Ash Warbow

[willie]

the ellipse shown in the post above is an example of how to draw one. It is not intended to represent any particular shape related to bows.

Yes, nice... but that's the problem with ellipses... just how much ellipse?

Del, I reviewed data collected on many of the mary rose warbows and averaged thicknesses widths and lengths to construct a "typical" example. I then entered the dimensions in a spreadsheet program to look at the bend profile and found a slightly stiffer handle area. The bend, at any stage of tiller, from a few inches to full draw can be fairly well seen in an ellipse with a major axis length 1.2 times as long as the nock to nock distance of the bow.
The height of the ellipse, will of course, vary with the stage of tiller. A flatter ellipse needed to judge the bow at brace height, etc.

As you note, some prefer a rounder full draw bend, but knowing what the braced bow bend should look like with out having built a lot of bows by the trial and error method is difficult to anticipate. I do know that many who set out to build warbows will often end up with a bow that bends too much in the handle. I have offered the 1.2 as a reasonable reference  for a beginner asking for advice.

Of course the other problem is how far round the ellipse do you expect the bow to follow... obviously not right round to the horizontal line PQ, but the shorter the portion of the ellipse that is chosen, the closer it becomes arc of a circle.

The 120% makes a very nice shape, but you will have to ignore the last 6" or so on each tip. let them be straight and not bend around so much as the ellipse.

[William M.]

willie, what would you recommend according to my last video? Should I take more away on the entire bow?

[willie]

William,

I am in agreement with Ryan, in that I find it hard to see well what is happening in your video. I do believe if you have something drawn out on a backdrop behind your tiller tree, it will be useful. I find when I tiller, I have to look at it multiple times and in different lighting.

[William M.]

Okay thank you! Today I had no time working on the bow. Tomorrow I gonna use the string and nail technique you wrote a few days ago. Maybe I gonna put a light directly over the tillerboard. Since the light right now is not in the middle of the tillerboard and throwing a wrong shadow on the bow

[RyanY]

Willie, that analysis of replica dimensions sounds super interesting. In your diagram is f1-f2 the nock to mock length?

[willie]

Willie, that analysis of replica dimensions sounds super interesting. In your diagram is f1-f2 the nock to mock length?

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! 

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. 

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"... (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.

[willie]

re: limb taper

the post linked below shows the width and thickness tapers of the "bow" I profiled in the spreadsheet and fitted the 1.2 x ellipse to.

http://www.primitivearcher.com/smf/index.php/topic,61640.msg862289.html#msg862289

[RyanY]

Del, Certainly those polycarbonate bows are close. Close enough for a pyramid taper to be "practically" even in thickness taper. I do notice some irregularities in the shape. Looking at both photos, one limb appears stiffer in the outer limb as indicated by Hickman. The other appears weak almost mid limb with more space between the circle and the tiller at that point (not sure what's going on there). Could be asymmetries but the point was not if it was practical or not, just that it's not entirely true that a straight profile will result in a perfectly circular tiller in a bow limb.

[Del the cat]

I think you can fit a better circle to the top one... (I'll do it if you like)
But I'd like to see the corrected pyramid fitting better!
Del

[William M.]

The radius of the circle is half the length of the bow?

[Digital Caveman]

No, the circle radius is unrelated, it changes based on how far the bow is drawn.