Traversing in geomatics engineering

1. MMJ14203
GEOMATICS ENGINEERING
MRS SITI KAMARIAH MD SA’AT
FKTM
UniMAP

2. TRAVERSING

3. TYPES OF COORDINATE
• It is split into four quadrants with the typical mathematical convention of the axis
to the north and east being positive and to the south and west, negative.
• The x-axis is referred to as the east-axis (E) and the y-axis as the north-axis
(N), with angles (a) measured clockwise from the N-axis, (E,N)
Rectangular Coordinate
• Polar coordinate used distance and whole circle bearing of the line
• Used to define the relative position of one point to another
• (d,β)
Polar Coordinate

4. RECTANGULAR COORDINATES
E=EB-EA
EA
NA
(EA,NA)
EB
N
B
(EB,NB)
Point A
Point B
North
East
N=NB-NA

5. RECTANGULAR COORDINATES

6. POLAR COORDINATES

d
North
East
Point A
Point B
 ~ whole-circle bearing/Azimuth
d ~ distance
Computing the polar for a line involves calculating E and N given the
horizontal distance (d) and WCB (β) of the line.

7. POLAR COORDINATES

8. COORDINATE CONVERSIONS
2
2
1
N
E
d
N
E
tan













 






cos
d
N
sin
d
E
Rectangular to polar Polar to rectangular
d

E
N d

E
N

9. EXAMPLE 6.1:
 Given the coordinates of A and the distance and bearing of
AB, calculate the coordinates of B.
EA = 48 964.38 m, NA= 69 866.75 m,
WCB AB = 299◦58’46”
Horizontal distance = 1325.64 m
Solution:
 EB= EA+ ∆EAB = 48 964.38 + dsinβ
= 48 964.38 + 1325.64 sin 299◦58’46”
=
 NB= NA+ ∆NAB = 69 866.75 + dcosβ
= 69 866.75 + 1325.64 cos 299◦58’46”
=

10. EXAMPLE 6.2:
 Given the following coordinates for two points A and B,
compute the length and bearing of AB.
EA = 48 964.38 m, NA = 69 866.75 m
EB= 48 988.66 m , NB= 62 583.18 m
Answer:
dAB = 7283.61 m
β= 179◦48’33”
2
2
1
N
E
d
N
E
tan













 

11. DEFINITIONS
Traverse
• Series of straight lines connecting
survey stations (begin at known points
as baseline)
Traversing
• Determination of horizontal coordinates
by measuring horizontal angles &
distances

12. WHAT IS A
TRAVERSE?
 Control survey
 A series of established stations tied
together by angle and distance.
 The angles are measured using
theodolites/total station/compass, while
distances can be measured using total
stations or tapes or EDM.

13. WHAT IS A TRAVERSE?
 A polygon of 2D (or 3D) vectors
 Sides are expressed as either polar coordinates (,d) or as
rectangular coordinate differences (E,N)
 A traverse must either close on itself
 Or be measured between points with known rectangular
coordinates.

14. TYPES OF TRAVERSES
 Open Traverse: Use as pipeline, highways, railways, etc.
 Closed traverse: Use to locate lakes, land boundaries and control mapping
A closed
traverse
A traverse between
known points

15. OPEN TRAVERSE

16. CLOSED TRAVERSE

17. WHY TRAVERSING?

18. APPLICATIONS OF TRAVERSING
 Establishing coordinates for new points
(

,
d
)
(,d)
(
,d)
(E,N)new
(E,N)new
(E,N)known
(E,N)known

19. APPLICATIONS OF TRAVERSING
 These new points can then be used as a framework for
mapping existing features
(

,
d
)
(
,d)
(,d)
(,d) (,d)
(

,
d
)
(E,N)new
(E,N)new
(E,N)new
(E,N)new
(E,N)new
(E,N)known
(E,N)known

20. APPLICATIONS OF TRAVERSING
 They can also be used as a basis for setting out new work
(E,N)new
(E,N)new
(E,N)known
(E,N)known

21. EQUIPMENT
 Traversing requires :
 An instrument to measure angles
(theodolite) or bearings (magnetic
compass)
 An instrument to measure distances
(EDM or tape)

22. EQUIPMENT
 Or use of total station that can measure both distance and angles

23. OBSERVATION OF TRAVERSE
 The methods used in observing angles and direction:
 Interior Angles
 To reduce mistakes in reading, recording and computing, always turned clockwise from
backsight station to foresight station
 Angles to the right
 To avoid ambiguity in angles to right, forward traverse station must be established.
 Deflection Angles
 For route survey
 Azimuth
 By total station, reading azimuth at all lines and thus eliminate the need to calculate
them.

24. OBSERVATION OF TRAVERSE
 Observation of traverse length
 By simplest and economical ways
 High precision
 Use stationing

25. CHOOSING LOCATION OF
TRAVERSE STATIONS
Some practical guidelines:
1. Minimum no. of stations (each line of sight as long as
possible)
2. Ensure: adjacent stations always inter-visible
3. Avoid acute traverse angles
4. Stable & safe ground conditions for instrument
5. Marked with paint or/and nail; to survive subsequent traffic,
construction, weather conditions, etc.

26. CHOOSING LOCATION OF TRAVERSE
STATIONS
6. Include existing stations/reference objects for checking
with known values
7. Traverse must not cross itself
8. Network formed by stations (if any): as simple as
possible
9. Do the above without sacrificing accuracy or omitting
important details

27. TRAVERSE FIELD NOTES

28. COMPUTATION SEQUENCE
1. Compute (E, N) or (X, Y) for each traverse line
2. Calculate linear misclose
3. Calculate accuracy and precision
4. Adjust linear misclose.

29. COMPUTATION OF LATITUDES AND
DEPARTURES
 Latitude-north/south rectangular component of line (North +;South -)
Latitude (ΔN) = distance(H) cos α
 Departure-east/west rectangular component of line (East +;West -)
Departure (ΔE) = distance(H) sin α
Where:
α = bearing or azimuth of the traverse course
H = the horizontal distance of the traverse course

30. LOCATION OF A POINT

31. CLOSURE OF LATITUDES AND DEPARTURES

32. (E,N) FOR EACH LINE
 The rectangular components for each line are computed from the polar
coordinates (,d)
 Note that these formulae apply regardless of the quadrant so long as
whole circle bearings are used






cos
d
N
sin
d
E

33. LATITUDE / DEPARTURE COMPUTATIONS

34. EXAMPLE: OBSERVATION SEQUENCE
7
7
.
1
9
99.92
6
0
.
6
3
129.76
3
2
.
2
0
A
B
C
D
E
2
3
o
53
o
1
6
8
o
227
o
3
0
1
o
1
2
1
o
Start at A

35. EXAMPLE: VECTOR COMPONENTS
Line Bearing, β Distance, d N
(Lat=
dcosβ)
E
(Dep=
dsinβ)
AB 23o
77.19 71.05 30.16
BC 53o
99.92 60.13 79.80
CD 168o
60.63
-
59.31 12.61
DE 227o
129.76
-
88.50
-
94.90
EA 301o
32.20 16.58
-
27.60

(399.70)
(-
0.05) (0.07)

36. CLOSURE ERROR AND CLOSURE
CORRECTION

37. LINEAR MISCLOSE &
ACCURACY
 Convert the rectangular misclose components to polar coordinates
 Precision is given by
2
2
1
N
E
d
N
E
tan













 
)
misclose
linear
/
length
traverse
(
:
1
Beware of quadrant when
calculating  using tan-1
Linear misclosure, E =
Precision= 1/(total distance/misclosure)

38. N
E


b positive
add 180
o
QUADRANTS AND TAN FUNCTION

+
b negative
add 180o
+

b negative
add 360
o
+
+
b positive
okay

39. FOR THE EXAMPLE…
 Misclose (E, N)
 (0.07, -0.05)
 Convert to polar (,d)
  = -54.46o
(2nd
quadrant) = 125.53o
 d = 0.09 m
 Accuracy
 1:(399.70 / 0.09) = 1:4441

40. COMPASS RULE (BOWDITCH METHOD)
– DISTRIBUTES THE ERRORS IN LAT/DEP.
Where:
C lat AB = correction in latitude AB
∑ lat = error of closure in latitude
AB = distance AB
P = perimeter of traverse
Where:
C dep AB = correction in departure AB
∑ lat = error of closure in departure
AB = distance AB
P = perimeter of traverse
C dep AB = AB
Σ dep P
C lat AB= AB
Σ lat P

41. THE EXAMPLE…
 East misclose 0.07 m
 North misclose –0.05 m
 Side AB 77.19 m
 Side BC 99.92 m
 Side CD 60.63 m
 Side DE 129.76 m
 Side EA 32.20 m
 Total perimeter 399.70 m

42. VECTOR COMPONENTS (PRE-ADJUSTMENT)
Side N E d CN CE Nadj Eadj
EA
71.05 30.16
77.19
AB
60.13 79.80
99.92
BC
-59.31 12.61
60.63
CD
-88.50 -94.90
129.76
DE
16.58 -27.60
32.20
Misc
(-0.05) (0.07)
399.7

43. THE ADJUSTMENT COMPONENTS
Side N E CN CE Nadj Eadj
1A
71.05 30.16
-
0.010 0.014
AB
60.13 79.80
-
0.012 0.016
BC
-
59.31 12.61
-
0.008 0.011
CD
-
88.50
-
94.90
-
0.016 0.023
D1
16.58
-
27.60
-
0.004 0.006
Misc
(-
0.05) (0.07) (-0.050) (0.070)
C lat AB= AB X Σ lat
P
C dep AB= AB X Σ dep
P

44. ADJUSTED VECTOR COMPONENTS
Side N E CN CE Nadj Eadj
1A
71.05 30.16
-
0.010 0.014 71.060 30.146
AB
60.13 79.80
-
0.012 0.016 60.142 79.784
BC
-
59.31 12.61
-
0.008 0.011
-
59.302 12.599
CD
-
88.50
-
94.90
-
0.016 0.023
-
88.484
-
94.923
D1
16.58
-
27.60
-
0.004 0.006 16.584
-
27.606
Misc
(-0.05) (0.07)
-
0.050 0.070 (0.000) (0.000)

45. SUMMARY OF INITIAL TRAVERSE
COMPUTATION
Balance the angle
1
Compute the bearing
or azimuth
2
Compute the latitude
and departure, the
linear error of closure,
and the precision ratio
of the traverse
3

46. SOURCES OF ERROR IN TRAVERSING
Poor selection of station resulting in bad sighting condition cause by
• shadow,
• Line of sight passing too close to the ground
• Lines are too short
• Sighting into the sun
Error in observations of angles and distances
Failed to observed angles an equal times direct and reversed

47. MISTAKES IN TRAVERSING
Occupying or
sighting the
wrong stations
Incorrect
orientation
Confusing
angles to the
right and left
Mistakes in note
taking
Misidentification
of station

48. QUIZIZZ
Let’s know your understanding to the topics

49. THANK YOU