Levelling Introduction

How to:Some Basic Principles forLevelingTilo SchneGFZ, [email protected]

Lecture OverviewEquipmentIntroduction to LevelingObservation, Field Notes, and ComputationErrors and their effects

Equipment

EquipmentLevel InstrumentTripodStaff/PoleChange plate (German: Frog/Frosch)Pole staff bubble (bull eye)Marker

Equipment: Level InstrumentAutomated LevelsEasy to use (not power!)Needs experienceRobust even in hostile environment

Digital LevelsPush-button techniqueNo reading errors, special staffReadings are stored and analyzed digitally

Automated Levels (Compensator)PendulumTribrachCourtesy: Deumlich, VermessungskundeBull Eye

Digital LevelsUses Barcode staffsInternal storage of dataDownload to the computerAutomated height computation + adjustmentNo feeling for quality anymoreYou frequently need power plugs

Equipment: TripodWooden design or aluminumFrom easy to sit to ops, this is high

Equipment: Staff/PoleWood, aluminumINVAR type for high precision levelingConventional (E-type)Barcode for Digital Levels

Equipment: Change PlateFor long survey linesAllows change of instrumentsBest is a metal change plateScrews e.g. at fencesSharp stones or nailsBeware of dark colorsIts not the Indonesian-German Dictionary, Its the nail!

Equipment: BubbleKeep the pole uprightAny tilt will disturb your readings

Survey MarkersGives you a fixed pointShould be of good qualityShould be long-termPreferable in bedrock, settled buildings, or bridgesDo not use fences or walls

Introduction to Leveling

Some Basic DefinitionsLevel surface (e.g. the geoid)A water surface with no motionGravity gradient is the normal to the level surfaceThe Instruments Bubble is in the normal (!)Horizontal surface At the instruments axis, the horizontal surface is tangent to the level surfaceOver short distances (

Basic Principle of LevelingMeasures height differences between pointsAlong a lineSeveral points from one occupationbsfsDh = bs - fs

DefinitionsBack sight (BS)The first reading from a new instrument stand point (i.e. take the height to the instrument)Fore sight (FS)The last reading from the current instrument station (i.e. give the height to a benchmark)Intermediate sight (IS)Any sighting that is not a back sight or fore sight

Reading a Staff1422 Read the [m], [dm] & [cm] Estimate the [mm]

Check yourself for frequent used numbers (2/3) or (7/8)

Basic Rules for LevelingAlways start and finish a leveling run on a Benchmark (BM or TGBM) and close the loopsKeep fore sight and back sight distances as equal as possibleKeep lines of sight short (normally < 50m)Never read below 0.5m on a staff (refraction)Use stable, well defined change pointsBeware of shadowing effects and crossing waters

Observation, Field Notes, and Computation

How to: A sample loop

How To: Field Notes13273982S2S1236509862347372437531101

BackInterForePointTHNB1NB2NB1TH

Date, Observer,InstrumentInstrument CheckForeBackSD

Compute levels132739820986372423652347375311011379265297929793-0001+1100 000100 000 0000 0001 (SOLL IST)73458624097 34598 72497 3480

BackInterForedhHCommentTHBM1BM2BM1TH

ISTSOLL

Loop misclosureMisclosure Error The difference of the measured height difference (DHmeas) to the known height (closed loops = 0, known benchmarks = height difference)Misclosure = DHSOLL DHISTPoint errors at double observed points

Achievable AccuracyInstrument dependentRoughly from the instrumentNI002 = 0,2mm/km (doubled line)NI025 = 2.5mm/km (doubled line)Survey line length dependentms = m1km s, s in kmmH = (m1km/2) s, s in km #(middle of the line)

An acceptable misclose?Small misclosures in closed level loops are expected because of the accumulation of random errors and can be adjustedIf the misclosure is large, the loop (or part of it) must be repeated

Misclosures can also result from errors in published BM levels and from BM instability

Testing the miscloseThe amount of misclosure acceptable using a specific instrument and survey line lengthFor our example, a second order leveling standard is adopted*misclosure 2,5s mmwhere s is the length of the line in km

*Dependent on your contrys rules and the instrument used

Our exampleThe misclosure is +1 mmThe length of the loop is 0.4 kmAcceptable error is2.5(0.4) = 1.6 mmThe misclosure of +1 mm is within the limitMean error for NB1 = 2.5/2* (0.4)

Errors and their effects

(many, but only a few addressed)

Errors in leveling, e.g.Collimation, ParallaxChange point / staff instabilityInstrument or Benchmark instabilityRefractionUncalibrated staff or levelsReading, booking, or computation errorsFore- and backsight distances different

Systematic and Random ErrorsEarth curvature RefractionCollimation errors

Effect of Earth CurvatureCurvature effectwww.fh-oow.de/institute/ima/personen/weber/VK_12/VL_VK1/geo_niv_6.htmHorizontal Level(r +Dh)2 = r2 + s2=>Dh s2/(2r)

Refractionwww.fh-oow.de/institute/ima/personen/weber/VK_12/VL_VK1/geo_niv_6.htmMean Gradient: 0,2 C / m

Collimation errorOccurs when the line of sight (as defined by the lens axis and cross-hairs) is not horizontalLeads to an incorrect staff readinghorizontal lineline of sighterror

Instrument test: Nhbauera1 = a1+e b1 = b1+2eh = a1b1 h1 = a1b1 = a1b1e = heWith h1+e = h2e h2h12a2 = a2+2eb2 = b2+e h = a2b2 h2 = a2b2 = a2+eb2 = h+eh =h2e e =

Summary

Procedure of levelingThe instrument must be check before use! (see lecture)The instrument and level must be stable settled-upThe bubble tube must be leveled before the readingBeware of sun exposure (will wander)Ensure the instruments pendulum is in-limitThe instrument must be set up in the middle between two staffsPrevents curvature effectsIf impossible, use the same distances, but opposite for the next readingsYou must not use the parallax screw between the backsight and foresight readings

Procedure of LevelingReadings must be taken 30-50 cm above the ground Surface refractionsBeware also of temperature gradients (inside/outside buildings) !!!!Staff should be set up verticallyA change plate should be usedLeveling must be done in two opposite directions but the same line (beware of gravity gradients)Staff should be calibrated, especially if INVARBe careful when crossing rivers (large water surfaces)Use same-time (mutual) observationsRepeat it during different times of the day

An Unhappy Surveyor having a 2 centimeter difference

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Levelling Introduction