Surveying I.

Lecture 2.

OutlineStructure of levelsAdjustment of levelsError sourcesProcedure of levellingLine levelling, detail point levellingProcessing levelling data

The principle of levellingdAlADHAB=lA-lB=(lA)-dA-(lB)+dBWhen dA=dB (spherical approximation, equal distance to A and B)DHAB=(lA)-(lB)equipotentialsurfaceLine of sight

The Surveyors levelTilting levelLevelling headTilting screwDiaphragmBubble tubeTilting axisClamping screw - to fix the telescope in one vertical plane

Tangent screw (slow motion screw) - to finely rotate the telescope along a vertical axisCircular bubble

Elements of Surveyors levelHow to set the line of sight to be exactly horizontal?

More general: how to set anything to be exactly horizontal?The bubble tube

The bubble tubeThe 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.

The bubble tubeThe determination of sensitivity:

Kepler-type telescopeObject lensEyepieceObjectVirtual imageNote that the virtual image is magnified and inverted!

The Surveyors telescopeThe diaphragm (cross-hairs)To provide visible horizontal and vertical reference lines in the telescope.Line of collimationWith adjustment screws the diaphragm can be moved in the telescope to adjust the line of collimation.

The Surveyors telescopeParallaxWhen 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!diaphragmimage

The Surveyors telescopeFocusing the telescopeExternal focusingInternal focusingFocusing lensVariable lengthFixed length

The Surveyors levelTilting levelTribrach (Levelling head)Tilting screwDiaphragmBubble tubeTilting axisClamping screw - to fix the telescope in one vertical plane

Tangent screw (slow motion screw) - to finely rotate the telescope along a vertical axisCircular bubble

The Surveyors level

The Surveyors level

The Surveyors levelTilting levelHow can we view the bubble tube?

Using a mirror (older instrument) Prismatic coincidence reader (modern instruments)Bubble tubePrismBubble tube is tiltedBubble tube is horizontal (leveled)Bubble tube

The Surveyors levelSetting up the level1. Fix the level on a tripod2. Center the circular bubble by adjusting the foot screws.(to approximately level the instrument)

The Surveyors levelSetting up the level3. 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.

The Surveyors levelAutomatic levelWe 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 Surveyors level

The Surveyors levelOperation of the compensatorAdvantage: faster observations, elimination of a possible reason of blundersDisadvantage: vibrations (wind, traffic, etc.) have a bad impact on the operation of the compensator

The levelling staff

OutlineStructure of levelsAdjustment of levelsError sourcesProcedure of levellingLine levelling, detail point levellingProcessing levelling data

Adjusting the levelThe two-peg testCollimation error - the line of collimation is not horizontal, when the level is levelledThe effect of collimation error cancels, when d1=d2.Thus the height difference is:How much is the collimation error (a)?Establish a test line on an approximately flat surface.

Compute the elevation difference between the test points (A and B)!

Adjusting the level5. The true elevation difference is already computed from the previous configuration: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:

OutlineStructure of levelsAdjustment of levelsError sourcesProcedure of levellingLine levelling, detail point levellingProcessing levelling data

Systematic error in levellingThe effect of curvatureSolution: 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.dAlAequipotentialsurfaceLine of sight

Systematic error in levellingThe refractionThe 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?

Systematic error in levellingSolution: 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.drradius of refractive curvedr

Systematic error in levellingThe effect of collimation errorSolution: 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 levellingTilting of the staffThe 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 verticaldidi=li-licosaa

Systematic error in levellingSettlement of the tripodSolution: the reading should be taken in both order, and the mean value of the height differences should be computed (assuming constant observation speed)ABdha1b1Measuring the height difference between A and B!Measuring the height difference between B and A!ABdha2b2Lets compute the mean value of the DHAB and DHBA:

Systematic error in levellingSettlement of the staffSolution: all lines should be run twice in the opposite directions; a change plate must be used to support the staff.Graduation error of the staffSolution: staffs must be calibrated regularly (the graduation must be checked in laboratories).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.

Systematic error in levellingIndex error of the staffProblem: The bottom of the staff is not aligned with the 0 unit of the scale.dThe effect of the index error on the reading:l = (l) + dWhere l is the reading taken, while d is the index error

Systematic error in levellingThe effect of index error on a single height difference:DH = lBS-lFSDH = [(lBS)+d1]-[(lFS)+d2)]=lBS-lFS+d1-d2When only one staff is used, then the effect of index error cancels out (d1=d2)Direction oflevellinglBSlFSStaff No. 1.Staff No. 2.DH

Systematic error in levellingWhat happens when two staffs are used?Single height difference:The sum of two height differences:12DH = [(lBS)+d1]-[(lFS)+d2)]=lBS-lFS+d1-d2Staff No. 1.Staff No. 2.Staff No. 1.DH = [(lBS)+d1]-[(lFS)+d2)]=lBS-lFS+d1-d2DH = [(lBS)+d2]-[(lFS)+d1)]=lBS-lFS+d2-d1

Systematic error in levellingDH1 +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.DH1 = [(lBS)+d1]-[(lFS)+d2)]=(lBS)-(lFS)+d1-d2DH2 = [(lBS)+d2]-[(lFS)+d1)]=(lBS)-(lFS)+d2-d1

OutlineStructure of levelsAdjustment of levelsError sourcesProcedure of levellingLine levelling, detail point levellingProcessing levelling data

Procedure of levelling1. 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 readings4. 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 levelling9. 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.

OutlineStructure of levelsAdjustment of levelsError sourcesProcedure of levellingLine levelling, detail point levellingProcessing levelling data

Line levellingPrinciple of levellingWhat happens, when we want to measure the height difference of two distant points?dAlAequipotentialsurfaceLine of sight

Line levellingThe previous procedure is repeated as many times as need to cover the distance between the points.DH=Dh1+Dh2+Dh3+Dh4The direction of levellingDHDh1Dh2Dh3Dh4DH=SlBS-SlFS

OutlineStructure of levelsAdjustment of levelsError sourcesProcedure of levellingLine levelling, detail point levellingProcessing levelling data

Processing Levelling DataLine levelling (one-way)

ABHAHB=?A11d=20m20121414580.244103.45522d=1919083313990.566d=153315147409130.561d=13B13086911250.2560.5611.066DHAB=SRise-SFall=-0.505 m102.950Line Levelling one way (the Rise&Fall Method)

PIDdBSFSRiseFallH

Line Levelling two-way (the Rise&Fall Method)DHAB=SRise-SFall=-0.505 mDHBA=SRise-SFall=+0.511mLets compute the mean height difference:HB=103.455-0.508=102.947m

PIDdBSFSRiseFallHA1214103.455120083314580.244219147413990.566315086909130.561B1311250.256

B1203111100109110.29221313531519-0.518318152209410.412A2211970.325

Detail Point Levelling The Height of Collimation MethodDetail Point Levelling: The elevation of some detail points (characteristic points of objects) should be determined.ABMSLReference levelHAHBThe elevation of the characteristic points of the ditch should be determined!

Detail Point Levelling The Height of Collimation MethodHeight 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.

Levelling - BookkeepingRise and fall method:

Levelling - BookkeepingHeight of Collimation method:

Thanks for the Attention!