Garrison stress graphs

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GeoF
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Garrison stress graphs

#1

Post by GeoF »

Hey everyone, I am new to the forum. I am a retired science teacher, avid fly fisherman, new to bamboo, and I like math and graphs. I have a question about The Book, "A Masters Guide...", by Hoagy. If this is the wrong forum for such a question, my apologies, and please redirect me. If someone previously has asked this question, (I would guess likely) again please direct me.

I have a disconnect when I read Chapter 14. Here is the issue:
p241 Hoagy states that the rod used as a model for all these calculations is the 8' model 212.
p257 This is a roughly parabolic graph, titled "2 piece 8'0" ", so I think this is the goal for this taper.
p275 is a chart of the second revision of this taper dimensions. The chart is within a thousandth or two of the p280 chart that gives the exact taper for the model 212 rod. Just small rounding errors are the difference I would guess. The chart on p280 matches exactly the taper on the Hexrod documentation for the model 212.
p277 is a graph titled "8'6" 212 ", which should at least be similar to the 8' version, or is this a typo and he meant to write 8' ??? Anyway, again this graph is roughly parabolic.
Finally, the Hexrod graph for the 8' 212, with taper measures that match p280 exactly, is a basically horiizontal graph with a slight negative slope. What Frank Stetzer would call a graph that is typical of Garrison tapers.

So there is the disconnect that I don't understand:
If the goal is the roughly parabolic graph on p257, then why does the finished rod not match that stress graph at all and instead make a mostly horizontal stress graph as seen on Hexrod??

p257 of The Book
Image

Model 212 from Hexrod
Image

Thanks for any insight,
George

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BigTJ
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Re: Garrison stress graphs

#2

Post by BigTJ »

George,

That taper is pretty linear. The slope of a parabolic taper is shallower in the butt than in the tip. The supposition it is parabolic is where you are getting confused.

Also I recall plot on 257 isn’t total calculated stress. The Garrison-calculated stress plot from Hexrod looks right.

There are three basic bamboo rod taper “families”. One that has a slope that increases with length, the straight line (+/-) and one where the slope decreases with length. There is a load of info on this on this board and on the internet.

Good luck,

John
Last edited by BigTJ on 03/07/22 21:46, edited 1 time in total.

trland
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Re: Garrison stress graphs

#3

Post by trland »

George, I believe it's just a matter of scale. If you take the hex rod stresses and plot the same points as the page 257 graph on a similar scale on the Y axis you get this:


Image


In other words, not very horizontal when you look at the tighter range that doesn't go from 0 to 200,000.
And welcome to the forum!

Mike

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BigTJ
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Re: Garrison stress graphs

#4

Post by BigTJ »

Changing the scale doesn’t make the taper parabolic though. I’m wondering where you got those numbers Mike they don’t match with the Op’s. Also what is a Dickerson 212 - is that a typo?

Keep in mind the Garrison calculated stresses have almost nothing to do with reality. In a fly rod the lowest stress is in the tip and the very butt. The highest stress is in the middle of the rod. Garrison stresses are a simple mathematical model based on beam theory. It’s not the end-all, be-all, but some find it useful.

Some people fee like they can better pick out the rod action from the stress curve. I prefer to interpret it from the taper itself. Different strokes.

John

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Re: Garrison stress graphs

#5

Post by trland »

John,

Yes, that was a typo. For some reason I had a Dickerson taper on my brain as I put a label to the graph. Sorry about that. I got the stress numbers from the same hexrod taper that George was describing. But his pic didn’t show the stresses, just the graph. I simply graphed the 5, and 10 through 80 inch numbers in 10 inch increments. They are the same numbers from his second graph from hexrod as shown below. He was describing a generally parabolic shape to the curve from the book. I don’t think he was referring to a parabolic action rod. At least that’s not how I took the meaning of his question. I was just pointing out that his confusion with the shapes of the graph, i.e. flat or a decreasing curve is just a matter of scale. I agree that the stresses are simply a model and is just another way of looking at a taper.

Mike
Image

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BigTJ
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Re: Garrison stress graphs

#6

Post by BigTJ »

The y axis labels are cut off in your photo so the “1” at the beginning is missing when the photo is clicked. That’s why the numbers don’t look the same.

John

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henkverhaar
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Re: Garrison stress graphs

#7

Post by henkverhaar »

Image

This is what the stress curve for a Garrison 212 in RodDNA looks like. If I set the tip impact factor to 3.75, the stress values agree very well with the numbers in the Book. And no, if you look at just the section from 140000 to 200000 it isn't flat at all. The deviations from a smooth line suggest to me that the numbers in RodDNA were taken off an actual rod, rather than from the Book, but I could be wrong there.

I also think the OP was referring to the parabolic shape of the stress curve (not really a parabolic section, but hey, does it matter much), not referring to a 'parabolic taper'. In fact Garrison stress curves represent fairly straight tapers.

Incidentally, stress is the second derivative of deflection, so if you were to integrate (numerically) the stress curve twice, you'd get the predicted deflection of a rod under static tip load. It'd be nice to do this some time, and then compare this predicted deflection with actual measured deflection. That would probably give a better answer to the question what Garrison stress curves have to do with 'reality' ;-)

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Re: Garrison stress graphs

#8

Post by trland »

Henk, (with apologies to George for getting off track)
FWIW Hexrod gets reasonably close to actual deflection measurements with the predicted. In other words, I would expect this actual rod to be deflected 1/3 of it’s length using somewhere close to 3 ounces of weight and have an angle at the tip of greater than 60 degrees. My crude deflection setup precludes me from measuring anything more though. It helps me to understand if I’m making, for example, an approximately 6 weight rod rather than a 5 weight rod and then if I’ve actually made a rod that will like a 6 weight line rather than a 5 weight. Just another comparison tool.


Image
Last edited by trland on 03/08/22 14:32, edited 1 time in total.

HexaMaineiac
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Re: Garrison stress graphs

#9

Post by HexaMaineiac »

Also, what is called a parabolic rod does not have a stress graph that looks like a parabola.

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henkverhaar
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Re: Garrison stress graphs

#10

Post by henkverhaar »

trland wrote:
03/08/22 07:25
Henk, (with apologies to George for getting off track)
FWIW Hexrod get’s reasonably close to actual deflection measurements with the predicted.
Yes - I know ;-) However, the Hexrod deflection prediction does not come from the Garrison stress calculation, but from a direct calculation method. What I was referring to was to use the Garrison calculation and back-calculate to deflection to see how well THAT corresponds to real world deflection. Or comparing it with the direct-calculation deflection would also be interesting already (as we know that calculated deflection is reasonably correspondent with actual deflection).

YMMV...

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Re: Garrison stress graphs

#11

Post by henkverhaar »

HexaMaineiac wrote:
03/08/22 07:46
Also, what is called a parabolic rod does not have a stress graph that looks like a parabola.
No, more like a ski jump slope ;-)

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BigTJ
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Re: Garrison stress graphs

#12

Post by BigTJ »

henkverhaar wrote:
03/08/22 01:55
Image

This is what the stress curve for a Garrison 212 in RodDNA looks like. If I set the tip impact factor to 3.75, the stress values agree very well with the numbers in the Book. And no, if you look at just the section from 140000 to 200000 it isn't flat at all. The deviations from a smooth line suggest to me that the numbers in RodDNA were taken off an actual rod, rather than from the Book, but I could be wrong there.

I also think the OP was referring to the parabolic shape of the stress curve (not really a parabolic section, but hey, does it matter much), not referring to a 'parabolic taper'. In fact Garrison stress curves represent fairly straight tapers.

Incidentally, stress is the second derivative of deflection, so if you were to integrate (numerically) the stress curve twice, you'd get the predicted deflection of a rod under static tip load. It'd be nice to do this some time, and then compare this predicted deflection with actual measured deflection. That would probably give a better answer to the question what Garrison stress curves have to do with 'reality' ;-)
You are 100% right, Bob MIlward did a deflection analysis to calculate stresses in a rod from stop-action photography, you can do the same on a deflection board. I'm a numerical modeler by trade, so I'm a huge fan of putting empirical data first and ensuring the mathematical model matches the key characteristics of that data accurately.

My bad on mis-interpreting "parabolic" from the OPs post. I am not a fan of the word I find it confusing, so many curves can be fit with a part of a parabola, so prefer progressive, regressive, straight line, they seem more descriptive. Also prefer Powell school of thought on tapers, EC Powell is my idol when it comes to rodmaking seriously the guy was a genius and incredibly gifted caster/thinker, he understood how fly rods work and how to make them work, but that's just me.

-John

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BigTJ
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Re: Garrison stress graphs

#13

Post by BigTJ »

HexaMaineiac wrote:
03/08/22 07:46
Also, what is called a parabolic rod does not have a stress graph that looks like a parabola.
Take a look at a Para 15, the stress graph looks like more of a part of a parabola than a straight line taper, but you can fit any curve with a part of a parabola if you play enough with the parabola, so it's sort of a meaningless word to me when related to rod tapers. As stated above, regressive taper seems a better name for it.

-John

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Re: Garrison stress graphs

#14

Post by Fcs »

I was just sitting down to answer the OP's question. It seems to be pretty well answered (a question of graph scaling) and now the discussion has split in several directions. As usual I'm late to the party.

A couple comments on Henk's remarks.
1. The 212 taper in RodDNA looks to be taken directly from the book, same as Hexrod. Once again the scaling of the graph magnifies small irregularities.
2. In Hexrod, on the "Casting Deflection" page, I give the stress curve for the deflected rod. My formula was the curvature value (which comes right out of the deflection calculation) times the MoE in ounces times 1/2 the rod dimension at the point in question. If you derive stresses from deflection, see if that agrees with your results.

Frank
"Wherever the fish are, that's where we go."
Richard Wagner

GeoF
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Re: Garrison stress graphs

#15

Post by GeoF »

Wow, a lot going on here. Thanks for the warm welcome to the forum and all the thoughtful responses. You have given me lots to think about! Fair warning, graph lover in the room.

I think Mike probably hit the nail on the head, and it may mostly come down to just a matter of scale. That is the simplest explanation, and the one that seems all too obvious once pointed out. Of course, that raises new questions.

The graph on p257 of The Book leads to the chart on p258. The goals for the stresses, if I understand correctly, are then 196000, 196000, 189000, and 180000 at stations 1", 5", 10", and 20" respectively. This is for a model 212 of 8'0", as Hoagy described on p241. All the 212s I have seen so far are 8'6" rods, including that pictured on p275 as well as the 212 on Hexrod. In fact, the graph on p275 gives 199000, 195000, and 187000 at stations 5", 10", and 20" respectively. The rod on p275 is not the rod Hoagy is building.

Mike changes the scale on the "Dickerson 212", which he means is a Garrison 212. That has 152300, 160000, and 155000 at stations 5", 10", and 20" respectively. So although the idea of scale adjustment is worthy, this is still not Hoagy's rod from The Book.

The graph from henkverhaar and RodDNA certainly has merit. But that graph shows 190000, 190000, and 175000 at 5", 10", and 20" respectively. That is still not Hoagy's rod.

So, I will assume for now that Mike is right. The most fundametal difference between the graph on p257 of The Book and the typical Garrison stress graphs on either Hexrod or RodDNA are a matter of scale. Yet, I still don't find a 1:1 match between the graph on p257 and any graph from Hexrod, or RodDNA, or anywhere else that match. Is that 8'0" model 212 just a figment of Hoagy's imagination? Is there a stress graph of that rod anywhere that matches the stress goals of the table on p258?

Thanks for considering,
George

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Re: Garrison stress graphs

#16

Post by Fcs »

George,

I think the answer to your question/concern is simply that there are a lot of minor (and maybe major) differences in the stress calculations between Garrison's hand work and what happens in Hexrod or RodDNA. I will list some here.

1. You will notice that some of the rod dimensions shown on the graph on p. 271 are slightly different than those in the 212 taper listing on p.280. Hexrod & RodDNA (H&R) are working from the latter.

2. The graph on p. 259 explicitly says the tip impact factor used is 2.5. H&R use, by default, 4.0. This is can be changed in the programs. Garrison's taper specifies and uses a 14/64 ferrule; H&R calculate a 13/64 ferrule is appropriate. (But Garrison's 14/64 and Hexrod's 13/64 seem to both weight 0.27 ounces.)

3. Each of the three use different methods of calculating the weight of the line on the tip and in the guides. Garrison (p. 242-3) takes the measured weight of the entire line and divides by the line length, to get grains per foot. Hexrod uses weight for each foot of line from tables once supplied by Cortland, for both DT and WF tapers. RodDNA (I believe) uses the weight of the first 30 feet (the AFFTA standard) and calculates weight per foot from that.

4. Garrison based his calculations on 5 inch intervals along the rod, corresponding to his planing form settings. H&R work at 1 inch intervals. That is bound to make some difference.

5. Garrison no doubt worked to limited decimal places. H and I assume R are performing all calculations to standard computer precision, typically 12 significant digits.

6. Hexrod uses a regression model to estimate the varnish weight from the rod dimension at that point. Garrison uses an average value for the entire rod (p. 244). In addition, I used weights of actual snake guides & strippers in Hexrod to try to improve on Garrison's calculations. (I'm sure this makes little if any difference.) I don't know how RodDNA calculates these, though its not hard to work backward and figure this out.

7. Hexrod & RodDNA differ in how they assign moments to points along the rod. In Hexrod, the bamboo, varnish, guide and line in guide moments for the segment between, e.g. the 6 and 7 inch points are assigned to point 7. RodDNA assigns these to point 6. I don't know if there is a most-correct way or not.

Maybe by making things more complicated, they become simpler???

Frank
"Wherever the fish are, that's where we go."
Richard Wagner

trland
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Re: Garrison stress graphs

#17

Post by trland »

GeoF wrote:
03/08/22 18:31
All the 212s I have seen so far are 8'6" rods, including that pictured on p275 as well as the 212 on Hexrod.
George,
The 212 in Hexrod is 8’0”. Look at the rod length in your second picture in your original post.
Mike

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Re: Garrison stress graphs

#18

Post by GeoF »

Frank,
Thank you for this thoughtful reply. I have already considered some of the points you raise.
1. I have noticed those small differences between p271 vs p280. Off by a thousandth or two, here or there, but essentially the same. Rounding error I guessed. I wonder if you put Hoagy's dimensions from p271 in Hexrod, will you get out his values of stresses that he lists on p258? Has anyone tried that? If so, I would love to see that graph and compare it to the Hexrod 212 graph at the beginning of my post. After all, it is those stresses on p258 that deliver his taper dimensions on p258-259. We should be able to go backward and forward, right?
2. Again, I would love to see a stress graph using Hoagy's dimensions, and certainly include this tip factor of 2.5 and the ferrule of 14/64. Let's compare apples to apples.
3. Yes, I noticed this issue as well. Using the total weight of the line and dividing by the length assumes a level taper to the line. Yet the line is a DT, so this adds some error. Since Hoagy does it this way, I say run with the error if someone is up to making a stress graph from Hexrod. Apples to apples again.
4. Yes, my first thought in reading Chap 14 was this lends itself to calculus rather than using 5" or 10" increments, or better yet use computers to nail it down at arbitrarily small increments.
5. Right, but using a slide rule and rounding to 3 sigfigs does bring back fond memories of high school for me. :-)
6. I noticed this varnish error right off. On p244 Hoagy mentions 55 gr of varnish on the typical 8'0" rod, but I was unable to generate his moment values for varnish and guides listed on the graph and table on p245. His moments for varnish and guides were higher than mine for varnish alone. Obviously guides moments were missing from my values. So I looked up the weight of a typical guide set and calculated guide moments with typical spacing, and added those to my varnish moments. Now my combined varnish and guide moments were larger than Hoagy's. Still, when we look at the magnitude of varnish and guide moments on p256, they are so small compared to moments of other components that the total moments only changed by a couple percent. Still, if we are going to bother to calculate moments for line, which is also small compared to total moments, I was puzzled why Hoagy appears to ignore the guides, and also assume the line was level??
7. I would assume that the correct way is to assign moments is to the station farther from the tip. That is the way Hoagy does it. I am not surprised Hexrod does that as well, since my understanding is Hexrod follows the Garrison math. I am surprised RodDNA does it the other way.

In conclusion, is anyone up for generating a Hexrod graph with Hoagy's original calculated taper dimensions, assuming level line, tip impact 2.5, 14/64 ferrule, etc., etc.?? I'd love to see that. And especially I would love to see if that graph regenerated the stresses on the table p258, rather than the stresses in the accepted Hexrod graph that uses the 212 taper on p280.

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Re: Garrison stress graphs

#19

Post by GeoF »

Mike,
My bad. You are correct, sir. My graph at the beginning off this thread is of the 8'0" model 212, which is the example used by Hoagy in Chap 14 of The Book.
My question in that regard, is why does this graph from Hexrod give stress values of 152651, 159987, 154657, and 151156 at 5", 10", 20", and 30" stations respectively. Yet on p258 of The Book the stresses Hoagy uses to generate this taper are 196000, 189000, 180000, and 172000 at those very same stations? Why do the stresses not match??

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canerodscom
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Re: Garrison stress graphs

#20

Post by canerodscom »

I have not looked at the examples yet, but a simple explanation could be that different values are used as the length of line outside the tiptop. Longer lines result in higher stresses. Check to make sure you are comparing apples to apples.

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