Any time you want to talk tapers, I'm your man.  I believe that the taper is the soul of the rod, the rest just window dressing (and while I strive to dress my rods as functionally as possible, and as aesthetically, I agree that it seems like some folks do get their priorities backwards focusing more on the wrappings, tipping, engraving, etc., than on a good action to start with).

I do quite a bit of "prototyping," building multiple tips with different actions for rods, to get a practical idea of what changing a taper, or designing one from scratch, really does.

I also have dozens of graphs of rod dimensions (which for the past few years I've found more helpful than stress curves) to help me compare tapers to actions (though charts are only useful if you've cast the rod, so you know what it does).

I do really appreciate ALL the discussion topics, from thread to glues to varnishes to gizmos, but I do agree that tapers sometimes get lost (though it is hard to convey what a rod feels like without letting someone else cast it, and God knows rodmakers are an opinionated bunch who don't often agree on what each prefers in rod action).  (Chris Obuchowski)

I was wondering ... How many customers actually are educated in tapers that buy cane rods??? I don't sell rods to cane fly fisherman, my rods go to family and friends that have never fished a cane rod while I learn to become more adept at building. I've always wanted to know more about the cane rod buying community. I know there's a faction that buys just for esthetics, but how many really are educated buyers???  (Bill Tagye)

I feel pretty comfortable in saying that somewhere around 20-25% of the folks who buy rods know their tapers pretty well.  This summer I had a customer who wanted a rod "sorta like a Perfectionist, but a little stiffer in the butt."  I had another customer last year who wanted a Payne 200L just like the one his dad fished.  Another one wanted a 6' 4 weight with  a stiff butt that would still handle 6x tippets and short casts.  I have a regular customer in Germany who really knows his stuff, and gets quite specific about the taper design in the rods I build for him.

On the other hand, I've had plenty of customers who ask things like "I fish a Scott glass rod, and really like it.  Can you build a bamboo rod like that?"  Or, "I'm new to fly fishing and want the best of everything.  I hear cane rods are the best.  What would you recommend?"  (Harry Boyd)

Therein lies the confusion. "You" take a person liking a stiff butt or a 200l for knowledge about tapers, I was trying to relate this to a stress function. something more measurable in result than a feel, although I agree that is the final test.

Don't take this all wrong, I'm not saying that the old rods or contemporary copies are not great rods, They simply don't tell you how they were engineered with out another tool

I handed a rod that I built as a slingshot taper to a guy who is a very good caster, and his comment was, this is really a fast rod.

so the test i am seeking is what was your design criteria and how do you know when it matches something you can measure. and is it modifiable without the add a few thousandths here or there. I accept the fact that R.N. and a few others can design a rod by feel, but can the skill be transferred.  (Jerry Foster)

Perhaps I should have distinguished between  knowledgeable and ignorant rod buying customers.  Ignorant, but able-to-be-educated, I can live with. I guess I lean more towards the touchy-feely than the empirical.  I haven't really thought a lot about relating how a rod feels to a stress value expressed in numbers.

One "number" that helps me visualize "feel" is a slope value of the rod taper.  Ray Gould describes the slope values well in his latest book, so I won't go into it in detail here.  The higher the slope of the taper, the stiffer the rod feels.  I think that's somewhat similar to the Powell ideas Chris Obuchowski described.

In my opinion, Garrison's math is a good guide for comparing tapers, and for making relatively minor changes to those tapers.  Enough rebuttals of his theories have been written to convince me that Garrison's math is really of quite limited usefulness beyond making comparisons and small changes; Milward, for example.  Don't get me wrong... I use Frank Stetzer's Online Hexrod and find it a great tool.  I greatly appreciate Frank putting it online and Wayne laying out the concepts.  But I think stresses as expressed by Garrison are quite limited as a design tool.  As a comparison tool, they somehow work.  Engineers almost universally agree that static stresses on a cantilevered beam are not an adequate model for describing how fly rods bend and straighten under increasing and decreasing loads.

You ask if the skill of designing tapers by feel can be transferred.  I don't know that it can be transferred, but I think it can be learned with practice and experience.  That's what I sought to express in urging us all to become better casters.  (Harry Boyd)

I have been trying to get my hands on Milward's book.

Perhaps someone can enlighten me as to the key principal in his work that is an overwhelming principal of design that makes his disciples discredit the results of beam deflection. (RK?)

Yes, Ray's targets for rate of change are valid also, just haven't had time to see how they fit into stress evaluation.

I had many talks with Press Powell (before his passing) about rod design and he was very firm that EC's formulas were the only rod design tools one needs.

So are we stuck here?   (Jerry Foster)

I read Milward's book, too.  To my experiment via my simulator, stress curve varies accordingly when a rod is flexed.  Stress point (high stress point) will move to mid of the rod and finally toward grip side.  Everybody knows about this in actual fishing situation.

Garrison's math does not move rod, of-course, and it focuses to one fixed situation, movement of the rod is fixed to the state of 4 x gravity (acceleration) situation (this is the translated rod of Don Phillips book), it does not assume the rod will be bent (within his math) since 5 inches interval are always 5 inches.

It is obvious that a flexed rod has different shape of stress curves from time to time.

But when we try to calculate desired dimension from such stress curves, cause and effect relationship will always result in the same dimension number. Flexed stress curve will also produce the same dimension numbers to the one from unflexed stress curve, since math will change to the effect.  Even MOE, change of angles are taken in account...

So, it is okay if we use Garrison's math to calculate dimension number from stress curve.  I confirmed this point by  calculating dimensions from fully bent stress curve.  The resulted dimension is same.  My program can calculate dimensions from rod flexure. Try to think like this, one rod can show  various stress curves, but it is the same rod.

It is not okay to try to draw a flex curve of a rod from Garrison's moment or stress curve. When a rod bend, moment calculation should  change the length of interval which is caused by bend.  To draw a deflection curve, we may need to consider the effects of gravity itself either as well as inertia of rod movement.  (Max Satoh)

My understanding of Max's post is that if you consider a fly rod as a lever with a line at the end along with its own distributed mass being accelerated, the more acceleration in the forward stroke the more bend in the rod- with bending increasing from tip to butt. However the degree bending changes the effective length of the lever (the more bend the shorter it gets). How acceleration changes effective length is a function of the rod taper. Steep tapers will bend mostly at the tip and remain long levers under large accelerations. Shallower tapers will shorten more under lighter loads.

So Max says that there is a family of bend forms created from a single rod taper under different accelerations. In terms of stress the highest stress will be in the part of the rod which is under load and bending. Once a portion of the rod straightens out and is in line with the fly line the bending stress goes toward zero. Milward did an experiment in which he measured the degree of bending at 5" stations along a rod at he maximum acceleration casting load by using high speed photography. He then used the standard formula to relate f(b) to the observed bend using the standard formula. He compares his stress  curve to the Garrison curve. They are, in fact very different. The major difference can be accounted for by the bending of the rod and the resultant shortening. This is I believe what Max means by saying the same rod can have different stress curves. Each bend form generated from a single taper will have a different stress curve. The tricky part is that the load and dimensions predict the bend forms however the stress curves for different bend forms of the same rod do not predict the same dimensions. This is because large parts of the rod tip are left out of the stress curve at large bending levels. This, I think, is why Garrison didn't let his rods bend.

I hope this is not a total distortion of your post Max.  (Doug Easton)

Thank you, thank you,  you did pick up what I wanted to say very much.  Thus,  a cooperation would have a good result.

The tricky part is that the load and dimensions predict the bend forms however the stress curves for different bend forms of the same rod do not predict the same dimensions.  This is because large parts of the rod tip are left out of the stress curve at large bending levels. This , I think, is why Garrison didn't let his rods bend.

I rather think a little romantic about this.

My calculation is like this;

add moment, calculate the bend, on time 1:

add moment, calculate the bend, on time 2:

Thus, moment value for time x becomes less and less on tip top. Finally the tip top part would have zero moment which means straightened by some force, by fish, line cast or tree.

Then you questioned why the straightened tip top could be reverse calculated to dimension? I say yes, we can get the same dimension if we get a set of cause-effect pairs of moment, bend, (as well as MOE, weight). Even if the tip is straighten out, the calculation algorithm include the length from tip top to butt end (I mean action length). Doing reverse calculation from butt side to tip side, subtraction effect will remain tip dimensions from 1 inch to another.

About the reason why Garrison didn't let his rod bend?:

* He did not have PC like now.

* By assuming the rod length to no bend, he could get higher stress value at tip top part oppositely. (since this is mere a division operation, M/Z, fixing M would result in more value then varying M according to bend)

* He possibly would like to make such a design formula by using the height of the stress value which would represent a nature of rod bend. So the slope of the curve from left to right would imply progressive nature of bend, or flat slope  for entire bending, and parabolic, etc..

* That is Stress Curve of Garrison.

* But actual world, Tip top (around 0-15 pt) does not have such high stress, then people start confusing...

Most people start calculating moment from tip top toward butt side, even if bending is taken into account. It will cause higher tip top moment since he is calculating straight  rod at the beginning.  Calculation from butt to tip considering bend, will result lower moment value on tip top.  These stress curve would not have high stress on the tip top.  (Max Satoh)

Just to stir the pot:

One "number" that helps me visualize "feel" is a slope value of the rod taper.  Ray Gould describes the slope values well in his latest book, so I won't go into it in detail here.  The higher the slope of the taper, the stiffer the rod feels.  I think that's somewhat similar to the Powell ideas Chris Obuchowski described.

And beyond that, the higher the slope IN STATIONS OF A TAPER make the rod a better distance, or roll, or close in rod.

Compare stress curves to slopes.   Look for the places where a rods slope increased or decreases.  

I compare my tapers to an average slope and have noticed that the taper usually has a "wiggle" around the ferrule.  flatter going in and steeper coming out. 

Anyone else see this in their tapers?   If so, why?  If not, why not?  (Terry Kirkpatrick)

The wiggle is the result of the diameter being bumped at the ferrule. A good representation of this in a slope can be found in the Fierabend article in The Wise Fisherman's Encyclopedia. Reed has the extract on his site.

First page.

Second page.  (Larry Blan)

Gould’s slope value idea is just a way of getting a quick idea of how fast the taper is, it is a bit misleading on some parabolics, as they have slower butt tapers than tip tapers.

I don't know why there is a wiggle at the ferrule, and I cannot think of a good reason.  (Robin Haywood)

Ah, now the question about the wiggle in the middle. I am assuming you mean the flattening of the taper at the ferrule location on my double parabolics. This is done for a specific purpose and that is that I believe that putting a nickel silver ferrule in the middle of a 2 section rod installs a stiff strong connector that will not bend at the same rate the cane does. Thus flattening the taper there offsets that difference and provides a smoother action to the cast.  (Ray Gould)

I didn't know what was meant by the wiggle, I imagined it as some kind of bulge at the time, which was probably stupid of me.

I quite liked the look of your double parabolics, but have not had the time to properly analyze them, there was something about them that concerned me but I can't find the graphs to look at to see what it was. It wasn't much though, in fact I remember thinking that the purists would probably not accept them as parabolics!  Was it that they have convex but tapers and I tend to like them concave? If it was not so late I'd go and find out, so advance apologies if I'm talking gibberish.  I certainly would not have worried about the flattening of the area around the ferrule since I like rods with the top third and the bottom half of a quicker taper and a slower bit in the middle, this is a bit of a reduction ad absurdam, but you can probably see what I mean.

Entirely off subject I like coil springs on cars that shape too, but whenever I have spoken to a suspension expert they go on about the difficulties of designing and making variable rate dampers. This is curious since a chum and I designed a perfectly viable design for one over 20 years ago which was tested and worked and now we have electronics and fluids which are electronically variable in viscosity. Since neither of us wish to emulate Tucker or, for that matter Citroen, in terms of grief per pound earned, we gave up with big sigh and shaking of heads! He was interested since he is by training an oil chemist of fairly exotic kind but I have recently learned that an ex-colleague is involved in electronic damper design, so, thirty years too late there may yet be hope!

Back on track I will say that I do not and never have liked step down ferrules for this reason.  I've never used them intentionally, even when there was no choice I built up the butt section to take the larger diameter female. In fact, I tend to build up both sections, even now, because I still have the heeby-jeebies about removing cane! But not always, I'm mellowing a bit with age, depends on the rod and sadly, what ferrules I have to hand, but don't tell anyone.  (Robin Haywood)

I don't believe most buyers have any knowledge of stress curves, nor should they. They buy rods for a lot of reasons, cosmetics, action, collectibility of the maker, etc. But the stress curve is in the dimensions, whether they know it or not.

Since it's raining here lets give a discussion about stress curves a start.  Although I'm not  the most qualified to do this..

1. Is there an overall agreement that Garrison had the optimum stress values for bamboo correct.  140k to 220k in oz's

I see a lot of rods that break this basic tenant and are beloved by their makers.

2. Every rod is built to optimize it's casting ability at one specific length of line.

A stress curve for 4 wt at 40' reflects the weight of the line beyond the tip

3. Wayne’s topic.. the stress curve reflects the character of the rod.

A parabolic is easy to see, the others (fast, slow, etc.) we will have to work on.

This should be a basic start.

Comments and next steps to understanding.  (Jerry Foster)

I think almost no one who has not made bamboo rods (and probably plenty who have but didn't read Garrison or Cattanach) are not familiar with stress curves.

1. I don't have a mechanical engineering background, so I don't know of any data from destructive testing regarding the "idea stress values" of bamboo.  My guess is that no formal destructive testing has been done with bamboo as a building material to provide empirically based numbers.  I don't recall how Garrison arrived at his numbers (I'll have to go back to the "Bible" tonight and see what I can learn).

I agree that there are a number of rods out there that violate these "rules", some that have been in use for decades without failure.

Having built a couple of Garrison tapers, I can say I like the smooth action, but they do seem to be slightly overbuilt (on the other hand, you can throw anything from small dries to huge heavily weighted stone flies, with split shot, and big strike indicators, with a rod like a 209e, a 5 wt, so maybe they really aren't "overbuilt" if your fishing swings from one extreme to another.  I probably wouldn't fish size #24 flies with 7 or 8x tippets though, at least not if I don't want to break off most of the fish).

As an all around fishing tool, covering the largest gamut of situations, I do think that Garrison rods are excellent.

2.  I agree with number 2.

3.  I agree that stress curves reflect the character of the rod. . .but I think you need to look at the actual dimensions to get an idea of line wt, and whether the rod will be strong, soft, etc. . .how it might perform in actual fishing situations.

For those interested in rod action, Ed Hartzell a number of years ago wrote a very concise little explanation of Powell rod actions (using the A, B, C system devised by EC Powell, and as described in several monographs and publications put out by the Powell rod company long ago),  that provide an excellent starting point, and common vocabulary, for discussing basic rod actions, and variations from them.  Oh, Ed's article was published in The Planing Form.  (Chris Obuchowski)

1. I agree with the general range of Garrison's optimum stress values, not to the extend that it is important that it defines a breaking point, but rather that it helps to gage at which stresses a rod is optimized during design.  For a set line weight/length, a rod that shows an average (lets call it 'average' though it isn't really) stress of 140k will be underlined.  There isn't enough line mass to load or flex the rod properly.  Conversely, one who's average is 220k will be overlined.

There is a magic spot, for me at least, around 180k that will allow me to define a rods proper line weight for progressive rods.  Look at the Garrison 209 in RodDNA for example.  Setting the line weight at 5 and the line cast at 45, I see an 'average' stress of around 165k or so.  To me this says that with up to 45' of line out the 209 is going to feel slightly underlined as I've found my optimum stress for accurately generating a progressive taper (using this line length for this rod weight) is around 180k.  As such, if I were to design a rod for a 5 wt line with a progressive action using the 209 as a template, I would lighten up the stresses until they neared that target.  I have empirically found this to be accurate for my personal fishing and casting preferences.

With tip action and parabolic rods the target of 180k moves around a bit, and is more difficult to pin down due to the nature of the graph, but again by doing some empirical testing I know wherein that optimum stress lies for each line weight and curve style.

This is just a little bit skewed as I don't use RodDNA nor Hexrod when designing a taper.  I have a heavily modified version of Paul Griffin's Excel spreadsheet (thank you Paul!) that I have setup to, among other things, view stress curves in a 3 dimensional format, with the X axis and Y axis being the standard values and the Z axis set as the amount of line cast from 2'-48' (variable of course).  Using this standard I can easily see the stresses, and rate of change of those stresses, under various line lengths for each taper.  And they look mighty cool! ;)

2. I think that a finished rod is made to optimize a certain range of line cast, or a few specific ranges in the case of rods with hinges etc., but not for one specific line length.  However, when a taper is being designed it is important to use a standard so that you are comparing apples to apples.  If you are using stress curves to design a 4wt, you don't want to use 40' of line cast for one taper and 50' for another, so in that sense you do need to use one line length to optimize the consistency when designing and comparing.

3. Thinking of stress curves as a tool that reflects the character of the rod is a perfect way to look at it.  Parabolic, progressive and tip action are all easy to see by the shape of the curve, and the overall stiffness (preferred line weight) is easy to see by the stresses exhibited.

The term action, and its overly simplified descriptions, will always give problems, especially when you're talking with a graphite convert or someone who isn't too familiar with cane.  I'm always careful to speak in terms of 'tip action', 'even or full flexing', 'flexible or soft butt section' and the like in such circumstances and not 'fast', 'medium' or 'slow'.  Way too many folks equate 'fast action' with 'stiff', 'slow' with 'soft' etc.

Some of this is akin, I suppose, to Powell's descriptions of A, B and C actions as Chris O. mentions.  As an aside, the original pamphlet can be read on Banjo's web site.   (Chris Carlin)

OK let's try this..

A customer comes to you and says " I'd like to buy a 3 wt rod that will punch 40' of line and drop a fly on the water without a ripple."

Where would you start?  (Jerry Foster)

A lighter line version of the 7 1/2 foot three piece 4 wt. Hardy Marvel? (David Zincavage)

I'm gonna assume it's for small dries and nymphs, small stream work. My favorite light rod is the Sir D, especially in Quad configuration (Bob Maulucci's version).

I'd run the taper thru Hexrod, adjusting first for the line weight conversion, then run in through a second time to do the hex to quad conversion. 

For those of you who don't have a computer but do have a hand calculator:

Divide the AFTMA #3 wt standard by the AFTMA #4 wt standard, to find out the percentage difference (the value will be unitless, but will give you a percentage how much less mass the 3 has compared to the 4).  Next, convert the diameter of the original taper at each station to cross sectional area.  Now multiply by the conversion factor to reduce the #4 cross sectional area values at each station to a #3. Finally, convert the area values for the #3 back into diameter.

In practice, this comes out very close to the values generated by Hexrod.  (Chris Obuchowski)

Great plan + a bunch of extra stuff.

I AM losing it. I was searching for a from scratch method.

For instance, how do you define the butt dimensions to get the punch, the tip for delicacy of presentation and stupid stuff like that.  What range of stresses, how much transition and where.. never mind  he he

By the way Dave's suggestion of a Hardy caught me off guard, I ran some stresses on it. It looks like a really neat taper, casts a 3 wt at 40 ft and a 6 wt at 50' and the stresses all stayed in range. Neat.  (Jerry Foster)

Okay, from scratch then.

• Ferrule for a 4 wt 12/64 (13 for  5 wt, 14 for a 6 wt); so I guess we'll use a #11 ferrule.
• Tip top #4 (4/64, .062 or so).
• Rod "speed" based on average slope over the working part of the rod. . .013 per 5" is medium, .016 medium fast
• Rod length 7 feet = 84"(10" grip, action length = 74")

Start at the ferrule station @ 42", and plot a straight taper forward to the tip dropping say .014/5" (.0171@42", .166@40", .152@35", .138@30", .124@25", .110@20", .096@15", .082@10", .068@5", and we'll fudge to give .060@0", the tip top, a #4)

Now go larger to the butt; 179@50, 193@55, 207@60, 221@65, 235@70, 249@75, and a constant .250 under the handle.   How do are  stresses look?  Actually, they look great - nice smooth curve, max of 209K at 10", 189K@15"

Anyone could build this taper and be very happy; a crisp medium fast 7' 3 wt, smooth progressive action.  But, the client wants a slightly stronger butt to the rod, to really punch out that 3 wt in the wind (okay, whatever).

So now we add the Powell A concept, with a constantly increasing slope (we'll keep the tip section constant, a B taper; the C taper had a constantly decreasing slope to generate a parabolic type rod).  EC often used a .___ + 2 , or a two ten thousandths of an inch increase at each 6" station (we'll use .0003/5" to increase the power in through butt.  Our     slope     now       becomes       .014+.0003@50", .014+.0006@55", .014+.0009@60", .0152@65", etc.  The new rod dimensions become: .060@0, 068@5, 082@10, 096@15, 110@20, 124@25, 138@30, 152@35, 166@40, 183@45, 197@50, 213@55, 227@60, 243@65, 259@70, 272@72.

If you want a more delicate tip, you can use the A system to decrease the tip diameter, or use a faster slope (.015 or .016/5"); I'd recommend the second option over either (giving you a B tip and an A butt).  With an A tip I'd worry about weakening it too much.

Now what do you think?  (Chris Obuchowski)

Ain't this great stuff?  I still think the customer was smokin' crack wanting a 3 wt wind rod.  But hey, it's his/her money.  Is it normal to start at the ferrule?  If so, how much does making it a 3 piece complicate the works?  (Mark Wendt)

It was interesting to superimpose your compound taper on mine (explained below), even though mine is 6" longer (the tips are very similar). I think it would be interesting to make the rods and compare the actions. I suspect that yours would be faster but mine might have more "reserve power." Both should cast fine in my book.  (Doug Easton)

There's that term again!  Would you mind defining what you mean by "compound taper", that's one I keep seeing but can't quite make up my mind what it means. I get progressive and parabolic, but compound seems to elude me. (John Channer)

ROFL! As Jerry pointed out, we don't all speak the same language. I know in my mind what I think a compound taper is, but I'll let Doug tell us all. I'm never sure that my explanation is correct, I once spent half a night arguing with some guy over what a hinge was.  (Larry Blan)

You guys must know the meaning of hinge in dictionary better than me. Hinge is the point where the bonnet of your  car is attached to the body. Sorry.

The hinge on a fly rod is a special term which  connote some specific action of a rod, or some special feeling of action of a casting.

My understanding came from this.  While I was flipping and flopping a rod with the line in about 30' or so, the rest of line are in my line hand.  I was walking up through a small stream watching the next casting point. There were many 1 feet size stones paved over the river so very slippery. Sometimes I lost the consciousness that I was moving the rod by looking for the next to step on.  But I kept moving the rod back and forth.

Then I felt something!!!

By moving the wrist just a little bit, say half an feet or so, the rod bent and pulled the entire line in the air and it continues backward too. The bend is around the point where the second peak of stress curve is drawn, it's hinge.  At the point, the rod bows back and forth.

Considering this situation, I understood that the rod was in the first resonance  vibration situation, that is, the vibration of the rod just matched to the nature of the rod in translated rod motion.

So I understood that the hinge is the point on a fly rod where the rod would bow back and forth, like the hinge of the bonnet, when the rod is in translated rod motion, further to say when the rod is in the first resonance vibration.

Additive:

You know what is the second resonance vibration of a rod? When you wiggle a rod right and left quickly, the rod will shape like two parenthesis overlapped.  That  is in the second resonance vibration. The things have their own vibration nature.  When it is moved slower, it would match to the first resonance vibration.  When it is moved twice faster, it would match to the second resonance vibration, it depends on the speed of motion, that is vibration.

A fly rod may only can match up to the second one maybe.  (Max Satoh)

Let me try this:

"drop a fly on the water without a ripple"

As this is the technique of a caster, I would neglect. But the rod should have enough power to do this for 40'. To land the fly silently, the loop which a rod would make should rather be a little wider than narrow? ... uuum, it still ability of a caster.

"3 wt rod "

Okay

"punch 40' of line "

I have an measure of "feeling of a cast" which is done by the figures of percentage of moment.  Like this.

At the hand grasp, we feel an aggregate force of "moment".  The force includes the sum of moment caused from each component of the rod.

Then, total moment is proportioned to two major components.

I will see the percentage of moment caused by the "rod", which includes bamboo and all the parts, and  by the "line weight to fish".

If the percentage of rod is greater, it says that "the feeling of a cast" is rod weight oriented.

If the percentage of line is greater, "the feeling of a cast" is line weight oriented.

Then,  does "punch" mean that with less feeling of fly line,  the rod should forward the line?  Or does it means that the caster feels enough of fly line weight at handgrasp?

Then I ask the client, which would you like better between faster rod or slower rod? Probably, he would reply as "faster" rod.

Then, I will face to my simulator and adjust taper so that the moment proportion becomes "line weight oriented," place stress curve around or  a little below the flex line (to realize faster action),  to cope with 40' of fly line.

There might be some conflict between the element of "line wt oriented" and faster action.  In that case, hollow build may be an candidate.  The most stiff hollow build is quad with 4 strips?

I hope the resulted rod is lighter in weight, faster action, sharp feeling of a cast.  (Max Satoh)

I still consider myself a novice at rod making and have a lot to learn about tapers, but I feel the start is to get a rod in the customer's hand and ask to check his casting style (Ability). A great caster can do this with just about any taper but what can your customer accomplish? If the customer can't get the rod to do what he wants then it will be a bad taper to him.   (Gary Jones)

I'm wondering if Jerry's original question was intended to be hypothetical in nature (made up customer, rod needs, etc.) to stimulate taper design discussion.

Jerry, could you better articulate what  you were intending by your initial question?   (Scott Turner)

Here is my sort of from scratch approach to the challenge. This is why it is sort of from scratch. I only know what I like and what other people seem to like. I will call that a rod style. To punch a line out hard with a tight loop, I like Gene Edwards style rods. I have a 7’6” 3 piece 5/6 wt Edwards Favorite that is very powerful and seems to charm most people who cast it. However it is a bit too powerful for the customer from hell. It is also very fast; which impair delicacy by promoting too much line speed. Using John Bokstrom's "Rod Design by Controlled Modification" as implemented in Larry Tusoni’s RodDNA program to analyze the taper, the “Rod Action Value” is 0.344. This represents an average straight line taper of  better than .003”/inch of rise. I decided to reduce the average slope to about .0026”/inch of rise (still pretty fast) with a tip size of 0.065. I used Frank’s Hexrod to make a straight line taper of that slope. I worked from there to modify the straight taper.  I did 4  things around  that taper:  1. I made  the tip section from stations 0-20 a bit concave (lighter) to gain some delicacy (particularly at short range). 2. I note from several rods  that have smooth actions and have good reserve power (Edwards, Granger, and the Sir D series have strong middles) so I made the rod somewhat convex in the middle, such that it uses a 12/64 ferrule. 3. I added a small hollow near the butt for better roll casting and (I think) better feel. 4. I put the modified taper through Rod DNA and checked the RAV and LWV. The RAV was nearly .315 (too steep) and when I looked at the maximum stress in the tip section it was > 250,000 PSI, so I generated a new rod model with a RAV of .275 and adjusted the Line Weight Value down from 0.058 to  0.054. This yields a rod with n average slope of 0.0026 in /inch rise and a maximum stress of about 225,000 PSI.

So how does this rod compare to others of the same length and approximate line wt.?  Well, without trying to do so, I ended up nearly duplicating a 7’6” Winston  which is in the rod DNA database.  Maybe John Gierach is right about one thing. “ All the good tapers have already been made.”   (Doug Easton)

This is about the clearest illustration of the relationship between small, subtle changes in the taper and the resulting changes in the stresses.

Combined with Doug’s explanation of how he arrived at the resultant rod.

This can be a baseline to discuss the stress curve. (Jerry Foster)

I'd be tempted to add some at the 5" station, bump the ferrule stations a bit, and level out the butt just before the grip. Then, I'd see how far from looking like a Para it really is. (Larry Blan)

I wonder if your request for the Design on the rod taper you described, I think it was a 2 piece 3 wt, is over, and if so how many replies did you get. Did any of  them meet your requirements, and if so, how did you determine that they were correct or incorrect. 

I think designing a rod using only a description would be very exciting thing, I don't know of anyone who has done that. If you could summarize the results of the tapers that you got I'm sure everyone would be very interested, I know I would. (Bob Norwood)

The question was more rhetorical than real, I have no customers, I was trying to stimulate those who have  a process to explain it. Not a making process, a design process. You witnessed most of the dialog, and I have now doubt that any of the processes discussed will work.  (Jerry Foster)

Since you asked the question. I, and I think many others thought you would tell us if the tapers were indeed 2 piece 3 weight rods that would throw a 40 foot line into the wind? This would be quite a feat to design a rod from a description. I don't know of many Makers who could do this, so my question is still, did the two designs really meet your requirements? I know that these makers put a lot of time and thought in to their tapers and to say that your question was simply rhetorical leaves me knowing no more now than I did before. The Question seemed real enough to me and I would think the answer should be also. Why ask if you can't answer?  (Bob Norwood)

My original intent was to stimulate a discussion about how to evaluate stress curves for the purpose of rod design and evaluation.

A few offered their view on  how they use stress curves. Chris O. asked me for my opinion, and I believe I posted that.

It overall ended up showing the diversity of opinion and process that I  expected.

I did not mean to mislead anyone into thinking that they had to define a taper, i was more interested in how they used their process to reach their conclusions. This was more of a follow-up to Wayne's question than anything else.

I think we got to the heart of rodmaking however, several of you discussed their modification or initialization process, and that was great. At a certain point I think we reached the place where the process was considered personal and proprietary, or too esoteric for anyone else to comprehend.  (Jerry Foster)

Your intents made a great success in drawing our, especially my, interests in viewing and posting what we have been doing. I guess it is more than tough work with stresses to receive various kind of punches.  I thank you for Jerry to have done it.

Don't you guys think so?  (Max Satoh)

Good stuff.

Now for fast. Is the height of the tip stress, the length of the descending curve, or the stress in the butt the deciding factor?

How about loop control. I think we know that the power factor is the wrist, wouldn't a high curve dictate a flexible tip which should translate to lots of tip movement..ergo..open loops? (Jerry Foster)

Empirically, my opinion is that a more uniform stress curve, without the "tip action" peak, should result in a more open loop (though a good caster can control loop size with any action rod).

For example; parabolics tend to have relatively low stresses in the tip half of the rod, and seem to throw a more open loop in the hands of an average caster.  The more "tip action", IE. "faster" rod, seems to throw a tighter loop (in the hands of an average caster).

Anyone agree?

On the other hand, "tip bounce," which I think you see more often with "soft tip" rods, can interfere with loop control.  A soft tip is more likely to collapse during a powerful cast, limiting distance severely.

I would suggest that it is the slope of descent from tip to butt that is the indicator of power (a more gradual descent means more power coming more uniformly from the length of the rod, rather than the rod having a "hinge").  (Chris Obuchowski)

I agree with you IF you look at the casting stroke as a strobe action.  But the casting stroke is a constantly changing form, and what happens before and after any given point in the casting stroke will influence the whole.  I have seen different casters with the same rod ( a parabolic of my design) make drastically different loops.  One Threw a loop so wide open that he only cast about 25-30 feet.  And he  is a certified FFF Casting instructor). Another cast the whole length of the line with a wee little bitty loop.  He was not an FFF casting instructor.  Any analysis of these two guys.  I am still convinced that the big dingus hanging on the end of the cork handle is the most vital controlling force in casting a fly line.  I even have a very good friend who can cast the entire length of a fly line with no rod at all.

Empirically, I'd opine that a more uniform stress curve, without the "tip action" peak, should result in a more open loop (though a good caster can control loop size with any action rod).

For example; parabolics tend to have relatively low stresses in the tip half of the rod, and seem to throw a more open loop in the hands of an average caster.   The more "tip action", ie. "faster" rod,  seems to throw a tighter loop (in the hands of an average caster).

Anyone agree?  (Ralph Moon)

I think another way to put it would be that rods whose effective length (length under load) is longer throw tighter loops than one's whose effective length is shorter.

Fast, tip action rods have a longer effective length while casting and thusly can more easily throw tight loops.  Parabolics, having a much shorter effective length due to significantly more flex in the rod, don't do tight loops as easily.

The Dingus definitely has the final word though.  (Chris Carlin)

I think another way to put it would be that rods whose effective length (length under load) is longer throw tighter loops than one's  whose effective length is shorter. 

Chris, I agree with all my heart, You have it right, BUT

Fast, tip action rods have a longer effective length while casting and thusly can more easily throw tight loops.  Parabolics, having a much shorter effective length due to significantly more flex in the rod, don't do tight loops as easily.

I must disagree most vehemently with the next paragraph, but then I don't know what you mean by effective length.

The Dingus definitely has the final word though. :D

I don't know the dingus, but if by that you mean the caster, I am with you.  (Ralph Moon)

My definition of effective length is the length of the rod from the hand (or perhaps even better from the elbow) to the tip of the rod as it is in a casting motion under a load.  A slower action rod bends more under the same casting circumstances and thusly has a shorter effective length than the same size rod in a faster action.

Of course the effective length is going to vary depending on where in the casting stroke the measurements are taken, but the easiest generalizations are made for a rod under maximum load, at or not long after the beginning of the fore stroke.

It seems to me that the more change in the vertical distance that the rod tip has to travel from the point of maximum stress (beginning of the fore cast) to the point of minimum stress (middle of the cast), the more open the loop wants to be.

The assumption is also that I'm talking about rods of the same 'real'  or static length when doing an action comparison.  I'm certainly not saying that a longer rod will necessarily cast a tighter loop than a shorter rod, and I wholeheartedly agree with both you and Ray that the caster is the final word,.  As such, I think that we're actually saying nearly the same thing:

"For example; parabolics tend to have relatively low stresses in the tip half of the rod, and seem to throw a more open loop in the hands of an average caster.  the more "tip action", IE: "faster" rod, seems to throw a tighter loop (in the hands of an average caster)."  (Chris Carlin)

I have frequently argued that the rod action and the line taper will demonstrate to the caster what is necessary to produce a successful cast.  If this requirement is compatible with the caster's ability and casting mechanics, the result is pleasing to the caster and the designs are considered good.  You could probably program a robot to wield the proverbial broomstick and produce great casts but with a motion that no person could or would want to duplicate.  (Jim Utzerath)

It seems to me that the tip of the rod  (maybe the top 10-15 inches) really works different from the rest of the rod, and the design principles are therefore going to be different.  Is this correct? I'd like to see a discussion of how to design a tip that will work with the rest of the rod.   I'm planing a tip tomorrow and its not too late to change the forms.  (Frank Stetzer, Hexrod, Taper Archive, Rodmakers Archive)

You've raised another very interesting issue re the first 10 or 15" of the tip section and how to design it. Let me refer you to page 272 of Garrison's book where he advocates making the first 5" a bit stronger than design because of the high stress in that area and proposes to draw a mostly horizontal line from 5" station to the "0" station. I have done that on most all of the rods I've made and have had no failures in that area. I did have one rod where the tip section splintered about half way between the tip and the ferrule but that was because my black lab "Moon" (no offense Ralph) jumped into my boat and landed on the rod.  (Ray Gould)

This has really been an interesting discussion. I'd opine that I'm in agreement with Chris regarding the slope of the stress curve from tip to butt indicating power (energy being used). If one looks at the comparison of stress curves for a straight line stress compared to a parabolic or semi-parabolic stress curve you will see that the stresses are higher in the last 20" of the butt section for the parabolics. In casting I feel that because of this I have more of the rod working for me and it's easier to cast. Now loop control is another matter. At the Great Western Rod gathering at Dunsmuir we had a casting instructor demonstrate (with the same rod) how to control the loop size which makes me think it's more technique than design. (Ray Gould)

Chime in with your work/observations on slope of change in dimensions predicting rod "speed". I agree with what you've published, and have both of your books, and what's more it agrees with my observations from graphing and casting rods.

I also agree (I think you said it in one of your books) that you need to look at average slope over the "working length" of the rod, and discount any fudge or deviation at the tip and butt (usually the first and last 15" - 20").  (Chris Obuchowski)

If the line follows the tip, if we agree on that, then how does a tip with a high stress 220k, flexible, naturally throw a narrow loop?  (Jerry Foster)

I think that in the case of very fine tips, what happens is the the tip folds over and gets out of the way and the rod effectively shortens itself to where it is stiff enough to push the line. Garrison designed his tapers with 3 tip diameters and said he recommended either the medium or heavy tip, and I can't argue with him from my experience. BTW, thanks for starting this conversation, I'm sure I've learned more today than I have in a long time.  (John Channer)

This is the effective length that was mentioned earlier. The tip bends more, the "shorter" length of rod describes a shorter arc, therefore produces a tighter loop, all else being equal.

Some time back, Darryl Hayashida did some work on tips and came up with a set of dimensions that he felt threw a tight loop naturally.  I don't have the dimensions handy, maybe Darryl is reading.  (Larry Blan)

While I was sleeping,  discussions heated up to interesting level.

First of all, my understanding of narrow loop or wide loop of cast fly line is, how the caster moved the tip top.

It is free from whether a rod is stiff or soft. A stiff rod can easily make wide loop if you turn it from 0 degree to 180 degree. 

I am sure the stiffness of a rod surely has a tendency to make narrower loop if the caster follow the instruction of ordinal casting style.

I believe that the loop width is the function of tip top movement, speed of tip top (that is line speed), and a pair of heights,  from the height where the tip top is most accelerated, to the height where the tip top releases the line.

Sorry, moment matter again.

Moment is a force which try to turn a bar.  Moment is the force which works perpendicular direction toward a bar. So, translated rod action (Don Phillips word), would gather the most moment at the grip of a rod. If a rod is in rotated rod action, though tip top moves longer travel, but grip does not move so long.  It happens in the same time frame (time length).  In this case, tip part will receive relatively more acceleration, resulted moment and resulted higher stress, then it becomes tip action type rod for a moment. Butt side section would not bend so much, but tip front would bend much, even if it has parabolic taper.(problem of degrees)  If we can know how the tip top behaves, we can adjust the height of tip top at the line release in a casting motion.  It will make a narrow loop or wide loop.

Of-course a rod has tendency.

A food for thought.  (Max Satoh)

We all really appreciate your information and knowledge.  I hope you have devised a better rod design program.  Outside of that, I was trying to focus on the last of your statements:  "Of-course a rod has tendency."

Assume same caster, same stroke, different taper, how do we predict what the rod does.  (Jerry Foster)

What I meant was, though the loop matter is so and so. Rod has tendency which  make a loop narrower or wider.

Soft rod (slower rod), will bend more during the cast.  It will delay the tip top movement than the faster rod.  It also mean that the line speed is not accelerated enough while the rod is under bending motion, right?   When the fly line is getting more acceleration? I guess it is when the rod starts unbending, probably when the wound up moment is released and when the rod return to almost straight position. Slower rod has longer time from full bend situation to straightened. This delay may cause some feeling to a caster. Further, since slower rod bend much, so called effective length of the rod is shortened much. When the caster stop the rod motion, the slower rod start unbending and turning around the grip with larger arc.  In larger arc, the tip top will follow the arc line. Thus tip top will have a pair of heights, highest and lowest, wider loop will be resulted.

Faster rod has less up down of tip top movement. On faster rod, the fly line start accelerated earlier than slower rod. While the faster rod is not fully bend, fly line start going forward. Since the tip top of the faster rod does not go up and down much, fly line has tendency to make narrower loop. And maybe, the caster might feel that it is rather easy to control the line.

An experienced old caster like me, like slower rod and enjoy how the line is speed up by the unbending force of the rod.  I like wider loop since it is safer from making line trouble.  (Max Satoh)

Thank You to all involved in this discussion. The responses have all been insightful and educational. We are all indebted.

Scott:

I hope it was hypothetical, and no I'm not on drugs this morning, yet.

If you know me you know I only build 5 wt's. If I tried to build a 3 wt. it would end up as a 5 wt.

Seriously, I believe we have surfaced at least 3 very good processes on the development of tapers.

These makers have an extraordinary  amount of talent and insight. The rest of you who are simply watching but interested should not pass up the opportunity to ask questions.

My overall intent was to try to raise awareness of some of design tools available. I am convinced that the best tool is a working mind. I am still trying to stress the value of stress curves, but some of the directions taken are much more tangible.

Now if I may;

It is very obvious that we do not have a common terminology to speak of tapers, so everyone is left to their own understanding and sense of feel as to what some of this means. (thank you Larry)

It appears that no one uses stress curves as a basic  design tool.  (I know some of you do).

Now, suppose we get this guy (the 3 wt one) in front of us before we make the rod.  And upon evaluation of his casting style, discern that he has a wimpy wrist. Or any of them casting maladies that effect we normal folk. Is there any adjustment that you would make to the rod to compensate? Aside from a casting class.  (Jerry Foster)

It appears that no one uses stress curves as a basic design tool. (I know some of you do).

Oh no, without stress curve, we cannot understand the entire balance of stress nor identify the line weight. I always verify my rod by looking at stress curve.

Now, suppose we get this guy (the 3wt one) in front of us before we make the rod. And upon evaluation of his casting style, discern that he has a wimpy wrist. Or any of them casting maladies that effect we normal folk. Is there any adjustment that you would make to the rod to compensate? Aside from a casting class.

Ahhha, this guy looks like me... I do not have strong wrist.

So the condition is quite different from the last case.  For weak wrist power, I usually select such a rod that a caster can throw the line only by wrist.  By just moving the rod a little forward, or by snapping the rod just a little, the rod would deflect. There also need some considerations about this rod, it should have soft tip to be balanced with the flexible butt.   The butt must endure  when he hooks a big fish, then I would implement a little swell just in front of the grip.

I would assume the rod is 7'6" for this guy.  This time, I assumed that this caster would require some additional power which is helped by the weight of the rod itself since he has wimpy wrist.  So, what I call "the feel of a casting" is rod weight oriented.

As most of you already knew, I will draw a stress curve (assume Garrison's stress curve).   I put a red line around 8,750 PSI (pound/sq. in. almost 140,000 oz/sq in.),  this is the possible flex line.  If the stress is around here,  the rod  normally flexes at the point, this is the rule of thumb.

I would draw such stress curve:

* draw a straight horizontal line just above the flex line around 9,000 PSI.  This means entire rod would evenly bend.

* implement a peak of stress curve at 20 inch point,  about 13,500 PSI.  This means tip will flex enough.

* implement a swelled butt from at pt 73" (17" from butt end) 8,000 PSI to pt 80" with 6,000 PSI.  This makes it easier to control entire rod and endure with strong power of a big fish.

* implement so called a hinge(second peak of stress mountain) for wrist casting at 60" pt with 11,000 PSI.  This will help a wimpy wrist can cast this rod very easily.

* moderate the stress curve in between the points above.  Smoother curve would result in smoother feel.

Frank Stetzer's stress curve drawing chart can moderate this automatically.

Then I make it to dimension.  Then I make the stress curve from the dimension again for verification. This is to my case only.  I will draw a deflection curve and simulate with various situations, quick cast, slow cast, pick up, hook the fish, etc..

Then this is done by every body, take the moment values of each rod component at 80" point which is in front of grip and take the  percentage of 1, line to fish, 2, bamboo (and other parts).  Try to compare to each other, which weight are larger?

This rod may become nearly equal to Payne L200 8' feeling.  (Max Satoh)

I do indeed use stress curves as  my basic design tool. I use the Garrison stress curve for most pentas and Zimny's stress curve for quads. Garrison's stress curve works also well for my trirods.   (Bill Fink)

As the relatively abrupt stop to set up the loop is intrinsic with casting, there is likely no cure but casting instruction.

Note: I said relatively abrupt stop. I find a good solid stop hard to do when "just fishing" and tend not to keep the loops as tight as possible so I guess it is off to casting school for me.  (Don Anderson)

There is no doubt that there are different casting styles and that different rods suit different casting styles. The expert casters are experts, however, because they can adjust their styles. They can adjust loop size primarily by adjusting the path that their hands follow and the acceleration of the casting cycle to compensate for the rods characteristics. This is why some casters can cast tight loops with parabolics whilst other struggle.

In order to really design a rod for a caster with a fixed style it would be critical to plot the path of his/her hand and the acceleration of their casting cycle. The distance the person casts would also have to be predetermined as the acceleration and acceleration period is different for different distances. The rod could then be suited to the person AS LONG AS THEY MAINTAIN THAT STYLE and cast mainly to that distance.

Surely a better process, all else being equal, would be to design a rod that assumes that the hand will follow a straight line (as advocated by many respected casters) and that the caster will learn to do so. This would then leave the choice simply as to what kind of loops the caster wants the rod to naturally throw and, to an extent, what the feel will be as a result of this choice.

Personally I find it easy to throw open loops, when this is required, with a rod that 'naturally' throws tighter loops (Chris Carlin's 'longer' rod). I can do so simply by slowing down the stroke (at least it feels like that although what is probably happening is that my hand path is dipping). On the other hand I find it more difficult to throw tight loops with a rod that naturally throws open loops (Chris's 'shorter' rod). This is because the hand path has to assume the correct curve with the correct timing (which is also faster) to keep the tip moving in a straight line. I think many people have similar experiences in this regard.  For this reason I prefer fishing with faster rods - they give me more options. How fast the rod is depends on the fishing conditions. There is nothing to beat a really fast rod when punching big flies into the wind is required.

In considering a truly empirical basis for designing and comparing rods I can't see how this can be done without computer software. I imagine the following would be critical issues in any empirical approach:

1.. The Elastic Modulus of bamboo would have to be determined or (unfortunately due to lack of research and variation from culm to culm), guesstimated.

2.. The same heat treating and rod finishing regime would have to be used

3.. The weight and placing of rod components determined

4.. As Max Satoh explains the rod would have to be considered dynamically, or at the very least assessed at fixed points in a casting cycle rather than at one point only.

5.. The casting 'style' would have to be fixed. e.g.. assuming a fixed rotation point, a fixed amount of hand movement in a fixed direction and a prescribed arc through which the rod moves in a prescribed time. (These could be varied for different assessments but would have to be fixed each time for  'apples with apples' comparisons)

6.. The force of the line (mass x acceleration) would have to be determined for each point in each cycle.

7.. The criteria of assessment would have to be prescribed egg. width of loop, recovery time at end of sequence etc.

8.. The criteria of assessment would have to be prioritized in order to assist in selecting the best design for the purpose .

Failing the computer software approach to design, the next best would probably be an experienced caster/rodmaker (Harry's point) starting with a design and applying a process of trial and error to refine it. This approach was probably used by most of the classic master builders.  (Stephen Dugmore)

As smug as it makes us bamboo nuts feel to disrespect our graphite brethren, right now they are far ahead of us in analyzing and systematizing (sp?) your points 5-8.  (For some reason the number changed when I snipped the post).

Sage has recently introduced a casting analyzer which is likely coming soon to your local fly shop.  Basically it's a gyroscope attached to the butt of a Sage rod and wired into a handheld computer.  It analyzes the motion of the rod being cast and compares it to composite baseline cast based on a panel of 20 experts ranging from Bruce Richards to Jason Borger to whoever else.  It measures such things as rate of angle change, degree of smoothness in acceleration, and so on.  I tried the analyzer in October and found it quite interesting.  It isn't a perfect tool, but is a great learning aid.

One thing it does well is force you to keep things simple.  Exactly forty feet of line beyond the tiptop is strictly controlled.  Hauling, double or single, is not allowed.  Thus it  monitors the criteria you highlighted in capital letters.

Our own Frank Paul has done some fascinating work analyzing both rods and casters.  He gave us a small glimpse over the weekend, and I hope we'll be hearing more about it in days to come.  (Harry Boyd)

Let me throw a monkey wrench into your interesting discussion on rod taper design.  Lets suppose you have designed a rod with a given taper and it has a fundamental modal (the static shape of the rod with a small tip load) frequency of lets say 2.5 Hertz (that is 2.5 cycles per second or 150 cycles per minute) - a medium speed rod. This fundamental frequency mode is the bending mode that you see when casting a fly rod.  Now this frequency is determined by rod design taper and EI stiffness modulus distribution along the rod. Remember the rod is a tapered beam and behaves not as a linear cantilever beam but as a nonlinear cantilever beam - this means - given a static load of 5 oz the tip deflection might be  'x', while if I double the load to 10 oz the tip deflection is not '2x' but something else.

So now I put a line on the this tapered rod design and put it in a fly casters hand who can hold the rod with out any elastic behavior between a hand and the rod grip.  I now look at the fundamental frequency mode of this flyrod,  line,  and caster -  A FLY CASTING SYSTEM - and the this mode drops by about 40 percent - that is it is 1.5 Hertz.  Quite a change that you may not think exists - but it does in reality. Now lets decide that the fly caster can not hold the rod so tight that there is elastic behavior between the rod grip and hand. Now looking at the fundamental frequency mode of the 'fly casting system' it drops by about 50 percent - that is it is about 1.25 Hertz. 

Now given that the rod taper design and line have not changed, what causes this difference? It is obviously the caster - and since each one has different arm  and body strengths and developments, the behavior of the flyrod casting SYSTEM changes. Now how do I know that. Well, recent completed research (my efforts at Clemson with a graduate student) that models a fly casting system demonstrates this phenomena which most 'old fart casters and rodmakers' have known for a long time. 

So what does this mean for fly rod taper designers? You better factor in the unknown casters physical capability in designing a rod taper to fit the caster and selected line - if that is your goal. This is obviously the reason when we have a Payne or Young or Dickerson or whomever, that one caster likes one rod better than another. Remember that when we are younger we like faster rods and as we age we usually like slower rods - physical abilities change and influence what we like in a rod design.   What have I learned - I think engineering analysis methods such as Garrison used guide us in taper design, but there is no way that we will ever create the ultimate flyrod design computer program to custom design a flyrod for "Old Joe".

Hope this adds to the discussion and stimulates some new thinking. My student and I have submitted two papers to an International Journal of Sports Engineering. Hopefully they will find the results of this work useful enough to publish after appropriate review.   (Frank Paul)

OK, I suppose I can agree with everything anyone has said, except the need to invalidate some engineering principals in rod design.

Here is a premise I guess I didn't throw out but I thought was understood.

To use any system (other than touchy feely) one must have some constants.

So the assumption was (is) that the rodmaker, glue, varnish, are all constants. I know these are all variables but for the sake of design there must be a standard for each maker.

The Bamboo taper itself was to be the only variable.

yes, we all know that bamboo is a wonder of nature and not a constant, but I dare you to put that in the equation and ever finish a rod