CIVL 1112
Surveying - Traverse Calculations
Surveying - Traverse
1/13
Surveying - Traverse
Introduction
 Almost all surveying requires some calculations to
reduce measurements into a more useful form for
determining distance, earthwork volumes, land areas,
etc.
 A traverse is developed by measuring the distance and
angles between points that found the boundary of a site
 We will learn several different techniques to compute the
area inside a traverse
Surveying - Traverse
Distance - Traverse
Methods of Computing Area
 A simple method that is useful for rough area estimates
is a graphical method
 In this method, the
traverse is plotted to scale
on graph paper, and the
number of squares inside
the traverse are counted
B
A
C
D
Distance - Traverse
Methods of Computing Area
B
a
A
Distance - Traverse
Methods of Computing Area
B
1
Area ABC  ac sin 
2
b

a
A
c
C
b

Area ABD 
1
ad sin 
2
Area BCD 
1
bc sin 
2

C
d
c
D
Area ABCD  Area ABD  Area BCD
CIVL 1112
Surveying - Traverse Calculations
Distance - Traverse
Surveying - Traverse
Methods of Computing Area
B
b
A
Area ABE 
c

Balancing Angles
C
a

D
e
2/13
Area CDE 
d
1
ae sin 
2
 Before the areas of a piece of land can be computed, it is
necessary to have a closed traverse
 The interior angles of a closed traverse should total:
1
cd sin 
2
(n - 2)(180°)
where n is the number of sides of the traverse
E
 To compute Area BCD more data is required
Surveying - Traverse
Surveying - Traverse
Balancing Angles
Balancing Angles
A
Error of closure
B
D
 A surveying heuristic is that the total angle should not
vary from the correct value by more than the square root
of the number of angles measured times the precision of
the instrument
 For example an eight-sided traverse using a 1’ transit,
the maximum error is:
1' 8  2.83 '  3'
C
Angle containing mistake
Surveying - Traverse
Surveying - Traverse
Balancing Angles
Latitudes and Departures
 If the angles do not close by a reasonable amount,
mistakes in measuring have been made
 The closure of a traverse is checked by computing the
latitudes and departures of each of it sides
 If an error of 1’ is made, the surveyor may correct one
angle by 1’
 If an error of 2’ is made, the surveyor may correct two
angles by 1’ each
 If an error of 3’ is made in a 12 sided traverse, the
surveyor may correct each angle by 3’/12 or 15”
N
N
B
Latitude AB
Bearing 
E
W
Bearing 
A
W
C
Departure AB
Latitude CD
S
Departure CD
D
S
E
CIVL 1112
Surveying - Traverse Calculations
Surveying - Traverse
3/13
Surveying - Traverse
Latitudes and Departures
Error of Closure
 The latitude of a line is its projection on the north–south
meridian
 Consider the following statement:
N
Latitude AB
E
W
Bearing 
A
“If start at one corner of a closed traverse and walk its lines
until you return to your starting point, you will have walked as
far north as you walked south and as far east as you have
walked west”
 The departure of a line is
its projection on the east–
west line
B
Departure AB
 A northeasterly bearing has:
+ latitude and
+ departure
 latitudes = 0
 Therefore
and
 departures = 0
S
Surveying - Traverse
Surveying - Traverse
Error of Closure
Error of Closure
 When latitudes are added together, the resulting error is
called the error in latitudes (EL)
 If the measured bearings and distances are plotted on a
sheet of paper, the figure will not close because of EL
and ED
 The error resulting from adding departures together is
called the error in departures (ED)
B
Error of closure
ED
Eclosure 
EL
A
C
Latitudes and Departures - Example
Precision 
2
  ED 
2
Eclosure
perimeter
 Typical precision: 1/5,000 for rural land, 1/7,500 for
suburban land, and 1/10,000 for urban land
D
Surveying - Traverse
 EL 
Surveying - Traverse
Latitudes and Departures - Example
A
N
N 42° 59’ E
S 6° 15’ W
234.58’
Departure AB
189.53’
B
W  (189.53 ft.)sin(615 ')  20.63 ft.
A
W
E
E
S 29° 38’ E
142.39’
175.18’
N 12° 24’ W
S 6° 15’ W
Latitude AB
189.53 ft.
S  (189.53 ft.)cos(615 ')  188.40 ft.
175.18’
D N 81° 18’ W
C
B
S
CIVL 1112
Surveying - Traverse Calculations
Surveying - Traverse
Surveying - Traverse
Latitudes and Departures - Example
Latitudes and Departures - Example
Bearing
Side
N
Departure BC
E  (175.18 ft.)sin(2938 ')  86.62 ft.
B
W
4/13
AB
BC
CD
DE
EA
degree
m inutes
6
29
81
12
42
15
38
18
24
59
S
S
N
N
N
Length (ft.)
Latitude
Departure
189.53
175.18
197.78
142.39
234.58
939.46
-188.403
-152.268
29.916
139.068
171.607
-0.079
-20.634
86.617
-195.504
-30.576
159.933
-0.163
W
E
W
W
E
E
175.18 ft.
Latitude BC
S 29° 38’ E
S  (175.18 ft.)cos(2938 ')  152.27 ft.
C
S
Surveying - Traverse
Surveying - Traverse
Latitudes and Departures - Example
Bearing
Side
AB
BC
CD
DE
EA
Eclosure 
S
S
N
N
N
 EL 
2
degree
m inutes
6
29
81
12
42
15
38
18
24
59
  ED  
Length (ft.)
Latitude
Departure
189.53
175.18
197.78
142.39
234.58
939.46
-188.403
-152.268
29.916
139.068
171.607
-0.079
-20.634
86.617
-195.504
-30.576
159.933
-0.163
A
S 77° 10’ E
W
E
W
W
E
 0.079 
2
Group Example Problem 1
2
  0.163   0.182 ft.
0.182 ft.
Eclosure

Precision 

939.46 ft.
perimeter
N 29° 16’ E
651.2 ft.
B
660.5 ft.
S 38° 43’ W
2
1
5,176
D
491.0 ft.
826.7 ft.
N 64° 09’ W
C
Surveying - Traverse
Surveying - Traverse
Balancing Latitudes and Departures
Group Example Problem 1
 Balancing the latitudes and departures of a traverse
attempts to obtain more probable values for the locations
of the corners of the traverse
Bearing
Side
AB
BC
CD
DE
S
S
N
N
Length (ft.)
degree
m inutes
77
38
64
29
10
43
9
16
E
W
W
E
651.2
826.7
491.0
660.5
Latitude
Departure
 A popular method for balancing errors is called the
compass or the Bowditch rule
 The “Bowditch rule” as devised by Nathaniel
Bowditch, surveyor, navigator and mathematician, as
a proposed solution to the problem of compass
traverse adjustment, which was posed in the
American journal The Analyst in 1807.
CIVL 1112
Surveying - Traverse Calculations
5/13
Surveying - Traverse
Surveying - Traverse
Balancing Latitudes and Departures
Balancing Latitudes and Departures
A
 The compass method assumes:
N 42° 59’ E
1) angles and distances have same error
2) errors are accidental
S 6° 15’ W
234.58 ft.
189.53 ft.
B
 The rule states:
E
S 29° 38’ E
“The error in latitude (departure) of a line is to the
total error in latitude (departure) as the length of the
line is the perimeter of the traverse”
142.39 ft.
175.18 ft.
N 12° 24’ W
175.18 ft.
D N 81° 18’ W
Surveying - Traverse
C
Surveying - Traverse
Latitudes and Departures - Example
Latitudes and Departures - Example
 Recall the results of our example problem
 Recall the results of our example problem
Bearing
Side
AB
BC
CD
DE
EA
S
S
N
N
N
Length (ft)
degree
m inutes
6
29
81
12
42
15
38
18
24
59
W
E
W
W
E
Latitude
Departure
Bearing
Side
189.53
175.18
197.78
142.39
234.58
AB
BC
CD
DE
EA
S
S
N
N
N
degree
m inutes
6
29
81
12
42
15
38
18
24
59
W
E
W
W
E
Length (ft)
Latitude
Departure
189.53
175.18
197.78
142.39
234.58
939.46
-188.403
-152.268
29.916
139.068
171.607
-0.079
-20.634
86.617
-195.504
-30.576
159.933
-0.163
Surveying - Traverse
Surveying - Traverse
Balancing Latitudes and Departures
Balancing Latitudes and Departures
N
N
Latitude AB
Departure AB
S  (189.53 ft.)cos(6 15 ')  188.40 ft.

A
W
E
Correction in Lat AB
LAB

EL
perimeter
S 6° 15’ W
189.53 ft.
B
W  (189.53 ft.)sin(615 ')  20.63 ft.
A
W
Correction in Lat AB 
EL  LAB 
189.53 ft.
B
Correction in Lat AB 
939.46 ft.
Correction in Dep AB
LAB

ED
perimeter
S 6° 15’ W
Correction in Dep AB 
perimeter
S
0.079 ft. 189.53 ft.
E

 0.016 ft.
ED  LAB 
perimeter
S
Correction in Dep AB 
0.163 ft. 189.53 ft.
939.46 ft.

 0.033 ft.
CIVL 1112
Surveying - Traverse Calculations
6/13
Surveying - Traverse
Surveying - Traverse
Balancing Latitudes and Departures
Balancing Latitudes and Departures
N
N
Latitude BC
Departure BC
S  (175.18 ft.)cos(29 38 ')  152.27 ft.

B
W
E
Correction in LatBC
LBC

EL
perimeter
175.18 ft.
S 29° 38’ E
Correction in LatBC 
C
S
Correction in LatBC 
EL  LBC 
E  (175.18 ft.)sin(2938 ')  86.62 ft.
B
W
E
S 29° 38’ E
939.46 ft.
ED  LBC 
Correction in DepBC 
perimeter
0.079 ft. 175.18 ft.
Correction in DepBC
LBC

perimeter
ED
175.18 ft.
perimeter
C
S
  0.015 ft.
Correction in DepBC 
0.163 ft. 175.18 ft.
  0.030 ft.
939.46 ft.
Surveying - Traverse
Surveying - Traverse
Balancing Latitudes and Departures
Balancing Latitudes and Departures
Length (ft.) Latitude
189.53
175.18
197.78
142.39
234.58
939.46
-188.403
-152.268
29.916
139.068
171.607
-0.079
Departure
-20.634
86.617
-195.504
-30.576
159.933
-0.163
Corrections
Latitude Departure
0.016
0.015
Balanced
Latitude Departure
0.033
0.030
Length (ft.) Latitude
189.53
175.18
197.78
142.39
234.58
939.46
-188.403
-152.268
29.916
139.068
171.607
-0.079
Departure
-20.634
86.617
-195.504
-30.576
159.933
-0.163
Corrections
Latitude Departure
0.016
0.015
0.033
0.030
Balanced
Latitude Departure
-188.388
-152.253
Corrected latitudes and departures
Corrections computed on previous slides
Surveying - Traverse
Surveying - Traverse
Balancing Latitudes and Departures
Balancing Latitudes and Departures
Length (ft.) Latitude
189.53
175.18
197.78
142.39
234.58
939.46
-188.403
-152.268
29.916
139.068
171.607
-0.079
Departure
-20.634
86.617
-195.504
-30.576
159.933
-0.163
Corrections
Latitude Departure
0.016
0.015
0.017
0.012
0.020
-20.601
86.648
0.033
0.030
0.034
0.025
0.041
Balanced
Latitude Departure
-188.388
-152.253
29.933
139.080
171.627
0.000
No error in corrected latitudes and departures
-20.601
86.648
-195.470
-30.551
159.974
0.000
Combining the latitude and departure calculations with
corrections gives:
Side
Corrections
Length (ft.) Latitude Departure Latitude Departure
Bearing
Balanced
Latitude
Departure
degree m inutes
AB
BC
CD
DE
EA
S
S
N
N
N
6
29
81
12
42
15
38
18
24
59
W
E
W
W
E
189.53
175.18
197.78
142.39
234.58
939.46
-188.403
-152.268
29.916
139.068
171.607
-0.079
-20.634
86.617
-195.504
-30.576
159.933
-0.163
0.016
0.015
0.017
0.012
0.020
0.033
0.030
0.034
0.025
0.041
-188.388
-152.253
29.933
139.080
171.627
0.000
-20.601
86.648
-195.470
-30.551
159.974
0.000
CIVL 1112
Surveying - Traverse Calculations
Surveying - Traverse
Surveying - Traverse
Group Example Problem 2
Group Example Problem 3
Balance the latitudes and departures for the following
traverse.
In the survey of your assign site in Project #3, you will
have to balance data collected in the following form:
Corrections
Balanced
Length (ft) Latitude Departure Latitude Departure Latitude Departure
450.00
-285.00
-164.46
0.54
339.00
259.50
-599.22
-0.72
B
N 69° 53’ E
A
N
600.0
450.0
750.0
1800.0
7/13
51° 23’
713.93 ft. 105° 39’
606.06 ft.
781.18 ft.
78° 11’
C
124° 47’
391.27 ft.
D
Surveying - Traverse
Surveying - Traverse
Calculating Traverse Area
Group Example Problem 3
In the survey of your assign site in Project #3, you will
have to balance data collected in the following form:
Side
Corrections
Length (ft.) Latitude Departure Latitude Departure
Bearing
Balanced
Latitude
Departure
degree m inutes
AB N
BC
CD
DA
69
53
E
713.93
606.06
391.27
781.18
Eclosure =
Precision =
 The meridian distance of a line is the east–west
distance from the midpoint of the line to the reference
meridian
 The meridian distance is positive (+) to the east and
negative (-) to the west
ft.
1
Surveying - Traverse
Calculating Traverse Area
N
Surveying - Traverse
Calculating Traverse Area
A
N 42° 59’ E
S 6° 15’ W
234.58 ft.
189.53 ft.
B
E
S 29° 38’ E
142.39 ft.
Reference
Meridian
 The best-known procedure for calculating land areas is
the double meridian distance (DMD) method
175.18 ft.
N 12° 24’ W
175.18 ft.
D N 81° 18’ W
C
 The most westerly and easterly points of a traverse may
be found using the departures of the traverse
 Begin by establishing a arbitrary reference line and using
the departure values of each point in the traverse to
determine the far westerly point
CIVL 1112
Surveying - Traverse Calculations
Surveying - Traverse
Surveying - Traverse
Calculating Traverse Area
Length (ft.) Latitude
189.53
175.18
197.78
142.39
234.58
939.46
Departure
-188.403
-152.268
29.916
139.068
171.607
-0.079
-20.634
86.617
-195.504
-30.576
159.933
-0.163
-20.601
-195.470
D
-30.551
E
D
Calculating Traverse Area
Corrections
Latitude Departure
0.016
0.015
0.017
0.012
0.020
B
0.033
0.030
0.034
0.025
0.041
N
Balanced
Latitude Departure
-188.388
-152.253
29.933
139.080
171.627
0.000
-20.601
86.648
-195.470
-30.551
159.974
0.000
Reference
Meridian
86.648
E
142.39 ft.
S 29° 38’ E
175.18 ft.
D N 81° 18’ W
C
Surveying - Traverse
DMD Calculations
DMD Calculations
The meridian distance of
line EA is:
A
N
Meridian distance
of line AB
N
B
 The meridian distance of line AB
is equal to:
A
the meridian distance of EA
+ ½ the departure of line EA
+ ½ departure of AB
B
 The DMD of line AB is twice the
meridian distance of line AB
A
E
E
C
189.53 ft.
N 12° 24’ W
Surveying - Traverse
D
S 6° 15’ W
234.58 ft.
E
C
C
Point E is the farthest
to the west
A
Reference
Meridian
N 42° 59’ E
175.18 ft.
159.974
N
A
B
A
B
8/13
E
DMD of line EA is the
departure of line
Surveying - Traverse
DMD Calculations
N
Meridian distance
of line AB
A
B
E
Surveying - Traverse
DMD Calculations
The DMD of any side is equal to
the DMD of the last side plus the
departure of the last side plus the
departure of the present side
Side
AB
BC
CD
DE
EA
Balanced
Latitude Departure
-188.388
-152.253
29.933
139.080
171.627
-20.601
86.648
-195.470
-30.551
159.974
The DMD of line AB is departure of line AB
DMD
-20.601
CIVL 1112
Surveying - Traverse Calculations
Surveying - Traverse
Surveying - Traverse
DMD Calculations
Side
AB
BC
CD
DE
EA
DMD Calculations
Balanced
Latitude Departure
-188.388
-152.253
29.933
139.080
171.627
-20.601 +
86.648 +
-195.470
-30.551
159.974
Side
DMD
-20.601
45.447
The DMD of line BC is DMD of line AB + departure of line AB
+ the departure of line BC
Surveying - Traverse
AB
BC
CD
DE
EA
DMD
-20.601
-20.601
45.447
86.648
-195.470 + -63.375
-30.551 + -289.397
159.974
Surveying - Traverse
AB
BC
CD
DE
EA
Balanced
Latitude Departure
-188.388
-152.253
29.933
139.080
171.627
DMD
-20.601
-20.601
45.447
86.648
-63.375
-195.470
-30.551 + -289.397
159.974 + -159.974
The DMD of line EA is DMD of line DE + departure of line DE
+ the departure of line EA
Traverse Area - Double Area
 The sum of the products of each points DMD and latitude
equal twice the area, or the double area
Balanced
Latitude Departure
-188.388
-152.253
29.933
139.080
171.627
DMD
-20.601
45.447
-63.375
Surveying - Traverse
DMD Calculations
AB
BC
CD
DE
EA
-20.601
86.648 +
-195.470 +
-30.551
159.974
The DMD of line CD is DMD of line BC + departure of line
BC + the departure of line CD
Side
The DMD of line DE is DMD of line CD + departure of line
CD + the departure of line DE
Side
-188.388
-152.253
29.933
139.080
171.627
DMD Calculations
Balanced
Latitude Departure
-188.388
-152.253
29.933
139.080
171.627
AB
BC
CD
DE
EA
Balanced
Latitude Departure
Surveying - Traverse
DMD Calculations
Side
9/13
-20.601
86.648
-195.470
-30.551
159.974
DMD
-20.601
45.447
-63.375
-289.397
-159.974
Notice that the DMD values can be positive or negative
Side
AB
BC
CD
DE
EA
Balanced
Latitude Departure
-188.388
-152.253
29.933
139.080
171.627
-20.601
86.648
-195.470
-30.551
159.974
DMD
Double Areas
-20.601
3,881
45.447
-63.375
-289.397
-159.974
 The double area for line AB equals DMD of line AB times
the latitude of line AB
CIVL 1112
Surveying - Traverse Calculations
Surveying - Traverse
Surveying - Traverse
Traverse Area - Double Area
Traverse Area - Double Area
 The sum of the products of each points DMD and latitude
equal twice the area, or the double area
Side
AB
BC
CD
DE
EA
Balanced
Latitude Departure
-188.388
-152.253
29.933
139.080
171.627
-20.601
86.648
-195.470
-30.551
159.974
DMD
Double Areas
-20.601
3,881
-6,919
45.447
-63.375
-289.397
-159.974
Surveying - Traverse
Balanced
Latitude Departure
-20.601
86.648
-195.470
-30.551
159.974
Surveying - Traverse
Balanced
Latitude Departure
1 acre = 43,560 ft.2
-20.601
86.648
-195.470
-30.551
159.974
 The sum of the products of each points DMD and latitude
equal twice the area, or the double area
AB
BC
CD
DE
EA
-188.388
-152.253
29.933
139.080
171.627
-20.601
86.648
-195.470
-30.551
159.974
DMD
Double Areas
-20.601
3,881
-6,919
45.447
-1,897
-63.375
-40,249
-289.397
-27,456
-159.974
 The double area for line EA equals DMD of line EA times
the latitude of line EA
 The sum of the products of each points DMD and latitude
equal twice the area, or the double area
Side
DMD
Double Areas
-20.601
3,881
45.447
-6,919
-63.375
-1,897
-289.397
-40,249
-159.974
-27,456
2 Area =
-72,641
Area =
Balanced
Latitude Departure
Traverse Area - Double Area
 The sum of the products of each points DMD and latitude
equal twice the area, or the double area
-188.388
-152.253
29.933
139.080
171.627
DMD
Double Areas
-20.601
3,881
-6,919
45.447
-1,897
-63.375
-289.397
-159.974
Surveying - Traverse
Traverse Area - Double Area
AB
BC
CD
DE
EA
-20.601
86.648
-195.470
-30.551
159.974
 The double area for line CD equals DMD of line CD times
the latitude of line CD
Side
DMD
Double Areas
-20.601
3,881
-6,919
45.447
-1,897
-63.375
-40,249
-289.397
-159.974
 The double area for line DE equals DMD of line DE times
the latitude of line DE
Side
-188.388
-152.253
29.933
139.080
171.627
Traverse Area - Double Area
 The sum of the products of each points DMD and latitude
equal twice the area, or the double area
-188.388
-152.253
29.933
139.080
171.627
AB
BC
CD
DE
EA
Balanced
Latitude Departure
Surveying - Traverse
Traverse Area - Double Area
AB
BC
CD
DE
EA
 The sum of the products of each points DMD and latitude
equal twice the area, or the double area
Side
 The double area for line BC equals DMD of line BC times
the latitude of line BC
Side
10/13
36,320 ft.2
0.834 acre
AB
BC
CD
DE
EA
Balanced
Latitude Departure
-188.388
-152.253
29.933
139.080
171.627
1 acre = 43,560 ft.2
-20.601
86.648
-195.470
-30.551
159.974
DMD
Double Areas
-20.601
3,881
45.447
-6,919
-63.375
-1,897
-289.397
-40,249
-159.974
-27,456
2 Area =
-72,641
Area =
36,320 ft.2
0.834 acre
CIVL 1112
Surveying - Traverse Calculations
Surveying - Traverse
Traverse Area - Double Area
11/13
Surveying - Traverse
Traverse Area - Double Area
 The word "acre" is derived from Old English æcer
(originally meaning "open field", cognate to Swedish
"åker", German acker, Latin ager and Greek αγρος
(agros).
 The word "acre" is derived from Old English æcer
(originally meaning "open field", cognate to Swedish
"åker", German acker, Latin ager and Greek αγρος
(agros).
 The acre was selected as approximately the amount of
land tillable by one man behind an ox in one day.
 A long narrow strip of land is more efficient to plough than
a square plot, since the plough does not have to be turned
so often.
 This explains one definition as the area of a rectangle with
sides of length one chain (66 ft.) and one furlong (ten
chains or 660 ft.).
 The word "furlong" itself derives from the fact that it is one
furrow long.
Surveying - Traverse
Traverse Area - Double Area
 The word "acre" is derived from Old English æcer
(originally meaning "open field", cognate to Swedish
"åker", German acker, Latin ager and Greek αγρος
(agros).
Surveying - Traverse
Traverse Area – Example 4
 Find the area enclosed by the following traverse
Side
Balanced
Latitude Departure
DMD
AB
BC
CD
DE
EA
600.0
100.0
0.0
-400.0
-300.0
Double Areas
200.0
400.0
100.0
-300.0
-400.0
2 Area =
1 acre = 43,560 ft.2
Surveying - Traverse
DPD Calculations
Area =
ft. 2
acre
Surveying - Traverse
Rectangular Coordinates
 The same procedure used for DMD can be used the
double parallel distances (DPD) are multiplied by the
balanced departures
 Rectangular coordinates are the convenient method
available for describing the horizontal position of survey
points
 The parallel distance of a line is the distance from the
midpoint of the line to the reference parallel or east–west
line
 With the application of computers, rectangular
coordinates are used frequently in engineering projects
 In the US, the x–axis corresponds to the east–west
direction and the y–axis to the north–south direction
CIVL 1112
Surveying - Traverse Calculations
Surveying - Traverse
Surveying - Traverse
Rectangular Coordinates Example
Rectangular Coordinates Example
In this example, the length of AB is 300 ft. and bearing is
shown in the figure below. Determine the coordinates of
point B
y
Latitude AB =300 ft. cos(4230’)
= 221.183 ft.
B
In this example, it is assumed that the coordinates of points
A and B are know and we want to calculate the latitude and
departure for line AB
y
A
Latitude AB = -400 ft.
x
Departure AB = x B – x A
Departure AB = 220 ft.
x B = 200 + 202.667 = 402.667 ft.
B
Surveying - Traverse
Rectangular Coordinates Example
Rectangular Coordinates Example
y
Consider our previous example, determine the x and y
coordinates of all the points
A
Side
AB
BC
CD
DE
EA
B
E
D
-20.601
86.648
-195.470
-30.551
159.974
x
C
Surveying - Traverse
Rectangular Coordinates Example
y
A
E
 x coordinates
E = 0 ft.
B
D
A = E + 159.974 = 159.974 ft.
x
C
B = A – 20.601 = 139.373 ft.
Side
AB
BC
CD
DE
EA
Balance d
Latitude De parture
-188.388
-152.253
29.933
139.080
171.627
-20.601
86.648
-195.470
-30.551
159.974
AB
BC
CD
DE
EA
D = C – 195.470 = 30.551 ft.
E = D – 30.551 = 0 ft.
Rectangular Coordinates Example
y
A (159.974, 340.640)
C = 0 ft.
D = C + 29.933 ft.
C
x
B (139.373, 152.253)
E = D + 139.080 = 169.013 ft.
Side
C = B + 86.648 = 226.021 ft.
Surveying - Traverse
 y coordinates
B
D
A
E
Balance d
Latitude De parture
-188.388
-152.253
29.933
139.080
171.627
x
Coordinates of Point B
(320, -100)
y B = 300 + 221.183 = 521.183 ft.
Surveying - Traverse
y
Latitude AB = y B – y A
Coordinates of Point A
(100, 300)
A
Departure AB =300 ft. sin(4230’)
= 202.677 ft.
N 42 30’ E
Coordinates of Point A
(200, 300)
12/13
Balance d
Latitude De parture
-188.388
-152.253
29.933
139.080
171.627
-20.601
86.648
-195.470
-30.551
159.974
(0.0, 169.013)
A = E + 171.627 = 340.640 ft.
E
B = A –188.388 = 152.252 ft.
(30.551, 29.933)
D
C = B –152.252 = 0 ft.
C (226.020, 0.0)
x
CIVL 1112
Surveying - Traverse Calculations
Surveying - Traverse
Surveying - Traverse
Area Computed by Coordinates
Group Example Problem 5
Compute the x and y coordinates from the following
balanced.
Side
Balanced
Length (ft.) Latitude Departure Latitude Departure
Bearing
Coordinates
x
y
Points
degree m inutes
AB
BC
CD
DE
EA
S
S
N
N
N
6
29
81
12
42
15
38
18
24
59
W
E
W
W
E
189.53
175.18
197.78
142.39
234.58
939.46
-188.403
-152.268
29.916
139.068
171.607
-0.079
-20.634
86.617
-195.504
-30.576
159.933
-0.163
-188.388
-152.253
29.933
139.080
171.627
0.000
13/13
-20.601
86.648
-195.470
-30.551
159.974
0.000
A
B
C
D
E
100.000
100.000
The area of a traverse can be computed by taking each y
coordinate multiplied by the difference in the two adjacent x
coordinates
(using a sign convention of + for next side and - for last
side)
Surveying - Traverse
Surveying - Traverse
Area Computed by Coordinates
Area Computed by Coordinates
y
A (159.974, 340.640)
Twice the area equals:
= 340.640(139.373 – 0.0)
 There is a simple variation of the coordinate
method for area computation
y
B (139.373, 152.253)
(0.0, 169.013) E
A (159.974, 340.640)
+ 152.253(226.020 – 159.974)
x1
y1
+ 0.0(30.551 – 139.373)
x2
y2
x3
y3
x4
y4
x5
y5
B (139.373, 152.253)
(30.551, 29.933)
+ 29.933(0.0 – 226.020)
D
(0.0, 169.013) E
Twice the area equals:
C (226.020, 0.0) x
+ 169.013(159.974 – 30.551)
= 72,640.433 ft.2
Area = 0.853 acre
Area Computed by Coordinates
 There is a simple variation of the coordinate
method for area computation
A (159.974, 340.640)
B (139.373, 152.253)
Twice the area equals:
159.974(152.253) + 139.373(0.0) +
226.020(29.933) + 30.551(169.013) +
0.0(340.640)
(0.0, 169.013) E
(30.551, 29.933)
- 340.640(139.373) – 152.253(226.020)
- 0.0(30.551) – 29.933(0.0)
– 169.013(159.974)
D
= x1y2 + x2y3 + x3y4 + x4y5 + x5y1
D
C (226.020, 0.0) x
- x2y1 – x3y2 – x4y3 – x5y4 – x1y5
Area = 36,320.2 ft.2
Surveying - Traverse
y
(30.551, 29.933)
C (226.020, 0.0) x
= -72,640 ft.2
Area = 36,320 ft.2
End of Surveying - Traverse
Any Questions?
x1
y1