Dec 232017

Calculate bicycle gearing. | |||
---|---|---|---|

File Name | File Size | Zip Size | Zip Type |

GEAR.DAT | 2684 | 553 | deflated |

GEAR.DOC | 13131 | 4895 | deflated |

GEAR.EXE | 36834 | 19216 | deflated |

GEAR.TPL | 486 | 204 | deflated |

# Download File GEARS.ZIP Here

## Contents of the GEAR.DOC file

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".

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

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

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

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.

Toggle between [Insert] and [Overstrike] modes.

Ctrl

Ctrl

Ctrl

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

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

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".

December 23, 2017
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