1. Measurement of Fly Rod Spines Graig Spolek

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

3. Mandrel Pre-Preg

4. Finished Rod Exhibits: Variable Diameter Variable Wall Thickness

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

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

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

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

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

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

11. 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

12.  F L Axial Rotation Rod

13. 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

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

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

16. Comparison of rod section to model

17. yiyi dA i

18. yiyi

19. MODEL RESULTS  F L

20. C, δ, E, L = constant

21. COMPARISON: MODEL & EXPERIMENT Experiment measures: Model predicts:

22. RESULTS 1234 PointRod 123Rod 114Rod 117Rod 118Rod 122 ExptModelOverlapExptModelOverlapExptModelOverlapExptModelOverlapExptModelOverlap 11.201.111201.141.08451.04 Missing 1.111.071201.131.1080 21.131.14901.161.10601.151.051501.181.11901.101.12105 31.101.13601.141.09751.061.001801.061.09501.111.09245 41.101.09301.12 1201.081.051501.04 151.06 Missing

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

24. Uncertainty in Moment of Inertia

25. Estimate for Partial Derivative

26. For small individual uncertainties

27. 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

28. 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

29. Estimate of ΔI max DODO t (n=4)θI max (*10 -5 )ΔI 0.350”0.028”90º17910 0.347”0.028”90º174150 0.350”0.028”85º17901 0.350”0.032”90º185564

30. Estimate of ΔI min DODO t (n=4)θI min (*10 -5 )ΔI 0.350”0.028”90º16230 0.347”0.028”90º157746 0.350”0.028”85º16158 0.350”0.032”90º167552

31. The final result is the ratio of the inertia values

32. Substituting values

33. Final value for ω Ratio

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

36. END