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Verifications

Purpose

The purpose of this section 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 density 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 to input data that has not yet been verified quantitatively.

Quantitative verifications:

Link to: Verification of fly rod

Link to: Falling horizontal line

Test cases verifying that equations are solved accurately:

Link to: Static, hanging chain

Link to: Static, towed line

Link to: Static, non-uniform beam

Link to: Dynamic, oscillating beam

Link to: Dynamic, hanging chain

Link to: Dynamic, travelling wave

Sensitivity analyses:

Link to: Fly line bending properties

Link to: 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 static and dynamic rod properties has been concluded to agree with experiment within about 0.2% and 4.0% respectively. 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 has been reported extensively in 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.