Figure 7-8.—Latitude and departure.
The latitude of a traverse line means the length of
the line as projected on the north-to-south meridian
running through the point of origin. The departure of a
traverse line means the length of the line as projected on
the east-to-west parallel running through the point of
origin. To understand this, you should examine figure
7-8. The point of origin is at O. The line NS is the
meridian through the point of origin; the line EW is the
parallel through the point of origin. The latitude of AB
is the length of AB as projected on NS; the departure of
AB is the length of AB as projected on EW. You can see
that for a traverse line running due north and south, the
latitude would equal the length of the line and the
departure would be zero. For a line running due east and
west the departure would equal the length of the line and
the latitude would be zero.
Now, for a line running other than north to south or
east to west, you can determine the latitude or departure
by simple triangle solution. Figure 7-9 shows a traverse
line 520.16 feet long bearing S61°25'E. To determine
the latitude, you solve the triangle ABC for the length
of the side AC. From the bearing, you know that the size
of angle CAB (the angle of bearing) is 61°25'. The
triangle is a right triangle; therefore
AC = 520.16 cos 61°25' = 248.86 ft.
The latitude of a traverse line, then, equals the
product of the length of the line times the cosine of the
angle of bearing.
To determine the departure, you solve the triangle
for the length of the side CB shown in figure 7-10.
CB = 520.16 sin 61°25' = 456.76 ft.
Figure 7-9.—Latitude equals length of traverse line times
twine of angle of bearing.
Figure 7-10.—Departure equals length of traverse line times
sine of angle of bearing.
The departure of a traverse line, then, equals the
length of the line times the sine of the angle of bearing.
The latitude of a traverse line is designated north or
south and the departure is designated east or west
following the compass direction of the bearing of the
line. A line bearing northeast, for example, has a north
latitude and east departure. In computations, north
latitudes are designated plus and south latitudes minus;
east departures are designated plus and west departures
minus.
7-9
