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Fly Line Stretch and Viscoelasticity

Moderator: Torsten

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gordonjudd
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Re: Fly Line Stretch and Viscoelasticity

#11

Post by gordonjudd »

For a database I'd keep it simple and choose what's closest to the actual usage of the line,
Torsten,
With that in mind what range of force values do you think we should use for our force vs deflection curves?

The tension applied when casting will only be a few Newtons at the rod tip and then will taper to near zero at the fly end of the fly leg. Thus the stretch from casting should be very small.

Do you know why the elongation value was measured for a 17.6 N load? Maybe we should focus our measurements around that load value as well.

Gordy
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gordonjudd
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Re: Fly Line Stretch and Viscoelasticity

#12

Post by gordonjudd »

have found that making force vs deflection measurements on a long length of line are frustrating to do since the repeatability is so bad. People doing those tests will find line does not return to the same zero force length after it has been stretched by a large load. Worse yet, the deflection to use for a new large load is also a moving target because of creep.
Here is an example of the hysteresis problems involved in making force vs deflection measurements on non-elastic fly lines. I used penny rolls to get different load values. Each roll has a mass of .125 Kg, so adding a new roll to the basket hanging from the line would increase the load by 1.227 Newtons. Once all the rolls had been added I then made deflection measurements for a decreasing loads by removing a roll from the basket. The line was a "stretchy" Snowbee ED 8wt line.

The force vs deflection curve found for this line is shown below.
snowjbee_f_vs_d.jpg
snowjbee_f_vs_d.jpg (42.97 KiB) Viewed 2344 times
The blue loop shows the hysteresis curve that was found with the first set of measurements. The red loop shows the loop for a second set of measurements that were made about 5 minutes after the first. You can see that these measurements do not repeat, and the area of the second loop was larger than the first set. Also note that when the decreasing load went to zero there was a residual deformation that was around 1cm.

The blue curve shows the force vs deflection curve was quite linear and had a nominal spring constant of 244 N/m. Using that spring constant for a 17.6 N load would give this line an estimated elongation value of 7.2%. Because the spring constant varies with load, the actual measured value for the elongation value would probably be different, but I did not have the 1.8Kg mass needed to make a confirming measurement.

As James noted:
the area described between the loading and unloading cycles (i.e. the hysteresis) is proportional to the mechanical loss.

If you calculate the PE values expected for the increasing load values and the decreasing load values you can get a measure of how the area of the hysteresis loop compares to the area under the increasing load vs deflection curve. As show below those calculations show the loop area is nearly 50% of the area under the increasing load vs deflection curve (the top red curve).
snowjbee_pe_up_dn.jpg
snowjbee_pe_up_dn.jpg (51.06 KiB) Viewed 2344 times
I have no idea of how the mechanical loss in the line would affect the casting distance, but I would expect the relative hysteresis loop area for a low stretch line would be much smaller than 50%.

Gordy
Torsten
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Re: Fly Line Stretch and Viscoelasticity

#13

Post by Torsten »

Hi Gordy,

about the 1,8 kg test weight:
I've asked them and it seems to be just an arbitrary choice; maybe not that bad because this force is much lower than the breaking strength of most fly lines and seems to be still within the linear range.

I tried today a similar static test with a chinese DT8F:
Chinese_DT8F.jpg
Same measurement procedure as yours, but in my case, no pause between the measurements.

--

However this is still a static test and a DMA analyzer is out of reach for a hobbyist. So my idea is a simple dynamic test: measure the step response with a test weight.
Data_Analysis2.png
I tried that with 1,6m #30 lbs running line:

* added a 500g test weight to the fly line section
* recorded the oscillations with my smart phone after I've pulled and released the test weight.
* analyzed the oscillations with the "Tracker" software (see https://physlets.org/tracker/)

For the analysis I've entered a equation for a damped sine wave,
see https://en.wikipedia.org/wiki/Damping

\(y(t) = A \cdot e^{-\lambda t} \cdot \cos(\omega t - \phi)\)

where

\(y(t)\) is the instantaneous amplitude at time ''t'';
\(A\) is the initial amplitude
\(\lambda\) is the decay rate
\(\phi\) is the phase angle
\(\omega\) is the angular frequency

I've slightly modified this function, because I've seen a linear offset, tuned then the parameters manually to get a match.
Data_Analysis.png
You can compute from the decay rate the damping ratio: \(\zeta = \lambda / \sqrt{\lambda^2 + \omega^2} \). Here the system is underdamped because \(\zeta < 0\). From the damping ratio you can then compute the damping coefficient and this can be used for a (damped) mass-spring simulation.

Torsten.
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gordonjudd
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Re: Fly Line Stretch and Viscoelasticity

#14

Post by gordonjudd »

Torsten,
Your data shows that I have a lot to learn about applying elastic spring equations to analyze viscoelastic fly lines.

It appears the area in the hysteresis loop for the second and third measurements where much smaller than the area for the first measurement. I wonder if James' DMA measurements will show the same effect.

Your f/d data shows that Chinese line (the king of stretch so far with an elongation value of 9%) had a nominal spring constant of 196 N/m. Longer lines would have lower spring constant values so the 1.6 m line length you used for your frequency measurement (kudos to Tracker for being able to track the small deviations involved in those measurements) would have an expected (expected by me at least) spring constant value of 122 N/m.

Assuming the oscillation frequency would equal sqrt(k/m) that would give an expected omega of 15.6 rad/sec, yet your measured value was 26 rad/sec. Does the line become much stiffer when it undergoes repeated stretch cycles?
I've slightly modified this function, because I've seen a linear offset, tuned then the parameters manually to get a match.
That slope looks like the 0 deflection point does reduce somewhat which implies the line stiffens a little bit with repeated stretch cylces but no where near the amount that would change the oscillation frequency from an expected value of 15.6 rad sec to your measured value of 26 rad/sec.

I was thinking of using a 3m length of line to get larger swing values that would be easier to measure with Tracker. How should that data be scaled to get the equivalent values expected for a 1 m length of line?

Gordy
Torsten
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Re: Fly Line Stretch and Viscoelasticity

#15

Post by Torsten »

Hi Gordy,

that are two different lines, for the static test a DT8 and for the dynamic test #30 running line. I've recorded the oscillations earlier and had not enough time to do it for the DT, sorry for the confusion.
For longer line lengths I'd assume it should scale simply like springs in series, so your equation would be right.

Torsten.
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gordonjudd
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Re: Fly Line Stretch and Viscoelasticity

#16

Post by gordonjudd »

that are two different lines, for the static test a DT8 and for the dynamic test #30 running line.
Torsten,
I am sorry I did not pay more attention to your description which specified what type of line was being used in your f/d and frequency tests. I just jumped to the conclusion your tests were done on the same line. My error not yours.

Did you try doing a f/d test with your stiffer running line? I would expect it would have a very high spring constant (over 500 N/m) to get an omega value of 26 rad/sec for 1.6 meter of line.

It appears these spring constant values vary all over the map depending on the core material used.

Gordy
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gordonjudd
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Re: Fly Line Stretch and Viscoelasticity

#17

Post by gordonjudd »

I have no idea of how the mechanical loss in the line would affect the casting distance, but I would expect the relative hysteresis loop area for a low stretch line would be much smaller than 50%.
Torsten,
Here is some data taken on a 9m length of a Barstool Ridge line with a low stretch "power core". The longer length increases the amount of deflection for different loads so it is easier to get measured deflection data. That data can then be reduced by a factor of 9 to get the corrected f vs d curve for our 1m length standard.

I also did three back to back tests with increasing and decreasing loads. The resulting hysteresis loops are shown below. The first set of measurements are in the blue curve. The second (red curve) and third (green curve) set of tests were almost overlays, so most of the residual deflection occurred in the first test. This data had very little creep for the maximum load of 12.2N used in these tests, but did show some creep for higher loads.
ridge_f_vs_d.jpg
ridge_f_vs_d.jpg (40.53 KiB) Viewed 2206 times
Extrapolating the 1181 N/m spring constant measured over this force range to a 17.6N load would give this line an elongation value of 1.5%.

You can see the area in the second and third hysteresis loops were much smaller than they were for the Snowbee line. The area in these loops were only 10.6% of the P.E. under the increasing f vs d curve.
ridge_pe_curve.jpg
ridge_pe_curve.jpg (49.48 KiB) Viewed 2206 times
Gordy
Torsten
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Re: Fly Line Stretch and Viscoelasticity

#18

Post by Torsten »

Hi Gordy,

thanks for the data. Indeed this line has less "creep" - I'm wondering if what kind of creep this is (see https://en.wikipedia.org/wiki/Creep_(deformation) ), the chinese line seems to show that effect very significantly, with a large retardation time. I'm thinking about building a line testing machine, something with a load cell and a stepper motor to automatize the measurement, should be possible with parts for less then 200$/€.

Greetings,
Torsten
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Re: Fly Line Stretch and Viscoelasticity

#19

Post by Torsten »

Hi,

pulled this thread up for Gordy - maybe you'd like to try my experiment in post #13 of this thread (?)

Has anyone an idea for a simple test setup to measure bending stiffness / losses ?

Greetings,
Torsten
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Merlin
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Re: Fly Line Stretch and Viscoelasticity

#20

Post by Merlin »

Since this is the thread for stretch and viscoelasticity, let me remind you what I found with a classic line flight model (Pearson):

Kinetic energy at start 3.8 J
remaining energy in the loop (zero fly leg) : 1.2 J
energy lost by the loop : 1.9 J
energy lost by the fly leg (skin drag) : 0.7 J

and from static analogy:
elastic energy in the fly leg: varies from 1 10-4 J to 1.2 10-4 J
energy from line bending: 0.0022 J

Consequently, if one expect to see an effect of elasticity or bending on the line flight, then we need to multiply those energies by a factor of at least 100 (e.g. 0.22 J for bending, to be compared to 0.7 J for skin drag).

I hardly believe that such a factor can be met, but anyway we shall see with measurements in James' lab.

Merlin
Fly rods are like women, they won't play if they're maltreated
Charles Ritz, A Flyfisher's Life
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