LESSON 8: TRAVERSE COMPUTATION, LATITUDE
AND DEPARTURE
50
TRAVERSE COMPUTATIONS
For any closed traverse the first step taken by the survey or should always be to
check if the observed angles fulfill the geometric conditions of the figure. Should there
be an angular error of closure it must be corrected to give a series of preliminary
adjusted directions. All linear distances should then be corrected since errors in
measured lengths will alter the shape of the traverse.
LATITUDES AND DEPARTURES
The latitude of a line is its projection onto the reference meridian or a north-south
line. Latitudes are sometimes referred to as northings or southings. Latitudes of lines
with northerly bearings are designated as being north (N) or positive (+); those in
southerly directions are designated as south (S) or negative (-). On the other hand, the
departure of a line is its projection onto the reference parallel or an east-west line.
Departures are east (E) or positive (+) for lines having easterly bearings and west (W)
or negative (-) for lines having westerly bearings.
LESSON 8: TRAVERSE COMPUTATION, LATITUDE
AND DEPARTURE
51
The relationship between a line and its latitude and departure is shown in the
figure below.
ERROR OF CLOSURE
The linear error of closure (LEC) is usually a short line of unknown length and
direction connecting the initial and final stations of the traverse. It is approximately
determined by plotting the traverse to scale, or more exactly by computing the
hypotenuse of a right triangle whose sides are the closure in latitudes and the closure in
departures, respectively. This quantity reflects the algebraic sum of all the accumulated
errors of measurement both in angles and distances when running the traverse. The
length of the linear error of closure and the angle that this line makes with the meridian
is determined by the following equations
LESSON 8: TRAVERSE COMPUTATION, LATITUDE
AND DEPARTURE
And
Where;
LEC= linear error of closure
CL= closure in latitude or the algebraic sum of north and south latitudes
CD= closure in departure or the algebraic sum of east and west departure
θ= bearing angle of the side of error
Problems
52
LESSON 8: TRAVERSE COMPUTATION, LATITUDE
AND DEPARTURE
53
1. LATITUDES AND DEPARTURES – given in the tabulation below are notes for an
open traverse. Determine the latitude and departure of each course and tabulate
observed and computed values accordingly.
COURSE
DISTANCE (M)
BEARING
AB
550.30
N 28°10´ E
BC
395.48
S 69°35´ E
CD
462.70
S 27°50´ E
DE
631.22
N 50°00´ E
EF
340.05
S 25°05´ E
FG
275.86
DUE EAST
Tabulated Solution
Lin
Dist
Bearing
AB
550.30
N 28°10´ E
BC
395.48
S 69°35´ E
CD
462.70
S 27°50´ E
DE
631.22
N 50°00´ E
EF
340.05
S 25°05´ E
FG
275.86
DUE EAST
e
Latitude
+N
Departure
-S
+E
-E
2. ERROR OF CLOSURE. Given in the accompanying tabulation are the observed data
for a closed traverse obtained from a transit-tape survey. Determine the following
LESSON 8: TRAVERSE COMPUTATION, LATITUDE
AND DEPARTURE
54
quantities: Latitude and departure of each course, linear error of closure, bearing of the
side of error, and the precision of the measurements. Tabulate observed and computed
values according to the usual format.
Line
DISTANCE (M)
AZIMUTH FROM NORTH
AB
233.10
122°30´
BC
242.05
85°15´
CD
191.50
20°00´
DE
234.46
333°35´
EF
270.65
254°08´
FA
252.38
213°00´
AZIMUTH
LINE
LENGTH
FROM
LATITUDE
DEPARTURE
NORTH
+N
AB
233.10
122°30´
BC
242.05
85°15´
CD
191.50
20°00´
DE
234.46
333°35´
EF
270.65
254°08´
FA
252.38
213°00´
-S
+E
-W
SUMS
3. ERROR OF CLOSURE. In a given closed traverse the sum of the north latitudes
exceeds the sum of south latitudes by 2.74 m and the sum of the west departures
exceed the sum of the east departure by 3.66 m. Determine the linear error of closure
and the bearing of the side of error.
LESSON 8: TRAVERSE COMPUTATION, LATITUDE
AND DEPARTURE
55