Jim Utzerath is the engineer and bamboo rod maker that created FlexRod in the late 90s. He has graciously agreed to share the history of the program and some thoughts about the future of taper analytics. If you know Jim, be sure to thank him for blazing the deflection trail for us. He can be reached at jutzerath@execpc.com. Here's his note as I received it a couple days ago:
Random reflections on FlexRod by its originator
Eight years have passed since FlexRod was created. I thought that it had vanished entirely, but thanks to David Bolin’s persistence, it seems to be struggling for life. Looking back, I thought I would pass on a few thoughts that occurred to me during its development, why it became what it is, and what I hoped it would be. Some of these thoughts might duplicate those of the program notes but not all.
The FlexRod project started from a paper written by D. Y. Barrer (You can still find it online: http://users.cybercity.dk/~bcc25154/Webpage/barrer.htm) which proposed a method to evaluate the equations for strain in a fly rod. A copy was sent me by my friend Bill Fink. I originally followed the scheme of the paper and soon found better ways to accomplish the calculation. The method is really quite simple. The stress is first calculated using moments ala Garrison but taking into account different angles at which the forces are applied. Then the strain (or deflection) is calculated using Euler’s rule that the beam bends to a radius of curvature proportional (by its MOE) to the stress. Since the curving rod changes the angles to which the moments are applied, you need to compute the stress again, then the strain again, then the stress, etc. till both remain the same as they were in the previous calculation.
In the Barrer analysis the moment was applied as force field acting in either or both the vertical and horizontal direction similar to the acceleration force used in the Garrison analysis. Though not completely realistic as a description of the casting motion, this method of applying force has several advantages. It duplicates the Garrison stress analysis, it correctly depicts a rod deflected by having a weight hung from it, and it avoids questions about the location of the pivots (elbow/shoulder/wrist) of the caster.
I began to work on FlexRod to support some of my experimental work involving stressing bamboo strips clamped in a fixture under a dial indicator. For what is worth, the textbook solution really is pretty accurate though the derivation of the formula assumes small displacement. Next I tried to match some of the Garrison analysis software for an unyielding rod (That’s why FlexRod has an option to hold the rod straight.). The weakest link in the analysis is that you have to guess the modulus of elasticity. As it turns out, the MOE does not stay the same from fly rod to fly rod and it varies with the thickness of the strip. Enter Bob Milward.
Bob Milward, I learned, had spent three or more years of research and was consulting with experts in physics, wood science, and botany from universities in California and British Columbia. He had tested hundreds of very precisely machined bamboo samples. When I first phoned him, he was very cautious about discussing his work because he was about a half year away from publishing. I swore on my mothers blessed remains that I wouldn’t do anything with his information till well after the book was out; so we ran up some huge phone bills talking about things bamboo. It was about this time that I distributed my files as you see them now (without adding any of the intended MOE modification features) through my friend Bill Fink and some other folks attending the Catskill Gatherings. FlexRod has remained essentially unchanged except for the enhancements that David Bolin created.
What happened next? My biggest concern was the estimation of MOE. When Bob Milward eventually published landmark book, Bamboo: Fact, Fiction and Flyrods, he states on page 42ff that the modulus measurements made on his thin samples proved there was a loss of stiffness from rind to pulp (no surprise here) and a loss from top to base of the culm. He later on writes that the predicted MOE of an assembled rod section is not what he would have expected from his samples. DARN, we are still left with an incomplete understanding of the stiffness of actual fly rods and hence how they bend.
Excuse me if digress here to comment a bit more about some of Bob’s work. The discrepancies between the MOE of his prepared samples and that of his completed sections were discovered as he was finishing his work and was of great consternation to him. He offered several explanations in the book but none completely satisfactory. When we spoke of it on the phone I thought it had something to do with the machining of the samples which might have altered the distribution of vascular fibers. It became more apparent than ever, to me, that we had to study the bending of the finished fly rod.
Another interesting item that you will find Bob’s book is his analysis of the curvature of the rod during the casting process. He used a different formula to compute strain than the Euler curvature relation suggested by Barrer. Instead he ed the fly rod as if it were divided into short cantilevered beams. Remember, all analyses of these kinds the fly rod as a series of short pieces that can be analyzed as simple un-tapered geometric solids. Garrison used 6” straight pieces. FlexRod uses circular arcs (which can be flat as well) of 1” (or any other specified) length. This type of analysis, sometimes referred to as FEA, is expected to become more mathematically accurate as the length gets smaller; so, I included a feature in FlexRod that lets the user diminish or enlarge the size of the pieces. I tried out the cantilevered beam method that Milward employed in a modified version of FlexRod and was pleased to see that as the size of the divisions got smaller and smaller, the answers tended to become exactly the same as my calculations based on arcs.
Anyone who does much mathematical ing realizes that the results must be verified against other s and validated against experimental data. FlexRod was verified against some of the Garrison implementations and against my own beam bending experiments and gave me reasonable confidence in the answers. In doing a lot of examples with different lengths of elements, an unexpected result was that: as the accuracy improved, the errors in the tip division (easily seen in a Garrison analysis where you must ignore the tip stress) could be reduced by pretending that the rod was half a division longer than actual. I included this “correction” as an option in FlexRod. The technique can be justified because the “tip error” happens because we calculate the load (moment, etc.) at the ends of the section and the stress in the middle; so there is a half element discrepancy.
I then turned my attention toward the deflected shape of actual fly rods. This, in itself, is nothing new; various manufacturers have used deflection methods to test finished products. Some methods are quite detailed and are reported by Philips in his book Technology of Fly Rods. When I wrote to Bill Fink about the possibility of measuring rods being cast, he offered to photograph one of his quad bamboo fly rods being cast by one his friends (Tom Smithwick, I think). Bill, I should explain, has his own pet interests in stress analysis one of which is to be able to translate the action of rods with conventional hex cross-section into his 5, 4, yes 3 side geometries. We hoped to match the curve in the photograph with a something generated by FlexRod to see what we could learn in comparing a quad with a similar hex. The result wasn’t very satisfactory because of difficulties scaling and correcting for optical foreshortening, etc. Even after a lot of work, the answers didn’t look quite right.
I figured that we were getting ahead of ourselves. Eventually we would like to analyze the rod during the casting process, but we should start with static testing. Sidenote here: Even though we talk about acceleration forces in our more advanced calculation we are still performing an analysis based on principles of static mechanics. If the analysis were truly dynamic, we would have to consider other properties of materials such as viscous damping and things that people don’t usually measure. I suspect that the MOE of bamboo under suddenly applied stress is higher than the static values we now use. Similarly the tensile strength of bamboo is probably also dependent upon the speed at which the load is applied since impacts appear to be more likely to break bamboo than steady pressure.
About this time there appeared in Rod Maker magazine a series of articles by William Hanneman describing a method he called Common Cents or CC. Though I didn’t think that the technique was as exactly the ultimate analysis, it did add an additional measurement which helps to describe the curvature of the rod tip; and the whole technique was easy to perform. And it proposed to provide additional information namely: the line weight and the tip action. I hoped that if the CC method might become used regularly by a few cane rod makers, there would be an abundance of data to describe static deflection. Then if a few more measurements could be added to better depict the behavior of the mid and mid tip regions of the deflected rod at, say 50 and 75 percent of the action length we could have a useful stress/strain analysis. For those unfamiliar with CC, the fly rod is clamped horizontally and weights are added till the tip dips to a third of the action length. We record the weight and the angle that the tip makes with the horizontal.
My friend Bill again obliged me by trying to promote CC at several of the Catskill group gatherings. The reception, he reported was disappointing. I think the cool reception had more to do with the inability of CC to predict the recommended line weight that the makers expected. And so the attempt to promote widespread use deflection measurements among bamboo all but failed. If the idea had caught on, I would have suggested the additional deflection distance measurements that would have described the arc of the loaded rod in such a way that the desired modulus data could have been derived. Incidentally, the amount of work required to go from the deflection data to the modulus measurements was very time consuming so I admit that I might be rightfully blamed for letting the project die.
My final effort in the study of stress analysis consisted of some correspondence in a forum started by Mike Montagne. He wanted to spearhead some technical discussions of stress analysis in bamboo fly rod making. After a few weeks of participation, the group apparently dispersed or maybe they tired of my verbose commentaries and simply ignored me. Mike M, incidentally had his own analysis method based on a geometric curve describing a deflected rod. I was interested in finding out whether his methods were general enough to describe any fly rod, not just those of his own design. That question remains unanswered.
Till my grandchildren are old enough to wade into streams, I have set aside my planing forms and pursue work and family and other interests for now. However if there are persons reading this little essay that are interest in advancing any of the above ideas, I would offer a plethora of assistance for the asking.