Loop Dynamics

[VGB]

In this case we have a constant linear mass density around the loop and R is constant but tangential speed is constantly varying. The centripetal force is constantly changing as we go around the loop. As I said previously I haven’t done a model but I expect the structure of the semicircular loop is not stable because of the non constant forces.

This for me is the crux of the discussion, it produces a completely different hypothesis to the moving frame that indicates that loops are stable for all fly line speeds.

Regards

Vince

[Merlin]

Is this a measured observation or a forecast from your model?

None of these Graeme

I repeat what I said differently: shooting line means that you increase rod leg mass and rod leg speed, in other words, you impart kinetic energy in that leg. Where can it come from? A magic spell or something?

Merlin

[Merlin]

The reference frame selected by Dr Perkins seems to produce a different outcome to the moving frame and I think that is worth investigating. I asked Gordy previously where he was taking his reference from and didn’t get an answer, perhaps you could explain it?

No Vince, I’m not interested in that comparison and let Gordy answer.

This for me is the crux of the discussion, it produces a completely different hypothesis to the moving frame that indicates that loops are stable for all fly line speeds.

May I state what I understand from this “crux”? In the moving frame, I can consider the tangential speed of the loop and calculate tension from centripetal forces and guess what, I can find the “string formula” for tension at the ends of the loop. But viewed in the earth frame, the speed at the top is tangential and equals Vfly whilst it is tangential and nil at the bottom. So on one end I anticipate a large centripetal force and zero at the other end. Consequently that suggests an asymmetry in forces on the loop which should morph. Generations of academics have missed that point.

You cannot be serious (John Mc Enroe). I have a number of dunce caps available.

Merlin

[VGB]

You cannot be serious (John Mc Enroe). I have a number of dunce caps available.

I can understand why you have so many Daniel

I can find the “string formula” for tension at the ends of the loop.

I take it from there that you now agree with Dr Gatti-Bono about the importance of bending stiffness in the low tension region at the bottom of the loop and that your model now predicts the same outcome as real life?

https://www.sexyloops.co.uk/theboard/vi ... 230#p45198

Consequently that suggests an asymmetry in forces on the loop which should morph. Generations of academics have missed that point.

No, only the ones here.

Vince

[Walter]

Merlin,

Glad to see you have made a speedy recovery. I hope that this isn’t getting you out of bed too soon. I know that when I had covid and I thought I was recovered, I wasn’t. It took an additional couple of days of rest to fully recover.

Let’s back up the train a bit.

What I have been talking about is the loop and only the loop. I thought that was clear but apparently not so. For discussions that follow I am only considering the loop to be the section of line from where the line begins to leave the fly leg and begins to accelerate around the loop to the point at the bottom of the loop where in the tethered cast the magnitude of the velocity is zero. Since it is currently a semicircular loop it is the portion of the line that is subtended by a 180 degree section of that semicircle whose central point in the x direction is one radius length from the loop nose and whose y location is the midpoint of the line that joins the x and y legs. The only role the fly and rod legs plays is that since they are parallel they set the orientation of the x axis for a horizontal cast in the earth frame. The energy of the rod leg is not part of this just as the energy of the fly leg is not part of it. They only provide reference points.

In making the transition from a tethered cast to the shooting cast I think it is acceptable to define the speed at the top and bottom of the cast in terms of the speed at the fly and rod legs. Up to now nobody has had a problem with the concept that, even though the fly leg is not part of the loop we can specify the speed of the top of the loop as the speed of the fly leg. If you have some way of disambiguating this for future discussion then please feel free to suggest it. Also, this is not a time based analysis (yet). It is a snapshot. Changing the magnitude of the velocity at the top and bottom of the is not considered at this time.

Thank you very much for the calculated value of the total am of the loop. I can use that to refine the model. As I described it, it is a finite element model. Given Gordy’s earlier statement that the accumulated am would be the same in both frames and having no other data to tune the model with I selected an element size based on obtaining the same am in both frames.

I will post additional results when I have refined the model.

[Paul Arden]

Welcome back Daniel. I hope you are feeling better. It certainly knocked me out for about a week. However I’ve knowingly avoided it twice since then.

Cheers, Paul

[Walter]

In the previous exercise without shooting, you calculate the AM at start, not its evolution as a function of time. Curiously I do not find the same amount of AM (around 0.0082 for you), I have something just below that level (0.00785). The calculation is: loop mass * squared loop diameter * rotation speed: 0.0157 * 0.5 ^2 * 10 / 0.5 = 0.0157*0.5 = 0.00785. Is it a question of rounded numbers?

Frankly speaking, I still do not see the benefit in understanding of using two frames for comparison of AM values.

Merlin

Hi Merlin,

Using a smaller step size the total angular momentum in the loop centric frame is .00785. The total angular momentum in the fixed frame is .00789. I'm not sure if you consider the difference between the two significant but going to a smaller size until we get convergence to several significant digits has diminishing returns in my opinion. I'll attach the updated charts.

I'm also unsure if there is any benefit but the work has been done so best to capture it. The total am around the loop in the loop centric frame matches the total am in the fixed frame for one specific cast only (parallel legs, tethered cast, semicircular loop) and even for that cast the distribution around the loop in the two frames is not the same. How that distribution affects the evolution of the loop over time is yet to be determined. I think that is worth discussing.

Here are the new charts.

Angular moment distributed hr.jpg (46.28 KiB) Viewed 260 times

Accumulated AM smaller steps.jpg (48.83 KiB) Viewed 260 times

[VGB]

The total am around the loop in the loop centric frame matches the total am in the fixed frame for one specific cast only (parallel legs, tethered cast, semicircular loop) and even for that cast the distribution around the loop in the two frames is not the same. How that distribution affects the evolution of the loop over time is yet to be determined. I think that is worth discussing.

That’s tidy work again Walter.

I’ll risk a penguining and suggest that I think that the relevance of the reference frame selection depends on the question you are asking. If it is “how much angular momentum is there in the loop?”, the frame doesn’t matter but the moving frame provides a much simpler calculation.

If the question is “where is loop momentum distributed relative to the intended direction of the cast”, the frame does matter because you are looking beyond the loop. As casters, I think we are interested in the direction of the cast.

[Walter]

Is this a measured observation or a forecast from your model?

None of these Graeme

I repeat what I said differently: shooting line means that you increase rod leg mass and rod leg speed, in other words, you impart kinetic energy in that leg. Where can it come from? A magic spell or something?

Merlin

Daniel,

Whether we shoot line or not the rod leg will gain mass. When we shoot line additional line is also being pulled through the rod guides and that line is added to the rod leg. I think that’s straightforward.

I’m confused by the idea that the rod leg is also increasing in speed. When the cast is tethered the rod leg speed is always zero but are you saying when shooting line that the entire rod leg speed is continuously increasing after its initial formation? I.e if I pick a point on the rod leg between the loop and the rod guides the speed of that point is continuously increasing? Are you referring to the part that is being pulled through the rod guides going from rest to some non zero speed?

Do you have any sort of mathematical function through your modeling efforts that would indicate the change in kinetic energy in the rod leg? That might make it easier to visualize.

If this from your modeling efforts are you treating the system from the point of view of energy conservation when shooting line? It seems to me that the interaction between the line joining the system as it gets pulled past the rod tip would be in the category of an inelastic, aka sticky, collision in which momentum, not energy, is conserved.

[Merlin]

Using a smaller step size the total angular momentum in the loop centric frame is .00785. The total angular momentum in the fixed frame is .00789

Hi Walter

Fair enough, hair splitting is not my cup of tea. Since the snapshot is at the very beginning of the cast, what is the point you chose for the earth frame? The bottom of the loop / rod tip? If so, then consider the situation if the loop was 5 or 10 meters beyond that point. Figures would not match I guess.

I’m confused by the idea that the rod leg is also increasing in speed. When the cast is tethered the rod leg speed is always zero but are you saying when shooting line that the entire rod leg speed is continuously increasing after its initial formation? I.e if I pick a point on the rod leg between the loop and the rod guides the speed of that point is continuously increasing? Are you referring to the part that is being pulled through the rod guides going from rest to some non zero speed?

As one shoots line, the rod leg moves forwards and pulls some line out of somewhere (e.g. the ground). The speed of the rod leg increases; continuously or not I have to check some old files.

Do you have any sort of mathematical function through your modeling efforts that would indicate the change in kinetic energy in the rod leg? That might make it easier to visualize.

I shall have a look in my old files, maybe I have to update them somehow.

If this from your modeling efforts are you treating the system from the point of view of energy conservation when shooting line? It seems to me that the interaction between the line joining the system as it gets pulled past the rod tip would be in the category of an inelastic, aka sticky, collision in which momentum, not energy, is conserved.

My god, another collision issue. I think I used something simpler. Give me some time to look at previous work I performed.

Merlin