Why is a crowned back favorable?

[Springbuck]

  I'm in the camp that says the main benefit here comes from a somewhat physically lighter limb, and a narrowed back that can still hold together in tension, rather than increased stretching of the back fibers.

Two things give me pause, though.   Bear with me.........

     I HAVE had several bows fail purely in tension. They were made of VERY thin ringed red elm, like paper thin summer rings over same thickness winter rings, in layers.  I just made, then quit on, a long flatbow made from a 5" tree.  I finished tillering, and was shooting the first 100 arrows or so, when I heard several little "tick"s.  I inspected the bow and saw no lifted splinters.  It kept happening.  Upon inspection with a magnifying glass, I found that all along the bow, the back had failed in small transverse cracks through the first growth ring.  There are like 15- 20 per limb.  I can dig a finger under them and flake up little chips about 1/32" thick, and see the winter ring underneath.

 The important thing here is THE BOW IS STILL SHOOTING.

 I have overdrawn it 4" or so.  No break, no set, just more lifting of these eggshell thin bits.  It is decrowning itself, as it were.

 It hasn't broken, has taken NO more set, and hasn't cracked again.

I am tempted to try decrowning it, but the stave is super knotty and lumpy, so I dunno.


The second thing is just Baker's test from TBB IV.  Taking a rectangle x-section bow and trapping it resulted in higher mass decrease than draw weight decrease, and in another test, the bows took less set. If a trapped bow takes less set than a rectangle bow of similar wood, how do we explaine this?



 Finally, this should be super easy to test.   We reverse Bakler's test.   We make a trapped pyramid bow out of a maple board or somewhat.  Shoot, measure, test.  Then we square the sides up with the back.  If the belly corners are truly "loafing", then we should lose almost no draw weight, and take very little more set, right?

[RyanY]

I think a lot of the bow tests seem to me to be anecdotal evidence. When comparing two bows, one trapped and one rectangular in cross section, how do we know that they are comparable with just bow length and draw weight? I think a better test would be to make two pieces piece of wood where the volume is equal, the thickness is equal, and the cross section is rectangular in one and trapezoidal in the other. This way we know that the mass of both pieces is the same but we can measure the resistance to deflection at a particular distance and compare that. The other comparison would be to test the pieces for set and breaking strength to see if the difference in cross section makes a difference in the tolerable bend radius. Maybe this has been done but I think it would be far more definitive than bow testing. It would tell us if trapping makes a difference in both energy storage and bend radius. And of course I think that several degrees of trapping would need to be tested such as 25%, 50%, 75%, to gain an idea of the benefits and risks. Unfortunately I don't have the engineering background to mathematically figure out how beam cross section effects energy storage but if I were to experimentally figure it out I think this would be the way to go. Thoughts?

[willie]

ryoon-
I woun,t  normally make suggestions for the other guy to try, but since you asked, I have been giving some thought about a way to easily test limb profiles and materiels.

if one settled on a single pyramid limb width and length profile, that was designed so that the thickness could be even and easily ripped with a table saw,

then perhaps 2 easily manufactured limbs could be clamped on a universal handle riser.

one could mix or match, share with others, save for later comparisons, or just plain shoot to see if some more subjective differences between limbs exist.

[Springbuck]

  I still think going from trap to rectangle would prove at least the one element intended, which is the claim/idea that the belly corners are loafing.

Tolerable bend radius WOULD be a good thing to test.  There is a lot of anecdotal evidence, by us, that tolerable bend radius is simply a threshold event.

I also think that it would be cool to purposely induce a hinge, and slow-mo film it while it breaks.

[Jim Davis]

  I still think going from trap to rectangle would prove at least the one element intended, which is the claim/idea that the belly corners are loafing.

I think it would prove that, though I can't imagine anyone thinking the belly corners are loafing...

[Jim Davis]

I wish there were a Paul Kolpsteg among us.

http://www.archeryhalloffame.com/Klopsteg.html

http://en.wikipedia.org/wiki/Paul_E._Klopsteg

[joachimM]

Actually, a pretty straightforward way of testing if trapped backs reduce set would be to start from flat boards and make ten identical pyramid bows with rectangular cross-section, for example made from maple or red oak boards or something easily accessible.

No grip, just two opposed triangles. They don't need to be live-size bows; miniature bows (75 cm  from a 0.5 cm thick board or c. 30" x 0.2") could do the trick.

Pyramid bows can be made such that there is no thickness taper from fades to nocks, which makes the bows easier to compare. For ease of making, forget about the handle, they don't need to actually shoot bows, you just need to put them on a tillering stick and draw them. Use only straight grained boards.
string them with the same slack string, put them on a tillering stick, draw them progressively and mark at which draw length they start to take set.  Measure draw weight at each interval for each bow. Continue, and mark at which draw length they take 1" of set. Continue and mark at which draw length the bow breaks or the back develops splinters.

There are two basic ways to test:

one is you divide these bows into two groups: one stays rectangular in cross-section as is, the other half is trapped, with the back being 2/3 as wide as the belly.
This allows you to compare some test statistics (see below) between the two groups. There are easy statistical tests (even online) where you can compare two groups of variables. (ANOVA, or t-test here, or a variant thereof)

The other method is by regression: you make a gradient of trapped (and reverse-trapped) bow-belly width going from 2/1 (back twice as wide as belly) to 1/2 (belly twice as wide as back). Here you relate draw length at which the bow starts to take set with the back/belly ratio and see if there's a linear relation.

You can also check if there's a trade-off with draw weight, and a trade-off with back failure (there's no point in having a bow that takes no set but always breaks).

I'll try to find good board wood here and test this sooner or later. But please if you have spare time and want the scoop, be my guest 

Now, this won't give you a magical back to belly ratio applicable to all future bows; these result will be very specific to the wood considered, and to the moisture content of the wood being used. But as a proof of principle it may be useful.

[Springbuck]

I think it would prove that, though I can't imagine anyone thinking the belly corners are loafing...
[/quote] 

This is actually the crux of the argument.  If they are NOT loafing, then you save weight, but store similar energy, and the belly is evenly strained.  If they ARE loafing, then there is no reason to trap a limb or use a crowned stave, and in fact the thinner edges hurt you by adding dead weight.

  Baker said that in TBB I, which champions the rectangular cross section for most woods in the Design and Performance section.  His testing and extrapolation to that point indicated that TOO small diameter a tree (crowned back) resulted in thick wood in the middle taking the brunt, and the thinner edges taking much less strain, thus storing less energy.

  In TBB IV, he was leaning toward trapping the limbs for weight reduction with minimal loss of draw weight.

[Springbuck]

joachim, Baker only did the one test I remember with a poplar bow.  I don't have exact numbers, but he took a poplar bow and trapped the limbs.  Weight was reduced by something like 20%, but draw weight only fell by 6%, (or some such) and the bow took no new set.

  Really basic pyramids like you describe would be perfect.  I think you could design a practical test by making two bows, purposely over built to take low set, one trapped and one rectangle cross section.   Measure and shoot, then start trapping the square one in stages to obtain the back to belly ratios you mentioned,  and squaring the trapped one.  Then just chart what happens regarding limb mass, draw weight, and set.  You could do this in stages until they break.  Square the trapped one and then trap the new narrower bow again.