## Is the cast itself a transverse wave?

Moderator: Paul Arden

### Is the cast itself a transverse wave?

the displacement of the line (particles) must be perpendicular to the tension vector.

Graeme,
Tension is an internal force, and thus will be aligned with the line, not perpendicular to it.

The direction of propagation (shown above) is always in the orientation of the average tension vector,

Not so.
When the line is tethered a wave will reflect from the anchor, and go back in the reverse direction (with a flip in in its orientation) as shown below.

youtu.be/L5qi4BoDvqY
The tension in the line did not change, and yet the wave will propagate in either direction.

It also helps explain why line tapers work (T and mass both approach zero)

That is a good point, so what is the effect of the taper on the loop velocity? In a whip wave the taper will cause the velocity of the wave to increase. Does it have the same effect for the propagation of the loop in casting?

Gordy

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### Is the cast itself a transverse wave?

Graeme H wrote:Now here's a rod attached. Please let me know if this one is not a transverse wave.

Rod.jpg

If no other action is taken at this point, a fly attached to the line at A will keep moving left because the momentum of the medium in the upper leg (the fly leg) is in that direction. This is a loop produced by moving the line side to side.

If you want to say the loop shown only looks like a transverse wave, please explain at which point above it STOPPED being a transverse wave.

Cheers,
Graeme

This hypothetical situation gives a nonsensical answer. Transverse waves require both mass and tension: cut the medium into small pieces to provide discrete masses and you remove the tension. It is impossible to transmit a transverse wave through disconnected points.

Discretisation is just calculus in lay-man's terms - perhaps you don't see the significance of this technique? By differentiating the positional information w.r.t time, i.e. dx/dt you get to see the velocity of every single point of the medium. Are you also about to argue that calculus is bollocks too?

With the calculus, or discretisation, it is very easy to show that your statement above "a fly attached to the line at A will keep moving left because the momentum of the medium in the upper leg (the fly leg) is in that direction" is just completely wrong. You think you see a moving fly leg in the transverse wave - but your thinking is fundamentally flawed.

For one, I reckon that you think point A (the fly in your example) follows a path down the line towards the front of the loop - it doesn't. Point A oscillates on a path that is perpendicular to the centre line, it's position will simply be sin(t) somewhere along that path, with the centre being zero - it will always move parallel to any other point on the line.

Secondly, you seem to think that all of your 'fly leg' is moving to the left and will continue to do so if allowed. Well it's not in a transverse wave. The simple calculus shows that the two ends are stationary and the centre of the fly leg has the highest velocity. So your fly cast is going to end up with a pretty weird shape. You can pick absolutely any moment in time and you will not find a single instance where a half wavelength (as in your picture) is all travelling in the same direction (again this is fundamental to transverse waves).

The above are the results that you get from using the transverse wave equations, there's no debating this because that's the transverse wave theory that's been laid out and accepted. So if you want a set of equations to describe some other result then you need to look elsewhere. I really don't see what your problem is with this.

Call a fly cast a 'transverse wave' if you wish (it's just as valid to call it an X-ray), but all you've got is a name, it means nothing. Apply some transverse wave equations and that will quickly become apparent to yourself, if you understand them. That square peg isn't going in that round hole.

James

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### Is the cast itself a transverse wave?

Graeme H wrote:
On a deeper level though, I really do think the question has impact on the how we understand the physics of casting. If the fundamentals are well understood, the details fall into place more elegantly. It bothers me that we (casters) invoke a special type of wave unknown to the rest of physics (the fly wave) to explain how a cast works when there is already a term in physics that describes it (the transverse wave).

G'day Graeme
I can see that it bothers you but after all that has been exchanged in this thread I still don't have any answers to the questions I posed back near the beginning. Nomenclature aside, what does it matter whether the loop is a transverse wave or a farnarkolipse?

For my \$0.02AUD all the obsession with loops and their shapes is misplaced attention to consequences instead of causes. To pick up your projectile theme, it's examining holes in things instead of chambering a round.

Cheers
Mark
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### Is the cast itself a transverse wave?

G'day Mark,

At work at the moment so not a lot of time to answer, but it boils down to one thing: WindKnotz asked this question.

I know this might not be a simple yes or no question, but can you guys explain if a standard fly cast can be interpreted as a transverse wave
.

Nomenclature aside, what does it matter whether the loop is a transverse wave or a farnarkolipse? He didn't actually ask about the farnarkolipse (RIP John Clarke ), he specifically asked if the loop is a transverse wave. We can't put nomenclature aside here. If an MCI wants an answer, then others will also ask.

If the combined SexyLoops community says "no" when in fact the answer is "yes", then we are all poorer for it.

The loop in a standard fly cast is the crest of a transverse wave, where the direction of propagation of the wave itself is vertical and the displacement of the medium is horizontal.

Cheers,
Graeme
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Graeme H

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### Is the cast itself a transverse wave?

Graeme H wrote: He didn't actually ask about the farnarkolipse (RIP John Clarke )

Yes mate, more's the pity, on both accounts I reckon.

Cheers
Mark
"The line of beauty is the result of perfect economy." R. W. Emerson.

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### Is the cast itself a transverse wave?

Hi Gordy,

gordonjudd wrote:Tension is an internal force, and thus will be aligned with the line, not perpendicular to it.

Tension in a string is not an internal force. Tension occurs when external forces act on a string. If tension were an internal force, the string would curl up on itself when not connected at both ends or hanging vertically under gravity's influence.

Put another way, a piece of string tied to a brick and sitting slack stays slack until we pull on the other end. We are an external force.

Some might say now that we can only have tension when both ends are tethered, but a string hanging from one end will also have tension in it due to gravity. The tension at any point in the string is exactly equal to the weight of the string below that point. You have already pointed this out in the post with the poodle picture. (This is actually very important. We simply can't do the physicists' intellectual trick of "ignoring gravity" and still maintain tension in a string with mass - unless we are also accelerating it through space.)

When the line is tethered a wave will reflect from the anchor, and go back in the reverse direction (with a flip in in its orientation)...

... The tension in the line did not change, and yet the wave will "propagate" in either direction.

I notice you have removed some of your post from earlier. However, it's still incorrect to say the wave is "propagating either direction" (implying sideways movement of the wave). I think you are actually referring to displacement rather than propagation here. The wave propagates along the rope here (because that's the direction of tensional force) while the rope is displaced sideways.

Regardless, this apparent reversal of displacement is only true if the rope is anchored to a solid tether point (a fixed boundary). If the rope end is allowed to move (an unfixed boundary), the wave displacement phase does not invert and stays on the same side. Watch this video from about 3:45 on for the demonstration of this. It's pretty cool and goes against our intuition.

youtu.be/SCtf-z4t9L8

Casting a fly line is an extreme example of an unfixed boundary condition in a transverse wave.

It also helps explain why line tapers work (T and mass both approach zero)

That is a good point, so what is the effect of the taper on the loop velocity? In a whip wave the taper will cause the velocity of the wave to increase. Does it have the same effect for the propagation of the loop in casting?

Gordy

I've been trying to research that question for a couple of years. The best I've been able to come up with is "It depends ..." It seems to depend a lot on how much energy is in the wave when the wave begins passing through the taper. If it's very high, the thin whip speeds up. If it's too low, the energy dissipates and fizzles (great for fly fishing). Applied to casting, I see line design as very important. Using a short taper is very different to using a long taper. Whip tapers are optimised for cracking, fly line tapers are optimised for delivering a fly.

I think finding an answer to this question is difficult because, as James rightly points out, no physicists have tackled the question of how a cast works using transverse wave physics as the starting point. Perhaps when they do, the answer will become apparent.

What I do know is that if an otherwise "nice cast" is rapidly pulled back from its intended path by increasing the tension in the rod leg rapidly, we can snap our fly. (Increasing tension in a string increases the velocity of wave propagation through the string.)

Cheers,
Graeme

(BTW, when I was looking again for the video I linked here (using the search term "Slinky transverse wave unfixed boundary", some really wonderful little videos appeared. They show how a transverse wave slows considerably when travelling from a light medium to a heavy medium. This is directly applicable to excessive overhang in fly casting. Check out this one from 1:35)
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Graeme H

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### Is the cast itself a transverse wave?

This is directly applicable to excessive overhang in fly casting

What is shown here is the problem linked to "impedance" of materials (e.g the transition between the fly line and the leader), but this cannot explain why there is a defined limit to overhang. This limit is linked to the relative importance of the rod leg versus the fly leg, assuming the loop has been shaped. Aitor's experiments demonstrated the existence of this limit. The lack of impedance fit between the fly line and the running line exists whatever the length of the overhang is, and I do not see how you can get an idea of the limit of overhang considering the impedance issue only.

When playing around with a simple model I just assumed that the running line had no mass at all. I have to find it in my old files, and get the equations leading to overhang limitation.

It would be nice if the author of the initial question could elaborate on what he would conclude if the answer to his question was yes or no. That would make our life easier

Merlin
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Merlin

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### Is the cast itself a transverse wave?

Graeme H wrote:If the combined SexyLoops community says "no" when in fact the answer is "yes", then we are all poorer for it.

The loop in a standard fly cast is the crest of a transverse wave, where the direction of propagation of the wave itself is vertical and the displacement of the medium is horizontal.

Hmmm. I'm not still convinced that yes or no have substantive consequences but I am hanging in there.

Have to say you are wearing me down on the nature of the loop. Hard to visualise vertical propagation and horizontal displacement in a horizontal line when the medium itself is moving horizontally. My intuition is pricked however. Will sleep on it.

Cheers
Mark
"The line of beauty is the result of perfect economy." R. W. Emerson.

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### Is the cast itself a transverse wave?

G'day James,

For one, I reckon that you think point A (the fly in your example) follows a path down the line towards the front of the loop - it doesn't. Point A oscillates on a path that is perpendicular to the centre line, it's position will simply be sin(t) somewhere along that path, with the centre being zero - it will always move parallel to any other point on the line.

No problems at all with that. Point A will move horizontally to the left of the image until it starts moving to the right, as will any other point on the line.

Can you see that the particles at the extreme right (the front of your loop) and the extreme left, marked A (the fly) have zero velocity? The particle that is moving the fastest is the one on the centre line - so this one will 'stretch' away from the fly. Between the two extremes there is a spread of velocities that are described, themselves, by a sine wave. The particles will therefore not move uniformly off to the left into a fly cast, they would simply smear out with the centre particles moving away from the extremities.

Okay, let's play dx/dt then. Your call. When you discretise this motion, velocities are out of phase with acceleration. The line at the rod tip and centre have maximum absolute velocities but minimum acceleration (equal to 0 ) while the points at A and in the loop have maximum absolute rates acceleration and minimum velocity. Left to its own devices at this point in time, point A will achieve the same velocity as the centreline velocity and not "smear out" as you predict.

Here's an old favourite. Sorry about this. Really, I am. I hated it last time and I hate it this time too, but it's required.

In the image shown, the rod tip is moving to the right at exactly the same speed as the line in the centre is moving to the left. The front of my loop and point A have zero velocity as shown. All agreed, no problems at all with your analysis, except the part about the part moving the fastest being the one on the centre line. The other point moving the same speed is the one at the rod tip, but to the right.

Let's assign the velocity of line at the centre point X m/s and the velocity of the rod tip -X m/s. The loop and A have velocities of 0 m/s.

However, we do not pull the rod tip back while the loop is moving forward: We keep it stationary. If we look at the picture with that as the frame of reference, so that the rod tip is NOT moving to the right and it has zero velocity, we see EVERYTHING else moving to the left with an apparent velocity of X m/s added to the earlier velocities.

Relative to the stationary rod tip, the loop moves to the left at a velocity of X m/s, the line at the centreline is moving left at 2X m/s and point A is moving at X m/s (more on this later.) In other words, the loop is travelling at half the speed of the fly leg. The rod leg is also moving at a velocity of zero. Does this look familiar?

Secondly, you seem to think that all of your 'fly leg' is moving to the left and will continue to do so if allowed. Well it's not in a transverse wave. The simple calculus shows that the two ends are stationary and the centre of the fly leg has the highest velocity. So your fly cast is going to end up with a pretty weird shape. You can pick absolutely any moment in time and you will not find a single instance where a half wavelength (as in your picture) is all travelling in the same direction (again this is fundamental to transverse waves).

Relative to the rod tip, the half wavelength between the loop and A is travelling at (approximately) the velocity of 2X m/s to the left. And as you say, it's moving parallel to all the other points, horizontally. The half wavelength shown is also called the fly leg.

The paradox of Point A travelling at X m/s instead of 2X m/s as the rest of the fly leg is doing is the result of the imaged waves being drawn from a "standing wave array" in a fixed boundary state. In reality, the fly hanging off the leader has already reached the equilibrium promised by being "left to its own devices long enough". Its acceleration maximum from the discretised figure before has meant its velocity has already reached the velocity of the rest of the fly leg because it has a mass approaching zero.

The other factor involved here is the "bend" in the rod and fly legs. Shown here, they follow the Sine wave. In reality, they do not follow a sine wave, but something closer to Chevron wave as shown below*. All points on that straighter leg are travelling in horizontally and parallel direction.

The above are the results that you get from using the transverse wave equations, there's no debating this because that's the transverse wave theory that's been laid out and accepted.

Agreed.

Cheers,
Graeme

(* Yes, I know it should be "Amplitude X 2" in the image. A typo I failed to notice at the time of posting the first time.)
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Graeme H

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### Is the cast itself a transverse wave?

Graeme

So in your conception, the "transverse wave" is illustrated by the full line and the amplitude is about the length of the line since the loop ends its trajectory to that point approximately.

This wave has little vertical speed, if any, which means that tension is very small with this representation (tension goes along with the square of the wave travelling speed, which is vertical here). How is it compatible with the tension created at the end of the tip as the rod is fully deflected? At this point wave equations are in trouble.

One of the problems with this approach is that the "crest" is moving from side to side after the original half wave from the tip has ceased. How can we justify that the amplitude of the wave is changing during the rollover whilst the source is in standstill? This is not a familiar characteristic of waves.

The loop IS the wave, and not the line: you throw the line as if you were throwing a ball, a javelin, of a spear with a smart flexible device allowing to follow a more or less straight trajectory, but since the medium (the line) is flexible the only way to send the fly in the distance is to make your "spear" rollover around a loop. Unfortunately, the loop does not fit the usual criteria defining longitudinal or transverse waves. You have to look at the tralectory of a point entering the wave. For a transverse wave, the point moves perpendicularly to the medium, and for a longitudinal wave it moves parallel to it. Here the point follows a cycloïd path, and moves in both directions, more in the parallel one than in the perpendicular one. Its an hybrid wave if I can say so, but you can find the usual wave relationships for tension as the loop is shaped. It is not the case for your giant wave.

Why make things simple when you can make them more complex is a French tale, I see it has been adopted by Australia

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

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