Geomatics / surveying III course: Module 5 hydrographic surveying, Module 6 interferometry, gyrotheodolites and gyrocompasseses

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Presentations in the course Surveying II in B.Sc. Geomatics at the University of Cape Town. Module 5 hydrographic surveying, Module 6 interferometry, gyrotheodolites and gyrocompassese


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30 Lectures , 5 AssignmentsRecommended Texts:Surveying :H Kahmen & W Faig

+ many other texts

APG3017DSURVEYING IIIHydrographic surveyingHydrographic surveyingTEXTS Hydrography for the Surveyor and Engineer - A E Ingham 3rd Edition - revised by V J Abbot (1992)Manual on Hydrography. Publication M-13, International Hydrographic Organisation, May 2005


Intro: Hydrographic surveyingMapping at seaPosition fixing at sea

How is this different from surveying on the land?Instantaneous position afloatWork outside the control frameworkNot precisePlatform a constant height above the geoid

Accuracies required:Position of the vessel - absoluteposition of the vessel wrt the sea bed and other structures or features relative

Repeatability?X, Y and depth, Z

Intro: Hydrographic surveyingIntro: Hydrographic surveyingUnits of measure:Sea mile: the length of 1 minute of arc along the meridian at the latitude of the position.International Nautical Mile: this is a constant 1852 metres (this is derived from the width of the English Channel). 1 land mile = 1.609 km; 1 nautical mile = 1.852 km.Fathom: is used to measure depth. 1 Fathom = 6 feet

TIDESTides affect the following concerns:fishinglaunching/berthing of vesselsmanagers of harbours and portsswimmerssurfersmicro-climatetidal currentshydrographic surveyor: correction for height of tide

Use of tidal dataReal Time: instant determination of water level and direct transmission to the user. Examples:on-line echo soundingshipping movement control in large portssurge and storm warnings - combinations of wind, weather and tide can be very destructive, in the South China Sea for examplecontrol of engineering activity - pipelines and harbour constructionHistorical/Statistical: Analysis of data after the event. Examples:control for hydrographic survey of the sea bedto determine MSL for the Land Levelling Datum (LLD)to determine the high water mark for cadastral purposesprediction of frequency of abnormalitiescompilation of co-tidal charts and tablesphysical or mathematical models of estuaries and lake systems movements for geodesyUse of tidal dataDefinitionstide:periodic vertical movement of the seatide raising forces:those exerted by the moon and the sun to generate tides and tidal streamstidal streams:periodic horizontal movements of the seacurrents:horizontal movements of the sea not caused by tide raising forces e.g. prevailing wind, differential salinity and water temperatureshigh and low water:the extremes reached in any tidal cyclesemi-diurnal tide:two highs and two lows in the lunar day (25 hours)lunar day: the moon returns to the same position w.r.t. the earth; 25hrs has an astronomical reason - relation to the angular velocity of the moon)Definitionsdiurnal tide:one high and one low in a lunar day (diurnal means occupying one day)mixed tide: diurnal and semi-diurnal on different occasionsrange of tide: difference between high and the preceding lowspring tides:when the average range of two successive tides is greatest, on two occasions in a cycle of 29.5 days (i.e. once a fortnight for 24 hours) when average declination of the moon is 23.neap tides:when the range is the smallest in the same cycleDefinitionsmean high water springs:average over a year of heights of two (MHWS) successive high waters at springs. Varies from year to year in a cycle of 18.6 years.mean low water springs:average of lows........ as above......(MLWS)mean low water neaps:average of neaps above.....(MLWN)low water of ordinary spring tides (LWOST):found in acts of parliament; no exact definition; not as low as MLWS

Definitionsmean sea level (MSL):average of hourly readings taken over one tidal cycle at least, or better a lunation (29.5 days) or 6 months or 18.6 years (one cycle of moons nodes). Length of period and date should be quoted.mean tide level (MTL):average of all highs and lows over a periodlowest astronomical tide:lowest level of sea under average meteorological(LAT)conditions. Can only be calculated by predicting tide levels over 18.6 years. Usually selected for chart datum for soundings. Will not be reached every year; excludes surges.DefinitionsLPLW:Lowest possible low water - used by France for its chart datum definitionsimilarly for high: HAT; HATOM (of the month); HATOY (of the year); HATOFF (of the foreseeable future). Also LATOM; LATOY; and LATOFF.chart datum:level to which soundings on a published chart are reduced; datum for tide tables, in SA = LATsounding datum:level to which soundings are reduced during a survey - may be the chart datumoff-shore datum:usually derived from the co-tidal chart

Definitionsstandard port:for which all data is published enabling high and low water to be calculatedLand Levelling Datum:generally mean sea level. In SA the (LLD)LLD is offset from MSL by varying amounts at different ports. For offsets of the LLD from the Chart Datum, see next slide.British Admiralty Chart Datum (B.A.C.D.):in SA until 1979 the B.A.C.D.=MSL - 1,1 (M2+S2)where M2 = semi -amplitude of lunar semi-diurnal cycle S2 = semi-amplitude of solar semi-diurnal tide

Datums in SA

Tidal TheoryTheory of Equilibrium (Darwin)Newtons Law of Universal Gravitation: A body attracts another with a force acting in a straight line between the bodies the magnitude of which is proportional to the product of their masses and inversely proportional the square of the distance between them.The close celestial bodies exert a force on the earth which causes ocean and crustal tides.Assumptions:Earth has a complete envelope of water of uniform depthThe inertia and viscosity of water is negligibleLunar Tides

G = centre of rotation of MoonTidal Theory Lunar Tide

Tidal Theory Lunar Tide

At A: superior lunar tide (tide of moons upper transit - over the meridian)At B: inferior lunar tide (tide of moons lower transit)Tidal Theory Lunar TideLUNATION: when the moon returns to its former phase i.e. new moon to new moonThe revolution of the moon is the same direction as the diurnal rotation of the earth (west to east).relative to the sun, one revolution = 29.53 earth days.LUNAR DAYInterval between transits of the moon across the observers meridian, or one earth rotation relative to the moonIn 29.53 solar (earth) days the moon transits 28.53 times. 29.53 days x 24 hours = 708.72 hours708.72 hours/28.53 days = 24 hrs 50.5 minutes =LUNAR DAY High tide is experienced at A every 12 hrs 25.25 min (SEMI-DIURNAL=one tide cycle per half day)

Tidal Theory Solar TidePeriod = 12 hoursApproximation: differential attraction, or tide-producing-force, is proportional to the mass of the attracting body and inversely proportional to the cube of the distance.i.e.: where S = 331000 x EarthM = 1/81 x Earths = 92 800 000 milesm = 239 000 milestherefore solar tide = 0.0458 x lunar tide

Combined Tide Raising ForcesRemember:tide:periodic vertical movement of the seatide raising forces:those exerted by the moon and the sun to generate tides and tidal streams

The relative positions of the sun and moon can strengthen or counteract each other. This is done in two ways:by variation in tidal range (springs and neaps)by variation in tidal day (priming and lagging)

Phases of the Moon

Springs and NeapsThe combined forces of the moon and the sun depend on their relative positions i.e. the phase of the moonIn alignment - SpringConjunction: on the same side of the earth max spring tide called spring tide of new moonOpposition: on opposite sides large spring tide called spring tide of full moonOut of alignment NeapElongation: angle to moon and sun are 90 deg apartNeap tide of first quarter elongation = 90 degNeap tide of last quarter elongation = 270 degPriming and LaggingVariation of the time of tide due to changing relative positions of moon and sun.High tide occurs either before or after the moon transits the observers meridian.Subject: TideObject: moons transitPriming: Tide occurs before moons transitLagging: Tide occurs after moons transitPriming and LaggingMoon in:ElongationPhaseMoons age TideRangeTiday DayConjunction0 degreesNew0 daysSpring (max)GreatNormalPrimingQuadrature90 deg1st 7.5 daysNeapSmallNormalLaggingOpposition180 degFull15 daysSpringGreatNormalPrimingQuadrature270 deg3rd 22 daysNeapSmallNormalLaggingConjunction360 degNew29.5 daysSpring (max)GreatNormalLong term effects ellipticity of orbitsMoon:ellipse with eccentricity of 0.055 (f)f=(1-0.055)/(1+0.055)Anomalistic month: the period of this disturbance between successive perigees = 27.55 days neaps and springs are increased at perigee and decreased at apogeeRange of the moon causes change of tide raising force of 15-20%the longitude of the perigee moves with a period of 8.85Long term effects ellipticity of orbitsEarth:ellipse with eccentricity of 0.0166 (f)neaps and springs are increased at perihelion and decreased at aphelionAnomalistic year: the period of this disturbance between successive perihelions = 365.26 daysRange of the sun causes change of tide raising force of 3%

Long term effects declination of orbitsSun:Plane of the sun varies 2327 N and S of Equatorial plane solsticesLine from the Earth to the sun = eclipticWhen declination 0, Sun crossing Equator equinoxesTropical Year: time between autumnal equinoxes = 365.24 days

Moon:Orbital plane varies 58 either side of the ecliptic2327 + 58 = 2835 ; 2327 - 58 = 1819Period =18.61 years: called nodal regression, or period of the moons nodesHence tidal data needs to be observed for 18.61 years to take into account full period of planetary effects.

Amplitude and Phase AngleInertia of the water mass: causes phase lagFriction against the seabed. Restriction of land masses. Shallow water effectsResonance of ocean basinsCorriolis ForceMeteorologicalSeismic activityOceanographicPrediction of TidesCosine curves one per effect (called a constituent)Harmonic analysis of tide data to determine these curves and coefficientsConstituents M (and O, N, etc.): lunar constituentsConstituents S(and R, T, etc.): solar constituentsOne cycle per day (diurnal) = suffix 1Two cycles per day (semi-diurnal) = suffix 261 constituents!

Prediction of TidesThere are four principal constituents which will be encountered (here we consider the earth stationary and the moon and sun revolving around it):M2 = Principal Lunar Constituent, moving at twice the speed of the mean moon (because it must happen twice in one lunation)S2 = Principal solar constituent, moving at twice the speed of the mean sunK1 = part of the effects of the Suns and the Moons declinationsO1 = remaining part of the Moons declination.SOUNDING DATUMSSounding is determination of depthA sounding datum is the reference surface for soundingIdeally: should agree with the Chart DatumArbitrary datum: established from using a tide gauge to take tidal observationstide should not fall under chart datum usuallydo not be too pessimisticthe datum should be in harmony with the datums of neighbouring surveysSounding DatumsLAT .... Tidal observations over 19 yearsChart Datum = LATLLD differs from CD -0.716m in East London to -1.055m in Luderitz. In Cape Town: -0.825m at Granger Bay and -0.843 at Simonstown

PreservationTGBM or FBMSounding DatumsObtaining a sounding datum:Is tidal regime diurnal or semi-diurnal?If x amplitude of the solar semi-diurnal constituent at Standard Port (i.e. (H of S ) x ) is greater than twice the sum of the amplitudes of the principal diurnal constituents (2 x (H of K + H of O )) the tide can be said to be semi-diurnal. Otherwise the tide may be regarded as diurnal.Diurnal and Semi-diurnal tides

Interpolate between known sounding datumsUse GPSTide corrections: cotidal charts

M2 tidal constituent: Amplitude is indicated by color, and the white lines are cotidal differing by 1 hour. The curved arcs around the amphidromic points show the direction of the tides, each indicating a synchronized 6-hour period.Cotidal chartsTime and height differences:Any time shift translates into a height of tide shiftMaximum at the half-tideTide corrections - Chart Datumthe vertical datum used for tidal observations should be connected to the general land survey datum via prominent fixed marks in the vicinity of the tide gauge/station/observatory. Ellipsoidal height determinations of the vertical reference marks used for tidal observations should be made relative to a geocentric reference frame based on ITRS, preferably WGS84, or to an appropriate geodetic reference level (IHO)Tide corrections - Chart Datumantenna correction, which is a purely geometric quantityGeometric offset/correctionthe height of the chart datum referred to the ellipsoid; this height is comparable to geoid heights in that it constitutes a connection between a geometrical surface - the ellipsoid - and the chart datum, which is a tidal dependent surfaceKnowledge of the LAT (Chart Datum) relative to the ellipsoid model similar to a geoid model

Chart datum modellingGNSS levelling at tide gaugesAt each tide gauge determine the height of the chart datum (LAT) above the ellipsoid. LAT computed at these stations from water level observations,use the heights of a quasi-geoid as preliminary reference surface for mean sea level determinationResult: chart datum heights above ellipsoidTide corrections using GNSS

Ellmer and Goffinet, Tide Correction Using GPS - The Determination of the Chart Datum. Shaping the Change, XXIII FIG Congress, Munich, Germany, October 8-13, 2006

(AA Mather, GG Garland, DD Stretch, African Journal of Marine Science 2009, 31(2): 145156)

(AA Mather, GG Garland, DD Stretch, African Journal of Marine Science 2009, 31(2): 145156)Tide Gauge Data sourced from Permanent Service for Mean Sea Level (PSMSL) level trendsSea level risingWest coast +1.87mm/yrSouth coast +1.48 mm/yrEast coast +2.74 mm/yrBarometric pressure contributesVertical crustal motion:Max East coast +1.1 mm/yr

(AA Mather, GG Garland, DD Stretch, African Journal of Marine Science 2009, 31(2): 145156)Error in tide reductions in SA The main problem with the South African tide gauge records is confined mainly to the period between 1998 and 2002 when the data for recorded tide levels were confused with the mean level (ML) at each site. In the derivation of the chart datum (CD) to land levelling datum (LLD) conversion, an error was inadvertently introduced. This error was first identified during the analysis of the Durban sea level records (Garland and Mather 2007) and has subsequently been found in other South African tide gauge records. The magnitude of the error varies between sites (Table 1). This over-correction resulted in artificially raising sea levels for the period 19982002 (Garland and Mather 2007). To obtain the correct LLD sea levels for the tide gauge locations, it was necessary to correct all records. This was achieved using Table 2, which is based on the South African Navys conversion table (SAN 2008).Due to these problems, we used the PSMSL revised local reference (RLR) data, excluding Durban, where additional data-correction processes have been applied. It should be noted that data for the period 19982002 have been largely removed from the RLR data by the PSMSL, possibly for the abovementioned reasons.(AA Mather, GG Garland, DD Stretch, African Journal of Marine Science 2009, 31(2): 145156)Offsets of the Chart Datum below LLD in SA

Walvis Bay -0.966Luderitz -1.055

Remember: Chart Datum is LAT, which is below mslApplication in SA

Ellmer and Goffinet, Tide Correction Using GPS - The Determination of the Chart Datum. Shaping the Change, XXIII FIG Congress, Munich, Germany, October 8-13, 20061D corrections calculated around the coast from tide gauge offsets from LLDNo offshore modelLLD WGS84 ellipsoid relies on geoid model

Tide Gaugesremove the effect of short term motion of the waterto isolate the effects due to tide raising forcesTypes:Flotationhydrostatic pressureAcoustic (in air and water)electronic

UNDERWATER ACOUSTICSSurveyor is blind cannot see what he/she is surveyingRelies on sensorsHazards may depend on the tideIncorrect charting renders navigators vulnerableDepth spot shots underwater (sounding)Many reductions.... Contour planInfill using other sensorsUnderwater acoustics - chartingWhat is charted:the positioning of navigational hazardsthe determination of the sea bed materialthe recommendations, with guaranteed safety, of clearing and leading linesthe position of topographical detail and conspicuous objects on shore of use to the navigatorthe delineation of the high and low water linesthe depiction to scale of shoreline view as seen from the seathe writing of recommendations for incorporation into the Sailing Directions regarding safe navigation in the area surveyed.Underwater acoustics - soundingSounding is the operation whereby an area is methodically covered by depth measurements (soundings) in order to portray the relief of the seabedDepth polesLIDARSonarEcho-sounding: like spot shots directly under the vessel for charting (off-shore charts: SAHO) and mapping for specific projects (e.g. FUGRO)

Underwater acoustics echo sounding

Underwater acoustics echo sounding

Underwater acoustics echo sounding

Underwater acoustics echo soundingUnderwater acoustics echo soundingOPERATIONAL CONSIDERATIONS-A bit like photogrammetry flight planning!Line SpacingFootprint of echosounderBeamwidth depth of the seabedIncrease if side-scan sonar availablethe sonar sweeps out at 90 degrees to the left and right of the direction of the vessel Reveals features between echo sounding lines

Underwater acoustics echo sounding2.Line Direction90 degrees to the slope Sandy bottoms form waves perpendicular to the direction of flow - side-scan sonar is useful.3.Sounding Speednavigational safetyfixing intervalEchosounder pulse repetition frequencySea state

Underwater acoustics echo sounding4.Scale of the Surveyaccuracy and density of the coverage requiredDetermines the sounding speed, fixing method and the line spacing.

SONARSONAR is an acronym for SOunding NAvigation and RangingSONAR instrumentation:Echo Sounder - fixed beam with a vertical axisUnderwater Acoustic Beacons and PositioningSide Scan SonarSector Scan SonarPassive (military) systemsMultibeam echosounderSONAR instrumentation

Range using SONARSpeed of propagation of acoustic energy in waterdetermine ranges speed of sound in sea water needs to be determinedJob of the hydrographic surveyorvaries with temperature, pressure and composition (salinity etc.)Sound velocity profileRange using SONARPropagation loss:Geometric spreadingAttenuationabsorptionscattering

Range using SONAR: shadow zone

Range using SONAR: speed adjMeasured depth needs to be corrected for speed of travel of sound in water: but we dont know c(t):

Measure cm : sound velocity profileUse a preset cp : correct for difference:

Range using SONAR: mean velocityCm :Bar check: lower bar to known depths and measure to determine correction in terms of cMeasure sound velocity directly using a velocimeter:Lower to depths and read velocity of sound through waterMeasure water characteristics:temperature, pressure, salinity at chosen depths in water columnDetermine Cm from tablesReduction of soundingsChart depth = Observed depth + Instrument correction + Sound Velocity Correction + Dynamic Draft Correction + Water level (Tidal) correction.Start with OBSERVED DEPTH: from raw measurement

Reduction of soundingsInstrument corrections: not necessary with electronic instrumentsNow we have ELAPSED TIME DEPTH

Reduction of soundingsVelocity correction for speed of sound in waterDynamic draft correction Static draftSquatSettlementNow we have ACTUAL DEPTH

Reduction of soundingsWater level (tidal) correctionMotion of vesselHeave: up and down: Averaging or IMURoll: sideways, Pitch (HRP): fore/aftHeading: vessel axis not aligned to motionTiming: latency of return echo signal


Reduction of soundingsCorrect offset between sounding datum and chart datum

Now we have CHART DEPTH

Operational Accuracy - influencesResolution Pulse duration: resolution = pulse length 2 objects within pulse length reflect once2 objects greater than pulse length apart reflect twiceAngle of incidenceSkew effective pulse length increasedDegrades resolutionSensitivity and resolution of recording mediumonly for analogueNature of targetFunction of density denser reflects stronger signalOperational Accuracy - influencesBeam width of transducerCone at which intensity that along the beams central axisNon-vertical beam or skew sea bed:Earliest return depth measurementError sourcesInstrumental: beam widthEnvironmental: c, waves, unwanted echoes (fish, bubbles), meterologicalOperational accuracy - specsStandard deviation of depth horizontal accuracyhorizontal accuracy with GPS 5m

where for d100m, a=1.0m and b=0.023

Much better accuracies are achievable with advanced DGPS : 2cm!

20m50m100m500m2000m0.56 m0.82 m1.39 m11.5 m46.0 mOperational accuracy - checksObserve cross lines:transverse (or between 45 and 90 degrees) to the direction of the echo soundingsaccuracy and reliability of surveyed depths and plotted locations

Side Scan SonarSwath 90 to direction of travelReflection of acoustic pulseMeasurement = strength of return pulse (not TOF)Picture of sea bedHigh resolution high frequency, short wavelengthTherefore : short distanceHigh qualityTowed behind vesselOne fishTwo fishes oblique to vessel

Side Scan Sonar

Detect 1m cube

Side scan sonar

Multibeam EchosoundingSwath 90 to direction of travelReflection of acoustic pulsesMeasurement = time of flight ... depthPicture of sea bedHigh resolution high frequency, short wavelength, short distanceHigh qualityIntegrated systems mix of different frequency instruments depth variations. 240 beams possible.Echo sounder transducer is beneath vesselOverlap or use with side scan sonar

Multibeam Echosoundingnear-nadir beam is required to detect objects with a high degree of accuracy side scan sonar in comboMany data pointsdepths 40 meters min detectable target size 10 % depth for horizontal dimensions5% depth for vertical dimensionsvertical resolution 1 centimetreMultibeam Echosounding

Positioning the survey vesselSome terminology:Acoustics: production, control, transmission, reception and effects of soundSound Waves: Alternating pressure compression/rarefactionParticles oscillateFrequency, wavelength, period, speed, direction (both = velocity), amplitude (pressure in decibels, dB; 0dB = 20Pa)Transponder: transmitter and responder (active reflector)Transducer: loudspeaker for signals (sounds) underwaterHydrophone: microphone for signals (sounds) underwater

Positioning the survey vessel

Positioning the survey vesselGPS for absolute positioning at seaStand aloneDGPS

Relative positioning w.r.t. sea bed/other objects:Acoustic positioningLocal, accurate, real-timeLong baseline (range-range): acoustic beacons (transducers) and transponderon sea bedhydrophone on vessel

Positioning the survey vesselShort baseline (range-range, range-bearing, time difference)1 or more submerged acoustic beacons3 or more transducers (hydrophones) on vesselrange-range:3 hydrophones in triangle below shipPoor geometryAffected by ships movementnoise fields surrounding each transducer: systematic errorRange-bearing (ultra-short baseline)Small hydrophone array on vesselBearing interpreted from relative phase of signals received at each hydrophonePoor resolutionTime differencePosition vessel over a location preciselyHydrophone on vesselTransponder on location eg well point

Specialized instrumentationLaser interferometerGyroscopic orientationGyrotheodoliteGyrocompassLaser interferometerPrinciples of measurementLaser interferometer

Gyroscopic orientationPrinciple of gyroscopic orientationGyrotheodolitesGyrocompassesPrinciples

How do we get orientation underground/at sea?

where we cannot see control?Gyroscopic orientationDifferent from gyroscopes):

A gyroscope (APG3016C) maintains the direction of its axis in relation to some distant fixed point in outer space due to conservation of angular momentum

A gyrotheodolite or gyrocompass automatically positions this same axis to true north by applying a torque due to the earths gravity. A weight is usually incorporated

Two elements:The rotating earthThe spinning mass element in the gyro

Gyroscopic orientationGyro: The Rotating EarthLike a flywheelAngular momentum = cosin horizontalAngular momentum = sinin verticalRH rule: L=I. Lbody=Ibody. E cosLbody E cos if Ibody small

Gyro: The spinning mass elementgyro flywheelAngular momentum: L G =I G. G

Gyro torque vector/precession momentCross Product of L G and Lbody :M= L G x Lbody

M= IG. G x E cos= L G x E cos

Gyro precession to NorthM area of L G and Lbody If L G and Lbody unidirectional, M= 0smallest when vector L G (along the spin axis of the gyro) is directed parallel to the meridianIf L G and Lbody 90, M= maximumvector L G (along the spin axis of the gyro) is directed East - WestTorque f(cos)maximum at the equator zero at the polesGyro precession to NorthIn summary; the angular momentum caused by the rotation of the earth around its axis is directed northwards, a component of this can be resolved in the horizontal plane. The angular momentum of the spinning gyro is also in the horizontal plane and directed along the gyro spin axis. These two angular momentums combine and induce a torque around the vertical axis at the gyro, causing it to precess until its spin axix is parallel to the gyros meridian and directed northwards.

ImagesPrecession and measurementGyrotheodoliteGyrotheodolitesGyromat 3000

Gyromat 2000, from: Brunner & Grillmayer, 2002from: inertia precession is an oscillation with decreasing range over timeModel this to determine North directionInstrument precision 1 North determined = the instantaneous rotation axis, and should be corrected for polar motion (0",3)Vertical axis = gravitational axis ellipsoid normalAstronomical meridian geodetic meridianAstronomical azimuth, not geodetic azimuth (correction required)Gyrotheodolites approx methodSet up, level, approx orientation to within 30-40 of Ngyro is set spinning and the brake is released, allowing the gyro to precess towards NorthTrack index mark on the gyro by turning the slow motion screw of the theodolite so that the index remains within the centre of the V-notchWhen index mark reverses its direction of motion (turning point), read the horizontal circleRepeatAverage two horizontal circle readings to get N to 2-3Gyrotheodolites - Turning Point MethodApprox method firstspinning gyro is set free to precesstrack continuously using the slow motion screw A multiple number of turning points is observed (usually 6 to 10)The processing of the observations takes into account the damping of the oscillations

Gyrotheodolites - Turning Point MethodSchler mean is used: = [ ( r1 + r3 )/2 + r2 ] /2= [ ( r2 + r4 )/2 + r3 ] /2= [ ( r3 + r5 )/2 + r4 ] /2 , etc.10" - 20"Gyrotheodolites - Transit MethodAprox methodClamp horizontal circlespinning gyro is set free to preceTime the passage of the index mark through the V-notchesIf oriented in the meridian, then the time spent by the index to the West of the notch = the time spent to the East of the notchdifference, t, is linearly related to the misorientation of the theodoliteGyrotheodolites - Turning Point MethodThe time intervals between passages through the V-notch are given by the first differences:differences will alternate between large and smallThe second differences, which should be constant in magnitude, provide a measure of the misalignment from N:

N = c.a. tGyrotheodolites - Turning Point MethodN = c.a. ta = mean amplitude of gyro swing in scale unitsRead on the scaleOscillation must be small enough to fit in the scale t : timing a number of passages of the gyro index through the V-notch and differencingc = proportionality factorDetermined from readings in two positions:N = N1 + c.a1. Dt1N = N2 + c.a2.Dt2

10" - 20"10" - 20"GyrotheodolitesIndex errorElectronic theodolites: R300 000 in 2001!1-2Mine surveyingTunnel surveyingImagesCalibration


Calibration of a gyrocompass in harbour:GPS heading of vesselGyrocompass readingBaseline on the jetty at the harbour fixed ground stationsBaseline on the vessel in fore/aft direction (would be heading) set up targetsSurvey vessel baseline from the two jetty points obs all 3 other stations from each jetty station.

At sea .Set GNSS software Geodetic ellipsoid parametersSet up DGNSS antennae at two Vessel baseline stationsObserve DGNSS position as (x,y)1 and (x,y)2Calculate join direction (geodetic azimuth)Compare to gyrocompass (astronomic azimuth)DGPS Integrity checkSet up GNSS antenna on Jetty station 1Compare DGNSS coordinate against known coordinate

The END!!!Please complete the course evaluations on VULA


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