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Mathematics and Fly Fishing

The Deflection Index

Knowing the stresses for a deflected rod, it is fairly simple to calculate the diameters for the rod. The procedure is very much similar to how we calculate a rod from a Garrison stress curve.

But how do we in even the most simple case of uniform stress for the whole length of the rod decide the value of the stresses.
Looking at the stress profiles of Garrison's rods, there is no apparent system in the constant stresses for the rods.

A systematic search after a dimensionless expression, which would give a clue as to how we can calculate one rod from another, showed that the deflection divided by the length used for calculating a rod, did not change much, they were all equal to 0.325 +/-8%.

Definition: The deflection index is the relative deflection divided by 0.325.

It is convenient to define the Deflection Index as the relative deflection divided by 0.325, the Index for Garrison's rods will then vary from 0.92 to 1.08, and the Deflection Index = 1 can be interpreted as an medium value for Garrison's rods.

The procedure for calculating a rod by NewUni is:
The program calculates a rod for a uniform stress of 120,000 oz./sq. inch, it then modifies the stress by a fraction of the difference between the calculated and required Deflection Index. The procedure is repeated till the difference in Index is < 0.0001.

An additional programming loop is required, if we have a stress reduction in the tip region.

The Rod Tip