The practical side of considering loops as waves: Teaching and Self Improvement

[Graeme H]

Q: What effect does an external force have on a string?

A: It removes slack, which is another way of saying external forces acting on a string produce tension.

Cheers,
Graeme

[Paul Arden]

I’m sorry Graeme, if that’s an answer to me then I don’t follow! That’s wasn’t my question. I’ll see if I can make it clearer.

With the loop on the floor, you say that it doesn’t propagate as a transverse wave because the line end is untethered (no tension). If it doesn’t propagate as a transverse wave then it is not a transverse wave.

But then when you cast the same loop in the air, you say it is a transverse wave with a wave direction in the same direction as gravity.

Why is the loop on the floor not a transverse wave but the one that is cast in the vertical plane you consider to be a transverse wave?

Thanks,
Paul

[Graeme H]

Sorry Paul, my mistake.

The loop on the floor is a transverse wave of sorts but it can't propagate away from the impulse source, so it tends to tangle. It's not really a good example of a wave because it can't transmit energy away from your rod tip.

Torsten said this earlier:

(b) mechanical waves don't transfer matter (but energy, movement of mass is limited),

Energy is transmitted in a wave, but if the wave can't propagate somewhere, it can't transmit the energy away from the energy source. That's what's happening in a floor wiggle.

Cheers,
Graeme

[Paul Arden]

However in the case of a fly cast you don’t have the loop’s transverse wave propagating outwards from the tip, instead you have it propagating downwards in the direction of gravity?

[Graeme H]

Wave propagation direction is not determined by the rod tip. It's the direction of tension in the line.

Amplitude is determined by the magnitude of the rod tip movement.

[Paul Arden]

Ok so I don’t really know the Tension layout in the loop. My understanding is that it is something like this, but maybe someone can confirm/deny?

Thanks,
Paul

[Paul Arden]

Amplitude is determined by the magnitude of the rod tip movement.

Lost me again! I thought you had it at length of the cast?

[Graeme H]

Lost me again! I thought you had it at length of the cast?

... which is determined by the magnitude of the tip movement. (Sorry, I really should have said "work done by the rod tip", so you're right to be confused - my fault. Magnitude is a poor word to use in this case.)


Maybe I can explain wave propagation and tension in a slightly different way that might help (or might not. )

Perhaps think of tension as a force pulling the wave away from the rod tip along the fly line.

If you tie your tippet to the bridge above you, the wave is pulled up. If you tie it to a tree, the wave is pulled towards the tree. If you stand on top of the bridge and dangle the line down and then wiggle the rod tip, the wave is pulled towards the ground by gravity. The tension pulls the wave and in turn the wave propagates towards the tension. (This is not quite accurate, but it's a simple way to think about wave propagation direction as opposed to "making a loop".)

In your picture, you have discounted gravity by only drawing Tmax to the left and right. Using the rod tip, you can add tension in the horizontal direction to the tension in the vertical direction, but you can't remove the tension due to gravity (the vertical tension.)

Once again, you are writing "tension in a loop" when it's tension in the line that we are considering. The loop is just a wave travelling along the line in the same way a mend travels along the line.

While it is true that tension is acting axially along the line at any single point in the line, the wave is placing a bend in the line that is deviating away from the sum of all tension components in the line (towards which the wave is travelling.) (Sorry, I've just re-read this sentence and it's a mess. I'll need to draw art to explain.)

Cheers,
Graeme

[Graeme H]

This might be a bit too esoteric but I'll try ...

Consider this a bird's eye view of a cast that was made to the north. A mend was made to the right and line tension is in the north-south direction (Tmax).

Inside the mend, we have components of tension to the right and left (TR and TL) and components in the north-south direction (Tm/2), two of which add up to Tm. The tension in the whole line is still north-south.

The tension in the line in the southern part of the mend is "the square root of (Tm/2) squared plus TR squared" (Pythagorus and all that shit). The tension in the northern part of the mend is "the square root of (Tm/2) squared plus TL squared". Together, they add up to Tmax.

In a cast, rotate that whole thing upwards so the the north arrow points up (as it does on the screen for me right now) and Tm is due to gravity. TR and TL are the tension to the left and right produced by your rod tip when you cast the line, but you had to aim that T up a little to counter the force of Tm.

Clear as mud, right? Sorry ...

(This will be so much easier to explain when I come to visit your ship. )

Cheers,
Graeme

[Paul Arden]

Well you are definitely not making life any simpler, Graeme

So let’s recap. Fly to bridge, the transfer wave travels up. Got it. It’s obviously slowed by gravity.
Line on floor. Not a transverse wave. Got that!
Loop in air. It’s a transverse wave that propagates to earth. Is this the same for an inverted loop? I assume so.
What about a side cast? Is this also a transverse wave? And is that also propagating to Earth?

I’ll have to think about the mend but I’m going for a Zwift ride now.

Cheers, Paul