《航海学》课程参考文献（地文资料）CHAPTER 01 INTRODUCTION TO MARINE NAVIGATION

CHAPTER 1INTRODUCTIONTOMARINENAVIGATIONDEFINITIONS100.The Art And Science Of Navigation.Celestial navigation involves reducing celestialmeasurements to lines of positionusing tables,Marine navigation blends both science and art. A goodspherical trigonometry,and almanacs.It is used pri-navigatorgathers informationfromeveryavailablesourcemarilyas a backupto satelliteand otherelectronicevaluatesthis information,determines afix,and comparessystems in the open ocean.that fix with his pre-determined“dead reckoning"position.Radionavigation usesradiowavestodeterminepoAnavigatorconstantlyevaluatestheship'sposition,anticipates dangerous situations well before they arise, andsition by eitherradio direction finding systems oralways keeps“ahead of the vessel."Themodern navigatorhyperbolic systems.must also understand thebasic concepts ofthe many navi-. Radar navigation uses radar to determine the dis-gation systems usedtodayevaluatetheiroutput'saccuracy,and arriveatthebestpossiblenavigational decisionstancefrom orbearingof objects whosepositionisNavigation methods and techniques vary with thetypeknown.This process is separate fromradar's use asof vessel, the conditions,and the navigator's experiencea collision avoidance system.Navigating apleasurecraft,for example,differsfromnav-.Satellite navigation uses artificial earth satellitesforigatingacontainership.Bothdifferfromnavigatinga navalvessel.The navigator uses the methods and techniques bestdetermination ofposition.suitedtothevesselandconditionsathandElectronic integrated bridge concepts are driving fu-Someimportantelementsofsuccessful navigationcan-notbeacquiredfromanybookorinstructor.Thescienceofture navigation system planning.Integrated systems takeinputs from various ship sensors, electronically display po-navigation can be taught, but the art ofnavigation must bedeveloped fromexperiencesitioning information,and providecontrol signals requiredto maintain a vessel on a preset course.The navigator be-101.Types Of Navigationcomesa system manager,choosing system presets,interpreting systemoutput,andmonitoringvesselresponseMethods of navigation have changed through historyInpractice,anavigatorsynthesizesdifferentmethodol-Eachnew method has enhanced themariner's ability toogies into a single integrated system.He should never feelcomplete his voyage safely and expeditiously.One of thecomfortable utilizing only one method when others aremost important judgments the navigator must make in-availablefor backup.Each method has advantages and dis-advantages.The navigator must choose methodsvolves choosing the best method to use.Commonlyrecognized types ofnavigation are listed below.appropriate to each particular situation.With theadvent of automated positionfixing and elec-tronic charts,modern navigation is almost completely an.Dead reckoning (DR) determines position by adelectronic process.The mariner is constantly tempted tovancing aknown position for courses and distancesrely solely on electronic systems.This would bea mistake.Aposition sodetermined is calleda dead reckoningElectronic navigationsystemsarealways subjecttofailure,(DR) position. It is generally accepted that onlyandtheprofessionalmarinermustnever forgetthatthecourse and speed determine the DR position. Cor-safety of his ship and crew may depend on skills that differrectingtheDRpositionforleeway,current effects.littlefromthosepracticed generations ago.Proficiency inand steering error result in an estimated positionconventional piloting and celestial navigation remainsessential.(EP).An inertial navigator develops an extremelyaccurateEP..Piloting involves navigating in restricted waters102.Phases Of Navigationwith frequent determination of position relative toFour distinct phases define the navigation process. Thegeographic and hydrographic features.1

1 CHAPTER 1 INTRODUCTION TO MARINE NAVIGATION DEFINITIONS 100. The Art And Science Of Navigation Marine navigation blends both science and art. A good navigator gathers information from every available source, evaluates this information, determines a fix, and compares that fix with his pre-determined “dead reckoning” position. A navigator constantly evaluates the ship’s position, antic￾ipates dangerous situations well before they arise, and always keeps “ahead of the vessel.” The modern navigator must also understand the basic concepts of the many navi￾gation systems used today, evaluate their output’s accuracy, and arrive at the best possible navigational decisions. Navigation methods and techniques vary with the type of vessel, the conditions, and the navigator’s experience. Navigating a pleasure craft, for example, differs from nav￾igating a container ship. Both differ from navigating a naval vessel. The navigator uses the methods and techniques best suited to the vessel and conditions at hand. Some important elements of successful navigation can￾not be acquired from any book or instructor. The science of navigation can be taught, but the art of navigation must be developed from experience. 101. Types Of Navigation Methods of navigation have changed through history. Each new method has enhanced the mariner’s ability to complete his voyage safely and expeditiously. One of the most important judgments the navigator must make in￾volves choosing the best method to use. Commonly recognized types of navigation are listed below. • Dead reckoning (DR) determines position by ad￾vancing a known position for courses and distances. A position so determined is called a dead reckoning (DR) position. It is generally accepted that only course and speed determine the DR position. Cor￾recting the DR position for leeway, current effects, and steering error result in an estimated position (EP). An inertial navigator develops an extremely accurate EP. • Piloting involves navigating in restricted waters with frequent determination of position relative to geographic and hydrographic features. • Celestial navigation involves reducing celestial measurements to lines of position using tables, spherical trigonometry, and almanacs. It is used pri￾marily as a backup to satellite and other electronic systems in the open ocean. • Radio navigation uses radio waves to determine po￾sition by either radio direction finding systems or hyperbolic systems. • Radar navigation uses radar to determine the dis￾tance from or bearing of objects whose position is known. This process is separate from radar’s use as a collision avoidance system. • Satellite navigation uses artificial earth satellites for determination of position. Electronic integrated bridge concepts are driving fu￾ture navigation system planning. Integrated systems take inputs from various ship sensors, electronically display po￾sitioning information, and provide control signals required to maintain a vessel on a preset course. The navigator be￾comes a system manager, choosing system presets, interpreting system output, and monitoring vessel response. In practice, a navigator synthesizes different methodol￾ogies into a single integrated system. He should never feel comfortable utilizing only one method when others are available for backup. Each method has advantages and dis￾advantages. The navigator must choose methods appropriate to each particular situation. With the advent of automated position fixing and elec￾tronic charts, modern navigation is almost completely an electronic process. The mariner is constantly tempted to rely solely on electronic systems. This would be a mistake. Electronic navigation systems are always subject to failure, and the professional mariner must never forget that the safety of his ship and crew may depend on skills that differ little from those practiced generations ago. Proficiency in conventional piloting and celestial navigation remains essential. 102. Phases Of Navigation Four distinct phases define the navigation process. The

2INTRODUCTIONTOMARINENAVIGATION·Coastal Phase: Navigating within 50 miles of themariner should choose the system mixthat meets the accu-racyrequirementsofeachphasecoast or inshore of the200meterdepth contour.. Ocean Phase: Navigating outside the coastal area in.Inland WaterwayPhase:Piloting in narrowcanals.the open sea.channels, rivers, and estuaries.The navigator's position accuracy requirements, his fix:Harbor/Harbor Approach Phase: Navigating to ainterval, and his systems requirements differ in each phase.harbor entrance and piloting in harbor approachThe following table can be used as a general guide for se-channels.lecting theproper system(s).InlandHarbor/HarborCoastalOceanWaterwayApproachXXxxxxxxxDRxxPilotingxxCelestialxxxRadioXRadarXSatelliteTable 102. The relationship of the types and phases of navigation.*Differential GPS maybe used ifavailableNAVIGATIONALTERMSANDCONVENTIONS103.ImportantConventions And Conceptsvoyage.Themeridian of London was usedasearlyas 1676,andThroughout the history of navigation, numerous termsover theyears its popularitygrewas England'smaritime in-and conventions have been established which enjoy world-terests increased.The system of measuring longitude bothwide recognition.The professional navigator,to gainafulleast and west through 180°may have first appeared in theunderstanding of his field, should understand the origin ofmiddle ofthe18th century.Toward the end of that century,certain terms, techniques, and conventions.The followingas theGreenwich Observatory increased inprominence,En-section discusses someof the importantones.glish cartographers began using the meridian of thatobservatoryas areference.ThepublicationbytheObserva-Defining a prime meridian is a comparatively recentdevelopment. Until the beginning ofthe19th century,theretory of thefirst British Nautical Almanac in 1767furtherwas littleuniformity among cartographers as to the meridi-entrenched Greenwich as the prime meridian. An unsuc-an from which tomeasure longitude.Thisdid not lead tocessful attempt wasmade in1810toestablishWashington,anyproblembecause there was no widespread method forD.C.astheprimemeridianforAmerican navigatorsandcar-tographers.In 1884,the meridian of Greenwich wasdetermining longitude accuratelyPtolemy,in the2nd century AD,measured longitudeofficially established as the prime meridian. Today,all mar-itime nations have designated the Greenwich meridian theeastwardfrom areferencemeridian 2degrees west of theprime meridian,except in afew cases where local referencesCanaryIslands.In 1493,PopeAlexanderVI established aline in the Atlantic west of the Azores to divide the territo-areusedforcertainharborchartsCharts are graphic representations ofareas ofthe earthries of Spain and Portugal. For many years, cartographersof thesetwocountriesusedthisdividinglineastheprimefor use in marine or air navigation.Nautical charts depictmeridian.In 1570 the Dutch cartographer Ortelius used thefeatures of particular interest to the marine navigator.Charts haveprobablyexisted sinceatleast600BC.Stereo-easternmost of the CapeVerde Islands.JohnDavis, in his1594The Seaman's Secrets, used the Isle of Fez in the Ca-graphic and orthographic projections date from the 2ndcentury BC. In 1569 Gerardus Mercator published a chartnariesbecausetherethevariationwaszero.Marinerspaidlittleattentiontotheseconventions andoften reckonedtheirusing the mathematical principle which now bears hislongitude from several different capes and ports duringaname.Some30years later,Edward Wrightpublished cor-

2 INTRODUCTION TO MARINE NAVIGATION mariner should choose the system mix that meets the accu￾racy requirements of each phase. • Inland Waterway Phase: Piloting in narrow canals, channels, rivers, and estuaries. • Harbor/Harbor Approach Phase: Navigating to a harbor entrance and piloting in harbor approach channels. • Coastal Phase: Navigating within 50 miles of the coast or inshore of the 200 meter depth contour. • Ocean Phase: Navigating outside the coastal area in the open sea. The navigator’s position accuracy requirements, his fix interval, and his systems requirements differ in each phase. The following table can be used as a general guide for se￾lecting the proper system(s). NAVIGATIONAL TERMS AND CONVENTIONS 103. Important Conventions And Concepts Throughout the history of navigation, numerous terms and conventions have been established which enjoy world￾wide recognition. The professional navigator, to gain a full understanding of his field, should understand the origin of certain terms, techniques, and conventions. The following section discusses some of the important ones. Defining a prime meridian is a comparatively recent development. Until the beginning of the 19th century, there was little uniformity among cartographers as to the meridi￾an from which to measure longitude. This did not lead to any problem because there was no widespread method for determining longitude accurately. Ptolemy, in the 2nd century AD, measured longitude eastward from a reference meridian 2 degrees west of the Canary Islands. In 1493, Pope Alexander VI established a line in the Atlantic west of the Azores to divide the territo￾ries of Spain and Portugal. For many years, cartographers of these two countries used this dividing line as the prime meridian. In 1570 the Dutch cartographer Ortelius used the easternmost of the Cape Verde Islands. John Davis, in his 1594 The Seaman’s Secrets, used the Isle of Fez in the Ca￾naries because there the variation was zero. Mariners paid little attention to these conventions and often reckoned their longitude from several different capes and ports during a voyage. The meridian of London was used as early as 1676, and over the years its popularity grew as England’s maritime in￾terests increased. The system of measuring longitude both east and west through 180° may have first appeared in the middle of the 18th century. Toward the end of that century, as the Greenwich Observatory increased in prominence, En￾glish cartographers began using the meridian of that observatory as a reference. The publication by the Observa￾tory of the first British Nautical Almanac in 1767 further entrenched Greenwich as the prime meridian. An unsuc￾cessful attempt was made in 1810 to establish Washington, D.C. as the prime meridian for American navigators and car￾tographers. In 1884, the meridian of Greenwich was officially established as the prime meridian. Today, all mar￾itime nations have designated the Greenwich meridian the prime meridian, except in a few cases where local references are used for certain harbor charts. Charts are graphic representations of areas of the earth for use in marine or air navigation. Nautical charts depict features of particular interest to the marine navigator. Charts have probably existed since at least 600 BC. Stereo￾graphic and orthographic projections date from the 2nd century BC. In 1569 Gerardus Mercator published a chart using the mathematical principle which now bears his name. Some 30 years later, Edward Wright published cor￾Inland Waterway Harbor/Harbor Approach Coastal Ocean DR X X X X Piloting X X X Celestial X X Radio X X X Radar X X X Satellite X* X X X Table 102. The relationship of the types and phases of navigation. * Differential GPS may be used if available

3INTRODUCTIONTOMARINENAVIGATIONrected mathematical tables for this projection,enablingthemetricformat.Considerations ofexpense,safety ofnav-cartographers to produce charts on the Mercator projection.igation, and logical sequencing will require a conversionThis projection is still widely in use.effort spanning many years.Notwithstanding the conver-Sailing directions orpilots have existed sinceat leastsiontothemetricsystem,thecommonmeasureofdistancethe 6th century BC.Continuous accumulation of naviga-at sea is the nautical mile.tional data,alongwithincreasedexploration andtrade,ledThecurrentpolicyof theDefenseMappingAgencytoincreasedproductionofvolumesthroughtheMiddleHydrographic/Topographic Center (DMAHTC) and theAges.Routiers"wereproduced in Franceabout 1500:theNationalOceanService(NOS)isto convertnewcompila-English referred to them asrutters."In 1584 Lucastions ofnautical, special purpose charts,and publications toWaghenaer published the Spieghel der Zeevaerdt (Thethe metric system.This conversion began on January 2,Mariner'sMirror),which becamethemodelfor suchpub-1970.Mostmodernmaritimenations havealsoadoptedthelicationsfor several generations of navigators.Theyweremeter as the standard measure of depths and heights.How-known as"Waggoners"bymostsailors.Modernpilotsever, oldercharts still on issue andthe chartsof someand sailingdirections arebased on extensivedata collec-foreign countriesmaynotconformtothis standard.tion and compilation efforts begun by Matthew FontaineThe fathom as a unit of length or depth is of obscureMaurybeginningin1842origin.Posidonius reported a sounding of more than 1,o00The compass was developed about 1000 years ago.fathomsinthe2ndcenturyBC.HowoldtheunitwasthenThe origin ofthe magnetic compass is uncertain, but Norseis unknown.Many modern charts are still based on the fath-menuseditinthe11thcentury.Itwasnotuntilthe1870sthat Lord Kelvin developedareliabledry card marine com-om, as conversion to themetric systemcontinues.pass.The fluid-filled compass became standard in 1906Thesailings refer tovarious methods ofmathematical-Variation was not understood until the 18th century,ly determining course, distance, and position.They have awhenEdmondHalleyledanexpeditiontomaplinesofhistoryalmostas oldasmathematics itself.Thales,Hippar-variation in the SouthAtlantic.Deviation was understoodchus, Napier, Wright, and others contributed theformulasat least as early as the early1600s,but correction ofcom-that permit computation of course and distance by plane,pass errorwas not possibleuntil Matthew Flinderstraverse, parallel, middle latitude, Mercator, and great cir-discovered that a vertical iron bar could reduce errors.Afcle sailings.ter 1840,British Astronomer Royal Sir George AiryandlaterLordKelvindevelopedcombinationsofironmasses104.TheEarthandsmall magnetsto eliminatemostmagneticcompasserror.The earth is an oblate spheroid (a sphereflattened atThe gyrocompass was madenecessary by ironandthepoles).Measurementsofitsdimensionsandtheamountsteel ships.LeonFoucault developed thebasicgyroscope inof its flattening are subjects ofgeodesy.However,for most1852.AnAmerican(ElmerSperry)andaGerman(Anshutznavigational purposes,assuminga spherical earthintroduc-Kampfe)bothdeveloped electrical gyrocompasses inthees insignificanterror.The earth's axis of rotation is the lineearlyyearsofthe20thcenturyconnectingtheNorth Poleand the South PoleThe log is the mariner's speedometer. Mariners origi-Agreat circle is the line of intersection ofa sphere andnallymeasured speedbyobservinga chipof woodpassingdownthesideofthevessel.Laterdevelopmentsincludedaa plane through its center.This is the largest circle that canwooden board attached toareel of line.Mariners measuredbedrawnonasphere.Theshortest lineonthesurfaceofaspeedbynotinghowmanyknotsinthelineunreeledasthesphere betweentwopoints on the surface ispart of a greatship moveda measured amountof time; hencethetermcircle.On the spheroidal earth the shortest line is called aknot.Mechanical logs using either a small paddle wheel orgeodesic.A great circle is a near enough approximation toa rotating spinner arrived about the middle ofthe 17th cen-ageodesicformostproblems ofnavigation.A small circletury.Thetaffrail log still in limited use today wasisthelineofintersectionofasphereandaplanewhichdoesdeveloped in 1878.Modern logs use electronic sensors ornot pass throughthe center.SeeFigure104aspinning devices that induce small electric fields propor-The term meridian is usually applied to the upper branchtional to a vessel's speed. An engine revolution counter orofthe half-circlefrompoletopolewhichpassesthroughagivenshaft log often measures speed onboard large ships.Dop-point. The opposite half is called the lower branch.pler speed logs areused on somevessels forveryaccurateA parallel orparallel of latitude is a circleon thespeed readings.Inertial and satellite systems also providesurface ofthe earth parallel to theplane of the equator.Ithighly accurate speed readings.connects all points of equal latitude.The equator is aTheMetricConversionAct of 1975and theOmnibusgreat circle at latitude 00. See Figure 104b.The poles areTradeandCompetitivenessActof1988established thesingle points at latitude 90o.All other parallels are smallmetric system of weights and measures in the UnitedStates.As a result, the government is converting charts tocircles

INTRODUCTION TO MARINE NAVIGATION 3 rected mathematical tables for this projection, enabling cartographers to produce charts on the Mercator projection. This projection is still widely in use. Sailing directions or pilots have existed since at least the 6th century BC. Continuous accumulation of naviga￾tional data, along with increased exploration and trade, led to increased production of volumes through the Middle Ages. “Routiers” were produced in France about 1500; the English referred to them as “rutters.” In 1584 Lucas Waghenaer published the Spieghel der Zeevaerdt (The Mariner’s Mirror), which became the model for such pub￾lications for several generations of navigators. They were known as “Waggoners” by most sailors. Modern pilots and sailing directions are based on extensive data collec￾tion and compilation efforts begun by Matthew Fontaine Maury beginning in 1842. The compass was developed about 1000 years ago. The origin of the magnetic compass is uncertain, but Norse￾men used it in the 11th century. It was not until the 1870s that Lord Kelvin developed a reliable dry card marine com￾pass. The fluid-filled compass became standard in 1906. Variation was not understood until the 18th century, when Edmond Halley led an expedition to map lines of variation in the South Atlantic. Deviation was understood at least as early as the early 1600s, but correction of com￾pass error was not possible until Matthew Flinders discovered that a vertical iron bar could reduce errors. Af￾ter 1840, British Astronomer Royal Sir George Airy and later Lord Kelvin developed combinations of iron masses and small magnets to eliminate most magnetic compass error. The gyrocompass was made necessary by iron and steel ships. Leon Foucault developed the basic gyroscope in 1852. An American (Elmer Sperry) and a German (Anshutz Kampfe) both developed electrical gyrocompasses in the early years of the 20th century. The log is the mariner’s speedometer. Mariners origi￾nally measured speed by observing a chip of wood passing down the side of the vessel. Later developments included a wooden board attached to a reel of line. Mariners measured speed by noting how many knots in the line unreeled as the ship moved a measured amount of time; hence the term knot. Mechanical logs using either a small paddle wheel or a rotating spinner arrived about the middle of the 17th cen￾tury. The taffrail log still in limited use today was developed in 1878. Modern logs use electronic sensors or spinning devices that induce small electric fields propor￾tional to a vessel’s speed. An engine revolution counter or shaft log often measures speed onboard large ships. Dop￾pler speed logs are used on some vessels for very accurate speed readings. Inertial and satellite systems also provide highly accurate speed readings. The Metric Conversion Act of 1975 and the Omnibus Trade and Competitiveness Act of 1988 established the metric system of weights and measures in the United States. As a result, the government is converting charts to the metric format. Considerations of expense, safety of nav￾igation, and logical sequencing will require a conversion effort spanning many years. Notwithstanding the conver￾sion to the metric system, the common measure of distance at sea is the nautical mile. The current policy of the Defense Mapping Agency Hydrographic/Topographic Center (DMAHTC) and the National Ocean Service (NOS) is to convert new compila￾tions of nautical, special purpose charts, and publications to the metric system. This conversion began on January 2, 1970. Most modern maritime nations have also adopted the meter as the standard measure of depths and heights. How￾ever, older charts still on issue and the charts of some foreign countries may not conform to this standard. The fathom as a unit of length or depth is of obscure origin. Posidonius reported a sounding of more than 1,000 fathoms in the 2nd century BC. How old the unit was then is unknown. Many modern charts are still based on the fath￾om, as conversion to the metric system continues. The sailings refer to various methods of mathematical￾ly determining course, distance, and position. They have a history almost as old as mathematics itself. Thales, Hippar￾chus, Napier, Wright, and others contributed the formulas that permit computation of course and distance by plane, traverse, parallel, middle latitude, Mercator, and great cir￾cle sailings. 104. The Earth The earth is an oblate spheroid (a sphere flattened at the poles). Measurements of its dimensions and the amount of its flattening are subjects of geodesy. However, for most navigational purposes, assuming a spherical earth introduc￾es insignificant error. The earth’s axis of rotation is the line connecting the North Pole and the South Pole. A great circle is the line of intersection of a sphere and a plane through its center. This is the largest circle that can be drawn on a sphere. The shortest line on the surface of a sphere between two points on the surface is part of a great circle. On the spheroidal earth the shortest line is called a geodesic. A great circle is a near enough approximation to a geodesic for most problems of navigation. A small circle is the line of intersection of a sphere and a plane which does not pass through the center. See Figure 104a. The term meridian is usually applied to the upper branch of the half-circle from pole to pole which passes through a given point. The opposite half is called the lower branch. A parallel or parallel of latitude is a circle on the surface of the earth parallel to the plane of the equator. It connects all points of equal latitude. The equator is a great circle at latitude 0°. See Figure 104b. The poles are single points at latitude 90°. All other parallels are small circles

4INTRODUCTIONTOMARINENAVIGATIONFigure 104a. The planes of the meridians meet at theFigure 104b. The equator is a great circle midwaypolaraxis.between thepoles.105.Co0rdinatestheprime meridian and themeridian ofapointon the earth,measured eastward or westward from the prime meridianCoordinates, termed latitude and longitude, can de-through180°.It is designated east (E)or west (W)to indi-fine any position on earth.Latitude (L, lat.) is the angularcatethedirectionofmeasurement.The difference of longitude (DLo) between two plac-distance from the equator, measured northward or south-ward along a meridian from 0°at the equator to 90°at thees is the shorter arc ofthe parallel or the smaller angle at thepoles.It is designated north (N)or south (S)to indicate thepolebetweenthemeridians ofthetwoplaces.Ifbothplacesdirectionofmeasurementareonthesameside(eastorwest)ofGreenwich.DLoistheThe difference of latitude (,DLat.)betweentwonumerical differenceof thelongitudes ofthetwoplaces;ifplaces is theangular length of arc of anymeridian betweenonoppositesides,DLoisthenumerical sumunlessthisex-theirparallels.Itisthenumericaldifferenceofthelatitudesceeds180°whenitis360ominusthesum.Thedistanceiftheplacesareon thesamesideoftheequator,it isthesumbetweentwomeridiansatanyparallel oflatitude,expressedof the latitudes if theplaces are on opposite sidesof theindistanceunits,usuallynauticalmiles,iscalleddepartureequator.Itmaybedesignated north(N)or south(S)when(p,Dep.).Itrepresentsdistancemadegoodeastorwestasa craft proceeds from one point to another.Its numericalappropriate.Themiddleormid-latitude(Lm)betweentwoplacesonthesamesideof the equatoris halfthe sumvalue between any two meridians decreaseswith increasedoftheirlatitudes.Mid-latitudeislabeledNorStoindicatelatitude,whileDLo is numericallythesameat anylatitudewhether it is north or south of the equator.Either DLo or p may be designated east (E) or west (W)Theexpressionmayreferto themid-latitude of twowhenappropriate.places on opposite sides of the equator. In this case, it isequal to half the difference between the two latitudes and106.DistanceOnTheEarthtakesthename oftheplacefarthestfrom the equator.How-ever,this usage is misleading because it lacks theDistance,as used bythe navigator, is the length of thesignificance usually associated with the expression.Whenrhumb line connecting two places.This is a line makingtheplaces areon oppositesides ofthe equator,twomid-lat-the same angle with all meridians.Meridians and parallelsitudes are generally used.Calculate these two mid-latitudeswhichalsomaintainconstanttruedirectionsmaybe consid-byaveraging each latitudeand00ered special cases ofthe rhumb line.Anyother rhumb lineLongitude(l, long.)is the angular distancebetweenspirals toward the pole,forming a loxodromic curve or

4 INTRODUCTION TO MARINE NAVIGATION 105. Coordinates Coordinates, termed latitude and longitude, can de￾fine any position on earth. Latitude (L, lat.) is the angular distance from the equator, measured northward or south￾ward along a meridian from 0° at the equator to 90° at the poles. It is designated north (N) or south (S) to indicate the direction of measurement. The difference of latitude (l, DLat.) between two places is the angular length of arc of any meridian between their parallels. It is the numerical difference of the latitudes if the places are on the same side of the equator; it is the sum of the latitudes if the places are on opposite sides of the equator. It may be designated north (N) or south (S) when appropriate. The middle or mid-latitude (Lm) between two places on the same side of the equator is half the sum of their latitudes. Mid-latitude is labeled N or S to indicate whether it is north or south of the equator. The expression may refer to the mid-latitude of two places on opposite sides of the equator. In this case, it is equal to half the difference between the two latitudes and takes the name of the place farthest from the equator. How￾ever, this usage is misleading because it lacks the significance usually associated with the expression. When the places are on opposite sides of the equator, two mid-lat￾itudes are generally used. Calculate these two mid-latitudes by averaging each latitude and 0°. Longitude (l, long.) is the angular distance between the prime meridian and the meridian of a point on the earth, measured eastward or westward from the prime meridian through 180°. It is designated east (E) or west (W) to indi￾cate the direction of measurement. The difference of longitude (DLo) between two plac￾es is the shorter arc of the parallel or the smaller angle at the pole between the meridians of the two places. If both places are on the same side (east or west) of Greenwich, DLo is the numerical difference of the longitudes of the two places; if on opposite sides, DLo is the numerical sum unless this ex￾ceeds 180°, when it is 360° minus the sum. The distance between two meridians at any parallel of latitude, expressed in distance units, usually nautical miles, is called departure (p, Dep.). It represents distance made good east or west as a craft proceeds from one point to another. Its numerical value between any two meridians decreases with increased latitude, while DLo is numerically the same at any latitude. Either DLo or p may be designated east (E) or west (W) when appropriate. 106. Distance On The Earth Distance, as used by the navigator, is the length of the rhumb line connecting two places. This is a line making the same angle with all meridians. Meridians and parallels which also maintain constant true directions may be consid￾ered special cases of the rhumb line. Any other rhumb line spirals toward the pole, forming a loxodromic curve or Figure 104a. The planes of the meridians meet at the polar axis. Figure 104b. The equator is a great circle midway between the poles

5INTRODUCTIONTOMARINENAVIGATION107.DirectionOnTheEarthDirection is the position ofone point relative to anoth-er. Navigators express direction as the angular difference indegrees from a reference direction, usually north or theship's head.Course (C, Cn) is the horizontal direction inwhich a vessel is steered or intended to be steered, ex-pressed as angular distance from north clockwise through360°.Strictly used, the term applies to direction through thewater, not the direction intended to bemade good over theground.The course is often designated as true,magnetic, com-pass, or grid according to the reference direction. Track2madegood (TMG)is the singleresultant direction fromthe point of departure to point of arrival at any given time.D.Course of advance(COA)is the direction intended to beCmade good over the ground, and course over ground(COG) is the direction between a vessel's last fix and anEP.Acourse line is a linedrawn onachart extending in thedirectionofa course.It is sometimes convenienttoexpressa course as an angle from either north or south, through 90oFigure106.Aloxodromeor 180°.In this case it is designated course angle (C)andshould be properly labeled to indicate the origin (prefix)loxodrome.SeeFigure106.Distancealong thegreat circleand direction of measurement (suffix).Thus, CN35°E=connecting two points is customarily designated great-cir-Cn035°(000°+35°),CN155°W=Cn205°(360°-155°)cle distance. For most purposes, considering the nauticalC S47°E=Cn133°(180°-47°).But Cn260°may be eithermile the length of one minute of latitude introduces no sigCN100oWorCS80W,dependingupontheconditionsofnificanterror.theproblemSpeed (S)is rateofmotion,ordistanceper unitof timeTrack (TR) is the intended horizontal direction ofA knot (kn.), the unit of speed commonly used in navigation,travel with respect to the earth. The terms intended trackisarate of 1 nautical mileper hour.Theexpressionspeed ofand trackline are used to indicate the path ofintended trav-advance (SOA) is used to indicate the speed to be madeel. See Figure 107aThe track consists of one or a series ofalong the intended track. Speed over the ground (SOG) iscourse lines, from the point of departure to the destination,the actual speed ofthevessel over the surface of the earth atalong which it is intended to proceed.A great circle whichany given time.To calculate speed made good (SMG) be-a vessel intends to follow is called a great-circle track,tweentwo positions,dividethe distance between thetwothough it consists ofa series of straight lines approximatingpositionsbythetimeelapsedbetweenthetwopositionsa great circle.UmknownCurrentDestinationelineiadirectioa ofcovrse steeredTrackCourointof DeparturePatOrCding.3frack Made GocPointofArrivalFigure107a.Course line, track,track madegood,and heading

INTRODUCTION TO MARINE NAVIGATION 5 loxodrome. See Figure 106. Distance along the great circle connecting two points is customarily designated great-cir￾cle distance. For most purposes, considering the nautical mile the length of one minute of latitude introduces no sig￾nificant error. Speed (S) is rate of motion, or distance per unit of time. A knot (kn.), the unit of speed commonly used in navigation, is a rate of 1 nautical mile per hour. The expression speed of advance (SOA) is used to indicate the speed to be made along the intended track. Speed over the ground (SOG) is the actual speed of the vessel over the surface of the earth at any given time. To calculate speed made good (SMG) be￾tween two positions, divide the distance between the two positions by the time elapsed between the two positions. 107. Direction On The Earth Direction is the position of one point relative to anoth￾er. Navigators express direction as the angular difference in degrees from a reference direction, usually north or the ship’s head. Course (C, Cn) is the horizontal direction in which a vessel is steered or intended to be steered, ex￾pressed as angular distance from north clockwise through 360°. Strictly used, the term applies to direction through the water, not the direction intended to be made good over the ground. The course is often designated as true, magnetic, com￾pass, or grid according to the reference direction. Track made good (TMG) is the single resultant direction from the point of departure to point of arrival at any given time. Course of advance (COA) is the direction intended to be made good over the ground, and course over ground (COG) is the direction between a vessel’s last fix and an EP. A course line is a line drawn on a chart extending in the direction of a course. It is sometimes convenient to express a course as an angle from either north or south, through 90° or 180°. In this case it is designated course angle (C) and should be properly labeled to indicate the origin (prefix) and direction of measurement (suffix). Thus, C N35°E = Cn 035° (000° + 35°), C N155°W = Cn 205° (360° - 155°), C S47°E = Cn 133° (180° - 47°). But Cn 260° may be either C N100°W or C S80°W, depending upon the conditions of the problem. Track (TR) is the intended horizontal direction of travel with respect to the earth. The terms intended track and trackline are used to indicate the path of intended trav￾el. See Figure 107a. The track consists of one or a series of course lines, from the point of departure to the destination, along which it is intended to proceed. A great circle which a vessel intends to follow is called a great-circle track, though it consists of a series of straight lines approximating a great circle. Figure 106. A loxodrome Figure 107a. Course line, track, track made good, and heading

6INTRODUCTIONTOMARINENAVIGATIONHeading (Hdg., SH) is the direction in which a vesselapoint on the earth.Arelativebearing ismeasuredrelativeis pointed, expressed as angulardistancefrom 000°clock-to the ship's heading from 000° (dead ahead) clockwisewise through 360o.Do not confuse heading and course.through360°.However,itis sometimesconvenientlymea-Heading constantlychanges asavessel yaws backandforthsured right or left from 0°at the ship's head through 180°This is particularly true when using the table for Distanceacross the course due to sea, wind, and steering error.Bearing (B, Brg.)is the direction of one terrestrialof anObjectbyTwoBearings.pointfrom another,expressed as angular distancefromTo convert a relativebearing to a true bearing,add the000°(North)clockwisethrough360°Whenmeasuredthrough 90° or 180°from either north or south, it is calledtrue heading:bearingangle(B).Bearingandazimutharesometimesusedinterchangeably,butthelattermoreaccuratelyreferstotheTrue Bearing =Relative Bearing + True Headinghorizontal directionofapoint on the celestial spherefromRelative Bearing=True Bearing-True HeadingFigure107b.RelativeBearingDEVELOPMENTOFNAVIGATION108.LatitudeAnd LongitudeDeterminationabilities of the average seaman. It was apparent that the so-lution lay in keeping accurate time at sea.In1714,theBritishBoard of Longitudewasformed.Navigators have made latitude observations for thou-offering a small fortune in reward to anyone who could pro-sands of years.Accurate sun declination tables have beenpublished for centuries, enabling experienced seamen tovidea solution to theproblem.computelatitudeto within I or 2 degrees.Mariners still useAn Englishman,John Harrison,responded to thechal-meridian observations of the sun and highly refined ex-me-lenge, developing four chronometers between 1735 andridiantechnigues.Thosewhotodaydeterminetheirlatitude1760.The most accurate of these timepieces lost only 15bymeasuring the altitude of Polaris are using a method wellseconds on a 156 dayround tripbetween London andBar-knownto15thcenturynavigators.bados.TheBoard,however,paid him onlyhalf theA method of finding longitude eluded mariners forpromised reward.TheKing finally intervened on Harri-centuries.Several solutions independentoftimeprovedtooson's behalf, and Harrison received his full reward off20.000at theadvanced ageof 80cumbersome.Thelunar distancemethod,whichdeterminesGMT by observing themoon's position among the stars,Rapidchronometerdevelopment ledtotheproblemofdetermining chronometer error aboard ship, Time balls,becamepopularinthe1800s.However,themathematicsre-quired bymost of these processes werefar above thelargeblackspheresmountedinportinprominentlocations

6 INTRODUCTION TO MARINE NAVIGATION Heading (Hdg., SH) is the direction in which a vessel is pointed, expressed as angular distance from 000° clock￾wise through 360°. Do not confuse heading and course. Heading constantly changes as a vessel yaws back and forth across the course due to sea, wind, and steering error. Bearing (B, Brg.) is the direction of one terrestrial point from another, expressed as angular distance from 000° (North) clockwise through 360°. When measured through 90° or 180° from either north or south, it is called bearing angle (B). Bearing and azimuth are sometimes used interchangeably, but the latter more accurately refers to the horizontal direction of a point on the celestial sphere from a point on the earth. A relative bearing is measured relative to the ship’s heading from 000° (dead ahead) clockwise through 360°. However, it is sometimes conveniently mea￾sured right or left from 0° at the ship’s head through 180°. This is particularly true when using the table for Distance of an Object by Two Bearings. To convert a relative bearing to a true bearing, add the true heading: True Bearing = Relative Bearing + True Heading. Relative Bearing = True Bearing – True Heading. DEVELOPMENT OF NAVIGATION 108. Latitude And Longitude Determination Navigators have made latitude observations for thou￾sands of years. Accurate sun declination tables have been published for centuries, enabling experienced seamen to compute latitude to within 1 or 2 degrees. Mariners still use meridian observations of the sun and highly refined ex-me￾ridian techniques. Those who today determine their latitude by measuring the altitude of Polaris are using a method well known to 15th century navigators. A method of finding longitude eluded mariners for centuries. Several solutions independent of time proved too cumbersome. The lunar distance method, which determines GMT by observing the moon’s position among the stars, became popular in the 1800s. However, the mathematics re￾quired by most of these processes were far above the abilities of the average seaman. It was apparent that the so￾lution lay in keeping accurate time at sea. In 1714, the British Board of Longitude was formed, offering a small fortune in reward to anyone who could pro￾vide a solution to the problem. An Englishman, John Harrison, responded to the chal￾lenge, developing four chronometers between 1735 and 1760. The most accurate of these timepieces lost only 15 seconds on a 156 day round trip between London and Bar￾bados. The Board, however, paid him only half the promised reward. The King finally intervened on Harri￾son’s behalf, and Harrison received his full reward of £20,000 at the advanced age of 80. Rapid chronometer development led to the problem of determining chronometer error aboard ship. Time balls, large black spheres mounted in port in prominent locations, Figure 107b. Relative Bearing

INTRODUCTIONTOMARINENAVIGATIONwere dropped at the stroke of noon, enabling any ship insides of the triangle were available.From these the meridianharborwhichcouldseetheballtodeterminechronometerangle was computed.The comparison of this with the Green-error. By the end of the U.S. Civil War, telegraph signalswich hour angle from the almanac yielded the longitude.were being used to key time balls.Use of radio signals toThe time sight was mathematically sound, but the navigatorsendtimeticksto ships well offshorebegan in 1904,andwas notalwaysawarethatthelongitudedeterminedwas onlyassoon worldwide signals wereavailableaccurateasthelatitude,andtogethertheymerelyformedapointon what isknowntodayasa lineof position.Iftheobserved109. The Navigational Trianglebody was on the prime vertical, the line of position ran north andsouth and a small error in latitudegenerally had little effect onModern celestial navigators reduce their celestial obser-the longitude.But when the body was close to the meridian, asmall error in latitude produced a large error in longitude.vations by solving a navigational triangle whose points aretheelevated pole,the celestial body,and thezenithofthe obThe line of position by celestial observation was un-server.The sides of thistriangle are the polar distance of theknown until discoveredin1837by30-year-old Captainbody (codeclination),its zenith distance (coaltitude), andThomas H.Sumner,a Harvard graduate and son ofa Unitedthe polardistance of the zenith (colatitude of the observer)States congressmanfromMassachusetts.Thediscovery ofA spherical triangle was first used at sea in solving lunanthe“Sumner line,"as it is sometimes called, was consid-distanceproblems.Simultaneousobservationsweremadeofered by Maurythecommencement of a new era inthealtitudes ofthemoon andthe sun ora star neartheeclipticpractical navigation." This was the turning point in the de-and the angular distance between the moon and the othervelopment of modern celestial navigation technique.Inbody.Thezenithof theobserver andthetwo celestial bodiesSumner's own words,the discovery took place in thisformed theverticesof a triangle whose sides werethetwomanner:coaltitudes and theangular distancebetweenthebodies.Us-ing a mathematical calculation the navigator“cleared"thisHavingsailed fromCharleston,S.C.,25thNovemberdistanceoftheeffectsofrefractionandparallaxapplicableto1837,bound to Greenock,a series ofheavy gales from theeach altitude.This corrected value was then used as an argu-Westwardpromisedaquickpassage,after passingthementfor entering thealmanac.The almanac gave thetrueAzores,thewindprevailedfromtheSouthward,withthicklunar distancefrom the sun and several stars at 3 hour inter-weather, afterpassing Longitude21oW,no observationvals.Previously,the navigator had set his watch or checkedwashaduntilneartheland:butsoundingswerehadnotfaritserrorandratewiththelocalmeantimedeterminedbyceas was supposed,from the edge ofthe Bank.The weatherlestial observations.The local mean time of the watch,wasnowmoreboisterous,andverythick,andthewindstillproperly corrected, applied to the Greenwich mean time ob-Southerly,arrivingaboutmidnight,17thDecember,withintained from the lunar distance observation, gave the40 miles, by dead reckoning,of Tusker light, the windlongitude.hauled SE,true,making the Irish coasta leeshore,the shipThe calculations involved were tedious.Few marinerswasthenkeptclose to thewind,and severaltacks madetocould solve the triangle until Nathaniel Bowditch published hispreserve her position as nearly as possible until daylightsimplified method in 1802in TheNewAmericanPracticalwhen nothing being in sight, she was kept on ENE underNavigator.short sail,withheavygales,at about 10 AM an altitude ofReliablechronometers were available in 1802,but theirthe sun was observed, and the Chronometertimenoted,high cost precluded their general use aboard most shipsbut,having run sofar without any observation, it was plainHowever,mostnavigatorscoulddeterminetheirlongitudetheLatitudeby dead reckoningwas liableto error,andusing Bowditch's method.This eliminated the need for par-could not be entirely relied on. Using, however, this Lati-allelsailing and the losttimeassociatedwithit.Tablesforthetude. in finding the Longitude by Chronometer. it waslunardistancesolutionwerecarriedintheAmericannauticalfoundtoputthe ship15'of LongitudeEfrom herpositionalmanac until the second decade of the 20th century.bydead reckoning,which in Latitude52°Nis9nauticalmiles:thisseemedtoagreetolerablywellwiththedead110.TheTime Sightreckoning:butfeelingdoubtfuloftheLatitude.theobservation was tried with a Latitude 10'further N, finding thisplaced the shipENE27nautical miles,oftheformerposi-Thetheoryofthetime sighthad beenknown tomathetion, it was tried again with a Latitude 20 N of the deadmaticians since the development of spherical trigonometry,reckoning,this also placed the ship still further ENE, andbut notuntil thechronometer was developed could it beusedstill 27 nautical milesfurther,thesethreepositions werebymariners.then seen to lie in the direction of Small's light.The time sight used the modern navigational triangle.TheIt then at once appeared that the observed altitudecodeclination,or polar distance,of thebody could be deter-minedfromthealmanac.Thezenithdistance(coaltitude)wasmust have happened at all the three points, and atSmall'slight, and at the ship,at the same instant oftime,determinedbyobservation.Ifthecolatitudewereknown.three

INTRODUCTION TO MARINE NAVIGATION 7 were dropped at the stroke of noon, enabling any ship in harbor which could see the ball to determine chronometer error. By the end of the U.S. Civil War, telegraph signals were being used to key time balls. Use of radio signals to send time ticks to ships well offshore began in 1904, and soon worldwide signals were available. 109. The Navigational Triangle Modern celestial navigators reduce their celestial obser￾vations by solving a navigational triangle whose points are the elevated pole, the celestial body, and the zenith of the ob￾server. The sides of this triangle are the polar distance of the body (codeclination), its zenith distance (coaltitude), and the polar distance of the zenith (colatitude of the observer). A spherical triangle was first used at sea in solving lunar distance problems. Simultaneous observations were made of the altitudes of the moon and the sun or a star near the ecliptic and the angular distance between the moon and the other body. The zenith of the observer and the two celestial bodies formed the vertices of a triangle whose sides were the two coaltitudes and the angular distance between the bodies. Us￾ing a mathematical calculation the navigator “cleared” this distance of the effects of refraction and parallax applicable to each altitude. This corrected value was then used as an argu￾ment for entering the almanac. The almanac gave the true lunar distance from the sun and several stars at 3 hour inter￾vals. Previously, the navigator had set his watch or checked its error and rate with the local mean time determined by ce￾lestial observations. The local mean time of the watch, properly corrected, applied to the Greenwich mean time ob￾tained from the lunar distance observation, gave the longitude. The calculations involved were tedious. Few mariners could solve the triangle until Nathaniel Bowditch published his simplified method in 1802 in The New American Practical Navigator. Reliable chronometers were available in 1802, but their high cost precluded their general use aboard most ships. However, most navigators could determine their longitude using Bowditch’s method. This eliminated the need for par￾allel sailing and the lost time associated with it. Tables for the lunar distance solution were carried in the American nautical almanac until the second decade of the 20th century. 110. The Time Sight The theory of the time sight had been known to mathe￾maticians since the development of spherical trigonometry, but not until the chronometer was developed could it be used by mariners. The time sight used the modern navigational triangle. The codeclination, or polar distance, of the body could be deter￾mined from the almanac. The zenith distance (coaltitude) was determined by observation. If the colatitude were known, three sides of the triangle were available. From these the meridian angle was computed. The comparison of this with the Green￾wich hour angle from the almanac yielded the longitude. The time sight was mathematically sound, but the navigator was not always aware that the longitude determined was only as accurate as the latitude, and together they merely formed a point on what is known today as a line of position. If the observed body was on the prime vertical, the line of position ran north and south and a small error in latitude generally had little effect on the longitude. But when the body was close to the meridian, a small error in latitude produced a large error in longitude. The line of position by celestial observation was un￾known until discovered in 1837 by 30-year-old Captain Thomas H. Sumner, a Harvard graduate and son of a United States congressman from Massachusetts. The discovery of the “Sumner line,” as it is sometimes called, was consid￾ered by Maury “the commencement of a new era in practical navigation.” This was the turning point in the de￾velopment of modern celestial navigation technique. In Sumner’s own words, the discovery took place in this manner: Having sailed from Charleston, S. C., 25th November, 1837, bound to Greenock, a series of heavy gales from the Westward promised a quick passage; after passing the Azores, the wind prevailed from the Southward, with thick weather; after passing Longitude 21° W, no observation was had until near the land; but soundings were had not far, as was supposed, from the edge of the Bank. The weather was now more boisterous, and very thick; and the wind still Southerly; arriving about midnight, 17th December, within 40 miles, by dead reckoning, of Tusker light; the wind hauled SE, true, making the Irish coast a lee shore; the ship was then kept close to the wind, and several tacks made to preserve her position as nearly as possible until daylight; when nothing being in sight, she was kept on ENE under short sail, with heavy gales; at about 10 AM an altitude of the sun was observed, and the Chronometer time noted; but, having run so far without any observation, it was plain the Latitude by dead reckoning was liable to error, and could not be entirely relied on. Using, however, this Lati￾tude, in finding the Longitude by Chronometer, it was found to put the ship 15' of Longitude E from her position by dead reckoning; which in Latitude 52° N is 9 nautical miles; this seemed to agree tolerably well with the dead reckoning; but feeling doubtful of the Latitude, the observa￾tion was tried with a Latitude 10' further N, finding this placed the ship ENE 27 nautical miles, of the former posi￾tion, it was tried again with a Latitude 20' N of the dead reckoning; this also placed the ship still further ENE, and still 27 nautical miles further; these three positions were then seen to lie in the direction of Small’s light. It then at once appeared that the observed altitude must have happened at all the three points, and at Small’s light, and at the ship, at the same instant of time;

8INTRODUCTIONTOMARINENAVIGATIONight.INELHAN96ES0to-InPOSITIONS OUTAINED FROMTHETHREE ASSUMEDLATITUDESa38N30*S84030*29-IW5Figure110.Thefirstcelestial lineofposition,obtainedbyCaptainThomas Sumner in1837and it followed, that Small's light must bear ENE, ifigator had no choice but to solve each triangle by tedious,the Chronometer was right.Having been convinced ofmanual computationsthis truth, the ship was kept on her course, ENE, theLord Kelvin, generally considered the father of modernwind being still SE., and in less than an hour, Small'snavigationalmethods,expressed interest inabookoftableswithlightwasmadebearingENE1/2E,andcloseaboardwhich a navigator could avoid tedious trigonometric solutions.However,solvingthemany thousandsof triangles involvedIn1843Sumnerpublishedabook,ANewandAccuratewould have made theprojecttoo costly.Computersfinallypro-Method of Findinga Ship'sPositionat SeabyProjection onvided apractical means of preparingtables.In1936thefirstMercator's Chart. He proposed solving a single time sightvolumeofPub.No.214wasmadeavailable;later,Pub.No.249wasprovidedforairnavigators.Pub.No.229,SightReductiontwice,usinglatitudessomewhatgreater and somewhatlessthan that arrived at bydead reckoning,and joining thetwoTablesforMarineNavigation,has replacedPub.No.214positions obtained toform the line of position.Modern calculators are gradually replacing the tablesThe Sumner method required the solution of two timeScientific calculatorswithtrigonometric functionscaneasi-sights to obtain each line ofposition.Many older navigatorslysolvethenavigationaltriangle.Navigationalcalculatorspreferred not to drawthelines on theircharts, buttofix theirreadily solve celestial sights and perform a variety ofvoyageposition mathematically by a method which Sumnerhadplanning functions.Using a calculatorgenerally givesmorealso devised and included in his book.This was a tediousaccurate lines of positionbecause it eliminates theroundingbutpopularprocedure.errors inherent in tabular inspection and interpolation.11l.NavigationalTables112.ElectronicsAnd NavigationSpherical trigonometry is the basis for solving everyPerhaps the first application of electronics to naviga-navigational triangle,and until about 80 years ago the nav-tioninvolved sendingtelegraphictime signalsin1865to

8 INTRODUCTION TO MARINE NAVIGATION and it followed, that Small’s light must bear ENE, if the Chronometer was right. Having been convinced of this truth, the ship was kept on her course, ENE, the wind being still SE., and in less than an hour, Small’s light was made bearing ENE 1/2 E, and close aboard. In 1843 Sumner published a book, A New and Accurate Method of Finding a Ship’s Position at Sea by Projection on Mercator’s Chart. He proposed solving a single time sight twice, using latitudes somewhat greater and somewhat less than that arrived at by dead reckoning, and joining the two positions obtained to form the line of position. The Sumner method required the solution of two time sights to obtain each line of position. Many older navigators preferred not to draw the lines on their charts, but to fix their position mathematically by a method which Sumner had also devised and included in his book. This was a tedious but popular procedure. 111. Navigational Tables Spherical trigonometry is the basis for solving every navigational triangle, and until about 80 years ago the nav￾igator had no choice but to solve each triangle by tedious, manual computations. Lord Kelvin, generally considered the father of modern navigational methods, expressed interest in a book of tables with which a navigator could avoid tedious trigonometric solutions. However, solving the many thousands of triangles involved would have made the project too costly. Computers finally pro￾vided a practical means of preparing tables. In 1936 the first volume of Pub. No. 214 was made available; later, Pub. No. 249 was provided for air navigators. Pub. No. 229, Sight Reduction Tables for Marine Navigation, has replaced Pub. No. 214. Modern calculators are gradually replacing the tables. Scientific calculators with trigonometric functions can easi￾ly solve the navigational triangle. Navigational calculators readily solve celestial sights and perform a variety of voyage planning functions. Using a calculator generally gives more accurate lines of position because it eliminates the rounding errors inherent in tabular inspection and interpolation. 112. Electronics And Navigation Perhaps the first application of electronics to naviga￾tion involved sending telegraphic time signals in 1865 to Figure 110. The first celestial line of position, obtained by Captain Thomas Sumner in 1837

9INTRODUCTIONTOMARINENAVIGATIONcheck chronometer errorTransmitting radio time signals114.Development OfHyperbolic Radio Aidsfor at sea chronometer checks dates to 1904Radio broadcasts providing navigational warnings, be-Various hyperbolic systems were developed fromgun in1907bytheU.S.NavyHydrographicOffice,helpedWorld War IL, including Loran A, This was replaced by theincrease the safetyof navigation at sea.more accurateLoran C system in use today.Using very lowBythe latterpartof WorldWarI thedirectional prop-frequencies,the Omega navigation system provides worlderties ofa loop antenna were successfully used in the radiowide, though less accurate, coverage for a variety ofdirection finder. The first radiobeacon was installed inapplications including marine navigation.Various short1921.Early20thcenturyexperimentsbyBehmandLan-range and regional hyperbolic systems have been develgevin led to the U.S. Navy's development of the firstoped by private industry for hydrographic surveying.practical echo sounder in1922offshore facilities positioning,and general navigation.Today,electronicstouches almosteveryaspectofnavi-gation.Hyperbolic systems, satellite systems, and electronic115.OtherElectronic Systemscharts all require an increasingly sophisticated electronicssuite.These systems'accuracy and easeofusemakethem in-TheNavyNavigation Satellite Svstem(NAVSAT)valuable assets to the navigator.Indeed, it is no exaggerationfulfilled a requirement established by theChiefofNaval Op-to state that, with the advent of the electronic chart and differential GPS,the mariner will soon be able to navigate fromerationsforan accurateworldwidenavigation systemfor allporttoportusingelectronicnavigationequipment alone.naval surfacevessels,aircraft,and submarines.The systemwas conceived and developed by the Applied Physics Labo-113.DevelopmentOfRadarratory of The Johns Hopkins University. The underlyingconcept that led to development ofsatellitenavigation datesAs early as 1904, German engineers were experimentingto1957andthefirstlaunchofanartificialsatelliteintoorbitwithreflected radiowaves.In1922twoAmerican scientists,NAVSAT has been replacedbythefarmore accurateandDr.A.HovtTaylorandLeoC.Young,testingacommunicawidely available Global Positioning System (GPS)tion system at theNaval Aircraft RadioLaboratory,notedThe first inertial navigation system was developed influctuationsinthesignalswhenshipspassedbetweenstations1942 for use in the V2 missile by the Peenemunde group underonoppositesides ofthePotomacRiver.In1935theBritishbe-the leadership of Dr.Wernher von Braun. This system used twogan work on radar.In 1937the USS Learytested the first sea-2-degree-of-freedomgyroscopes and an integrating accelerom-going radar. In 1940 United States and British scientists com-eter to determine the missile velocity.By the end of World Warbinedtheirefforts.WhentheBritishrevealedtheprincipleofI,thePeenemundegrouphaddevelopedastableplatformwiththemulticavitymagnetron developedbyJ.T.Randall and Hthree single-degree-of-freedom gyroscopes and an integratingA.H.Bootat theUniversityof Birmingham in1939,microaccelerometer.In1958 an inertial navigation system was usedtowaveradarbecamepractical.In1945,at theclose of WorldWar Il,radar becameavailable for commercial use.navigate the USS Nautilus under the iceto the North Pole.NAVIGATION ORGANIZATIONS116.GovernmentalRolesnavigation systems. Many maritime nations have similarorganizations performing similar functions.InternationalNavigation only a generation ago was an independentorganizations also playa significant role.process, carried out by the mariner without outside assis-117.The Coast And Geodetic Surveytance.Withcompass and charts, sextant andchronometerhe could independently travel anywhere in the world.TheThe U.S. Coast and Geodetic Survey was founded inincreasinguse of electronic navigation systems has made1807 when Congress passed a resolution authorizing a sur-thenavigatordependentonmanyfactorsoutsidehiscon-trol.Governmentorganizationsfundoperate,andregulatevey of thecoast,harbors,outlying islands,and fishingsatellites,Loran,and other electronic systems.Govern-banks oftheUnited States.PresidentThomasJeffersonap-ments are increasingly involved in regulation of vesselpointed Ferdinand Hassler, a Swiss immigrant andprofessorofmathematics atWestPoint,thefirstDirectorofmovements through traffic control systems and regulatedthe“Survey of the Coast."The survey became the"Coastareas. Understanding the governmental role in supportingSurvey"in1836and regulating navigation is vitally important to the mari-ner.In the United States,there are a number of officialThe approachestoNew Yorkwere the first sections oforganizations which support the interests of navigators.the coast charted,andfrom there the work spread northwardSome have apolicy-making role, others build and operateand southward along the eastern seaboard.In1844 thework

INTRODUCTION TO MARINE NAVIGATION 9 check chronometer error. Transmitting radio time signals for at sea chronometer checks dates to 1904. Radio broadcasts providing navigational warnings, be￾gun in 1907 by the U.S. Navy Hydrographic Office, helped increase the safety of navigation at sea. By the latter part of World War I the directional prop￾erties of a loop antenna were successfully used in the radio direction finder. The first radiobeacon was installed in 1921. Early 20th century experiments by Behm and Lan￾gevin led to the U.S. Navy’s development of the first practical echo sounder in 1922. Today, electronics touches almost every aspect of navi￾gation. Hyperbolic systems, satellite systems, and electronic charts all require an increasingly sophisticated electronics suite. These systems’ accuracy and ease of use make them in￾valuable assets to the navigator. Indeed, it is no exaggeration to state that, with the advent of the electronic chart and dif￾ferential GPS, the mariner will soon be able to navigate from port to port using electronic navigation equipment alone. 113. Development Of Radar As early as 1904, German engineers were experimenting with reflected radio waves. In 1922 two American scientists, Dr. A. Hoyt Taylor and Leo C. Young, testing a communica￾tion system at the Naval Aircraft Radio Laboratory, noted fluctuations in the signals when ships passed between stations on opposite sides of the Potomac River. In 1935 the British be￾gan work on radar. In 1937 the USS Leary tested the first sea￾going radar. In 1940 United States and British scientists com￾bined their efforts. When the British revealed the principle of the multicavity magnetron developed by J. T. Randall and H. A. H. Boot at the University of Birmingham in 1939, micro￾wave radar became practical. In 1945, at the close of World War II, radar became available for commercial use. 114. Development Of Hyperbolic Radio Aids Various hyperbolic systems were developed from World War II, including Loran A. This was replaced by the more accurate Loran C system in use today. Using very low frequencies, the Omega navigation system provides world￾wide, though less accurate, coverage for a variety of applications including marine navigation. Various short range and regional hyperbolic systems have been devel￾oped by private industry for hydrographic surveying, offshore facilities positioning, and general navigation. 115. Other Electronic Systems The Navy Navigation Satellite System (NAVSAT) fulfilled a requirement established by the Chief of Naval Op￾erations for an accurate worldwide navigation system for all naval surface vessels, aircraft, and submarines. The system was conceived and developed by the Applied Physics Labo￾ratory of The Johns Hopkins University. The underlying concept that led to development of satellite navigation dates to 1957 and the first launch of an artificial satellite into orbit. NAVSAT has been replaced by the far more accurate and widely available Global Positioning System (GPS). The first inertial navigation system was developed in 1942 for use in the V2 missile by the Peenemunde group under the leadership of Dr. Wernher von Braun. This system used two 2-degree-of-freedom gyroscopes and an integrating accelerom￾eter to determine the missile velocity. By the end of World War II, the Peenemunde group had developed a stable platform with three single-degree-of-freedom gyroscopes and an integrating accelerometer. In 1958 an inertial navigation system was used to navigate the USS Nautilus under the ice to the North Pole. NAVIGATION ORGANIZATIONS 116. Governmental Roles Navigation only a generation ago was an independent process, carried out by the mariner without outside assis￾tance. With compass and charts, sextant and chronometer, he could independently travel anywhere in the world. The increasing use of electronic navigation systems has made the navigator dependent on many factors outside his con￾trol. Government organizations fund, operate, and regulate satellites, Loran, and other electronic systems. Govern￾ments are increasingly involved in regulation of vessel movements through traffic control systems and regulated areas. Understanding the governmental role in supporting and regulating navigation is vitally important to the mari￾ner. In the United States, there are a number of official organizations which support the interests of navigators. Some have a policy-making role; others build and operate navigation systems. Many maritime nations have similar organizations performing similar functions. International organizations also play a significant role. 117. The Coast And Geodetic Survey The U.S. Coast and Geodetic Survey was founded in 1807 when Congress passed a resolution authorizing a sur￾vey of the coast, harbors, outlying islands, and fishing banks of the United States. President Thomas Jefferson ap￾pointed Ferdinand Hassler, a Swiss immigrant and professor of mathematics at West Point, the first Director of the “Survey of the Coast.” The survey became the “Coast Survey” in 1836. The approaches to New York were the first sections of the coast charted, and from there the work spread northward and southward along the eastern seaboard. In 1844 the work

10INTRODUCTIONTOMARINENAVIGATIONwith the log book data,were compiled into the“Wind andwasexpanded andarrangements madetochart simultaneous-lythegulf and east coasts.Investigationof tidal conditionsCurrentChartoftheNorthAtlantic"in1847.This isthean-began, and in 1855 the first tables of tidepredictions werecestor of today's Pilot Chart.The United States instigatedpublished.The Californiagold rush necessitated a surveyofan international conference in1853to interestother nationsthe west coast.This survey began in 1850,the year Californiain a system of exchanging nautical information.The plan,becameastate.CoastPilots,orSailingDirections,fortheAt-which was Maury's,was enthusiasticallyadopted by otherlanticcoastof the United States wereprivatelypublished inmaritime nations.In 1854 theDepot was redesignated thethe first half of the 19th century. In 1850 the Survey began"U.S.Naval Observatory and Hydrographical Office."InaccumulatingdatathatledtofederallvproducedCoastPilots1861, Maury, a native of Virginia, resigned from the U.S.The1889PacificCoastPilotwasanoutstandingcontributionNavy and accepted a commission intheConfederateNavytothesafetyofwestcoastshippingatthebeginning ofthe CivilWar.This effectively ended hisIn1878thesurveywasrenamed"CoastandGeodeticcareer as a navigator, author,and oceanographer.At war'sSurvey."In 1970 the survey became the"National Oceanendhefledthecountry.Maury'sreputationsufferedfromSurvey,"and in1983it becamethe"National Ocean Ser-hisembracing theConfederatecause.In1867,whileMauryvice."The Office of Charting and Geodetic Serviceswas still absent from the country to avoid arrest for treason,accomplished all charting and geodeticfunctions.In1991George W. Blunt, an editor of hydrographic publications,the namewas changed back to theoriginal "Coast and Geo-wrote:detic Survey,"organized under the National Ocean Servicealong with several other environmental offices.Today itIn mentioning what our government has doneto-provides themariner with the charts and coast pilots of allwards nautical knowledge, I do not allude to thewaters ofthe United States and its possessions,andtideandworks ofLieutenantMaury,becauseIdeem themtidal currenttablesformuch oftheworld.Its administrativeworthless....They havebeen suppressed sinceorderrequirestheCoastandGeodeticSurveytoplanandthe rebellion by order of the proper authorities,directprograms toproduce charts and related informationMaury's loyalty and hydrography being alike infor safe navigation of the Nation's waterways, territorialquality.seas, and national airspace.This work includes all activitiesrelated to theNational Geodetic Reference System, survey-After Maury's return to the United States in 1868, heing, charting, and data collection; production andservedasaninstructorattheVirginiaMilitaryInstitute.Hedistribution of charts; and research anddevelopment ofnewcontinued atthis position until his death in1873.Sincehistechnologiestoenhancethesemissionsdeath, his reputation as one of America's greatest hydrographershasbeenrestored118.TheDefenseMappingAgencyIn1866CongressseparatedtheObservatoryandtheHydrographic Office, broadly increasing the functions ofIn the first years of the newlyformed United States ofthelatter.TheHydrographicOfficewas authorized tocarryAmerica, charts and instruments used by the Navy and mer-outsurveys,collectinformation,and print everykind ofchantmariners were left over from colonial days or werenautical chartand publicationfor thebenefit anduseofobtainedfromEuropeansources.In1830theU.S.Navyes-navigators generally."tablished a“Depot of Charts and Instruments”inThe Hydrographic Ofice purchased the copyright ofWashington,D.C.It was a storehousefrom whichavailableThe NewAmericanPractical Navigator in 1867.The firstcharts.sailingdirections.andnavigationalinstrumentsNoticetoMarinersappearedin1869.Dailybroadcastofwere issued to Naval ships.Lieutenant L.M.Goldsboroughnavigational warnings was inaugurated in 1907.In1912and oneassistant, Passed Midshipman R.B.Hitchcock,following the sinking of the Titanic,theInternational Iceconstituted theentirestaff.PatrolwasestablishedThe first chart published by the Depot was producedIn 1962 the U.S. Navy Hydrographic Office was redes-from data obtained in a survey madeby Lieutenant Charlesignated the U.S. Naval Oceanographic Office. In 1972Wilkes,who had succeeded Goldsborough in 1834.Wilkescertain hydrographic functions of the latter office werelaterearnedfameastheleaderofa UnitedStatesexpeditiontransferred to the Defense Mapping Agency Hydrograph-to Antarctica.From 1842until 1861LieutenantMatthewicCenter.In 1978 theDefense Mapping AgencyFontaineMaury served as Officer in Charge.Under hisHydrographic/Topographic Center (DMAHTC) as-command the Depotrose to international prominencesumed hydrographic and topographic chart productionMaurydecided upon an ambitious plan to increase themar-iner's knowledge ofexisting winds,weather,and currents.functions.DMAHTC provides support to theU.S.Depart-ment of Defense and other federal agencies on mattersHe began bymaking a detailed record of pertinent matterincluded in old log books stored at the Depot.He then inau-concerningmapping,charting,andgeodesy.Itcontinuestofulfill the old Hydrographic Office's responsibilities toguratedahydrographicreportingprogramamongshipmasters, and the thousands of reports received,along"navigators generally

10 INTRODUCTION TO MARINE NAVIGATION was expanded and arrangements made to chart simultaneous￾ly the gulf and east coasts. Investigation of tidal conditions began, and in 1855 the first tables of tide predictions were published. The California gold rush necessitated a survey of the west coast. This survey began in 1850, the year California became a state. Coast Pilots, or Sailing Directions, for the At￾lantic coast of the United States were privately published in the first half of the 19th century. In 1850 the Survey began accumulating data that led to federally produced Coast Pilots. The 1889 Pacific Coast Pilot was an outstanding contribution to the safety of west coast shipping. In 1878 the survey was renamed “Coast and Geodetic Survey.” In 1970 the survey became the “National Ocean Survey,” and in 1983 it became the “National Ocean Ser￾vice.” The Office of Charting and Geodetic Services accomplished all charting and geodetic functions. In 1991 the name was changed back to the original “Coast and Geo￾detic Survey,” organized under the National Ocean Service along with several other environmental offices. Today it provides the mariner with the charts and coast pilots of all waters of the United States and its possessions, and tide and tidal current tables for much of the world. Its administrative order requires the Coast and Geodetic Survey to plan and direct programs to produce charts and related information for safe navigation of the Nation’s waterways, territorial seas, and national airspace. This work includes all activities related to the National Geodetic Reference System; survey￾ing, charting, and data collection; production and distribution of charts; and research and development of new technologies to enhance these missions. 118. The Defense Mapping Agency In the first years of the newly formed United States of America, charts and instruments used by the Navy and mer￾chant mariners were left over from colonial days or were obtained from European sources. In 1830 the U.S. Navy es￾tablished a “Depot of Charts and Instruments” in Washington, D. C. It was a storehouse from which available charts, sailing directions, and navigational instruments were issued to Naval ships. Lieutenant L. M. Goldsborough and one assistant, Passed Midshipman R. B. Hitchcock, constituted the entire staff. The first chart published by the Depot was produced from data obtained in a survey made by Lieutenant Charles Wilkes, who had succeeded Goldsborough in 1834. Wilkes later earned fame as the leader of a United States expedition to Antarctica. From 1842 until 1861 Lieutenant Matthew Fontaine Maury served as Officer in Charge. Under his command the Depot rose to international prominence. Maury decided upon an ambitious plan to increase the mar￾iner’s knowledge of existing winds, weather, and currents. He began by making a detailed record of pertinent matter included in old log books stored at the Depot. He then inau￾gurated a hydrographic reporting program among shipmasters, and the thousands of reports received, along with the log book data, were compiled into the “Wind and Current Chart of the North Atlantic” in 1847. This is the an￾cestor of today’s Pilot Chart. The United States instigated an international conference in 1853 to interest other nations in a system of exchanging nautical information. The plan, which was Maury’s, was enthusiastically adopted by other maritime nations. In 1854 the Depot was redesignated the “U.S. Naval Observatory and Hydrographical Office.” In 1861, Maury, a native of Virginia, resigned from the U.S. Navy and accepted a commission in the Confederate Navy at the beginning of the Civil War. This effectively ended his career as a navigator, author, and oceanographer. At war’s end, he fled the country. Maury’s reputation suffered from his embracing the Confederate cause. In 1867, while Maury was still absent from the country to avoid arrest for treason, George W. Blunt, an editor of hydrographic publications, wrote: In mentioning what our government has done to￾wards nautical knowledge, I do not allude to the works of Lieutenant Maury, because I deem them worthless. . . . They have been suppressed since the rebellion by order of the proper authorities, Maury’s loyalty and hydrography being alike in quality. After Maury’s return to the United States in 1868, he served as an instructor at the Virginia Military Institute. He continued at this position until his death in 1873. Since his death, his reputation as one of America’s greatest hydrog￾raphers has been restored. In 1866 Congress separated the Observatory and the Hydrographic Office, broadly increasing the functions of the latter. The Hydrographic Office was authorized to carry out surveys, collect information, and print every kind of nautical chart and publication “for the benefit and use of navigators generally.” The Hydrographic Office purchased the copyright of The New American Practical Navigator in 1867. The first Notice to Mariners appeared in 1869. Daily broadcast of navigational warnings was inaugurated in 1907. In 1912, following the sinking of the Titanic, the International Ice Patrol was established. In 1962 the U.S. Navy Hydrographic Office was redes￾ignated the U.S. Naval Oceanographic Office. In 1972 certain hydrographic functions of the latter office were transferred to the Defense Mapping Agency Hydrograph￾ic Center. In 1978 the Defense Mapping Agency Hydrographic/Topographic Center (DMAHTC) as￾sumed hydrographic and topographic chart production functions. DMAHTC provides support to the U.S. Depart￾ment of Defense and other federal agencies on matters concerning mapping, charting, and geodesy. It continues to fulfill the old Hydrographic Office’s responsibilities to “navigators generally