Measurement of Fly Rod Spines Graig Spolek

Modern fly rods Hollow, tubular, and tapered Manufactured of carbon fiber reinforced plastic Formed by layering pre-preg (graphite imbedded cloth) around a mandrel

Mandrel Pre-Preg

Finished Rod Exhibits: Variable Diameter Variable Wall Thickness

Increasing Wall Thickness Wall thickness adjusted by varying overlap of pre-preg 3 wraps3 ¼ wraps 3 ½ wraps

Rod Spine Preferential plane of bending Align rod hardware to maintain bending during fish fighting that causes static bend in rod.

Rod Resists Bending in this Direction Rod Freely Bends in this Direction

Increasing Wall Thickness No Spine Increasing Spine Maximum Spine Decreasing Spine No Spine 3 wraps3 ¼ wraps 3 ½ wraps

Push Down Here Hold Tip Rotate Rod Rest Rod Butt on Floor Method for Location of Rod Spine

Static test Yields average spine orientation over whole rod Maximum influence of spine orientation at point of maximum deflection

Measurement of Rod Spines Measures local spine Measures magnitude of spine by comparing maximum and minimum force required for specified deflection Allows location of spine orientation

 F L Axial Rotation Rod

Model of Spine Due to Pre-Preg Overlap Develop model of material distribution Calculate Moment of Inertia (I) due to distribution of material Accommodate different orientation

Model Inputs Measured from actual production rods Outside diameter - D O Wall Thickness - t Angle of Layer Overlap - θ

DoDo θ t Outside diameter - D O Wall Thickness - t Angle of Layer Overlap - θ

Comparison of rod section to model

yiyi dA i

yiyi

MODEL RESULTS  F L

C, δ, E, L = constant

COMPARISON: MODEL & EXPERIMENT Experiment measures: Model predicts:

RESULTS 1234 PointRod 123Rod 114Rod 117Rod 118Rod 122 ExptModelOverlapExptModelOverlapExptModelOverlapExptModelOverlapExptModelOverlap Missing Missing

QUESTION: Do these agree? Can the differences be attributed to measurement uncertainty or is the model incorrect?

Uncertainty in Moment of Inertia

Estimate for Partial Derivative

For small individual uncertainties

So the uncertainty in I can be estimated by the root mean square of the finite perturbations in I, ΔI, due to the measurement uncertainties

DoDo θ t Outside diameter - D O = 0.350” ± 0.003” Wall Thickness - t = 0.028” ± 0.004” Angle of Layer Overlap - θ = 90º ± 5º

Estimate of ΔI max DODO t (n=4)θI max (*10 -5 )ΔI 0.350”0.028”90º ”0.028”90º ”0.028”85º ”0.032”90º185564

Estimate of ΔI min DODO t (n=4)θI min (*10 -5 )ΔI 0.350”0.028”90º ”0.028”90º ”0.028”85º ”0.032”90º167552

The final result is the ratio of the inertia values

Substituting values

Final value for ω Ratio

Comparison of Model and Experiment Model Uncertainty:± 6.26% Experimental Uncertainty: ± 5%

END