segments of each of the six scales. Each of the
six scales is designated by a number representing
the number of graduations that particular scale
has to the linear inch. On the 10 scale, for
example, there are 10 graduations to the inch; on
the 50 scale there are 50. You can see that the 50
scale has 50 graduations in the same space
occupied by 10 on the 10 scale. This space is
1 linear inch.
To determine the actual number of gradu-
ations represented by a numeral on the engineer’s
scale, multiply the numeral by 10. On the 50 scale,
for instance, the numeral 2 indicates 2 x 10, or
20 graduations from the 0. On the 10 scale, the
numeral 11 indicates 11 x 10, or 110 graduations
from the 0. Note that the 10 scale is numbered
every major graduation, while the 50 scale
is numbered every other graduation. Other
scales on the engineer’s scale are the 20, 30, 40,
and 60.
Because it is decimally divided, the engineer’s
scale can be used to scale dimensions down to any
scale in which the first figure in the ratio is 1 in.
and the other is 10, or a multiple of 10.
Suppose, for example, that you wanted to
scale a dimension of 150 mi down to a scale
of 1 in. = 60 mi. You would use the 60
scale, allowing the interval between adjacent
graduations to represent 1 mi. To measure
off 150 mi to scale on the 60 scale, you would
measure off 2.5 in., which falls on the 15th
major graduation.
Suppose now that you want to scale a dimen-
sion of 6,500 ft down to a scale of 1 in. = 1,000
ft. The second figure in the ratio is a multiple of
10 times a multiple of 10. You would therefore
use the 10 scale, allowing the interval between
adjacent graduations on the scale to represent 100
ft, in which case the interval between adjacent
numerals on the scale would indicate 1,000 ft. To
measure off 6,500 ft, you would simply lay off
from 0 to 6.5 on the scale.
To use the engineer’s scale for scaling
to scales that are expressed fractionally, you
must be able to determine the fractional
equivalent of each of the scales. For any scale,
this equivalent is simply 1 over the total number
of graduations on the scale, or 1 over the
product of the scale number times 12, which
comes to the same thing. Applying this rule, the
fractional expressions of each of the scales is as
follows:
10 scale = 1/120
20 scale = 1/240
30 scale = 1/360
40 scale = 1/480
50 scale = 1/600
60 scale = 1/720
Suppose you wanted to scale 50 ft down to
a scale of 1/120. The 10 scale gives you this scale;
you would therefore use the 10 scale, allowing the
space between graduations to represent 1 ft, and
measuring off 5 (for 50 ft). The line on your paper
would be 5 in. long, representing a line on the
object itself that is 120 in. x 5 in., or 600 in., or
50 ft long.
Similarly, if you wanted to scale 50 ft down
to a scale of 1/600, you would use the 50 scale
and measure off 5 for 50 ft. In this case, the line
on your paper would be 1 in. long, representing
a line on the object itself that is 1 x 600, or 600
in., or 50 ft long.
When it is not required that the drawing be
made to a specified scale—that is, when the
dimensions of lines on the drawing are not
required to bear a specified ratio to the
dimensions of lines on the object itself—the most
convenient scale on the engineer’s scale is used.
Suppose, for example, that you want to draw the
outline of a 360-ft by 800-ft rectangular field on
an 8-in, by 10 1/2-in. sheet of paper with no
specific scale prescribed. All you want to do is
reduce the representation of the object to one that
will fit the dimensions of the paper. You could
use the 10 scale, allowing the interval between
adjacent graduations to represent 10 ft. In
this case, the numerals on the scale, instead
of representing 10, 20, and so on, will represent
100, 200, and so on. To measure off 360 ft to
scale, you should measure from 0 to the 6th
graduation beyond the numeral 3. For 800 ft you
should measure from 0 to the numeral 8.
Because you allowed the interval between
adjacent graduations to represent 10 ft, and
because the 10 scale has 10 graduations to the in.,
the scale of your drawing would be 1 in. = 100 ft,
or 1/1,200.
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