Hexrod Documentation

Table of Contents

  1. Program Origin and History
  2. Overview
  3. Start Here
    1. First screen: entering rod fundamentals
    2. Second screen: entering rod taper
    3. Other ways of entering a taper
      1. Entering rod stresses
      2. Entering a straight taper
      3. Entering a Powell taper
  4. Design Report Screen
    1. Settings
    2. Graphs
    3. Tables
    4. Modify the rod
      1. Dimensions
      2. Fundamentals
      3. Geometry
      4. Controlled modification
      5. Editing the stress curve
      6. Hollowing
      7. Modification by deflection
    5. Rod Libraries
      1. Creating a library and saving a rod
      2. Comparing rods
  5. More detail on special topics
    1. Various definitions, assumptions and quirks
    2. Specifying ferrule weights
    3. Powell taper calculator
    4. Modifying fundamentals
    5. Hollowing
    6. Static deflection
    7. Casting deflection
    8. Modify rod by deflection
    9. Bokstrom's Controlled Modification

Program Origin and History

Hexrod is a set of tools to aid in the design and analysis of tapers for split cane (bamboo) flyrods. At the core is the stress analysis conceived by Everett Garrison. Stress analysis is a widely used method to analyze, compare and modify tapers. Besides stress analysis, Hexrod also implements John Bokstrom's method of controlled modification, and does more mundane tasks such as graphing tapers, computing ferrule sizes and form settings for ordinary planing forms and Morgan hand mills. In Hexrod, you can also save your tapers in a library for later retrieval and use.

This online version of Hexrod is based on Wayne Cattanach's Hexrod program, Rev 7-92, which was graciously supplied by Wayne. It uses Web "forms" to pass information between a set of cgi scripts written in Perl.

Wayne's Hexrod program was based on Everett Garrison's formulas, published in "The Book".

I was also inspired by Bruce Conner's Windows version of Hexrod.

For in introduction to stress analysis as used in Hexrod, see this document. You can find an archive of information about cane rods, the Hexrod program, and cane rod tapers at Jerry Foster's excellent Rodmakers Web Site. Jerry's site has a paper by Wayne describing the math behind the Hexrod program.

Some important milestones:

  • December 17, 1996: First released.
  • May 2002: Complete rewrite of the program, adding many new features.
  • July 2002: Added the ability to set up private taper libraries.
  • Spring 2009: Major revisions, most important a rehosting to a commercial web server and moving all rods and user libraries to a MySQL database.
  • July 2015: Added rod slope measures (Bokstrom RAV and LWV).
  • September 2015: Better support for metric data users and some simplification
  • November 2015: Compute rod stress for a hollow rod.
  • August 2018: Modify a rod based on Bokstrom's Controlled Modification.
  • April 2020: Calculation of static and casting deflection, and modification by holding constant casting deflection.
  • April 2021: Changes to change geometry operation

Overview

Before using Hexrod, take a few minutes to study this flowchart of its main parts:



There are three ways to get a rod taper into Hexrod for analysis: (1) enter the details of the rod, including its taper; (2) retrieve a rod previously saved in a Hexrod private library; or (3) retrieve a classic rod from the Rodmakers library. Libraries will be discussed below.

If you enter a rod, the first screen is where you enter the basic rod parameters, what I like to call fundamentals: things like the geometry (hex, penta, or quad), rod length, line weight and number of pieces. You can also choose between American and metric units, and the pixel width of graphs, depending on the size of your computer screen.

Then you have to enter the taper. There are four options: (1) enter the actual rod dimensions at points along the rod (e.g. five inch intervals); (2) enter the stress curve (for the advanced user); (3) specify a straight taper; or (4) specify a taper from the Powell taper system.

After an extra click or two, you are at the Design Report page. You have specified all the necessary details of the rod, and it is ready for analysis or modification. This is the central page of Hexrod; you will always return to this page.

Start here

The opening screen has a link to the Hexrod program. It also has links to other useful things, such as documents, libraries of tapers and guide spacing programs. We will return to some of these later.



First screen: Entering rod fundamentals

The first input page is titled Basic Rod Design Parameters. For short we call these the fundamentals. Half of these are self explanatory. The others are used in the Garrison stress calculations. Saving and retrieving a rod from a library will be discussed below.



These are the items on the top half of the Fundamentals screen:

  1. Rod description A short name for the taper.
  2. Design notes Whatever you need.
  3. Geometry Hex Penta or Quad
  4. Output units
  5. Decimal separator
  6. Graph width For display on your computer screen.
  7. Rod length
  8. Action length To top of grip or butt swell. This is where stress calculations end.
  9. Line details Stress calculations depend on the weight of all the rod components and the line. If you are interested in the stress numbers, put realistic values in here.
    1. Standard or spey line
    2. Line weight & type
    3. Length of line cast



These are the items on the bottom half of the Fundamentals screen:

  1. Number of pieces 1 through 4. All rod sections are assumed to be the same length. See note below on inputting rods with unequal sections.
  2. Ferrule details Ferrules are a major source of weight, and figure large in the stress calculations. Ferrules are assumed to be nickel silver, either standard length or truncated. For a rod with ferrules of a different type see the notes below. There is no special provision for step-down ferrules, although one may be forthcoming.
    1. Ferrule type Standard or truncated.
    2. Ferrule sizes In 64-ths if known.
    3. Compute ferrule sizes If ferrule sizes unknown; you must specify where to round up to the next 64-th size from the flat-to-flat dimension.
  3. Tip impact multiplier For computing stresses; see the stress analysis document for discussion; rarely changed from value of 4.
  4. Cane density For computing stresses; rarely changed from value of 0.668.
  5. Rod data input This is where you enter the rod taper, by one of four methods:

Second screen: Entering rod taper

The most common method of getting your rod taper into Hexrod is to enter rod dimensions at measured points along the rod.



Pairs of numbers are entered into the box, with first number being the distance from the rod tip (of the assembled rod) and second being the rod dimension at that point. Distances do not have to be at any particular spacing (although five-inch intervals are common) nor do the pairs need to be in any order. You can specify input units, amount to substract from dimensions (e.g. varnish), and a multipler. The top of the screen has more details.

After clicking Continue, the data will be checked for obvious errors and dimensions interpolated to one-inch points will be displayed for you to check.

Other ways of entering a taper

Entering rod stresses

It is possible to get rod dimensions indirectly by starting with stress values and working backward. This option is for the hard-core user.

Entering a straight taper

To start with a simple straight taper, give the dimensions at the 0, 5 and 10 inch stations and then a taper slope for the rest of the rod:



Powell taper calculator

You can calculate tapers in the Powell "A", "B", and "C" taper schemes. This is based on the article by Ed Hartzell in The Planing Form, number 54 (1998). More detail on Powell tapers is below. See also the paper by Mike McGuire on his website.



Design Report screen

Once the rod fundamentals and taper has been entered, Hexrod takes you to the Design Report screen. The top of the screen gives the rod fundamentals and taper: dimensions and stresses at five inch intervals, ferrule locations and sizes and tiptop size.



The middle of the screen gives you options to get additional information in the form of graphs and tables, and to modify the rod taper to achieve some end. All of these options return to this page after completing their task.



Graphs

These are the graphs, most are self explanatory:
  1. Stresses: the usual Garrison-style stress curve
  2. Dimensions
  3. Combined: both stresses and dimensions on a single graph
  4. All-in-One: stress graph, dimension graph and a table of dimensions at five inch intervals
  5. Rod Slope Parameters: these are related to John Bokstrom's rod analysis method; see details below
  6. Rod speed: numeric score for rod speed based on stress values (my invention)
  7. Marinaro: as described in Whittle and Harms: Split and Glued by Vince Marinaro
  8. Regression: Linear, quadratic and cubic regression of rod dimensions against the stations
  9. Static Deflection: Deflection of the rod due to a force (weight) applied to the tip. see details below.
  10. Casting Deflection: Deflection of the rod due the weight of rod components and line being cast, along with an impact factor G. see details below.

Tables

More tables for specific analyses are found in other sections, such as the Deflection and Hollowing.
  1. Detailed numbers: this table has the dimensions, stresses, and individual stress components at one inch intervals
  2. Planing form settings: by default settings are given at 5 inch intervals for each rod section; you can change these as needed; you can also add or subtract a fixed amount from each setting or multiply by a constant.
  3. Morgan Hand Mill settings
  4. Rod Action Measures

    These measures are somewhat experimental. They may be useful for comparing rod tapers.

    1. Measurements from Garrison Stress Curves. These describe the distribution of stress values across the length of the rod. The first 10 inches (25cm) of the tip is ignored, and the remainder of the action length is split into three equal sections, as in this example:
      The area (sum of stresses) in the A1, A2 and A3 regions is caclulated. The three measures are defined as follows:
      • "Tip Action" captures the concentration of high stresses in the A1 region as T=2A1/(A2+A3).
      • "Middle Strength" captures the concentration of low stresses in the A2 region. M=(A1+A3)/(2A2). Middle strength is sometimes associated with rods casting more than one line weight well, or casting at a variety of distances effectivley. YMMV of course.
      • "Parabolic" captures high stresses in the A3 region. P=2A3/(A1+A2).
      These three measures are scaled to sum to 1.0 in the table.
    2. A series of papers by Jon Hoffmann and Matthew Hooper explore the application of engineering theory to fly rods, in particular the "natural frequency" of tapered cantilever beams, and what it can tell us about the action of rods. In the paper "Fly Rod Performance and Line Selection" (Proceedings of DETC'97/ 1997 ASME Design Engineering Technical Conferences/ September 14-17, 1997, Sacramento California), they analyze the frequency of 19 contemporary graphite rods, and apply the theory to derive estimating equations for rod stiffness, natural frequency, and line weight. This table gives some of engineering quantities as estimated for the bamboo blank. They may prove useful in comparing rods.
    3. The Estimated for Bamboo table takes the above measures from Hoffmann and Hooper and adjusts them for bamboo, based on the measured frequency for a small number (10) trout sized rods of hexagonal construction. Please do not take these as more than crude guesses. The line weight predictions were tested on 26 "classic" trout tapers; the estimates are too high for more parabolic rods.

Modify the rod

One of the uses of Hexrod is to modify an existing taper in a systematic way. There are several options for doing this.
  1. Modify dimensions: If you want to replace the taper in a certain region with different dimension numbers (e.g. to strengthen a tip or add a hinge), you can directly change the numbers in that region. The example below beefs up the tip from 0 to 10 inch stations.



  2. Modify fundamentals. You can change the fundamentals of the rod, such as length, line weight and number of pieces. The new rod taper is created by either Holding Constant Dimensions, which means shortening or lengthening the rod at the butt end, or (more commonly) Holding Constant Stresses, which stretches or compresses the Garrison stress curve and works backward to the taper that gives the curve.

    Additional information on taper modification at the end of this documentation.



    Modify Geometry gives two alternative conversions between Hex, Penta and Quad construction dimensions. See Additional information below.



  3. Controlled modification. John Bokstrom's method of controlled modification is a simple technique for replicating a taper in a rod that is a little longer or shorter, lighter or heavier than the original. It starts with a straight line taper drawns from the 10% and 60% points along the rod length. Deviations of the actual from this straight taper are calculated. The method of controlled modification then stretches or squeezes these deviations to change the rod length, or shifts the straight taper up or down to change line weight.

    Additional information at the end of this documentation.



  4. Edit stress curve. The editor presents the stress curve graph as a series of dots at one-inch intervals. Use your computer mouse to move the points of the curve to increase or decrease stress in regions of the rod. Then the dimensions will be computed for this new curve. It is not the most elegant tool but serves the purpose.



  5. Output units: Change between American and metric output units.
  6. Hollowing: Hollowing should be the last thing you attempt in Hexrod, after other modifications and adjustments are complete.

    Hexrod allows for hollowing by scallops and dams, where it assumed the dams are as small as practical. In Hexrod, hollowing accomplishes two things. First, you can adjust the dimensions to account for the hollowing with either of three alternative methods, and you will add the hollowing (wall thickness) to the planing form report for your reference. Stress computation incorporates the hollowing.

    The hollowing procedure consists of two parts. First is specifying the wall thickness. This is done separately for each section of the rod. You can indicate where the hollowing begins and ends, and the wall thickness for that segment at the beginning and end points. This allows the wall thickness to have a linear taper. Up to four separate beginning/ending segments are allowed for each rod section. See the example below.

    The second part is how dimensions are adjusted to compensate for the hollowing. First option is leave the dimensions unchanged, which is most appropriate when the degree of hollowing is modest. Second is to increase the taper to maintain equal stiffness. This option uses the cubic formulas derived by Mike McGuire and given in a paper "Dimension Compensation for Hollowing Bamboo Rods" on his website. It is probably the most used method. Unless the hollowing is extreme, the increase in outside dimenions will probably be very small, at most a few thousanths of an inch.

    The third is to adjust the taper for equal stress, which may actually mean a decrease in dimension because of the decreased weight. Weight reduction depends on the density of the cane, which is initially set at 0.668 ounces per cubic inch (Garrison's calculation for Tonkin cane). This can be changed on the Modify Fundamentals page. Finally, the fourth way is by equal casting deflection. Like equal stresses, dimensions in part of the rod may decrease while others are increased, because of reduced bamboo weight. This is equal to maintaining deflected stress. Again, actual external dimension changes will be small.



    The following options (Report, Change, and Unhollow) are only available for newly-hollowed rods (since 20-JAN-2010).

    After hollowing, there is a report which gives the change in bamboo weight from the original taper for each inch and section of the rod. This does not include what you leave for dams, which might be 10-20 % of the weight reduction.

    The hollowing specifications can be changed and the rod dimensions recalculated. The hollowing can also be cancelled and returned to the original solid taper.

    It is recommended NOT to change the length or geometry of a hollowed rod. Do this operation first on a solid rod, then hollow.

    Additional information at the end of this documentation.

  7. Modification by deflection curve. See additional documentation below.

Rod libraries



You can set up a private library to save your tapers. Choose a name for the library you will remember; the first time you save a rod your library will be created. You will be asked for your name and email; this will help me solve problems later (like people forgetting their library name). Library names are case sensitive. You can set up more than one library if that suits your purpose.

Each taper in the library will have a distinct name (the Rod ID), and date. You can also assign a group name to the taper. In listings of tapers, rods will be listed by group.

To retrieve a rod from your library, enter the Rod ID and Library on the first Rod Design Parameters page. If you enter a Library with no Rod ID, you will see all rods in the Library and you can retrieve the one you want.

You can compare the current rod to one previously saved in a library. The comparison gives graphs and tables for dimensions and stress values.

A list of your tapers can be sent to you (or someone else) by email.

More detail on special topics

Various definitions, assumptions and quirks

Tip sizes get tiny
If you go back and forth, calculating stresses from dimensions then recalculating dimensions from stresses, the dimension values in the first few inches of the rod tip get tiny. Garrison did not use the dimensions near the tip from his math either; he considered these computed dimensions impractically small.
Browser reload
Because of the way information is passed between program screens, a browser "Reload" will sometimes bring back a screen without data. Use the "Back" button to go back to a good screen, reload it, and go forward again. This can affect how you correct entry errors; you may have to return and fill in the entire screen again.
Units
Hexrod allows specification of American (inches) or Metric (millimeters) for three separate operations:
  1. Input of the rod (stations and dimensions)
  2. Output of tables and graphs
  3. Planing form settings
The length of rod and the action length are input in American units (feet and inches) on the first form page. After this point, you have the choice to input dimensions and stations in inches or millimeters.

Planing form settings seem to be standardized on 5 inch (127mm) stations so these are the default, and ferrule sizes are in 64'ths of inch, with metric sizes and weights displayed.

All input rod measurements, American or metric, are interpolated to 1-inch segments for stress calculations and then back again to metric for display.

Ferrule size are in 64ths of inch and stress values are computed and displayed in American (ounce-inches), as are Morgan hand mill settings, at least for the present. Its harder to explain than to use.

Rod and action length
In case there is any confusion, the Rod Length refers to the entire assembled rod, from tip to butt. The Action Length is the length from the tip to as far as you want to analyze dimensions and stresses.

The action length may end at the front of the grip, or may extend into the grip and reel seat. It should never be longer than the rod length.

If you have a two-piece rod with unequal sections, you can analyze it by cheating a little. Specify the action length as usual, but specify the rod length as twice the tip length, whatever that is. That will place the ferrule where it should be for the stress calculations.

Line weight & taper
Separate line weights are used for DT and WF lines. These were compiled/computed from the Cortland website by Chris Carlin. They specify the weight of each foot of line for each taper and line weight from 2 through 12. One-weight lines are extrapolated from 2-weight data using the AFTMA line weight standards.

Line weights 3/0, 2/0 and 0 were extrapolated from the data for 1-weight lines by using the info on Bill Byrd's website www.byrdultrafly.com/sagelines.htm. To my knowledge, there are no AFTMA standards for these line weights.

Spey lines
For spey-type lines, enter the weight of the entire head section (including any added tip) and the length of the running line cast. E.g. for a 35-foot head section and a 80 foot total cast, the running line cast is 80-35=45 feet. There are many sorts of running lines on the market. It is assumed to weight 3.0 grains per foot, which seems typical.
Tip impact factor
Garrison incorporated this parameter (estimated to be 4.0) in his stress equations. This number servs as a multiplier for all the moments (line, bamboo, guide, varnish) to account for the stress created by pulling the line through the air during the cast. Increasing it will increase the stress values calculated. Change it if you like, but make sure its the same when comparing stress numbers of two rods.
Tip factor
is the weight of the line beyond the tip (and the weight of the tip guide, fwiw).
Cane density
Garrison calculated the denisty of Tonkin cane as 0.668 ounces per cubic inch. This parameter may be adjusted if you are building with another material.

Specifying ferrule weights

From the point of view of stress calculations, the only thing about a ferrule that matters is its weight (and its location, of course).

Ferrule weights are supplied for sizes 8 thru 32 -64th in standard and truncated lengths. They correspond most closely to nickel silver Super Swiss style ferrules of the type produced by CSE. Some of the weights come from Wayne's original program, from measurements others have sent me, and from my own limited measurements. Some in-between sizes I've estimated as best I could. (Yes, someone requested ferrules as large as 32/64!)

If you are using a ferrule that is unusual in material, type or size. and you know its weight in ounces, use the table below to choose the size and type (standard or truncated) that most closely matches the weight, and then use that ferrule "as if" it were the correct one. Tell the program not to adjust the ferrule size.

Wt (Oz/g) Size Type Wt (Oz/g) Size Type
0.075/2.126 8 Truncated 0.437/12.389 17 Standard
0.084/2.381 9 Truncated 0.442/12.530 24 Truncated
0.095/2.693 10 Truncated 0.466/13.211 25 Truncated
0.117/3.317 11 Truncated 0.477/13.523 18 Standard
0.120/3.402 8 Standard 0.490/13.891 26 Truncated
0.135/3.827 9 Standard 0.514/14.572 27 Truncated
0.141/3.997 12 Truncated 0.516/14.628 19 Standard
0.162/4.593 10 Standard 0.537/15.224 28 Truncated
0.163/4.621 13 Truncated 0.556/15.762 20 Standard
0.194/5.500 11 Standard 0.560/15.876 29 Truncated
0.197/5.585 14 Truncated 0.584/16.556 30 Truncated
0.225/6.379 12 Standard 0.595/16.868 21 Standard
0.238/6.747 15 Truncated 0.607/17.208 31 Truncated
0.247/7.002 16 Truncated 0.630/17.860 32 Truncated
0.271/7.683 13 Standard 0.633/17.945 22 Standard
0.272/7.711 17 Truncated 0.672/19.051 23 Standard
0.297/8.420 18 Truncated 0.711/20.156 24 Standard
0.321/9.100 19 Truncated 0.749/21.234 25 Standard
0.328/9.299 14 Standard 0.787/22.311 26 Standard
0.346/9.809 20 Truncated 0.825/23.388 27 Standard
0.358/10.149 15 Standard 0.863/24.466 28 Standard
0.370/10.489 21 Truncated 0.900/25.515 29 Standard

Powell taper calculator

E.C. Powell tapers are created from a formula, starting with "A", "B" or "C" families. Powell "B" tapers start with a tip size and a linear taper, given in thousanths of an inch per six inches of rod strip. E.g. a B-8 taper has the strip increasing 0.008 per six inches (the total rod dimension increasing 0.016 per six inches.) A B-9.2 taper increases 0.0092 per six inches.

"A" and "C" tapers modify the linear "B" taper formula by adding (A) or subtracting (C) a fixed amount to the strip each 6 inches after the frist 6-inch station. This amount is given as a fraction of a thousanth of an inch; 1/5 is 0.0002 inches. An A-8 X 1/5 taper has the strip increasing 0.008 from the tip to six inches, 0.008+0.0002=0.0082 from six to 12 inches, 0.0084 from 12 to 18, 0.0086 from 18 to 24 inches, etc. Powell characterized the A-series rods as "progressive."

"C" tapers substract the fraction at each 6-inch station after the first. These are "regressive" tapers.

Powell tapers are most commonly used for longer (8 foot plus) rods in heavier (5+) line weights, and are usually hiollow-built. There is no fixed formula for choosing the initial tip size or line weight of a rod. If you create a taper and take it into Hexrod, you can adjust the line weight after viewing the stress values.

Input for Powell taper calculator is in American units. If you specified Metric output, this will appear on subsequent screens.

The Hexrod implementation of Powell tapers is based on the article by Ed Hartzell in The Planing Form, number 54 (1998).

Modifying fundamentals

This approach to modifying a rod's fundamentals seems to be the safest:
  • First, make changes to the original rod's simple properties such as changing length, number of pieces, ferrule type, line weight or length of cast.
  • Second, if desired, change the rod's geometry.
  • Finally, again if desired, hollow the taper to your specifications.

Changing Simple Properties

Changing one or more "fundamentals" of a rod without changing the taper will change the stress values, or conversely, fundamentals can be changed while preserving the stress values which will change the taper. In Hexrod this is accomplished by choosing the “Modify Fundamentals” option, changing one or more fundamentals, then choosing either "Hold Constant Dimensions" (for new stresses) or "Hold Constant Stresses" (for a new taper.) When calculating a new taper for a changed rod by holding constant stresses, be aware that the sizes of the ferrules may change. In Hexrod, be sure to click the checkbox under Ferrule sizes Unknown.

Many builders have found that, making modest changes to a rod while holding constant the stress values will result in a rod with a similar "feel." For example, changing a 7.5 foot 4 weight rod to a 8 foot 5 weight is reasonable. Going from that rod to a 9 foot 7 weight is not likely to succeed.

Number of pieces
A common modification is to change the number of pieces in a rod by adding or removing ferrules from the taper. Adding a ferrule (say from a 2 to 3 piece) adds considerable weight at certain points, which increases moments and increases stress. Adding a ferrule will add stress from that location back toward the butt. If we want a new rod with the same stress characteristics, we will have to increase the taper dimensions from that point backward to support the additional weight without increasing the stress.

Changing the number of ferrules will involve computing not only the locations but the sizes of the ferrules.

Naturally, adding ferrules does more than add weight. It also introduces a flat spot to the taper. Not all tapers will respond well to changing ferrule locations. In general, ferrules are least objectionable in a fairly low stress part of the taper. Many classic tapers used step down ferrules; the taper was designed for a ferrule at that particular location and moving it will alter the feel of the rod. Besides the number of ferrules, it is possible to change ferrule types, from standard to truncated or the opposite. This will change the weight, which will change the stress, or change the taper to achieve the same stresses.

Line weight
Changing the weight of the line, or the type of the line (weight forward, double taper, or spey), or the length of the line cast will alter the stresses. Conversely you can hold constant stresses and derive a new taper that will give the same stresses with the new weight. Logically, adding line weight will increase moments which will increase stresses; to achieve the same stresses the taper will have to be beefed up.
Rod length
Following Garrison, stress values are calculated starting at the tip and ending at the top of the grip. This is called the "action length". For a typical trout rod, it is about 10 inches shorter than the entire rod. Action and rod lengths can be changed in Hexrod. If dimensions are held constant, a shorter rod just means ending the taper earlier, and a longer rod extends the taper near the grip a little longer. If stresses are held constant, then the stress curve is compressed to shorten the rod or stretched to lengthen it. The new taper is computed from this altered stress curve.

Changing the Geometry

There are two methods available to change the geometry:
  1. Find a new taper with equal cross section at each station to the original. This is the "traditional" method. It results in a rod with equal weight to the original. The constants involved and their derivation can be seen here in section 7.
  2. New taper has equal stiffness (Moment of Inertia) to the original. This is the preferred method of many builders. The constants are in section 9 of the above reference. A series of spread sheets are available to do the conversion has been created by Gabriele Gori and is available here
The option to modify geometry by equivalent Garrison (static) stress curve has been removed as of April 2021. It tended to give impractical tapers. The option to change geometry by equivalent casting deflection curves has been removed until a problem with convergence is resolved.

Hollowing

There are many hollowing schemes in use. Hexrod assumes scalloping with dams in its calculations.

The effect of hollowing on stress is hard to predict in advance. Hollowing reduces weight of the rod (the "bamboo moment"); this reduces stress compared to a solid rod, the difference increasing as you move toward the grip and becomes magnified in longer (e.g. spey) rods. Countering this, hollowing also decreases the stiffness (Modulus of Elasticity) of the rod at each point; this increases stress values. Which one of these effects dominates depends on the degree of hollowing and length of the rod. It is possible that stresses decrease in some areas of a rod while increasing in others. Placement of ferrules can also affect how these two components balance out. Most often, the effect of modest hollowing on stress values is quite small for a trout-sized rod, but can be significant for a longer rod.

The formulas for stress in a hollow rod can be found in the toward the end of the paper by Claude Freaner on this website.

Computing dimensions while holding constant stresses (e.g. a hollow rod with the same stress curve as a solid rod) is an iterative process, working down the rod from tip to butt. Iteration at an inch-point stops when stresses are within 10 ounce/inches of the target stress, or change in dimension is less than 0.0001 inches. Then the process advances to the next inch. This will typically take a couple seconds.

Be aware that bamboo is not of uniform strength. Milward's book "Bamboo: Fact Fiction and Fly Rods" documents how rapidly the stiffness (Modulus of Elasticity) decreases as you go from enamel to pith. Hollow building is removing much weaker material than what remains. This fact does not enter into the stress calculations. Therefore, building a hollow rod with equal stress to a solid rod will probably result in a stiffer rod than you anticipate.

Static Deflection

Static deflection calculates the bend of the rod assuming a force (weight) suspended from the tip of the rod. It uses mechanical engineering concepts for deflection of a cantilever beam, as implemented by Bennett Scully in his Honors thesis. Deflection calculations rely on a fairly complex set of assumptions, some of which are
  1. Small deflection theory is implemented by treating the rod as a set of small increments, and then accumulating the deflection. Hexrod uses increments of length 0.2 inches. Large deflection theory is significantly more complex.
  2. Static deflection ignores other forces which cause a bamboo rod to deflect. It ignores the weight of the rod components (bamboo, ferrules, varnish and guides), the weight of the line being cast and the line in the guides. It also ignores the forces involved in casting. These are treated in dynamic or casting deflection analyses.
  3. Modulus of elasticity (MOE or E) is a measure of the inherent stiffness of the bamboo. Several researchers have measured the MOE of Tonkin cane, most often used in rodbuilding. But there is considerable variability between culms and even between strips in the same culm. Due to the decline in power fibers from enamel to pith, there is also an expected decline in MOE from tips (built from just the outer portion of the strip) to butt. I worked with the MOE results published by Bob Milward in Bamboo: Fact Fiction and Flyrods, and arrived at a default MOE of 5.3 million psi (= 36.54 gigapascals); this value can be changed by the user. Max Satoh's DynaRod program contains MOE values for various species of Japanese bamboo.

Usage

The output from static deflection includes a graph and a table. The graph starts by default with the force necessary to deflect the rod 30 percent of its length. E.g. for an 8 foot rod (96 inches), this is a deflection of 96 x 0.3 = 28.8 inches. The user can then change the deflection percent or the force. The MOE can also be changed from the default. The table contains deflection values by inch.

The option to compare the active rod with another in your library will give a graph comparing the static deflection curves for the rods on the assumption of 30 percent deflection.

Casting Deflection

Casting deflection (as contrasted with static deflection) includes the weight of the rod and components involved in the cast: weight of bamboo, ferrules, varnish and guides, the line in the guides, and the line being cast. These are the same components, along with the "impact multipler" (G force), that are involved in computing the traditional Garrison stress curve, which tradionally uses the impact factor at 4G. In addition, the casting deflection involves the resistance to bending (MOE) of the bamboo.

(I chose the name "casting deflection" rather than the more obvious "dynamic deflection" because it leaves out many elements that would be included in a realistic "dynamic" analysis: the variable input of force from the caster at different points during the cast, the changing angle of the line to the rod, etc.)

Calculation of casting deflection employs the same algorithm by Scully used in static deflection, with several modifications. It requires many iterations and will sometimes take 5-10 seconds to display the initial page.

The casting stress values are calculated from the curvature of the deflected rod, the MOE and rod dimensions. It is interesting (to me :-) to compare these stress curves for various impact factors to the Garrison curves for the undeflected rod. The total area under the stress curve may have no intrinsic meaning but provides a metric for comparing curves under different assumptions.

The graph of the casting deflection curve includes a casting torque measure, which is the rod moments calculated using the deflected length, summed at the end the the action length, usually the start of the grip. It may be useful for comparing the perceived rod weight of different rods which are casting the same weight and length of line.

Modifying a rod by deflection

This procedure has been temporarily (April 2021) removed until I have time to investigate some convergence issues.

Bokstrom's Controlled Modification

John Bokstrom developed a graphical system for creating a new rod by modifying an existing taper which he called Controlled Modification. It was written up in The Planing Form issue 45. It is intended to allow modest changes in rod length and line size while maintaining the same feel. This is how it works.

Dimensions of the existing rod at two points, 10% and 60% of the rod length from the tip, are used to define a straight line with an intercept and a slope (expressed in inches of rod dimension per 100 inches of rod length). Then at each inch-point the deviation of the actual rod from this straight line taper is calculated. The essence of Bokstrom's method is to replicate these same deviations from the straight line in a new rod of a different length.

To create a new taper for a longer or shorter rod, the straight line taper is extended or shortened, and then the curve of the original deviations is stretched or compressed and applied to the straight taper. If a different line weight is desired, the intercept of the straight taper is adjusted by appoximately 0.007 inch per unit of additional line weight.

If desired, you can change the 10% and 60% start/end points for determining the straight line taper. Also, you can magnify or reduce the deviations around the straight line for the new row by a multiplier. Intuitively, you may want a multiplier less than 1.0 if shortenting the new rod, or greater than 1.0 if lengthening.

The Bokstrom modification is just applied to the action-length portion of the rod. The dimension beyond the action length (e.g. under the rod handle) is given no taper. If the rod changes length, ferrule locations and sizes are allowed to change.

Finally

If you find any bugs, have suggestions for improvements, etc. let me know at fcstetzer at gmail dot com.

Just for the record, I promise not to peek at anyone's rod designs :)

Back to the Hexrod Program

--
Frank Stetzer
Bellingham Washington, USA