Faculty of Applied Engineering and Urban Planning

1. Faculty of Applied Engineering and Urban Planning Civil Engineering Department Surveying First Semester 2010/2011 Leveling Part II: Differential Leveling Lecture 10- Week 6

2. Content • Computation of elevations using Method of Instrument Height • Calculations Check • Computation of elevations using Method of Rise and Fall • Calculations Check

3. Measuring Elevation Difference Using a level • The basic operation in differential leveling is the determination of elevation differences between two points • Consider two points A and B as shown • Set up the level so that readings may be made on a staff held vertically at A and then at B B A

4. Rise 2.56 0.93 C B AC = 2.56 – 0.93 = 1.63 m A Second reading smaller than first reading represents a rise

5. Fall 0.64 2.97 K M NK = 0.64 – 2.97 = -2.33 m N Second reading greater than first reading represents a fall

6. Calculation of Elevation The height of instrument method Elevation of Point A = 520.43 m AMSL Height of Instrument HI = Elevation Of A + Staff Reading = 520.43 + 2.56 = 522.99 m AMSL Elevation of B = HI – Staff Reading at B = 522.99 – 0.93 = 522.06 m AMSL 0.93 2.56 C B A

7. Calculation of Elevation The height of instrument method Elevation of Point M = 520.43 m AMSL Height of Instrument HI = Elevation Of M + Staff Reading = 520.43 + 0.64 = 521.07 m AMSL Elevation of N = HI – Staff Reading at N = 521.07 – 2.97 = 518.10 m AMSL 0.64 2.97 K M N

8. Calculation of Elevation The rise and fall method Elevation of Point A = 520.43 m AMSL Elevation Difference = Elevation Of A - Elevation Of B = 2.56 – 0.93 = 1.63 m (rise) Elevation of B = Elevation at A + rise = 520.43 + 1.63 = 522.06 m AMSL 0.93 2.56 C B A

9. Calculation of Elevation The rise and fall method Elevation of Point M = 520.43 m AMSL Elevation Difference = Elevation Of M - Elevation Of N = 0.64 – 2.97 = - 2.33 m (fall) Elevation of N = Elevation at M + fall = 520.43 - 2.33 = 518.10 m AMSL 2.97 0.64 K M N

10. Definitions Backsight (BS) This is the first reading taken by the observer at every instrument station after setting up the level Foresight (FS) This is the last reading taken at every instrument station before moving the level Intermediate Sight (IS) This is any reading taken at an instrument station between the backsight and the foresight Turning point (TP) This point at which both a foresight and a backsight are taken before moving the staff

11. Calculation of Elevation B A 1 C G D F E BM RL = 98.76 m AMSL Plan G F 1 BM B E C D A 0 20 40 60 80 100 120 Distance (m) Longitudinal Section

12. Calculation of Elevation Instrument Station 1 P BM RL = 98.76 m AMSL Plan Backsight (BS) 0.663 1 BM 0 Longitudinal Section Distance (m)

13. Calculation of Elevation B A 1 C P G D F E BM Q RL = 98.76 m AMSL Plan 2.270 2.787 1.218 0.646 1.153 1.946 1.008 1.585 0.663 G F Q 1 BM B P E C D A 0 20 40 60 80 100 120 Longitudinal Section Distance (m)

14. HI = RL + BS

15. Calculation of Elevation B A 1 C P BM RL = 98.76 m AMSL Plan Intermediate Sights (IS) 1.153 1.946 1.008 0.663 1 BM B P C A 0 20 40 Distance (m) Longitudinal Section

16. RL = HI - IS

17. Calculation of Elevation B A 1 C P D BM RL = 98.76 m AMSL Plan Foresight (FS) 1.153 1.946 1.008 1.585 0.663 1 BM B P C D A 0 20 40 60 Distance (m) Longitudinal Section

19. Calculation of Elevation B A 1 C P D BM Q RL = 98.76 m AMSL Plan Turning Point (TP) Backsight (BS) 2.787 1.153 1.946 1.008 1.585 0.663 Q 1 BM B P C D A 0 20 40 60 Longitudinal Section Distance (m)

20. HI = RL + BS

21. Calculation of Elevation B A 1 C P G D D F E BM Q RL = 98.76 m AMSL Plan 2.270 2.787 1.218 0.646 1.153 1.946 1.008 1.585 0.663 G F Q 1 BM B E P C D A 80 100 120 0 20 40 60 Longitudinal Section Distance (m)

23. Check 1 No. of BS = No. of FS No. of BS = 2 No. of FS = 2

24. Check 2 ΣBS - ΣFS = RL of last point - RL of first point ΣBS - ΣFS = 3.450 – 2.231 = 1.219 RLlast - RLfirst = 99.979 – 98.760 = 1.219

25. Check 3 ΣRL – RLfirst point = [Σ (No. of IS and FS × HI)] - Σ IS- Σ FS ΣRL – RLfirst point = 689.741 [Σ (No. of (IS and FS) × HI)] - Σ IS- Σ FS = [ 99.423×4 + 100.625×3] – 7.595 – 2.231 = 689.741

26. Calculation of Elevation B A 1 C P G D F E BM Q RL = 98.76 m AMSL Plan 2.270 2.787 1.218 0.646 1.153 1.946 1.008 1.585 0.663 G F Q 1 BM B P E C D A 0 20 40 60 80 100 120 Longitudinal Section Distance (m)

27. Calculation of Elevation The rise and fall method Elevation of Point A = 520.43 m AMSL Elevation Difference = Elevation Of A - Elevation Of B = 2.56 – 0.93 = 1.63 m (rise) Elevation of B = Elevation at A + rise = 520.43 + 1.63 = 522.06 m AMSL 0.93 2.56 C B A

28. Calculation of Elevation The rise and fall method Elevation of Point A = 520.43 m AMSL Elevation Difference = Elevation Of A - Elevation Of B = 0.64 – 2.97 = - 2.33 m (fall) Elevation of B = Elevation at A + rise = 520.43 - 2.33 = 518.10 m AMSL 2.97 0.64 C A B

29. Calculation of Elevation B A 1 C G D F E BM RL = 98.76 m AMSL Plan G F 1 BM B E C D A 0 20 40 60 80 100 120 Distance (m) Longitudinal Section

30. Calculation of Elevation Instrument Station 1 P BM RL = 98.76 m AMSL Plan Backsight (BS) 0.663 1 BM 0 Longitudinal Section Distance (m)

31. ΔH1A = BS – IS = 0.633 – 1.946 = -1.283 (fall)

32. Calculation of Elevation B A 1 C P D BM RL = 98.76 m AMSL Plan Intermediate Sights (IS) Foresight (FS) 1.153 1.946 1.008 1.585 0.663 1 BM B P C D A 0 20 40 Distance (m) Longitudinal Section

34. Calculation of Elevation B A 1 C P D BM Q RL = 98.76 m AMSL Plan Turning Point (TP) Backsight (BS) 2.787 1.153 1.946 1.008 1.585 0.663 Q 1 BM B P C D A 0 20 40 60 Distance (m) Longitudinal Section

36. Calculation of Elevation B A 1 C P G D D F E BM Q RL = 98.76 m AMSL Plan 2.270 2.787 1.218 0.646 1.153 1.946 1.008 1.585 0.663 G F Q 1 BM B E P C D A 80 100 120 0 20 40 60 Longitudinal Section Distance (m)

38. Check 1 No. of BS = No. of FS No. of BS = 2 No. of FS = 2

39. Check 2 ΣBS - ΣFS = ΣRise – ΣFall = RLlast – RLfirst 3.450 – 2.231 = 3.079 – 1.860 = 99.979 - 98.760 1.219 = 1.219 = 1.219

40. Questions?!