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, anticipates 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 navigation 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 navigating 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 cannot 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 involves choosing the best method to use. Commonly recognized types of navigation are listed below. • Dead reckoning (DR) determines position by advancing 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. Correcting 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 primarily as a backup to satellite and other electronic systems in the open ocean. • Radio navigation uses radio waves to determine position by either radio direction finding systems or hyperbolic systems. • Radar navigation uses radar to determine the distance 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 future navigation system planning. Integrated systems take inputs from various ship sensors, electronically display positioning information, and provide control signals required to maintain a vessel on a preset course. The navigator becomes a system manager, choosing system presets, interpreting system output, and monitoring vessel response. In practice, a navigator synthesizes different methodologies 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 disadvantages. The navigator must choose methods appropriate to each particular situation. With the advent of automated position fixing and electronic 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 accuracy 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 selecting 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 worldwide 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 meridian 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 territories 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 Canaries 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 interests 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, English cartographers began using the meridian of that observatory as a reference. The publication by the Observatory of the first British Nautical Almanac in 1767 further entrenched Greenwich as the prime meridian. An unsuccessful attempt was made in 1810 to establish Washington, D.C. as the prime meridian for American navigators and cartographers. In 1884, the meridian of Greenwich was officially established as the prime meridian. Today, all maritime 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. Stereographic 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 corInland 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 navigational 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 publications for several generations of navigators. They were known as “Waggoners” by most sailors. Modern pilots and sailing directions are based on extensive data collection 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 Norsemen used it in the 11th century. It was not until the 1870s that Lord Kelvin developed a reliable dry card marine compass. 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 compass error was not possible until Matthew Flinders discovered that a vertical iron bar could reduce errors. After 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 originally 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 century. 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 proportional to a vessel’s speed. An engine revolution counter or shaft log often measures speed onboard large ships. Doppler 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 navigation, and logical sequencing will require a conversion effort spanning many years. Notwithstanding the conversion 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 compilations 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. However, 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 fathom, as conversion to the metric system continues. The sailings refer to various methods of mathematically determining course, distance, and position. They have a history almost as old as mathematics itself. Thales, Hipparchus, Napier, Wright, and others contributed the formulas that permit computation of course and distance by plane, traverse, parallel, middle latitude, Mercator, and great circle 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 introduces 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 define any position on earth. Latitude (L, lat.) is the angular distance from the equator, measured northward or southward 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. However, 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-latitudes 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 indicate the direction of measurement. The difference of longitude (DLo) between two places 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 exceeds 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 considered 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-circle distance. For most purposes, considering the nautical mile the length of one minute of latitude introduces no significant 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) between 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 another. 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, expressed 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, compass, 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 travel. 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