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Verifications

Purpose

The purpose is to demonstrate how verification of the simulation model has been conducted and to highlight remaining uncertainties in need of further work.

Background

Quantitative verification of real casts requires simultaneous measurement versus time of:

· Hand movements at the rod handle (rotation and translation).

· Hand movement hauling/feeding line.

· Rod and line positions.

Also, rod, line and fly data must be known with sufficient accuracy (diameter, mass per unit length and bending stiffness). Currently, no complete set of data that can be used for verification of a complete cast exists to my knowledge.

From a simulation perspective the uncertainties to be verified, may be summarized as follows:

• Is the model correct / is reality described by the equations?

– Equations of motion (Newtons equations), YES!

– Kinematic equations, YES!

– Bending behavior of line and rod. Approximate.

– Air drag is based on experimentally determined equations. Approximate.

• Are the equations solved correctly?

– Extensively checked, YES!

Method

Verification is currently pursued as follows:

· Quantitative verification on parts, see examples on fly rod and falling line below.

· Animated casts are evaluated to agree qualitatively with observations.

· Around 25 test cases have been derived. These test cases represent simplified (but relevant) situations for which exact solutions can be derived. Numerical results obtained by the simulation model are compared with exact solutions. The test cases verify that the equations are solved accurately (verifying that the numerical scheme is 2^nd order accurate), see examples below.

· Sensitivity analyses on input data that have not yet been verified quantitatively.

Quantitative verifications:

Static verification of fly rod

Dynamic verification of fly rod

Falling horizontal line

Test cases verifying that equations are solved accurately

Static, hanging chain

Static, towed line

Static, non-uniform beam

Dynamic, oscillating beam

Dynamic, hanging chain

Dynamic, travelling wave

Sensitivity analyses

Fly line bending properties

Modeling of axial air drag

Concluding remarks

· Correct numerical solution of the equations has been verified for all terms. Six examples are given as examples of the methodology above.

· The modeling of the static and dynamic rod properties has been concluded to agree with experiment within about 3 %. Therefore, the fly rod is considered to be calculated with sufficient accuracy.

· The modeling of bending stiffness for the fly line is using a Young’s modulus for which no accurate experimental data is at hand. However, the sensitivity of a calculated cast has been shown not to change significantly by changes in the Young’s modulus. Therefore, the bending stiffness is considered to be calculated with sufficient accuracy.

· Normal air drag has been verified with the falling horizontal line experiment. Experimental data of normal drag versus Reynolds number have been investigated by many workers and been reported in the scientific literature. Therefore, the normal air drag is concluded to be modeled with sufficient accuracy.

· The modeling of axial drag, however, is considered as the only remaining uncertainty of significance. More work is encouraged to decrease this uncertainty.