Is ERN enough? - rod and line classification

[gordonjudd]

Merlin,
Here is the non-linear spring function for another full flex rod that shows how well the cubic fit matches the measured force vs deflection data. Lamiglass rates this as an 8wt rod, and I like using it with a 20 gr shooting head line made by Rasmus Hansen in Denmark. His use of specified line mass values for his lines makes more sense to me than the non-linear AMFTA line weight system.

As noted in the comments in this plot the K3/K1 ratio for this rod was around .4 with a natural frequency of 3.17 Hz k0=1.87 N/m, and a mo of 4.7 gr.

As with the Kane Klassics rod its non-linearity has an exponential slope factor of 3.1 which is quite close to having a non-linearity factor given by a x.^3 deflection term.


Gordy

[FlyAlf]

" the ERN/AA data gives me a broad view of a rod, but not an idea of its performance." Disagree: The ERN (and AA) gives an idea of its performance. You would surely agree that to have some objective number of stiffness (even at one given load) would say something of its performance.

"This does not tell me how fast is the rod". To tell how fast you need to measure frequency.

"...and how it reacts to load" Disagree. This is exactly what ERN does. It says something about stiffness. But I agree that one normally uses such as spring constant to measure ... a spring. More correct would be to state "and how it reacts to different loads"?


Influence of mass?

"Change the mass of the blank using stiffer material but keeping stiffness the same, and you shall see that rod performance will completly change while ERN/AA are likely to remain the same." Yes, and? If the stiffness is the same, its the same . If the AA is the same its the same . So these two rods should in my not-so-humble opinion have the same action, and handle the same lines since they are equally stiff. They would not "perform" equally in the meaning of "feeling". To better understand this part of the "performance" I would measure the frequency.

"We use the rod dynamically but we like making static measurements (most rod companies do the same)"
Yes, because some understanding of the rod can be achieved by such static measurements. Its easy to do and understand, and for some it good enough. And most rod companies do not share even the basic static parameters with us. Instead the paint some meaningless arbitrary number on the rod indicating that all casters are the same as their test caster and prefer the same stiffness instead of trying to tell how stiff the rod is and letting us choose.


Dynamically versus static measurements?

Im not sure that I understand the difference clearly. If you by "dynamic" mean as a part of a caster-rod system we have other tools such as the caster analyzer.

If you by dynamic mean sampling over time then measurements of frequency is one such dynamic method.

If you mean how the rod reacts to different loads that is for me inherent by knowing the AA/ERN- AA tells me something about action, and ERN about stiffness.


I do look forward to better understand your purpose though.

Fly Alf

While ERN does give a view of stiffness it has limited utility. Traditionally, stiffness for a cantilever beam is a measure of force vs deflection and the measured value is comparable for any shape/size of beam. Because of the way CCS measures stiffness, an ERN of 6 is different for 6, 9 or 12 ft rod and a correction factor would need to be applied to make any comparison between different rod lengths. It would be simpler and more meaningful to use the standard stiffness measurement technique.

Similarly, using a 1/3 of the rod length to gain a deflection to take the ERN/AA measurement assumes that the angler is only interested in the top third of the rod. The 2nd third is also of interest to the competition casters on here who want lots of grunt and to the armchair fisherman like me who like to feel a presentation rod flex through its length and to make the fish feel bigger than they are. Similarly, the lake fisherman hauling up 50ft of Di-8 does not want the rod to fold on him as he pulls the line up form the bottom.

Rods are designed to fill all of the above purposes and use compound tapers to meet these requirements. This is why so many have ERN that are higher than the stated line weight because some rods may have tapers that produce power within the 1/3 deflection.

As you know, tapered rods are non-linear and the CCS measurement is taken at a single deflection point. From that measured point you do not know if the rod gets stiffer, softer or stays the same as it bends past the 1/3rd deflection. I have no problem with using CCS, the DBI gives me a better mental picture of a rod that I have not touched than manufacturers data alone. However, a user needs to understand its limitations and know that it is not an answer to a maidens prayer.

regards

Vince

P.S Marc, the rabbit was not a happy bunny this morning and I let it run

"While ERN does give a view of stiffness it has limited utilit". Yes indeed. But is it helpful for me to understand how stiff the rod is independent of length?

I have measured AND fished a lot of rods betwenn 5' and 9'6''. For lengths between 6'6'' and 9'6'' I would say that ERN is *good enough* to choose line weight (along with AA).

So I would argue that you dont need a correction factor for these lengths. For longer I don't know. For very short rods I have limited experince, but would say that I need to choose softer (lower ERN) rods that expected.

So could you please give an example of how "it would be simpler and more meaningful to use the standard stiffness measurement technique" to choose correct line/rod?


"Similarly, using a 1/3 of the rod length to gain a deflection to take the ERN/AA measurement assumes that the angler is only interested in the top third of the rod. ".
Sorry to say, but you are incorrect. You have to remember that at any load all the rod is bending, not only the top third.


"Rods are designed to fill all of the above purposes and use compound tapers to meet these requirements. This is why so many have ERN that are higher than the stated line weight because some rods may have tapers that produce power within the 1/3 deflection."

Rods do NOT have ERN higher or lower than line weight. Rods have an ERN. Its up to us to decide how stiff rods we want, and to choose line weight based on knowing the rod (stiffness and action).


"From that measured point you do not know if the rod gets stiffer, softer or stays the same as it bends past the 1/3rd deflection."

I would assume that all modern rods are progressive, meaning they get stiffer gradually beyond 1/3 up to a point where they start getting "overloaded". And also I would assume the higher the AA, the more progressive. I have not seen any rods with a truly flat action meaning that they would not get stiffer the more you load them.

[FlyAlf]

OK we restart. The final objective is to put the finger on what non linearity does in terms of rod response. Several criteria will be used to compare two rods of a given ERN and different AA, but AA does not designate the line fit, does it?...

Thanks for you patience,

Can you please give us at least one example of "compare two rods of a given ERN and different AA? Im having a hard time reading this from the rest of the text.

And can you please show how to use this example in order to choose a line/rod combination or appliance of rod you would NOT choose based on ERN/AA alone?

Again back to the "why". As a theoretical exercise this is well, but I still struggle to see how we intend to use this.

[Marc LaMouche]

so what is properly loaded fly rod?

a sufficient bend in the rod that delivers the amount of line, leader and fly in the desired manner.

this has nothing to do with rod or line specifications but only of the caster and how he/she moves the rod to match the casting stroke at that specific point in time.

cheers,
marc

[Michal Duzynski]

Hi Marc
That is what I tought.
Cheers
mike

[Michal Duzynski]

...Just one more thing
Clearly, who ever says: "dont buy this fly line, because it doesnt load properly the rod, get this one insted" has simply no idea what PROPER CASTING IS?
..am I right?
Cheers
mike

[gordonjudd]

so what is a properly loaded fly rod?
and
a sufficient bend in the rod that delivers the amount of line, leader and fly in the desired manner.

Marc,
The load or bend in the rod is not the main factor that impacts the initial line speed required to reach a distant target. I.e., the bend in the rod and the potential energy associated with that bend is only 20% or so of the energy we produce in most most fishing casts.

It is the deflection force from the tip of the rod and the distance that force is applied to the line that is important to determining how far the fly will go. As you note the way the caster moves the rod tip during the cast is just as important as how much bend he is putting into the rod.

Because the rod is a flexible beam the deflection force will not be a linear function of its deflection. That non-linearity is further accentuated by the taper in the rod. Merlin is trying to come up with a way to characterize that non-linearity rather than using a single point deflection measurement to define the spring constant of the rod.

That is a useful endeavor and should give more information about how a rod might perform over a range of casting distances, but I think most good casters will still determine a preferred rod/line combination by test casting, not by looking at measured data.

Gordy

[Merlin]

Bill,

The point raised by Mike is relevant of the actual situation, and you do not need a definition of speed at this point, since there are as many speeds as loads. A caster adpats his cast to the conditions, and does not try to always get the same response from the rod.

I however understand that the definiton you give is part of your CCSystem, and I am not going to argue about if the wording is adequate or not, this is not the question.

Merlin

[Merlin]

Hi Gordy

We are just using the Duffing equation differently, but come to the same results:

You model F = k1 x + k3 x^3
I model F/x = k1 + k3 x^2

OK? We find the same order of magnitudes for the range of K3/k1 (last finding, a rod at k3/k1 = 1).

I shall give a look at your log log method, but this remembers me a story.

I was visiting a scientific lab some 20 years ago and they were two graphics hanged on the wall of a corridor. The first one was a set of points linked with lines that looked like a monkey. The coordinates were linear. Next to it there was another graphic with the same set of points converted in log log. And the picture looked like a pig. This is why I do not try that change coordinates very often.

Merlin

[Merlin]

Alf

As I said I proceed step by step. The figures you are interested in will come during the week end.

Hope Magnus will catch up.

Merlin

[gordonjudd]

You model F = k1 x + k3 x^3
I model F/x = k1 + k3 x^2

Merlin,
I should have paid more attention to your formulation. Are the F/x curve values compute with F/x=k1+k3*x^2 equal to the Kavge (rise/run) values shown in the dotted line back in post#2?


With either formulation we agree that that the non-linearity in the force vs deflection curve is proportional to the deflection cubed and the non-linearity in the normalized spring constant (f/x) will be proportional to the deflection squared. That means the ratio of our k3/k1 values should have the same value.

Do you see the same relationship that k3/k1 ratios around .8 go with fast tip flex rods and ratios around .3 are found in slower full flex rods?

Gordy

[gordonjudd]

I have measured AND fished a lot of rods betwenn 5' and 9'6''. For lengths between 6'6'' and 9'6'' I would say that ERN is *good enough* to choose line weight (along with AA).

So I would argue that you dont need a correction factor for these lengths.

Alf,
Did you use the fixed deflection magnitude of 36 inches defined in Bill's system when you make those measurements or are you using a deflection value that is around 37% of the clamped length?

Because of the non-linearity in the spring constant of the rod I would be surprised the ERN value you would get for a normalized deflection of 36/(78-11)=53% of the clamped length of a 6'6" rod would be match the ERN value Bill derived based on a 37% normalized deflection for a 9 foot rod.

The L.^3 sensitivity of the deflection relative to the clamped length (L) of a cantilever beam would imply that you need to use normalized deflection values (not a fixed deflection of 36 inches) in coming up with an ERN value to characterize the nominal rod stiffness.

I don't think you would have the same experience if you were measuring tip flex rods that have higher k3/k1 ratios.

Gordy

[FlyAlf]

I have measured AND fished a lot of rods betwenn 5' and 9'6''. For lengths between 6'6'' and 9'6'' I would say that ERN is *good enough* to choose line weight (along with AA).

So I would argue that you dont need a correction factor for these lengths.

Alf,
Did you use a fixed deflection magnitude of 36 inches when you make those measurements or are you using a deflection value that is around 37% of the clamped length?

Because of the non-linearity in the spring constant of the rod I would be surprised the ERN value you would get for a normalized deflection of 36/(78-11)=53% of the clamped length of a 6'6" rod would be match the ERN value Bill derived based on a 37% normalized deflection for a 9 foot rod.

The L.^3 sensitivity of the deflection relative to the clamped length (L) of a cantilever beam would imply that you need to use normalized deflection values (not a fixed deflection of 36 inches) in coming up with an ERN value to characterize the nominal rod stiffness.

I don't think you would have the same experience if you were measuring tip flex rods that have higher k3/k1 ratios.

Gordy

Hi,

I used 1/3 deflection of total length and clamping at the handle.

Btw: Its been a while since a read a discussion on how different casters "feel" and chose line for rods with same ERN and different AA. Same goes for same ERN different length, etc...Time to start with real life examples?

[Merlin]

Now the Big picture...

Hi everybody

Let’s make one step forward by defining two rods of same ERN (5.5 corresponding to a #5 line along the CCS scaling system) but different non linearity. Below are the main features of these rods:



For those who know about CCF, you can see that these two rods differ by approximately one line number in terms of loaded frequency. Rod B has a faster speed of recovery by comparison to rod A.

Here is an example of what we can get when making a complete set of measurements (mo, ko):



too big an image likely...

This difference in line number for a given loaded frequency comes from the influence of mo (you can see examples of mo in the graphic). If I wanted to match the frequencies, I would have to increase further mo for the A rod, beyond the limits of reality, or to reduce it for rod B, again beyond the limits of reality. If I bring mo values close together, the difference achieves two line numbers in terms of loaded frequency. This is possible in real life.

There is no AA value quoted here but this will be the cherry on the cake at the end. Have a look at the trends given by a non linear casting model. The casting style is oversimplified, with an increase in casting arc with load and a constant timing. It is the same for both rods to have a starting point. It is likely that casters adapt their style to the rod in reality, but let’s do with the trends.



It shows that the more non linear rod (B) is better suited for a heavier line (casting with higher speed), although the linear estimates (dotted lines) would let us think the opposite (low linear loaded frequency for a given line).

For light loads, rod A gives higher line speeds despite the short casting arc considered. Rod B with its lower k1 is likely more pleasant to use, we do not need speed at this point, but control. It may well happen that we shall cast a heavier line with rod A in that case, to cool it down and reduce the speed for a given casting arc.

Magnus, do you see the compatibility of that with your own comments? That drew my attention on the indication given by AA, because I was reading what the casting model was telling. As I started producing k3/k1 data for some rods, I also computed AA for the 1/3 L rod deflection. Although I can model a cast with k3/k1 since it has a physical meaning, I could see that after a careful analysis, AA may be an indicator of the non linearity. Not exactly this one, but as would say Gordy a “normalized” non linearity. How to get it? Just by multiplying the k3/k1 ratio by the square of the length of the rod. The reason why is below:

1 +3/4* k3/k1* x2 = 1+3/4 *k3L^2/k1 *(x/L)^2

I just multiplied and divide by L^2 to make the relative deflection appear. So the normalized ratio is k3* L^2 / k1.

In fact, when I do the calculation, I take only the free length of rod outside the embedment used for measuring (see the graphic). The results are more precise. Same thing for k1 and k3: I use the change in deflection from the no load position, not the absolute position from a supposed to be clearly identified horizontal line, and this complies with the physics of stiffness measurements.



Below you can see the variation of the normalized non linearity ratio with AA:



Not that bad, isn’t it? Rods are from 6’6 to 10 feet, with a majority of 9 feet rods. You see for the first time the only existing correlation between non linearity and AA. And it is free of charge on top of that. If more data can confirm this relationship (or help to create a more statistically significant one); then we could derive AA range values that can be classified in terms of non linearity. For Rod A, the AA estimate is 45 degrees (very low); and for rod B, it is 65 degrees with this correlation.

Conclusion: if confirmed through correlation (highly likely) AA has something to do with non linearity: high values indicate the possibility to take advantage of a higher line number, and vice versa. There is nothing explaining that in the CCS system, it was observed by experienced casters like Magnus. From this you may conclude k1 is not worth knowing, but it is so easy to get and then compare the normalized non linearity with AA that it is a valuable opportunity.

Here is an example taken from the database showing that sometimes either rod samples differ significantly, either the methodology of CCS needs more accuracy (e.g. specify the embedment length). These are the results for a TCR890 in terms of ERN/AA: 9.66/65; 9.83/67; 10.7/73; 9.96/66; 10/68. The spreads are important, especially for AA.

From this experience, I conclude that ERN is not enough to recommend a line number, but that AA can compensate this “weakness” since it has a meaning in terms of line fit through the effect of non linearity (and not only in terms of “action”, or “speed”). But that it can be improved, thanks to understanding rod behavior through modeling.

Not sure Bill is ready to buy in…

Merlin

[gordonjudd]

Merlin,
Thanks for sharing all of your work.

I think you have made an important step in coming up with an approach to take the non-linear spring characteristics into account.

For those like me who get more understanding with the use of plots rather than tables here is a comparison of the frequency vs tip mass characteristics of your two rods.


This shows that rods with larger m0 values tend to maintain higher loaded frequency values for longer line lengths.

Gordy