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Surveying I. Lecture 2. Sz. Rózsa: Surveying I. – Lecture 2.

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Presentation on theme: "Surveying I. Lecture 2. Sz. Rózsa: Surveying I. – Lecture 2."— Presentation transcript:

1 Surveying I. Lecture 2. Sz. Rózsa: Surveying I. – Lecture 2

2 Outline Structure of levels Adjustment of levels Error sources Procedure of levelling Line levelling, detail point levelling Processing levelling data Sz. Rózsa: Surveying I. – Lecture 2

3 The principle of levelling A B (l A ) (l B ) AA  H AB lAlA BB lBlB  H AB =l A -l B =(l A )-  A -(l B )+  B When  A =  B (spherical approximation, equal distance to A and B)  H AB =(l A )-(l B ) topography equipotential surface Line of sight

4 The Surveyor’s level Tilting level Levelling head Tilting screw Diaphragm Bubble tube Tilting axis Clamping screw - to fix the telescope in one vertical plane Tangent screw (slow motion screw) - to finely rotate the telescope along a vertical axis Circular bubble Sz. Rózsa: Surveying I. – Lecture 2

5 The Surveyor’s telescope Object lens Eyepiece Object Virtual image Note that the virtual image is magnified and inverted! Sz. Rózsa: Surveying I. – Lecture 2

6 The Surveyor’s telescope The diaphragm (cross-hairs) To provide visible horizontal and vertical reference lines in the telescope. Line of collimation With adjustment screws the diaphragm can be moved in the telescope to adjust the line of collimation. Sz. Rózsa: Surveying I. – Lecture 2

7 The Surveyor’s telescope Parallax When focusing the telescope, the real image formed by the objective lens is made to coincide with the diaphragm. What is the parallax? When viewing two distant objects approximately along a straight line, and the eye is moved to one side, then the more distant object moves relative to the other in the same direction. This can lead to observation errors (wrong reading, wrong sighting). If the real image formed by the objective lens does not coincide with the diaphragm a parallax is observed -> the reading depend on the position of the eye! diaphragm image Sz. Rózsa: Surveying I. – Lecture 2

8 The Surveyor’s telescope Focusing the telescope External focusing Internal focusing Focusing lens Variable length Fixed length Sz. Rózsa: Surveying I. – Lecture 2

9 The Surveyor’s level Tilting level Tribrach (Levelling head) Tilting screw Diaphragm Bubble tube Tilting axis Clamping screw - to fix the telescope in one vertical plane Tangent screw (slow motion screw) - to finely rotate the telescope along a vertical axis Circular bubble Sz. Rózsa: Surveying I. – Lecture 2

10 The Surveyor’s level Tilting level How can we view the bubble tube? Using a mirror (older instrument) Prismatic coincidence reader (modern instruments) Bubble tube Prism Bubble tube is tiltedBubble tube is horizontal (leveled) Bubble tube Sz. Rózsa: Surveying I. – Lecture 2

11 The Surveyor’s level Setting up the level Primary axis Secondary axis 1. Fix the level on a tripod 2. Center the circular bubble by adjusting the foot screws. (to approximately level the instrument) 3. Sight the levelling staff, and eliminate the parallax. 4. Adjust the sensitive bubble tube by the tilting screw. Sz. Rózsa: Surveying I. – Lecture 2

12 The Surveyor’s level Automatic level We must adjust the bubble tube before every reading when using the tilting level -> takes a lot of time, may cause blunders (large mistakes in the observations) An automatic level contains an optical device, which compensates the tilting of the telescope - called compensator. Sz. Rózsa: Surveying I. – Lecture 2

13 The Surveyor’s level Operation of the compensator Advantage: faster observations, elimination of a possible reason of blunders Disadvantage: vibrations (wind, traffic, etc.) have a bad impact on the operation of the compensator Sz. Rózsa: Surveying I. – Lecture 2

14 The levelling staff Sz. Rózsa: Surveying I. – Lecture 2

15 Outline Structure of levels Adjustment of levels Error sources Procedure of levelling Line levelling, detail point levelling Processing levelling data Sz. Rózsa: Surveying I. – Lecture 2

16 Adjusting the level The two-peg test Collimation error - the line of collimation is not horizontal, when the level is levelled The effect of collimation error cancels, when d 1 =d 2. Thus the height difference is: Sz. Rózsa: Surveying I. – Lecture 2 How much is the collimation error (  )? 1.Establish a test line on an approximately flat surface. 2.Compute the elevation difference between the test points (A and B)!

17 Adjusting the level 5. The true elevation difference is already computed from the previous configuration: Sz. Rózsa: Surveying I. – Lecture 2 3. Move the instrument to an external point on the extension of the AB line. 4. Compute the elevation difference from the observations (note that the elevation difference contains the effect of the collimation error)! 6. Thus the collimation error is:

18 Outline Structure of levels Adjustment of levels Error sources Procedure of levelling Line levelling, detail point levelling Processing levelling data Sz. Rózsa: Surveying I. – Lecture 2

19 Systematic error in levelling The effect of curvature Solution: Since the equipotential surface is approximately spherical, the effect of curvature is a function of the instrument-staff distance. When the backsight and foresight distances are equal, the effect of curvature cancels out. Sz. Rózsa: Surveying I. – Lecture 2 (l A ) (l B ) AA  H AB lAlA BB lBlB topography equipotential surface Line of sight

20 Systematic error in levelling The refraction The air has different optical properties everywhere. Air pressure, humidity etc. Have an impact on the refractivity. Thus the light does not propagate along a straight line, but along a curve: For points with the same elevation, the effect of refraction can be neglected. What to do, when they are not? Sz. Rózsa: Surveying I. – Lecture 2

21 Systematic error in levelling Solution: the instrument should be set up exactly in the middle between two points, thus the effect of curvature is the same for the backsight and foresight. Sz. Rózsa: Surveying I. – Lecture 2 d r’ radius of refractive curve rr

22 Systematic error in levelling The effect of collimation error Solution: the instrument should be set up exactly in the middle between two points and the collimation error must be constant, thus the effect is eliminated Sz. Rózsa: Surveying I. – Lecture 2

23 Systematic error in levelling Tilting of the staff The effect depends on the: tilting angle reading (the higher the reading is, the bigger the error is) Solution: staffs should be equipped with circular bubbles and kept vertical Sz. Rózsa: Surveying I. – Lecture 2 ii  i =l i -l i cos  

24 Systematic error in levelling Settlement of the tripod Solution: the reading should be taken in both order, and the mean value of the height differences should be computed (assuming constant observation speed) Sz. Rózsa: Surveying I. – Lecture 2 A B hh a1a1 b1b1 Measuring the height difference between A and B! Measuring the height difference between B and A! A B hh a2a2 b2b2 Let’s compute the mean value of the  H AB and  H BA :

25 Systematic error in levelling Settlement of the staff Solution: - all lines should be run twice in the opposite directions; - a change plate must be used to support the staff. Graduation error of the staff Solution: staffs must be calibrated regularly (the graduation must be checked in laboratories). Sz. Rózsa: Surveying I. – Lecture 2 Problem: The staff has a subsidence during the observations. a change plate must be used to support the staff. Problem: The cm graduation on the staff is not accurate. The units have different lengths.

26 Systematic error in levelling Index error of the staff Problem: The bottom of the staff is not aligned with the 0 unit of the scale.  The effect of the index error on the reading: l = (l) +  Where l is the reading taken, while  is the index error Sz. Rózsa: Surveying I. – Lecture 2

27 Systematic error in levelling The effect of index error on a single height difference:  H = l BS -l FS  H = [(l BS )+  1 ]-[(l FS )+  2 )]=l BS -l FS +  1 -  2 When only one staff is used, then the effect of index error cancels out (  1 =  2 ) Sz. Rózsa: Surveying I. – Lecture 2 Direction of levelling l BS l FS Staff No. 1. Staff No. 2. HH

28 Systematic error in levelling What happens when two staffs are used? Single height difference: The sum of two height differences: 1 2 Sz. Rózsa: Surveying I. – Lecture 2  H = [(l BS )+  1 ]-[(l FS )+  2 )]=l BS -l FS +  1 -  2 Staff No. 1. Staff No. 2. Staff No. 1.  H = [(l BS )+  1 ]-[(l FS )+  2 )]=l BS -l FS +  1 -  2  H = [(l BS )+  2 ]-[(l FS )+  1 )]=l BS -l FS +  2 -  1

29 Systematic error in levelling  H 1 +  H 2 =  (l BS )-  (l FS ) When two staffs are used, an even number of stations have to be created in the levelling line. In this case the effect of the index error of the staff cancels out. Sz. Rózsa: Surveying I. – Lecture 2  H 1 = [(l BS )+  1 ]-[(l FS )+  2 )]=(l BS )-(l FS )+  1 -  2  H 2 = [(l BS )+  2 ]-[(l FS )+  1 )]=(l BS )-(l FS )+  2 -  1

30 Outline Structure of levels Adjustment of levels Error sources Procedure of levelling Line levelling, detail point levelling Processing levelling data Sz. Rózsa: Surveying I. – Lecture 2

31 Procedure of levelling 1. The instrument must be set up with the same distance to the staffs. 2. The bubble tube must be levelled before each reading (tilting level). 3. You must not use the parallax screw between the backsight and foresight readings 4. The bubble tube must not be affected by strong heat. 5. Readings must be taken 30-50 cm above the ground. 6. Staff should be set up vertically. 7. A change plate should be used to place the staff on the ground. 8. Levelling must be done in two opposite directions. Sz. Rózsa: Surveying I. – Lecture 2

32 Procedure of levelling 9. All the observations should be made with a constant speed. 10. Observations should be made only in suitable weather: cloudy sky, constant temperature, early morning, or late afternoon. 11. Staff should be calibrated. 12. If there are three hairs in the diaphragm, one should use all of them to take a reading. 13. When two staffs are used, an even number of stations must be used to create the levelling line. Sz. Rózsa: Surveying I. – Lecture 2

33 Outline Structure of levels Adjustment of levels Error sources Procedure of levelling Line levelling, detail point levelling Processing levelling data Sz. Rózsa: Surveying I. – Lecture 2

34 Line levelling Principle of levelling What happens, when we want to measure the height difference of two distant points? Sz. Rózsa: Surveying I. – Lecture 2 (l A ) (l B ) AA  H AB lAlA BB lBlB topography equipotential surface Line of sight

35 Line levelling The previous procedure is repeated as many times as need to cover the distance between the points. H=h1+h2+h3+h4H=h1+h2+h3+h4 The direction of levelling HH h1h1 h2h2 h3h3 h4h4 Sz. Rózsa: Surveying I. – Lecture 2  H =  l BS  l FS

36 Outline Structure of levels Adjustment of levels Error sources Procedure of levelling Line levelling, detail point levelling Processing levelling data Sz. Rózsa: Surveying I. – Lecture 2

37 Processing Levelling Data Sz. Rózsa: Surveying I. – Lecture 2 Line levelling (one-way) A B MSL Reference level HAHA H B =?

38 A B HAHA Sz. Rózsa: Surveying I. – Lecture 2 PIDdBSFSRiseFallH A 1 1 d=20m 20 12 14 58 0.244 103.455 2 2 d=19 19 08 33 13 99 0.566 d=15 3 3 15 14 74 09 13 0.561 d=13 B 13 08 69 1125 0.256 0.561 1.066  H AB =  Rise -  Fall =-0.505 m 102.950 Line Levelling – one way (the Rise&Fall Method)

39 PIDdBSFSRiseFallH A1214103.455 120083314580.244 219147413990.566 315086909130.561 B1311250.256 B1203 111100109110.292 213 531519-0.518 318152209410.412 A2211970.325 Sz. Rózsa: Surveying I. – Lecture 2 Line Levelling – two-way (the Rise&Fall Method)  H AB =  Rise -  Fall =-0.505 m  H BA =  Rise -  Fall =+0.511m Let’s compute the mean height difference: H B =103.455-0.508=102.947m

40 Sz. Rózsa: Surveying I. – Lecture 2 Detail Point Levelling – The Height of Collimation Method Detail Point Levelling: The elevation of some detail points (characteristic points of objects) should be determined. A B MSL Reference level HAHA HBHB The elevation of the characteristic points of the ditch should be determined!

41 Sz. Rózsa: Surveying I. – Lecture 2 Detail Point Levelling – The Height of Collimation Method Height of collimation: The elevation of the horizontal line of sight. It can be computed by adding the elevation of the backsight point and the backsight reading. A MSL Reference level HAHA HoC=H A + A l BS A l BS Steps of Computation: 1.Compute the corrected elevation of the intermediate points! 2.Compute the Height of Collimation at each station! 3.Compute the elevation of the detail points ( HoC-l IS )!

42 Detail Point Levelling – The Height of Collimation Method Sz. Rózsa: Surveying I. – Lecture 2 A B MSL Reference level HAHA HBHB I1I1 I2I2 I3I3 101 102 103 104 PIDd Backsight (BS) Intersight (IS) Foresight (FS) Rise/Fall Height of Collimation Elevation A1214103.455 I1I1 08331458 1011104 1021421 1031428 1041067 I2I2 14741399 I3I3 08690913 B1124102.947 -0.244 -0.566 +0.561 -0.255  = -0.504  = -0.508  =-4mm True - Observed (-1) 103.210 102.643 103.203 104.043 102.939 102.622 102.615 102.976

43 Thanks for the Attention! Sz. Rózsa: Surveying I. – Lecture 2


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