Surveying I. Lecture 2.

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

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 1

The principle of levelling Line of sight dA dB (lA) lA equipotential surface A (lB) lB DHAB topography B DHAB=lA-lB=(lA)-dA-(lB)+dB When dA=dB (spherical approximation, equal distance to A and B) DHAB=(lA)-(lB) Sz. Rózsa: Surveying I. – Lecture 1

The Surveyor’s level Tilting level Bubble tube Diaphragm Tilting screw Tilting axis Circular bubble 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 Sz. Rózsa: Surveying I. – Lecture 1

Elements of Surveyor’s level How to set the line of sight to be exactly horizontal? More general: how to set anything to be exactly horizontal? The bubble tube Sz. Rózsa: Surveying I. – Lecture 1

The bubble tube The radius determines the sensitivity of the bubble tube: Sensitivity: how much the bubble moves due to a given amount of inclination. The more the bubble moves, the more sensitive the bubble tube is. Sz. Rózsa: Surveying I. – Lecture 1

The bubble tube The determination of sensitivity: Sz. Rózsa: Surveying I. – Lecture 1

Kepler-type telescope Object Eyepiece Object lens Virtual image Note that the virtual image is magnified and inverted! Sz. Rózsa: Surveying I. – Lecture 1

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 1

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 1

The Surveyor’s telescope Focusing the telescope External focusing Variable length Focusing lens Internal focusing Fixed length Sz. Rózsa: Surveying I. – Lecture 1

The Surveyor’s level Tilting level Bubble tube Diaphragm Tilting screw Tilting axis Circular bubble 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 Sz. Rózsa: Surveying I. – Lecture 1

The Surveyor’s level Sz. Rózsa: Surveying I. – Lecture 1

The Surveyor’s level Tilting level • 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) Sz. Rózsa: Surveying I. – Lecture 1

The Surveyor’s level 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) Sz. Rózsa: Surveying I. – Lecture 1

The Surveyor’s level Setting up the level 3. Sight the levelling staff: first: rotate the telescope in the direction of the staff second: use the fine motion screws to ensure precise sighting (note: on some instruments the fine motion screw works only, when the alidade is fixed using the fixing clamp) 4. Adjust the levelling bubble using the levelling screw. Sz. Rózsa: Surveying I. – Lecture 1

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 1

The Surveyor’s level Sz. Rózsa: Surveying I. – Lecture 1

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 1

The levelling staff Sz. Rózsa: Surveying I. – Lecture 1

Adjusting the level 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: Sz. Rózsa: Surveying I. – Lecture 1

Adjusting the level • 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: Sz. Rózsa: Surveying I. – Lecture 1

Systematic error in levelling The effect of curvature Line of sight dA dB (lA) lA equipotential surface (lB) lB 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. Sz. Rózsa: Surveying I. – Lecture 1

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 1

Systematic error in levelling d dr r’ radius of refractivecurve 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 1

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 1

Systematic error in levelling 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 Sz. Rózsa: Surveying I. – Lecture 1

Systematic error in levelling Settlement of the tripod Measuring the height difference between A and B! Measuring the height difference between B and A! dh dh a1 b1 b2 a2 A A B B Let’scomputethemeanvalue of theDHAB 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) Sz. Rózsa: Surveying I. – Lecture 1

Systematic error in levelling 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). Sz. Rózsa: Surveying I. – Lecture 1

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) + d Wherel is thereadingtaken, whiled is the index error d Sz. Rózsa: Surveying I. – Lecture 1

Systematic error in levelling 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) Sz. Rózsa: Surveying I. – Lecture 1

Systematic error in levelling 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 Sz. Rózsa: Surveying I. – Lecture 1

Systematic error in levelling 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. Sz. Rózsa: Surveying I. – Lecture 1

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 1

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 1

Line levelling Principle of levelling Line of sight dA dB (lA) lA equipotential surface (lB) lB DHAB topography What happens, when we want to measure the height difference of two distant points? Sz. Rózsa: Surveying I. – Lecture 1

Line levelling The previous procedure is repeated as many times as need to cover the distance between the points. The direction of levelling Dh1 Dh2 DH Dh3 Dh4 DH=Dh1+Dh2+Dh3+Dh4 DH=SlBS-SlFS Sz. Rózsa: Surveying I. – Lecture 1

Processing Levelling Data Line levelling (one-way) A B HA HB=? MSL Reference level Sz. Rózsa: Surveying I. – Lecture 1

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

Line Levelling – two-way (the Rise&Fall Method) 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 Sz. Rózsa: Surveying I. – Lecture 1

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 HA HB The elevation of the characteristic points of the ditch should be determined! MSL Reference level Sz. Rózsa: Surveying I. – Lecture 1

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. Sz. Rózsa: Surveying I. – Lecture 1

Levelling - Bookkeeping Rise and fall method: Sz. Rózsa: Surveying I. – Lecture 1

Levelling - Bookkeeping Height of Collimation method: Sz. Rózsa: Surveying I. – Lecture 1

Surveying I. Lecture 2.