Del's Pyramid Taper Test!

[Del the cat]

Sometimes you just gotta do the test, all the theory and pontificating in the world won't make you right if it ain't so!
After some discussion on another thread I couldn't get a consensus on what was a good test.
So I made two symmetrical bows, straight tapers 40" long (plus 1" for nocks) tapering from 3" wide to nothing and the other from 1.5" wide to nothing.
I drew 'em on the tiller rig to 20" and 22" draw whilst videoing 'em with the camera position fixed on a tripod.
One thing that showed up is it's surprisingly hard to get 'em sawn out perfectly and mounted dead straight.
The result did rather shock me, the curves we near as dammit identical (within the positional/sawing errors I've just mentioned).
The pics shown are the 20" draw as I felt this was a more realistic draw. The 22" draw is very much the same result... damn near identical.
There have been plenty of learned papers written on this sort of thing, and as a kid I spent hours pondering if the centre width mattered as long as it tapered to a point, after all regardless of the grip width it would always be half that width at half that length... did it sort of automatically regulate itself?
Anyhow it only took me 40 years to do the test
Del
PS. Anyone who want's to say "I told you so!" be my guest ... but seeing is believing

[Hrothgar]

Interesting tests Del. Did you happen to check and compare the perspective weights when drawn?

[SLIMBOB]

I am wondering what your analysis of the test is.  As a rule I am not in the "pyramid with no thickness taper" camp as a practical matter, but I am curious about the physics of it all.
They both appear to be a tad round in the handle.  I would have expected the wider one to be less so.

[Gaust]

Never tried a pyramid.  I've read that you don't actually do any thickness tapering, just pick a dimension for draw weight and let it ride all the way to the tips.  Is that right?  Then maybe all you add is the grip lamination for thickness there, cut it out, and you're done?  Seems simple enough.  Would this work for any kind of wood?
George

[adb]

Didn't this just prove what we already knew?

[Del the cat]

Didn't this just prove what we already knew?

I don't profess to be able to speak for "We" !
Maybe you already knew it... I didn't... I didn't spend the time doing it on a whim.
I fact I've just re-done it setting up more carefully to get better pics so that I can be confident in the result.
I'm a great believer in the empirical but will allow others to draw their own conclusions.
Del

[Del the cat]

Interesting tests Del. Did you happen to check and compare the perspective weights when drawn?

Yeah, the wide one was much heavier (presumably twice the weight).
They are too light to weigh accurately.
Del

[Del the cat]

I am wondering what your analysis of the test is.  As a rule I am not in the "pyramid with no thickness taper" camp as a practical matter, but I am curious about the physics of it all.
They both appear to be a tad round in the handle.  I would have expected the wider one to be less so.

I've just re-done the test with a more careful set up. All it shows is that the skinny one has one limb stiffer than the other. It's difficult to cut a thin limb V accurately on the band saw. I think it's pretty conclusive that the grip width has little if any effect on the curve in a straight "taper to a point" design. It does effect the draw weight tho'.
There is no 'handle' as such and in the re done shots I actually support the centre on an off cut of arrow shaft.
they look pretty much arc of a circle to me (try holding a CD up to it). I've added another ipc with a circle centred on the draw point of the string...
In the re- done shots the draw length is half the bow limb length.
Mind... of course we all knew this 

[Gaust]

Thanks, Del, for showing us this.  Now I know.
George

[bubby]

Nothing wrong with challenging the status quo, if nothing else to prove to yourself what you think is right, not everything you read or see on the internet is true, thanks for doing the test now try it with a stiff handle

[DC]

Thanks Del, you saved me from sawing up my last piece of plastic(I can't spell polycarbonate)

[Carson (CMB)]

Nice simple test Del. Thanks for taking the time to share it with us.   
Glad you posted the second set of photos, much clearer to see just how near identical and nice the bends are.
While I didnt see it spelled out (which aint to say it wudnt spelled out  ), and not sure if it matters or not, but I am assuming these are the same thickness, is that right?

[bradsmith2010]

thanks Del,very nice test,,I really made things more clear for me about the tiller,, I appreciate your time and effort,, B

[Del the cat]

Nice simple test Del. Thanks for taking the time to share it with us.   
Glad you posted the second set of photos, much clearer to see just how near identical and nice the bends are.
While I didnt see it spelled out (which aint to say it wudnt spelled out  ), and not sure if it matters or not, but I am assuming these are the same thickness, is that right?

Yeah, cut out from the same sheet of plastic. (about 1/8" thick)
Del

[JW_Halverson]

To me this both makes sense and is utterly counterintuitive.  I think we all owe a debt of gratitude to Del for clearly illustrating the principle.