measurement of fly rod spines graig spolek. modern fly rods hollow, tubular, and tapered...

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 wraps 3 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

NoSpine

IncreasingSpine

MaximumSpine

DecreasingSpine

NoSpine

3 wraps 3 ¼ wraps 3 ½ wraps

Push Down Here

Hold Tip

Rotate Rod

Rest Rod Butt on Floor

Method for Location of Rod Spine

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

AxialRotation

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 - DO

• Wall Thickness - t

• Angle of Layer Overlap - θ

Do

θ t

Outside diameter - DO

Wall Thickness - t

Angle of Layer Overlap - θ

Comparison of rod section to model

yi

dAi

dAyI 2

yi

dAi

ii dAyI 2

MODEL RESULTS

F

L

3L

IECF

MODEL RESULTS

min

max

min

max

I

I

F

F

C, δ, E, L = constant

COMPARISON: MODEL & EXPERIMENT

min

max

I

I

Experiment measures:

Model predicts:

min

max

F

F

RESULTS

1 2 3 4

Point Rod 123 Rod 114 Rod 117 Rod 118 Rod 122

  Expt Model Overlap Expt Model Overlap Expt Model Overlap Expt Model Overlap Expt Model Overlap

1 1.20 1.11 120 1.14 1.08 45 1.04 Missing Missing 1.11 1.07 120 1.13 1.10 80

2 1.13 1.14 90 1.16 1.10 60 1.15 1.05 150 1.18 1.11 90 1.10 1.12 105

3 1.10 1.13 60 1.14 1.09 75 1.06 1.00 180 1.06 1.09 50 1.11 1.09 245

4 1.10 1.09 30 1.12 1.12 120 1.08 1.05 150 1.04 1.04 15 1.06 Missing Missing

QUESTION: Do these agree?

Can the differences be attributed to measurement uncertainty or is the model incorrect?

,, tDfI o

21

222

I

t

I

D

ItD

oI o

Uncertainty in Moment of Inertia

Estimate for Partial Derivative

ii X

R

X

R

For small individual uncertainties

iXiX

iii XXi

Xi

RX

R

X

R

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

21222

IIItDoI

Do

θ t

Outside diameter - DO = 0.350” ± 0.003”

Wall Thickness - t = 0.028” ± 0.004”

Angle of Layer Overlap - θ = 90º ± 5º

Estimate of ΔImax

DO t (n=4) θ Imax (*10-5) ΔI

0.350” 0.028” 90º 1791 0

0.347” 0.028” 90º 1741 50

0.350” 0.028” 85º 1790 1

0.350” 0.032” 90º 1855 64

8164150 21

222

maxI

Estimate of ΔImin

DO t (n=4) θ Imin (*10-5) ΔI

0.350” 0.028” 90º 1623 0

0.347” 0.028” 90º 1577 46

0.350” 0.028” 85º 1615 8

0.350” 0.032” 90º 1675 52

7052846 21

222

maxI

The final result is the ratio of the inertia values

21

2

min

2

max

min

max

minmax

IIRatio

I

IRatio

IIRatio

Substituting values

0625.01623

70

1791

81

10.11623

1791

21

22

Ratio

Ratio

Ratio

Final value for ωRatio

069.010.1

069.00625.0*10.1

Ratio

Ratio

Comparison of Model and Experiment

Model Uncertainty: ± 6.26%

Experimental Uncertainty: ± 5%

ROD 114

1.00

1.05

1.10

1.15

1.20

1.25

0 1 2 3 4 5

Expt

Model

END