Understanding Casting

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Grizzle Duster

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Perhaps I can introduce myself as a new forum member with a few comments on the physics of fly casting: fly-fishing is my hobby, but physics has been my day job at a university for more than 40 years. James9118 has already made some good contributions above, and perhaps I can also chip in alongside him to help explain some of the basic physics for those who are curious.

As the discussion in this thread illustrates, it's quite complicated to analyse the mechanics of both the rod and line together. Even very bright physics undergraduate students would find it challenging. So, to understand the formation and propagation of the all-important loop in the forward cast, it's best to concentrate first on understanding the mechanics of the fly line itself.

To make the problem simpler (as physicists are prone to do), we neglect gravity and air resistance and also assume that the fly line is perfectly flexible (i.e., we neglect its stiffness). In that case, one can show (from Newton's 2nd Law) that the radial component of acceleration of a fly line that is curved into a loop of radius R is T/(mu.R), where T is the tension in the fly line and mu is its mass per unit length. (The radial acceleration acts towards the centre of the circular loop, in much the same way as an object undergoing circular motion requires a 'centripetal' force acting towards the centre. In general, a curved fly line does not form an exactly circular loop. However, at each point on the line, R is then the local radius of curvature, and the acceleration formula is still valid.)

The tension T in the fly line (exerted by the caster holding on to the stationary end of the line) is absolutely crucial to the propagation of the rolling loop in the forward cast. The motion of the rolling loop is quite similar to a wheel rolling along the ground (without slipping). So, if a semi-circular loop rolls forwards (away from the caster) with speed v, the base of the loop (equivalent to where the rolling wheel touches the ground) is stationary, whilst the top of the loop moves forwards with speed 2v (i.e., the line speed is twice the speed of the rolling loop). The radial (or centripetal) acceleration of the rolling loop is then (v*v)/R = T/(mu.R), where R is the radius of the loop. Hence, the speed v of the rolling loop is equal to the square root of T/mu. This is exactly the same formula as the speed of transverse waves (mentioned by James above) on a stretched string (like a piano or guitar string). Hence, if the rod tip vibrates after the flick at the end of the cast, then you see transverse waves (ripples in the fly line) chasing after the rolling loop.

It follows that, to cast a tight loop (with small radius R), we must impart a large radial acceleration to the fly line at the rod tip. During the forward cast, the rod tip first accelerates smoothly forwards (parallel to the fly line) in a straight-line path (the 'SLP'). This pulls on the fly line, and the tension in the line loads the flexible fly rod. If the rod tip moves along the SLP, there is no radial acceleration during this part of the forward cast. However, the accelerating 'power stroke' finishes with a slight forward flick (or tap), at the end of which the casting hand stops abruptly. This suddenly flexes the rod tip, which then flicks forwards in an approximately circular arc as it unloads, and (some of) its stored elastic energy is transferred to the fly line. So, it is the flick at the end of the power stroke that initiates the circular motion of the rod tip, and this creates the large radial acceleration that forms the tight loop. A smaller radial acceleration (for a given line velocity) produces a wider loop, whilst deviation from the SLP during the power stroke creates ripples in the line that may produce a tailing loop.

The above (albeit simplified) analysis describes some of the basic physics of fly casting. Of course, you don't need a physics degree to cast a fly. But it's fun to see how Isaac Newton can help us understand what, to the uninitiated, may seem almost like magic. Or, as Albert Einstein put it rather more elegantly: "Joy in looking and comprehending is Nature's most beautiful gift."

Neil.
 

geenomad

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I agree..I think... the concept of the rod as a spring has for years smothered the important job that the rod bend does for the cast.
Hi Alan
Don't want to get sucked into tackle or distance casting rabbit holes but yes the bendiness of the lever is useful in ways we seldom well understand. There is a delay at the beginning and end of the stroke which are useful to us. Caster power on - delay - line begins to move. Caster power off - delay - rod continues to accelerate line as "the spring" unloads. Counterflex gets the tip out of the way. These delays are easier on the software - us and our soft tissue and joints.

As Mark Surtees explained, while cluing me into the notion of Impulse, much of our preference in rod action (bendiness character) is due to what length of delay suits us as casters.

I think folks keep banging on about how well "line X loads rod Y" because they are expressing a feel thing, the feedback they are getting in the rod hand. It's often the heavier lines that are favoured for "rod Y". Improved casting technique can lead to different tackle preferences or needs but all that's another story.

Cheers
Mark
 
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andygrey

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Surely there's nobody alive that still thinks of the rod as a spring? I've been here 6 years and never heard anyone say it. (I've seen the words 'spring', and 'load', trigger a few land mines but I've never had the impression that the user thought that rods were just catapults,

Time to just let it go. Boing.

Can you explain this a bit more?
The 'spring' myth is alive and well. This is an extract from a website of a UK fishing guide...

The cast uses the weight of the line to load the rod like a spring or a catapult before throwing the line in the direction of the fish.
 

James9118

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@Grizzle Duster
Neil - good luck!
With regard to transverse waves, perhaps we could discuss the difference in conditions that exist in the rod-leg versus the fly-leg. Transverse waves in the rod leg i.e. wobbles from the rod tip counter-flexing, aerial mends etc., are much more 'predictable' due to the tension in that portion of the line. The fly-leg, where 'tailing loops' appear, is a much more complicated scenario, and I've found wave analogies to break down pretty quickly here.
 
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Tangled

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Welcome Neil, pick up a stump and set awhile - great to have another mind on this.

I'd also like to hear more about tailing loop formation and propagation - I have questions!
 

Tangled

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Bead chain falling. Loop shape looks very familiar.

Mind numbing fact, the arrow on the left is a metal bead released at the same moment as one leg of the chain. The chain is accelerating faster than gravity.


page2image1467474112


The reason is conservation of energy

"This is because whenan object is suspended it has initial potential energy mgh . When it is dropped and2 reaches the bottom of its fall, it has zero potential energy and kinetic energy 12 mv. This energy must be conserved, however, and in the case of the chain, the mass of the moving section is constantly decreasing. To compensate and maintain the same energy, the velocity is higher than if the mass were constant, as in a free falling object."

(Been looking at whips, people have done more work on them than fly rods)

 

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aenoon

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Bead chain falling. Loop shape looks very familiar.

Mind numbing fact, the arrow on the left is a metal bead released at the same moment as one leg of the chain. The chain is accelerating faster than gravity.


View attachment 43798

The reason is conservation of energy

"This is because whenan object is suspended it has initial potential energy mgh . When it is dropped and2 reaches the bottom of its fall, it has zero potential energy and kinetic energy 12 mv. This energy must be conserved, however, and in the case of the chain, the mass of the moving section is constantly decreasing. To compensate and maintain the same energy, the velocity is higher than if the mass were constant, as in a free falling object."

(Been looking at whips, people have done more work on them than fly rods)

So how is single bead actually catching up on the head of the loop then?
 

Rhithrogena

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Good stuff here; closest I have yet come to understanding how a cast can 'defy gravity' (or seem to...)
Light bulb moment💡
 

Grizzle Duster

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Thanks for the words of welcome above - sorry I haven't yet got the hang of quoting individual posts.

To understand a fairly complex mechanical problem like fly casting, it's best to strip away as many complications as you can, without throwing away the essentials. Of course, gravity plays a role in real-life casting, but it doesn't amount to much more than having to angle a bow and arrow slightly upwards to achieve distance. Pace Mr Hird (who is a obviously a very good caster), it's not really relevant to the central idea of loop formation and propagation. Moreover, despite what he says in his video, the propagation of the rolling loop is indeed a type of wave motion. However, it's not a 'harmonic' wave (like a small-amplitude ripple, which has a definite wavelength and frequency). It's more akin to a 'solitary' wave, or 'soliton', which is a large-amplitude wave that propagates (ideally) without change of shape in a non-linear medium - the Severn Bore is a well-known example.

James's point about the difference in the waves in the rod leg and the fly leg is a fair one. In the simplified picture that I outlined, the tension is constant in the rod leg, so the wave velocity there is the same as the loop velocity. However, in the fly leg, the tension decreases progressively from the loop towards the fly, so the wave velocity in that leg must also decrease owing to the square-root dependence of velocity on tension. (For a real fly line, one should also consider the effect of the line taper.). The fly leg moves forwards at 2v, so I think backward-propagating ripples on the fly leg will still move forwards relative to the caster.

James also pointed out early in the thread that some ideas in published scientific articles on fly casting are circumspect. That's generally true of science, because ideas are developed and tested over time and some are discarded. One paper that impressed me (and which I think has stood the test of time) arose from a collaboration between Bruce Richards and Prof Noel Perkins at Michigan University. There's mo maths in this paper and it's accessible to everyone at https://link.springer.com/content/pdf/10.1007/BF02844862.pdf. To study the physics of Bruce's expert casting, they attached a gyro sensor to the rod butt to measure it's angular velocity, and they also filmed the casts in slow motion. In addition to the paper, there are two nice videos on Youtube showing a tight loop at
and a tailing loop at
. Studying these videos and the paper should answer many questions for those who are trying to understand the physics of fly casting.

They also summarize the essence of casting very succinctly:

"...both the forward and back casts begin with the same smooth increase in angular velocity (modest angular acceleration), followed by a quick ‘stop’ (large angular deceleration). The stops are followed by a 'rebound’ during which the fly rod flexes (vibrates in fundamental bending mode), providing a reaction moment on the caster’s hand. The amount of this rebound is indicative of how much the fly rod flexed as the caster ‘loads’ the rod during casting, and good casters load the rod significantly while casting long distances. The loop is formed during the stop and the best loops are formed by a well defined stop (i.e. very large angular deceleration)."

To me, the tight-loop video (and gyro measurements) show the importance of loading (and unloading) the 'spring' of the rod. So, I don't think it is a 'myth', despite some of the comments above. It's also in accord with my own (limited) experience with a fly rod. But I'm not an expert caster, so maybe someone can post a video of them casting tight loops with a broomstick (or some other kind of rigid lever) to show us that they don't need the fly rod to flex.
 

Grizzle Duster

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Sorry, but this is a very long thread! I'll look back to find James's broomstick/lever bit.

As an experiment, I tried to cast a French leader on grass the other day with a #3 rod - no rod flex and could not create a decent loop, but I'm only an average-ish caster.

Neil.
 

Tangled

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Sorry, but this is a very long thread! I'll look back to find James's broomstick/lever bit.

The received wisdom is that good casters can cast with an inflexible rod but not as far as a flexible one. Loops are apparently tight but it's not good on joints.

Thanks for the words of welcome above - sorry I haven't yet got the hang of quoting individual posts.

It depends a little on the device and browser that you use, but if you click on the reply button at the bottom right of the thread, the whole post will be quoted.

If you then go to the top of the post, you'll see QUOTE= etc inside square brackets.

You can go from there to the end of the paragraph you want to quote enter a carriage return and it should put the paragraph in a grey box and allow you to type your reply.

If that doesn't work, just put the bit you want to quote like this - using square brackets instead of round brackets

(QUOTE) This makes a quote (/QUOTE)

It comes out like this

This makes a quote

You can name who you're quoting like this

(QUOTE=Tangled) This makes a quote (/QUOTE)


Tangled said:
This makes a quote
 

LukeNZ

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What? you mean the tangled view of gravity? rather than Newtons?

The irony of all this, is that some of us can cast a line much better, and further than Newton would have ever been able to, despite him being able to explain more ably than any of us how it works….

Tangled wants to understand and explain to the casting world what exactly?

In light of the above, most likely; nothing useful…


🙃
 

Tangled

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I found this graph fascinating. Showing how symmetrical the forward and back cast is with an expert caster and also how smooth the acceleration to a dead stop is.

Screenshot 2021-09-25 at 11.00.18.png
 

James9118

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I've been out to do some casting with a 'broomstick' this morning. Actually its the bottom three sections of my competition salmon casting (S55) rod, I think some would describe this rod as a 'broomstick' even with the tip section in place, with it removed what's left is incredibly stiff. On this I put a #5 line.

There's a couple of things that are immediately obvious, firstly there are no wobbles, wrinkles etc. in the rod leg (just a bit of sag due to gravity) - this is because the rod didn't bend so there's no counter-flexing etc. Secondly the very front of the loop looks a little odd - I believe this is because the stiffness of the line doesn't really want to go around the bend radius that this sort of outfit produces in terms of the loop front.

I'd forgotten how much hard work it is casting 'bromsticks' so I gave up quite early to protect my elbow. Given a bit more time I would get the loop a lot tighter than in the photo. The distance cast was an easy 80ft plus.

Broomstick_Moment (2).jpg
 
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