1. TOPIC 5 TRAVERSING MS SITI KAMARIAH MD SA’AT LECTURER
SCHOOL OF BIOPROCESS ENGINEERING

2. Stationing Stations are dimensions measured along a baseline.
The beginning point is described as 0+00.
A point 100 ft(m) from the beginning is 1+00.
A point ft(m) from the beginning is
Points measured before the beginning station are 0-50, -1+00, etc.

3. Baseline Stations and Offset Distances

4. Overview In this lecture we will cover :
Rectangular and polar coordinates
Definition of a traverse
Applications of traversing
Equipment and field procedures
Reduction and adjustment of data

5. Rectangular coordinates
Point A
Point B
North
East EB NB
(EB,NB)
N=NB-NA EA NA
(EA,NA)
E=EB-EA

6. Polar coordinates North Point B d  Point A  ~ whole-circle bearing
East
Point A
Point B d 
 ~ whole-circle bearing
d ~ distance

7. Whole circle bearings North Bearing are measured 0o
clockwise from NORTH
and must lie in the range
0o    360o
4th quadrant
1st quadrant
West
270o
East
90o
3rd quadrant
2nd quadrant
South
180o

8. Coordinate conversions
Rectangular to polar
Polar to rectangular E N d  d  E N

9. 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, while distances can be measured using total stations, steel tapes or EDM.

10. 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
A closed
traverse
A traverse between
known points

11. Types of Traverses Open Traverse using deflection angles.
Closed traverse using interior angles.

12. Open Traverse

13. Closed Traverse

14. Applications of traversing
Establishing coordinates for new points
(E,N)known
(,d)
(,d)
(,d)
(E,N)new
(E,N)new

15. Applications of traversing
These new points can then be used as a framework for mapping existing features
(E,N)new
(E,N)known
(E,N)new
(E,N)new
(E,N)new
(,d)
(,d)

16. Applications of traversing
They can also be used as a basis for setting out new work
(E,N)new
(E,N)known

17. Equipment Traversing requires :
An instrument to measure angles (theodolite) or bearings (magnetic compass)
An instrument to measure distances (EDM or tape)

18. Computation of Latitudes and Departures
Latitude-north/south rectangular component of line (North +;South -)
Latitude (ΔY) = distance(H) cos α
Departure-east/west rectangular component of line (East +;West -)
Departure (ΔX) = distance(H) sin α
Where:
α = bearing or azimuth of the traverse course
H = the horizontal distance of the traverse course

19. Location of a Point

20. Closure of Latitudes and Departures

21. Latitude / Departure Computations

22. Measurement sequence C B D A E 232o 168o 60.63 99.92 56o 352o 205o
77.19
129.76
21o A
118o
32.20
303o
48o E

23. Computation sequence Calculate angular (bearing/azimuth) misclose
Adjust angular (bearing/azimuth) misclose
Calculate adjusted bearings
Reduce distances for slope etc…
Compute (E, N) for each traverse line
Calculate linear misclose
Calculate accuracy
Adjust linear misclose.

24. Calculate internal angles
Point
Foresight
Bearing
Backsight
Internal
Angle
Adjusted A
21o
118o
97o B
56o
205o
149o C
168o
232o
64o D
352o
120o E
303o
48o
105o
 =(n-2)*180
Misclose
Adjustment
At each point :
Measure foresight bearing
Measure backsight bearing
Calculate internal angle (back-fore)
For example, at B :
Bearing to C = 56o
Bearing to A = 205o
Angle at B = 205o - 56o = 149o

25. Calculate angular misclose
Point
Foresight
Bearing
Backsight
Internal
Angle
Adjusted A
21o
118o
97o B
56o
205o
149o C
168o
232o
64o D
352o
120o E
303o
48o
105o
 =(n-2)*180
535o
Misclose
-5o
Adjustment
-1o

26. Calculate adjusted angles
Point
Foresight
Bearing
Backsight
Internal
Angle
Adjusted A
21o
118o
97o
98o B
56o
205o
149o
150o C
168o
232o
64o
65o D
352o
120o
121o E
303o
48o
105o
106o
 =(n-2)*180
535o
540o
Misclose
-5o
Adjustment
-1o

27. Compute adjusted bearings
Adopt a starting bearing
Then, working clockwise around the traverse :
Calculate reverse bearing to backsight (forward bearing 180o)
Subtract (clockwise) internal adjusted angle
Gives bearing of foresight
For example (bearing of line BC)
Adopt bearing of AB 23o
Reverse bearing BA (=23o+180o) 203o
Internal adjusted angle at B 150o
Forward bearing BC (=203o-150o) 53o

28. Compute adjusted bearings
Line
Forward Bearing
Reverse Bearing
Internal Angle AB
23o
203o
150o BC
53o CD DE EA
53o B
150o D
203o A E

29. Compute adjusted bearings
Line
Forward Bearing
Reverse Bearing
Internal Angle AB
23o
203o
150o BC
53o
233o
65o CD
168o DE EA
233o
65o
168o B D
23o A E

30. Compute adjusted bearings
Line
Forward Bearing
Reverse Bearing
Internal Angle AB
23o
203o
150o BC
53o
233o
65o CD
168o
348o
121o DE
227o EA
53o
348o B
121o D
23o
227o A E

31. Compute adjusted bearings
Line
Forward Bearing
Reverse Bearing
Internal Angle AB
23o
203o
150o BC
53o
233o
65o CD
168o
348o
121o DE
227o
47o
106o EA
-59o
301o
53o
168o B D
23o
47o A
106o
301o E

32. Compute adjusted bearings
Line
Forward Bearing
Reverse Bearing
Internal Angle AB
23o
203o
150o BC
53o
233o
65o CD
168o
348o
121o DE
227o
47o
106o EA
301o
98o
23o (check)
53o
168o B D
23o
227o
98o A
121o E

33. (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

34. Vector components Line Bearing Distance E N AB 23o 77.19 30.16 71.05BC
53o
99.92
79.80
60.13 CD
168o
60.63
12.61
-59.31 DE
227o
129.76
-94.90
-88.50 EA
301o
32.20
-27.60
16.58 
(399.70)
(0.07)
(-0.05)

35. Closure Error and Closure Correction

36. Compass Rule – distributes the errors in lat/dep.
C lat AB= AB
Σ lat P
C dep AB = AB
Σ dep P
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

37. Linear misclose & accuracy
Convert the rectangular misclose components to polar coordinates
Accuracy is given by
Beware of quadrant when
calculating  using tan-1

38. Quadrants and tan functionE + 
negative
add 360o +
positive
okay 
positive
add 180o  +
negative
add 180o

39. For the example… Misclose (E, N) Convert to polar (,d) Accuracy
(0.07, -0.05)
Convert to polar (,d)
 = o (2nd quadrant) = o
d = 0.09 m
Accuracy
1:( / 0.09) = 1:4441

40. Bowditch adjustment
The adjustment to the easting component of any traverse side is given by :
Eadj = Emisc * side length/total perimeter
The adjustment to the northing component of any traverse side is given by :
Nadj = Nmisc * side length/total perimeter

41. The example… East misclose 0.07 m North misclose –0.05 m
Side AB m
Side BC m
Side CD m
Side DE m
Side EA m
Total perimeter m

42. Vector components (pre-adjustment)
Side E N
dE
dN
Eadj
Nadj 1A
30.16
71.05 AB
79.80
60.13 BC
12.61
-59.31 CD
-94.90
-88.50 D1
-27.60
16.58
Misc
(0.07)
(-0.05)

43. The adjustment components
Side E N
dE
dN
Eadj
Nadj 1A
30.16
71.05
0.014
-0.010 AB
79.80
60.13
0.016
-0.012 BC
12.61
-59.31
0.011
-0.008 CD
-94.90
-88.50
0.023
-0.016 D1
-27.60
16.58
0.006
-0.004
Misc
(0.07)
(-0.05)
(0.070)
(-0.050)

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

45. Summary of initial traverse computation
Balance the angle
Compute the bearing or azimuth
Compute the latitude and departure, the linear error of closure, and the precision ratio of the traverse

46. THANK YOU