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Merlin's Metric Measurement System - rod and line fit

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Merlin
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Merlin's Metric Measurement System - rod and line fit

Post by Merlin »

Hi Folks,

I’m starting a new thread about rod / line fit. The basic idea is to take advantage of the interpretation of non linearity, and make a bridge with CCS/URRS. Data analysis shows that AA can be linked to non linearity, although the actual link is not perfect. Using ERN, and CCF to a lesser extent, one can derive new parameters that can be used to analyze a rod. These new parameters are the normalized linear stiffness and the normalized non linearity. Normalized means that these values apply to rod of any length. You can then compare properties of short versus long rods.

I took the opportunity to define a more “engineered” concept that can give better estimates of the normalized characteristics. The description of frequency variation with load is taken on board, and, cherry on the cake, the use of a casting model allows illustrating what can be done with rods. The objective is to give a panorama of lines that can be used with the rod. This includes the line type (DT, WF, S head) for some typical rods.

For the time being, this is on an Excel spreadsheet. The Rosetta stone is included, no need to calculate many things, just use the gram unit to define ERN (and you can see how many grains, cents, etc. it corresponds to). The “dashboard” control is a little bit messy for the time being, but this is a draft.

I take the example of the usual suspect, the TCR 590. In the CCS system, this is a rod for a number 7 line, final point. In the engineering approach, it can use lines between a number 5, the minimum, and number 8, the maximum. The minimum line number corresponds to the value of the normalized linear stiffness of the tip. This is the stiffness for a “reasonable” deflection of the tip (small load).

Image

The maximum line number is obtained from two key parameters which are the normalized linear stiffness of the rod (and not the tip) and the normalized non linear coefficient of the rod. Both are used to predict the rod deflection for an “average” cast, with the help of my numerical casting model. That deflection is limited to 50% of rod length which allows calculating the maximum mass of line that would be casted. Once the limits are known for various values of parameters, you do not need to care about the model; we just use correlations to get the final result. In the TCR case, it says a number 8. The difference between the maximum weight and the minimum line number allows estimating the total carry you can take for that rod with the lightest line: here we get 48 feet #5 without hauling. That is likely small for competitors, but the purpose is not to classify casting rods, although the system can be adapted to them just by changing the casting style in the model. If someone says that should be closer to 60 feet without haul, it can be adjusted.

To decide about what may be the best choice for you, you have to consider the loaded speed of the rod with 30 feet of line (see the graphic below giving the speed in Hz vs the line number). The 5 is really on the high speed side, but this was the intention of the designer. An 8 turns the rod into a softer stuff that may be too slow in practice. The 7 is OK for casters liking a moderate tempo, and the 6 might well be the choice of a number of casters interested in speed. This rod is however a bit on the edge; it is difficult to consider it as a “normal” fly fishing tool.

Image

Interesting?

Merlin
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Post by gordonjudd »

The maximum line number is obtained from two key parameters which are the normalized linear stiffness of the rod (and not the tip) and the normalized non linear coefficient of the rod.

Merlin,
Is the "normalized linear stiffness of the rod (and not the tip)" the measured k1 of the butt (lower two pieces) times the cantilever length of the butt?

I don't understand what you mean by (and not the tip) in that statement.

Is the normalized non-linear coefficient of the rod equal to:
k1*L(1 + k3/k1*L^2*s^2) where s is equal to .33 or .5 depending on how much the rod tip is deflected?
I take the example of the usual suspect, the TCR 590. In the CCS system, this is a rod for a number 7 line,

Does that mean it has an ERN of 7.5 using the CCS approach? The data Magnus measured appears to vary somewhat about an ERN value of 7 or a line wt of 6.5:
Image
I never understood why an ERN of 7.5 is the CCS match for a 7 wt line.

Both are used to predict the rod deflection for an “average” cast, with the help of my numerical casting model.

Are you using the values for the Paradigm cast as the input to that model and then vary the line mass for different lengths of line to see what the normalized deflection (s=.5 or so) would be?

Would your normalized k1 vs mass curve be linear if the x axis was given in grams rather than the mass of 30 feet of different fly line weights?

Gordy
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Post by Merlin »

Hi Gordy
Is the "normalized linear stiffness of the rod (and not the tip)" the measured k1 of the butt (lower two pieces) times the cantilever length of the butt? I don't understand what you mean by (and not the tip) in that statement.


The normalized linear stiffness of the rod is the product of its stiffness for small deflections (e.g. 1 N/m) multiplied by the cantilever length of the rod (e.g. 2.5 m, the length of the part which is not embedded for measurements); then k1L = 1 * 2.5 = 2.5 (Newtons)

The normalized stiffness of a tip is the same, using the cantilever length of the tip and its own linear stiffness. Let’s take another example: k1 (tip) = 1.8 N/m and cantilever length = 1.3 m; then k1 L = 1.8 * 1.3 = 2.34

Usually the value for the tip is smaller than for the rod, this is why I took it as the “reference” for the minimum line number, but you could use the rod value to define a line number for that rod. In the case of the TCR, it says this is a number 6. And yes, if I plot the actual weight values, this gives a straight line. The reason is that the stiffness must go along with mass.

When evaluating the carry, I must take the normalized values of the full rod, this is why I said “and not of the tip”.

Is the normalized non-linear coefficient of the rod equal to:
k1*L(1 + k3/k1*L^2*s^2) where s is equal to .33 or .5 depending on how much the rod tip is deflected?


Nearly yes, there is a problem of definition here. One should use the actual change in deflection due to load by comparison to no load. Since there is some initial deflection when measuring a rod horizontally, you have to discard that initial value, even if it is small. So “s” is a little bit less than 0.33 or 0.5

Speaking about the TCR CCS data, I took Bill’s measurement (7.5). The variability of data shows that there can be a rod to rod variation and a measurement to measurement variation if the methodology is not clearly defined. Anything between 7.0 and 7.99 is a #7 in Bill’s system, a 7.5 corresponding exactly to the weight of a #7 (185 grains).

The model I use to simulate the cast is a numerical non linear one tuned on a timing (0.44 s) and a casting arc (95 deg) which are close to the Paradigm cast. Then I look for the load giving a deflection equivalent to the total length of the rod divided by 2 (a little bit more than the cantilever length). Changing k1 and k3 values allows defining a mass, and surprise, the relationships with normalized values are linear. Changing the parameters of the cast changes the evaluation of the “carry”.

This system can be used in different ways. You can put carefully computed values of k1 and k3 obtained from a series of measurement, added to the classical m0 and k0 values for rod frequency variation with load. This is a purely engineered approach. If you do not have these means, the idea is to bridge the CCS data with a few extra measures (the k1 values), and then get k3 values from AA. For the time being, this methodology works for some rods and not for others (like the TCR), meaning that the relationship between AA and non linearity is weak. On another side, CCF is a mean to bridge with frequency values.

Beyond that you can incorporate a more sophisticated approach taking MOI on board for example. That MOI has an effect on the torque you have to develop to cast the rod and line, so it does influence your line choice. Let’s take the TCR example: if I find the MOI of the TCR too high for me, I shall be inclined to rotate with less speed and in that case, I may opt for the 7 instead of the 6 line.

Merlin
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Post by gordonjudd »

meaning that the relationship between AA and non linearity is weak. On another side, CCF is a mean to bridge with frequency values.

Merlin,
Tom looked at how well AA is correlated with the natural frequency and found there was considerable scatter in that relationship as well.
Image

Makes me think that the static bend profile with the rod tilted at a 45 degree angle that Tim Rajeff (and other manufacturers) use might be a better way to measure the "action" of a rod.
Image
Have you looked at how well mo fits with action or the natural frequency? I would expect that mo has a very strong correlation with the natural frequency, and rods with small mo values would also tend to be tip action rods.

Here are some other examples of the differences of some 8wt rods that were measured in the [url=http://yellowstoneangler.com/FlyRodComp ... asandThoma



sSt.CroixOrivsZeroGravityOrvisT3RedingtonCPSAlbrightXXSageXi2SageZaxisLoomiscrosscurrentLo



omisNativeRun.asp]8 wt shootout[/url] at Yellowstone Anglers a few years ago.
Image
With a fixed tip mass you can also see how a rod's tip deflection varies for the different Loomis Cross Current 10, 9, 8 and 7 wt rods in this photograph.
"Flyfishing: 200 years of tradition unencumbered by progress." Ralph Cutter
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Post by gordonjudd »

Since there is some initial deflection when measuring a rod horizontally, you have to discard that initial value, even if it is small. So “s” is a little bit less than 0.33 or 0.5

Merlin,
I think the deflection due to inertial loading and any set curve in the blank should be removed such that the deflection for a zero Newton tip force should be zero (as given by F=-kx), not some small offset value.

In your example if you used a very small deflection of L/30 that initial offset can give a misleading f/d value if you do not remove it.

If you rotate the rod any curve in the blank will cause that initial offset to vary, so I think it is best to just subtract it and then always use the cantilever length (not the full length of the rod) to get your normalized spring constant values and reference deflection values.

It is the cantilever length not the total length of the beam that is used in engineering measurements to account for different cantilever lengths, so I would not mix apples and oranges in an"engineering approach" to looking at the range of line weights you might recommend for for a rod.

As you say aside from the L/30 deflection measurement that offset is a small effect, but from an engineering standpoint I think it would be best to just subtract it, and not use different L values in the s=d/L normalized deflection values.

Gordy
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Post by VGB »

Excellent work again Merlin, I would have been surprised if there had been a strong correlation between AA & non-linearity as it is difficult to discern how regular internal tapers are. I have looked at some old fibreglass rods that have internal plugs that stiffen up the profile and seem to change the non linear chracteristics part way through the deflection.

I have been thinking about the variable values of K and suspect that if we looked at the rod fequency response with a spectrum analyzer that we may see something similar to a Chirp waveform. Which would imply that it may have bandwidth & selectivity
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Post by Merlin »

Gordy

Personally I discard initial deflection, but in the CCS system, there is no clear indication about that point. Is the "1/3 of total rod length" including that or not, it is not clear to me.

Thanks to Bill if he can clarify this point.

The problem with the 45 deg angle is to make a test bed, hoping the angle is correct, because the lever arm effect is not negligible. Apart from that, it would be difficult to connect such picture with rod behavior.

I said AA is connected to the normalized non linearity, that is to say to k3 L^2 / k1 (L being the cantilever lenght). Statistically, the fit is better than comparing AA with Fo. I put some hope in that in order to bridge the CCS with my actual prototype metric system


Vince,

Internal plugs have an effect on stability, this is one of the spectacular tricks Harry Wison used on his glass rods. He took a rod which was very sensitive to instability and put a few tiny plugs inside until the rod was quite stable. This comes from the stiffening effect of the plugs. Now where to place the plugs is a problem...

Merlin
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Post by VGB »

No names on the 2 I had, the plugs were also quite large. They felt odd so I blasted a big light through them. I sectioned one of them and the plug was solid white, probably e-glass. I also spoke to someone with a novel approach to doing similar. I won't post it here as I suspect it was a trade secret
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Post by gordonjudd »

Internal plugs have an effect on stability, this is one of the spectacular tricks Harry Wison used on his glass rods. He took a rod which was very sensitive to instability and put a few tiny plugs inside until the rod was quite stable. This comes from the stiffening effect of the plugs.

Merlin,
If stability refers to the after bounce vibrations, i.e.:
Instability is tip wobbling at the end of a cast, sending waves in the line.

It would seem to be a better tradeoff to increase the diameter at different points in the tip (with ferrule like overlaps) to make it stiffer rather than making it solid. The increase in stiffness will increase as d^4 while the added mass would only increase as d^2. Thus as was done with hollow built bamboo rods you could increase the stiffness/mass ratio more effectively by keeping a hollow cross-section rather than a solid one..

That assumes what Don Phillips says is the source of the tip bounce problem:
When fiberglass rods became available, rod designers found they could make rods with very flexible and strong rod tips. Although these rods were delightful for short to medium casting distances, tip after-bounce became a real problem with long casts.

The inertia of the relatively heavy fiberglass material flexed the rod tip excessively and its slowness to recover was ill-timed to the performance of the casting stroke.

was the mass density of the fiberglass in relationship to its stiffness.

I know Phillips used solid tips in his boron rods, but that was to prevent buckling failures even though it reduced the natural frequency of the rods due to the added mass of the solid tips.

To get a spectacular change in the recovery damping there must be something else going on with the use of those short plugs rather than just stiffening.

Haun looked at different ferrule positions in two piece rods (effectively a short stiffer section) and found that:
The results show very little change in modal behavior and frequency with the addition of the ferrule.

So there may have been some other effect than just stiffening going on to produce a big change in the after bounce characteristics of those rods.

Now where to place the plugs is a problem...

Agreed, and for me the physics of the added damping they provided is a mystery as well.
Gordy
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Post by gordonjudd »

Is the "1/3 of total rod length" including that or not, it is not clear to me.

Merlin,
In Bill's description of how to do the deflection measurement he shows the horizontal butt having a distance off the floor of 64 inches. For a 8' 6" rod he computes the 1/3 L deflection as 34" and then adds pennies until the tip is at a height of 30" off the floor.

Thus the initial x0 deflection due to inertial loading and any blank curvature is included in his quasi L/3 deflection measurement.

That is the difference between doing an ERN measurement and a spring constant measurement. Any normalized deflection in an engineering measurement would be related to the length of the cantilever not the length of the beam. Also the initial deflection would be subtracted such that the f=kx equation would hold and a zero force would have a zero deflection.

Theo found the initial inertial deflection adds a small bit of additional stiffening to downward deflections. Thus it takes slightly more force to bend the tip down 2 cm from the initial deflection point than it does to bend it up 2 cm from that zero reference point.
Since that inertial deflection impacts his 3.75 degree measurement for heavier rods he came up with a scheme to compensate for it by:
What I tried now is a second 3,75° scaling or lets say better a minus 3,75° scaling. What I do is I push the rod tip upward until it bends 3,75° and measure the force necessary with a scale.

So I have 2 results - one with the mass hanging on the tip and the second one as explained above. Now I add both and divide by 2.


He might have some examples of that in the 15 degree method thread, but as I remember that small force difference was in the noise by the time you measured the force required to get up or down deflections of .25 L.

Gordy
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Post by gordonjudd »

I said AA is connected to the normalized non linearity, that is to say to I said AA is connected to the normalized non linearity, that is to say to k3 L^2 / k1 (L being the cantilever length)

Merlin,
I think the Orvis flex index was derived by looking at the distance down the blank where the slope in those tilted bendforms was zero. For a full flex rod that point might be at around .5*L while for a tip flex rod it could be around .8*L.

It probably would not be linear, but I would expect there would be a strong correlation between those zero slope distance values and your (k3 L^2 / k1) spring non-linearity values.

Gordy
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Post by Eugene Moore »

IMHO separate the performance aspects of the tip and butt.
By looking at the total blank there is far too much generalization of the taper both in dynamic and static performance.
The least stable rods I've cast consisted of a fairly nice tip with an under-powered butt section. The flex in the butt contributed a great deal of tip oscillation even though the rod was correct overall for ERN and AA. This has been my major gripe with the current systems of blank measurement. The non-linearity of taper is the heart of the blank and is different between the butt and the tip.

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Post by gordonjudd »

The non-linearity of taper is the heart of the blank and is different between the butt and the tip.

Eugene,
Could you measure the outside diameter of that blank every 6 inches or so to show what you mean by a non-linearity in the taper?

I will do that for one of my full flex saltwater rods to see if there is much of a difference in the taper Lamiglass used from section to section in that rod.

Merlin says that many rods being made today use different stiffness (Young's modulus) graphite in different rod sections as well so that could also produce some discontinuities.

Gordy
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Post by Merlin »

Gordy

I have no information of how Orvis is proceeding (butt angle from horizontal, weight at tip). Only calculation with model rods would make the concept palatable in order to understand the relationship with non linearity.

Eugene,

Typical description of a classical stability problem, and you cannot detect that from any measurement like CCS or mine. The story is quite complex (several parameters).

Merlin
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Post by Eugene Moore »

Gordy,

I've actually measured blanks at 2" spacings and can derive where the mandrel transitions are located. IPC not withstanding.
The conventional transitions are less than 6" long and can not be easily found.
I've an 8' 8 weight IM7 med fast blank that casts very well. I'll make the measurments this weekend and send you the raw data.

Merlin,

I believe I've sent you the spreadsheet I created for finding that instability problem. The dimensions for the rod I experienced the problem in are both 9' IM6 blanks. Line weight was 4 and 5 and are located in the data base at top. Both rods were true to overall power but the butt section was slow and weak with a heavy taper tip. I believe the relationship to be quantifiable. At least that's what I read from the analysis.

Gene
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