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Fly Fishing’s Fundamental Formula: A = 4 Delta - A = 4 Delta
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Fly Fishing’s Fundamental Formula: A = 4 Delta - A = 4 Delta
Fly Fishing’s Fundamental Formula: A = 4 Delta
While it is recognized the Answer to Life, the Universe, and Everything is 42, and practically everyone is familiar with Einstein’s formula E = mc2, few anglers know the formula which relates rod power and line weight, to the distance cast, frequency, and feel. That formula is A = 4 Delta (where Delta = ERN - ELN), and where A is defined as the “Adjustment” required to coordinate line, rod, and feel. In the following paragraphs, I shall explain.
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Background
There is only one “universally recognized” standard related to fly lines, and it was developed nearly 50 years ago by the AFTMA. They assigned an integral number (e.g., No. 5) to represent the weight in grains of the first 30 feet of that line. All subsequent descriptions of fly lines and their applications to fly rods trace their origins to that standard. Unfortunately, a standard for describing the intrinsic properties of fly rods was never developed.
Originally, when a fly rod was fabricated, it was labeled with a number corresponding to the AFTMA fly line which its designer believed should be used on that rod. It was “understood” the designer was basing his recommendation on the angler aerializing 30 feet of the designated line to load the rod. Consequently, a rod designed for use with a No. 5 line was commonly called a 5-Weight rod, and a 5-Weight rod was always more powerful than a 4-Weight rod and less powerful than a 6-Weight rod.
However, with the advent of newer, lighter, and stronger materials, this distinction is no longer valid. Today, one company’s 5-Weight rod might be identical to another company’s 4-Weight rod or a third company’s 6-Weight rod. Consequently, if an angler is unhappy with how his rod feels, he can try using different lines until he finds one which “adjusts” it to fit his desires. “A” represents the “Adjustment” necessary to make the rod “feel right.”
Matching Rod and Line
By means of CCS measurements anyone can determine a rod’s Effective Rod Number (ERN) and Common Cents Frequency (CCF). For any given fly line, one can easily determine its Effective Line Number (ELN). Combined, these properties allow one to characterize the Feel of one’s rod and reel combination and determine the overall adjustment (A) one must make due to any change of line or distance cast.
The basic premise of the CCS is there is a fundamental relationship between the stiffness or ERN of a fly rod and the weight of fly line (WL) or ELN which will “load” that rod. When ERN = ELN, the rod-line system is balanced according to the CCS. A balanced rod-line system will also exhibit an intrinsic Common Cents Frequency (CCF) of about 84 cpm..
However, one must recognize this does not guarantee such an outfit will please every angler. It only means the weight of the line matches the strength of the rod. Each angler must individually determine his own preference relative to this balance, i.e., the degree of unbalance, if any, he finds most pleasurable.
Now, having defined a balanced outfit, we can characterize an unbalanced one. For this, the term Delta was created. One unit of Delta corresponds to the “Adjustment” equivalent to that resulting from a change of one AFTMA line number, or a change of rod of one ERN number. Delta is defined as the numerical difference between ERN and ELN, or Delta = ERN - ELN.
For a balanced system, Delta equals zero. For an “over-loaded” rod, where the line is “too heavy” for the rod, Delta has a negative value. For an “under-loaded” rod, Delta has a positive value.
For example, using an AFTMA #5 line (ELN = 5.5) on an ERN = 7.5 rod produces Delta = 7.5 - 5.5 = 2.0. Such values are typical with Sage’s touted TCR (Technical Casting Rod). This is a very fast responding (high frequency) combination and is one with which one can cast great distances in competitions. However, it is no one’s favorite for a leisurely day of fishing—it feels too stiff.
Common Cents Frequency and Feel
The “feel” of any fishing rod is determined by its stiffness and its frequency. Stiffness is measured in units of ERN, and frequency in units of CCF.
When fitted with a fly line, modern graphite fly rods exhibit a CCF of about 84. This value will change about 4 for each change of one Delta. Thus the expression A = 4 Delta. The reader must recognize this value as being a “first approximation” rather than a “universal constant.”
In the case of the aforementioned TCR where Delta = 2, this combination exhibited a frequency of 94. However, when fitted with a fly line two AFTMA Numbers greater (ELN=7.5), its CCF dropped to 86. Now, one might expect it to feel and cast much more like a typical graphite fly rod.
A nostalgic angler might even want to fit this rod with an AFTMA No. 10 line. This might reduce its frequency enough to make it feel almost like his old bamboo rod.
Matching Line to Rod
Many anglers slavishly match their fly line to the number inscribed on their rod, in the belief doing otherwise might damage their rod. This is completely unwarranted. One can cast a No. 10 line on an ERN=2 rod without a problem, but it probably won’t feel good, as A= 4 (10-2) = 32 and the combination will feel like a very very noodlie bamboo rod.
Now, going to the other extreme, if one fits a No. 2 line on an ERN=10 rod, one will get the feeling of casting with a broomstick.
From this one can postulate the major purpose the fly line serves is to provide the necessary weight to “load” the rod sufficiently to give your fishing outfit a CCF of about 84 and thus make it “feel good, like a fly rod should.”
Matching Line to Distance
It is recognized, if one wishes to fish “close in,” one should use a line at least one ELN heavier, i.e., Delta = -1 to -2. This is necessary to counteract the effect of the lesser weight of the shorter line in loading the rod.
On the other hand, for casting a greater distance, e.g., 60 feet, a line one ELN lighter is recommended, i.e., (Delta =1). This is because the weight of the additional 30 feet of line is equivalent to a Delta value of -1, and A will consequently remain zero.
Conclusions
An expert caster can quickly adapt to any fly rod by “Adjusting” his casting stroke. On the other hand, a less experienced angler might be better served by using his “normal” casting stroke and “Adjusting” his tackle to provide the most satisfaction. This can be accomplished by the judicious consideration of rod power and line weight relative to the distance cast, frequency, and feel. The unifying equation is A = 4 Delta.
© 2008 W. W. Hanneman
While it is recognized the Answer to Life, the Universe, and Everything is 42, and practically everyone is familiar with Einstein’s formula E = mc2, few anglers know the formula which relates rod power and line weight, to the distance cast, frequency, and feel. That formula is A = 4 Delta (where Delta = ERN - ELN), and where A is defined as the “Adjustment” required to coordinate line, rod, and feel. In the following paragraphs, I shall explain.
-------------
Background
There is only one “universally recognized” standard related to fly lines, and it was developed nearly 50 years ago by the AFTMA. They assigned an integral number (e.g., No. 5) to represent the weight in grains of the first 30 feet of that line. All subsequent descriptions of fly lines and their applications to fly rods trace their origins to that standard. Unfortunately, a standard for describing the intrinsic properties of fly rods was never developed.
Originally, when a fly rod was fabricated, it was labeled with a number corresponding to the AFTMA fly line which its designer believed should be used on that rod. It was “understood” the designer was basing his recommendation on the angler aerializing 30 feet of the designated line to load the rod. Consequently, a rod designed for use with a No. 5 line was commonly called a 5-Weight rod, and a 5-Weight rod was always more powerful than a 4-Weight rod and less powerful than a 6-Weight rod.
However, with the advent of newer, lighter, and stronger materials, this distinction is no longer valid. Today, one company’s 5-Weight rod might be identical to another company’s 4-Weight rod or a third company’s 6-Weight rod. Consequently, if an angler is unhappy with how his rod feels, he can try using different lines until he finds one which “adjusts” it to fit his desires. “A” represents the “Adjustment” necessary to make the rod “feel right.”
Matching Rod and Line
By means of CCS measurements anyone can determine a rod’s Effective Rod Number (ERN) and Common Cents Frequency (CCF). For any given fly line, one can easily determine its Effective Line Number (ELN). Combined, these properties allow one to characterize the Feel of one’s rod and reel combination and determine the overall adjustment (A) one must make due to any change of line or distance cast.
The basic premise of the CCS is there is a fundamental relationship between the stiffness or ERN of a fly rod and the weight of fly line (WL) or ELN which will “load” that rod. When ERN = ELN, the rod-line system is balanced according to the CCS. A balanced rod-line system will also exhibit an intrinsic Common Cents Frequency (CCF) of about 84 cpm..
However, one must recognize this does not guarantee such an outfit will please every angler. It only means the weight of the line matches the strength of the rod. Each angler must individually determine his own preference relative to this balance, i.e., the degree of unbalance, if any, he finds most pleasurable.
Now, having defined a balanced outfit, we can characterize an unbalanced one. For this, the term Delta was created. One unit of Delta corresponds to the “Adjustment” equivalent to that resulting from a change of one AFTMA line number, or a change of rod of one ERN number. Delta is defined as the numerical difference between ERN and ELN, or Delta = ERN - ELN.
For a balanced system, Delta equals zero. For an “over-loaded” rod, where the line is “too heavy” for the rod, Delta has a negative value. For an “under-loaded” rod, Delta has a positive value.
For example, using an AFTMA #5 line (ELN = 5.5) on an ERN = 7.5 rod produces Delta = 7.5 - 5.5 = 2.0. Such values are typical with Sage’s touted TCR (Technical Casting Rod). This is a very fast responding (high frequency) combination and is one with which one can cast great distances in competitions. However, it is no one’s favorite for a leisurely day of fishing—it feels too stiff.
Common Cents Frequency and Feel
The “feel” of any fishing rod is determined by its stiffness and its frequency. Stiffness is measured in units of ERN, and frequency in units of CCF.
When fitted with a fly line, modern graphite fly rods exhibit a CCF of about 84. This value will change about 4 for each change of one Delta. Thus the expression A = 4 Delta. The reader must recognize this value as being a “first approximation” rather than a “universal constant.”
In the case of the aforementioned TCR where Delta = 2, this combination exhibited a frequency of 94. However, when fitted with a fly line two AFTMA Numbers greater (ELN=7.5), its CCF dropped to 86. Now, one might expect it to feel and cast much more like a typical graphite fly rod.
A nostalgic angler might even want to fit this rod with an AFTMA No. 10 line. This might reduce its frequency enough to make it feel almost like his old bamboo rod.
Matching Line to Rod
Many anglers slavishly match their fly line to the number inscribed on their rod, in the belief doing otherwise might damage their rod. This is completely unwarranted. One can cast a No. 10 line on an ERN=2 rod without a problem, but it probably won’t feel good, as A= 4 (10-2) = 32 and the combination will feel like a very very noodlie bamboo rod.
Now, going to the other extreme, if one fits a No. 2 line on an ERN=10 rod, one will get the feeling of casting with a broomstick.
From this one can postulate the major purpose the fly line serves is to provide the necessary weight to “load” the rod sufficiently to give your fishing outfit a CCF of about 84 and thus make it “feel good, like a fly rod should.”
Matching Line to Distance
It is recognized, if one wishes to fish “close in,” one should use a line at least one ELN heavier, i.e., Delta = -1 to -2. This is necessary to counteract the effect of the lesser weight of the shorter line in loading the rod.
On the other hand, for casting a greater distance, e.g., 60 feet, a line one ELN lighter is recommended, i.e., (Delta =1). This is because the weight of the additional 30 feet of line is equivalent to a Delta value of -1, and A will consequently remain zero.
Conclusions
An expert caster can quickly adapt to any fly rod by “Adjusting” his casting stroke. On the other hand, a less experienced angler might be better served by using his “normal” casting stroke and “Adjusting” his tackle to provide the most satisfaction. This can be accomplished by the judicious consideration of rod power and line weight relative to the distance cast, frequency, and feel. The unifying equation is A = 4 Delta.
© 2008 W. W. Hanneman
- Paul Arden
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There is a fundamental error here Bill. If you're fishing close you don't use a heavier line, instead you use a narrower casting arc. Rods bend progressively. They bend a little bit with a short line, and a lot more with a long length of line. Rods were never designed around casting 30 feet of line. This is a myth. They are designed around expected application. This is why small stream rods are relatively softer than saltwater or most Stillwater rods.
I explained this to you before and had it backed by Sage and SA, but I know you don't believe us!
Cheers, Paul
I explained this to you before and had it backed by Sage and SA, but I know you don't believe us!
Cheers, Paul
- Hal Jordan
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In the world of spey casting it is accepted that the same rod can have several different ideal line weights depending on the type of line.
With a shooting head the rod casts "off the tip" and only the top part of the rod is under serious load.
With a mid line which may weigh 50% more the rod bends further into the blank
With a long spey the line can weigh twice what a shooting head suitable for the same rod the rod bends fully into the butt.
Surely this is the same for all rods?
With a shooting head the rod casts "off the tip" and only the top part of the rod is under serious load.
With a mid line which may weigh 50% more the rod bends further into the blank
With a long spey the line can weigh twice what a shooting head suitable for the same rod the rod bends fully into the butt.
Surely this is the same for all rods?
- Paul Arden
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Hi everybody
Two things:
CCF varies non linearly with mass, CCF(load) = CCF no load / sqrt (1 + load / rod equivalent mass); so the equation given by Bill is an approximation and bad luck, it lacks precision.
The equivalent mass of the rod is an important parameter which varies first with rod length: a long rod have little variation in speed with load and can accomodate a larger variation in line mass by comparison to a short one.
Merlin
Two things:
CCF varies non linearly with mass, CCF(load) = CCF no load / sqrt (1 + load / rod equivalent mass); so the equation given by Bill is an approximation and bad luck, it lacks precision.
The equivalent mass of the rod is an important parameter which varies first with rod length: a long rod have little variation in speed with load and can accomodate a larger variation in line mass by comparison to a short one.
Merlin
Fly rods are like women, they wont´play if they're maltreated.
Charles Ritz, A Flyfisher's Life
Charles Ritz, A Flyfisher's Life
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I've just got the catalogue...I was a poor student in 1981 and certainly couldn't afford the £89 in addition to the essential beer and herbal necessities.
Come to think of it my rod of choice in those days was a Sue Burgess 9ft AFTM 4-7. A bit of a change from my current favoured Gatti which I was told worked best with a Rio Gold as the line is really an AFTM 5.25!
Malcolm
Come to think of it my rod of choice in those days was a Sue Burgess 9ft AFTM 4-7. A bit of a change from my current favoured Gatti which I was told worked best with a Rio Gold as the line is really an AFTM 5.25!
Malcolm
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Merlin wrote:The equivalent mass of the rod is an important parameter which varies first with rod length: a long rod have little variation in speed with load and can accomodate a larger variation in line mass by comparison to a short one.
Merlin
WOW - so this explains the Spey Rod to Line puzzle .... ?
Craig
- Hal Jordan
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Paul Arden wrote:So what line weight should I string up on my ERN7 for a three foot cast?
Well you would use one of those new clear lines in about a 28 wt to build a leader out of and the resulting A value would be -84 but that would certainly affect frequency and feel.
I'm just not quite sure how I would actually apply this, and forgive me if that's point you are trying to make Paul. I have a rod that I don't really like the feel of so because it's too stiff and I always fish in 20 foot wide streams so I put on a different line. Does the formula tell me what line I should use? What I would currently do is start with using AFTMA rating todetermine what line at 20 ft match my rod rating and then bump it up a weight or two. What does this do better? And now that I've found a line I like what is knowing that it has an A value of -16 going to do for me?
- Marc LaMouche
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Paul,Paul Arden wrote:There is a fundamental error here Bill. If you're fishing close you don't use a heavier line, instead you use a narrower casting arc.
Cheers, Paul
That's one way to get it done and the one I too prefer but Bill is also correct. There are many fishermen out there that do as he says - especially when Tarpon come in close.
Craig
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