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Ash Warbow
willie:
--- Quote from: RyanY on March 09, 2021, 07:48:01 pm ---Willie, that analysis of replica dimensions sounds super interesting. In your diagram is f1-f2 the nock to mock length?
--- End quote ---
No, the diagram is a generic illustration of how to draw an ellipse.
there is a bit of trial and error in locating the nails for any particular ellipse, But in this example for a shallow ellipse, I would proceed as follows.....
72" nock to nock distance times 1.2 is 86.4"
draw a line 86.4 and find the midpoint at 43.2" from the midpoint measure out 42? inches each way and locate your nails. your string will need to be 86.4 long. it should draw an ellipse enclosing the line. The center 60" of one side of the ellipse is all's that's needed. you only need the center 60 " because the tips need to be stiffer and not wrap around the ellipse all the way.
the arc will be shallower if the nails are further apart, and deeper if the nails are closer together. but the 1.2 factor holds true fairly well for a bow that is somewhat stiffer in the handle area, whether representing a shallow brace or closer to full draw.
A more bendy handle will be an ellipse of different proportion to the nock to nock length.
RyanY:
How did you come up with the 42” from 43.2? Is there a ratio you follow? Seems like shorter bows of the same draw length would need a more circular shaped ellipse.
willie:
ryan , 42 is just a guess for creating a shallow curve, maybe less than brace even. You just move the nails in to generate a curve that will match the bow at a longer drawlength. a shorter bow will have a different major axis length ellipse.
Del the cat:
Regarding the post about Pyramid taper. (We all realise of course that a warbow isn't a pyramid bow)
Not sure I agree with the mathematical analysis!
You have to remember that maths is a tool to explain reality...not the other way round!
I reckon any mathematical analysis of a bow is a series of compromises and simplifications.
Let's just look at a real life test:-
https://bowyersdiary.blogspot.com/search?q=pyramid+taper+test
Can you really see or measure any deviation from arc of a circle?
Mind TBF
Having reviewed the Mathematical analysis a bit closer I see two huge difference.
1. The Mathematical analysis include a stiff grip section (yes ok... that's actually far more realistic)
2. the work was done by Hickman! I'm a great fan of Hickman therefore I beieve it! ;D
It rather reminds me of the story about the mathematician and the engineer in the bar. They are 32' away from the bar.
The mathematician bets that the engineer can't get to the bar if he moves half the distance towards it each time he moves. The wager being to buy the beers.
The engineer accepts the bet, despite knowing that theoretically he will never reach the bar.
He walks 16'...then 8'... then 4'...then 2'...then 1'...
Having moved 31' he calls to the barman, reaches out his arm and picks up the beers.
It just shows that close enough is good enough for many real life applications. ;D
Some very good discussion on this thread.
I especially like Willies's work with the Mary rose averages :)... but is "slightly stiff at the grip" the same as "elliptical"... >:D (shut up Del!)
Del
Please note: I always reserve the right to be wrong!
Digital Caveman:
I'm starting to understand the Hickmann adjustment better. The bit about the cantilever beam is what I was thinking of when I said that the bow should have straight sides, but I didn't account for the component of the force pulling the limbs inward, only backward. The component inward would be cancelled out on a straight cantilever beam, but not on a bending bow. I need to figure out more math before I can quantify this.
This all makes sense because if you sharply bend a straight slat between your hands you get most bend in the middle, whereas if you bend a straight cantilever beam you get most bend and the base.
This would imply that bows with greater bend should have more mass in the center. Think of the west coast paddle bows.
I'd like to figure out a way to find width as a function of distance from the handle for any given bow, assuming a flat limb, so that the stress is uniform across the limb.
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