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Leveling Part II: Differential Leveling

Faculty of Applied Engineering and Urban Planning. Surveying. Second Semester 2009/2010. Leveling Part II: Differential Leveling. Content. Computation of elevations using Method of Instrument Height Calculations Check Computation of elevations using Method of Rise and Fall

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Leveling Part II: Differential Leveling

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  1. Faculty of Applied Engineering and Urban Planning Surveying Second Semester 2009/2010 Leveling Part II: Differential Leveling

  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 A AC = 2.56 – 0.93 = 1.63 m

  5. Fall 0.64 2.97 K M NK = 0.64 – 2.97 = -2.33 m N

  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 2.97 0.64 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 + rise = 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 Distance (m) Longitudinal Section

  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 Distance (m) Longitudinal Section

  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

  18. 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

  19. HI = RL + BS

  20. 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 Distance (m) Distance (m) Longitudinal Section

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

  22. 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

  23. 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

  24. 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 Distance (m) Longitudinal Section

  25. 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

  26. 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

  27. 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

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

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

  30. 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

  31. 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

  32. 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 Distance (m) Distance (m) Longitudinal Section

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

  34. 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

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