GEAR - A program for optimizing bicycle gearing.
Copyright 1986 by Peter Esherick and Paralegal Services
1105 Sagebrush Tr. S.E., Albuquerque, N.M. 87123

Permission is hereby granted to NON-COMMERCIAL USERS to freely use,
copy and/or distribute this program. This program is distributed
without warranty as to its utility or functuality. It is distributed
entirely on an 'as is' basis. However even in this 'as it is' form we
hope you find it fun and/or useful.

What does the program do ?
The primary function of the GEAR program is to calculate all of the
possible gear ratios that you can get given the number of teeth on the
front and rear gears of your bicycle. The results are expressed in
terms of "equivalent wheel diameter".
If you have read about the history of bicycles you will remember the
great high wheeled bikes of 1890's that had the pedals attached directly
to the front wheel. Since bicycles of those days lacked gears, the only
way you could go faster was to pedal a bigger wheel. When geared
bicycles were introduced it became possible to get the same effect by
turning a smaller wheel more than one turn for each rotation of the
pedals. The "equivalent wheel diameter" is thus the actual wheel
diameter multiplied by the number of wheel revolutions that occur for
each full turn of the pedals.
The GEAR program works a lot like a mini-spreadsheet: there are
blanks (or "cells") on the screen where you fill in values for things
like wheel diameter and the number of teeth on a front or rear gear
sprocket. At the bottom of the screen there is a pseudo graphic display
of the equivalent wheel diameters for all of the possible combinations
of gears that you have entered. As you enter or change the data, the
display at the bottom is updated each time you type the (or
) key.
In addition to the graphic display, GEAR also calculates a more
comprehensive numeric display of the gear ratios. This table is

displayed when you press either the or key on the cursor
pad. The table lists the front and rear sprocket number, the number of
teeth on each, the equivalent wheel diameter, the percentage change from
the gear listed above, the speed obtained in this gear for the specified
cadence, and finally the gradient hill that can be climbed at this speed
given the horsepower and weight of the cyclist.


Getting started:

The GEAR program consists of three essential files:

GEAR.EXE is the main executable file.
GEAR.TPL is the screen template which can be customized.
GEAR.DAT is the data file containing default values.

In general it is assumed that all three files are contained in the
current default directory. The program can then be run by simply typing
"GEAR" at the DOS command line. (Provisions for harddisks and
subdirectories are described at the end of these instructions.)

Once loaded the program will display an introducion and then a short
screen of instructions. Type any key to go on to the next screen.
After the initial help screen you will arrive at the main data entry
screen. The data entry screen looks something like this:

-----------------------------------------------------------------------------
Gear: A program for optimizing bicycle gearing.

Gear Optimization for ________________________________________

Wheel Size ____ (inches) Cadence ___ (rpm)
Weight ___ (lbs) Power ____ (HP) Drag ____ E-5

Front 1 2 3 4 Rear 1 2 3 4 5 6 7
Gear __ __ __ __ Gear __ __ __ __ __ __ __
Percent ____ ____ ____ ____ ____ ____ ____ ____ ____

Rear Front
5 . . . . 1 . . . . . . . . . .
4 . . . . . . 1. . . . . . . . .
3 . . . . . . . . 1 . . . . . .
2 . . . . . . . . . . . 1 . . . .
1 . . . . . . . . . . . . . . 1
30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Equivalent Wheel Diameter (inches)
-------------------------------------------------------------------------------

At this point the GEAR program is running much like a specialized
spread-sheet program. The underlined blanks above show up on the screen
in reverse video. These are the blanks or empty cells where you enter
the data you want to use. The cursor pad arrow keys are used to move
around the form, and then new values are entered in any cell location to
modify the parameters and gears used in the calculations. The graphic
display at the bottom of the screen and the percentage difference
between gears are updated when you type . In this display each
line corresponds to a gear position on the freewheel and the numbers
plotted give the equivalent wheel diameter for each corresponding
chainwheel position.

Moving around the screen:

Keyboard: Action:

Arrow keys: Move left/right char or up/down line.
Ctrl <- and Ctrl -> Move to previous or next field.
or Move to beginning or end of current line.
Toggle between [Insert] and [Overstrike] modes.

Update display, filling in blanks if necessary.
or Shft Update display while changing field.

Ctrl Clear current entry.
Ctrl Clear entry from cursor to end of field.
Ctrl or Clear all Front or Rear sprocket entries.

PgUp or PgDn Display detailed gear ratio table.
F1 Display this help screen.
F3 Read in pre-set data from disk (Advanced version.)
F9 Print the current table on printer.


The following general information can be entered at the top of the page:

Label: This is just a place where you can enter some text which
might serve as a reminder on a printed copy later on. Put in
anything you want here as a label.

Wheel size: This is where you enter the bicycle's wheel diameter in
inches. It will be used for calculating the effective wheel
diameter for each gear ratio, as well as for speed calculations.
According to the Cateye cyclometer manual, the following values
should be used for metric 700 series wheels:
700 x 25C 26.4"
700 x 28C 26.8"
700 x 32C 27.0"

Cadence: Enter how fast you typically pedal, in rpm. If you don't
know, a good guess would be around 80.

Weight: In this case we want to enter the combined weight of the
rider plus the bicycle. If you don't know what your bike
weighs, it is probably around 30 pounds. If it weighs less than
that you probably paid extra for that weight savings and you
know exactly what it weighs.

HP: Here is where the ego gets involved: you get to estimate how
much power you can put out on a steady basis. If your a
recreational cyclist and honest, you should be in the range 0.1
to 0.3 HP. If you race and don't come in last, maybe 0.4. If
you regularly compete in the Tour de France, I might give you
0.5 HP. For Albuquerque cyclists, a power output of 0.25 HP
will lift 190 pounds from the Sandia Crest turnoff on North 14
to the top of Sandia Peak in 90 minutes.

Drag: Coefficient of drag in hp/(mph*3). The number you enter here is
used for calculating how much of your energy goes towards
countering wind resistance. The units are weird, but they come
from the approximation that the energy required is proportional
to the cube of your velocity. A value of 3.5x10-5 appears to be
a good value for riding a touring bike with your arms fairly
straight. (You only have to enter the 3.5. The program assumes
the correct value for the exponent.) For a hunched over racing
position 3.0 is probably reasonable, while straight up on a
mountain bike you better use 4.0. A little research wouldn't
hurt here, but for the crude application here, these values are
probably OK.

How to enter values for the FRONT and REAR gears:

The rest of the blanks are for entering values for the number of teeth
on the front and rear sprockets of the bicycle's gears. There are
several ways that this can be done:

1. Direct entry:
Enter the number of teeth for each gear wheel directly on the
line labeled "Gear". For example a typical 10 speed bike would
have two entries, say 52 and 42, entered for the front
chainrings. The five sprockets on the freewheel are entered in
the table under "Rear", for example 14, 17, 20, 24 and 28. Note
that the program expects the gears to be entered with the highest
gear first and then progressing to successively lower gears.
Thus for the front chain rings the numbers decrease, while for
the freewheel sprockets the numbers increase.

2. Minimum/maximum entry:
Lots of times you will want to try something like "how about a
five sprocket freewheel going from a 14 to a 32 tooth gear?" The
GEAR program makes this easy by allowing you to fill in 14 in
position 1, blanks in positions 2, 3, and 4, and then 32 in
position 5. When you press the key, GEAR will fill in
the blanks assuming as smooth a geometric progression as can be
accomplished with integral values for the number of teeth on each
sprocket.

3. Percentage difference entry:
When you enter sprocket values explicitly, GEAR calculates the
percentage difference between every pair of values entered. (The
Percent change is displayed below each pair of gears.) If you
wish, you can enter one explicit value, say 14 for the first rear
position gear, and then move down one line to the Percent entry
blanks. When you enter a value in a Percent field all empty gear
fields on the line above a filled in with the specified percent
change between each gear. For example, clear the Rear gear field
using , enter 14 in the first position, then move down
a line and over 4 cells. Now enter 20 to get a five speed
freewheel with approximately 20% spacing between gears.

A note on "percentage differences" as calculated by GEAR:

How one calculates a percentage difference between two numbers X and
Y depends on whether you compare (X-Y) to Y or (Y-X) to X. If X is 10%
larger than Y (X=1.1Y) it is not true that Y is 10% smaller than X,
although it's close. To get a number that doesn't care how you do the
comparison you have to get tricky. The way I chose to get tricky was to
calculate the difference in the natural logarithyms of gears I was
comparing, and then multiply by 100. The result is a number that is
equal to percent difference in the limit of small differences, but with
the advantage that these numbers can be added to get the relative change
over several gears. For what it's worth, that how it's done here.

Playing the game:

Start out by entering what you have on your bike now. After getting a
display of the effective wheel diameter for each position of the front
and rear gears, check to see if the available gears are evenly spaced
and give you the kind of range you want. Then the fun begins: you play
the game of trying different gear combinations and see if you can
improve the way your bike is set up. A few weekends and $50 later you
quit playing these games and get back to actually riding your bike.


Notes on sub-directories:

In general it is assumed that all three GEAR files are contained in the
current default directory. The program can then be run by simply typing
"GEAR" at the DOS command line. Alternatively one can specify on the
command line where the program should look for the two data files. This
is particularly useful on hardisk systems where the data files are
contained in a different subdirectory. For example if the data files
are in a subdirectory C:\BIKE you could run the program by entering
"GEAR C:\BIKE", assuming GEAR.EXE can be found in the currently
specified PATH. Using DOS 3.x you could put all the files in the
subdirectory \BIKE and then call the program (perhaps with a batch file)
by typing "\BIKE\GEAR \BIKE".