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Analysing loop propagation

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Graeme H
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Re: Analysing loop propagation

#81

Post by Graeme H » Tue Sep 29, 2020 8:45 am

Paul Arden wrote:
Tue Sep 29, 2020 8:25 am
I suppose another difference when fly casting is that the 1/2 wave length decreases in size as the loop unrolls, usually disappearing to zero?
I don't understand this at all. The half wave length? How is that measured?
Whereas with tethered string one would expect the transverse wave to propagate at 90 degrees away from tip path, with a maintained constant wave length?
Sort of. Changing the tension in the line with the rod tip changes the frequency and wavelength. Pulling away from wave propagation direction with the tip or by check hauling shortens the wave length. Is that what you mean? (Tethered or not, this is true.)

You can see both tethered and untethered waves in action in this video. In fact, you can see the tethered wave become an untethered wave as it happens. Does it answer your question or not?



I actually don't understand why you can't see this happening in the video Paul. What is it you're objecting to in the video? What are you seeing in that video that I'm not seeing? I can't do CGI - this is an exact demonstration of how a loop is an untethered transverse wave. The wave that is undeniably a transverse wave becomes a loop. I did nothing different at the rod.

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Graeme
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Merlin
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Re: Analysing loop propagation

#82

Post by Merlin » Tue Sep 29, 2020 12:17 pm

A word on string analogy

In the teaching forum Graeme explains to us his interpretation of the mechanisms allowing controlling the line. The basic equation of transverse waves is used: tension in the string equals the linear mass of the line multiplied by the squared speed of the wave in the string. Change one parameter and the other two follow: increase linear mass under given tension and the wave speed diminishes. Increase tension for a given linear mass and the speed increases. Simple and straightforward at first sight, and the reading made me think of Berlin’s explanations (see “a week with Berlin” in the special guest forum).

The same approach is applied to leaders, using impedance as a guideline (impedance is tension divided by speed for a string and equals linear mass multiplied by speed). I recommend to reread wthe discussion on leader tapers.

There is however a big assumption hidden here, because this relationship applies to a string held tight in between two fixed points like a guitar string, there is no free end like for a line, and no rollover as well. At some stage there is a contradiction with known situations: the following one relates to a snap cast:
The linear mass of the string decreases as the wave travels through the taper, so the wave speed increases.
That should be applicable to the end of the rollover then; the tapered line section should show acceleration since the linear mass decrease along the string approach. But if you cast a level line, you can see that the final acceleration is much more pronounced than for a tapered one and ends with a kick back: there is too much energy left in the line. The statement above illustrates the fact that nothing coming from the actual situation of a loop (drag) is considered with the string approach. There is something well known however: as the diameter of a line decreases, drag forces take progressively the lead on line momentum change and at some stage (a small diameter), the line decelerates. You can have both trends following each other as the taper enters the loop: an acceleration trend caused by a favorable change in momentum within the loop, followed by a deceleration due to the size of the line. And this is the one which always wins at the end given the diameter of leaders.

There is a wave speed increase with snap, pull back, and check casts because the caster applies a force on the rod leg which results in an acceleration of the “wave” speed (the tangential velocity around the loop, which I often call the “rotation speed” of the loop). This happens whatever the taper of the line is. The physics behind has little to do with strings, but with the application of Newton laws on the line (loop and legs). The same physics show that the travel speed of the loop is reduced and seems to nearly stop or even go backwards sometimes, but after a short while it reaccelerates again. The taper of the line has its say but it is not the main parameter of this late acceleration.

Among the equations needed to simulate a cast, there is the “angular momentum” (AM) one (recommended by James). Months ago I was on the “string side” but when I realized I was unable to simulate a pull back correctly, I restarted from the beginning and finally found a way to better simulate, and consequently better understand, what is going on with such cast. In this equation, there is a “morphing term”, which is represented by the possible variation of the radius of a semi circular (idealized) loop. This equation is not easy to solve if you do not assume that morphing is negligible, but you do not need to solve it if you want to understand what can happen on the morphing side. An important parameter is the “wave” speed. You can increase it with a pullback and then the AM equation tells you that for a level line the size of the loop should reduce. If on top of that the diameter of the line increases, this trend is reduced and if the diameter of the line decreases, the trend is amplified. As an example, if you pull back late enough during the time the front taper enters the loop, then the loop size should reduce. If you push forward instead, the loop size should increase. There are several possibilities in fact (e.g. PB during the time a reversed taper enters the loop) some of them giving mitigated results (little morphing) in terms of loop size.

Although it is simple and easy to use, the string wave speed equation has been established for a specific situation which is not encountered for a loop (fixed ends). Taking the time (and the pain) to write correctly equations for a variable mass system allows understanding the internal mechanisms governing particular actions like PB of snap. And despite the reasoning with the string approach may conclude sometimes similar things by comparison to the actual physics of the line; it is just inappropriate on the technical ground and can end with false conclusions.

There can be some true transverse waves in the line, like a mend or a dangle, which can travel along the line, reflect at the end like any transverse wave. They belong to a different category by comparison to a loop. To such waves you can apply the string theory, but not to the loop.

Merlin
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Paul Arden
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Re: Analysing loop propagation

#83

Post by Paul Arden » Tue Sep 29, 2020 12:45 pm

This reminds me of a question asked during an AAPGAI exam, “what is the purpose of the taper at front of the flyline and leader?” “Good question”, though I. The candidate did not know and so the head examiner, who had asked the question said, “it was to speed it up” and was quite proud of the fact that he did not need physicists to tell him this, only “common sense”, and then he went on to explain that he knew this because when he put a nozzle on a hose pipe the water spurted faster and further!

After he exam I tried to correct him and told him to cut the leader off and cast with a level line instead and he would end up with the opposite (and correct) conclusion that it was ultimately in fact to slow it down. But apparently he still asks this question and loves his hosepipe.

I do see what Graeme is driving at, but I still can’t call it a transverse wave because it never propagates 90 degrees away from tip path. Not unless the loop is cast upside down. Put the line on the floor and a transverse wave should propagate at 90 degrees to the applied motion and it doesn’t. It would be nice if they did because then you could defy gravity, although you’d probably spend more time unhooking flies from trees.

Cheers, Paul
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Graeme H
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Re: Analysing loop propagation

#84

Post by Graeme H » Tue Sep 29, 2020 1:42 pm

Paul Arden wrote:
Tue Sep 29, 2020 12:45 pm
Put the line on the floor and a transverse wave should propagate at 90 degrees to the applied motion and it doesn’t.
Maybe that's because you put it on the floor?



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Graeme
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Paul Arden
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Re: Analysing loop propagation

#85

Post by Paul Arden » Tue Sep 29, 2020 1:52 pm

True I put it on the floor and I can get it to behave as a loop. But I can’t get it to behave like a transverse wave. I can get it to behave like a transverse wave if I tether the other end, or suspend it under gravity. But once the chain is near my finger I can’t get it to wiggle outwards. A transverse wave by its very nature should propagate at 90 degrees away from my finger’s direction. Despite being nimble I still can’t accomplish this feat.

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Paul Arden
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Re: Analysing loop propagation

#86

Post by Paul Arden » Tue Sep 29, 2020 2:17 pm

[media] [/media]
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Graeme H
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Re: Analysing loop propagation

#87

Post by Graeme H » Tue Sep 29, 2020 11:01 pm

Paul Arden wrote:
Tue Sep 29, 2020 1:52 pm
But once the chain is near my finger I can’t get it to wiggle outwards. A transverse wave by its very nature should propagate at 90 degrees away from my finger’s direction. Despite being nimble I still can’t accomplish this feat.
Which direction is 90 degrees from the line you trace on the floor with your rod tip? Why do you think that MUST be outwards along the floor?

Try this: Slip a pencil between your middle and ring finger and hold it there with your hand straight. Your index finger is pointing 90 degrees from the pencil's direction.

hand_d.jpg
hand_d.jpg (7.78 KiB) Viewed 263 times
hand_c.jpg
hand_c.jpg (9.83 KiB) Viewed 263 times

In the pictures above, my finger is pointing upwards. In the one below, it's pointing horizontally:

hand_b.jpg
hand_b.jpg (7.06 KiB) Viewed 263 times


And in this one it's pointing downwards.
hand_a.jpg
hand_a.jpg (7.7 KiB) Viewed 263 times


In all cases, my finger is 90 degrees from the pencil's orientation.

The pencil represents the line you are tracing on the floor with your rod tip. My hand occupies a plane representing an infinite number of directions, all of which are 90 degrees from that line. Some are up, some are down and some are away. A transverse wave simply needs to propagate in ONE of those directions to honour the condition you want to apply. However, you're physically removing all but two options (away from you and towards you) by only considering this as a 2 dimensional problem.

Of course the wave you make on the floor is not going to move away from you if you don't tether it. It requires tension in that orientation to move away from the rod tip. A transverse wave in a medium is propagated away from an impulse in the direction of tension. If you place a floor below the medium to remove gravity as a source of tension (and fail to replace it with another source) then the wave must fail. That's one prediction from the wave equation and you are simply proving it.

Tension can be provided by the tether or it can come from gravity. Remove all sources of tension and we fail to propagate a wave. ("Slack is the enemy of the cast.")

So I'll ask once again - since you seem to be avoiding answering this question - what do you observe in this video? Can you see a transverse wave travelling up the string? Can you see that same transverse wave become a loop? If not, what are you observing and how do you explain what you see?





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Graeme
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Paul Arden
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Re: Analysing loop propagation

#88

Post by Paul Arden » Wed Sep 30, 2020 1:47 am

Indeed I do see the transverse wave become a loop. Which point does this happen for you? When the tether is released or slightly later?

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Graeme H
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Re: Analysing loop propagation

#89

Post by Graeme H » Wed Sep 30, 2020 5:14 am

As I've been saying all along in this thread, I see it as a transverse wave. I make no distinction between "a loop" and "a transverse wave", so it became a loop as soon as the rod tip stopped moving to the left of screen (i.e. well before the tether was released.)

Why is there a difference for you? What is the distinction you're making to choose the tether release as a time of reference between the two? Did the string change its state at that time? Did the energy being transferred by the wave become something else at that time? Did that energy diminish or increase at that time? Did it change its direction of propagation along the string?

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Re: Analysing loop propagation

#90

Post by Paul Arden » Wed Sep 30, 2020 12:26 pm

Ah right. I thought by “ Can you see a transverse wave travelling up the string? Can you see that same transverse wave become a loop? ” you had made a distinction. Well for me I think it stops becoming a transverse wave the moment it becomes untethered. Ie it stops moving vertically (in this case) which would be the transverse direction. Without that tethering, or without gravity working on the line dangled below, then the wave fails to propagate transversely.

I must have missed something above. The loop height being half the wave length question refers to how transverse waves are normally measured. Ie a full wave length. Top to bottom of a loop would be half a wave length. But that wave length doesn’t maintain itself in the case of a loop, but instead diminishes to zero.

Incoming storm.

Cheers, Paul
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