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English Longbow Help (with image)

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willie:
mike
does this progressive bend add anything to the performance or handling of the bow? could you point to a photo that exemplifies this nuance of tillering?
thanks
willie

Ian.:
Bend a small piece of wood and it will return to shape. Bend a massive piece of wood and it will break long before it bends much at all.

Wooden Spring:
We talk a lot about bows bending in an "arc of a circle" but the only true way to do that without the bow suffering undo fiber stress (exploding) is to taper a bow's width with a constant thickness. Whenever the bow's thickness is tapered, it will always bend into an ellipse provided that the fiber stress is even along its length.

Remember: R/T = E/2S
Where:
R = radius of curvature
T = Thickness
E = Modulus of Elasticity
S = Modulus of rupture

Your bow looks fantastic to my eyes.

willie:
Wooden Spring

"it will always bend into an ellipse....." seems like a bit of an absolute. I was under the impression that if the thickness taper is too litttle, then the bend happens more at the handle, and if too much, then more bending happens towards the tips. Isn't there a thickness taper that gives the circular bend? Of course we often taper both the thickness and the width, and I am sort of partial to a constant thickness taper, where the tips are 1/2 the thickness of the handle, combined with some width narrowing in the outer third of each limb,at least for a bow that is 2.3 longer than the draw length, as over drawing and under drawing seem to change the relative shape.

willie

Wooden Spring:

--- Quote from: willie on December 15, 2016, 03:52:13 pm ---Wooden Spring

"it will always bend into an ellipse....." seems like a bit of an absolute. I was under the impression that if the thickness taper is too litttle, then the bend happens more at the handle, and if too much, then more bending happens towards the tips. Isn't there a thickness taper that gives the circular bend? Of course we often taper both the thickness and the width, and I am sort of partial to a constant thickness taper, where the tips are 1/2 the thickness of the handle, combined with some width narrowing in the outer third of each limb,at least for a bow that is 2.3 longer than the draw length, as over drawing and under drawing seem to change the relative shape.

willie

--- End quote ---

Well, we live in a universe governed by laws, whereby everything that moves, moves according to universal and absolute principles established at creation, and mathematics is one of the tools that we have of making sense of those laws - the structure and motion of an archery bow are just as absolute as the laws of thermodynamics.

One may well get a thickness tapered bow to bend in the arc of a circle, but the inevitable result will be that it will suffer uneven fiber stress. It is the reason of uneven fiber stress that is why a Welsh Long Bow is not the most efficient of bow shapes. This is not to say that it isn't a "good bow," it's just not very efficient.

A bow's thickness may be obtained by
T = [(2S)(R)]/E
Where:
T = Thickness
S = Modulus of Rupture
E = Modulus of Elasticity
R = Radius of curvature at a particular point along the limb

It's width may be defined by
W = (6PD)/(S)(T)(T)
Where:
W = Width
P = Tension in string (about 12% more than draw weight)
D = Distance in inches from the fade to the string measured perpendicularly to the string at full draw
S = Modulus of Rupture
T = Thickness

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