1. ANGLE AND DIRECTION MEASUREMENT
TOPIC 4
ANGLE AND DIRECTION MEASUREMENT
MS SITI KAMARIAH MD SA’AT
LECTURER
SCHOOL OF BIOPROCESS ENGINEERING

2. Introduction
An angle is defined as the difference in direction between two convergent lines.

3. Types of Angles
Vertical angles
Zenith angles
Nadir angles

4. Definition
A vertical angle is formed by two intersecting lines in a vertical plane, one of these lines horizontal.
A zenith angle is the complementary angle to the vertical angle and is directly above the obeserver
A Nadir angle is below the observer

5. Three Reference Directions - Angles

6. Meridians
A line on the mean surface of the earth joining north and south poles is called
meridian.
Note:
Geographic meridians are fixed, magnetic meridians vary with time and location.
Figure 4.2
Relationship between “true” meridian and grid meridians

7. Geographic and Grid Meridians

8. Horizontal Angles
A horizontal angle is formed by the directions to two objects in a horizontal plane.
Interior angles
Exterior angles
Deflection angles

9. Closed Traverse

10. Open Traverse

11. Directions Azimuth Bearing
An Azimuth is the direction of a line as given by an angle measured clockwise (usually) from the north.
Azimuth range in magnitude from 0° to 360°.
Bearing
Bearing is the direction of a line as given by the acute angle between the line and a meridian.
The bearing angle is always accompanied by letters that locate the quadrant in which line falls (NE, NW, SE or SW).

12. Azimuths

13. Bearing

14. Relationships Between Bearings and Azimuths
To convert from azimuths to bearing,
a = azimuths
b = bearing
Quadrant
Angles
Conversion NE
0o  90o
a = b SE
90o  180o
a = 180o – b SW
180o  270o
a = b +180o NW
270o  360o
a = 360o – b

15. Reverse Direction In figure 4.8 , the line
AB has a bearing of N 62o 30’ E
BA has a bearing of S 62o 30’ W
To reverse bearing: reverse the direction
Line
Bearing AB
N 62o 30’ E BA
S 62o 30’ W
Line
Bearing AB
N 62o 30’ E BA
S 62o 30’ W
Figure 4.7
Figure 4.8
Reverse Directions
Reverse Bearings

17. Reverse Direction Line Azimuths CD has an azimuths of 128o 20’
DC has an azimuths of 308o 20’
To reverse azimuths: add 180o
Line
Azimuths CD
128o 20’ DC
308o 20’
Figure 4.8
Reverse Bearings

18. Counterclockwise Direction (1)
Start
Given

19. Counterclockwise Direction (2)

20. Counterclockwise Direction (3)

21. Counterclockwise Direction (4)

22. Counterclockwise Direction (5)
Finish
Check

23. Sketch for Azimuth Computation

24. Clockwise Direction (1)
Start
Given

25. Clockwise Direction (2)

26. Clockwise Direction (3)

27. Clockwise Direction (4)

28. Clockwise Direction (5)
Finish
Check

29. Finish
Check
Start
Given

30. Azimuth Computation
When computations are to proceed around the traverse in a clockwise direction,subtract the interior angle from the back azimuth of the previous course.
When computations are to proceed around the traverse in a counter-clockwise direction, add the interior angle to the back azimuth of the previous course.

31. Azimuths Computation
Counterclockwise direction: add the interior angle to the back azimuth of the previous course
Course
Azimuths
Bearing BC
270o 28’
N 89o 32’ W CD
209o 05’
S 29o 05’ W DE
134o 27’
S 45o 33’ E EA
62o 55’
N 62o 55’ E AB
330o 00’
N 30o 00’ W

32. Azimuths Computation
Clockwise direction: subtract the interior angle from the back azimuth of the previous course
Course
Azimuths
Bearing AE
242o 55’
S 62o 55’ W ED
314o 27’
N 45o 33’ W DC
29o 25’
N 29o 05’ E CB
90o 28’
S 89o 32’ E BA
150o 00’
S 30o 00’ E

33. Bearing Computation
Prepare a sketch showing the two traverse lines involved, with the meridian drawn through the angle station.
On the sketch, show the interior angle, the bearing angle and the required angle.

34. Bearing Computation
Computation can proceed in a Clockwise or counterclockwise
Figure 4.11
Sketch for Bearings Computations

35. Sketch for bearing Computation

36. Comments on Bearing and Azimuths
Advantage of computing bearings directly from the given data in a closed traverse, is that the final computation provides a check on all the problem, ensuring the correctness of all the computed bearings

37. Angle Measuring Equipment
Plane tables (graphical methods)
Sextants
Compass
Tapes (or other distance measurement)
Repeating instruments
Directional instruments
Digital theodolites and total stations

38. Determining Angles – Taping
Lay off distance d either side of X l
Swing equal lengths (l)
Connect point of intersection and X X
Need to: measure 90° angle at point X

39. Determining Angles – Taping
Measure distance AB Measure distance AC Measure distance BC
Compute angle  B  A C
Need to: measure angle  at point A

40. Determining Angles – Taping A B C
Lay off distance AP Establish QP AP Measure distance QP
Compute angle  P Q
Need to: measure angle  at point A

41. Determining Angles – Taping A B C D
Lay off distance AD Lay off distance AE = AD Measure distance DE
Compute angle  E
Need to: measure angle  at point A

42. Repeating Instruments
Very commonly used
Characterized by double vertical axis
Three subassemblies

43. Directional Instruments
Has single vertical axis
Zero cannot be set
More accurate but less functional

44. Total Stations
Combined measurements
Digital display

45. Measuring Angles Instrument handling and setup
Discussed in lab
Procedure with repeating instrument

46. Angles Backsight: The baseline or point used as zero angle.
All angles have three parts
Backsight: The baseline or point used as zero angle.
Vertex: Point where the two lines meet.
Foresight: The second line or point

47. Repetition and Centering
Repetition provides advantages
Centering process

48. “Centering”

49. Measuring Angles Procedure with directional instruments
Most total stations are directional instruments

50. Angle Measuring Errors and Mistakes
Instrumental errors
Natural errors
Personal errors
Mistakes

51. THANK YOU