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Mathematics and Fly Fishing

Introduction

What is presented here is a tool for investigating rod tapers and calculates new tapers based on the assumption that the stress distribution in the deflected rod is what contributes most to the rod action. The programs are based on classical theory of elasticity as taught in elementary engineering and in advanced bike-mending.
By coincidence? The programs find a very interesting and simple explanation for Garrison's tapers.
Looking at programs available to rod builders I have to ask myself: was Garrison the only engineer ever to build fly rods.
I am not a rod builder myself. So let me say this before someone else do I have absolutely no idea of how a fly rod should be designed. Of course I could not write about all the thoughts behind the programs without expressing some beliefs; but regard it as ideas to consider and not as opinions of an expert. Consequently, you may find yourself disagreeing with my conclusions, or my approach to the subject. If so, I look forward to hearing from you. It may be that we will end up disagreeing, but I am certainly willing to hear your critique. If you think that something needs to be added or corrected, please contact me and I'll attempt to fix the problems in a future version.

It all started in 1994, when I first met Preben Torp Jacobsen. I did not know the first thing about fly-fishing. I had just finished an instruction class in fly-casting and had begun reading everything I could find about fly-fishing including rod design. I knew more about mathematics, than I knew about fly-fishing. So I told Torp that I had found some errors in his book on rod building, to which he answered: "I know, but can you do it better?"
I accepted the challenge and for a couple of years we exchanged programs on rod calculations.
It was Torp's idea, that all the secrets of a bamboo fly rod was to be found in the static deflection curve. So I started looking for a way to calculate the deflection using a Commodore 64. When I finally succeeded, I could calculate a deflection curve in about 45 minutes.
Later I got a PC and wrote the program in Pascal. It was Torp's idea that we should switch to Excel.
The programs are a result of Torp asking questions and me trying to come up with some answers. Torp is still asking question, and I am about to run out of answers.

The Garrison Stress Curve