Transversing and Transverse Computation
Transverse
a series of lines connecting successive points whose lengths and directions have
been determined from field measurements
Latitudes and Departures
N (+) B
Lat. AB ʆab
W (-) E (+)
Reference line A Dep. AB
Reference line
S (-)
Latitude of a Line
Its projection onto the reference meridian or a north-south line
Northings or Southings
Departure of a Line
Its projection onto the reference parallel or an east-west line.
Error of Closure
Linear Error of Closure (L.E.C.)
A short line of unknown length and direction connecting the initial and final station
of the traverse. It is approximately determined by plotting the traverse to scale, or
more exactly by computing hypotenuse of a right triangle whose side are the closure
in latitudes and closure in departures respectively.
LEC = CL2 + CD2
TAN Ө= -CD
-CL
Where:
C L = Closure in latitude or the algebraic sum of North and South latitudes.
C D = Closure in departure or the algebraic sum of East and West departures.
Ө = bearing angle of the side of error.
Sample Problem:
Given in the accompanying tabulation are the observed data for a closed traverse obtained from a
transit-tape survey. Determine the following quantities: latitude and departure of each course, linear
error of closure, and the bearing of the side of error. Tabulate observed and computed values according
to the usual format.
Line Length(m) Azimuth from Latitude Departure Bearing
North
+N -S +E -W
AB 233.10 S 1220301 E 125.24 196.59 S 590 301 E
BC 242.05 N 850151 E 20.04 241.22 N 200001 E
CD 191.50 N 200001 E 179.95 65.50 N 850151 E
DE 234.46 S 3330351 W 209.98 104.31 N 260251W
EF 270.65 S 2540081 W 74.00 260.34 S 440081W
FA 252.38 S 2130001 W 211.66 137.46 S 330001 W
∑NL= 409.97 ∑SL= -410.90 ∑ED= 503.31 ∑WD= -502.11
CL= ∑NL+∑SL
= 409.97+ (-410.90)
CL=-0.93m
CD=∑ED+∑WD
=503.31+ (-502.11)
CD=1.20m
LEC = CL2 + CD2
LEC= (-0.93)2+ (1.20)2
LEC= 1.52m
tanӨ = -CD
-CL
= -1.20
0.93
= -1.29m
Ө= 52°13127.34ll
Bearing = N 520 131 W
Traverse Adjustment
Compass Rule
Cl= CL(d/D) Cd= CD(d/D)
Where:
Cl= Correction to be applied to the latitude of any course
Cd= Correction to the applied to the departure of any course
d= Length of any course
D=Total length or perimeter of traverse
Lat’= Compute Lat. ± Cl
Dep’= Compute Dep. ± Cd
L’= √(Latitude)2+ (Departure)2
tanʆ= Departure’
Latitude ‘
L’= Adjusted length of a course
Lat’= Adjusted latitude
Dep’= Adjusted departure
Ө= Adjusted horizontal angle bet the reference meridian and a course
Sample Problem:
Given the tabulation of observed data from a survey, determine the latitudes & departures of each
course and balance these quantities by employing the compass rule. Also determine the lines error of
closure, bearing of the side of error, adjusted length and bearing of each course. Tabulate value
accordingly.
Line Distance Bearing Latitude Departure Correction Adj. Latitude Adj. Departure Adj. Adj.
Length Bearing
+N -S +N -S Lat. Dep +N -S +E -N
.
AB 495.85 N5°30’E 493.57 47.53 1.67 1.79 491.70 45.74 494.02 N5°19’E
BC 850.62 N46°02’E 590.53 612.23 2.36 3.08 587.67 609.15 846.442 N46°02’E
CD 855.45 S67°38E 325.53 791.09 2.88 3.09 328.41 788.00 858.43 S67°23’E
DE 1020.87 S12°25’E 996.99 219.51 3.43 3.69 1000.42 215..82 1023.43 S12°10’E
EF 117.26 S83°44’W 121.96 1110 3.76 4.04 125.72 1114.60 1121.67 S83°34’W
FA 660.08 N55°09’W 377.19 541 2.22 2.39 374.97 544.09 660.78 N55°26’W
5,000.13 1,461.29 1,444.48 1.65
Transit Rule
Cl= Lat (CL) Cd= Dep (CD)
∑NL-∑SL ∑ED-∑WD
Sample Problem:
Given the tabulation of observed data from a survey, determine the latitudes & departures of each
course and balance these quantities by employing the transit rule. Also determine the lines error of
closure, bearing of the side of error, adjusted length and bearing of each course. Tabulate value
accordingly.
Line Distance Bearing Latitude Departure Correction Adj. Latitude Adj. Departure Adj. Adj.
Length Bearing
+N -S +N -S Adj. Adj. +N -S +E -N
Lat. Dep
.
AB 495.85 N5°30’E 493.57 47.53 2.86 1.79 491.70 45.74 494.02 N5°19’E
BC 850.62 N46°02’E 590.53 612.23 3.42 3.33 587.67 609.15 846.442 N46°02’E
CD 855.45 S67°38E 325.53 791.09 1.88 4.31 328.41 788.00 858.43 S67°23’E
DE 1020.87 S12°25’E 996.99 219.51 5.77 1.19 1000.42 215..82 1023.43 S12°10’E
EF 117.26 S83°44’W 121.96 1110 0.70 6.04 125.72 1114.60 1121.67 S83°34’W
FA 660.08 N55°09’W 377.19 541 2.18 2.15 374.97 544.09 660.78 N55°26’W
5,000.13 1,461.29 1,444.48 1.65
