Topographic Maps and Digital Elevation Models

102 Part III Maps and Images
scale on Figure 6.9 is I:24,000 (or
1124,000), which means that one unit (for
example, an inch) on the map equals
24,000 of the same units on the ground.
A graphic scale usually consists of a
scale bar subdivided into divisions corresponding
to a mile or kilometer (see Fig.
6.9). One mile or kilometer segment on
the scale bar is commonly subdivided to
allow more precise measurements of distance.
The subdivided units are commonly
placed to the left of zero on a scale bar, as
in Figure 6.9. A graphic scale is helpful
because it is readily visualized and stays
in true proportion if the map is enlarged or
reduced. It also provides a convenient way
of measuring distances between points on
a map: lay a strip of paper between the
points and make pencil marks next to
each point. Then lay the paper along the
graphic scale at the bottom of the map and
determine the distance.
A verbal scale is commonly used to
discuss maps but is rarely written on
them. People usually say, "I inch equals
I mile," which means, "I inch on the map
represents, or is proportional to, 1 mile
on the ground." Because I mile equals
63,360 inches, a common fractional scale
of 1:62,500 on older maps corresponds
closely to the verbal scale "I inch to
I mile." Many U.S. maps, and essentially
all foreign maps, use metric scales, making
common fractional scales easily convertible
to verbal scales: scales of
I:50,000, I: 100000, and I:250,000 correspond
to I centimeter equaling 0.5, 1.0,
and 2.5 kilometers, respectively.
4° quadrangle maps are drawn at a
fractional scale of I: I,000,000; 2° quadrangles
at I:500,000; I° at I:250,000; 15' at
I:62,500 or I:50,000; and 7'.1.' at 1:24,000
or 1:25,000. Both graphic and fractional
scales are shown at the bottom center of the
map (see Fig. 6.9).
These different scales are used to
show larger or smaller areas of the Earth's
surface on conveniently sized maps. For
example, it may be possible to show a
small city on a map where I inch on the
map represents 12,000 inches (1000 ft) on
the ground. This map would have a scale
of I: 12,000. However, to show a midsized
state, such as Indiana, on a map of
similar size, the scale would have to be
much smaller, say I inch on the map to
500,000 inches (approximately 8 miles) on
the ground. In general, the larger the area
shown, the smaller the scale of the map
(smaller because the fraction 1!500,000 is
a smaller number than 1/12,000).
Converting Among
Scales
Verbal to fractional scale
conversion:
I. Convert map and ground distances
to the same units.
2. Write the verbal scale as the fraction:
I. Convert both map and ground distances
to the same units, inches:
5000 X 12" = 60,000". The verbal
scale is now 2.5 inches on the map
represents 60,000 inches on the
ground.
2. Write the verbal scale as the fraction:
2.5" (distance on map)
60,000" (distance on ground)
3. Divide the numerator and denominator
by the value of the numerator:
2.5"/2.5"
60,000"/2.5"
Distance on map
Distance on ground
3. Divide both numerator and denominator
by the value of the numerator:
Distance 0/1 map/distance on map
Distance on ground/distance on map
Example: Convert the following verbal
scale to a fractional scale: 2.5 inches on
the map represents 5000 feet on the
ground.
I
24,000 or 1:24,000
Fractional to verbal scale
conversion:
I. Select convenient map and ground
units to relate to each other (for
example, inches and miles or centimeters
and kilometers).
2. Express fractional scale using the
map units (inches or centimeters).
3. Convert the denominator to the
ground units (miles or kilometers).
4. Express verbally as "I inch [or
I centimeter] equals X miles [or
kilometers]."
Example: Convert a fractional scale of
I:62,500 to a verbal scale of I map inch
equals X miles on the ground.
I. Units to be related are inches and
miles.
2. 1:62,500 = 1"/62,500"
3. Convert 62,500" into miles by dividing
by the number of inches in
I mile. One mile = 5280 feet and
1 foot = 12 inches. So, 1 mi =
5280' X 12" = 63,360". Working
out the division:
62,500 inches .
63 360 ' I . = 0.986111/
, mc 1es per 1111
4. Expressed verbally, I inch on the
map equals 0.986 mile on the
ground.
Magnetic
Declination
Maps are usually drawn with north at
the top. North on a map refers to true
geographic north. At most places on
Earth, however, a compass needle does
not point toward the geographic north
pole but toward the magnetic north pole.
The magnetic north pole is in the
Canadian Arctic, but its exact position
changes. For example, in 1955, it was
located north of Prince of Wales Island
near latitude 74° N, longitude 100° W;
its last measured location in 200 I put it
in the Canadian Arctic Ocean (81.3° N,
110.3° W) headed northwest toward
Siberia at 40 km/year.
The angular distance between true
north and magnetic north is the magnetic
declination. Because the location
of the magnetic pole changes, the magnetic
declination generally varies with
time. If you are navigating or doing geologic
research using a compass, you
must adjust the declination of the compass
for local conditions. Without
adjustment, compass errors in excess of
10° to 20° are possible along the west
and east coasts of North America! The
magnetic declination is shown at the
bottom of most USGS maps by two
arrows (see Fig. 6.9). One points to true
north (commonly marked with a star, or
T.N.) and one points toward magnetic
north (commonly marked M.N.). The