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## Fly Line Stretch and Viscoelasticity

Moderator: Torsten

gordonjudd
Posts: 1448
Joined: Sat Jan 19, 2013 11:36 pm
Location: Southern California

### Re: Fly Line Stretch and Viscoelasticity

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

gordonjudd
Posts: 1448
Joined: Sat Jan 19, 2013 11:36 pm
Location: Southern California

### Re: Fly Line Stretch and Viscoelasticity

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 (42.97 KiB) Viewed 79 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 (51.06 KiB) Viewed 79 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
Posts: 259
Joined: Tue Jan 22, 2013 7:34 pm

### Re: Fly Line Stretch and Viscoelasticity

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:
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.
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.
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.

gordonjudd
Posts: 1448
Joined: Sat Jan 19, 2013 11:36 pm
Location: Southern California

### Re: Fly Line Stretch and Viscoelasticity

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