Hollow Limb Design and the Mass Principle

[Slackbunny]

When reading the thread with Simson's hollow limb bow, I had a moment of inspiration. But I didn't want to hijack, and I thought this topic might be good enough to merit its own thread

My thinking is that a hollow limb cross-section could be significantly more efficient than a standard cross-section bow because of its unique geometry.

Its like steel I-Beams. They have similar strength characteristics to solid steel beams, but with far less mass. This principle doesn't just apply to metals, its a geometry thing that should apply to all solid materials.

So in theory a hollow-limbed bow with a certain mass should pull heavier than a standard bow with the equivalent mass because its geometry gives it a better strength-weight ratio.

If my thinking is correct, then the hollow limb geometry would require a major adjustment to the mass principle in order for it to be accurate.

What are you thoughts?

[Onebowonder]

Getting out my slide ruler, pocket protector, and making popcorn.  this should be interesting in a geeky sort of way!

OneBow

[PatM]

Just ask simson to shoot the bow and tell us the mass and draw weight and tell you how it compares to a bow of the same weights in regular configuration. 

[Wiley]

All other things being as equal as wood can be, 2 bows of the same length, same mass, I am pretty sure the HLD design will have significantly stiffer limbs.

Grab yourself a sheet of printer paper. Let's consider this a simple cellulose analog to the wood in the bow. Whatever way you fold it, the mass stays the same. It does not take much effort to bend it into a U shape from top to bottom. Now bring the two edges together in a similar shape the HLD limbs would be. Put your thumbs in the bottom of the concave shape on top and bottom of the paper and try to bend that piece of paper in on itself, this concave shape is noticeably more stiff.  A piece of paper probably isn't the greatest example, but its an easy example of why this would result in a stiffer limb.

For a better analog one could go out and find a suitable sapling for a break test. split it in half. Hollow one side out until its bending good, take the other side from the same tree and scrape it down until the mass is the same and preform a break test. If it goes as expected it should take more to break the HLD, or at least the HLD should be stiffer than the the flat backed sample.

[Holten101]

My thoughts are...that I cant shake the thought of all that stress concentrated in two narrow ridges. Im sure that material/stress simulations that would shed light on this exsist.

Simsons bows are thought provoking (in so many ways)....I am just pretty sure he could get the same effect with a none hollow, but more narrow same-mass design.

Cheers

[Slackbunny]

My thoughts are...that I cant shake the thought of all that stress concentrated in two narrow ridges. Im sure that material/stress simulations that would shed light on this exsist.

But the concave also provides a much greater surface area on the belly to distribute the stress. That may help to offset the effect that you are talking about.

[Holten101]

My thoughts are...that I cant shake the thought of all that stress concentrated in two narrow ridges. Im sure that material/stress simulations that would shed light on this exsist.

But the concave also provides a much greater surface area on the belly to distribute the stress. That may help to offset the effect that you are talking about.

It may....and it may not. The ridges will be farthest away from the back at all time and should take most, if not all the compressive stress (I say "should", because it being wood there will be a lateral flex too....the limb ridges will be pushed out as well as compressed. And I cant anticipate what effect that has). If anyone can show me a hollow limb design with a fret in the midline, I will bow my head and leave in silence;-)

[Wiley]

Simson should correct me on this if I am not correct, but I think I read that when the HLD is drawn the limbs will actually begin to flatten. The stresses are being distributed along the curved limb. It's sort of a dynamic distribution of stress that to me seems a little more complicated than simple compression/tension, but a process that seems to distribute those forces in a very acceptable manner.

Case in point being this bow of Simson's. If this design wasn't a good one, this bow wouldn't have worked. He took a piece of wood rotting from the inside out that few people would have done anything with other than throw it in the fireplace and turned it into an HLD bow.
http://www.primitivearcher.com/smf/index.php/topic,41217.0.html

[Badger]

  I tend to agree with you Wiley, I feel like it might slightly flatten out. I have no idea how it would relate to the mass principle. If I try to duplicate the action with my tape measure it just twistsithout bending and then kinks, not sure why it seems to be effective with wood.

[Holten101]

It will flatten out (that is what I mean by saying the ridges will be pressed outwards).

Simpson is an expert no doubt about that, and finding a bow inside that mess of half roten laburnum was good bowyering.

But its not enough to convince me that hollowlimb design is more effective that than other designs.

Cheers

[Wiley]

I think simson has proved that the design works when using a high crowned stave. In terms of mass I think that a rectangular cross section bow vs a HLD bow of the same mass would result in a stiffer limb in the HLD, If both were reduced to the same weight of pull the HLD limb bow would have less final mass. I imagine a lower mass bow of the same weight of pull would probably result in a higher efficiency, low hand shock, and shoot faster. I am not a bowyer but I soak up things that interest me like a sponge, so i'm just going on what i've read.

[Slackbunny]

Hmm, if it flattens out, then that might change things. Now instead of dealing with a single cross-section for the duration of the draw, we have a cross-section that is changing dynamically. That complicates things. We're leaving the realm of simple geometry and stress-strain and getting into the realms of calculus now.

The limbs flattening out may be the only reason the design works at all. What Holten said about the stress concentration in the ridges is probably true. But if the bow flattens out when it is at its maximum stresses, then all of the sudden we don't have that issue anymore, because we no longer have ridges, just a really wide flat bow.

It seems to me like an ideal design. It changes its cross-section to the ideal state at any given point in the draw and the release. It is narrow with ridges early on to give high initial draw weight storing more energy early on. Then as the stresses increase, it becomes wide and flat, a cross-section that we know deals better with greater tension. Then it narrows as it accelerates through the release, becoming more aerodynamic as it gains velocity.  And it does all of this while seemingly being of lower mass than a comparable standard bow.

I don't know if all that is true, but that is how my mind is processing it at the moment. Feel free to bring me back to reality.

[Badger]

  I don't think it actually flattens as much as it does attempt to flatten or possibly even turn itself inside out. It really is interesting, I can figure out why the steel tape will not duplicate the bend unless it is because it lacks tapering.

[Onebowonder]

While I suspect the slightly improved aerodynamics of the limb as it is released and re-shapes itself into a high crowned geometry would be very hard to quantify in any assessment of the performance of the bow, ...the rest made sense to me.  The effectiveness of the improved aerodynamics would require a medium with a viscosity something like pudding before I imagine it would show up in the overall performance of the bow.

However; the bit about dynamic redistribution of the forces, both tension and compression, during the draw and release do sound like they would make significant physical difference to the performance of the bow.

Simpson - If you are monitoring this thread, it would be great to have any performance measurements you might have for this little bow.  ...and if by any chance you had a similar stats bow made in one of the more traditional crossections, some comparables would be of interest.

OneBow

[xXKyojinXx]

Well it's a sort of concave form, yeah? It creates an arch (like a 'U')? Arches are among the strongest structures. If it bears a stress on it's top side (the opposite side of the hollowed side) it will divert the tensile stress, increasingly, towards the bottom of the arch's form. The more rounded the portion of the arch is, the more it will evade tensile stress. The straighter portion of the arch will take on that stress. Eggs are arches as well, in fact. That's why you can lay a heavy weight on the top of an egg without it breaking, yet if you lay it on the side, it will be crushed. So wouldn't it stand to reason that a hollowed limb bow like that would possess a heavier draw weight but be able to build up more 'potential energy'? I don't know honestly, I'm just going on my layman's understanding of physics and bow making.