## Is the cast itself a transverse wave?

Moderator: Paul Arden

### Is the cast itself a transverse wave?

Ok Graeme, let ‘s stay on earth with Mr Newton.

Using your video and the pic with the yellow zebra, it seems that the vertical wave at the beginning is going down at about 1 m/s: taking an estimate of the slowing down of the video at 2.5, and a wavelength of about 1m. For this transverse wave, the tension would thus be 0.001 N, in other words peanuts, if I consider a line weighting approximately 1 gram per meter.

Then you make a soft transition to a casting motion, but in between the nature of your motion has changed, even if visually this does not seem to be so. Let’s review the tension history of a cast from a scientific publication (Gatti-Bono – Perkins).

There are three parts: the acceleration of the line up to maximum speed, the shaping of the loop with the quick compression making difficult to shape a loop with a soft running line, and since the fly leg keeps on moving forward the disappearance of slack is felt through a tug in the line, and finally the rollover of the loop at a more or less constant speed for the major part of it.
Tension history fly cast.JPG (42.11 KiB) Viewed 559 times

For the point indicated on the graphic at tension 0.2 N and timing 0.65s, using a linear density of one g/m for the #5 line used by the authors, we find that the loop travelling speed is square root (0.2/0.001) = SQRT(200) = 14 m/s, and the fly leg speed is the double (28 m/s). This corresponds to the level of speed reported by the authors.
For a transverse wave to propagate, two conditions must be met. There must be tension in the medium and the medium must have mass. With those, we can calculate the velocity of propagation of the wave as V = sqrt(Tension/Mass per unit length).

If you want to consider that all the sequence of line acceleration before loop shaping is (part of) a transverse wave which would embrace the whole cast and line flight, then the corresponding tension values indicate the vertical speed of loop propagation at any time. For 1.2 N, that would correspond to SQRT (1.2/0.001) = SQRT (1200) = 34.6 m/s for the transverse wave: either it goes down to the ground immediately, either it rockets towards the sky at this point in time. This is nonsense obviously and tells us that we do not face a wave here, but the throwing of a projectile to take your words. Such level of tension can be calculated from rod deflection or line mass and its acceleration.

The line tension is increasing during the throwing phase and any disturbance like a dip in the tip trajectory will start propagating in the fly leg: does the vertical transverse wave explain the propagation of tailing loops (horizontal transverse wave) in the fly leg?

Same after loop shaping, any wobble from the tip will follow the loop on the rod leg as long as the cast is tethered. Wobbles also are transverse waves travelling horizontally. The loop is the wave, propagating approximately horizontally; it is a hybrid type of wave, something like 60% longitudinal and 40% transverse, following the definition of such waves (displacement relative to the medium).

You can also consider mends performed with the rod tip, they send transverse waves in various plans according to the motion of the caster whilst the loop is propagating.
Gravity provides the tension vector required for a transverse wave to propagate in an untethered fly line.

I totally disagree here; you can explain the propagation of an untethered line without gravity at all, just using Newton’s laws (momentum, energy). I can’t see how a transverse vertical wave can explain that but would be please to learn, for me only the dynamics of the (horizontal) loop can do it. If you take gravity on board, it will contribute to loop morphing which is not really easy to calculate and this is often left aside given the complexity.

When I speak of overall complexity of your explanation, I refer to the fact that there is no need to use the vertical transverse wave concept: you throw a line, and it rolls over thanks to a loop (the only wave we would like to see during the cast). That is simple to understand, one can use a rope lying straight and his arm to watch it: translate the rope forward with increasing speed and stop it to create a loop. I cannot imagine explaining that we should start by wig wagging the rope until we can make a transition to a cast. With a fly rod I can do the same with circles and move progressively to a Belgium cast, and finally to an overhead cast when the large circle will be flat and thin enough. For sure, I am not going to explain the virtues of the circle to comment the overhead cast.

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

Merlin

Posts: 1072
Joined: Wed Jan 09, 2013 8:12 pm
Location: France

### Is the cast itself a transverse wave?

Thanks Merlin. I really like that answer. I'm going to have to think about it for a bit now.

Separately, I've come up with an experiment and I'll need to run it and see what falls out of it.

Cheers,
Graeme
IFFF CCI

Graeme H

Posts: 1202
Joined: Fri Jan 25, 2013 2:54 pm
Location: Perth, Western Australia

### Is the cast itself a transverse wave?

A quick question Merlin: In your opinion, how would the tension profile in the graph differ if the elements of the line being accelerated were part of a wave instead of being projectiles only?

How would the graph change when a wave medium undergoes displacement from (say) the left to the right? How would it compare with a projectile of the same mass being launched from the left to the right?

Still thinking on the rest of the answer, but I'm heading off to run a lesson shortly.

Cheers,
Graeme
IFFF CCI

Graeme H

Posts: 1202
Joined: Fri Jan 25, 2013 2:54 pm
Location: Perth, Western Australia

### Is the cast itself a transverse wave?

Merlin wrote:The travelling speed is half of the sum of leg speeds. If you haul you improve both speeds (rotation, travelling). If you pullback you improve rotation but you reduce travelling speed, this is why it should be used as an adjustment.

Thanks Merlin. Makes sense.... I think. When a whip is cracked that is a mighty improvement of dat dere rotation stuff Dude.

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

Posts: 302
Joined: Tue Aug 06, 2013 10:11 pm
Location: Melbourne

### Is the cast itself a transverse wave?

Graeme H wrote:That's okay Mark. It's not really that important unless you're trying to answer certain questions (such as "What was Berlin on about?")

If all you're really chasing is a visualisation of vertical propagation and horizontal displacement, go back to the video I made. It's clear that the waves are moving downwards while the line is moving sideways.

G'day Graeme
Shorter version of potentially much longer response.
I'm a fly fisher with an interest in fly casting. Not the other way around. Casting and physics? Same answer.

Back in Post 3 I stated my position and so far I haven't changed it but not because I'm stupid, obstinate or competitively insecure. I am always open to change. That's the fun part. I may be stuck in the celestial spheres but like to fit in with the rest of the universe and stay relative/dynamic. Some practical incentive would certainly help my escape. Chasing slippery rabbits down moving and multiplying holes? Not my gig mate.

I'm left handed and right brained and I take great delight in mentally holding the absolutes of Newtonian physics within a universe of relative and interactive space time. As you say, light as particle and wave simultaneously is very cute. OTOH maths and formulae are to me like arduous bouts of portage between interesting floats on the river with rapids to negotiate. Shooting a rapid, literally or metaphorically, is a perfect example of risk and reward.

As ever à chacun son goût.

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

Posts: 302
Joined: Tue Aug 06, 2013 10:11 pm
Location: Melbourne

### Is the cast itself a transverse wave?

Hi Merlin,

I've had a little bit of time to think on things and I'm still very happy with your post.

Firstly, I'm extremely pleased you calculated a tension value of approximately zero in your calculations. I actually hope you overestimated it by 0.001 N. Why am I happy? The system was in equilibrium, left oscillations balancing right oscillation and upward force (me lifting the line) balanced by the weight of the line (not accelerating vertically.)

I was aiming for no net acceleration up, down, left or right. It looks like I got very close to that aim. I don't think I could have gotten closer to zero if I had just dangled the line from the tip of the rod.

However, it turns out the default slow speed for iPhone videos is 12%. I'm sorry I didn't know that, and I don't know what it does to your equations. Maybe we'd end up at 0.004 N? I'll still take that!

Forgive me, but I don't think I understand how the tension was derived though. I actually think the method you have used is not the correct one for calculating tension in a string in this case. If all of the line were simply hanging unsupported from the tip, the tension in the line (at the tip) can be calculated with T = Mg, where M = the line mass supported by the tip (which was everything outside the tip). Let's estimate the line was 15m and I'll also assume 1 g/m, so the vertical component of tension measured at the tip due to gravity should be ~0.15 N, since I am not accelerating the line upwards at any point (it's globally in vertical equilibrium.)

(There will be times when the horizontal component is higher as the rod is accelerated left and right, but they are balanced for the duration of the time while I'm holding the array. No net left or right force is being applied.)

I hope you're with me to this point. I hope I've established that T is vertical, and I hope we've already established that the direction of propagation of the wave is also vertically down. I'm really focusing hard on this point because it's crucial. There's a mistake in the underlying assumptions of your calculations from the graph and the conclusions based on those calculations.

Once again, transverse waves are defined as waves in which the direction of displacement is perpendicular to the direction of propagation. The velocity vector of wave propagation shares the orientation of the tension vector (from the equation for velocity).

In the pictured case, the direction of propagation is vertical and medium displacement is horizontal. Vector analysis will show that displacing the line horizontally has no effect on the (vertical) tension derived from gravity.

Tension is a vector. Applying tension to displace the line horizontally during a cast does not modify the tension in the vertical direction and thus does not have any effect on the velocity of propagation of the transverse wave.

In the graph, I assume the majority of the tension is derived from accelerating the line in the horizontal direction, as is common during a cast. There is no indication of the vector direction. Can you shed some light on that? Did they publish vector analysis or was tension supplied as a scalar value only?

I recognise that in the real world, we do need to add some upward trajectory in each phase of the cast. There will be some small upward component of the cast measured for the graph. To get a better picture of any increase in vertical wave propagation speed you'll need to establish the vertical component of the tension of 1.2 N. It's going to be small though*. (How long was the cast? We might be able to make some assumptions and apply them.)

Gravity provides the tension vector required for a transverse wave to propagate in an untethered fly line.

I totally disagree here; you can explain the propagation of an untethered line without gravity at all, just using Newton’s laws (momentum, energy). I can’t see how a transverse vertical wave can explain that but would be please to learn, for me only the dynamics of the (horizontal) loop can do it.

Please read the piece you quoted again. I specifically referred to the propagation of transverse waves, not the medium through which they travel. Waves propagate with a velocity through space that is non-zero. The velocity of a transverse wave through a medium is defined by the equation V=sqrt(T/rho), so if T=0, V=0. There cannot be velocity of the wave through the medium without a source of tension.

You've disagreed by citing examples of the medium itself moving through space, which indeed can be explained with Newton's Laws (and should be.)

Cheers,
Graeme

* I haven't done any calculations but I believe the net effect of false casting is another "balanced array" of waves similar to the small one I filmed. The amplitudes will be significantly higher though, so the line gets to fall further in each phase.

I also think the inclination of those wave legs the the "yellow zebra" tells a story about the total tension in the line. The horizontal and vertical components could be analysed with vector analysis. The vertical component should be ~0.15 N. I don't know how we could use it though - maybe predict how far the line would travel horizontally without further input?
IFFF CCI

Graeme H

Posts: 1202
Joined: Fri Jan 25, 2013 2:54 pm
Location: Perth, Western Australia

### Is the cast itself a transverse wave?

I think I've already stated it somewhere before, but any planar bend that travels through a line is a transverse wave (which obviously includes the ones you've listed Merlin). The trick with the biggest of all the bends is working out where the wave is propagating from and to. We can easily see the medium being displaced, but we never glimpse the wave that the loop is the crest of. Without taking gravity into account, it's easy to see the loop progressing horizontally across the water as not propagating vertically.

However, on Newton's Earth, the line is always falling. When we propagate the wave vertically upwards at just the right velocity, the crest rises at the same velocity as the line is falling, so the whole line appears to defy gravity. But ONLY until the crest reaches the tippet, at which point in time, the whole line continues to fall to earth and the magic is gone.

So many people here have tried to explain the apparent lift generated by the loop or the floating of the line as the cast progresses. They attempt to explain it because it does indeed appear to defy physics. It certainly doesn't behave like a ballistic object. Watch those casts by Christopher Rownes in his video. Magic flows from the wand in his hand.

A transverse wave propagated upwards at the right speed will offer the solution. This is one of the outcomes of breaking the Celestial Sphere.

Cheers,
Graeme
IFFF CCI

Graeme H

Posts: 1202
Joined: Fri Jan 25, 2013 2:54 pm
Location: Perth, Western Australia

### Is the cast itself a transverse wave?

A quick question Merlin: In your opinion, how would the tension profile in the graph differ if the elements of the line being accelerated were part of a wave instead of being projectiles only?

You would see a low level of tension, nearly constant or changing slowly, that depends on external forces like air drag. It could look like the right part of the graphic (loop propagation). A wave is a disturbance within a medium so it does not require a lot of energy. Throwing all the medium needs much more energy.
How would the graph change when a wave medium undergoes displacement from (say) the left to the right? How would it compare with a projectile of the same mass being launched from the left to the right

I cannot visualize that, could you give us an example,? Do you speak of a medium where a wave is already travelling from left to right and you decide to move that medium from left to right too? As I said above the energy required to disturb a medium is small compared to the energy needed to move the entire medium. The medium itself cannot be considered as a wave, or we are in another world of physics.

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

Merlin

Posts: 1072
Joined: Wed Jan 09, 2013 8:12 pm
Location: France

### Is the cast itself a transverse wave?

Now a lot of questions are coming up and need some time to answer (globally I hope)
I shall do my best to avoid a contest, but the starting point does not looks so good

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

Merlin

Posts: 1072
Joined: Wed Jan 09, 2013 8:12 pm
Location: France

### Is the cast itself a transverse wave?

Merlin wrote:I cannot visualize that, could you give us an example,?

No, sorry about the questions. I couldn't delete the post after I realised they were redundant. You can ignore them

Cheers,
Graeme
IFFF CCI

Graeme H

Posts: 1202
Joined: Fri Jan 25, 2013 2:54 pm
Location: Perth, Western Australia

PreviousNext