《航海学》课程参考文献（地文资料）CHAPTER 02 GEODESY AND DATUMS IN NAVIGATION

CHAPTER 2GEODESYANDDATUMSINNAVIGATIONGEODESY,THEBASISOFCARTOGRAPHY200.Definitionequal and to which thedirection ofgravity is always perpen-dicular.The latter is particularly significant because opticalGeodesy is the science concerned with the exact posi-instruments containing level devices are commonly usedtotioning of points on the surfaceofthe earth.It also involvesmake geodetic measurements. When properly adjusted, thethestudyofvariationsoftheearth'sgravity,theapplicationvertical axis ofthe instrumentcoincides withthedirection ofof thesevariations to exactmeasurements on the earth,andgravity and is, therefore, perpendicular to the geoid.the study ofthe exact size and shape ofthe earth.These fac-Thegeoid is that surface to which the oceans would con-tors were unimportant to early navigators because of theform over the entireearth if freeto adjust to the combinedrelative inaccuracyoftheirmethods.Theprecise accuracieseffect of theearth's mass attraction and thecentrifugalforceoftoday'snavigationsystems and theglobal natureofsat-of theearth's rotation.The ideal ocean surface would befreeelliteandother long-rangepositioningmethods demandaof ocean currents and salinity changes.Uneven distributionmore complete understanding ofgeodesy than has everbe-of the earth's massmakes the geoidal surface irregular.forebeenrequiredThe geoid refers to the actual size and shape of theearth,but such an irregular surfacehas serious limitations201.The Shape Of The Earthas amathematical earthmodelbecause:The irregular topographic surface is that upon which·Ithasnocompletemathematicalexpressionactual geodetic measurements are made. The measure-.Small variations in surface shape over time intro-ments, however, are reduced to the geoid. Marineduce small errors in measurement.navigation measurements are madeon theocean surfacewhichapproximatesthegeoid.The irregularity of the surface would necessitate aThegeoid is a surface along which gravity is alwaysprohibitive amount of computations:GEOID-ELLIPSOIDRELATIONSHIPSElutratitieslatheuthmtGEOID UNDULATIONGEONEOID UNDULATIONEANSEASURFACEGEOIDPERPENOICULAR TO GEOID(PLUNSLINE)PERPENDICULAR TO ELLIPSOIDDEFLECTION OFTHEVERTICALFigure201,Geiod,ellipsoid,andtopographic surface oftheearth,anddeflection ofthevertical duetodifferences inmass.15

15 CHAPTER 2 GEODESY AND DATUMS IN NAVIGATION GEODESY, THE BASIS OF CARTOGRAPHY 200. Definition Geodesy is the science concerned with the exact posi￾tioning of points on the surface of the earth. It also involves the study of variations of the earth’s gravity, the application of these variations to exact measurements on the earth, and the study of the exact size and shape of the earth. These fac￾tors were unimportant to early navigators because of the relative inaccuracy of their methods. The precise accuracies of today’s navigation systems and the global nature of sat￾ellite and other long-range positioning methods demand a more complete understanding of geodesy than has ever be￾fore been required. 201. The Shape Of The Earth The irregular topographic surface is that upon which actual geodetic measurements are made. The measure￾ments, however, are reduced to the geoid. Marine navigation measurements are made on the ocean surface which approximates the geoid. The geoid is a surface along which gravity is always equal and to which the direction of gravity is always perpen￾dicular. The latter is particularly significant because optical instruments containing level devices are commonly used to make geodetic measurements. When properly adjusted, the vertical axis of the instrument coincides with the direction of gravity and is, therefore, perpendicular to the geoid. The geoid is that surface to which the oceans would con￾form over the entire earth if free to adjust to the combined effect of the earth’s mass attraction and the centrifugal force of the earth’s rotation. The ideal ocean surface would be free of ocean currents and salinity changes. Uneven distribution of the earth’s mass makes the geoidal surface irregular. The geoid refers to the actual size and shape of the earth, but such an irregular surface has serious limitations as a mathematical earth model because: • It has no complete mathematical expression. • Small variations in surface shape over time intro￾duce small errors in measurement. • The irregularity of the surface would necessitate a prohibitive amount of computations. Figure 201. Geiod, ellipsoid, and topographic surface of the earth, and deflection of the vertical due to differences in mass

16GEODESYANDDATUMSINNAVIGATIONThe surfaceof thegeoid,with some exceptions,tendsThis ratio is about 1/300 for the earth.to rise undermountains and to dip above ocean basins.Forgeodetic,mapping,andchartingpurposes, itis necessary to usea regular or geometric shape which closelya-bapproximatestheshapeofthegeoid eitheronalocal orglo-f:3bal scaleandwhichhas a specificmathematical expression.This shape is called the ellipsoidThe separations of the geoid and ellipsoid are calledgeoidal heights, geoidalundulations, or geoidalThe ellipsoidal earth model has its minoraxis parallel to theseparations.earth'spolaraxis.The irregularities in density and depths of the materialmaking up the upper crust of the earth also result in slight203.Ellipsoids AndTheGeoid As Reference Surfacesalterations of the direction of gravity.Thesealterations arereflected in the irregular shapeofthegeoid, the surfacethatSince the surface of the geoid is irregular and the sur-is perpendicular toaplumb line.face of the ellipsoid is regular, no one ellipsoid can provideSince the earth is in fact flattened slightly at the polesother than an approximation of part of the geoidal surfaceand bulges somewhat at the equator, the geometric figureFigure 203illustrates an example.The ellipsoid that fitsused ingeodesytomostnearlyapproximatetheshapeofthewell in North America does not fit well in Europe; there-earth is the oblate spheroid or ellipsoid ofrevolution.Thisfore, itmust bepositioneddifferentlyis the three dimensional shape obtained by rotating an el-lipse about its minor axis202.DefiningTheEllipsoidNNAAn ellipsoid of revolution is uniquely defined by spec-ifying twoparameters.Geodesists, by convention, use thesemimajor axis and flattening.The size is represented bythe radius at the equator,the semimajor axis.The shape ofthe ellipsoid is given by the flattening, which indicates howclosely an ellipsoid approachesa spherical shape.Theflat-tening is the ratio of the difference between the semimajorand semiminor axes ofthe ellipsoid and the semimajor axisSee Figure 202. If a and b represent the semimajor andsemiminor axes, respectively, of the ellipsoid, and f is theO,flattening,N15CFigure 203.The geoid and two ellipsoids, illustrating howthe ellipsoid which fits well inNorth America will not fitbwell in Europe, and must have a different origin(exaggeratedfor clarity)A number of reference ellipsoids are used in geodesyandmappingbecause anellipsoid is mathematically sim-plerthanthegeoid204.CoordinatesFigure202.An ellipsoid of revolution,with semimajoraxis (a), and semiminor axis (b)The astronomic latitude is the angle between the

16 GEODESY AND DATUMS IN NAVIGATION The surface of the geoid, with some exceptions, tends to rise under mountains and to dip above ocean basins. For geodetic, mapping, and charting purposes, it is nec￾essary to use a regular or geometric shape which closely approximates the shape of the geoid either on a local or glo￾bal scale and which has a specific mathematical expression. This shape is called the ellipsoid. The separations of the geoid and ellipsoid are called geoidal heights, geoidal undulations, or geoidal separations. The irregularities in density and depths of the material making up the upper crust of the earth also result in slight alterations of the direction of gravity. These alterations are reflected in the irregular shape of the geoid, the surface that is perpendicular to a plumb line. Since the earth is in fact flattened slightly at the poles and bulges somewhat at the equator, the geometric figure used in geodesy to most nearly approximate the shape of the earth is the oblate spheroid or ellipsoid of revolution. This is the three dimensional shape obtained by rotating an el￾lipse about its minor axis. 202. Defining The Ellipsoid An ellipsoid of revolution is uniquely defined by spec￾ifying two parameters. Geodesists, by convention, use the semimajor axis and flattening. The size is represented by the radius at the equator, the semimajor axis. The shape of the ellipsoid is given by the flattening, which indicates how closely an ellipsoid approaches a spherical shape. The flat￾tening is the ratio of the difference between the semimajor and semiminor axes of the ellipsoid and the semimajor axis. See Figure 202. If a and b represent the semimajor and semiminor axes, respectively, of the ellipsoid, and f is the flattening, This ratio is about 1/300 for the earth. The ellipsoidal earth model has its minor axis parallel to the earth’s polar axis. 203. Ellipsoids And The Geoid As Reference Surfaces Since the surface of the geoid is irregular and the sur￾face of the ellipsoid is regular, no one ellipsoid can provide other than an approximation of part of the geoidal surface. Figure 203 illustrates an example. The ellipsoid that fits well in North America does not fit well in Europe; there￾fore, it must be positioned differently. A number of reference ellipsoids are used in geodesy and mapping because an ellipsoid is mathematically sim￾pler than the geoid. 204. Coordinates The astronomic latitude is the angle between the Figure 202. An ellipsoid of revolution, with semimajor axis (a), and semiminor axis (b). Figure 203. The geoid and two ellipsoids, illustrating how the ellipsoid which fits well in North America will not fit well in Europe, and must have a different origin. (exaggerated for clarity) f a b – a = . -

17GEODESYANDDATUMSINNAVIGATIONplumblineata station and theplaneofthecelestial equatorof the geodetic meridian at a station and the plane of theIt is thelatitudewhichresults directlyfromobservations ofgeodetic meridian at Greenwich.A geodetic longitude dif-celestialbodies.uncorrectedfordeflectionoftheverticafers from the corresponding astronomic longitude by thecomponentin the meridian(north-south)direction.Astro-primevertical componentof the localdeflectionofthever-nomiclatitudeappliesonlytopositions ontheearth.Itistical divided by the cosine of the latitude.The geodeticreckonedfromtheastronomic equator(oo),north and southcoordinates areusedformapping.through90°The geocentric latitude is the angle at the center oftheThe astronomic longitude is the angle between theellipsoid (usedtorepresenttheearth)betweentheplaneofplane of the celestial meridian at a station and the plane ofthe equator,anda straight line (or radius vector) to a pointthe celestial meridian at Greenwich. It is the longitudeon the surface of the ellipsoid.This differs from geodeticwhichresultsdirectlyfromobservationsofcelestialbodieslatitudebecause the earth is approximated more closely byuncorrectedfordeflection ofthevertical componentinthea spheroid than a sphere and the meridians are ellipses, notprime vertical (east-west) direction.These are the coordi-perfectcircles.nates observed bythe celestial navigator using a sextant andBoth geocentric and geodetic latitudes refer to the ref-averyaccurateclockbased on theearth's rotationerence ellipsoid and notthe earth.Sincetheparallels ofAstronomic observations by geodesists are made withlatitude are considered to be circles,geodetic longitude isoptical instruments(theodolite,zenith camera,prismaticgeocentric,anda separateexpression is not used.astrolabe)which all contain leveling devices.When proper-Because of the oblate shapeof the ellipsoid.thelengthly adjusted, the vertical axis of the instrument coincidesofa degree of geodetic latitude is not everywhere the same,with the direction of gravity,and is, therefore,perpendicu-increasing fromabout 59.7nautical miles at the equator tolar to thegeoid.Thus,astronomic positions are referencedabout 60.3nautical miles at thepoles.to thegeoid. Sincethegeoid is an irregular, non-mathemat-A horizontal geodetic datum usually consists of theical surface,astronomic positions are whollyindependentastronomic and geodetic latitude,and astronomic and geo-ofeachotherdeticlongitudeofaninitialpoint(origin):anazimuthofaThe geodetic latitude is the angle which the normal toline(direction);theparameters (radius andflattening)ofthethe ellipsoid at a stationmakes withtheplane of thegeodet-ellipsoid selectedforthecomputations,andthegeoidal sep-ic equator.In recording a geodetic position, it is essentialaration at the origin.A change in any of these quantitiesthatthegeodeticdatumonwhichitisbasedbealsostatedaffects every point on the datum.A geodetic latitude differs from the correspondingastro-For this reason, while positions within a given datum arenomic latitudeby theamountofthemeridian component ofthelocaldeflectionoftheverticaldirectlyandaccuratelyrelateable,thosefromdifferentdatumsThe geodetic longitude is the angle between the planemustbetransformedtoacommondatumforconsistencyTYPESOFGEODETICSURVEY205.TriangulationTo establish an arc of triangulation between two wide-lyseparated locations,the baselinemay bemeasured andThemostcommontypeofgeodetic surveyisknownaslongitudeandlatitudedeterminedfortheinitialpointsateachlocation.Thelinesarethenconnectedbyaseriesoftriangulation.Triangulation consists ofthe measurementadjoining triangles forming quadrilaterals extendingfromoftheanglesofaseriesoftriangles.Theprincipleoftrian-gulation is based on plane trigonometry.If the distanceeach end.All angles ofthe triangles are measured repeated-ly to reduce errors. With the longitude, latitude, andalong one side ofthe triangle and the angles at each end areazimuth of the initial points, similar data is computed foraccuratelymeasured, theothertwo sides and theremainingeach vertex of thetriangles,thereby establishing triangula-anglecanbe computed.Inpractice,all of theanglesofev-erytrianglearemeasuredtoprovideprecisemeasurements.tionstations,orgeodeticcontrolstations.ThecoordinatesAlso,the latitude and longitude ofone end of the measuredofeachofthestationsaredefinedasgeodeticcoordinatesside along with the length and direction (azimuth)of theTriangulation is extended over large areas by connectside providesufficient datato compute the latitude and lon-ingandextendingseriesofarcs toforma networkongitude of the otherend of the sidetriangulation system.The network is adjusted in a mannerThe measured side ofthe basetriangle is called a basewhich reduces the effect of observational errors to a mini-line.Measurementsaremadeascarefullyandaccuratelyasmum.Adenserdistributionofgeodeticcontrolisachievedpossible with specially calibrated tapes or wires ofInvar,anin a system by subdividing orfilling in with other surveys.alloyhighly resistant tochanges in length resulting fromThere are four general classes or orders of triangula-tion.First-order(primary)triangulation is the most precisechanges in temperature. The tape or wires are checked pe-riodically against standardmeasures of length.and exacttype.Themost accurate instrumentsand rigorous

GEODESY AND DATUMS IN NAVIGATION 17 plumb line at a station and the plane of the celestial equator. It is the latitude which results directly from observations of celestial bodies, uncorrected for deflection of the vertical component in the meridian (north-south) direction. Astro￾nomic latitude applies only to positions on the earth. It is reckoned from the astronomic equator (0°), north and south through 90°. The astronomic longitude is the angle between the plane of the celestial meridian at a station and the plane of the celestial meridian at Greenwich. It is the longitude which results directly from observations of celestial bodies, uncorrected for deflection of the vertical component in the prime vertical (east-west) direction. These are the coordi￾nates observed by the celestial navigator using a sextant and a very accurate clock based on the earth’s rotation. Astronomic observations by geodesists are made with optical instruments (theodolite, zenith camera, prismatic astrolabe) which all contain leveling devices. When proper￾ly adjusted, the vertical axis of the instrument coincides with the direction of gravity, and is, therefore, perpendicu￾lar to the geoid. Thus, astronomic positions are referenced to the geoid. Since the geoid is an irregular, non-mathemat￾ical surface, astronomic positions are wholly independent of each other. The geodetic latitude is the angle which the normal to the ellipsoid at a station makes with the plane of the geodet￾ic equator. In recording a geodetic position, it is essential that the geodetic datum on which it is based be also stated. A geodetic latitude differs from the corresponding astro￾nomic latitude by the amount of the meridian component of the local deflection of the vertical. The geodetic longitude is the angle between the plane of the geodetic meridian at a station and the plane of the geodetic meridian at Greenwich. A geodetic longitude dif￾fers from the corresponding astronomic longitude by the prime vertical component of the local deflection of the ver￾tical divided by the cosine of the latitude. The geodetic coordinates are used for mapping. The geocentric latitude is the angle at the center of the ellipsoid (used to represent the earth) between the plane of the equator, and a straight line (or radius vector) to a point on the surface of the ellipsoid. This differs from geodetic latitude because the earth is approximated more closely by a spheroid than a sphere and the meridians are ellipses, not perfect circles. Both geocentric and geodetic latitudes refer to the ref￾erence ellipsoid and not the earth. Since the parallels of latitude are considered to be circles, geodetic longitude is geocentric, and a separate expression is not used. Because of the oblate shape of the ellipsoid, the length of a degree of geodetic latitude is not everywhere the same, increasing from about 59.7 nautical miles at the equator to about 60.3 nautical miles at the poles. A horizontal geodetic datum usually consists of the astronomic and geodetic latitude, and astronomic and geo￾detic longitude of an initial point (origin); an azimuth of a line (direction); the parameters (radius and flattening) of the ellipsoid selected for the computations; and the geoidal sep￾aration at the origin. A change in any of these quantities affects every point on the datum. For this reason, while positions within a given datum are directly and accurately relateable, those from different datums must be transformed to a common datum for consistency. TYPES OF GEODETIC SURVEY 205. Triangulation The most common type of geodetic survey is known as triangulation. Triangulation consists of the measurement of the angles of a series of triangles. The principle of trian￾gulation is based on plane trigonometry. If the distance along one side of the triangle and the angles at each end are accurately measured, the other two sides and the remaining angle can be computed. In practice, all of the angles of ev￾ery triangle are measured to provide precise measurements. Also, the latitude and longitude of one end of the measured side along with the length and direction (azimuth) of the side provide sufficient data to compute the latitude and lon￾gitude of the other end of the side. The measured side of the base triangle is called a base￾line. Measurements are made as carefully and accurately as possible with specially calibrated tapes or wires of Invar, an alloy highly resistant to changes in length resulting from changes in temperature. The tape or wires are checked pe￾riodically against standard measures of length. To establish an arc of triangulation between two wide￾ly separated locations, the baseline may be measured and longitude and latitude determined for the initial points at each location. The lines are then connected by a series of adjoining triangles forming quadrilaterals extending from each end. All angles of the triangles are measured repeated￾ly to reduce errors. With the longitude, latitude, and azimuth of the initial points, similar data is computed for each vertex of the triangles, thereby establishing triangula￾tion stations, or geodetic control stations. The coordinates of each of the stations are defined as geodetic coordinates. Triangulation is extended over large areas by connect￾ing and extending series of arcs to form a network or triangulation system. The network is adjusted in a manner which reduces the effect of observational errors to a mini￾mum. A denser distribution of geodetic control is achieved in a system by subdividing or filling in with other surveys. There are four general classes or orders of triangula￾tion. First-order (primary) triangulation is the most precise and exact type. The most accurate instruments and rigorous

18GEODESYANDDATUMSINNAVIGATIONcomputation methods are used. It is costly and time-con-leveling It is often the only practical method of establishingsuming,andisusuallyusedtoprovidethebasicframeworkaccurateelevationcontrol inmountainousareasIn barometric leveling,differences in height are deter-of control dataforan area, and thedetermination of thefig-ure of the earth. The most accurate first-order surveysminedbymeasuringthedifferences in atmosphericpressurefurnish control points which can be interrelated with an ac-at various elevations.Air pressure is measured by mercurialcuracy rangingfrom1part in25,000over shortdistancestoor aneroid barometer, or a boilingpoint thermometer.Al-approximately 1 part in 100,000 for long distances.though theaccuracyofthis method is not as great as either oftheothertwo,itobtainsrelativeheights veryrapidlyat pointsSecond-order triangulation furnishes points closer to-gether than in the primary network. While second-orderwhicharefairlyfarapart.Itisusedinreconnaissanceandex-ploratory surveys where moreaccurate measurements will besurveys may cover quite extensive areas, they are usuallytiedtoaprimarysystemwherepossible.Theproceduresaremadelateror wherea high degree ofaccuracy is not requiredless exacting and the proportional error is 1part in 10,o00Third-order triangulation is run between points in asecondary survey. It is used to densify local control nets andposition the topographic and hydrographic detail of the ar-ea.Triangle errorcan amounttoIpart in 5,o00The sole accuracy requirement for fourth-ordertrian-gulation is that the positions be located without anyappreciableerroronmaps compiled on thebasisof thecon-trol. Fourth-order control is done primarily as mappingcontrol206. Trilateration, Traverse, And Vertical SurveyingTrilateration involvesmeasuringthesides ofachainoftri-angles or other polygons. From them, the distance and directionfrom A to B can be computed.Figure 206 shows this process.Traverse involves measuring distances and the anglesbetweenthem withouttrianglesforthepurposeofcomput-ingthedistance anddirectionfromAtoB.SeeFigure206Vertical surveying is the process of determining eleva-tions above mean sea-level. In geodetic surveys executedprimarily for mapping, geodetic positions are referred to an el-lipsoid, and the elevations of thepositions arereferred to thegeoid. However, for satellite geodesy the geoidal heights mustbe considered to establish the corectheight above thegeoid.Precise geodetic leveling is used to establish a basicnetworkofvertical control points.Fromthese,the height ofotherpositions inthe surveycan bedetermined by supple-mentary methods. The mean sea-level surface used as areference(vertical datum) is determined by averaging thehourly waterheights for a specified period of timeatspec-ifiedtidegauges.There are three leveling techniques: differential, trig-onometric, and barometric.Differential leveling is themost accurate of the three methods.With the instrumentlocked in position,readings are made on two calibratedstaffs held in an upright position ahead of and behind the in-strument.The differencebetweenreadings is the differenceinelevationbetween thepoints.Trigonometric leveling involves measuring a verticalanglefrom aknown distance with a theodoliteand comput-ing the elevation of the point. With this method, verticalmeasurement can be made at the same time horizontal anglesare measured for triangulation.It is, therefore,a somewhatmoreeconomical method but less accuratethan differential

18 GEODESY AND DATUMS IN NAVIGATION computation methods are used. It is costly and time-con￾suming, and is usually used to provide the basic framework of control data for an area, and the determination of the fig￾ure of the earth. The most accurate first-order surveys furnish control points which can be interrelated with an ac￾curacy ranging from 1 part in 25,000 over short distances to approximately 1 part in 100,000 for long distances. Second-order triangulation furnishes points closer to￾gether than in the primary network. While second-order surveys may cover quite extensive areas, they are usually tied to a primary system where possible. The procedures are less exacting and the proportional error is 1 part in 10,000. Third-order triangulation is run between points in a secondary survey. It is used to densify local control nets and position the topographic and hydrographic detail of the ar￾ea. Triangle error can amount to 1 part in 5,000. The sole accuracy requirement for fourth-order trian￾gulation is that the positions be located without any appreciable error on maps compiled on the basis of the con￾trol. Fourth-order control is done primarily as mapping control. 206. Trilateration, Traverse, And Vertical Surveying Trilateration involves measuring the sides of a chain of tri￾angles or other polygons. From them, the distance and direction from A to B can be computed. Figure 206 shows this process. Traverse involves measuring distances and the angles between them without triangles for the purpose of comput￾ing the distance and direction from A to B. See Figure 206. Vertical surveying is the process of determining eleva￾tions above mean sea-level. In geodetic surveys executed primarily for mapping, geodetic positions are referred to an el￾lipsoid, and the elevations of the positions are referred to the geoid. However, for satellite geodesy the geoidal heights must be considered to establish the correct height above the geoid. Precise geodetic leveling is used to establish a basic network of vertical control points. From these, the height of other positions in the survey can be determined by supple￾mentary methods. The mean sea-level surface used as a reference (vertical datum) is determined by averaging the hourly water heights for a specified period of time at spec￾ified tide gauges. There are three leveling techniques: differential, trig￾onometric, and barometric. Differential leveling is the most accurate of the three methods. With the instrument locked in position, readings are made on two calibrated staffs held in an upright position ahead of and behind the in￾strument. The difference between readings is the difference in elevation between the points. Trigonometric leveling involves measuring a vertical angle from a known distance with a theodolite and comput￾ing the elevation of the point. With this method, vertical measurement can be made at the same time horizontal angles are measured for triangulation. It is, therefore, a somewhat more economical method but less accurate than differential leveling. It is often the only practical method of establishing accurate elevation control in mountainous areas. In barometric leveling, differences in height are deter￾mined by measuring the differences in atmospheric pressure at various elevations. Air pressure is measured by mercurial or aneroid barometer, or a boiling point thermometer. Al￾though the accuracy of this method is not as great as either of the other two, it obtains relative heights very rapidly at points which are fairly far apart. It is used in reconnaissance and ex￾ploratory surveys where more accurate measurements will be made later or where a high degree of accuracy is not required

19GEODESYANDDATUMSINNAVIGATIONN4LINEBASEOBTRIANGULATIONZ+OBTRILATERATIONANPBTRAVERSEFigure 206.Triangulation, trilateration, and traverse.DATUMCONNECTIONS207.DefinitionsThe North American Datum, 1927 (NAD 27) has beenused in the United States for about 50 years, but it is being re-A datum is defined as any numerical or geometricalplaced by datums based on the World Geodetic Systemquantity or set of such quantities which serves as a refer-NAD27coordinatesarebasedonthelatitudeand longitudeofencepointtomeasureotherquantitiesa triangulation station (thereferencepoint)at Mead's Ranch inIn geodesy,as well as in cartography and navigation, twoKansas, the azimuth to a nearby triangulation station calledtypes of datums must be considered: a horizontal datum andWaldo, and the mathematical parameters of the Clarke Ellip-a vertical datum.The horizontal datum forms the basis forsoid of1866.Other datums throughout the world use differentcomputationsof horizontal position.Thevertical datumpro-assumptions as to origin points and ellipsoids.vides the reference to measure heights. A horizontal datumTheorigin oftheEuropeanDatum isat Potsdammaybedefined atan origin point on the ellipsoid (local datum)Germany.Numerous national systems have been joinedsuch that the center of the ellipsoid coincides with the Earth'sinto a large datum based upon the International Ellipsoid of1924 which was oriented by a modified astrogeodetic meth-center of mass (geocentricdatum).Thecoordinatesforpointsin specific geodetic surveys and triangulation networks areod. European, African, and Asian triangulation chains werecomputedfrom certain initial quantities,ordatums.connected, and African measurements from Cairo to CapeTown were completed.Thus, all of Europe, Africa, and208.PreferredDatumsAsia are molded into one great system. Through commonsurveystations,itwasalsopossibletoconvertdatafromtheIn areas of overlapping geodetic triangulation networks,Russian Pulkova, 1932 system to the European Datum, andeach computed on a different datum, the coordinates of theas a result, the European Datum includes triangulation aspoints given with respectto one datum will differfrom thosefar east as the 84th meridian. Additional ties across thegiven with respect to the other. The differences can be used toMiddle Easthave permitted connection of the Indian andderivetransformation formulas.Datums areconnected byde-EuropeanDatums.veloping transformation formulas at common points, eitherThe Ordnance Survey of Great Britain 1936Datumbetweenoverlapping control networksor by satellitehas no point of origin.The data was derived as a bestfit be-connections.tweenretriangulationandoriginalvaluesofIlpointsoftheMany countries have developed national datums whichearlier Principal Triangulation ofGreat Britain (1783-1853).differfrom those of theirneighbors.Accordingly,nationalTokyo Datum has its origin in Tokyo. It is defined inmaps and charts often do not agree along national borders.terms of the Bessel Ellipsoid and oriented by a single astro-

GEODESY AND DATUMS IN NAVIGATION 19 DATUM CONNECTIONS 207. Definitions A datum is defined as any numerical or geometrical quantity or set of such quantities which serves as a refer￾ence point to measure other quantities. In geodesy, as well as in cartography and navigation, two types of datums must be considered: a horizontal datum and a vertical datum. The horizontal datum forms the basis for computations of horizontal position. The vertical datum pro￾vides the reference to measure heights. A horizontal datum may be defined at an origin point on the ellipsoid (local datum) such that the center of the ellipsoid coincides with the Earth’s center of mass (geocentric datum). The coordinates for points in specific geodetic surveys and triangulation networks are computed from certain initial quantities, or datums. 208. Preferred Datums In areas of overlapping geodetic triangulation networks, each computed on a different datum, the coordinates of the points given with respect to one datum will differ from those given with respect to the other. The differences can be used to derive transformation formulas. Datums are connected by de￾veloping transformation formulas at common points, either between overlapping control networks or by satellite connections. Many countries have developed national datums which differ from those of their neighbors. Accordingly, national maps and charts often do not agree along national borders. The North American Datum, 1927 (NAD 27) has been used in the United States for about 50 years, but it is being re￾placed by datums based on the World Geodetic System. NAD 27 coordinates are based on the latitude and longitude of a triangulation station (the reference point) at Mead’s Ranch in Kansas, the azimuth to a nearby triangulation station called Waldo, and the mathematical parameters of the Clarke Ellip￾soid of 1866. Other datums throughout the world use different assumptions as to origin points and ellipsoids. The origin of the European Datum is at Potsdam, Germany. Numerous national systems have been joined into a large datum based upon the International Ellipsoid of 1924 which was oriented by a modified astrogeodetic meth￾od. European, African, and Asian triangulation chains were connected, and African measurements from Cairo to Cape Town were completed. Thus, all of Europe, Africa, and Asia are molded into one great system. Through common survey stations, it was also possible to convert data from the Russian Pulkova, 1932 system to the European Datum, and as a result, the European Datum includes triangulation as far east as the 84th meridian. Additional ties across the Middle East have permitted connection of the Indian and European Datums. The Ordnance Survey of Great Britain 1936 Datum has no point of origin. The data was derived as a best fit be￾tween retriangulation and original values of 11 points of the earlier Principal Triangulation of Great Britain (1783-1853). Tokyo Datum has its origin in Tokyo. It is defined in terms of the Bessel Ellipsoid and oriented by a single astro￾Figure 206. Triangulation, trilateration, and traverse

20GEODESYANDDATUMSINNAVIGATIONNORTHAMERICANOKYOCAPEARCAUSTRALIANFigure 208. Major geodetic datum blocks.nomic station.Triangulation ties through Korea connect theon the Everest Ellipsoid with its origin at Kalianpur, in cen-Japanesedatum withtheManchuriandatum.Unfortunately,tral India. It is largely the result of the untiring work of SirTokyo is situated on a steep slope on the geoid,and the single-George Everest(1790-1866),Surveyor General in Indiastation orientation has resulted in large systematic geoidal sep-from1830to1843.Heisbestknownbythemountainarations as the system is extended from its initial pointnamedafterhim,but byfar his most important legacywasTheIndianDatum is thepreferreddatumforIndia andthesurveyoftheIndiansubcontinentseveral adjacentcountries in Southeast Asia.It is computedMODERNGEODETICSYSTEMS209.DevelopmentOfTheWorldGeodeticSystemcombined leadingto thedevelopmentof theDoDWorldGeodeticSystemof1960(WGS60)By the late1950's the increasing range and sophistica-InJanuary1966.aWorldGeodeticSvstemCommitteetion of weapons systemshad renderedlocal ornationalwas charged with the responsibility for developing an imdatums inadequatefor military purposes;these newweap-proved WGSneededto satisfymapping,charting,andons required datums at least continental in scope.Ingeodeticrequirements.Additional surfacegravityobserva-response to these requirements, the U.S. Department of De-tions,results from the extension of triangulation andfense generated a geocentric reference system to whichtrilaterationnetworks,andlargeamountsofDopplerandop-different geodetic networks could be referred and estab-tical satellitedata had become available sincethedevelopment of WGS 60.Using the additional data and imlished compatibility between the coordinates of sites ofinterest.Efforts of theArmy,Navy,and AirForcewereprovedtechniques,theCommitteeproducedWGS66which

20 GEODESY AND DATUMS IN NAVIGATION nomic station. Triangulation ties through Korea connect the Japanese datum with the Manchurian datum. Unfortunately, Tokyo is situated on a steep slope on the geoid, and the single￾station orientation has resulted in large systematic geoidal sep￾arations as the system is extended from its initial point. The Indian Datum is the preferred datum for India and several adjacent countries in Southeast Asia. It is computed on the Everest Ellipsoid with its origin at Kalianpur, in cen￾tral India. It is largely the result of the untiring work of Sir George Everest (1790-1866), Surveyor General in India from 1830 to 1843. He is best known by the mountain named after him, but by far his most important legacy was the survey of the Indian subcontinent. MODERN GEODETIC SYSTEMS 209. Development Of The World Geodetic System By the late 1950’s the increasing range and sophistica￾tion of weapons systems had rendered local or national datums inadequate for military purposes; these new weap￾ons required datums at least continental in scope. In response to these requirements, the U.S. Department of De￾fense generated a geocentric reference system to which different geodetic networks could be referred and estab￾lished compatibility between the coordinates of sites of interest. Efforts of the Army, Navy, and Air Force were combined leading to the development of the DoD World Geodetic System of 1960 (WGS 60). In January 1966, a World Geodetic System Committee was charged with the responsibility for developing an im￾proved WGS needed to satisfy mapping, charting, and geodetic requirements. Additional surface gravity observa￾tions, results from the extension of triangulation and trilateration networks, and large amounts of Doppler and op￾tical satellite data had become available since the development of WGS 60. Using the additional data and im￾proved techniques, the Committee produced WGS 66 which Figure 208. Major geodetic datum blocks

21GEODESYANDDATUMSINNAVIGATIONservedDoDneedsfollowing itsimplementation in1967210.TheNewNorthAmericanDatumOf1983The same World Geodetic System Committee beganwork in 1970 to develop a replacement for WGS 66. Since theTheCoastAnd Geodetic SurveyoftheNational Oceandevelopment of WGS 66, large quantities of additional dataService(NOS),NOAA,is responsiblefor charting Unitedhad becomeavailablefrombothDopplerandoptical satellites,States waters.From 1927 to 1987,U.S.charts were basedsurfacegravity surveys,triangulation and trilateration surveys,on NAD27, using the Clarke 1866ellipsoid. In 1989, thehighprecisiontraverses,andastronomicsurveys.U.S.officiallyswitched toNAD83(navigationally equiva-In addition, improved capabilities had been developedlent to WGS 84 and other WGS systems)for all mappinginbothcomputersandcomputersoftware.Continuedreand charting purposes, and all new NOS chart production issearchincomputational procedures and erroranalyses hadbased on this new standard.produced better methods and an improvedfacilityfor han-Thegrid ofinterconnected surveys whichcriss-crossesdling and combining data. After an extensive effortthe United States consists of some250,000 control pointsextending overa period of approximatelythreeyears,theeach consisting of the latitude and longitude of the point,Committee completed the development ofthe Departmentplus additional data such as elevation.Converting theNADofDefenseWorldGeodeticSystem1972(WGS72)27coordinatestoNAD83involved recomputing theposi-Further refinement of WGS 72 resulted in the newtion of each pointbased on the newNAD83datum.InWorldGeodeticSystemof1984(WGS84).Asof 1990addition to the 250,000U.S.control points,several thou-WGS84 is being used for chartmakingbyDMA.For sur-sand more were added to tie in surveys from Canadafacenavigation,WGS 60, 66,72and thenewWGS84areMexico,andCentralAmericaessentiallythesame,sothatpositionscomputedonanyConversion of new edition charts to the new datums,WGS coordinates can beplotteddirectlyontheotherswith-eitherWGS84orNAD83,involvesconvertingreferenceoutcorrection.points on each chart from the old datum to the new, and ad-TheWGS system isnotbased onasinglepoint,butmanyjusting the latitude and longitude grid (known as thepoints,fixed withextremeprecisionby satellitefixesandstatisgraticule)so that itreflects thenewly plotted positions.Thistical methods. The result is an ellipsoid which fits the realadjustment of the graticule is the only difference betweensurface oftheearth,orgeoid,farmoreaccuratelythan any other.The WGS system is applicable worldwide. All regional datumscharts which differ only in datum.All charted features re-can bereferenced toWGS oncea surveytiehas been mademaininexactlythesamerelativepositions.IMPACTSON NAVIGATION211.DatumShiftsgether.For example, theNAD27to NAD 83 conversionresults in changes in latitude of 40 meters in Miami, 11One impact of different datums on navigation appearsmeters in New York, and 20 meters in Seattle.Longitudewhen a navigation system provides a fix based on a datumchanges for this conversion are about 22 meters in Miami,35meters in NewYork,and 93meters in Seattle.different from that used for the nautical chart.The resultingMost charts produced by DMA and NOS show a“datumplottedpositionmaybedifferentfromtheactual locationon that chart.This difference isknown as a datum shiftnote."This note isusuallyfound in the titleblock or intheupperleftmargin ofthechart.Accordingtotheyearof thechartedi-Anothereffectonnavigationoccurswhenshiftingbetion,the scale,and policy atthetime ofproduction,the notemaytween charts that havebeenmade using different datums.Ifany position is replotted on a chart of another datum usingsayWorld Geodetic System1972(WGS-72)""World Geo-onlylatitudeand longitudefor locating thatposition,thedetic System 1984 (WGS-84)",or"World Geodetic Systemnewlyplottedpositionwill notmatchwithrespecttoother(WGS)"Adatumnotefora chartforwhich satellitepositionschartedfeatures.Thisdatumshiftmaybeavoidedbyre-canbeplottedwithoutcorrectionwillread:Positionsobtainedplotting using bearings and ranges to common points.Iffrom satellite navigation Systems referred to (REFERENCEDATUM) can be plotted directly on this chart."datumshiftconversionnotesfortheapplicabledatumsareDMA reproductions of foreign chart's will usually begiven on the charts,positions defined bylatitudeand longi-tudemaybereplottedafterapplyingthenoted correctioninthedatum orreferencesystem of theproducingcountryThepositionsgivenforchartcorrections intheNoticetoIn these cases a conversion factor is given in the followingMariners reflecttheproperdatumforeach specificchart andformat:“Positions obtained from satellite navigation sys-edition number.Duetoconversion ofchartsbased onoldda-tems referred to the(Reference Datum)must bemovedtumstomoremodernones,andtheuseofmanydifferentX.XXminutes(Northward/Southward)andX.XXminutes(Eastward/Westward)toagreewiththis chart.datumsthroughouttheworldchartcorrectionsintendedforone editionofa chartmaynotbe safelyplotted on anyother.Somecharts cannotbetied intoWGSbecauseof lackThesedatum shifts arenot constant throughout a givenof recent surveys.Currentlyissued charts of someareas arearea, butvaryaccordingtohowthediffering datumsfit to-based on surveys or usedata obtained in the age of sailing

GEODESY AND DATUMS IN NAVIGATION 21 served DoD needs following its implementation in 1967. The same World Geodetic System Committee began work in 1970 to develop a replacement for WGS 66. Since the development of WGS 66, large quantities of additional data had become available from both Doppler and optical satellites, surface gravity surveys, triangulation and trilateration surveys, high precision traverses, and astronomic surveys. In addition, improved capabilities had been developed in both computers and computer software. Continued re￾search in computational procedures and error analyses had produced better methods and an improved facility for han￾dling and combining data. After an extensive effort extending over a period of approximately three years, the Committee completed the development of the Department of Defense World Geodetic System 1972 (WGS 72). Further refinement of WGS 72 resulted in the new World Geodetic System of 1984 (WGS 84). As of 1990, WGS 84 is being used for chart making by DMA. For sur￾face navigation, WGS 60, 66, 72 and the new WGS 84 are essentially the same, so that positions computed on any WGS coordinates can be plotted directly on the others with￾out correction. The WGS system is not based on a single point, but many points, fixed with extreme precision by satellite fixes and statis￾tical methods. The result is an ellipsoid which fits the real surface of the earth, or geoid, far more accurately than any other. The WGS system is applicable worldwide. All regional datums can be referenced to WGS once a survey tie has been made. 210. The New North American Datum Of 1983 The Coast And Geodetic Survey of the National Ocean Service (NOS), NOAA, is responsible for charting United States waters. From 1927 to 1987, U.S. charts were based on NAD 27, using the Clarke 1866 ellipsoid. In 1989, the U.S. officially switched to NAD 83 (navigationally equiva￾lent to WGS 84 and other WGS systems) for all mapping and charting purposes, and all new NOS chart production is based on this new standard. The grid of interconnected surveys which criss-crosses the United States consists of some 250,000 control points, each consisting of the latitude and longitude of the point, plus additional data such as elevation. Converting the NAD 27 coordinates to NAD 83 involved recomputing the posi￾tion of each point based on the new NAD 83 datum. In addition to the 250,000 U.S. control points, several thou￾sand more were added to tie in surveys from Canada, Mexico, and Central America. Conversion of new edition charts to the new datums, either WGS 84 or NAD 83, involves converting reference points on each chart from the old datum to the new, and ad￾justing the latitude and longitude grid (known as the graticule) so that it reflects the newly plotted positions. This adjustment of the graticule is the only difference between charts which differ only in datum. All charted features re￾main in exactly the same relative positions. IMPACTS ON NAVIGATION 211. Datum Shifts One impact of different datums on navigation appears when a navigation system provides a fix based on a datum different from that used for the nautical chart. The resulting plotted position may be different from the actual location on that chart. This difference is known as a datum shift. Another effect on navigation occurs when shifting be￾tween charts that have been made using different datums. If any position is replotted on a chart of another datum using only latitude and longitude for locating that position, the newly plotted position will not match with respect to other charted features. This datum shift may be avoided by re￾plotting using bearings and ranges to common points. If datum shift conversion notes for the applicable datums are given on the charts, positions defined by latitude and longi￾tude may be replotted after applying the noted correction. The positions given for chart corrections in the Notice to Mariners reflect the proper datum for each specific chart and edition number. Due to conversion of charts based on old da￾tums to more modern ones, and the use of many different datums throughout the world, chart corrections intended for one edition of a chart may not be safely plotted on any other. These datum shifts are not constant throughout a given area, but vary according to how the differing datums fit to￾gether. For example, the NAD 27 to NAD 83 conversion results in changes in latitude of 40 meters in Miami, 11 meters in New York, and 20 meters in Seattle. Longitude changes for this conversion are about 22 meters in Miami, 35 meters in New York, and 93 meters in Seattle. Most charts produced by DMA and NOS show a “datum note.” This note is usually found in the title block or in the upper left margin of the chart. According to the year of the chart edi￾tion, the scale, and policy at the time of production, the note may say “World Geodetic System 1972 (WGS-72)”, “World Geo￾detic System 1984 (WGS-84)”, or “World Geodetic System (WGS).” A datum note for a chart for which satellite positions can be plotted without correction will read: “Positions obtained from satellite navigation systems referred to (REFERENCE DATUM) can be plotted directly on this chart.” DMA reproductions of foreign chart‘s will usually be in the datum or reference system of the producing country. In these cases a conversion factor is given in the following format: “Positions obtained from satellite navigation sys￾tems referred to the (Reference Datum) must be moved X.XX minutes (Northward/Southward) and X.XX minutes (Eastward/ Westward) to agree with this chart.” Some charts cannot be tied in to WGS because of lack of recent surveys. Currently issued charts of some areas are based on surveys or use data obtained in the age of sailing

ships.The lack of surveyed control points means that they cannot be properly referenced to modern geodetic systems. Inthis case there may be a note that says: "Adjustments to WGS cannot be determined for this chart."Afewchartsmayhavenodatumnoteat all, butmay carrya notewhichsays:From various sourcesto (year)."Inthesecasesthereisnowayforthenavigatortodeterminethemathematical differencebetweenthelocal datumandWGSpositionsHowever, if a radar or visual fix can be very accurately determined, the difference between this fix and a satellite fix candetermineanapproximatecorrectionfactorwhichwillbereasonablyconsistentforthat local area212.MinimizingErrors Caused ByDifferingDatumsTominimizeproblemscausedbydifferingdatumsPlot chart corrections only on the specific charts and editions for which they are intended. Each chart correction is specific toonly one edition ofa chart. When the same correction is made on two charts based on different datums,the positions for thesamefeaturemaydifferslightly.This difference is equal to thedatum shiftbetweenthe two datums for that area. Try to determine the source and datum of positions of temporary features, such as drill rigs. In general they are given in thedatum used in the area in question. Since these are usuallypositioned using satellites, WGS is the normal datum.A datumcorrection, if needed,mightbefoundona chartofthearea.Remember that ifthe datum ofa plottedfeature is notknown,position inaccuraciesmay result It is wiseto allowamarginoferror ifthere is anydoubt about thedatum..Know howthe datum ofthepositioning system you areusing (Loran, GPS,etc.)relates to your chart.GPS and otheimodernpositioning systems usetheWGS datum.If your chart is onany otherdatum,youmustapplyadatum cor.rectionwhenplottingtheGPSpositionofthechart.Modern geodesy can support the goal of producing all the world's charts on the same datum. Coupling an electronicchart with satellitepositioningwilleliminate theproblemofdifferingdatums becauseelectronicallyderived positions andthevideochartsonwhichtheyaredisplayedarederivedfromoneofthenewworldwidedatums

ships. The lack of surveyed control points means that they cannot be properly referenced to modern geodetic systems. In this case there may be a note that says: “Adjustments to WGS cannot be determined for this chart.” A few charts may have no datum note at all, but may carry a note which says: “From various sources to (year).” In these cases there is no way for the navigator to determine the mathematical difference between the local datum and WGS positions. However, if a radar or visual fix can be very accurately determined, the difference between this fix and a satellite fix can determine an approximate correction factor which will be reasonably consistent for that local area. 212. Minimizing Errors Caused By Differing Datums To minimize problems caused by differing datums: • Plot chart corrections only on the specific charts and editions for which they are intended. Each chart correction is specific to only one edition of a chart. When the same correction is made on two charts based on different datums, the positions for the same feature may differ slightly. This difference is equal to the datum shift between the two datums for that area. • Try to determine the source and datum of positions of temporary features, such as drill rigs. In general they are given in the datum used in the area in question. Since these are usually positioned using satellites, WGS is the normal datum. A datum correction, if needed, might be found on a chart of the area. • Remember that if the datum of a plotted feature is not known, position inaccuracies may result. It is wise to allow a margin of error if there is any doubt about the datum. • Know how the datum of the positioning system you are using (Loran, GPS, etc.) relates to your chart. GPS and other modern positioning systems use the WGS datum. If your chart is on any other datum, you must apply a datum cor￾rection when plotting the GPS position of the chart. Modern geodesy can support the goal of producing all the world’s charts on the same datum. Coupling an electronic chart with satellite positioning will eliminate the problem of differing datums because electronically derived positions and the video charts on which they are displayed are derived from one of the new worldwide datums