August
2004, Issue 169
Ham
Radio Repeater Locator
ACCURACY
AND MATH
Precise
distances to repeaters are not required, so to simplify
calculations and make the code smaller, I decided to
shoot for an accuracy of approximately plus or minus
two miles for repeaters that are within approximately
100 miles.
Various
factors affect accuracy: repeater locations are stored
to an accuracy of about one mile; the exact locations
of the repeaters are unknown; the algorithm for determining
distances has a small error under certain situations;
and the integer arithmetic used is subject to truncation
and rounding errors. Tests on the finished algorithms
show errors within the desired range.
Given
two points on the surface of the earth, a straightforward
trigonometry formula gives the distance between the
points. Although the Zilog C compiler includes floating-point
libraries, I used integer arithmetic throughout in order
to avoid the size of floating-point arithmetic and transcendental
routines. Speed is not really an issue for this project,
but integer routines are faster of course.
The
distance between two points on the same longitude (a
north-south line) is about 69 miles per degree of latitude.
For points on the same latitude (an east-west line),
the distance is 69 miles per degree of longitude only
at the equator, shrinking to zero at the poles. The
formula for the distance along a line of constant latitude
is 69 miles per degree of longitude multiplied by the
cosine of the latitude.
The
HRRL program calculates the legs of a right triangle
using the formulas in Figure 1. The correction factor
for the leg of constant latitude is taken to be the
cosine of the average latitude of the two points, and
the cosine is calculated with a look-up table. The error
caused by this approximation is negligible for distances
less than 100 miles.
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(Click
here to enlarge)
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Figure
1—Given two points on the surface of the earth,
a spherical trigonometry formula gives the distance
between the points. In order to avoid lengthy code,
the familiar formula for the length of the hypotenuse
of a right triangle is used instead, with an accuracy
that’s close enough (within a mile or so) for any
repeaters within range. |
Division
is slow and takes noticeable code space, even for integers.
The HRRL code does no division except by powers of two,
which can be implemented by shifts. For example, to
convert delta latitude—which is expressed in grees (a
“gree” is defined as one-fiftieth of a degree)—to miles,
it’s necessary to multiply by the ratio 69/50. The code
uses the ratio 11/8 to avoid an integer divide, with
a resulting error of only approximately one-third of
a mile in 100 miles.
DATABASE
There
are about 8,000 repeaters in the U.S. and Canada, so
it’s necessary to carefully design the data storage
in order to fit all the repeater information and the
program into the 64 KB of flash memory available in
the Z8F6401. Experience with the first version of the
program led me to add the call letters of each repeater
station to the database. This made it impossible to
fit all 8,000 repeaters in the available memory. But,
a substantial fraction fit, enough to satisfy anyone
who is driving through 49 states (Hawaii is not included)
and Canada.
Table
1 shows the required database information and the
number of bits of storage allocated. A change in latitude
of 1 gree is equal to slightly greater than one mile,
which is judged to be sufficient resolution for the
HRRL.
The
database is stored sorted by frequency in order to reduce
the number of bits required for frequency information.
Frequencies are in the range of 144 to 148 MHz, and
all stations are on 5-kHz increments.
REPEATER
INFORMATION
I
had hoped to find an Internet site with repeater locations
and frequencies available for download, but no such
service is offered. There are some localized databases
for certain states, and users in those locations may
be able to make use of them.
The
printed ARRL repeater directory costs approximately
$10, but manually entering the data is tedious. The
translation to latitude-longitude is also tedious and
inaccurate because the locations of the repeaters are
given as the names of cities and geological features.
The
ARRL sells a CD containing the locations, but it’s pricey
and the CD database has the locations of the repeaters
encrypted for some strange reason. It isn’t too difficult
to extract the necessary latitude-longitude information,
which I did for my project. Refer to the LCC program
listings on the Circuit Cellar ftp site for the details.
Because the information is copyrighted, I included only
a small sample database as part of the project files.
If
you only need repeaters for a small area, you can manually
create a text file with one line per repeater. Tabs
separate fields, and all fields must be present (enter
zero for the tone field if no tone is required). The
fields, in order, are: latitude in degrees, longitude,
frequency in megahertz, plus or minus for offset, call,
and tone in hertz. Figure 2 is an example line.
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(Click
here to enlarge)
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Figure
2—The repeater database text file has one line per
repeater. Tabs separate the fields. All fields must
be present. (Enter zero for the tone field if no
tone is required.) The fields, in order, are as
follows: station latitude in degrees, station longitude
in degrees, frequency in megahertz, plus or minus
for offset, call, and tone in hertz. An auxiliary
program converts the data to the format needed by
the microcomputer. |
Several
programs have been written to aid in the creation of
the repeater database. For example, the datagen program
converts a text file in the aforementioned format to
the C data array used by the microcomputer. The auxiliary
programs were written with the free Windows lcc-win32
compiler.
