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.

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.

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.

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.

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.

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.

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 7½ 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. 

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 ½ 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

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. 

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. 

Parts 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

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.