Topographic maps are drawn to scale. This means
that distances on a map are proportional to distances on the
ground. For example, if two cities 20 miles apart are shown 2
inches apart on a map, then any other locations that are two inches
apart on the map are also 20 miles apart. This proportion, the map
scale, is constant for the map so it holds for any points on
the map. In our example the proportion between equivalent
distances on the map and on the ground is expressed as a scale of 1 inch
= 10 miles, that is 1 inch on the map is equal to 10 miles on the
ground. Map scales can be expressed in three forms. We will look at all
The simplest form of map scale is a VERBAL
SCALE. A verbal scale just states what distance on a map is equal
to what distance on the ground, i.e. 1 inch = 10 miles from our example
above. Though verbal scales are easy to understand, you usually will not
find them printed on topographic maps. Instead our second type of
scale is used.
Fractional scales are written as fractions (1/62500)
or as ratios (1:62500). Unlike verbal scales, fractional scales do
not have units. Instead it is up to the map reader to provide
his/her own units. Allowing the reader of the map to choose his/her own
units provides more flexibility but it also requires a little more
work. Basically the fractional scale needs to turned in to a
verbal scale to make it useful.
First lets look at what a fractional scale
means. A fractional scale is just the ratio of map distance to the
equivalent distance on the ground using the same units for
both. It is very important to remember when we start
changing a fractional scale to a verbal scale the both map and ground
units start the same. The smaller number of the fractional scale
is the distance on the map. The larger number in the scale is the
distance on the ground.
So if we take our example scale (1:62500) we can
choose units we want to measure distance in. Lets chose
inches. We can rewrite our fractional scale as a verbal scale:
1 inch on the map = 62500 inches on
We can do the same thing used with any unit of
length. Some examples of verbal scales produced using various
units from a 1:62500 fractional scale are given in the table:
||1 inch on the map
= 62500 inches on the ground.
||1 foot on the map
= 62500 feet on the ground
||1 cm on the map =
62500 cm on the ground
||1 m on the map =
62500 m on the ground
Notice the pattern. The numbers are the same,
only the units are changed. Note that the same units are used on
both sides of each of the verbal scale.
While these verbal scales are perfectly accurate, they
are not very convenient. While we may want to measure distance on
a map in inches, we rarely want to know the distance on the ground in
inches. If someone asks you the distance from Cleveland to
Columbus they do not want the answer in inches. Instead we need to
convert our verbal scale into more useful units.
Lets take our example (1 inch on the map = 62500
inches on the ground). Measuring map distance in inches is OK, but
we need to come up with a better unit for measuring distance on the
ground. Lets change 62500 inches into the equivalent in feet (I
choose feet because I remember that there are 12 inches in 1
foot). If we multiple 62500 inches by the fraction (1 ft / 12 in)
inches in the numerator and denominator cancel leaving an answer in
feet. Remember, since 1 ft = 12 inches, multiplying by (1 ft / 12 in) is
the same as multiplying by 1. The result of this multiplication gives:
62500 inches x (1 ft /
12 in)= 5208.3 ft
So we can rewrite our verbal scale as 1 inch on
the map = 5208.3 feet on the ground.
This is also a perfectly valid verbal scale, but what
if we wanted to know the distance in miles instead of feet. We
just need to change 5208.3 feet into miles (we could change 62500 inches
into miles but I never remember how may inches are in 1 mile).
Knowing that there are 5280 feet in a mile:
5208.3 ft x (1 mi/5280 ft) = 0.986
So our verbal scale would be: 1 inch on the map =
0.986 miles on the ground. For most practical purposes we can
round this off to 1 inch on the map ~ 1mile on the ground, making
this scale much easier to deal with.
We can do the same type of conversions
using metric units. One of the ways to express a fractional scale
of 1:62500 as a verbal scale using metric units is 1 cm on the map
= 62500 cm on the ground (see table above). As with inches, we
really do not want ground distances in cm's. Instead we can
convert them into more convent units.
Lets convert our ground distance from cm's into
meters. Recall that there are 100 cm in a meter. So:
62500 cm x (1m / 100cm) = 625
So we can write a verbal scale of 1 cm on
the map = 625 m on the ground.
What if we want our distance in kilometers (km).
We just change 625 m into km by multiplying by (1km/1000m). The
result is a verbal scale of 1 cm on the map = 0.625 km on the ground.
So for any fractional scale we can choose the same
units to assign to both sides and then convert those units as we see fit
to produce a verbal scale. Given all of the
possible map scales and all of the possible combination of units that
can be used it may seem that scales on topographic maps a very
complicated. In fact there are only a few scales commonly used,
and each is chosen to allow at least one simple verbal scale. The
most common fractional scales on United States topographic maps and
equivalent verbal scales are given in the table below.
||SIMPLE VERBAL SCALE
||1 in = 2000 ft
||1 in ~ 1 mi
||1 cm = 1 km
||1 in ~ 2 mi
||1 in ~ 4 mi
After all this, why would anyone
want to deal with fractional scales. Well, first as the table
above shows its not that bad, and second, they allow us to get the most
precise measurements off a topographic map. If we are not that
concern about being precise we can use the third type of scale,
A bar scale is just a line drawn on a map of known
ground length. There are usually distances marks along the
line. Bar scales allow for quick visual estimation of distance. If
more precision is needed just lay the edge of a piece of paper between
points on the map you want to know the distance between and mark the
points. Shift the paper edge to the bar scale and use the scale
like a ruler to measure the map distance.
Bar scales are easy to use, but there is one
caution. Look at the typical bar scale drawn below. Note
that the left end of the bar is not zero. The total length of this
bar is FIVE miles, not four miles. A common error with bar scales
is to treat the left end of the line as zero and treat the whole bar as
five miles long. Pay attention to where the zero point on the bar
actually is when you measure with a bar scale.
In addition to their ease of use, there is one other
advantage of a bar scale. If a map is being enlarged or reduced, a
bar scale will remain valid if it is enlarged and reduced by the same
amount. Fractional and verbal scales will not be valid (unless
they are adjusted for the enlargement or reduction, more fun
calculations we will not worry about). This is a problem with the maps
you are looking at on this web site. The actual scale of the
map will vary depending on your computer monitor and its setting.
For the maps on this site only bar scales are included since the size of
the bar will also change with the size of the map.
Topographic Map Page
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