Good post with valid scientific considerations. Perhaps stiff and fast are more closely associated than I would propose by such thinking. However I feel that the rate of deflection of a uniform rod with a load on one end is not an applied analysis of what happens during fly casting because of the effect of rod taper and feedback to the caster who operates the tool.
The player with the biggest arms is not the best man to put onto the mound, technique has a lot to do with it not just brute force.
I have to believe there is some critical thinking being missed with the classic stiffness model above. So how do we factor taper and it's effect on loading the rod and transitioning energy into the loop in our analysis?
Let's consider the level line verses a weight forward line - the taper makes all the difference in the world in the way the line transfers energy along it's length. And although the modulus of graphite does not change over the length of the rod, the flexibility of the rod and the way it transitions energy along changes proportionately to the taper and graduation of taper thus it is unndeniably a factor in the way a rod operates.
Where material stiffness varies little, taper varies much more between rod designs. Let's say that one rod has a very stiff butt section that tapers parabolically to a very soft tip. Another has a stiff butt section tapering uniformly (circularly) to a stiff tip. A third is a level rod as in your example. Each of these rods will have a dramatically different feel on the wrist and thumb verses the other and a dramatically different effect on the line. In fact the third one, the uniform stiff rod, would essentially be useless.
My (anecdotal) experience has been that a soft rod loads up but does not unload well unless you baby it, a stiff rod does not load well unless you drive it harder than you need to.
In the middle are several rods that I consider not stiff, but quite fast - meaning they load comfortably but recoil with a vengeance due to good taper design.
Crap there's that irony again!
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