Angular Momentum

[Graeme H]

I'll ignore Gordy because we've covered that ground already.

I've been working on the question about how a taper can be utilised to both dissipate and increase the velocity of the fly within the same line by modifying the tension in the rod leg.

James got me thinking about angular momentum so I analysed a few of my videos with that concept in mind, seeing if I can work out why sometimes the fly can accelerate beyond the breaking strain of the tippet, while at other times it can be placed most delicately on the water surface. During casting, I've noticed:

• Rapidly pulling the line as the loop approaches the leader can cause a "crack of the whip", especially if there is no fly attached to the tippet. (Velocity increased)
• Lowering the rod tip as the loop approaches the leader can let the fly touch softly down (Velocity dissipated)

Increasing tension in the rod leg speeds up the fly, while decreasing rod leg tension slows it down.



I don't know exactly why that's happening, but if the answer is "angular momentum", then it might be explained by the amount of line following a curved path as it enters the loop. If more line is subject to angular momentum, perhaps more accelerative force from that line is applied to the fly leg? If that's the case, then pullback at the right time can crack a whip, and with the same line, we can also wipe off speed by dipping the rod tip at the right time.

If the line in the rod leg is stationary, about a quarter of an oval is occupied:

Capture from halted rod leg

If the line in the rod leg slides forward, less of the fly leg is pulled into an oval shaped path:

Capture from rod leg sliding forward

If the rod leg is pulled back during the cast, nearly half an oval is occupied:

Capture from snap cast

In the snap cast, we have a LOT of line moving rapidly in a curved path. If angular momentum in a fly line is real, there is a lot of it in a snap cast, and we also see the fly leg accelerate markedly in the snap cast. We can enhance turnover in a failing cast by pulling back on the rod leg near the end of the cast.

In a delicate cast, we can soften the impact by pushing the rod tip forward, inhibiting turnover.

As I say, I don't know if this is the answer to Will's question, but it's something that's working for me right now. I'll keep thinking on it.

Cheers,
Graeme

[Graeme H]

I'd love to have markers on this line to run through Tracker:



Alas, there's not much chance of finding good values for angular momentum.

Cheers,
Graeme

[Torsten]

Hi James,

Torsten, so by the same reasoning you'd dismiss hypotheses based on conservation of linear momentum then, i.e. most of the published papers on fly casting?

Many papers that I've read derive the basic equation of motion by the conservation of energy rather than conservation of momentum and include also losses (such as Spoleks paper). Conservation of momentum is not applicable, because constrained motions and external forces. One simple example where conservation of momentum is not valid is the pendulum, you can derive the basic equations of motions by the conservation of energy principle - for instance using Lagrangian mechanics. Once you have these equations you can include losses (damping coefficients etc.) as well.

--

Graeme:
Angular (or rotational-) momentum is applicable for any rotating solid. It's more a question of significance, e.g. most parts of the loop do not rotate. I could imagine however, that it plays a certain role for acceleration of the top leg. All your above examples show some kind of acceleration; this is only possible if a certain force at the loop front pulls at the remaining fly leg (else the fly leg would only deaccelerate due losses). I'd say that both the transfer of linear and also rotational momentum is happening at the loop front when it's unrolling.

Because of losses we don't see that much acceleration for basic casts - I think fly lines are also designed to dissipate energy, else we would get a horrible presentation of the fly. Spolek's paper shows also only a slight acceleration for ordinary fly line tapers and including air drag. With some kind of extreme triangle taper we should see a more significant acceleration.

It should be possible to compute both rotational and linear momentum from your videos, maybe Gordy has some ideas to derive that from the video material.

[gordonjudd]

Even with that in mind I think the conservation of angular momentum helps to explain why the loop diameter reduces when the heavier linear mass momentum of a sink tip line enters the loop as shown below for a Tenny 450 line.

To self,
Wrong again.

In looking at Mike Hendry's thesis I think he would explain that the reduction in loop size is due to the conservation of vertical momentum in the loop not angular momentum per se.

Gordy

[gordonjudd]

The plan is to cast them in different configurations alongside a “control” line and film the loop morph.
and
With some kind of extreme triangle taper we should see a more significant acceleration.

Paul,
Torsten's suggestion is a great test case.

If you can I would like to see the relative loop velocity of a triangular taper vs the propagation with a reversed triangular taper. I would expect the reverse taper would win out, but only a controlled test case will tell.

If it was the tip of a heavier floating line would it still narrow or open?

It is the linear mass density that is important to the vertical momentum component, so the loop going from a section of #5 line to a #9 line should narrow.

Just as with terminal velocity the form drag increases with the diameter, while the linear mass density scales with the square of the diameter. Thus the loop speed in the heavier #9 line should increase faster than the loop speed for a #5 line.

Again only a test case will tell for sure.

Gordy

[gordonjudd]

Many papers that I've read derive the basic equation of motion by the conservation of energy rather than conservation of momentum

Torsten,
Same here. I did a word search for "conservation of linear momentum" in the papers I have in my records, and came up empty every time.

That is why I am interested to see the papers that James referred to when he said:

Torsten, so by the same reasoning you'd dismiss hypotheses based on conservation of linear momentum then, i.e. most of the published papers on fly casting?

I thought I had copies of most of the technical papers related to fly casting, but obviously not if some researchers are basing their analysis on the conservation of linear momentum.

Gordy

[Graeme H]

It should be possible to compute both rotational and linear momentum from your videos, maybe Gordy has some ideas to derive that from the video material.

Hi Torsten,

That type of computation is built into the Tracker software. I've only been showing the video representation of the data but there's a panel with graphs I've been excluding. When I get home tonight, I'll screen capture a few of them for you. I can also export data files with X-Y positions, velocities, momentum, angular velocities, etc.

Unfortunately, the calculations are approximations because I can't get true frame rates out of the iPhone's capture and I don't have exact mass values for each marker. The distance calibration is carried out on two of the markers themselves too, so there is distance error due to the tolerance of my markings on the line. But the values work on a relative basis within each video.

Cheers,
Graeme

[Graeme H]

In looking at Mike Hendry's thesis I think he would explain that the reduction in loop size is due to the conservation of vertical momentum in the loop not angular momentum per se.

So the loop - uniquely within the universe - is immune to the effects of gravity? Its vertical momentum is conserved rather than increasing over time?

No wonder they call the fly rod "The Long Wand".

Cheers,
Graeme

[Merlin]

Hendry’s thesis is on my desk, and he calculated the rate of change of vertical momentum to draw his conclusion. It is clearly non conservative.

Sorry for the confusion raised by Gordy’s post on this point.

Merlin

[Merlin]

In the snap cast, we have a LOT of line moving rapidly in a curved path. If angular momentum in a fly line is real, there is a lot of it in a snap cast, and we also see the fly leg accelerate markedly in the snap cast

Graeme,

In the thread "Anatomy of a snap cast", in the tech forum, I simulated one of yours and I never needed to consider angular momentum to get close to measurements. I used momentum in the direction of the cast. So I would say that if there was an impact of angular momentum, assuming we can evaluate it, it should remain small.

Merlin