Sz. Rózsa: Surveying I. – Lecture 2

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

The principle of levelling Sz. Rózsa: Surveying I. – Lecture 2 Line of sight dB lB (lA) dA (lB) lA equipotential surface topography A B DHAB DHAB=lA-lB=(lA)-dA-(lB)+dB When dA=dB (spherical approximation, equal distance to A and B) DHAB=(lA)-(lB)

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

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

The Surveyor’s telescope Sz. Rózsa: Surveying I. – Lecture 2 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.

The Surveyor’s telescope Sz. Rózsa: Surveying I. – Lecture 2 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

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

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

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

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

The Surveyor’s level Automatic level Sz. Rózsa: Surveying I. – Lecture 2 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.

The Surveyor’s level Operation of the compensator Sz. Rózsa: Surveying I. – Lecture 2 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

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

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

Adjusting the level The two-peg test Sz. Rózsa: Surveying I. – Lecture 2 The two-peg test How much is the collimation error (a)? Collimation error - the line of collimation is not horizontal, when the level is levelled Establish a test line on an approximately flat surface. Compute the elevation difference between the test points (A and B)! The effect of collimation error cancels, when d1=d2. Thus the height difference is:

Adjusting the level 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)! 5. The true elevation difference is already computed from the previous configuration: 6. Thus the collimation error is:

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

Systematic error in levelling Sz. Rózsa: Surveying I. – Lecture 2 The effect of curvature Line of sight (lA) dA dB lB (lB) lA equipotential surface DHAB topography 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.

Systematic error in levelling Sz. Rózsa: Surveying I. – Lecture 2 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?

radius of refractive curve Systematic error in levelling Sz. Rózsa: Surveying I. – Lecture 2 d dr r’ radius of refractive curve 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.

Systematic error in levelling Sz. Rózsa: Surveying I. – Lecture 2 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

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

Systematic error in levelling Sz. Rózsa: Surveying I. – Lecture 2 Settlement of the tripod Measuring the height difference between A and B! Measuring the height difference between B and A! dh dh a1 b1 a2 b2 A B A B Let’s compute the mean value of the DHAB and DHBA: Solution: the reading should be taken in both order, and the mean value of the height differences should be computed (assuming constant observation speed)

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

Systematic error in levelling Sz. Rózsa: Surveying I. – Lecture 2 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) + d Where l is the reading taken, while d is the index error d

Systematic error in levelling Sz. Rózsa: Surveying I. – Lecture 2 The effect of index error on a single height difference: Direction of levelling Staff No. 1. Staff No. 2. lBS lFS DH DH = lBS-lFS DH = [(lBS)+d1]-[(lFS)+d2)]=lBS-lFS+d1-d2 When only one staff is used, then the effect of index error cancels out (d1=d2)

Systematic error in levelling Sz. Rózsa: Surveying I. – Lecture 2 What happens when two staffs are used? Single height difference: DH = [(lBS)+d1]-[(lFS)+d2)]=lBS-lFS+d1-d2 Staff No. 1. 1 Staff No. 2. 2 Staff No. 1. The sum of two height differences: DH = [(lBS)+d1]-[(lFS)+d2)]=lBS-lFS+d1-d2 DH = [(lBS)+d2]-[(lFS)+d1)]=lBS-lFS+d2-d1

Systematic error in levelling Sz. Rózsa: Surveying I. – Lecture 2 DH1 = [(lBS)+d1]-[(lFS)+d2)]=(lBS)-(lFS)+d1-d2 DH2 = [(lBS)+d2]-[(lFS)+d1)]=(lBS)-(lFS)+d2-d1 DH1 +DH2 = S(lBS)-S(lFS) 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.

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

Procedure of levelling Sz. Rózsa: Surveying I. – Lecture 2 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.

Procedure of levelling Sz. Rózsa: Surveying I. – Lecture 2 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.

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

Line levelling Principle of levelling dA dB (lA) lA (lB) lB DHAB Sz. Rózsa: Surveying I. – Lecture 2 Principle of levelling Line of sight (lA) dA dB lB (lB) lA equipotential surface DHAB topography What happens, when we want to measure the height difference of two distant points?

The direction of levelling Line levelling Sz. Rózsa: Surveying I. – Lecture 2 The previous procedure is repeated as many times as need to cover the distance between the points. The direction of levelling Dh1 DH Dh2 Dh3 Dh4 DH=Dh1+Dh2+Dh3+Dh4 DH=SlBS-SlFS

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

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

Line Levelling – one way (the Rise&Fall Method) Sz. Rózsa: Surveying I. – Lecture 2 d=19 d=20m d=15 d=13 A 1 HA HB=? 2 3 B PID d BS FS Rise Fall H A 12 14 103.455 1 20 08 33 14 58 0.244 2 19 14 74 13 99 0.566 3 15 08 69 09 13 0.561 B 13 11 25 0.256 102.950 0.561 1.066 DHAB=SRise-SFall=-0.505 m

Line Levelling – two-way (the Rise&Fall Method) Sz. Rózsa: Surveying I. – Lecture 2 PID d BS FS Rise Fall H A 12 14 103.455 1 20 08 33 58 0.244 2 19 74 13 99 0.566 3 15 69 09 0.561 B 11 25 0.256 03 10 01 0.292 53 -0.518 18 22 41 0.412 97 0.325 DHAB=SRise-SFall=-0.505 m DHBA=SRise-SFall=+0.511m Let’s compute the mean height difference: HB=103.455-0.508=102.947m

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

Detail Point Levelling – The Height of Collimation Method Sz. Rózsa: Surveying I. – Lecture 2 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. Steps of Computation: Compute the corrected elevation of the intermediate points! Compute the Height of Collimation at each station! Compute the elevation of the detail points (HoC-lIS)! AlBS A HoC=HA+AlBS HA MSL Reference level

Detail Point Levelling – The Height of Collimation Method Sz. Rózsa: Surveying I. – Lecture 2 A 101 104 I1 I2 I3 B HA 102 HB 103 MSL Reference level PID d Backsight (BS) Intersight (IS) Foresight (FS) Rise/Fall Height of Collimation Elevation A 1214 103.455 I1 0833 1458 101 1104 102 1421 103 1428 104 1067 I2 1474 1399 I3 0869 0913 B 1124 102.947 -0.244 (-1) 104.043 103.210 102.939 102.622 102.615 102.976 -0.566 (-1) 102.643 +0.561 (-1) 103.203 -0.255 (-1) S= -0.504 S= -0.508 True - Observed D=-4mm

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