The truth of Stress Curve

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3-November-2019 (Sun)
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12-December-2019 (Thu)
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Rod Design by Deflection
In the world of designing bamboo fly rod, Everett Garrison invented his method to calculate a rod taper from the expected stress curve in old days. This method has been considered as a scientific method of designing a bamboo rod for a long time and it is still vital even now.
To brief the Mr. Garrison's method, assume that there is a rod which taper (dimensions) is known. As the rod is made from bamboo, the rod sections (each 5 inches length sections, for example) have weight. And the rod parts which are attached on the rod, e.g. ferrule (connection parts), guides, varnish, fly line along with the rod, all have their weight respectively. These respective weight will produce force of inertia when the entire rod is moved (cast) by the physical phenomenon of inertia. The force of inertia will generate a torque which we call as Moment. Each part of the rod will generate Moment, then he accumulats all the Moments which are generated by all the rod parts for each specific point of the rod (for instance, each 5 inches interval on the rod). When Moment value is calculated, the stress value can be calculated on the specific point of bamboo rod. The plot of this stress value on each rod point is a graph, which is called as Stress Curve. By looking at the stress curve, he could know what kind of rod it is.
In the beginning, it is hard to understand what the stress curve means. But after repeating to make rods based on the stress curves, one can gradually feel to understand the relationships between the actual feeling of the rod and the stress curve patterns.
Once we could feel to understand the relationship between the rod and its stress curve, we would like to draw a probable stress curve and want to reverse calculate its taper (dimensions) from the stress values on the rod. Mr. Garrison invented this method by using slide rule.
The truth of Stress Curve
The truth of Stress Curve No.2
Introducing DynaRod
Rod Deflection in Casting
Rod Action
Line Weight
Designing the Rod Angle
In more older days than Mr. Garrison's, the method of rod design was "Try and Error". In this method, he makes a basic rod. Then evaluate the rod and adjust needed dimension by flipping and casting. When he feels like that he would like to bend this part of the rod a little more, he planes out that part a little more and again evaluates the rod. Even if we use any kind of design tools, this factor may remain in rod making.
Well, let me introduce the design method which I invented.
Though I long used Mr. Garrison's method, I couldn't have a confidence if I surely defines the desired rod by means of his stress curve. I could feel that the stress curve may be all right but I could not be for sure if the rod is really what I desires. Then I started to doubt if this is the correct way. The stress curve might not be a should-be target to design a rod taper. It is because Mr. Garrison's calculation is for structural engineering which tries to calculate the internal force of stress within a non flexure materials. As the result, when a rod is fully deflected, the stress curve around tip front section goes high even though the tip front section is stretched out actually. Thus the stress curve which I draw when I design a rod, is also not a real one.
Mr. Garrison's Stress Curve
The two graphs below are made through Mr. Garrison's mathematics. One is the Stress Curve and the other is a rod deflection which is calculated from the Stress Curve.
The assumptions are: Payne 200 8 feet 3 pieces #4 line, line length to fish is 75 feet, rod movement is translated in the speed of 4G, the speed which forces the rod 4 times of gravity acceleration.
The word PH1-PH4 on the graph legend means that the rod movement is divided into 4 phases and the calculation is made for each phase. Phase 4 is the last phase of rod movement.
First look at the stress curve at left around rod point 0 to point 30. The stress values are around 25,000 psi (pound per square inch). It might over the breaking point of bamboo? This is caused by the structural engineering type calculation which assumes that the rod should not bend.
Though it is not meaningful, I drew a rod deflection graph from the stress values. Right side graph is the one. Though the rod moves in horizontal direction, its tip top faces downward at phase 4. In actual world, its tip top must face to the direction where the fly line is pulling, that is toward right horizontally.
click the graph to enlarge
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These graphs were made by a program, CastRod, which is previous version to DynaRod.
Though this is dynamic type calculation but the math is by the one of structural engineering.

I researched what can be the most practical objective which becomes the should-be target when designing a rod for more than 8 years. Consequently, I reached to the conclusion that the rod deflection be the most appropriate design objective as it can be equally seen by everybody. Under a certain assumption, if I can draw a rod which flexures like this and to this extent, it is good to have a program to reverse calculate the dimension of the rod from the deflection data. First I should think about the rod deflection and bend pattern as objectives of my rod. Once the objectives could be defined, a computer can calculate the rod dimensions.
Rod deflection is also difficult to draw. We cannot see how the rod deflects while casting the rod. But we can look at the deflection when our friend is casting. Anyway, it is sure that the rod deflection is more practical bjective than stress curve.
Then, I developed an Excel tool to draw an objective rod deflection. This tool can draw any kind of rod deflection in a good shape. The resulted data is passed to DynaRod and DynaRod produces the rod dimensions through making various complex calculations.
The most difficult thing in developing DynaRod was its dynamic calculation. Where time duration must be considered. The calculation is made by chasing the shape of the rod from time to time. This costs computer time a little but the result shows the realistic shape of the rod and stress curve. When a rod is fully bent, tip top will be stretched and the stress curve reflect this either.
Stress Curve of DynaRod
The next graphs are the output of DynaRod. Left is the one for rod deflection and right is corresponding stress curve. Assumptions are exactly same to the one which is shown above. Payne 200 8 feet 3 pieces #4 line, line length to fish is 75 feet, rod movement is translated in the speed of 4G, the speed which forces the rod 4 times of gravity acceleration.
On the rod deflection graph at left, horizontal fly line is pulling the tip top toward horizontal right direction. On the stress curves, the stress values of tip front becomes lower to show that the part is stretching from phase to phase.
click to enlarge
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These are the output of DynaRod
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