Rod basics
Rules (kinda)
taper Graphs
taper Slope
Stress curves

Notes on Tapers

Early in my re-building experience it became clear that I'd have to learn a little about tapers.  I couldn't just glue ferrules on pieces of bamboo and expect them to be anything I'd want to cast.   I soon discovered that bamboo rod tapers get passed around and everyone knows a good one, but few know why it's good.  Of course people who are good at it can take one look at a chart, or graph, or some other table and tell exactly what a rod will do.   I can sorta tell, but I'm often still not sure exactly what I'm looking at. 

There are a lot of ways of judging a rod's character from it's taper.  Some people chart the taper on graph paper.   Others  use formula.  Still others computer models, such as Hexrod.   Some use "deflection."  Orvis started doing this with their "flex index" but the idea isn't really new. 

To use any of these method you have to have some idea about what a fly rod's doing and how well it's doing it.   Reading this page won't make you an expert but it will give you a starting place.  You have to go out and cast rods, then compare the tapers. 

But there are some general rules.

The Tool
To start to understand tapers you have to understand the tool we call a fly rod and how it works.   A rod has two basic functions -- to cast a fly line and fight a fish.  Sometimes these functions come into conflict, so most rods are a compromise. 
The cast
A good cast is like the green line on the chart,  power is added at a steady rate all the way through the cast until the very end, where it drops off sharply.  The red line represents what would be a terrible cast.   The rod is jerked into motion (extreme stress applied at point A) but very little additional power is added.   The cast dies an evil death at point B.  Most casters apply power somewhere between these two extremes. 

No matter what casting skill the fisher has, the rod has to be able to stand up to the forces placed on it.

A rod is both a lever and a spring.  The rod acts as a spring when we start and end the cast. As a  spring it both stores energy and smoothes out the cast.  At the end of the cast it can return the stored energy at the right --or wrong -- time.  In fighting fish it keeps delicate tippets from being over stressed and fish from breaking off. 

As a lever the rod works just the opposite of most levers.  Most levers are used to multiply force from the end of the lever to the fulcrum.  In a fly rod power is delivered through the lever's fulcrum, somewhere under the casting hand of  the fisher.   From there power is passed outward to the tip.   There is a formula that is used to figure the center of gravity for aircraft.  The force it measures is called moment.  What it says is for every foot a pound is moved away from the Center of gravity, it's effect increases in foot/pounds (ft/lb).   Something that weighs a pound that's 2 ft from the C.G. (center of gravity) is said to be  2 ft/lb. while a pound of something  that's  three feet away is said to be 3ft/lb  The difference is 1ft/lb.  With a fly rod we can also measure  in/oz.

How does this apply to a fly rod? 

Here's a very simple test that you can try.  Hook a pound of lead sinkers on your rod at the stripper guide.  while you're standing up, point the rod straight out from your shoulder.  Now, move the sinkers out to the half way point and pick the rod up again.   Try it a third time, only move the sinkers out to the tip of your rod.  You'll be amazed at the difference in weight you feel, even though the sinkers total only one pound.

Think of the old bamboo fly rods that were six, seven and even eight ounces.  Today's rods are all around 2 to 5 ounces.  Most of us wouldn't think much of a difference of 4 or 5 oz.  That's not even half a pound.   But when you start waving it around in a 9 ft rod, you'll soon feel how the weight is multiplied.  And you've got the line on the end of that rod.  That's more weight.   Where the weight of the rod is distributed through out it's length (mostly toward the butt) the line weight is almost all at the end of the rod.   No wonder fly fishing can be such good exercise!

A rod is tapered because of the counter  forces on the rod. When you're fighting a fish, the force is the same all along the rod ( unless you put more force on the tip or the butt).  But when you're casting the force comes from your hand and goes through the rod.  It has to move all the rod and because you cast in an arc, the tip travels further than any other part of the rod. (Back to my airplane analogy again.  This could be thought of as something a bit  like "G" force, though it's different)   You'd have to give a lot of pressure on a rod that wasn't tapered, to get the mass at the tip moving.  And once the tip got started, it wouldn't want to stop.  Or you would be casting something built like a broomstick.  So the rod is tapered to balance the longer arc the tip travels with lighter weight. 

Why not make a rod thin all the way down to the butt?  Because the force applied at your hand is a lot higher than the force applied further out the rod.  The force at the butt has to move everything out to the tip in an ever larger arc.  The middle of the rod moves further than the section above your hand but does less work to move itself and the rest of the rod outward to the tip.  The tip only has to move itself and the line.

Any point on a rod has to be able to withstand the counter forces of (1) the power applied by the caster and (2) the total inertia of the mass of the rod and line from that point to the tip.   If it can't it will break.
So the taper is always larger at the butt and progressively smaller as you move to the tip. This is often referred to as the "slope." The steeper the slope, the faster the rod. 
In general a slope of .034 to .038 inches in a foot is a fast action: .028" to .033" is a medium action; .023 to .028 is a slow action rod.
Of course rods are thicker as line weight goes up.   If the tiptop for a 4 wt is .065" then you can expect similar taper for a 5 wt to go around .070" to .072". 
A rods general taper will increase by about  .006" (Plus/minus) for each increase in line wt.
Two piece rods have more "flex" then three or four piece rods.  The ferrules are considerably stiffer then the surrounding bamboo.  That area of flexibility has been removed from the taper.  While a 2 piece rod loses about 2 to 2 inches under the ferrule, a 3 piece rod loses at least twice that.
Generally, the more sections a rod has the faster is will cast.
Now that's some VERY general rules of thumb and not all tapers abide by them.  But it is a place to start

How to measure a rod
In the old days rods were measured from the butt to the tip.  In the seventies, Garrison and Carmichael wrote the book A Masters Guide to Building a Bamboo Flyrod.  In that book Garrison used a mathematical model that required starting at the tip.  Over the next twenty five years almost all rods came to be measured from the tip.  Although one, three, and six inch increments are used,  the interval most used is five inches because it's easy 
to use in calculations. 

Although some rods were built to 64ths of an inch, today's rod cross sections are measured in  thousandths (.001) of an inch.   To do this some kind of special measurement tool is needed.  The two basic tools used for measuring rods are a micrometer or calipers.  While venire calipers can be used (and can be accurate to .0001 in) most rods are measured with a dial caliper.  It's the quickest way and accuracy usually suffers less then .001. 

One other thing to take into consideration is that you're not actually measuring the bamboo,  You're measuring the bamboo and any finish on the outside of the bamboo. Usually, you'll want to subtract .002 to .004 inches from your reading for varnish. 

I find that my old friend, masking tape, comes in handy when measuring a bamboo rod section.  I can put a small strip of tape at each station (say every five inches from the tip.) and butt the side of my calipers against this tape.   I know that I'll get the same readings each time.  And it's a lot quicker then first finding then measuring each station, one at a time.

Make a chart.  It should look something the one at the right.  It contains space for all the basic data you'll need to record about your rod.  The Title and date are very important.  I've got tables of numbers that  have no associated rod information with them.  It's very easy to create the information in the table, then forget what it refers to.  Include as much information as you can.  For example:  "Second Tip section for 8 ft. 3p 5wt. Wright and McGill field and stream. To create duplicate tip section for Jimmy.   Done July 15, 2001Always put down more information then you need because you'll always need it somewhere down the road.. 

The fields in the chart are as follows, Station is the position along the length of the section in inches.  A, B and C are the flat to flat measurements of each of the three sides.   Avg. is the average of the three sides. (you'll find that almost every rod you measure will be off from .001 to as much as .015 between different sides.)  Slope is the difference between the current and preceding station.  An example: Station 5 slope = the number in the station 5 average box minus the number in the Tip Average box.

Station  A B C Avg. Slope
tip       a.  
5       b.  c.

A typical layout for storing data about one rod section
a. Average tip size
b. Average station 5 size
c. Slope for station 5
Work with a good light. It makes the measuring device easy to read.   Keep clear of everything else.  It's easy to turn around, looking for something and break a rod section on a desk or a table leg.  Record each reading as you make it. (I usually take all three readings at once and then write them down. i.e. .071,.074, .078) 
If you create the data table using a computer spreadsheet it's easy to calculate the information.  In fact you don't even have to put in the decimal point.  (a + b + c)/3000 will convert 71 + 74 + 78 into .074333 or .074. 

If you find a  station that is under a guide wrap, or in the middle of a ferrule, you have two choices.   You can interpolate, taking the size above and below and create an increment of  the slope, add it to the smaller number.  Or you can measure both sides add them together, and average them . Either one should get you within tolerance.  Surprisingly it's usually the slope that's more important then the actual dimensions. 

Once you've got all the numbers you'll be able to see a few things right away.   You'll notice the slope can go from .006 to .022 over two five inch stations.  You'll also notice that several stations have the same slope or a slope very much alike (.002+/- difference).  They could be considered straight. 

A sudden change of .005 to .015 in a slope signifies a 'hinge'  They seem like they're actually increasing stress, but in some ways, they relive stress around critical points.  Hinges give a rod it's personality. 

In looking for the slope of a rod, don't consider the full length of the action ("tip to grip") because tips and the area just in front of the cork grip are often special cases.  Let's take a 7 ft rod as an example.  the rod is 90 inches long, but the bottom 11 inches are taken up by the reel seat and grip.  The action is 79 inches long. (most rod actions don't extend under the grip.  A few do.)  To find the slope of this rod, divide the action length by two and round to the nearest 5 inches.  79 / 2 = 39.5 rounded to 40".  Next, using 5" increments, add and subtract an equal number of inches from that station.  Using  20" we get  40 - 20 = 20 and 40 + 20 = 60.  The slope between station 20 and 60 give us the slope in 40".   We want to figure the slope in feet, so slope / 40 gives us the slope per inch. Multiply that slope by 12 for feet. 

Notice we don't have to use 20 inches as our base line.   We could use 25" which would give us a slope from station 15 to station 65.   Thirty inches would give us a slope from station 10 to station 70.  However, the first and last 10 inches of an action are usually designed differently then the rest of the rod and if we include them in our calculations they can throw us off. 

The slope is only part of the information we use to evaluate a rod.   Remember a rod doesn't have to have a consistent slope.   Some of the best rods have slopes that change from the tip to the butt.  For example some rods  have a hinge close to the butt.  This gives them a "kick"   Others have stiff butts and tips but a more "modest" mid section.  ( Often called Parabolic or Simi-parabloic,  they require a modified casting stroke to get the most out of them, but people who like them won't trade them for anything.)  It might not be a bad idea to check the slope for the first, second and third 1/3 of the action length. 

Of course one easy way to compare tapers is to graph them on graphing paper.  Things like hinges are easy to see when you compare two rods or compare a rod to it's slope. ( Yes you can chart the slope of a rod to see where it might be above or below the slope.)   Once again, the tip and butt sections of a rod taper may be special considerations and may not give an exact indication of what they rod will actually cast like, but they are apparent if you're graphing the taper.
The illustration above is a graph of three very similar rods.  The rod marked series 4 is the fastest of the three rods, while Series 3 is the slowest.  Beyond this we see several places where the graph seems to flatten out.  Those are the hinges for these rods.  Without casting rods with similar hinges, it would be hard to tell if we really wanted a rod with these characteristics.

In the example, measuring from  station 15 to station 65,  the rod has a constant slope of about .014 per 5 inches. 
If we were to look only at the actual slopes between each point, it wouldn't tell us much.  For example, what does the slight drop around station 75 mean?  That's where the average slope number comes in.   Remember we're only using the main part of the taper for our average.  Using the tip and butt can lead to entirely different (and some would say erroneous) information.
It looks like we'll have a slightly fast tip, with a hinge starting somewhere between stations, 20 and 25.  that hinge will continue until we get close to station 35.  Another hinge is between stations 45 and 65. 
There will be a slight hinge close to station 75 but it won't be as significant as the other two. 

There are many ways to measure slope.  It can be the difference between each station or the percent change per station.  I once plotted slope using 4 methods and found that the plots all fell almost exactly in line with each other,   So use what the method you like best.    I chart slopes using the "between station" numbers. 

Changing tapers using slope 
You can change a taper using slope by doing all the work in percents.  This allows you the ability to change the length or line weight and still have a starting point. DON'T expect to use on this technique alone to come up with a good taper.  To change a rod's length, you'd have to change the slant of the avg. taper line from horizontal, either up or down.   In other words, everything else being equal, a rod that's 8 ft long will have a larger butt then a like taper on a 6 ft. rod. They may cast much the same (the hinges will be at about the same relative location and the action will feel about the same)  but they'll be have different measurements.  The use of slopes can be a starting point, but proceed with care. 

For more information on understanding how changes in slope change a fly rods action check out the articles "A discussion of rod Tapers," by Don Anderson; "Rod Design by Controlled Modification," by John Bokstrom and "Taper Design, by Frank Neunemann,  all in The Best of the Planing Form

Stress Curves
Stress curves were popularized in rod building by Garrison and Carmichael in their book A Master's Guide to Building a Bamboo Fly Rid .   Stress curves are used to show the amount of stress any given point on a rod can handle. The idea is this will show how the rod will react when loaded.  Very simply, where it will bend the most and at what point it will break. 

The stress at each point has to be calculated before the stress at the next point can be attained.  Because the work is usually done in inches, and the calculation is very complex,  very few people used them until the advent of the P.C.  The Personal computer allowed the calculations be performed quickly and accurately.  The only thing that was lacking was someone to write the program.   That person was Wayne Cattanach, who included a floppy disk the first edition of his Handcrafting Bamboo Fly Rods.   While the original program was primitive by today's standards, it revolutionized rod building.  In the 2nd edition of Handcrafting... Wayne explains, in detail, the math behind the program. 

Cattanach 7'6" (1) DT#5 2 pc.

Example of a Stress Curve for a 7 ft. rod.
The best short explanation for stress curves and graphs was done by Darryl Hayashida.  He's allowed me to reprint it here in it's entirety.  (I've tried to adapt his ASCII art to graphics.  I hope he'll accept my humble attempts.) 

   "In it's most basic use a stress curve shows you how close split cane rod is to breaking with the weight and length of line you specified. Garrison believed 200,000 ounces per square inch was a good, safe upper level. In reality you can go up to 220,000 or 230,000 without any problems.  Garrison himself went up to 220,000 on his lighter rods.  Garrison believed that below the 140,000 point the bamboo stopped flexing. 

   "As you get deeper into stress curves you can begin to pick out certain characteristics that tell you what kind of action the rod has, or will have if it hasn't been made yet. A Garrison rod, which I consider to be slow, has a well rounded "hump" near the tip and a fairly slow drop off as it goes towards the handle. 
   "The rod that I'm always raving about, the Cattanach 7' 0"4 wt, I consider to be fairly fast. It has a stress curve like this: 
   "The blip near the handle is the Cattanach hinge, and it greatly enhances roll casting. Don't forget to  put it in. I did and the rod I made was a terrible roll caster. It isn't as necessary on longer rods, but on shorter rods it's definitely needed.
   "A Paul Young Para 15, what is described as a parabolic action looks like this: 
   "Looking at this rod, and never having cast one, I would guess that it would feel fairly slow, due to the enhanced bending near the handle, but able to throw a lot of line, due to the stiff mid section. I would also guess that it could roll cast really well.
   "There are as many variations of stress curves as there are rodmakers.  This covers the slow, fast and parabolic actions." 
-Darryl Hayashida

Deflection Graphs
In his book The Technology of Fly Rods Don Phillips expounds on the old idea that you can tell a lot about how a fly rod will cast by placing weight at various places along the rod and measuring how far the rod bends.   Don's original article appeared in 1973 in Flyfisherman, but even then It wasn't really new.  Some rod companies would send out a large graph that could be placed on a wall and rigged to hold a rod by it's handle. A weight would be attached to the tiptop.  The rod cold then be compared to lines on the graph, to tell the prospective buyer what they were getting. 

Today a few companies such as Orvis give information on the action of fly rods by reporting were they "flex."  Don comes from an engineering background, so it's not surprising that  his explanation is much more detailed and designed along engineering lines. 

The idea is fairly simple.  If you immobilize a rod at some point, then place a known weight a known distance from the point the rod will bend -- in other words "flex."  How far it will flex is measured as deflection.  Most deflection measurements of the past were from the handle to the tip.  Don points out that there are limitations to this approach.  It will tell you how far a rod will flex, (and in Orivs' case, the point of greatest flex.) but it won't tell you much more.  Don overcame this limitation by testing about 5 inches of the rod at a time.  Do this to enough points you can come up with a deflection chart .  The appeal of this method is it's portability.   In theory, if two rods have the same deflection, then they should cast the same, no matter what they're made of.  Like so much else in the rod building business this isn't completely true.  The speed that a material will return from deflection and the material's weight are both variables that won't show up in a deflection curve. 

You'll need a jig to do the actual test.  Here's a suggestion for building one. 
A. Rod section being tested 
B. Test section clamp 
C. Index arm. 
D. Index plate 
E. Index Scale 
F. Index link 
G. Test Weight 
H. Index plate adjustment knob 
J. Index arm counter weight 
K. Jig back plate.
Critical points
 Length of test section (1) must be equal to distance between index arm axis (2) and index link axis (4).  Lines dropped from the index arm axis (3) and the index link axis (5) must be parallel.  The test weight must be attached (6) directly below the index link axis (5).

There are three related variables, the length of the rod section being tested (in, in, in, etc.), the weight placed on the tested section (usually oz.) and the distance the tested rod section deflects, or bends (in inches). 

For example, a tip tested at five inches will flex under very little weight  where a butt section tested at 9 inches will require much more weight to flex the same amount.  It's easy to see that a way to give some commonality to the three is needed.   Don came through for us again.  It's an engineering formula.  El = Pl3/3y
I built a deflection jig using stuff around the workroom.  One thing that I needed was a way to be very accurate with the actual measurement. I could adjust the distance between the the front of the vice and the weight attachment point by using an old piece of molding, cut to length, as a gauge.  I could use the same weights for each measurement.  But actually measuring the distance the rod deflected to very accurate tolerances proved to be a problem. 
El = Pl3/3y
Where EI = stiffness 
P = applied weight 
l = test section length 
y = deflection.

 The answer I came up with was to use an idea borrowed from a lot of tools.  For example the micrometer uses a rotating drum to expand very small space into something we can read.  Each revolution of the drum moves the head in or out about .1 of an inch, but the drum itself is marked in .01 of or even .001 of an inch. 

Picture one shows how I made my extended scale.  I dropped a vertical line from my zero line(A).  Then I marked it in 10th of an inch(B).  I had to be very careful here.  If this wasn't right nothing else would be.  Once I had the 10th marked I dropped two other lines on each side of my measuring line(C).  These two lines have to be exactly the same distance and parallel to the centerline for this to work. Then lay a straight edge from the  index axis through each of the lines at each .1 increment(D).  Mark from parallel line to parallel line.  This line will represent each tenth of an inch at the center vertical line, no matter where you measure it.  Now connect the lines as in the illustration at right(E).  These lines are for more exact measurements. You can read to hundredths (.00) and interpolate to thousandths (.000).  You read these lines from right to left. 

Picture two shows how to read the scale.  In the example the pointer cuts the index line at A , B, and C.   We read the scale vertically for the first reading A is between .4' and .5".  we read the scale horizontally (remember to read it from right to left  The major line on the right is .4 and the major line on the left is .5) .  A. is .4 + .030 = .430.  B. is = .7 + .085 = .785.  C. is .9 + .055 = .955.

You plot the just like anything else, but Don suggests using a log graph because the amount grows so quickly, 

Picture one

picture two

All these system are good ways to judge the taper of a fly rod.  There are rod builders who swear by each one.  Of course each has it's strong and weak points -- just as each has it's defenders and detractors.  And I've only scratched the surface of each system.  Once you find a system you like, you'll find all kinds of "tweaks" you can make so it will work it's best for you. 

But until you actually cast a few rods that you've graphed, or charted, you won't really know what you're looking at.  So go find some of those rods of the old masters (or the new masters, for that matter) and see what they feel like. Then plot them out.  Or better yet, go to the rod makers taper page and see if someone has already done a lot of the work for you! 

But remember, it starts with you casting a rod.  Nothing else will do.

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