Thickness vs width questions

[mmattockx]

Bottom limb looks hinged? It looks like it could lose quite some weight off those mid/outer limbs

Zing! It does look like a hinge, but is where the underlay starts that I used to add material to those skinny levers. The spreadsheet says I don't really need them but I was being conservative with my first try of this style. When I cut the back profile those levers looked so narrow and delicate, but they are rock solid on the tree so what do I know?


Mark

[PatM]

Maybe Mike was talking about the video.

[mmattockx]

Maybe Mike was talking about the video.

After watching the video I think you are correct. No harm done either way, mine looks like there is a hinge on the left limb as well...


Mark

[Allyn T]

That video had to be a joke.

[Selfbowman]

That video had to be a joke.

I think so to. Or not real knowledgeable.

[scp]

I am wondering if there are two advantages to wide thin bows. The first being that thin limbs will be under less strain and are less likely to take set. The second being that a higher percentage of working wood is closer to the surface with less non working wood in the middle/neutral plane of the limb possibly leading to lower mass.

In a rectangular cross section limb the percentage thickness that is contributing the most work is always the same. The gradient of stress/strain is a straight line in the rectangular cross section, from zero on the neutral axis to maximum at the surface of the limb.

I am going to tinker a bit with your idea about the wider limb having more wood at a higher strain level, there could be something to that.

Mark

Interesting points. I can guess but not sure. Can you explain "the straight line gradient" in ordinary language, please?

[mmattockx]

Can you explain "the straight line gradient" in ordinary language, please?

It's really a graphical thing and so much easier to understand with a diagram of what is going on:



The stress through the thickness of the limb goes linearly from the maximum at the surface to zero at the neutral axis. This is a diagram of a portion of a beam in bending, like looking at the side of a bow while the limb is bent. The bow limbs would be oriented horizontally as the diagram is drawn. In this diagram the top surface would be the belly (in compression) and the bottom surface the back (in tension).


HTH,
Mark

[willie]

I haven't watched the video yet, but "over penetration"

in a culture where more work was expended on arrow making than bow making, loosing a good arrow on a shoot through was painful.

[scp]

Can you explain "the straight line gradient" in ordinary language, please?

It's really a graphical thing and so much easier to understand with a diagram of what is going on:

Thanks. That's what I thought you meant. Then, why do they say that the top 10% of back does most of the (tension) work?

[PatM]

A pass through is more likely to preserve an arrow for retrieval than one getting  slapped by trees as the animal flees and then falls down on it.

   If you are worried about your arrow when hunting, you will  likely miss.

[Don W]

I haven't watched the video yet, but "over penetration"

in a culture where more work was expended on arrow making than bow making, loosing a good arrow on a shoot through was painful.

This is true, but I agree with Pat. I would think a full passthrough would be the easiest to find and the least likely to break. I am trying to think of a scenario where this would not be true, and can't come up with one.

[Allyn T]

I would say not getting an animal because you didn't get a pass through would be more painful, and it would probably leave with your arrow as well so that's a double whoopsie

[mmattockx]

Thanks. That's what I thought you meant. Then, why do they say that the top 10% of back does most of the (tension) work?

This is hard to explain in a short forum entry of text. Attached is a picture of the basic calculations to help illustrate. You may have to zoom in on the picture to see it clearly.

The basic idea is that the area under the curve (in this case the triangle) gives the total force generated. This allows us to calculate what portion of the total force is generated by different layers in the limb.



The picture shows the same triangle representation, representing the tension side of the limb in this case. I added dimensions to illustrate:

t = the distance from the neutral axis to the outer surface of the limb
F = the maximum stress on the outer surface of the limb

Say we split the thickness t into half, representing the outer half of the tension side of the limb and the inner half. Call the outer portion Area1 and the inner portion Area2. We can easily see that Area1 is much bigger than Area2. The calculations show that Area1 is 3/4 of the total area and Area2 is 1/4, which means that the outer half is generating 3/4 of the total force.

This calculation can be carried out for any slice of the limb thickness to show how much of the total force that particular layer is generating. If you work it backwards you can calculate out that the outer 29.3% of the thickness carries 50% of the total load. For a rectangular section limb the triangle depth t is half the total limb thickness. This means 50% of the work in that limb is being done by a layer that is 14.65% of the total limb thickness on the back and belly surfaces.

To put this into real numbers, say your limb is 0.5" thick. 50% of all the work is done by 0.073" thick layers on the belly and back surfaces. The other 0.354" in the core is doing the other 50%, which means the core isn't doing much overall.

Clear as mud?


Mark

[scp]

Clear as mud?

Clear as a bell. But you are saying the same thing.
I am too lazy to do the calculation myself.
What is the percentage of work done by the top 10%?

It is possible that the bow stave is not quite homogeneous
and the top layer selected is quite stronger in tension
than the layers below, as in the case of bamboo.

It is also possible that the neutral plane is not quite in the middle,
as wood is usually much stronger in tension than in compression.

[mmattockx]

Clear as a bell. But you are saying the same thing.

The same as what?

I am too lazy to do the calculation myself.
What is the percentage of work done by the top 10%?

The outer 10% (of total thickness) does 36% of the work.

It is possible that the bow stave is not quite homogeneous
and the top layer selected is quite stronger in tension
than the layers below, as in the case of bamboo.

Yes, that is correct. The above analysis assumes a homogeneous material. It can be applied to non-homogeneous materials with adjustments but that gets more complicated.

It is also possible that the neutral plane is not quite in the middle,
as wood is usually much stronger in tension than in compression.

The ultimate strength doesn't influence the neutral axis but the stiffness does. The above analysis assumes the stiffness is the same in tension and compression, which may not be the case. This was discussed here a while back and there was no conclusive answer as to where the usual bow woods fell on this question. The analysis method is still valid regardless of where the neutral axis is located, I just kept it symmetrical for simplicity and because that is a common situation on bows.


Mark