Angles and Directions in Measurement Techniques

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

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 • 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

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 Figure 4.7 Figure 4.8 Reverse Directions Reverse Bearings

17. Reverse Direction • CD has an azimuths of 128o 20’ • DC has an azimuths of 308o 20’ To reverse azimuths: add 180o 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. Start Given Finish Check

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

32. Azimuths Computation • Clockwise direction: subtract the interior angle from the back azimuth of the previous course

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

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

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

41. Lay off distance ADLay off distance AE = ADMeasure distance DE Compute angle  B D  A E C Determining Angles – Taping 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 • 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. Instrumental errors Natural errors Personal errors Mistakes Angle Measuring Errors and Mistakes