflexed bow is there a point where a denser bow will become more unstable because it's narrower. Or does the density maintain the torsional stiffness? Boy, I'm having a tough time explaining this, I hope it's clear what I'm asking.

[Pat B]

DC, on highly reflexed bows and recurves with big hooks lateral bending is more likely on narrower bows. Straight limbed bows, not so much. I'm sure it's possible on R/D and recurves but the alignment and good tillering are more critical.

[Bayou Ben]

I get what you're asking DC.  I had the same thoughts when Jeff (upstatebowyer) asked about the width of ipe. 
I would think the torsional stiffness and density more or less go hand in hand.  That is, a denser wood will have more torsional stiffness or resistance to twist.  I don't believe this is a common value used in wooden structure design, so going deeper than just a guess would require some experimentation.

 

[Halfbow]

My intuition here is that it will just depend on the ratio between width and thickness. If you have limbs that are 3x as wide as they are thick, it will be pretty torsionally stable, whether the wood is dense or light, and whether there's a lot of volume there or not. And conversely if you have limbs that are as wide as they are thick, it will be unstable whether it's a dense or light. When the wood is deciding which direction to go, its only opponent is itself.

[Selfbowman]

Halfbow I want to agree with you . But I think this would be a overbuilt design. Pyramid bows will hold true to this till about mid limb. Then it needs to be pretty straight grain or you better be good at tiller. I haven’t built many recurves but reflex all my bows the last 8-10”. The best ones work 5-6 “ of the 8-10”. That’s when I do my part correctly. Just thoughts here guys . Arvin

[Bayou Ben]

My intuition here is that it will just depend on the ratio between width and thickness. If you have limbs that are 3x as wide as they are thick, it will be pretty torsionally stable, whether the wood is dense or light, and whether there's a lot of volume there or not. And conversely if you have limbs that are as wide as they are thick, it will be unstable whether it's a dense or light. When the wood is deciding which direction to go, its only opponent is itself.

I'll try and do a simple experiment tonight....So you are saying 2 bows with the same exact dimensions (width, thickness, length) will have the same torsional stability regardless of what they are made of?  Ipe and pine?  I don't think so. 

[Halfbow]

Halfbow I want to agree with you . But I think this would be a overbuilt design. Pyramid bows will hold true to this till about mid limb. Then it needs to be pretty straight grain or you better be good at tiller. I haven’t built many recurves but reflex all my bows the last 8-10”. The best ones work 5-6 “ of the 8-10”. That’s when I do my part correctly. Just thoughts here guys . Arvin

Sure, I think we agree. My statement was just about the cross section of a limb at any given point. On most bows that cross section will change at different points on a limb. I wasn't suggesting a design, I was just saying the limb will be most stable where it's wider/thinner. Stability kind of matters less the farther out you are on the limb, so you can get away with more. Many bows even get narrower than they are thick at the tips. But if you tried to make a bow that was narrower than it is thick near the handle, you'd run in to problems.

But even toward the tips you have to think about it some. I've made a holmegaard style bow where I narrowed the tips too much, they were much thicker than they were wide, and they started to want to bend sideways. Oops. (Add the constraint of a bow string, and sideways bend shows up as twist and torsional instability)

I'll try and do a simple experiment tonight....So you are saying 2 bows with the same exact dimensions (width, thickness, length) will have the same torsional stability regardless of what they are made of?  Ipe and pine?  I don't think so. 

Not exactly. I'm talking about ratios of width to thickness. So let's say a board of eastern red cedar that is 1.5" x .5", and a board of ipe that is .6" x .2" have the same stiffness. The same "draw weight", if you will. (I don't know what the real numbers would be, I'm just imagining) Both these boards are 3 times as wide as they are thick, and I'd imagine they'd both be quite torsionally stable as a bow.

Now if we imagine boards with a square cross section, say erc that's 1" x 1" vs ipe that's .3" x .3". If they have the same stiffness, I'd imagine they'd both be equally unstable.

[Del the cat]

IMO The torsional stiffness is more about the cross section than the species of wood...
Del

[willie]

IMO The torsional stiffness is more about the cross section than the species of wood...
Del

I agree. as most torsion bars are round or square.
to have a closer to square sectioned bow limb, the wood would need  both high stiffness (to minimize width), and high elasticity to maximize thickness.

[DC]

I agree. as most torsion bars are round or square.

That was my thinking too, but it's kind of standard(I thought) to make the limb wider to increase stability

IMO The torsional stiffness is more about the cross section than the species of wood...
Del

I agree but do the dimensions trump the density? I want to build a high performance(hopefully) bow with Ocean Spray, SG 1.2. If I leave the limbs big enough so they don't twist off will I be paying a penalty in mass?

[willie]

That was my thinking too, but it's kind of standard(I thought) to make the limb wider to increase stability

of course you are correct. the twisting limb is more a case of eccentric loading rather than pure torsion.
for just a wild ass guess, dimensions trump density

[Selfbowman]

My record flight bow is very stable. It’s osage , pyramid 2-3/8 at the fade ,67” long 10” handle and straight pyramid to the 5/16 tips . Weighs 28 oz. the mass is all mid limb to handle. I think the mid limb is close to 1-1/4 wide. 2-1/2 inch reflex when built . Most in the last 10” of the limb. Held all but 1/2” of the reflex. . Hope that might help. Arvin

[Eric Garza]

It seems to me that the relevant number with respect to stability is a ratio of width to thickness, not width by itself. Maybe that is what folks mean by cross section?

Dense wood can be made narrower, but not so narrow that you end up with a width to thickness ratio that approaches 1:1. Even when folks use ipe, they do not make these bows so narrow that you end up with a 1:1 ratio of width to thickness, at least not in portions of the limb that bend.

[DC]

I'm just concerned with what the density does to the torsional stiffness. Obviously if you change the shape the stiffness will change. Maybe an imaginary way of looking at it is if you take a piece of wood with a .5 SG and magically compress it in width and thickness until it has an SG of 1 will it still have the same rotational stiffness? Hmmmm, I'm starting to think no.

[Bayou Ben]

I'm just concerned with what the density does to the torsional stiffness. Obviously if you change the shape the stiffness will change. Maybe an imaginary way of looking at it is if you take a piece of wood with a .5 SG and magically compress it in width and thickness until it has an SG of 1 will it still have the same rotational stiffness? Hmmmm, I'm starting to think no.

That's what I thought your original question was.  I think the rotational stiffness will be close. 
The mass may be a little more in the higher SG, but not enough to make much of a noticeable speed difference.  This is just a guess.
As Steve's mass principle implies, SG and strength go hand and hand.  It would make sense that torsional stiffness would also be proportional to the SG.