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Leveling Part II: Differential Leveling

Faculty of Applied Engineering and Urban Planning. Surveying. Civil Engineering Department. 2 nd Semester 2007/2008. Leveling Part II: Differential Leveling. Content. Definitions Basic Principle of A Level Bubble Tube Equipment Measuring Elevation Difference using A Level. Definitions.

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Leveling Part II: Differential Leveling

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  1. Faculty of Applied Engineering and Urban Planning Surveying Civil Engineering Department 2nd Semester 2007/2008 Leveling Part II: Differential Leveling

  2. Content • Definitions • Basic Principle of A Level • Bubble Tube • Equipment • Measuring Elevation Difference using A Level

  3. Definitions Leveling Leveling is the operation required in the determination or, more strictly, the comparison, of heights of points on the surface of the earth.

  4. Definitions Datum If a whole series of heights is given relative to a plane, this plane is called a datum, In topographical work the datum used is the mean level of the sea (MSL)

  5. Definitions Horizontal Line Line of Sight Vertical Line Level Surface Level Line

  6. Definitions Vertical Line at a point The line formed by the string of a plumb bob when the tip is located directly over the point. Horizontal Line at a point The straight line perpendicular to the vertical line at that point Level Surface The continuously curved surface that is perpendicular to the direction of gravity at all points.

  7. Definitions Level Line A line that lies on the level surface. Difference in Elevation between two points The vertical distance between the two level surfaces passing through these two points Line of Sight or Collimation Neither horizontal nor level. Affected by atmospheric refraction. Horizontal Line Line of Sight Vertical Line Level Surface Level Line

  8. Definitions Bench Mark A marked point whose elevation has been accurately measured. Height of Instrument The line of Collimation above the datum after setting up the level above a certain point Horizontal Line Line of Sight Vertical Line Level Surface Level Line

  9. Differential Leveling • Differential Leveling Requires: • a device which gives a truly horizontal line (the Level), • a suitably graduated staff for reading vertical heights (the Leveling Staff) .

  10. Level • Level consists mainly of: • Telescope for Sighting • A leveling device for maintaining the line of sight horizontal.

  11. Equipments • Equipments needed for differential leveling • Level • Dumpy Level : In this type of instrument the line of sight defined by the center of the cross hairs and the optical center of the objective lens - the line of collimation - is fixed at right angles to the vertical axis of rotation of the instrument. When level, the line of collimation should describe a true horizontal plane around the instrument • 2. Tilting Level: the telescope is hinged near the top of the vertical axis to allow a limited degree of movement with respect to the vertical axis. Like the dumpy level the spirit level is attached to the telescope.

  12. Equipments • 3. Automatic Level : Many modem levels use a system of self leveling • compensators within the optical system of the telescope. • This requires the observer to level the instrument within the working range of the compensator, which is usually about +20' of the horizontal. The vertical axis may be supported by a three-screw • 4. Electronic Digital : This kind of level combines the merits of the automatic level with the fact that it is user friendly and easy to use. All the user has to do is aim the staff, adjust the focus and then - with a single touch of a key - the level will accurately measure and record the staff reading on a display. • Tripod • Staves(Level Rods) • Spirit Level

  13. Questions?!

  14. Rise 2.56 0.93 C B A AC = 2.56 – 0.93 = 1.63 m

  15. Fall 0.64 2.97 C A BC = 0.64 – 2.97 = -2.33 m B

  16. Questions?!

  17. 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

  18. 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 + 0.64 = 521.07 m AMSL Elevation of B = HI – Staff Reading at B = 521.07 – 2.97 = 518.10 m AMSL 2.97 0.64 C A B

  19. 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

  20. 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

  21. Content • Computation of elevations using Method of Instrument Height • Calculations Check

  22. 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

  23. 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

  24. 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 + 0.64 = 521.07 m AMSL Elevation of B (RL)= HI – Staff Reading at B = 521.07 – 2.97 = 518.10 m AMSL 2.97 0.64 C A B

  25. -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 foresight readings. • Turning Point (TP). This a point at which both a foresight and a backsight are taken before moving the staff.

  26. 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

  27. 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

  28. HI = RL + BS

  29. 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

  30. RL = HI - IS

  31. 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

  32. HI = 98.760 - 0.663 = 99.423 m Calculate the RL of points A, B, C and D as follows: RL of A = HI - IS at A = 99.423 - 1.946 = 97,477 m RLof B =HI -IS at B = 99.423 - 1.008 = 98.415 m RL of C = HI - IS at C = 99.423 - 1.153 = 98.270 m RL of D = HI - FS at D = 99.423 - 1.585 = 97.838 m These reduced levels are entered in the RL column in the corresponding lines.

  33. 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

  34. HI = RL + BS HI = 98.760 - 0.663 = 99.423 m Calculate the RL of points A, B, C and D as follows: RL of A = HI - IS at A = 99.423 - 1.946 = 97,477 m RLof B =HI -IS at B = 99.423 - 1.008 = 98.415 m RL of C = HI - IS at C = 99.423 - 1.153 = 98.270 m RL of D = HI - FS at D = 99.423 - 1.585 = 97.838 m These reduced levels are entered in the RL column in the corresponding lines.

  35. 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

  36. Calculate the next height of instrument. This is equal to: HI = RL of point D + BS reading at point D = 97.838 + 2.787 = 100.625 m (This value is entered in the same line as point D, but in the HI column). Calculate RL of points E, F and G as follows: RL of E = HI - IS at E = 100.625 - 2.270 = 98.355 m Rl of F =HI-IS at F = 100.625- l.218 = 99.407m RL of G = HI - FS at G = 100.625 – 0.646 = 99.979 m These reduced levels are again entered in the RL column in the Corresponding lines

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

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

  39. 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

  40. Questions?!

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