Monday, 6 August 2012

Bow Geometry Explanation

I mentioned how adding a riser section changes the bow geometry in an earlier post, here's an attempt at a 'proof'
The diagram is just the top half of the bow, I'm assuming its lower half is completely symmetrical.
The black limbs at the top represent the upper limb of a bow at brace and full draw.(BOW 1)
The string is length L. and the full draw length is at B (On the big fat red horizontal centre line).
If we now extend the limb downwards into a rigid riser section,  also of length L (BOW 2), we see the string is now length 2L. The limb bends exactly as it did before to point A (not strictly true, due to the slight change of string angle, but this is my simplified model)
Now drawing an arc for the string of radius 2L centred on point A, we see it intersects the new horizontal centre line at point D which is our new draw length.
So you can see it is drawing further.
If the limbs return to brace at the same time, then the arrow is travelling further in the same time and is thus faster!
Blimey, my brain hurts now.

1. This comment has been removed by the author.

2. But surely, if you extend the flexible limb so it is the same length as the total of limb+riser then the draw is even greater due to the angle of the string.
So I am unsure of the point you are trying to prove.
If however, you are limited by available materials to shorter limbs of lesser strength, then a static riser will increase the draw & speed of cast & thus power of the bow.
Theoretically of course as the the length of the splice (and subsequent loss of length of 'active' limb)and outer limb mass to speed ratio would effect cast too?

Forgive my presumption, these are just my views. After all you are the bowyer not I.
(sorry too many typos in original comment)

3. Indeed you are correct, and personally I tend to favour an arc of a circle tiller which will share the stress over the longer limb.
I was trying to show a possible reason why 'eliptical tiller' and a stiffer centre section is seen as better for flight bows. But really it's to illustrate how counter intuitive somethings are, and how (as the Who so succinctly put it), the simple things in life are all complicated!
'Common sense' might lead one to think that if the working part of the limb remains the same then sticking a stiff section in the middle would merely create a more cumbersome bow without changing the performance.
I don't usually go in for maths or geometry, being of the empirical school of design. I'd mentioned the effect in a previous post and felt obliged to justify my assertion.
Even the most learned dissertations on bow geometry seem to make a lot of assumtions and simplification, although I expect moder CAD systems can do a better job of the analysis.
Fear not, I'm back to honest simple bowmaking!

4. It was fun pondering on the topic, as it rapidly progressed into insane complexity. :)

5. I don't think the arrow should go faster in the end, since I'm pretty sure the pull over the now longer distance will be weaker to make for the same work (or amount of energy)in the end. The bow should be more gentle to shoot, though. But then, the angle of the string is different. And the string is heavier, since its longer by the lenght of the riser. Lots of things play in. The whole thing is so complex it can only be handled by intuition.

6. Bows are built backwards. To control arrow flight in the acceleration phase, is what bows are all about. Think what we are doing by pushing an arrow from the farthest tips of an object(bow) as possible, and expect perfect symmetry.
Start over: reverse the pivot points by moving the tips to the hand grip area, and securing the spring member at the ends of a rigid member that has the handle in the middle. Now redesign the cam take up function to accommodate the new string speed and add dampeners to end-of-stroke to eliminate shock wave effects.
This is a paradyme shift for the bow making industry, but so are cell phones to the land line industry.
Get a grip on leadership, with your experience, developing the next gen bow is clearly in your lap.
God's speed