| Home | Mathematics and Fly Fishing The Stress Profile

As in all theories, let us start with a definition and a theorem.

Definition: The stress profile is a curve for the stresses in the deflected rod; but without specifying the size of the stresses.

The Bike-Mender's Theorem: The deflection and the stress distribution (the stress profile) in the deflected rod determines the action of a rod.

The BM-theorem is equivalent to the Garrison/Carmichael theory, that the rod action is determined by the Garrison stress curve.

The important difference between a Garrison stress curve and the stress profile is, that the Garrison curve is calculated using arms of moments without considering the deflection, that makes the stresses fictive and the curve is only valid for the rod for which is was calculated.
I do not reject the Garrison stress curve, but I caution the use of it.
Knowing the Garrison stress curve, we can calculate the stress profile, and vice versa.

The programs do not consider a swell a the bottom of the rods. In cases where it is obvious, that the Garrison taper at the bottom is starting to swell, the diameters have been changed to obtain a straight taper down to a point 20" from the butt. This is in agreement with Garrison's remark, that the tapering at the bottom should be almost straight. Ref.:Garrison, page 237. The straight taper at the bottom is a consequence of the stress being uniform.
A Garrison stress curve for a rod with light tip will transform into a straight line in the diagram for the stress profile.
A Garrison curve for a regular or heavy tip will transform into a straight line for the main length of the rod and then decrease as a smooth curve.
Irregularities in the stresses will make themselves apparent in a similar way in both diagrams.
Look at the diagrams for 206 further down.

A frequently asked question is: How important is it, that the Garrison stress curve is smooth -without humps?

The answer is: We don't know how much we can deviate from the theoretical curve without changing the action of the rod. But humps on the curve will change the curvature of the deflected rod, it will not be noticeable to the eye - but the deflection curve will be wavy.
On the other hand, just removing the humps from a wavy Garrison stress curve may not result in a better rod. It could be that the points that look like humps were the points that charaterized the action of that particular rod, and the points that looked most smooth were the points that should be changed.

Garrison Rod 193

The first row in the tables above show the diameters of Garrison's rod 193.
The second row has been modified by an amount less than +/-0.00049", so it has no effect as far as the rod builder is concerned. In fact the rod builder will say that the two rods are identical.
When we look at the stress curves below, an idea of how Garrison designed his rods emerges.

Changing the modified rod diameters less than 0.00040" in four places, turns the stress curve into a straight line.

When we consider, that the stress curve for the deflected rod is calculated from classical theory of elasticity, well known to Garrison, it will be difficult to reject the hypothesis, that Garrison's basic idea was to calculate his tapers to give a uniform stress distribution in the rods.
The diagram below compares Garrison stress curves. The rod 193 is calculated using Garrison's truncated diameters the other is calculated by the program NewUni.

Garrison Rod 201

This was Garrison's favorite fly rod, built with what he called a "progressive" taper.

Clearly, the main part of the rod must have been calculated for a uniform stress.
That leads to the conclusion, that a "progressive" taper is just another word for uniform stress.

But how do we interpret the stress at point at 5" and 10"?
If we use NewUni to calculate the rod with a tip factor = 0, we get a difference in diameters in two places.
The Garrison curves below show, that something special has been done to the diameters near the tip, a feature that is characteristic for many of Garrisons rods.

Garrison Rod 206

Each of Garrison's rod tapers presents a puzzle.
For the 206 the solution could be that the stress reduction starts at 30" below the tip, with a tip factor = 5.
There are other possibilities. We could try calculating a best fit for the stress profile, but it would result in higher stresses for points 5" and 10", Which would be contrary to everything Garrison said.

I do not want to use the easy explanation, that some diameters are miscalculated. On the other hand, it would be strange if there are no calculation errors. We all made calculation errors in the pre-computer age.
And come to think of it, it's still possible.

The diagram shows, where we will get a difference in diameter.

The difference between Garrison's 206 and the rod calculated by NewUni is not significant. Except for one point, they are within the tolerances obtainable even by a skilled rod builder.

A closer agreement with Garrison's diameters can be obtained by having Excel calculate a trendline for Garrison's stress curve, from which UniRod could calculate the corresponding diameters. It may sound like a good idea, but it is not.
The purpose is not to make a program calculate the Garrison tapers, we have them already in his book.
The purpose is to find the ideas behind Garrison's design.

The Deflection Index

This page was modified August 11, 2001
Copyright © 1998, Falka Gregersen. All rights reserved.