Even as a kid making crossbow prods I wondered what was the optimum taper on a bow limb of even thickness, or did it matter?
Last week there was a thread on Primitive Archer (PA) which skirted around the question and some people mentioned learned papers or said they'd done the test but only hinted at the result. Only one person had the balls to say they thought it didn't matter.
Or will the narrower bow bend more like a dead straight bow with most bend in the middle?
Why can you never find a straight answer to the simple question?
Well after 40 years I've done the test!
Two test bows 40" long (plus 1" for tiny slim nocks) one tapering from 3" at the centre to zero and the other from 1.5" to zero. These were sawn on the bandsaw from Polycarbonate sheet. The sawing isn't perfect so the tiller isn't exactly symmetrical.
Just for completeness I've done a parallel limbed one. The difference in curve is clear to see.
The curve is near as dammit identical within the limits of my sawing.(Especially considering the huge difference in width at the centre)
One helpful soul on PA said, "Doesn't this just prove what we already knew?"
There is a huge difference between being directed to learned papers and having people allude to the fact that they've done it and actually seeing the test.
On a bow limb of constant thickness tapering to a point, does the width of the limb at the wide end change the curve of the limb?
No not with the constraints of a realistic bow limb and a realistic deflection ( according to this test... terms and conditions apply etc!)
Does it effect the draw weight? Yes.
Now we didn't need any differential calculus for that now did we?