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Quantifying the Amount of Spine in Fly Rods

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gordonjudd
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Quantifying the Amount of Spine in Fly Rods

#1

Post by gordonjudd »

Dave Tulteman’s methods for finding the magnitude and alignment of spine in golf shafts can readily be applied to fly rods since the spine affect is related to the varying amount of scrim overlap along the length of the shaft (golf) or rod (fishing).

To make sense of this thread it would be well to study his excellent analysis of what causes the tip of a rod to whirl when it vibrates. He discusses the physics behind the Lissajous patterns formed by shaft whirl here and goes into to the details of finding the flat line oscillation (FLO) plane here.

Be forewarned if you skip reading his articles the nomenclature and results of this thread will be very confusing for you.

Tutleman reduces the complexity of spine by realizing that to first order it can be reduced to assuming the rod has slightly different spring constants in two primary bending planes that are 90 degrees apart from eachother. The spring constant in the weak or NBP plane is a bit less than it is in the strong or spine plane as shown below.
Image.

For fly rods that stiffness difference is due to the varying amount of scrim overlap along the length of the rod rather than having an oval shape. Graig Spolek has given an extensive analysis of how that overlap effects the spring constant in fly rods in this paper.
Spolek, G (2005). Measurement of fly rod spines. Proceeding of SEM annual conference on experimental and applied mechanics, Portland, Or, 7-9 June 2005.
But I could not find a free source for it on line.

In essence the amount of scrim overlap varies along the blank and thus the spine angle orientation varies along the length of the rod as well. Thus its final effect for a full rod is an integrated effect of the varying spine along the length of the blank. Fortunately, to first order at least, the complexities involved with the spine spiraling along the length of the rod can still be reduced to Tutleman’s simple model of two orthogonal springs. It is rather remarkable that something as complex as spine can be reduced to the properties of two orthogonal springs.

In reality the overall spine axes orientation will vary depending on the tip load in the static case or the magnitude and higher mode contributions to the bendform shape in the dynamic case but finding Tutleman’s flat line oscillation planes in a vibrating fly rod can still be used to get a good estimate of the amount of spine in a rod just as it does for a golf shaft.

The key to finding the FLO planes resolves around finding a vibration plane where the angle of the vibration plane is matched to the restoring force given by the combined restoring force of the two spring constants as shown below.
Image

Tutleman shows that the tangent of the angular difference of those angles is given by:
\(tan(B-A) = s *tan(A) / (1 + (1+s) tan^2(A)) \)

Thus the restoring force direction will be in line with the deflection direction when s is zero (no spine), when the deflection angle is at 0 degrees, or when tan(A) has very large values when A is near 90 degrees. Thus even though a rod has a considerable spline it should still have a nearly straight line tip path when its deflection is on the stronger flat oscillation plane or the weaker neutral bending plane.

Taking the inverse tangent of that tan(A-B) function shows how the phase difference between the deflection and restoring angles depends on the relative spring constants in the weak and strong directions as shown in the first plot below:

You can see that for relative spring constant values of around 10% the restoring force will be 2.75 degrees away from the deflection angle when the oscillation plane is half way between the flat line oscillation planes. That phase difference will produce an oval Lissajous pattern that will cause the tip whirl to increase and rotate over time since the oscillating frequency of the two FLO planes is different.

An example of the expected Lissajous pattern expected for a rod with s=.065 and an initial deflection angle of 140 degrees is shown in the second plot below.

Applying this theory to quantifying the magnitude of the spine in a fly rod will be covered in the next post.

Gordy
restoring_force_phase_difference.jpg
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gordonjudd
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Re: Quantifying the Amount of Spine in Fly Rods

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Post by gordonjudd »

I picked this rod as a test of Tutleman’s method because it had so much tip whirl when doing frequency vs. tip mass tests. That whirl made it difficult to get good frequency measurements with small tip loads as Merlin has mentioned. It was made with high modulus graphite in China and sold for less than $100. As such I was hoping it could be purchased to sell to some students at the annual beginning casting classes at the Long Beach Casting Club. High shipping costs ended up making that choice impractical.

The frequency vs. tip load measurements showed it had a reasonably high natural frequency (3.56 hz) and a low effective mass value of .0032 Kg. Not bad numbers especially for the price.
Image

The challenge in this test was to find the flat oscillation plane as the tip whirl was very pronounced for most orientations of the clamped rod butt. I finally homed in on one of the straight line oscillation planes as shown for the tip paths of the first two oscillation cycles as digitized with Tracker.
Image

These paths were nearly straight lines and in this case the second cycle shown in yellow was actually more narrow than the first cycle that is shown in red. The measured loaded frequency in this case with a tip load of 16 grams was 1.477 Hz.

To get the loaded frequency in the other FLO plane I released the tip from an offset horizontal direction. The measured tip paths for the horizontal vibration mode is shown below.
Image

It was difficult to gauge the height of the horizontal release and thus these tip paths were not as straight as they were for the vertical vibration plane. These paths show the typical case where the second vibration cycle shown in yellow was wider than the narrow oval shape of the first cycle. In retrospect I should have clamped the rod butt with a 90 degree rotation from the first and then vibrated the rod vertically since it is easy to sight down the rod and determine when the tip is directly above the butt of the rod before it was released. I settled for this measurement rather than setting up the experiment again, but think the measured frequency in that FLO plane of 1.431 would be very close the actual value.

To determine the relative spring constant of these two orientation you can assume the loaded frequency of the rod is given by
\(freq=1/(2*pi)*sqrt(k/(mo + m_{load}) \)
Thus assuming mo is the same for both orientations you can determine that the ratio of the spring constants in the two orientation is equal to the square of the frequency ratio which gives:
\(k2=k1*(1.478/1.431)^2\)
Or k2=1.067*k1. Thus the s factor for the spine in this rod was relatively high value of .067.

To check on the validity of Tutleman’s predictions of the Lissajous pattern expected for this rod I released the tip of this rod from a deflection angle of 140 degrees. The paths measured by Tracker for that oscillation plane is shown below.
Image
That initial deflection angle is around the maximum phase difference for the restoring force direction, and thus results in a much fatter oval shape where the second cycle’s path in yellow was much wider than the path of the first cycle in red. Those paths match the predicted Lissajous pattern quite closely as shown in the first topic.

I also used this approach to measure the spine of the upper half of Loomis rod was designed for the Trout fly game. It's s factor was .028 or less than half of the s factor for the Sky Gold rod.

Thus Tutleman’s FLO concept gives a very accurate way to measure the amount of spine in a fly rod. Too bad that it has taken this long to apply it to measure an important characteristic of fly rods..

Gordy
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Re: Quantifying the Amount of Spine in Fly Rods

#3

Post by James9118 »

Have you measured the spine in a carbon blank caused by how the carbon is wrapped, or have you measured a spine created by whipping guides to it? Or a combination of both (i.e. the manufacturer has already determined the spine before adding the guides).
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Re: Quantifying the Amount of Spine in Fly Rods

#4

Post by gordonjudd »

Or a combination of both (i.e. the manufacturer has already determined the spine before adding the guides)
James,

Both. As mentioned this rod had a lot of whirl when it was tested on the guide plane. I have no idea how they chose to orient the guides on the blank. Would not doubt that they placed the guides to get the straightest looking finished rod since they are not on the static NBP either.

Here is an interesting observation about the C.G. of the tip weight relative to the center of the shaft from Tutleman's site:
TECH NOTE 29: In the spine alignment process we try to determine the two planes in a shaft that produce flat line oscillation, i.e. no wobble. This is very often done with a tip weight rather than the actual clubhead. The questions arises," will the FLO change when I install the head because its center of gravity is offset from the centerline of the shaft?" Golfsmith claims it will not change. I was curious. If a change in FLO does occur is it due to the change in cg or because it's hard to twang the club straight up and down when your finger is twanging somewhere out on the clubhead rather than on the centerline of the shaft?
To test this I built a tip weight with an arm sticking out of the side of the piece that attaches to the shaft. This piece weighed about 100 grams. I placed another weight on this arm and held it in place with a setscrew. This second weight also weighs about 100 grams. This arrangement allowed me to vary the cg of the test weight by more than an inch in a direction at right angles to the shaft. I attached a very small key chain laser to the tip weight. I built a trigger release system to eliminate any variations due to finger plucking. I placed a 10" disc on the butt end of the shaft. With degree lines on this disc it was easy to repeat alignments as I searched for the FLO. I determined the FLO plane as accurately as I could with the laser projected about 20 feet across the room. I then adjusted the side weight to move the cg about an inch. I did not find any variation in the FLO plane. I guess Golfsmith was right.
Gordy
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gordonjudd
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Re: Quantifying the Amount of Spine in Fly Rods

#5

Post by gordonjudd »

Have you measured the spine in a carbon blank caused by how the carbon is wrapped, or have you measured a spine created by whipping guides to it?
James,
That brings up an interesting question as to the guide placement relative to the strong FLO plane.

If you wanted to reduce the spine would you put the guides on the strong FLO plane of the blank or its weak FLO plane?

That same question applies to aligning the spine in a four piece rod. How would you align the strong FLO axis of the upper sections to the strong FLO axis of the butt to minimize the overall spine in the rod?

Gordy
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Re: Quantifying the Amount of Spine in Fly Rods

#6

Post by Merlin »

Hi James

Years ago, Graig Spolek now retired professor from Oregon State University (a friend of mine and Gordy) studied spine in several blanks and compared calculated spine versus measured spine. To identify the number of turns he cut splices in blanks (a destructive test procedure). The stiffness asymmetry (higher stiffness divided by lower stiffness) can rise up to 20% depending on the number of wraps and he got pretty good comparisons between measurements and calculations.

I did something similar last year, comparing sections overall stiffness asymmetry for the tip of a rod of known design (number of wraps). For the tip I calculated 1.075 for 1.07 measured, and for the tip mid I calculated 1.14 for 1.11 measured. Guides are included in measurements which means that the spine contribution of guides can create local disturbance but pretty little effect on the overall characteristic of a rod section. I calculated the spine for butt sections as well but was unable to measure the stiffness assymetry correctly. In that case both butt sections exhibited spiral spine.

For a synthetic rod, the main axis of inertia can swap together which makes the rolling test sometimes surprising.

Merlin
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Re: Quantifying the Amount of Spine in Fly Rods

#7

Post by James9118 »

What are your thoughts on the 'D-Flex' rods that have recently re-appeared on Facebook (looking for kick-starter funding). The USP of these seems to be a very high stiffness asymmetry (produced by a non-conventional blank cross sectional profile) - would the 'whirl' on these be greatly exaggerated, how do you think one would cast?

James.
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Re: Quantifying the Amount of Spine in Fly Rods

#8

Post by Merlin »

I think I have already seen that type of rod (the releaux cross section I guess), let me have a check.

I calculated the stiffness effect of guides on the rod I mentionned above (which is 37% stiffer than the one I used before, in the thread about guides) and the stiffening is very low: 0.5%. This could explain why I can simulate the stiffness ratio due to spine rather easily.

Merlin
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Re: Quantifying the Amount of Spine in Fly Rods

#9

Post by Paul Arden »

Would be weird to have to constantly adjust arcs between back and forward casts. If there is a significant difference I would think Snake Rolls will be extremely odd too!

Cheers, Paul
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Re: Quantifying the Amount of Spine in Fly Rods

#10

Post by gordonjudd »

The USP of these seems to be a very high stiffness asymmetry (produced by a non-conventional blank cross sectional profile)
James,
What is USP and how does it relate to the relative spring constant magnitudes in the two flat line oscillation (FLO) planes?

Regardless of the factor the produces the spring constant differences (in this case I assume it is due to an oval cross-section) Tutleman's approach would still apply. The s factor of those rods (which quantifies the amount of spine in a rod) could well be larger than it is for conventional rods. If so they would exhibit more whirl when vibrated on a non-FLO axis.

It would be rare for the bending axis plane to remain constant when we cast so I don't think it would be easy to keep the rod bending strictly on one of the FLO planes. That would be especially true when trying to cast only on the strong FLO plane. Thus I would expect an asymmetrical rod would tend to twist in the hand when trying to cast it on the strong FLO plane.

The only way to find out would be to cast it.

Gordy
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