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## Two heads cast at the same time

Moderator: Torsten

gordonjudd
Posts: 1298
Joined: Sat Jan 19, 2013 11:36 pm
Location: Southern California

### Re: Two heads cast at the same time

Obviously there is more than one factor at play here.
Paul,
There are two primary considerations going on here.

1. There is a positive acceleration force on the fly leg due to the tension at the top of the loop that is due to the momentum change of the moving mass going around the loop. That positive force is nominally proportional to the linear mass density of the line and the square of the loop velocity over the ground (assuming a tethered cast).

2. There is a negative acceleration force on the fly leg due to the drag losses on the loop, trailing line, and fly. The skin drag depends on the diameter squared of the trailing line, the square of its velocity (=2*loop velocity) and the length of the fly leg. There is also a form drag component on the fly that depends on the diameter of the fly and the square of its velocity. If the fly leg tilts down (the general case) then it will also have a sizeable form drag component that depends on sin(angle of the tilt), line diameter, velocity squared, and the length of the fly leg.

At the start of the cast the drag losses are large due to the length of the line. In the case where the fly leg is very long the combined drag losses will in general be larger than the positive tension force and the fly velocity will tend to decelerate at the beginning of the loop propagation.

Near the end of the cast the drag losses on the line are much smaller and the loop will tend to accelerate. That is especially true for a level line that has a constant linear mass density over its entire length.

However, if the end of the line is tapered then that will reduce the positive acceleration force due to the reduction in the linear mass density of the line. The linear mass density(rho_l) depends on the square of the diameter so halving the line diameter will cause a factor of 4 reduction in rho_l.

If that taper is enough then the positive acceleration force will be smaller than the drag force (at the end of the cast the drag forces on the fly may be the dominate drag loss) and the fly velocity will decrease. That is especially true when a long leader starts going around the loop. The thin leader will have a much smaller rho_l that pretty much guarantees the fly velocity will decrease and produce a smoother turn over of the fly. This is what Merlin is referring to when he talks about exponential deceleration

It takes a complicated ODE to keep track of the competing acceleration and deceleration forces as the fly propagates even for a level line. When the line is tapered it becomes a programming nightmare, and my hat is off to Lingard, Spolek, and Gatti-Bono for figuring it out.

Gordy

gordonjudd
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Joined: Sat Jan 19, 2013 11:36 pm
Location: Southern California

### Re: Two heads cast at the same time

At least one of them must be a steaming pile of horse manure right?
James,
If you have read those papers then you would understand they are using the same formulation of the ODE required to model the expected fly velocity history.

The difference in their results is due to the different values they used for the loop diameter and especially the skin drag coefficient. For some reason Gatti-Bono used a value of .075 while Lingard was using the value given by White that is around .0022. Thus Gatti-Bono's value was about 15 times too high and Lingard's value was about half the measured value of .005 given by Gaddis.

Rest assured, if you use the same input values, the ODEs developed by Lingard and Gatti-Bono will produce the same result for the expected fly history.
If you want more details you can find them in this topic viewtopic.php?p=15501#p15501 on the old board that attempted to debunk the use of the conservation of momentum concept to predict what the fly velocity history would be for a given cast.

To save you the trouble, here is the relevant graph that shows the closed form equation that Gatti-Bono produced for a level line (the blue curve below) is an overlay to Lingard's model(green curve).

Have you found a technical paper reference that back ups your contention that:
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?
Somehow I think that is an impossible task since aside from analyzing what happens in a collision I don't think I have any published papers that use the conservation of momentum concept especially ones dealing with fly casting.

Gordy

gordonjudd
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Location: Southern California

### Re: Two heads cast at the same time

The information given by Josh and Bruce is fine as long as we neglect air drag,
Merlin,
I think you are being a bit kind.

I was disappointed to see a reference to the "big spring" theory
The potential energy stored in a bent rod is transformed into kinetic energy in the line.
and using COM to explain the speed up of the line during a cast.
The final part of all of this is momentum which is governed by this equation: p=m*v (p=momentum, m=mass in motion, v=velocity). So a rear biased line travels faster, but has less moving mass at the end of the loop.
Also if they mentioned rho_l*v_loop.^2 in regards to producing the positive acceleration force on the rod leg I missed it. That is half of what is going on, so I was surprised to see it left out of their discussion.

Gordy

Merlin
Posts: 1372
Joined: Wed Jan 09, 2013 8:12 pm
Location: France

### Re: Two heads cast at the same time

You are right Gordy, I skipped the big spring and COM (which would be ok for an untethered cast), COE is the baseline when you neglect air drag.

It shows us that one can make lines (valid for rods as well) without knowing the physics in detail

I guess we could find a qualitative consensus to satisfy Paul, but maybe I am optimistic.

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

Paul Arden
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Location: Belum Rainforest
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### Re: Two heads cast at the same time

Thanks Gordy, so in effect you have accelerating force from the loop front vs drag forces on the line - post 21, a very clear answer. I can understand that.

Alas I think there may be some disagreement. Graeme, James - Gordy posts a very clear explanation as to why and how a front taper can result in both acceleration and deceleration of the loop. I’m fairly sure that you’re going to have a different explanation?

I’d love to hear it.

Thanks,
Paul
It's an exploration; bring a flyrod.

Flycasting Definitions

Merlin
Posts: 1372
Joined: Wed Jan 09, 2013 8:12 pm
Location: France

### Re: Two heads cast at the same time

The answer is in air drag Paul. You can have better acceleration conditions due to the fact that more mass leaves the loop by comparison to the mass entering the loop at the same time, but air drag can, under some circumstances, spoil that trend to the point that there is no acceleration any more and a deceleration takes place. It depends of several parameters (e.g. loop size, fly drag, etc.) and on line diameter.

As the front taper enters the loop, it contributes to accelerating the line but at some stage the situation is going to be reversed because the line within the loop becomes too sensitive to air drag. If you use #15 line, the deceleration might never show up, but if you use a #5, that deceleration is very likely.

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

Will
Posts: 292
Joined: Thu Jan 10, 2013 9:44 pm

### Re: Two heads cast at the same time

Merlin wrote:
Wed Jun 19, 2019 7:03 am
I agree with Torsten, comparisons are made out of the full context (assumptions). The information given by Josh and Bruce is fine as long as we neglect air drag, but this is the source of losses. And by the way I do not understand that sentence (Graeme in another thread).
Energy was dissipated in the taper because the mass of each dot was less than the one preceding it into the loop.
Where is air drag?

If one introduces air drag in the assumptions, then one can find that this phenomenon is related to the diameter of the line section. There are two limits in diameter which depends on various conditions (loop height, fly drag, etc.).

A first one (approximately 0.85 mm for a 2 feet loop and a dry fly) is the dimension corresponding to a rather constant fly leg velocity. Below this diameter the line decelerates, which explains why a #3 is not designed for distance and why the front taper can finally decelerate the line. A second one (approximately 0.45 mm in the same conditions, which may correspond to the butt of a trout leader) below which the deceleration becomes exponential.

This explains the final deceleration due to the leader, and also this remark from Bruce about the tip of the MED:
The MED is designed with a rather long front taper for smooth turnovers, but with an oversize tip to insure it does turnover at distance.
Hope this helps to understand the questioning about the final stage of rollover.

Merlin
This is a very interesting statement Merlin. Can I infer from this that at diameters above 0.85mm drag is not as important and a taper will accelerate? That would explain Lee’s Scandi line comparison where we have a couple of chunky lines which are prob >0.85 for most of their length.

Could you perhaps say something about the maths that set the limits you mention?

Cheers

Will
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Will
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Joined: Thu Jan 10, 2013 9:44 pm

### Re: Two heads cast at the same time

Cross-posted! I think you just answered my question!
Lineslinger
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"The only advice it is necessary to give the angler… is to avoid any approach to foppery, as trout have the most thorough contempt for a fop…”
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Will
Posts: 292
Joined: Thu Jan 10, 2013 9:44 pm

### Re: Two heads cast at the same time

Still be interested in the maths principles which set the limits you mention! Many thanks.

Will
Lineslinger
Barrio Pro-team
SGAIC
AAPGAI

"The only advice it is necessary to give the angler… is to avoid any approach to foppery, as trout have the most thorough contempt for a fop…”
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Graeme H
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Joined: Fri Jan 25, 2013 2:54 pm
Location: Perth, Western Australia

### Re: Two heads cast at the same time

Paul Arden wrote:
Thu Jun 20, 2019 7:47 am
Thanks Gordy, so in effect you have accelerating force from the loop front vs drag forces on the line - post 21, a very clear answer. I can understand that.

Alas I think there may be some disagreement. Graeme, James - Gordy posts a very clear explanation as to why and how a front taper can result in both acceleration and deceleration of the loop. I’m fairly sure that you’re going to have a different explanation?

I’d love to hear it.

Thanks,
Paul
Yes, I disagree with Gordy. I've explained why numerous times in the past and it's a waste of time doing it again. The message isn't getting through.

I'll show you why he's wrong when we catch up next month.

Cheers,
Graeme
FFi CCI