REALLY tiller on the edges?

[Del the cat]

The statement "The curvature will not change by narrowing the triangle" (by Asharrow) caught my eye.
I'm not sure I agree...
I'd already been considering this subject, indeed I've been pondering it for about 50 years.
There must surely be an optimum taper for a bow of even thickness to give the arc of circle curve. ( ? )
IMO this is self evident because if you take the taper to one extreme* e.g zero taper (parallel) we all know most of the bend is near the grip.
OR... maybe the whole thing is self compensating and the theoretical taper is always to zero tip width and the actual angle doesn't matter ...
It's one of those things I mean to try sometime as I have a load of polycarbonate sheet which could be cut out into nice trial shapes.
Del
Of course the real extreme is tapering the wrong way with tip wider than grip

[Jim Davis]

I highly recommend Paul Klopsteg's review of this subject in Archery the Technical Side. Clarence Hickman looks at it too in the same book. Also, a look at the mechanical data for flat springs in Machinery's Handbook is revealing--and encouraging.

Jim Davis

[George Tsoukalas]

Good observation, Del. In a pyramid bow the tiller should be rounded. That means the wider, near handle wood needs to do its share of the bending. Otherwise, set will be impacted.
Jawge

[Del the cat]

Right let's design an experiment!
My polycarbonate sheet is 3mm thick.
I can cut out several bows 40" ntn . If they are all 40" ntn with no grip at all, (e,g straight line symmetrical taper from the centre line to the tip) that's one less variable to consider.
What do we think is the best taper?
What is the best starting width for a 20" limb?
I'd suggest maybe going extreme as we can cut 'em down after.
Say 3" wide tapering to 3" (e.g.Parallel, although this may break... mind polycarbonate is pretty tough)
Then 3" tapering to 2"
3" tapering to 1"
3" tapering to 1/8"
I can use the same string on each and a low brace, say 1" and draw to 16" ?
Now obviously I don't want to do a load of work and have folk say I should have done it different... so if we reach some sort of concensus I'll do the test and take the pics. I can keep a fixed camera set up.... heck I can even take video, edit it togethjer , put music to it and release it in time for Christmas.
What do the gang think?
Del
(IMO. A well designed experiment trumps pages and pages of theory)

[DC]

I think that in order for it to be an arc the taper has to go to zero. So I think you need to cut a poly limb say 4" tapering to zero, bend it, take a picture, slice it in half(2" to zero), bend it , take a picture and then do it again. That will give you three pictures to compare. I'm not sure what the 3" tapering to 1" will do. It might be an arc too

[bradsmith2010]

if the wood is consistent in density etc etc,,you can cut it out and it will be tillered,, but wood usually has variations from one part of the stave to the other,  then you have too look at how it is bending and remove wood as needed,,, part of the limb may react to the compression differently and start to take a set more than the other,, then it will need to be adjusted by eye,,,, not a caliper,,

[Knoll]

Or make polycarbonate limbs with profile similar to what a bow's would be.  Ala, 3",2", 1" tapering to 3/8".

[Del the cat]

Or make polycarbonate limbs with profile similar to what a bow's would be.  Ala, 3",2", 1" tapering to 3/8".

Yeah, that's reasonable.
Any other offers? 4" to 3/8" ?
The more extreme the variation the easier it will be to see the change..
Maybe 4", 2" and 1" all going to 3/8 ?
Del

[scp]

I gather the objective of experiment is to verify that "The curvature will not change by narrowing the triangle" (by Asharrow). If so, I think it would be easier to model just one limb and even simpler if you model one lengthwise half of one limb. That way you only need to cut one straight line differently for each test, leaving all other lines straight and perpendicular to each other. You can even use the same material for all tests, cutting it narrower for each test and recording the curvature. Good luck.

[Del the cat]

The purpose of the test is simply to see what curves result and which is the best approximation to an arc of a circle.
It can sometime be a mistake to assume the result before the test as it can lure one into misinterpreting the result to favour one's preconceived notion.
But in reality, I'm sure we all know what we expect to see .
(My view is that narrowing the triangle WILL change the curve (but tell anyone I said that  )
We should each draw our expectations and seal them in a manilla envelope only to be opened when the experiment is complete in the presence of the Great Panjandrum himself! A gold star can be awarded to the closest!
(Sorry drifting off a tad there... better get back to cooking the chilli  )
I'm off on a shoot in Windsor Great Park tomorrow*... so I can't do it then...(hope maybe Monday)
Del
*We are registering for the shoot at the barracks of the household cavalry and they are going to arrange a cavalry charge at us!!! (We won't be allowed to shoot at 'em) I hope to get some video for the blog. (I'll be taking spare underware )

[bubby]

this is all good and well, but with all the variables in a stick of wood I'm not really sure this experiment is really going to prove anything with regards to a wood bow

[Del the cat]

this is all good and well, but with all the variables in a stick of wood I'm not really sure this experiment is really going to prove anything with regards to a wood bow

Whaaaa?
That can't be right.
We can't all swan through life muttering mantras like.... "front profile dictates tiller" and "Pyramid bows should be arc of a circle " without trying to pin some of it down a bit.
How "pyramid" is Pyramid"? After all a parallel limb is just a 0 degree taper!
If we taper to zero thickness maybe it's automatically right.... but how wide do you start?
I'm all for practical rather than theory, but an empirical test like this could actually show us... how a simple board bow should be such and such taper )or thereabouts.
Sure, we don't have to all build 'em like that that, but knowing the optimum can help when we have to make compromises.
Mind, having said all that I take your point.... you can only use the wood in front of us.
Now look what you've done...
I'm arguing with myself...
No I'm not!
Yes I am....
Del

[bubby]

Del I propose someone get a fully quartersawn board, any flavor will do, rip them into let's say 1/4" thickness's for four tests, then cut your front profile taper in diminishing widths, at least then you are using the same materials that the bows are made of, I know I've made a lot of board bows in pyramid style with the working limbs ripped on a tablesaw and they don't always have "perfect tiller" like mentioned in the bible's, seems like most guy's leave the last six or so inches stiff anyway so that kinda screw's the pooch as far as " front profile dictates tiller" and "pyramid bows are arc of circle" anyway, righhhhht

[DC]

Oh Bubby, that's a waste of a perfectly good piece of wood. Nobody gives a hoot if we waste a chunk of plastic. Besides we're trying to prove an idea so we need the most homogeneous material we can find. Once we prove what a "perfect" material can do then we can apply our new-found knowledge to wood. Not that it matters, I'll still tiller by bend.

[DC]

Sorry Del, I kept saying "we" as if I had something to do with this experiment.