Physics FOR Fly Casting – The Einstein Series

What the Line Does – Really

Short Version

This is where the going gets harder. Sorry, but there is no short version available.


There is an awful of argument, online and offline, about fly casting, especially about what the fly line is doing and why it’s doing it. The lack of agreement and the surplus of BS which arguments seem to produce are why I decided to write this series.

What follows is my best attempt at explaining simply the things that might matter to a curious caster trying to improve their casting. Trust me, what goes on with the flyline is really quite complex. I’m still getting my head around it all, even as I write the series. Casting isn’t either easy or simple, despite what a lot of (usually average) casters will tell you – at least not when you aspire to excellence.

A grasp of the basic principles of line mechanics provides enough knowledge to reach the objective of better casting. Even that doesn’t come easily. We will need to sift and separate those principles from the hyper technical analysis and, of course, we will need to avoid stepping in the BS. It follows that this episode won’t attempt to give an exhaustive account of the physics of fly line behaviour. That means some things other people find meaningful might get left by the side of my road. As ever, one man’s trash is another person’s treasure.

What do people notice most when they watch fly casting? The loop. The way that beautiful thing sails away from the fly rod and seems to defy gravity is fascinating. Magic eh? Good place to start the story of loops in fly lines.

Lines and Loops – Part 1

In the previous episode I said:

“When the rod straightens fully the acceleration party is over. The line now overtakes the rod tip and a loop is formed. Hold that thought. You will need it for the next part of the series.”

Well, here we are and now you need that thought again.

One last thing before we dive in. For this episode it will be helpful to assume we are considering a standard overhead cast. That might be a basic cast with no hauls and no line being shot or it might include one or both of these add-ons plus others. I will keep you posted on what is in and what isn’t.

Loop Formation

As soon as the rod tip slows the fly line begins to overtake it. The rod tip obligingly moves out of the way to avoid a collision. The flyline stays attached to the rod so when it overtakes the rod tip the flyline divides itself into two legs. The upper leg is known as the fly leg. The lower leg is known as the rod leg. The loop, then, is the transition from a single leg into two legs. The loop/transition moves along the line from the moment of its formation to the completion of turnover, the point at which two legs have again become just one.

Loop Propagation, Loop Travel and Velocity

Such a loop, moving along the fly line from the rod tip to the end of the fly line, is said to be “propagating”. The loop also travels away from us. In other words a loop has two elements of motion – propagation and travel. Understanding the difference is important for understanding how to manipulate these things to our advantage.

The two elements of loop movement get be a bit tricky to grasp. Here is how I look at them. When something is moving, say a car along a highway, it appears to move away from a person standing behind it and towards a person standing some distance away in front of the car’s position. In other words these two people have different perspectives or frames of reference for the moving car. We have no problem getting this duality because it is commonplace.

Loop propagation and travel are also two different perspectives or frames of reference. Propagation through the line is an internal frame of reference. The loop is like a wave passing through the ocean. It is the wave that moves and not the whole ocean. The ocean is displaced upwards but it doesn’t move otherwise. Imagine you are the line and a loop travels through you from head to toe.

Loop travel is an external frame of the reference. If you are standing on the beach facing the sea the waves are travelling towards you. Imagine I am casting and you are standing beside me watching the loop sail out across the water. It is travelling away from us.

These two aspects of loop motion occur at measurable speeds and both movements are in a direction. That means we can talk about them as having velocity. The velocity of loop propagation (Vp) is the movement/speed of the loop through the line. The velocity of loop travel (Vt) is the movement/speed of the loop over the ground.

Velocity, my friends, is exactly what we are trying to produce – line speed in the intended direction of our cast. Remember net Force and Work and how they are applied in a single direction? They are what we use and line velocity is what we want from them. Controlled line velocity, by the way, is the fundamental objective of everything we do in casting.

The loop is where transition happens. The fly leg has velocity (Vfl) which is lost as the fly leg progressively turns into the rod leg. During this process loop travel (Vt) occurs at half the rate of fly leg movement. Vt = ½ Vfl. Like you, probably, my first response to this was “Huh? Why half?” I still don’t know why exactly but it obviously has to do with the fly leg having to change direction to become the rod leg via the loop. Trust me on this one, loops travel at half the speed of the fly leg.

When the rod leg remains still after loop formation then the velocities of loop travel and loop propagation will be the same. Vt=Vp.

However, when the rod leg moves it will also have a velocity (Vrl). Accordingly, our understanding of loop travel needs an adjustment and we need to consider the relative movement and velocity of the two legs. (Vfl – Vrl) So our equation becomes Vt= ½ (Vfl – Vrl).

Bear with me while I explore what happens when rod leg moves a) in the opposite direction to the fly leg and then b) in the same direction. I know it is tricky to keep a mental hold on four velocities at the same time – one for each of the two legs of the line, one for loop propagation and one for loop travel. Not my fault though, this is what is going on and I’m just the messenger so don’t shoot me ok.

Snap Cast

When we make a snap cast the loop seems to hover. That shows it is possible to have lots of propagation (Vp) and very little travel (Vt). What’s going on? The rod leg has been made to move at least as fast as the fly leg – the exact opposite of what we do in a basic cast where the fly leg is made to move faster than the rod leg. In a snap cast we enhance propagation at the expense of travel.


If we use the rod to pull back on the rod leg and move it in the opposite direction to the fly leg it will also affect the relative speeds of the line legs and enhance propagation – though not as much, of course, as a snap cast which is pullback on steroids.

Shooting Line

When we shoot line the rod leg begins to move away from us as well as the fly leg. Now, from the loop’s perspective, the rod leg has velocity which adds to the velocity of the fly leg and, of course, the velocity of loop travel over the ground. Again we need to alter the equation slightly. Vt= ½ (Vfl – Vrl) +Vrl.

If we shoot line and then check the shoot then we first enhance travel and then enhance propagation.


Hauling shows just how sensitive to changes in rod and fly leg velocity loop travel can be. If we haul before loop formation (ideally just before) then we add line velocity into what will become the fly leg – remember at this point the line has only one leg. If we haul after loop formation we are pulling back on the rod leg instead of pulling forward on what will become the fly leg. This reduces travel velocity and increases propagation velocity.


The take away from all this is that the two legs of the fly line are both connected and related. The behaviour of one affects the other. The loop is the transitional zone between them. In various ways we can change the relationship to our advantage. (Equally, we can do things which are disadvantageous.) For example we can manipulate the velocity of loop propagation and loop travel. In a snap cast we enhance propagation and restrict travel velocity. When we shoot line we enhance travel and, yes, we restrict propagation velocity. When hauling we can do one or the other depending on our timing.

Casting is fundamentally about creating line velocity – speed in the desired direction of the cast.

Lines and Loops – Part 2


In Part 1 we considered loop and line behaviour (mostly) from the perspective of velocity – speed in a direction. In this part we will look at loops and lines (mostly) from the perspective of forces which also have directions. In any cast, of course, there is no separation of force and velocity. My reason for separating them as perspectives was to reduce some of the complexity, at least temporarily!

The loop is the most obvious feature of a fly line being cast. Its size and shape can tell an experienced observer quite a lot about what the caster has done during the cast to make a loop like that – ie it provides data useful in analysing casting technique. For these reasons and probably others I have missed, an influential bunch of casting people tend have a “loop centric” view of what is going on when we cast. Some of them even consider the loop to be some sort of engine of the cast – the fly leg of line being pulled along by it. I am not one of those people. I consider the loop to be fundamentally a consequence of the force(s) we applied during a casting stroke and where we made the rod tip go.

Push Me, Pull Me, Tension

After the rod finishes accelerating the line and begins to slow down, the line overtakes the rod tip and a loop forms. The fly leg rocks on with all the kinetic energy we put into it and it wants to keep going where it was sent. This complies with Newton’s First Law of motion, namely that an object will remain in motion unless acted on by an external force. Of course, the first external force our fly leg encounters is restraint that comes from us keeping the rod tip more or less still. That resistance is applied to the rod leg and then to the fly leg via the loop – the transition zone.

So, the fly leg is pushing forwards and the rod leg is pulling backwards.That might seem a bit odd at first. I mean, after a standard cast, without a haul or some line shoot, the rod tip has pretty much stopped a little while after we stopped moving the rod butt. How then can it be pulling backwards against something pulling it forwards?

Look at it this way. If we weren’t holding the rod still then it would be pulled forward by the fly line. So we are applying a restraining force opposing the force or kinetic energy of the fly leg. Newton’s Third Law, probably the best known of the three, is that for every action there is an equal and opposite reaction. The fly leg pushing forward is an action. (To be precise, a part of the fly leg that is pushing forward is continually being deviated by the restraint of the rod leg and this is the “action”.) The caster holding the rod still is an equal and opposite reaction, that is, the caster is pulling backwards on the rod leg.

Tension is what happens in a string when two forces pull on it in opposite directions so now we can say that after loop formation some tension is created in the rod leg. Push me from the fly leg. Pull me from the rod.


Hauls which end before loop formation add velocity and energy to the fly line. Hauls that end after the rod is stopped add tension to the rod leg and as discussed earlier they enhance loop propagation.


Pulling back on the line with the rod would likewise increase tension and enhance propagation.

Shooting Line

Shooting line probably releases some tension on the rod leg and (via the loop) on the fly leg. I say “probably” because I don’t know how much tension is maintained by line friction against the guides and the blank and by the resistance of the line being towed up off the ground and out through the rod tip.

Is that it? From my perspective as a fly fisher who likes fly casting and wants to improve my casting the short answer is yes, that’s about all I need to know. Like I said at the start, it isn’t simple and easy to understand.

From another perspective, say distance casting competitions and the occasional extra long fishing cast there is potentially something else. At the very least it is interesting.

Acceleration of the Fly Leg Later in the Cast

It is true that in a standard cast the rod leg is pulling on the fly leg via the loop and that causes a change of direction. Technically speaking then, force is applied to the fly leg so as to “accelerate” it. To the vast majority of casters and their typical casting this is almost always insignificant. For it to be significant we would need clear evidence of it helping us to make longer casts or any cast for that matter, by actually speeding up the fly leg after we finish the casting stroke. I can’t offer you such clear evidence.

The most extreme example of a late acceleration phenomenon, when it does become significant, can be observed in a snap cast which is itself an example of extreme pullback.

Watch this video clip. It’s slo-mo footage of one of my Advisory Group, Graeme Hird, making a snap cast. The rod and line are slowly lifted up and then the rod is snapped down. For the first few seconds the rod leg pulls the loop downwards. At about 8 seconds we see that the rod leg has hit the ground. After 10 seconds, the loop begins to hover and then to climb slightly. The fly leg turns over completely, leader and all, and the leader climbs noticeably at the end. Seemingly, the only reasonable explanation for this that the fly leg has been accelerated by the rod leg in the common or garden meaning of acceleration. It is has been speeded up.

What this apparently demonstrates is that it is possible for the fly leg to be pulled on by the rod leg hard enough to make it move faster. Later in the video we see evidence of the fly leg speeding up during the last little bit of a standard overhead cast. No question the fly leg is being accelerated by something(s). It could well be the rod leg again. However, it could be other things as well, including remnant kinetic energy in the fly leg now affecting reducing mass (front taper of the fly line and leader). It could even include a bit of help by gravity. The line is falling so the big G is starting to pull the fly leg downhill at the same time as it is still going forwards which would speed it up a tad.

If that sounds like I don’t know exactly what is going on you are correct. Next question, who cares? Supplementary question, does it matter, to whom and in what circumstances might it be significant?

Going back to first paragraph of this section then yes, it might matter to someone making very long casts and looking for a poofteenth extra – loop travel and/or propagation. You often see distance casters make a little lift right at the end of the stroke which could tighten the rod leg, narrow the loop a touch, enhance propagation and maybe, just maybe, even increase fly leg speed. I sometimes use them with overhead casts. Graeme also suggests it can be useful in making roll/spey casts and we will get to those later on.

Try it and make up your own mind.

The Opposition Forces

Every time we cast we are opposed by gravity and by drag. Gravity, the big G, is effectively constant. We deal with it by using line speed and by changing the trajectory of our cast like a javelin thrower does – aiming up to optimise distance and counter gravity’s efforts to pull us down to earth. For short to medium casts we often aim the backcast up and the forward cast down (in line with the backcast). When we do that the forward cast is partly opposed by gravity and partly assisted by it. The steeper the angle the greater the assistance and the less the opposition.

Drag is rather more interesting to us. Newton’s Third Law again. When we push something through the air the air pushes back. Drag comes in two varieties, skin drag and form drag. Skin drag is about the surface texture of an object being pushed through the air. The rougher the texture the greater the drag. Not much we do about that one, a fly line is what it is in terms of smoothness. Clean lines might be marginally smoother than dirty ones but nothing much there to get intense about.

Form drag is dependent on the shape of the object being pushed through the air. The greater the surface area the greater the drag. Now we have something we can work on. The bigger the loops we throw the greater the surface area presented to the air. Narrow loops are more aerodynamically efficient. So are thinner lines.

Secondly, when we make tracking errors – casting outside of a straight line forward and back – we present more line surface area to the air. In distance cycling races like the Tour de France we see a peloton of riders. The guys up front are pushing a hole in the air for the guys behind them. Riding outside the line of the peloton means losing that advantage. Greater drag will be experienced, requiring more effort to keep up with the group.

It is harder to cast into a head wind because the air is pushing harder against our fly line. The answer is not simply more effort. That usually takes us off the right path and into offences against the Straight Line Rule. The answer is greater efficiency of effort – better technique and narrower loops to give the air less to push against.

This bring us to another interesting factoid about drag. It is proportional to speed. The faster we go the more drag increases because more air molecules are hitting the line in a given amount of time. This is the same as when we cast into the wind. More line speed away from us or more airspeed towards us creates the same effect – more air molecules banging into the line during the same time period.

In fact if the passage of the line through the air creates turbulence, drag can even increase at the square of velocity. Double the velocity and quadruple the drag. Regardless of proportion, faster lines experience increased drag. This is one of the things that makes going longer more difficult.

Making Waves: Lines and Loops – Part 3

Making Waves

I learned a lot about waves, producing them and controlling them to do interesting things by playing around with a garden hose attached to a tap. Hoses are nice and thick and heavy and waves in them are fairly slow and easy to see. Have a play yourself but take it easy or you might rip the fittings off the hose at the tap end. A heavy rope tied to something solid like a tree or fence post will also work.

Here’s where we are going. The hose is a string medium like a fly line. Waves travel along string media differently depending on the density of the medium and the tension it is under.

Tension is produced by opposing forces, forces pulling on the medium in different directions. For our purposes density is about the mass contained in a given length of a string medium. This is referred to as linear density. Hence forward I’ll talk about density and assume you know it is linear density that we are discussing. Garden hoses have meaty density. They are thicker and heavier per metre than any fly line I’ve ever used. We can make and watch nice waves with them.

We don’t need to understand everything about the physics of waves to improve our casting but the concepts of tension and density can be very useful. Generally speaking waves are good when we intentionally create and control them. Likewise they are usually bad when we create them unintentionally and have no control of them after that.

Let’s get the principal bad guy out of the way first and doing that will ease us into some of the technical stuff we can use to advantage.

Tailing Loops

These are everyone’s least best friend. Accounts of what causes them vary a bit but most people agree they are caused by the rod tip dipping and rising back up again. This produces a concave tip path and a wave in the fly line.

We can create the dip and rise in various ways but the most common cause is lumpy acceleration during the casting stroke. Speeding up puts more bend in the rod. Slowing down allows it to unbend a bit. Voila – dip and rise which makes a wave. Not hard to see this happening when we go for that heroic bit extra on the delivery cast, rotate too much too early and then run out of gas. That’s how I make most of my tails – that in combination with miss-timed hauls which start (rod tip dips) and finish too early (rod tip bobs up).

So, in wave terms, we have created a wave which disturbs/displaces the medium – the rod leg of the fly line. As we proceed with the cast the wave rocks on down the line toward the fly. ie It propagates.

Meanwhile we have produced a loop so now we have two legs in the fly line. The wave we made in the rod leg is now propagating in the fly leg. So far, so good and no problem. However, if we made our cast with a tracking error (as well as lumpy acceleration) we could be in trouble. The tracking error makes the two legs cross paths and if the wave is big enough it makes a part of the fly leg dip below the rod leg. As the line paths cross, they can collide and they do collide with maddening frequency.

The wave we put into the line propagates in a direction. The medium is displaced at right angles to the direction of propagation. What we produce then, is called a transverse wave. Tracking error and a transverse wave in the fly leg = tailing loop trouble.

Line Tension

Having unintentionally created a transverse wave we are not in control of it. The more net Force we put into that delivery cast the faster our line will travel. The transverse wave will also travel faster. That has nothing to do with line speed but a lot to do with line tension.

Back to the garden hose. Let’s assume it’s about 20m long. You have one end in your hand and the other end attached securely to something solid. Start by putting a bunch of slack, loops and wiggles, into the hose so that there is now only about 10m distance between the fixed end and the one in your hand. We are going to make a whip action with the hose. Quickly lift up above the holding position, then drop below that position and then lift back up to the holding position. What happens? I guessing not much. A wave was created but it fizzled out well before it reached the other, fixed end.

Ok. Now back up until all the hose is straight. Doesn’t have to be taut, just in a straight line on the ground will do. Repeat the lift and drop routine. You should feel the weight of the hose as it comes tight during the lift and feel it go light again as you drop. What happens this time? Completely different result. A wave shoots along the hose and smacks into the far end. Quite possibly you will see a return wave coming back toward you.

The point? You have just demonstrated that tension in a string medium makes waves travel faster along it. Yep, you are right, it also means they travel more efficiently assuming you applied roughly the same amount of force to the straight hose as you did to the slack one. Now we have some things we can vary and hopefully control.

Tension, Mends and Such

Anybody who fishes moving streams or even tidal water will need to mend upstream from time to time. Whether you do this in the air or on the water the principle is the same; a mend is a wave and waves travel more efficiently in tense lines than in slack ones. Many mends and casts rely on creating waves and manipulating tension to shape and position the line as desired. Not saying it’s easy but it is definitely doable.

If, for instance, you want to aerially mend the rod leg upstream it will be far easier to do this after making a nice tidy cast than if you had made a poor cast with a lazy loop. The tidy cast will create more tension in the rod leg as the moving mass of the fly leg pushes ahead while the rod tip restrains the rod leg. Pulling back will further increase tension. Pushing the rod forward will release some.

We can put a wave into a normal delivery cast and drop the line to the water before the wave has fully propagated to add slack or avoid an object. Wiggle casts are a series of waves dropped to the water before wave propagation is significant. These casts also deliberately induce slack.

Overpowered casts and curve casts can rely on a rebound wave to kick the fly, leader and even some of the fly line down or around at the end of the cast.

You get the idea. Play, practice and use it as you like. This series isn’t about making specialty casts. It’s about understanding the physics which will help us create and execute them.

Density, Line Tapers and Mass Distribution

The taper of a fly line, floating or sinking, is far more than the outer shape of the line. It is a profile of its volume and, more particularly, of the distribution of its mass. Same material but more of it in one section than in another of the same length means different mass in those two sections. That means the linear density of the line can vary between sections with different tapers.

The implications of this go way beyond how far we can launch one when we wind up from the two bob seats. It has a lot to do with how waves travel along our fly lines. It influences loop propagation or turnover. It affects what a rod feels like when we cast lines with different profiles and different weights – as in AFFTA line designations as well as mass. It affects air drag. In fact there isn’t much it doesn’t have an effect on. Hence all of the variation in line tapers out there and all the marketing bumpf and BS that goes with them.

Once upon a time if you fished for trout you used double taper lines. Then weight forward lines largely took over. Now “brick on a string lines”, essentially integrated shooting heads, are becoming increasingly popular, especially, it has to be said, with people of average casting ability. But before I descend fully into rant mode let’s go back to waves and line density.

In general terms a wave travelling along a fly line will have less speed in the denser sections and more speed in the less dense sections. How that plays out for us will vary with the profile of the line sections we are casting or mending. A wave moving along a fly line tapering down will move faster as it proceeds. However, a wave moving along a fly line that is getting thicker will slow down. Obviously then a wave in a double taper line can behave differently to a wave in a weight forward line. In a weight forward line the wave might be passing from thinner to thicker and back down to thinner line. That will mean faster, slower, then faster wave speed. At the extreme end, with a shooting head, a wave in the running line will effectively run into a brick wall when it reaches the head.

In summary then. Double tapers are handy to mend. Weight forward lines can be ok and shooting heads are usually complete bastards. What do I like? For most of my fishing I like long belly weight forward lines.

It is a similar situation with loop propagation in that as net Force is used up it is handy to have progressively less mass at the end of the fly line (the forward taper) and then leader. More mass can turnover less mass more easily.

If for some strange reason we tried going the other way – trying to turnover fly line with the leader, the cast would most likely fail. Less mass trying to turnover more mass is a serious problem. That is what happens when we get too much “overhang” into the carry of a shooting head line – or for that matter a weight forward line with too steep a rear taper. You might cast further with shooting heads but will be less able to mend and shape them – brick on a string lines included!

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