©GaryC.Kessler,2012-2018

AShortCourseonNauticalChartsandBasicPlottingFortheRecreationalBoater

GaryC.Kessler

gck@garykessler.nethttps://www.garykessler.net/scuba

Version5.1(04/28/2018)

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TableofContentsListofFigures................................................................................................................................iii

Introduction...........................................................................................................................1

Part1.NauticalCharts............................................................................................................21.1.PurposeandRoleofNauticalCharts...............................................................................2

1.1.1.TypesofCharts.....................................................................................................21.1.2.SourcesofCharts..................................................................................................3

1.2.SupplementaryResources...............................................................................................31.2.1.ChartNo.1............................................................................................................41.2.2.U.S.CoastPilot®....................................................................................................41.2.3.USCGLightList......................................................................................................61.2.4.NoticetoMariners................................................................................................7

1.3.LatitudeandLongitude....................................................................................................81.4.TheAnatomyofaNauticalChart.....................................................................................9

1.4.1.ChartReferenceData..........................................................................................101.4.2.TheCompassRose..............................................................................................141.4.3.Landmarks...........................................................................................................141.4.4.MarginalNotes...................................................................................................151.4.5.AidstoNavigation,andCoastalandUnderwaterFeatures................................16

1.5.AidsToAndRulesOfNavigation...................................................................................221.6.Summary........................................................................................................................27

Part2:Plotting......................................................................................................................282.1.WhichWayisNorth?.....................................................................................................28

2.1.1.TheCompassRose,Revisited..............................................................................282.1.2.Deviation.............................................................................................................292.1.3.PuttingitallTogether.........................................................................................30

2.2.InstrumentsforPlotting................................................................................................312.2.1.ParallelRuleandRollerPlotter...........................................................................312.2.2.DividersandCompass.........................................................................................33

2.3.ArithmeticforPlotting...................................................................................................332.3.1.MeasuringDistance............................................................................................332.3.2.ManipulatingTimeValues..................................................................................352.3.3.Distance,Speed,andTime..................................................................................36

2.4.PlottingProblems..........................................................................................................372.4.1.FindingLatitudeandLongitude..........................................................................382.4.2.PlottingaPosition...............................................................................................402.4.3.FindingaTrueBearingandCompassCourse......................................................402.4.4.FindingDistanceandSpeedMadeGood............................................................422.4.5.EstimatingTimeofArrival...................................................................................422.4.6.DeadReckoning..................................................................................................432.4.7.FindingSetandDrift...........................................................................................442.4.8.PlottingACourseWithKnownSetandDrift......................................................45

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2.4.9.ObtainingaFixWithLinesofPosition................................................................472.4.10.TakingaRunningFix.........................................................................................482.4.11.DoubletheAngleontheBow...........................................................................49

2.5.Summary........................................................................................................................51

AppendixA:DMS,GPS,andDecimalNotations....................................................................52

AppendixB:MercatorandPolyconicProjections..................................................................56

AppendixC:TheLengthofaDegree.....................................................................................58

AppendixD:NavigatorsQuickReferenceCard......................................................................59

AppendixE:SampleProblemChart.......................................................................................61

AcronymsandAbbreviations................................................................................................63

ReferencesandFurtherReading...........................................................................................64

Acknowledgements..............................................................................................................66

AbouttheAuthor.................................................................................................................66

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ListofFigures1.1.ChartNo.1:NauticalChartSymbolsAbbreviationsandTermsusedonPaperandElectronic

NavigationalCharts..............................................................................................................41.2.U.S.CoastPilot®(Regions4and6).........................................................................................51.3.LightList(VolumeI:AtlanticCoastandVolumeIII:AtlanticandGulfCoasts)......................61.4.NoticetoMariners(No.10fortheweekending10March2018)andLocalNoticeto

Mariners(9thweekof2018--February--coveringUSCGDistrict7)..................................71.5.Latitudeandlongitude...........................................................................................................81.6.Chart14782(CumberlandHeadtoFourBrothersIslands)..................................................101.7.Chartnumberanddateofpublication(Chart14782).........................................................101.8.Charttitleandotherinformation(Chart14782)..................................................................111.9.LatitudeandlongitudescalesonChart14782.....................................................................121.10.LegendsfordistanceonChart14782.................................................................................131.11.SoundinginformationforChart14782..............................................................................131.12.Compassrose.....................................................................................................................141.13.LandmarksinthecityofBurlington(Chart14782)............................................................151.14.NOTEAfromChart14782..................................................................................................161.15.AppletreeBay,fromChart14782......................................................................................171.16.ColchesterReefandColchesterShoal,fromChart14782..................................................181.17.Burlingtonharborbreakwater,fromChart14785(BurlingtonHarbor)............................201.18.DeerIslandandPresidentRoadssectionofChart13267(MassachusettsBay).................201.19.U.S.AidstoNavigation.......................................................................................................231.20.Green(can)andred(nun)buoys.......................................................................................231.21.Redtriangularandgreensquaredaymarkers...................................................................241.22.AreaaroundPoncedeLeonInletfromChart11485(IntracoastalWaterwayTolmatoRiver

toPalmShores)..................................................................................................................251.23.DaytonaBeachMunicipalYachtBasininsetfromChart11485.........................................261.24.NavigationRulesandRegulationsHandbook.....................................................................272.1.Compassrose........................................................................................................................292.2.Parallelruler.........................................................................................................................312.3.Parallel,orroll,plotter.........................................................................................................322.4.Protractortriangle................................................................................................................322.5.Dividers.................................................................................................................................332.6.Placingthedividersontwopoints.......................................................................................342.7.Placingthedividersonthelatitudescale.............................................................................342.8.60DSTmnemonic................................................................................................................372.9.Nauticalsliderule.................................................................................................................372.10.Findinglatitudeandlongitude............................................................................................392.11.Plottingposition.................................................................................................................402.12.Findingatruebearingandcompasscourse.......................................................................412.13.Findingdistanceandspeedmadegood.............................................................................422.14.Estimatingtimeofarrival...................................................................................................43

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2.15.Deadreckoning...................................................................................................................442.16.Determiningsetanddrift...................................................................................................452.17.Plottingwithknownsetanddrift.......................................................................................462.18.Obtainingathree-bearingfix..............................................................................................472.19.Takingarunningfix............................................................................................................482.20.Anisoscelestriangle..........................................................................................................502.21.Doubletheangleonthebow............................................................................................50B.1.Mercatorprojection.............................................................................................................56B.2.Polyconicprojection.............................................................................................................57

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Introduction

Thismanualisintendedfortherecreationalboaterwhowantstounderstandtheelementsofthenauticalchartsthatweemploytolearnhowtonavigatethroughanewbodyofwaterandperformbasicplottingtasks.Themotivationformetowritethisissimple--asarecreationalboatermyself,Icametorealizethatwhilereadingachartdoesnotappeartobeallthatdifficult,thereweremanyitemsofinformationthatIhadnotrealizedwereeventhere,eitherbecauseIdidnotusethatinformationformyboatingexcursionsorbecausethechartsthatIcommonlyusedidnotcontaincertainelementsofinformation.Priortotakingacoursein2011toacquiremycaptain'slicense,IknewnothingabouttheCoastPilot®orLightList,sourcesofanincredibleamountofinformationofinteresttomastersofavesselofanysize.Inaddition,thegeneralbookstowhichrecreationalboatersareoftendirectedareexcellentinmanywaysbutrarelytacklethesubjectofevensimpleplotting.Thismanualisdividedintotwoparts.Part1describesnauticalchartsfromtheperspectiveofarecreationalmariner.Thissectiondescribesplaceswhereonecanacquirechartsand,moreimportantly,wherereferencematerialscanbeobtainedthatcanhelpamarinerinterpretthemarkingsonthecharts,fromthemeaningofaidstonavigationandtheperiodofalighthouselighttothecompositionoftheseabedandheightofabridge.Someofthegeneralinformationinthispartofthemanualappliestoanynauticalchartanywhere,althoughthefocusisonUnitedStatesnauticalcharts.MostoftheexamplesarefromLakeChamplain(NewYorkandVermont)becausetheseweremyhomewatersuntil2014;nowtheyaretheHalifaxRiver,AtlanticOceanoffofPoncedeLeonInlet,andthenorthernMosquitoRiverLagoon.Part2ofthemanualdescribesbasicplotting.Thissectionsstartsbyanexplanationoftherelationshipbetweenmagneticnorth(asshownonacompass),truenorth(asshownonachart),andship'snorth(i.e.,asshownonyourvessel'scompass),andintroducestheconceptsofvarianceanddeviation.Thatisfollowedbyadescriptionoftheinstrumentsthatareneededinordertoplotcoursesonnauticalcharts.Thebulkofthechapterdescribesanumberofrudimentaryplottingproblemsandhowtosolvethem,suchasdeterminingpositionbydeadreckoning,estimatingtimeofarrival,andcompensatingforcurrentwhenplottingacourse.Thefocusofthisdocumentisonprintedcharts,andreadingandplottingusinghandtools.MarineelectronicsmakealotofthesetasksautomaticbutIhavealwaystakentheposturethatpeopleneedtoknowthebasicprocessbehindwhatourautomatedandcomputer-basedtoolsaretellingus.Inthatspirit,Iofferthistutorial.Hopefully,readerswillbeinspiredtoreadsomeofthemoreexcellent,in-depthtextsreferencedattheendofthispaper.Suggestions,corrections,and/oranyothercommentsaboutthismanualarewelcome.

GaryC.KesslerOrmondBeach,FL

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Part1:NauticalChartsThissectionpresentsanintroductiontonauticalcharts.Inaddition,supplementaryresourcematerialsthatcanaidintheinterpretationofthesymbolsonthechartandyieldabetterunderstandingofthecoastalandnavigationalfeaturesdepictedonthechartswillalsobeintroduced.Thiswillbefollowedbysomespecificexamplesofchartfeaturesandsymbols.1.1.PurposeandRoleofNauticalChartsNauticalchartsare,ofcourse,the"roadmap"ofwaterways.Butthechartsaresomuchmore.Onastreetmap,prettymuchallyougetarethestreets;maybeyouwillalsoseeidentifiersforsomebuildings,parks,andotherstructures,butyouwon'tfindalistingofallofthetrafficsignalsandthedurationofaredandgreenlight.Andstreets,ofcourse,highlyregulatewhereyoucangoinyourcar;ifonatwo-wayroad,youdriveontherightside(intheU.S.).Lakesandoceansarealittlelessorganized.Insomeareas,therearenauticaltrafficlanesbutboatmovementisnotsorestrictedonthevastmajorityofthewaterways.Ifyouaremorethanacoupleofmilesawayfromland,knowingthelandmarksandstructurescanhelpyouorientyourselftoyourposition.Navigationalaidsofalltypeshelpyoufindyourwayorkeepoutofdanger.Chartsshowsignificantlymoreinformationthanastreetmap.Chartsdescribenotonlywherethewaterisbutalsothecharacteristicsofthewaterwayandseabed.Theyshowtheshapeofthecoast,locationofislandsandhazards,navigationmarkers,warningsofhazards,theheightofbridgesandotherobstructions,andoffermuchmoreadditionalinformation.Nauticalchartsareanessentialitemonboardanyvessel,evensmallrecreationalboatsthatdonotwanderveryfarfromland.Unexpectedeventsfromweathertocurrentcantakeyouabitfurtherthanyouintendedtogoandthechartscanhelpyougettowhereyouwanttobeortoaportofrefuge.1.1.1.TypesofChartsTheNationalOceanicandAtmosphericAgency(NOAA)producesU.S.nauticalcharts.Chartsaregenerallycategorizedbytheirscale;large-scalechartsshowalotofdetailoverasmallgeographicarea,whilesmall-scalechartsshowalesseramountofdetailoveralargearea.Ingeneral,then,marinerswouldusesmall-scalechartswhenontheopenseasgoingfromoneplacetoanotherandwouldusethelargestscalepossiblefornavigatingnear-shore.NOAAusesthefollowingchartclassifications:1

• Sailingchartshaveascaleof1:600,000andsmaller.Thesechartsarefordetermining 1FromU.S.CoastPilot®.

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positionalongthecoastwhenapproachingfromtheopenocean,orforsailingbetweendistantcoastwiseports.

• Generalchartshaveascalebetween1:150,000and1:600,000.Thesechartsareprimarilyforcoastalnavigationoutsideofnear-coastalreefsandshoals.

• Coastchartshaveascalebetween1:50,000and1:150,000.Thesechartsareforinshorenavigationleadingtosizeablebaysandharbors,andfornavigatinglargeinlandwaterways.

• Harborchartshaveascalelargerthan1:50,000andarefornavigatingharbors,anchorageareas,andsmallerwaterways.

1.1.2.SourcesofChartsThereareavarietyofsourcesfornauticalcharts.Mostboatersbuyachartforlocalwatersatalocalmarinestore.Chartsforjustaboutanypartoftheworldcanbeobtainedfromanynumberofsourcesonline.TheofficialNOAAsiteforchartsisattheOfficeofCoastSurveyWebsite.2Linksfromthatpagewillassistyouinobtainingpapercharts,electroniccharts,publicationswithadditionalinformation,andhistoricalcharts.ThissitealsolistsanumberofretailersthatsellNOAAcharts.NOAAhaschartsavailableinanumberofformats,including:

• Printondemand(POD)chartsareprinteduponrequestandshippedtothecustomer.• BookletchartsaredownloadablechartsinPDFformatthatcanbeprintedforfree.3• ChartViewerallowsallNOAAchartstobeviewedonline.• Electronicchartsaredownloadablechartsforusewithcommercialsoftware.Downloads

areavailableasRasterNavigationalCharts(NOAARNC®)in.BSBformatforrasterdisplaysystemsorasElectronicNavigationalCharts(NOAAENC®)forelectronicchartingsystems.Neitheroftheseformatsisdesignedforprinting.Electronicchartsareconstantlyupdated.

1.2.SupplementaryResourcesNauticalchartsarethegraphicalrepresentationofthewaterwaysandcoastalzones.Likeallgraphicalrepresentations,however,theirsymbolsmayseemarcanetotheuntrainedeyeand,inanycase,itisimpossibleforthediagramstohavecompleteinformation.Forthatreason,thereareanumberofdocumentsthatprovideimportantinformationthatsupplementsthecharts.

2http://www.nauticalcharts.noaa.gov/3Mostofthechartfragmentexamplesinthisdocumentcomefrombookletcharts.

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1.2.1.ChartNo.1ThesinglebestreferencewithwhichtounderstandthesymbolsandmarkingsonU.S.nauticalchartsisadocumentcalledChartNo.1:Symbols,AbbreviationsandTermsusedonPaperandElectronicNavigationalCharts(Figure1.1),publishedbytheNationalOceanService.ChartNo.1canbedownloadedfromtheNOAAWebsite.4

Figure1.1.ChartNo.1:Symbols,AbbreviationsandTerms

usedonPaperandElectronicNavigationalCharts.ChartNo.1isdividedintofivesections:

• Introduction:Generalintroductiontothedocument,andanoverviewofthesymbolsandinformationthatcanbefoundonanauticalchart.

• General:Symbolsandinformationrelatedtochartidentification,distance,directions,andthecompass.

• Topography:Chartsymbolsrelatedtofeaturesfoundonland.• Hydrography:Chartsymbolsrelatedtofeaturesrelatedtothewaterandseabed.• NavigationAidsandServices:Chartsymbolsrelatedtoaidstonavigation.SectionsQ

(Buoys,Beacons)andU(SmallCraftFacilities)provideinformationonthelateralsystemofnavigationbuoysusedworldwide(although,ofcourse,therearetwosystemsindifferentregionsoftheglobe,makingthisparticularlyusefulifyouwilloperateavesseloutsideofyournormalboatingzone).

1.2.2.U.S.CoastPilot®TheUnitedStatesCoastPilot®supplementsnauticalchartsbyprovidingdetailedinformationaboutcoastalfeaturesthatwouldbeimpossibletoincludeonachart.PublishedbytheNationalOceanService,U.S.CoastPilot®documentscanbedownloadedfromtheNOAAWebsite.5 4https://nauticalcharts.noaa.gov/publications/docs/us-chart-1/ChartNo1.pdf5https://nauticalcharts.noaa.gov/publications/coast-pilot/index.html

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Figure1.2.U.S.CoastPilot®(Regions4and6).

TheU.S.CoastPilot®isaseriesofninedocuments(Figure1.2),eachcoveringadifferentregionoftheUnitedStates:AtlanticCoastRegions

1. Eastport,MainetoCapeCod,Massachusetts2. CapeCod,MassachusettstoSandyHook,NewJersey3. SandyHook,NewJerseytoCapeHenry,Virginia4. CapeHenry,VirginiatoKeyWest,Florida5. GulfofMexico,PuertoRico,andU.S.VirginIslands

GreatLakesRegion

6. GreatLakesandConnectingWaterwaysPacificCoastRegions

7. California,Oregon,Washington,Hawaii,andPacificIslands8. Alaska-DixonEntrancetoCapeSpencer9. Alaska-CapeSpencertoBeaufortSea

EachCoastPilothasthesamegenerallayout.Chapter1istitledGeneralInformationandisawealthofinformationabouthowtousetheCoastPilot,themeaningofvariousterms,genericinformationaboutnauticalcharts,noticestomariners,aidstonavigation,communicationandassistanceprocedureswhenindistress,radiousage,pollutionregulations,andsomuchmore;6thischapteraloneisextraordinarilyvaluableevenintheabsenceoftherestofthedocument.Chapter2istitledNavigationRegulationsandcoversvariousrulesandregulationsaffectingnavigationinthejurisdictionscoveredbythisparticulardocument.Eachsubsequentchaptercoversapartoftheregion;theRegion6CoastPilot,forexample,has12additionalchapterscoveringtheGreatLakes,St.LawrenceRiver,LakeChamplain,andtheconnectingwaterways.Eachchapteridentifiesthepertinentnavigationalchartsthatcoverthe

6ThereisalsoasectiontitledMineclearing:Caution.

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regionandprovidesdetaileddescriptionsofpertinentlandmarks,waterways,andotherreferencepointsusefulfornavigation.Anchorageareas,specialharborregulations,U.S.CoastGuardfacilities,small-craftfacilities,andothergenerallyusefulinformationisalsoprovided.1.2.3.USCGLightListTheU.S.CoastGuardLightListdescribeslights,buoys,beacons,soundsignals,andotheraidstonavigationfoundintheUnitedStates.Thelightlistprovidesdetailedinformationabouttheaidstonavigationthatcouldnotfitontothenauticalchartitself.Achart,forexample,mightshowalighthousebuttheLightListwillcontainadditionalinformationsuchasthelatitudeandlongitude,seasonalvariations,andothercommentary.PublishedbytheU.S.GovernmentPrintingOffice,LightListdocumentscanbedownloadedfromtheU.S.CoastGuardNavigationCenterLightListWebsite.7

Figure1.3.LightList(VolumeI:AtlanticCoastandVolumeIII:AtlanticandGulfCoasts).

TheLightListsareaseriesofsevenvolumes(Figure1.3)coveringthefollowinggeographicregions:

I. AtlanticCoast:St.CroixRiver,MainetoShrewsburyRiver,NewJerseyII. AtlanticCoast:ShrewsburyRiver,NewJerseytoLittleRiver,SouthCarolinaIII. AtlanticandGulfCoasts:LittleRiver,SouthCarolinatoEconfinaRiver,Florida(including

PuertoRicoandtheU.S.VirginIslands)IV. GulfofMexico:EconfinaRiver,FloridatoRioGrande,TexasV. WesternRivers:MississippiRiverSystemVI. PacificCoastandPacificIslands

7http://www.navcen.uscg.gov/?pageName=lightlists

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VII. GreatLakes:GreatLakesandtheSt.LawrenceRiverabovetheSt.RegisRiverEachLightListhasthesamegenerallayout.Thebeginningofthedocumentincludesanexcellentoverviewofthelateralnavigationsystemincludingexamplesofthemarkersasseenduringthedayandduringthenight,aswellasthoseusedontheIntracoastalWaterwayandthewesternrivers.Thisisfollowedbyatablethataidsthemarinerindeterminingthedistancefromwhichalightcanbeseenbaseduponitsstatednominalrangeandactualvisibilityconditions.Adescriptionofaidstonavigationandaglossaryoftermsprecedethelistoflights.Lightsarelistedinanumericalorderthatisusedbytheindex.UpdatestothelightlistareissuedbyperiodicNoticetoMarinersanddocumentsontheLightListWebsite.1.2.4.NoticetoMarinersNeitherthecharts,CoastPilot®,norLightListaretotallyerror-free.Furthermore,manyofthefeaturesanditemsonthosedocumentschangeovertime;astorm,forexample,mightknockdownastructureindicatedonthelandorcauseanunderwaterwrecktoshiftposition,oranunlightedbuoymightbereplacedwithalightedone.Inanycase,informationcontainedinanyofthesepublishedreferencescanchangeovertime.

Figure1.4.NoticetoMariners(No.10fortheweekending10March2018)and

LocalNoticetoMariners(9thweekof2018--February--coveringUSCGDistrict7).Twoseriesofdocumentsprovideupdatestothesepublications.TheNoticetoMariners(NtM)ispublishedweeklybytheNationalGeospatial-IntelligenceAgency(NGA)incooperationwiththeNationalOceanServiceandUSCG(Figure1.4,left).Bydesign,theNtMdocumentsonly

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providechartcorrectionspertinenttoocean-goingvessels.NtMdocumentscanbedownloadedfromtheNGA'sNoticetoMarinersWebpage.8LocalNoticetoMariners(LNM)documentsprovideweeklyupdatestochartsandotherpublications(Figure1.4,right).DistributedbytheUSCGNavigationCenterWebsite,9LNMsareorganizedbyUSCGdistrict.1.3.LatitudeandLongitudeInordertoreadachart--and,ofcourse,inordertodoanyplottingonachart--onemustbefamiliarwithlatitudeandlongitude(Figure1.5).Linesoflatituderuneast-westandareusedtomeasurepositionontheglobeinthenorth-southdirection.Becauselinesoflatitudedrawnontheglobeappearsasconcentriccircles,alineoflatitudeisalsoreferredtoasaparallel.Latitudeismeasuredasanumberbetween0°and90°,where0°istheEquator,90°north(N)istheNorthPole,and90°south(S)istheSouthPole.Insomecases,a"+"or"-"signprecedesthevalue;positivelatitudes(+)areinthenorthernhemisphereandnegativelatitudes(-)refertothesouthernhemisphere.

Figure1.5.Latitudeandlongitude.10

Linesoflongituderunnorth-southandareusedtomeasurepositionontheglobeintheeast-westdirection.Linesoflongitudedrawnontheglobeappearlikethesectionallinesofanorange,comingtogetheratthenorthandsouthpoles.Alineoflongitudeisalsoreferredtoasameridianandcantakeonavaluebetween0°and180°;0°isthePrimeMeridianandrunsthroughtheRoyalObservatoryinGreenwich(London)and180°istheInternationalDateLine.Insomecases,a"+"or"-"signprecedesthevalueinsteadofaneast(E)orwest(W)designation;positivelongitudes(+)areintheeasternhemisphereandnegativelongitudes(-)refertothewesternhemisphere.

8http://msi.nga.mil/NGAPortal/MSI.portal?_nfpb=true&_pageLabel=msi_portal_page_619http://www.navcen.uscg.gov/?pageName=lnmMain10http://en.wikipedia.org/wiki/File:Latitude_and_Longitude_of_the_Earth.svg

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Nauticalchartsareorientedsothatgeographic(true)northistowardsthetop.Theverticallinesarethemeridians(longitude)andthemarkingsontheleftandrightbordermeasurelatitude.Thehorizontallinesaretheparallels(latitude)andthemarkingsonthetopandbottombordermeasurelongitude.Notethatthelatitudeandlongitudescalesarenotthesame(exceptattheEquator).Latitudeandlongitudearemeasuredindegrees(°),minutes('),andseconds(").Adegreeiscomposedof60minutes,which,inturn,comprises60seconds.Nauticalchartsgenerallyexpresslatitudeandlongitudeinadegree,minute,second(DMS)format,sometimesdenotedDD°MM'SS".GlobalPositioningSystems(GPS),mobilephones,GoogleMaps,andothersystemsoftenuseotherformatstodenotelatitudeandlongitude.TheGPSformatuseswholedegrees,wholeminutes,andsecondsexpressedasafractionofaminute,sometimesdenotedDD°MM.MM'.Decimalnotationuseswholedegreesandexpressesminutesandsecondsasafractionofadegree,sometimesdenotedDD.DDD°.Asanexample,thelatitudeandlongitudeofthewreckoftheO.J.WalkerinBurlingtonHarbor(Vermont)couldbeshownas44°28'43"N,073°14'26"WinDMSnotation,as44°28.72'N,073°14.44'WinGPSnotation,oras44.479°N,073.241°Windecimalnotation.AppendixAdescribeshowtoconvertbetweenthesethreenotations.1.4.TheAnatomyofaNauticalChartAsstatedearlier,nauticalchartsarethegraphicalrepresentationofwaterwaysandthenearbycoast.Nearlyeveryonewhoownsoroperatesaboathasreferredtoachartatleastonceinordertoobtainarudimentaryunderstandingoftheoveralllayoutofthelandandwater.Chartsalsocontainawealthofinformation,includingaidstonavigation,landmarks,hazards,attractions,anchorageareas,etc.Recreationalboatersusethesamechartascommercialshipssotheinformationcontainedonthechartshastosufficeforthebiggestofvessels.Figure1.6showsNOAAChart14782,whichcoverstheCumberlandHeadtoFourBrothersIslandsareaofLakeChamplaininNewYorkandVermont.Mostnauticalchartsareatleastacoupleoffeetineachdirection,agoodfitforaship'splottingtablebutrequiringfoldingonasmallboat.Evenwiththeverysmallsizeshowninthefigure,onecanseethatthereisalotofinformationwrittenonthechartthatisoftenasimportantasthewaterwaydataitself.

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Figure1.6.Chart14782(CumberlandHeadtoFourBrothersIslands).

1.4.1.ChartReferenceDataThesinglebestidentifierforachart,ofcourse,isthechartnumberthatisclearlymarkedontheouterboundaryinallfourcorners.Additionalinformation,suchasdateofpublication,isgenerallyshowninoneplace;theinformationinFigure1.7appearsinthelowerleftcornerofchart14782.Thischartisinits25thedition,publishedinJanuary2006;ithasbeencorrectedbaseduponNMsthroughJanuary14,2006andLNMsthroughJanuary10,2006.Thechartnote,inpurple,confirmsthatthischarthasbeencorrectedfromNMsandLNMs.

Figure1.7.Chartnumberanddateofpublication(Chart14782).

Chartsalsohaveanamethatidentifiesthespecificgeographicareathattheycover,aswellasthepublisherofthechart.Figure1.8clearlyidentifiesthischart'sgeographiccoverageaswellasNOAAasthepublisher.AllcurrentnauticalchartsintheU.S.comefromNOAAand,insomecases,additionalagencies(particularlytrueinwatersthatborderothercountries).

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Figure1.8.Charttitleandotherinformation(Chart14782).

Chart14782hasascaleof1:40,000,puttingitintheharborchartclass.Theidentificationsectionalsoindicatesthatthechartusesapolyconicprojection,asdomostU.S.chartscoveringtheGreatLakesanditsconnectingwaterways.(MostnauticalchartsontheopenseasemployaMercatorprojection.AppendixBdescribesthedifferencebetweenthetwoprojections.)Figure1.9showsaportionofChart14782thatshowsthelatitudeandlongitudeaxes.Theverticallinesarethemeridians,orlinesoflongitude,onwhichnorth-southpositionismeasured.Theverticallineontherightedgeofthechartshowtheregionbetween44°25'Nto44°30'Nlatitude.Therearetenblackandwhiteboxesbetweenthesetworeferencepoints,soeachrepresentshalfaminute,or30".Thehorizontallinesaretheparallels,orlinesoflatitude,onwhicheast-westpositionismeasured.Thehorizontallineonthebottomedgeofthechartshowstheregionbetween073°10'Wand073°15'Wlongitude.Again,eachalternatingblackandwhitelineis30".Notethatthelongitudescale(horizontal)appearstobegeographicallyshorterthanthelatitudescale(vertical).Thisisbecauseonedegreeoflatituderepresentsthesamelineardistanceregardlessofyourpositionontheglobe,whereasadegreeoflongitudegetslinearlysmalleras

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thelinesapproachthepoles(wherethelinescometogether).11OnlyattheEquatorisadegreeoflatitudeandadegreeoflongitudeequaltothesamelineardistance.(AppendixCdescribesthisissueinmoredetail.)

Figure1.9.LatitudeandlongitudescalesonChart14782.

11Thefactthatonedegreeoflongituderepresentsadifferentlineardistancedependingonlatitudewasasignificantproblemformarinerspriortothedevelopmentofaccurateclocksinthe1700s.ForanexcellentdescriptionoftheLongitudeActof1714andthedevelopmentofprecisenauticalclocks,seeLongitude(Sobel,1995).

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Onedegreeoflatitude(andonedegreeoflongitudeattheEquator)represents60nauticalmiles.Therefore,aminuterepresentsonenauticalmile,whichequals1.15statute(land)milesor6,076.12feet(1,852meters).Asecondisapproximately101.27feet(30.9meters).

Figure1.10.LegendsfordistanceonChart14782.

Figure1.10showsthelegendonChart14782forthedistancescalesonthechart.Notethatonenauticalmileisthesamelengthasoneminuteonthe(vertical)latitudescaleonthechart;oneminuteonthe(horizontal)longitudescaleislessthananauticalmile.Anauticalmilecanalwaysbedeterminedfromthelatitudeaxisofalmostanynauticalchartandcangenerallyneverbedeterminedfromthelongitudeaxis.(Thiswillcomeupagainintheplottingexercises.)

Figure1.11.SoundinginformationforChart14782.

Numbersoverwateronthechartrepresentthedepthofthewateratvariouspoints.Itisimportanttoknowinwhatunitsthedepthsaremeasuredandthereferencepointfordeterminingthosedepths.AsFigure1.11shows,depthsoundingsonChart14782areinfeet;thisstatementisactuallypresentonthechartinatleastthreeplaces.Theplaneofreferenceis93.0feet,whichisthelowlakelevel.Itmakessensetotakesoundingswhenthewaterisatitslowestbecausethesoundingsthenrepresentthemostconservativemeasurementsofdepth.Themarinerisstillresponsibletoknowwhattheactuallakelevelgivenlocalconditionsinordertoensurethatthesoundingsstillpaintanaccuratepictureatanygivendayandtime.12Manycharts(includingthisone)provideaconversiontablebetweenfeet,fathoms,andmeters.Afathomis6feet. 12Tidetables,whicharenotdiscussedinthistutorial,assistthemarinerinknowinghowthewaterdepthfluctuatesonadailybasis,whichcanaidinplanning.TheNOAATides&CurrentsWebpagecanbefoundathttp://tidesandcurrents.noaa.gov/.

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1.4.2.TheCompassRoseOneofthemostprominentfeaturesoneverynauticalchartisthecompassrose(Figure1.12).Thecompassroseprovidesthereferencefordeterminingthedirectionofthevessel.Northonthecompassroseisat0°,eastis90°,southis180°,andwestis270°.Thecompassroseisgenerallydepictedastworings.Theouterringrepresentstrue,orgeographic,north.Theinnerringrepresentsmagneticnorth,theheadingthatisgenerallyshownonthecompassofmostrecreationalboats(sincetheyaregenerallymadeofwood,fiberglass,orsomeothernon-magneticmaterial).

Figure1.12.Compassrose.13

Detailsaboutthemagneticcompassandvariationwillbediscussedinthesectionsonplottinganddeterminingnorthonthechartandcompass.SectionBofChartNo.1describesthecompassrosetothelevelnecessaryfortherecreationalmariner.1.4.3.LandmarksChartsareprimarilyarepresentationoffeaturesofwaterwaysbutadescriptionofmajorlandmarksisprovidedtoassistinnavigationanddeterminingone'slocation.Figure1.13showsthecityofBurlingtonfromChart14782.Thedetailhereshowsafewofthemajorroadsandthelocationofanumberofspiresindowntown;notethepresenceoftopographiclinesofelevationrepresentingthehillonwhichBurlingtonisbuilt.ThenoteindicatesthatevenmoredetailcanbefoundusingChart14785. 13http://en.wikipedia.org/wiki/File:Modern_nautical_compass_rose.svg

15

Figure1.13.LandmarksinthecityofBurlington(Chart14782).

Thechartalsoshowsatankandradiomasttotheeastofdowntown(onthetopofthehill).Thetankhastwoverticalocculting14redlightsonit,whiletheradiomasthasanoccultingredlightandtwofixedredlightsinaverticalconfiguration.TheCoastPilot(Volume6)containsadditionalinformationaboutBurlington(referencingCharts14782and14785):

(48) Burlington, VT, just N of the entrance to Shelburne Bay, is the largest port on Lake Champlain. Several companies have dock facilities for receipt of petroleum products by barge. The Radisson Hotel, with a red lighted sign, is the most prominent object in the harbor approach. (49) Burlington Breakwater North Light (44°28'50"N., 73°13'47"W.), 35 feet above the water, is shown from a white square lighthouse on the N end of the N breakwater.

1.4.4.MarginalNotesAdditionalinformationonthechartsappearsintheformofmarginalnotes,whichareprintedinpurple.ThereferencetoChart14785inFigure1.13,forexample,issuchanote.TothewestofdowntownBurlingtonisaspecialanchorageareawithastatementto"(seenoteA)."NoteAcanbefoundlookingelsewhereonthechart(Figure1.14).

14Anoccultinglightisonewherethelightisonforanoticeablylongertimethanitisoffduringtheperiodofthelightcycle.

16

Figure1.14.NOTEAfromChart14782.

1.4.5.AidstoNavigation,andCoastalandUnderwaterFeaturesTheprimarypurposeofnauticalcharts--andtheprimaryreasonthatrecreationalboatersrefertothem--istolearnaboutthecharacteristicsofthewaterratherthantheland.Theprimarycharacteristicsaretheaidstonavigation,aswellascoastalandunderwaterfeatures.Theexamplesbelowaremeanttointroducesomeofthedetailsandsymbolsonachartthatmighthavebeenoverlookedbyarecreationalmariner;ifyouarenotlookingforadivesite,asanexample,youmightnotcaremuchaboutwrecks.Whilenavigationalmarkersareshownanddescribed,thisisnotatutorialaboutthelateralsystem.ChartNo.1andtheLightListscoverthistopicquitewell.ThefirstchartsnippetshowstheAppletreeBayportionofChart14782(Figure1.15).Allofthefollowinginformationcanbefoundonthischart:

• Allofthenumbersthathavenoothercontextualmeaningaredepthsoundings.Thelegendonthischartindicatesthatsoundingsareinfeet.Notethatthewaterwithdepthsat6feet(1fathom)orlessareshadedindarkblue;depthsbetween7-12feet(2fathoms)areshadedinlightblue.

• Theupperleftofthechartareashowsabuoy(thegreendiamondatanangletoasmallwhitecircle)tothesouthwestofashoal.ThecolorandtheletterGindicatethisasagreenbuoy.TheletterCindicatesthatthisisa"can,"referringtothebuoy'ssquareshape.The"39"indicatesthenumbermarkedonthisbuoy.15Thewhitecircleatthebottomofthediamondrepresentsthe(intended)actualpositionofthebuoyandthatthisbuoyisnotlighted.

• JusttotheeastofAppletreePoint--andjustsouthofanothershoal--isanotherunlightedgreencanbuoy,thisonemarkedwitha"1".

• ThereisathirdbuoyjustsouthofAppletreeShoal.Theredcoloredcircleindicatesthatitisalightedbuoy(butdoesnotindicatethecolorofthelight).The"greenoverred"

15Inthelateralnavigationsystem,greenbuoysaregenerallycan-shapedandhaveanoddnumber,redbuoysarenun-shapedandhaveanevennumber,andpreferredchannelmarkersmayhavelettersbutwillneverhaveanumber.Forareferencetothenavigationbuoys,seeU.S.CoastGuard(2011).

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colorofthebuoyindicatestwothings;first,thisisapreferredchannelmarker(withthetophalfbeinggreenandthebottomhalfbeingred)andsecond,thelightisgreen.ThelettersGRareadditionalindicatorsthatthisagreen-over-redcoloredbuoy,markedwiththeletters"AS".Thelightisagreenlightthatflashestwice,rests,thenflashesonce,andrests,allinasix-secondcycle;thisisindicatedonthechartbythelettersFl(2+1)G6s.

Figure1.15.AppletreeBay,fromChart14782.

• Twopotablewaterintakes(PWI)canbefoundsouthofLoneRockPoint.Bothterminate

incribsthatareinabout43feetofwater(perthewordingonthechart).Apipeline(possiblydisused)leadstoeachofthecribs.

• Awreckcanbefoundtotheeastofthetwocribsandbetweenthetwopipes.Becausethepositionofthewreckisnotknownexactly,itismarkedPA(positionapproximate).16

• Thereddashedlinerepresentstherouteofaferry.17 16ThewreckindicatediscalledtheHorseFerry,theonlyknownwreckofahorse-poweredvesselinNorthAmerica.17ThisferryrunsbetweenBurlingtonandPortKent,NewYork.

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AlloftheinformationfoundherecanbeinterpretedusingtheinformationinChartNo.1.Forthischartfragment,thefollowingsectionsofChartNo.1areparticularlyhelpful:

• SectionB:Positions,Distances,Directions,Compass• SectionK:Rocks,Wrecks,Obstructions• SectionL:OffshoreInstallations• SectionQ:Buoys,Beacons

AdditionalinformationaboutmarkersinAppletreeBaycanalsobefoundintheLightListfortheregion.18Theentriesforbuoys"1"and"AS"areshownbelow,andincludethelatitudeandlongitude.19Inaddition,theentryforthe"AS"buoynotesthatitcanbeseenuptoanominaldistanceof3nauticalmilesandthatitisaseasonalmarker,replacedbyacanfromNovember1toMay1.

Figure1.16.ColchesterReefandColchesterShoal,fromChart14782.

Figure1.16showsanotherexamplefromChart14782inordertodemonstrateafewmorechartsymbols.Theinformationthatisrecordedhereincludes:

18LakeChamplaininformationisinVolumeI:AtlanticCoast(St.CroixRiver,MainetoShrewsburyRiver,NewJersey).19Notethatlatitudeandlongitudeareexpressedtothethousandthofasecond,whichisroughly1.2inches(3cm).

19

• ThereisawhitelightatthenorthendofColchesterReef(theabsenceofanyothercolorcodeindicatesthatthelightiswhite).Thelightflashesonceever4seconds,stands51feethigh,andhasanominalvisibilityof7statutemiles(Fl4s51ft7StM).

• TheseabedaroundColchesterReefandColchesterShoalisrocky("rky").• Justsouthofthereef(positionapproximate)isawreck,markedbyayellowbuoy,

denoted"E."20Thisbuoyisprivatelymaintained.• ThereisagreenbuoyatthenorthendofColchesterShoal,withthenumber"35".Thisis

alightedbuoy,withagreenlightthatflashesevery2.5seconds(FlG2.5s).• Thereisagreencanbuoymarkedwiththenumber"37"atthesouthendoftheshoal.

TheLightListprovidesinformationaboutthesefourmarkers,asshownbelow.Asbefore,theentriesshowthelatitudeandlongitude;sincethewreckisdenotedwithaPAandthetwobuoysarenotfixed,themostreliablepositionofthefouristhelightonthereef.TheColchesterReefLightentrystatesexplicitlythatitisawhitelightandstands51feethigh;thenominalvisibilityinthelightlistisgiveninnauticalmilesratherthanstatutemiles,whichiswhythatentryshowsa6whereasthechartshowsa7.TheentriesforthebuoysonColchesterShoalindicatethattheyareonlyseasonallymaintained.Finally,theLightListshowsthattheyellowbuoy"E"isayellowsphericalmarkermaintainedbytheLakeChamplainUnderwaterPreserve.

:

:

:

Figure1.17showsaportionofChart14785(BurlingtonHarbor).Theinformationshownhereincludes:

• Thelightjusttothenorthofthebreakwater--naturallycalledNorthBreakwaterLight--flashesredevery2.5seconds;standingat35feet,thenominalvisibilityofthelightis14statutemiles(FlR2.5s35ft14StM).

• Justsouthofthelight,attheopeninginthebreakwater,isawhitedaybeacon(WBn).• Apipe(blackdashedline)extendspastthenorthendofthebreakwater,running

roughlyeast-west.Thereisalsoasubmarinecable(redsquigglyline)inthatarea,leadingtothelight.

• Therouteoftheferry(reddashedline)isjusttothenorthofthelight.

20ThiswreckiscalledthePhoenix.

20

Figure1.17.Burlingtonharborbreakwater,fromChart14785(BurlingtonHarbor).

Figure1.18.DeerIslandandPresidentRoadssectionofChart13267(MassachusettsBay).

AfinalexampleshowstheDeerIslandandPresidentRoadsportionofMassachusettsBay(Figure1.18).ThefirstitemofparticularinterestisthelighttothesouthofDeerIsland.Thecodesunderthe"DEERISLAND"labelonthechartmean:

• Thisisanalternatingwhite/redlightwitha10srotationperiod.Thelightstands53feethighandcanbeseenfromanominaldistanceof11(nautical)miles.

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• Thelighthasahorn.• Thereisafixedredlightataheightof15feetthatcanbeseenfromadistanceof6

(nautical)miles.Thelabel"LTOBSC"canbeseennorthofthelight(infact,northofthetank).Thisreferstoaregionwheretheviewofthelightisobstructed.Inaddition,thelabel"REDSEC"appearsroughlynortheastofthelight,referringtothesectorwhereavesselatseacanseetheredlight.ThechartprovidesalotofinformationbutthisisanexamplewheretheLightListprovidessomuchmore.TheVolumeILightListhasthisentryforDeerIsland:

TheLightListprovidestheexactlocationofboththeprimarylightandthereddangerlight,andindicatesthatthehornsoundsaone-secondblastevery10seconds.Theentryalsoindicatesthatthelightisobscuredintherangeof112°to186°;thesebearingsaretruecompassheadingsfromtheperspectiveofthevessel.Inaddition,thereddangerlightcanbeseenfromavesselatseafromthetrueheadingsbetween198°to222°.TheotherfeaturesofinterestonthechartaretheshippingchannelstotheeastofPresidentRoads.RememberthatinthelateralnavigationsystemusedintheU.S.,redbuoysarekepttotheportside(left)ofthevesselwhengoingouttoseaandthegreenbuoyskepttothestarboard(right)side.ThechannelstartsbetweentheDeerIslandlightandthegreenbuoy("15")tothesoutheastoftheDeerIslandlight.Thisbuoyhasabellandhasaquicklyflashinggreenlight(QG).Continuingnortheasttowardsthechannelisalightedgreen-over-redbuoy("PR"),whichisapreferredchannelmarker.Sincethetopbandisgreen,thisbuoyindicatesthatvesselsshouldgenerallyproceedtowardtheBostonNorthChannel(i.e.,keepingthisbuoytothevessel'sstarboardside).Thisbuoyflashesagreenlighttwice,andthenflashesonce,inasix-secondcycle(Fl(2+1)G6s).Thenorth(left,asyougoouttosea)sideoftheBostonNorthChannelismarkedbyfiveredbuoyswiththefollowingcharacteristics:

• "10"--Alightedbuoywithabellandaquickflashingredlight.• "8"--Alightedbuoywitharedlightthatflasheseverysixseconds.• "6"--Alightedbuoywithabellandwitharedlightthatflasheseveryfourseconds.• "4"--Alightedbuoywitharedlightthatflashesevery2.5seconds.

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• "2"--Alightedbuoywithabellandaquickflashingredlight.Thesouth("right")sideoftheBostonNorthChannelismarkedbyfourgreenbuoyswiththefollowingcharacteristics:

• "9"--Alightedbuoywithagreenlightthatflasheseverysixseconds.• "7"--Alightedbuoywithagreenlightthatflasheseveryfourseconds.• "5"--Alightedbuoywithagreenlightthatflashesevery2.5seconds.• "3"--Alightedbuoywithaquickflashinggreenlight.

Avesselmightchoosetotakethesouthchannel.Thenorth("left")sideofthesouthchannelismarkedwithtworedbuoys:

• "10"--Alightedbuoywithaquickflashingredlight.• "6"--Alightedbuoywitharedlightthatflasheseveryfourseconds.

Thesouth("right")sideofthesouthchannelismarkedwithsixgreenbuoys:

• "13"--Acanbuoy.• "11"--Acanbuoy.• "9"--Alightedbuoywithaquickflashinggreenlight.• "7"--Acanbuoy.• "5"--Alightedbuoywithagreenlightthatflasheseveryfourseconds.• "3"--Acanbuoy.

1.5.AidsToAndRulesOfNavigationAlthoughwellbeyondthescopeofthispaper,thenextstepaftergraspingthemarkingsonthenavigationalchartsistoturnthatunderstandingintoactiononthewater.Findingthebuoysonthechartsinonethings;doingtherightthingonthewaterisanother.ThemarkingsystemofnavigationaidsisdefinedbytheInternationalAssociationofMarineAidstoNavigationandLighthouseAuthorities(IALA)21.Thesystemisverywelllaidoutandisquitelogicaltothosewhounderstandit;itisjustabunchofcoloredfloatingthingsonthewatertothosewhodonot.Whilethesystemitselfisveryconsistent,itcanappearconfusingtothosewhodonotknowwhycertaincolorsareusedincertainplaces.OneofthebestreferencestothebuoysystemintheUnitedStatesistheU.S.CoastGuard'sU.S.AidstoNavigationSystem22(Figure1.19).Thissectionincludessomebriefcommentsabouttheaidstonavigationprimarilyasaveryhigh-levelintroductionandtosuggestwhyadditionaltrainingandexperienceisrequired. 21http://www.iala-aism.org/22http://www.uscgboating.org/images/486.PDF

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Figure1.19.U.S.AidstoNavigation(USCG,2011).

MostboatersintheU.S.arefamiliarwiththemnemonicdeviceredrightreturningasaremindertokeeptheredbuoystotherightoftheboatwhenreturningfromsea.Asgoodamechanismasthisis,itisnothelpfulonmanyinlandwaterways.Furthermore,theruleisonlycorrectintheIALA"B"systemusedinthewesternhemisphereandafewcountriesinAsia;therestoftheworldusestheIALA"A"systemwhichusestheoppositecolorings.23IntheU.S.(andIALA"B"system),therulesforthecolorofchannelmarkerbuoysare,ingeneral,asfollows:

• Redisontherightwhenreturningfromsea.

• Redisintherightwhengoingfromalargertosmallerbodyofwater(e.g.,fromalakeintoabayorfromamainchannelintoasmallerchannel).

ThethirdruleisthatontheIntracoastalWaterway(ICW)andinlandrivers(e.g.,MississippiRiver),redisonyourrightasyoutraversearoundthecountryinaclockwisedirection.Onemnemonicforthisruleisthatredistowardstheinteriorandgreenistowardstheopenwater(AtlanticOceanorGulfofMexico).

Figure1.20.Green(can)andred(nun)buoys.[Photosbytheauthor.]

23TheIALA"A"systemmnemonicistomatchcolorswhenreturningfromsea;i.e.,greenbuoyontherighttomatchtheboat'sgreenlightandredbuoyonthelefttomatchtheboat'sredlight.

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Themostcommonaidstonavigationareredandgreenmarkerbuoys(Figure1.20).Thereareseveraldifferentstylesofbuoysbutthemostcommononesaregreencanbuoysandrednunbuoys.Asshownonthecharts,thegreenbuoysareassignedanoddnumberandredbuoysanevennumber.

Figure1.21.Redtriangularandgreensquaredaymarkers.(Notetheyellowsquareon#39A,

indicatingthatthismarkerisintheICW.)[Photosbytheauthor.]Daymarkersareredtriangleswithanevennumberandgreensquareswithanoddnumber(Figure1.21).OntheICW,daymarkershaveayellowtriangleorsquare.Ingeneral,ayellowtriangleisonaredmarkerandayellowsquareonagreenmarker.24Therearemanysubtletiesandnuancesrelatedtoproperlyinterpretingtheaidstonavigationandmarinersarewelladvisedtostudythechartsintheirboatingareaand,wherepossible,learnthelocalwatersfromlocalboaters.Someexamplesofthemixedrulesinunderstandingthebuoyscanbefoundinthefollowingcharts.Figure1.22showsaportionofChart11485(IntracoastalWaterwayTolmatoRivertoPalmShores),whichshowsPoncedeLeonInlet,southofDaytonaBeach,Florida.ThefollowingexampleisforaboatenteringtheinletandheadingnorthtoadockinDaytonaBeach.Asthechartshows,onewouldenterthechannelbetweenredbuoy#2andgreenbuoy#3,shownatthelowerrightofthefigure;thisisasexpectedwithredbuoystotheright(andgreenbuoystotheleft)whenreturningfromsea.Theentrycontinuesbetweenredbuoy#4andgreenbuoy#5.Withthejettyontheright,thesafepassageistotherightofgreenbuoy#5A,betweengreenbuoy#7andredbuoy#8,andthenbetweengreenbuoy#7Aandredbuoy#8A.

24TherearetimeswhentheICWcrossesawaterwaymarkedaccordingtotheIALAlateralsystem.AlthoughthedaymarkersontheICWaregenerallyredwithayellowtriangleandgreenwithayellowsquare,onemightseeayellowtriangleonagreencanbuoyorayellowsquareonarednunbuoywhentheICWcrossesalateralsystem-markedchannel.Inthosecases,theshapeoftheyellowsymbolprevailsastheICWchannelmarkerregardlessofthecolorofthebuoy(i.e.,theyellowtrianglesmarkthemainlandsideoftheICWevenifonagreenbuoy).

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TogoontoDaytona,followthecharttothenorth,whichmeansarightturnkeepingredbuoy#8Btotheleft.Atthispoint,thecolorrulesfollowtheICWconventions.Inthiscase,thesafechannelcontinuestothenorthwhereredbuoys#4,#2B,and#2Aareontheleft(i.e.,towardsthemainland)andgreenbuoy#1isontheright.ThetrueICWisjoinedatthejunctionneargreenbuoy#3.

Figure1.22.AreaaroundPoncedeLeonInletfromChart11485

(IntracoastalWaterwayTolmatoRivertoPalmShores).OnceontheICW,markersareasexpectedwhentravelingnorthontheeastcoastoftheU.S.;namely,redmarkersaretotheleft(towardsthemainland)andgreenmarkersaretotheright.NowconsiderwhathappenswhenapproachingthedockattheDaytonaBeachMunicipalYachtBasin(Figure1.23).TheICWchannelisfoundwithgreenmarker#39Aofftotheright,thenbetweenredmarker#38andgreenmarker#39.JustsouthoftheMemorialBasculeBridge(intheupperrightofthechart)istheentrychanneltothecitydock.Noteherethattheredmarker

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#2istotherightandgreenmarker#1istotheleft(consistentwiththecolorruleswhengoingfromalargerbodyofwatertoasmallone).Thesafechannelherecontinuesbetweenredmarker#4andgreenmarker#3,andthenredmarker#6andgreenmarker#5.

Figure1.23.DaytonaBeachMunicipalYachtBasininsetfromChart11485.

Thediscussionaboveglossesoverthedetailsofthemarkersystemanddoesnotbegintodescribeothermarkerbuoytypes;thissectionismeantonlytodescribewhyadditionaleducationalresourcesareessentialforproperlyinterpretingtheaidstonavigationandsafelynavigatingthewaters.Butevenunderstandingtheaidstonavigationisnotsufficient;boatersneedtounderstandtherulesoftheroad,includingsafepassingmaneuvers,howtohandlecrossingsituations,whichvesselshavepriorityoverothervessels,lightingandsoundrequirements,andmuchmore.Themariner'srulesoftheroadarecontainedinadocumentcalledtheNavigationRulesandRegulationsHandbook25(Figure1.24).Knownasthecollisionregulations(orcolregs),this

25http://www.navcen.uscg.gov/pdf/navRules/Handbook/CG_NAV_RULES_20140910.pdf

27

documentdescribestheprotocolforvesselsininlandandinternationalwaters.Allmarinersshouldbefamiliarwiththebasicsofthecolregs.

Figure1.24.NavigationRulesandRegulationsHandbook(USCG,2014).

1.6.SummaryTherearemanyreasonsthattherecreationalmarinershouldhaveathoroughunderstandingofnauticalcharts.Theprimaryreason,obviously,issafety.Thechartsprovidenecessaryinformationthatcanhelpyouavoidhazards,particularlywhengoingintounfamiliarwaters.Butknowledgeofchartscanalsoaddanelementofenjoymentbyhavingagreaterunderstandingoffamiliar,andevenunfamiliar,waters.Thissectionprovidesaverybasic,rudimentaryoverviewofissuesrelatedtoobtainingandreadingcharts,andaccessingsupplementaryresourceswithwhichtobetterunderstandthem.Thefocusherehasbeenonpapercharts.Indeed,anincreasingnumberofrecreationalboatersemploymarineGPSunits.TherearemanyissuesrelatedtokeepingtheGPSunitup-to-date,andmanagingthedifferencesbetweentheelectronicandpapercharts.Readersareurgedtocontinuereadingotherresources,suchasHowtoReadaNauticalChart(Calder,2012),toobtainmoredetailedinformation.

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Part2:PlottingThissectionpresentsbasicinformationaboutthetoolsusedforchartingandsomeofthebasicarithmeticneededinordertosolvesimplenavigationproblem.Thesectionwillalsoreviewtherelationshipbetweengeographicnorth,magneticnorth,andthecompassonyourvessel.Severalsimplenavigationandchartingproblemswillalsobeintroducedwithmethodsinwhichtosolvethem.2.1.WhichWayisNorth?Nauticalchartsarealwaysorientedsothattrue(geographic)northistowardsthetopofthechartandverticallinesruntruenorth-south.Compasses,however,pointtowardsmagneticnorth--andthedifferencebetweentrueandmagneticnorthisdifferentatdifferentpartsoftheglobe.Issueswiththecompassareexacerbatedbytheaffectofnearbymetalonthecompass.Thissectionwilldescribetherelationshipbetweenthedifferentperspectivesofnorthandhowtheyrelatetoeachother.Understandingtheserelationshipsisessentialtobeingabletosolvenavigationalproblemsandthenactuallyturningthesolutionsintoactionableplansforyourvessel.2.1.1.TheCompassRose,RevisitedFigure2.1showsthecompassrose,acommonpresenceoneverynauticalchart.AsdescribedinPart1ofthismanual,thecompassrosehastwoconcentricrings,wheretheouterringrepresentsheadingsrelativetotruenorthandtheinnerringrepresentsheadingsrelativetomagneticnorth.Ontheouterring,000°pointstotrue,orgeographic,northandalwayspointstowardsthetopofthechart.Onthisring,090°istrueeast,180°istruesouth,and270°istruewest.Ithaslongbeenknowntogeologistsandgeographersthatthemagneticnorthpoleisnotinthesameplaceasthegeographicnorthpole.Thedifferencebetweentrueandmagneticnorth--calledthevariation--willdependuponwhereyouarelocatedontheglobe.Theproblemisexacerbatedbythefactthatthemagneticnorthpoleisactuallyconstantlymoving,aphenomenonisknownasthewanderingmagneticpole.26Thus,thevariationbetweenmagneticandtruenorthatanygivenspotischangingeveryyear.Thecenterofthecompassroseinthefigureindicatesthatwhenthisrosewasdrawn(1985),thevariationbetweentrueandmagneticnorthwas4°15'W.Lookcloselytoseethat,indeed,magneticnorth(i.e.,0°ontheinnerring)correspondstoapproximately356°ontheouterring. 26SeeNOAA(2011)foranexcellentexplanationandmapsofthewanderingmagneticnorthpole.

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Thelabelinthecenterofthecompassrosesaysthatthevariationdeceasesannuallyby8'(i.e.,8'E).Thisisimportantinformationbecausethecompassroseonmostchartsthatrecreationalboatersusemightbefive,ten,ormoreyearsinage.Twenty-nineyearselapsedbetweenwhenthisparticularcompassrosewasdrawnandthecurrentversionofthismanual.Thevariation,therefore,hasdecreasedby3°52',meaningthatthevariationin2014isonly23'W,welllessthanhalfadegree.

Figure2.1.Compassrose.27

2.1.2.DeviationThecompassroseindicateshowthecompasspointingtomagneticnorthrelatestotrue,geographicnorth.Metalnearacompass,however,affectsthecompassreading.Mostrecreationalboatershavevesselsthataremadeofwood,fiberglass,and/orothernon-magneticmaterials,thustheconstructionofthevesselhasminimalaffectonthecompass.Shipsthataremadeofmetal,however,mayhaveasignificantadditionalimpactonthecompassreading.Thisadditionalaffectiscalledthedeviation.

27http://en.wikipedia.org/wiki/File:Modern_nautical_compass_rose.svg

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Thedeviationhasaconstantaffectontheship'scompass(i.e.,itdoesn'tchangebaseduponlocationontheglobe)andcanbemeasured.Thedeviationwillgenerallybeofadifferentmagnitudeindifferentheadings,sothemeasurementswillbestatedonadeviationtablethatisneartheship'scompass.Anexampledeviationtableisshownbelow:

Heading Deviation Heading Deviation Heading Deviation0° 1°E 120° 1°E 240° 2.5°W 30° 1.5°E 150° 0° 270° 2°W 60° 2°E 180° 1°W 300° 0° 90° 3°E 210° 2°W 330° 0.5°E

Inpractice,deviationappliesonlytoaship'scompass.Noadditionalcorrectionisappliedtoahandheldcompassbecauseitisimpractical,ifnotimpossible,tomeasureitsdeviation.Forahandheldcompass,adeviationof0°isused.2.1.3.PuttingitallTogetherWhenacourseislaidout,theheadingisdeterminedfromthechartrelativetotruenorth.Accountingforvariationanddeviationisnecessarytodeterminetheproperheadingontheship'scompass,whichisreferredtoasthecoursepersteeringcompass.Simplystated,thecoursepersteeringcompassisthesumofthetrueheading,variation,anddeviation.Variationordeviationvaluesthataretothewestareadded,whilevaluestotheeastaresubtracted.So,forexample,ifthetrueheadingis032°,thevariation3.5°W,andthedeviation1.5°E,then: CoursePerSteeringCompass=32+3.5-1.5=34°Thereareanumberofcommonacronymsthatareusedtoteachthisrelationship.Themostpoliteacronymappearstobe: Tele TRUE Vision Variation Makes MAGNETIC Dull Deviation Children COURSE addWonder addWest(subtracteast)Applyingtheexamplefromabove,then,yields:

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Tele TRUE 32° Vision Variation +3.5°W Makes MAGNETIC 35.5° Dull Deviation -1.5°E Children COURSE 34°Moving(downward)fromtruetocompasscourseheading--i.e.,havingdeterminedtheheadingfromthechartandconvertingtoaheadingtouseontheship'scompass--iscalleduncorrectingthecompass.Converting(upward)fromasteeringcompassheadingtoatrueheadingiscalledcorrectingthecompass.ThereareseveralWebsitesthatexplainthisinmuchmoredetailandgivesampleproblems.282.2.InstrumentsforPlottingAnincreasingnumberofmarinerstodayrelyonautomatedtoolssuchasGPSfornavigationandgettingfromonepointtoanother.Indeed,agoodmarineGPSwillnotonlyreplicateachart'sdetails,butcanaidindeterminingcourse,distance,elapsedtime,andposition.Nevertheless,auserofanyformoftechnologyshouldknowsomethingaboutwhat'shappening"underthehood."Inthatspirit,thissectionintroducessomeofthehandtoolsusedtomanuallyperformroutinenavigationaltasksusinganauticalchart.2.2.1.ParallelRuleandRollerPlotterOneofthetoolsmostcommonlyassociatedwithnavigationistheparallelruler(Figure2.2).29Aparallelrulerismostcommonlyusedtodeterminetheheadingonthecompassrosefromalineofdirectionfromachart(orviceversa).The"arms"connectingtheupperandlowerpartoftherulerallowittobemovedacrossthechartwithoutchangingitsorientation;thisiscalled"walking"theruler.

Figure2.2.Parallelruler.

28Onesuchsiteishttp://captnmike.com/2011/11/13/tvmdc-%E2%80%93-practice-%E2%80%93-correcting-and-un-correcting-the-compass/.29InstrumentsshownherearefromWeems&Plath.Picturesareforexamplepurposesonlyandshouldnotbeinterpretedasarecommendationorproductendorsement.

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Useofaparallelrulercanbemasteredwithalittlebitofpractice.ThereareanumberoftutorialsontheInternetthatmightinterestthereaderincluding"HowtoUseParallelRulers"(http://www.boatsafe.com/navigation/rules1.htm)and"HowtoUseaParallelRulerandCompassRosetoDetermineDirection"(http://www.youtube.com/watch?v=xKSBYfscA80).Theparallelrulercanalsobeusedasastraightedgewhenconnectingtwopointsonachart.Someparallelrulers(suchastheoneinthefigure)haveadditionalprotractormarkingsaroundtheedgesallowingthecourseheadingtobedeterminedbymovingtheruletoanylineofmedian(longitude)onthechartratherthanonlythecompassrose.

Figure2.3.Parallel,orroll,plotter.

Aparallel,orroll,plotter(Figure2.3)isanalternativetoaparallelruler.Aparallelplotterhasarollerthatallowsthedevicetobemovedacrossachartwithoutchangingitsorientation.Mostrollplottershaveprotractormarkings,allowingtheheadingtobedeterminedwithouthavingtomovetoacompassrose.Theplottercanalsobeusedasaregularstraightedge.

Figure2.4.Protractortriangle.

Anothercommontoolistheprotractortriangle(Figure2.4).Inadditiontobeingastraightedge,itcanalsohelpfindtheheadingwhenusedinconjunctionwithaparallelrulerorrollplotter.

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2.2.2.DividersandCompassThesecondtoolmostcommonlyassociatedwithplottingandnavigationisapairofdividers(Figure2.5).Dividersareusedtomarkthedistancebetweentwopointsonthechartortomarkpointsonthechartatwhichtoplacearuler,parallelruler,orrollplotter.

Figure2.5.Dividers.

Notethatthedividershavetwopointsattheend.Replacingonepointwithapencilorleadmarkerturnsthisintoacompass.Althoughnotdiscussedfurtherhere,acompasscanbeusedinchartingtomarkacircle(e.g.,aswingcirclewhendeterminingtheareaforananchorage)oranarc(e.g.,whenestimatingpossiblepositions).2.3.ArithmeticforPlottingThereareanumberofbasicarithmeticskillsthatareessentialtobeingabletosolvesimplechartingproblems.Thissectionwillbrieflyreviewhowtomeasuredistancewithdividers,howtomaketimecalculations,andtherelationshipbetweentime,distance,andspeed.2.3.1.MeasuringDistanceDistancescanbedeterminedusingdividersoraruler,althoughtheformerismorecommonlyemployedbecauseitcanbeusedwithmoreprecision.Themostcommonwaytodetermineadistanceistosetthedividerstothelengthofthelineconnectingtwopoints.Thedividersarethenplacedagainstascaleonthecharttofindtheactualgeographicdistance.Inmostcases,plottingproblemsrequiredeterminingdistancesinnauticalmiles.Rememberthataminuteoflatitudeisequaltoonenauticalmile.Thus,thedistanceofalineonachartcanbedeterminedbyholdingthedividersuptothelatitude(vertical)scaleonthesideofachart.Neverusethelongitude(horizontal)scaletodeterminethedistancebetweentwopoints.Asanexample,supposewewanttomeasurethedistancebetweentwopointsonachart(inthisexample,betweentwobuoys).First,setthedividerstothetwopointsoverwhichtomeasurethedistance(Figure2.6).Next,placethedividersagainstthelatitudescaleonthecharttofindthedistance,whichisapproximately3.8nauticalmiles(Figure2.7).

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Figure2.6.Placingthedividersontwopoints.

Figure2.7.Placingthedividersonthelatitudescale.

Ifthelineconnectingthetwopointsislargerthanthespanofthedividers,setthedividerstoaspanrepresentingaknowndistance,andthencountthenumberofincrementsofyourcompassspaninordertocoverthelengthoftheline.Atutorialcalled"Howtousedividers"(http://www.boatsafe.com/navigation/divide1.htm)alsoshowsthisprocedure.

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2.3.2.ManipulatingTimeValuesForpurposesofplottingandnavigation,timesshouldbeexpressedusinga24-hourformat,where:

• Midnightisexpressedas0000• 12:01-11:59a.m.isexpressedas0001-1159• Noonisexpressedas1200• 12:01-11:59p.m.isexpressedas1201-2359

Expressingtimeina24-hourclockgreatlysimplifiestimecalculationsthatareoftennecessaryinordertodeterminethenumberofhoursandminutesbetweentwoevents.Forexample,todeterminetheelapsedtimebetween1113(11:13a.m.)and1345(1:45p.m.),merelysubtracttheearliertimefromthelatertimetofindtheanswer(2hours,32minutes): 1345 -1113 --------- 2:32Iftheminutesvalueoftheendingtimeislargerthantheminutesvalueofthestartingtime,weneedto"borrow"additionalminutes;adding60totheendingminutesandsubtractingonehouraccomplishesthis.Forexample,todeterminetheelapsedtimebetween1822(6:22p.m.)and2010(8:10p.m.),usethefollowingstepstofindtheanswer(1hour,48minutes): -1 +60 19 70 2010à 2010à 2010 -1822 -1822 -1822 --------- --------- ---------- 1:48Ifthestartingandendtimescrossoveradayboundary(i.e.,thestarttimeisbeforemidnightandtheendingtimeisaftermidnight),merelyadd24hourstotheendingtime,forpurposesofthecalculation.Forexample,todeterminetheelapsedtimebetween2215(10:15p.m.)and0137(1:37a.m.),usethefollowingstepstofindtheanswer(3hours,22minutes): +24 25 0137à 0137à 0137 -2215 -2215 -2215 --------- --------- ---------- 3:22

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Finally,itisoftennecessarytoconvertthetimetominutes.Todothis,multiplythehoursby60andaddtheminutes,asshownbelow:

• 2hours,32minutes=2×60+32=152minutes• 1hour,48minutes=1×60+48=108minutes• 3hours,22minutes=3×60+22=202minutes

Toconvertminutesbacktohoursandminutes,merelydividetheminutesby60;thewholepartoftheansweristhenumberofhoursandtheremainderisthenumberofminutes.Thus,

• 108minutes=108min÷60min/hr=1hr,48min• 152minutes=152min÷60min/hr=2hr,32min• 202minutes=202min÷60min/hr=3hr,22min

2.3.3.Distance,Speed,andTimeManychartingproblemsinvolvedistancetraveled,speedmadegood(i.e.,actualspeedofthevessel),andtheelapsedtimetogetfromoneplacetoanother.Theseproblemsaregenerallysetupthatyouknowtwoofthesevariablesandneedtofindthethird.Forpurposesoftheseexercises,thefollowingassumptionsandsymbolswillbeused:

• Distance(D)isgiveninnauticalmiles(nm)• Speed(S)isgiveninnauticalmilesperhour,orknots30(kn31)• Time(T)isgiveninminutes

Thesethreevariablesarerelatedbyaformulathatcanbemanipulateddependinguponwhichtwofactorsareknownandwhichoneisunknown.Acommonlyusedmnemonicforthisformulais"60DStreet,"abbreviated60DST(Figure2.8).Inthefigure,findtheunknownfactor,replacethenearestdivisionoperator(÷)withanequalsign(=),andthencontinuemovinginthatsamedirectionaroundthecircletoapplytheremainingfactorsandarithmeticoperators.Example1:Youhavetraveled18nm(D)in72minutes(T).Whatwasthespeedmadegood? S=60×D÷T=60min/hr×18nm÷72min=15knExample2:Youhavebeenunderwayfor75minutes(T)ataspeedof14knots(S).Howfarhaveyoutraveled?

30Notethatthespeedometeronmanysmallrecreationalboatsusesmilesperhour(MPH)astheunitofmeasurementratherthanknots.IfyouperformthesecalculationsusingMPH,distanceswillbeinstatutemilesratherthannauticalmiles.31Theabbreviationktisalsocommonlyusedforknotsalthoughknistheinternationalstandard.

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D=T×S÷60=75min×14kn÷60min/hr=17.5nmExample3:Youneedtotravel16nm(D)andcanmakeaspeedof12knots(S).Howlongshouldyourtriptake? T=60×D÷S=60min/hr×16nm÷12kn=80min=1hr20min

Figure2.8.60DSTmnemonic.

Anauticalsliderule(Figure2.9)canaidthemarinertoquicklyperformthesecalculations.

Figure2.9.Nauticalsliderule.

2.4.PlottingProblemsTheparagraphsbelowwillintroduceanumberofroutineplottingproblemsandthemethodsbywhichtheycanbesolved.Keepinmindthatwhentryingtosolveanavigationalproblem,youneedtofirstdeterminewhatitisyouaretryingtofindoutandwhatpertinentinformationyoualreadyknoworneedinordertosolvetheproblem.Youcanignoreirrelevantfacts.32 32E.g.,supposeyouknowthedistancetoyourdestination,courseheading,andspeed,andareaskedtodeterminehowlongthetripwilltake.Tosolvefortime,youneedonlyknowdistanceandspeed;headingisirrelevant.

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Chartingtaskscoveredinthissectioninclude:

1. Findinglatitudeandlongitude2. Plottingaposition3. Findingatruebearingandcompasscourse4. Findingdistanceandspeedmadegood5. Estimatingtimeofarrival6. Deadreckoning7. Findingsetanddrift8. Plottingacoursewithknownsetanddrift9. Obtainingafixwithlinesofposition10. Gettingarunningfix11. Doublingtheangleoffthebow

Intheproblemsbelow,paycarefulattentiontothecourseheading,whichmightbeexpressedasdegreestrue(T),magnetic(M),orpersteeringcompass(C).Rememberthatallheadingstakenfromachartaretruewhereasheadingsthatwillbeusedbythevessel'scompassarepersteeringcompass.Fortheexamplesinthissection,maketheassumptionthatitistheyear2002.Accordingtothecompassroseonthechart,thevariationwas4°15'Win1985withanannualdecreaseof8';after17years,thevariationwouldhavedecreasedby2°16'tobeapproximately2°W.Similarly,thefollowingdeviationtablewillbeusedforallexamples:

Heading Deviation Heading Deviation Heading Deviation0° 1°E 120° 1°E 240° 2.5°W 30° 1.5°E 150° 0° 270° 2°W 60° 2°E 180° 1°W 300° 0° 90° 3°E 210° 2°W 330° 0.5°E

Anumberofabbreviationsandnotationalsymbolswillbeusedonthechartsinthissection,andwillbeexplainedasintroduced.AppendixDprovidesaNavigator'sQuickReferenceCard33withasummaryofthenotationandabbreviationsusedhere.Finally,allchartsinthissectionusethesamplechartshowninAppendixE.ThechartinAppendixEiswhollyfictitious.Donotattempttorelatethischarttoanythingintherealword.2.4.1.FindingLatitudeandLongitudeDeterminingthelatitudeandlongitudefromapointonthechartisafundamentalskillandisrelativelystraightforward.Theeasiestwaytodeterminelatitudeistoorienttheparallelruler 33Fromhttp://captnmike.com/2009/10/01/piloting-and-navigators-quick-reference/

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onahorizontallineonthechartandthen"walk"theparallelruleruntilitmeetsthepointofinterestandlinesupwiththechart'shorizontalscale;thelatitudecanbereadfromthescale.Longitudecanbefoundinasimilarwayexceptthatyoulineuptheparallelruleralongaverticallineonthechart.

Figure2.10.Findinglatitudeandlongitude.

Figure2.10showsanexampleofthisprocess.Inordertofindthepositionofgreenbuoy#3onthechart,startbypositioningtheparallelrulerthroughtheverticallineat83°15'andthenwalktherulertorunthroughthebuoy'spositionandtheverticalscale.Next,positiontheparallelrulerthroughthehorizontallineat54°35'Nandwalktherulertorunthroughthebuoyandthehorizontalscale.Thelinesshowthepositionofthebuoytobe54°35.5'N,083°12.8'W.Ifthepositionofinterestisfurtherfromtheedgeofthechartthanthelengthoftheparallelruler,youcanfindthelatitudeandlongitudebyemployingdividers.Lineuptherulerwithanyverticalorhorizontallineonthechart,movetothepositiontomeasure,andusethedividerstoseehowfaryouarefromtheline.Then,usethedividersontheverticalorhorizontalscaletofindthelatitudeorlongitude,respectively.Thevideotitled"MeasuringLatandLongw/Dividers"(http://www.youtube.com/watch?v=K02gFTAz5Mo)alsoshowsanicedemonstrationofthistechnique.Asanaside,notethatthischartdoesnotspecificallyindicatewhetherthelocationisnorthorsouthoftheEquator,oreastorwestofthePrimeMeridian.Youcandeterminethisinformation,however,fromthecontextofthelatitudeandlongitudemarkingsonthechart.Rememberthatchartsarealwaysorientedwithtruenorthtowardsthetop.Whenlookingatthischart,noticethattheminutesontheverticalscaleincreasegoingfrombottomtotop;thismeansthatthischartisinthenorthlatitudes.Similarly,theminutesalongthehorizontalscaleareincreasingfromrighttoleft,meaningthatthechartisinthewesternlongitudes.

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2.4.2.PlottingaPositionPlottingapositionfromlatitudeandlongitudeistheoppositeofdeterminingthosecoordinates.Inthiscase,youaregiventhelatitudeandlongitude,andneedtofindoutwhereyouareonthechart.Thisisaccomplishedmuchlikethestepsabove.

Figure2.11.Plottingposition.

SupposeyouneedtofindLAT54°34.5'NLONG083°21.7'Wonthechart.Useyourparallelrulertomarkalineattheproperlineoflatitudeandanotherattheproperlineoflongitude;theintersectionofthetwolinesisyourposition(Figure2.11).2.4.3.FindingaTrueBearingandCompassCourse34Whenlayingoutacourseonachart,itisimportanttorememberthatallheadingsarerelativetotruenorth.Therearetimeswhenyouneedtoaccountforvariationanddeviation--suchaswhenyouobtainamagneticheadingfromacompassorneedtodeterminewhatcompassheadingtosteeronyourvessel--butplottingroutesonachartarealwaystrue.Findingthetrueheadingrequirestwopoints,aparallelruler(orrollplotter),andthecompassrose.Theprocedureisasfollows:Findthetwopointsonthechart,drawalinebetweenthepoints,aligntheparallelrulertotheline,andwalktheparallelrulertothecompassrose.

34Thissectiondescribeshowtofindthecompasscourseknowinganinitialpointandanintendeddestination;anothertermforthisistheintendedcourse.Ifyouknowthetwopointsandwanttofindthecoursebetweenthem,thisissometimesreferredtoasthecoursemadegood,whichistheactualcourseyoutookbetweenthetwopointsafteraccountingforcompassvarianceanddeviation,wind,tide,current,andotherfactors.Bowditch(2002)recommendsusingthephrasetrackmadegood.

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Asanexample,supposeyouneedtoplotyourcoursefromLAT54°35.5'NLONG083°20.5'Wtoredbuoy#4(Figure2.12):

1. Findthetwopointsanddrawalinebetweenthem;thisiscalledthetrackline.

2. Lineupyourparallelrulerand"walk"ittothecompassrose.

3. Notethatyourlinewillintersectthecompassroseintwoplaces.Toselecttheproperheading,youneedtorecallthatyoustartedacoupleofmileseastofTheFaceandheadedtowardsthebuoy;therefore,youknowthatyouwillbegoingroughlysouthwest,whichmeansthatyouwanttobeinthesouthwestquadrantofthecompassrose.Alternatively,ifyouwereatthecenterofthecompassrose,youwouldbemovingdownandtotheleft.Ineithercase,youshouldseethatthelineintersectstheoutercompassringat211°true.

Figure2.12.Findingatruebearingandcompasscourse.

Toactuallysteerthiscourse,youneedtoconvertthecompassbearingtoacompasscoursetoactuallysteer.Todothis,usetheTVMDC+Wcalculation.Remember,forthismanualthevariationis2°WandthedeviationcomesfromthetableinSection2.4: T TRUE 211° V Variation +2°W M MAGNETIC 213° D Deviation +2°W (Deviationis2°Wfor210°magnetic) C COMPASS 215°

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2.4.4.FindingDistanceandSpeedMadeGoodAsdescribedinSection2.3.1,measuringdistanceisajobforthedividers.Tomeasurethedistancebetweenthetwopointsabove,merelyplacethetwoendsofthedividersonthetwopoints.Then,findaconvenientlocationonthevertical(latitude)scaleandmeasurethedistance.Inthiscase,thetwopointsareapproximately3.3nauticalmilesapart(Figure2.13).

Figure2.13.Findingdistanceandspeedmadegood.

Determiningthespeedmadegoodmeanstocalculateyourspeedoversomedistance.AsshowninSection2.3.3,usethe60DSTformulatocalculatespeedifdistanceandelapsedtimeareknown.Inthisexample,thetripstartedat1017andtheredbuoywasreachedat1031;thus,theelapsedtimeis14minutes.Applyingtheformulatofindspeed,weget: S=60×D÷T=60min/hr×3.1nm÷14min=13.3kn2.4.5.EstimatingTimeofArrivalEstimatingthetimeofarrivalatadestinationisanothertime-speed-distanceproblem.InFigure2.14,weleavethemouthoftheinletsouthofJigsawPointandwouldlikeanestimatedtimeofarrival(ETA)atthesmallbaytothewestofBulgeIsland,assumingthatweplanonmakingaspeedof10kn.

1. Thestarttimeis1452.

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2. Thetracklineonthechartshowsthatthedistanceis5.4nm.Knowingdistanceand

speed,wecansolvefortime: T=60×D÷S=60min/hr×5.4nm÷10kn=32min

3. TheETAis32minutesafterwestarted,or1524.

Figure2.14.Estimatingtimeofarrival.

2.4.6.DeadReckoningDeadreckoningisamethodbywhichavessel'spositioncanbeestimatedwhenthestartingposition,speed,course,andelapsedtimeareknown.Inthisexample(Figure2.15),thestartingpositionisjustoffthemostwesterlypointofAltamontIslandat1554.Thevesselisheadingonacourseof330°Tataspeedof15kn.Whatisthevessel'spositionat1615?

1. Createatracklineusingtheinitialpointandcourse.(Thetrianglearoundthestartingpointindicatesthatthisisaknownposition.)

2. Thesecondpointonthetracklinecanbeestimatedgiventhestartingpoint,course,and

distance.Thedistancecanbecalculatedusingthe60DSTformulabecausethespeedandelapsedtime(21minutes)areknown:

D=T×S÷60=21min×15kn÷60min/hr=5.3nm

3. Plotthelatitude(54°28.6'N)andlongitude(083°23.9'W)oftheestimatedposition.(Thearcaroundthepointindicatesthatthisisadeadreckoningestimate.)

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Deadreckoningisacrude,buteffective,estimationtechnique.Itdoesnotaccountfor--buthelpsusmeasure--theeffectsofwinds,tides,andcurrents,asubjectthatwillbediscussedinthenexttwosections.

Figure2.15.Deadreckoning.

2.4.7.FindingSetandDriftDeadreckoningprovidesanestimatedpositionbaseduponspeedandheading,assumingseasthathaveneitherwind,tide,norcurrent.Muchmoreprecisemeasuresareavailablefordeterminingtheactualposition,suchasusingaGPSortakingfixesfromknownpointsonland.Combiningdeadreckoningestimatesandprecisemeasures,however,allowsforthecalculationoftheeffectofwind,tides,andcurrentand,armedwiththatinformation,fordeterminingamoreeffectivechoiceofheadingtoefficientlygettoanintendeddestination.Thesetanddriftreferstotheeffectofwindandseasontheactualcoursethatavesseltakes.Thiseffectcanbemeasuredbycomparingtheestimatedpositionbasedupondeadreckoningandtheactualpositionbaseduponsomemoreprecisemeans.Setreferstothedirectionofthesea'seffectanddriftreferstothespeed.35ThesetanddriftprocessisshowninFigure2.16:

1. AdeadreckoningpositionisdeterminedtobeLAT54°28.6'NLONG083°23.9'Wat1615.

35Withoutgettingtoomuchintothetopicofvectoranalysis,somereadersmighthavealreadyrecognizedthatatracklineisavector.Inphysics,avectorisalinethathasbothdirection(e.g.,heading)andmagnitude(e.g.,distance).Addingthetwovectorsofadeadreckoningtracklineand"setanddrift"yieldstheactualposition.

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2. Theactualpositionisfoundtobe(54°28.0'N,083°24.6'W)byGPS.

3. Thetracklinefromtheestimatedpositiontowardstheactualpositionshowsthe

direction(set)tobe218°trueandthedistancetobe0.8nm.Usingthe60DSTformula(withD=0.8nmandT=22min),wefindthespeed(drift)tobe2.2kn.

Figure2.16.Determiningsetanddrift.

2.4.8.PlottingACourseWithKnownSetandDriftKnowingthesetanddriftpriortoplottingacoursecanallowanavigatortodeterminethemostdirectcoursetoadestination.Inthisexample,wewishtoplotacoursefromapositionnearthebaseofJigsawPointtoadivesiteacoupleofmileseastofAltamontIsland(Figure2.17).Inthiscase,weplanonmakingaspeedof5knandthereisaknowncurrentof1.5knat085°true.

1. Toplotthecourseaccountingforsetanddrift,startbyplottingatracklinebetweenthestartingposition(labeledA)andtheintendedendingposition.Thiswillbeacourseof137°trueforadistanceof6.4nm.

2. DrawatracklinerepresentingthesetanddriftfrompointAforadistancerepresenting

onehourofdrift(i.e.,1.5nm).LabeltheendpointofthatlineB.

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3. Ontheoriginaltrackline,drawapointwherethevesselwouldbeafteronehour;labelthispointC.Thiscorrespondstothefactthatwedrewaone-hourset-and-drifttracklinebecauseusinganhouriseasyforcalculations.Sincethevessel'sspeed5kn,itwilltravel5nminonehour.

4. DrawalineconnectingpointsBandC.Determinetheheadingofthatlinetofindthe

mostdirectcoursetomakegoodinordertoarriveatthedestinationwithoutconstantlyhavingtocorrectforthesea'seffects.Inthiscase,thisresultsinacourseof153°true.ConvertthistoacompasscourseusingtheTVMDC+Wcalculation:

T TRUE 153° V Variation +2°W M MAGNETIC 155° D Deviation 0° (Deviationis0°for150°magnetic) C COMPASS 155°

Figure2.17.Plottingwithknownsetanddrift.

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2.4.9.ObtainingaFixWithLinesofPositionAlineofposition(LOP)isacompassbearingtakenonaknownpoint.Ifsightingsaretakenoftwoknownpoints,thepositionofthevessel(fix)canbeobtainedbyfindingwherethetwoLOPsintersect.ObtainingafixusingthreeLOPsusesasimilarmethodologyandisgenerallymoreprecisebecausetherearethreepointsofreferenceinsteadoftwo.ThissectionwilldescribeobtainingafixwiththreeLOPsbuttheprocessisthesamewithtwo.Intheexampleinthissection,theLOPheadingsareobtainedusingahand-heldcompass.Toconverttotruenorth,wehavetocorrectthemagneticheadingbythevariation.Wecanignoretheeffectsofthevesselitself,however,sodeviationwillnotbeanissue.

Figure2.18.Obtainingathree-bearingfix.

SupposeourvesselislyingtotheeastofJigsawIsland.At1315,inordertoobtainourposition,threeheadingsaretakenusingahand-heldcompass.Sincethecompassgivesareadingrelativetomagneticnorth,theheadingsmustbeadjustedtotruenorth(variation=2°W):

LOPTarget Compass TrueToweronBulgeIsland 122°M 120°T"Nose"ofTheFace 310°M 308°TTipofJigsawPoint 245°M 243°T

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Afterconvertingthereadingsfromthecompasstotrueheadings,theLOPsaretransferredtothechart,alsonotingthetimethattheheadingsweretaken(Figure2.18).ThepointatwhichthethreeLOPsintersectisthecurrentposition.Whentakingthreebearings,thethreeLOPsmightintersectinsuchawayastoformasmalltriangle.Inthatcase,thefixisgenerallytakenasthemiddleofthetriangle.Whenusingthisprocedurewithtwobearings,thetwoLOPsalwaysintersectatonepoint.2.4.10.TakingaRunningFixArunningfixisawaytoobtainanestimateofpositionwhilethevesselisunderway.Therunningfixdependsontakingtwocompassreadingsononeknownpointattwodifferenttimeswhilekeepingtrackofthecourseandspeedofthevessel.Figure2.19showstheprocessofobtainingarunningfixbasedupontwosightingsofgreenbuoy#7northofAltamontIsland.

Figure2.19.Takingarunningfix.

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1. At1424,thebuoyisfoundtobeatabearingof057°byhandheldcompass.Adjustingforvariationyieldsabearingof055°truefromthevessel.AnLOPisdrawntothebuoy.

2. Atthistime,thevesselisrunningonaheadingof003°trueataspeedof14kn.Drawa

tracklinerepresentingthiscourse.(ItdoesnotmatterwherethetracklineisdrawnaslongasitintersectstheLOP.)

3. At1439,anothersightingistakenofthebuoybyhandheldcompass.Thisheadingis

foundtobeat136°magnetic,or134°true.DrawasecondLOP.

4. ThetwoLOPobservationsweretaken15minutesapart.Usingthe60DSTformula,wecandeterminethatthedistancetravelledinthatamountoftimeataspeedof14kn;namely,3.5nauticalmiles.Usingtheparallelrulerorrollplotter,copythefirstLOP(1424)3.5nauticalmilesupthetrackline(labeledhereasthe1424-1439LOP).

5. Therunningfixat1439isthepointofintersectionbetweenthe1439and1424-1439

LOPlines.Arunningfixworksbecauseitismeasuringatrianglewhereonepoint(thebuoy,inthiscase)isknownaswellasthreeanglesofatriangle.Itisnotnecessarytoknowtheexactlengthofthethreesidesofthetriangle,whichiswhyisdoesnotmatterwherethetracklineisdrawn.NotethatifthetracklineinthisexampleweredrawnnearertoAltamontIsland,thepointofintersectionwouldbethesameandpossiblytotheleftofthetrackline.Infact,theonlypurposeofthetracklineistoprovideareferencefor"moving"thefirstLOPtomeetthesecondLOP.2.4.11.DoubletheAngleontheBowDeterminingyourpositionusingthedoubletheangleonthebowmethodisasimplewaytoestimatepositionwhenonlyasingleknownpointisvisible.Putsimply,themethodworksasfollows:

1. Whenonagivenheading,determinetheangleoftheknownpointfromthebowofthevessel.

2. Maintainspeedandheading,andmoveforwarduntiltheangleoftheknownpointonthebowdoublesfromthefirstsighting.

3. Calculatethedistancetraveledfromthefirsttosecondsighting;thatisalsothedistanceawayfromtheknownpointatthelastsightedangle.

Thegeometrybehindthismethodisthatofanisoscelestriangle,whichisatrianglewheretwosidesareofequallength.Figure2.20showssuchanisoscelestriangle,wheretwosidesareoflengthA.Sincetwoanglesofthetrianglearex°andthetotalnumberofdegreesinatriangleis180,theremainingangleis180-2x°.Thismethodtakesadvantageofisoscelestrianglessothat

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thesightingstakenatthebeginningandendofoneofthe"sides"ofthetrianglewillrepresentboththedistancetraveledaswellasthedistancefromaknownpoint.

Figure2.20.Anisoscelestriangle.

Figure2.21.Doubletheangleonthebow.

Figure2.21showsanexampleusingthesesteps.Supposeavesselisoncourse012°trueataspeedof18kn,withBulgeIslandtotheeast.

1. At1535,thefirelookouttowerisfoundtobeatabearingof057°true,whichis45°totheeastoftheboat'scurrentheading.

2. Theboatcontinuesonatthecurrentspeedandheadingand,at1542,thetower

appearsatabearingof102°true(i.e.,90°totheeastoftheboat'sheading).

3. Proceeding7minutes(0.12hours)ataspeedof18knmeansthattheboathastraveledapproximately2.1nm.Thisalsomeansthattheboat'sestimatedpositionis2.1nmfromthelookouttoweratabearingof102°T(or,258°Tfromtheperspectiveofthetower).

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2.5.SummaryThissectionhasprovidedanoverviewofsomeofthebasicchartingandnavigationtasksthatarecreationalmarinermightneedtoperform.Asstatedintheintroduction,automateddevices,particularlymarineGPSdevices,canperformallofthesechartingandnavigationfunctionstoday.Nevertheless,knowinghowtoperformthesetaskswilladdtoyourownknowledgeandprovideabackuptotheelectronics.

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APPENDIXA:DMS,GPS,andDecimalNotations

Latitudeandlongitudeareexpressedindegrees(°),minutes('),andseconds(")notation(DD°MM'SS")onnauticalcharts.Manynewertechnologies,suchasGPSdevices,mobilephones,andsomeWebsites,expresslatitudeandlongitudeinadecimalformat,showingthenumberofdegreesandfractionsofadegree(DD.DDD°),orindegrees,minutes,andfractionsofaminute(DD°MM.MM').Thesectionsbelowwillshowhowoneconvertsfromonenotationtotheother.WhilethereareseveralWebsitesthatwillperformthisconversion,36itisusefultounderstandthearithmeticbehindtheconversion.Thekeypointtorememberwhenconvertingfromonenotationtotheotheristhatadegreeiscomposedof60minutes,eachofwhichisfurthersubdividedinto60seconds.Therefore,adegreecomprises3,600seconds.Toobtainafractionofadegree,youneedtofindthenumberofsecondsanddivideby3600;toobtainthefractionofaminute,youneedtodividethenumberofsecondsby60.ConvertingDMStoDecimalandGPSThelocationofthewreckoftheO.J.WalkerisgivenasLAT44°28'43"NLONG073°14'26"WinDMSnotation.WhatisthelatitudeandlongitudeindecimalandGPSnotations?Todeterminedecimalnotation,converttheminutesandsecondstoafractionofadegree,whichismerelythetotalnumberofsecondsdividedby3600.ToconverttoGPS,convertthesecondstoafractionofaminute,whichismerelythesecondsdividedby60.Example1:44°28'43" Fraction_of_degree =(minutes×60+seconds)÷3600 =(28×60+43)÷3600 =(1680+43)÷3600 =0.4786666666... Decimal =degrees+Fraction_of_degree =44+0.478666666... =44.479°

36Onesuchsiteishttp://www.csgnetwork.com/gpscoordconv.html.TherearealsoappsavailableforAndroidandiOSplatforms.AspreadsheetandPerlprogramforperformingthesecalculationscanalsobefoundathttp://www.garykessler.net/software#latlong.

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Fraction_of_minute =seconds÷60 =43÷60 =0.71666666... GPS =degrees,minutes+Fraction_of_minute =44,28+0.71666666... =44°28.71667'Example2:73°14'26" Fraction_of_degree =(14×60+26)÷3600 =(840+26)÷3600 =0.24055555... Decimal =73+0.24055555... =73.241° Fraction_of_minute =26÷60 =0.4333333... GPS =73,14+0.4333333... =73°14.43333'ConvertingDecimaltoDMSandGPSThelocationofthewreckofthePhoenixisreportedas(44.666°N,073.335°W)indecimalnotation.WhatisthelatitudeandlongitudeinDMSandGPSnotations?ConvertingfromdecimalnotationtoDMSandGPSnotationistheinverseoftheexamplesabove.Thehardestpartisconvertingthefractionaldegreebacktominutesandseconds.ToobtainaDMSvalue,convertthefractionbacktosecondsbymultiplyingby3600,andthendividingby60;thenumberofminutesisthewholenumberpartoftheanswerandthenumberofsecondsistheremainder.ToobtainaGPSvalue,convertthefractionbacktosecondsbymultiplyingby60.Example1:44.666° Minutes_and_seconds=Fraction_of_degree×60 =0.666×60 =39.96minutes

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minutes =39 seconds =(0.96×60) =57.6 DMS =degrees,minutes,seconds =44°39'58" GPS =degrees,Minutes_and_seconds =44,39.96000 =44°39.96000'Example2:73.335° Minutes_and_seconds=0.335×60 =20.1 minutes =20 seconds =0.1×60=6 DMS =73°20'06" GPS =73,20.10000 =73°20.10000'ConvertingGPStoDMSandDecimalThelocationoftheHorseFerrywreckisreportedas(44°29.12000'N,073°14.58000'W)inGPSnotation.WhatisthelatitudeandlongitudeinDMSanddecimalnotations?ToobtainaDMSvalue,convertthefractionofsecondtoactualsecondsbymultiplyingby60.Toobtainthedecimalvalue,converttheminutes(includingthefractionofaminute)toafractionofadegreebydividingby60.Example1:44°29.12000' seconds =Fraction_of_minute×60 =0.12×60 =7.2 DMS =degrees,minutes,seconds =44°29'07" Decimal=degrees+(minutes+Fraction_of_minute)÷60

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=44+(29.12÷60) =44+0.48533333... =44.485°Example2:73°14.58000' seconds =0.58×60 =34.8 DMS =73°14'35" Decimal=73+(14.58÷60) =73+0.243 =73.243°

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APPENDIXB:MercatorandPolyconicProjections

Mapsandchartsaredrawnonatwo-dimensionalplane,suchasapieceofpaperorGPSscreen.Theyare,however,arepresentationofathree-dimensionalobject,namely,theEarth.Thereareanumberofwaystopresentthepictureoftheglobeintwodimensionsandthesearecalledprojections.

FigureB.1.Mercatorprojection.37

Mercatorprojections(FigureB.1)aretheoldestwayofrepresentingnavigationmapsandcharts(developedbyGerardusMercatorin1569).Mercatorprojectionsrepresentlatitude(parallels)andlongitude(meridians)asstraightlinesthatintersectatright(90°)angles.Thisisnotatruerepresentationoftheparallelsandmeridiansontheglobe,ofcourse;linesoflatitudeare,indeed,concentriccirclesthathavesmallerandsmallercircumferencesastheyapproachthepoleswhereaslinesoflongitudeareallthesamelength.38MostnauticalchartsaredrawnusingaMercatorprojection.Onanyparticularchart,thedistancesbetweenmeridiansareequalbutthedistancesbetweenparallelsincreaseprogressivelyfromtheEquatortowardthepoles.OneadvantageofaMercatorprojectionisthataconstantcoursebetweenanytwopointsonthechartcanberepresentedasastraightline,calledarhumbline(orloxodrome).ThispropertyoftheMercatorprojectionistheprimaryreasonthatitispreferredforusewithnauticalcharts.

37http://mathworld.wolfram.com/MercatorProjection.html38ItisbecauselinesoflongitudearethesamelengththatdistanceisalwaysmeasuredontheverticalscaleofanauticalchartusingMercatorprojections.Thehorizontalscaleshowsdegreesoflongitude,whichvaryindistancedependinguponhowfarnorthorsouththeyare.

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Polyconicprojections(FigureB.2),firstdescribedinthe1825byFerdinandRudolphHassler,lookdownonaflatrepresentationoftheglobewiththeEquatorandPrimeMeridianintersectingatrightanglesinthemiddle.Withthistypeofprojection,parallelsoflatitudeappearasnonconcentricarcs,andmeridiansoflongitudeappearascurvedlinesthatconvergeatthepoles.Thescaleiscorrectalonganyparallelandalongthecentralmeridianofthechart.Alongothermeridians,thescaleincreasesasdistanceincreasesfromthecentralmeridian.PolyconicprojectionsareusedonmostU.S.nauticalchartsfortheGreatLakesanditsconnectingwaterways.

FigureB.2.Polyconicprojection.39

Thisinformationisincludedherebecauseitispertinenttocharting.Thatsaid,formostnauticalchartsusedbytherecreationalboater,itdoesnotmakethatmuchdifferencebecausethedistancescoveredbythechartsaresosmall.

39http://mathworld.wolfram.com/PolyconicProjection.html

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APPENDIXC:TheLengthofaDegree

Thereareseveralplacesinthisdocumentthatstatethatadegreeoflatitudeisequalto60nauticalmileswhereasthelineardistanceofadegreeoflongitudevarieswithlatitude.Indeed,adegreeoflatitudeisapproximately60nauticalmileswhileadegreeoflongitudeisroughly60nauticalmilesattheEquatorandgetsshorterasthelatitudeapproachesthepoles.Theobviousquestion,ofcourse,ishowtodeterminethelineardistanceofadegreeoflongitude.Onecommonformulastates: lengthofonedegreeoflongitude(inmeters)=1852.3-9.4xcosine(2xlatitude)Meeus(1999)providesawonderfulsetofformulasrelatedtocalculatingmanythingsrelatedtocalendars,time,andtheplanets.Fromthisbook,R.L.HutchisoncreatedatableathisWebsite(formerlyhttp://www.zodiacal.com/tools/lat_table.php)thatprovides(mostof)thefollowinginformation:

Latitude

Onedegreeoflatitude Onedegreeoflongitudesm nm km sm nm km

Equator(0°) 68.71 59.75 110.57 69.17 60.15 111.3210° 68.73 59.77 110.61 68.13 59.24 109.6420° 68.79 59.82 110.70 65.02 56.54 104.6530° 68.88 59.90 110.85 59.85 52.04 96.4940° 68.99 60.00 111.03 53.06 46.14 85.3950° 69.11 60.10 111.23 44.55 38.74 71.7060° 69.23 60.20 111.41 34.67 30.15 55.8070° 69.32 60.28 111.56 23.73 20.63 38.1980° 69.38 60.33 111.66 12.05 10.48 19.39

Poles(90°) 69.40 60.35 111.69 0 0 0 Key:sm=statutemiles;nm=nauticalmiles;km=kilometersTheWebsitehttp://www.csgnetwork.com/degreelenllavcalc.htmlprovidesa"LengthofaDegreeofLatitudeandLongitudeCalculator."

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APPENDIXD:NavigatorsQuickReferenceCard

Thesequickreferencecardsarefromhttp://captnmike.com/2009/10/01/piloting-and-navigators-quick-reference/

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APPENDIXE:SampleProblemChart40

40Thischartwascreatedforexamplepurposesonly.Thechartiswhollyfictitious.APDFversioncanbedownloadedfromhttp://www.garykessler.net/scuba/library/SampleChart.pdf.

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AcronymsandAbbreviationsDMS Degree,minute,andsecondnotationGPS GlobalPositioningSystemkn Knots(nauticalmilesperhour)LMN LocalNoticetoMarinersLOP LineofpositionNGA NationalGeospatial-IntelligenceAgencyNtM NoticetoMarinersnm NauticalmilesNOAA NationalOceanicandAtmosphericAgencyUSCG U.S.CoastGuard

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ReferencesandFurtherReading

Bowditch,N.(2002).TheAmericanPracticalNavigator:AnEpitomeofNavigation.PublicationNo.9.Bethesda,MD:NationalImageryandMappingAgency.Retrievedfromhttp://msi.nga.mil/NGAPortal/MSI.portal?_nfpb=true&_pageLabel=msi_portal_page_62&pubCode=0002

Brogdon,B.(2001).BoatNavigationfortheRestofUs,2nded.Camden,ME:InternationalMarine/RaggedMountainPress.

Calder,N.(2012).HowtoReadaNauticalChart,2nded.Camden,ME:InternationalMarine/RaggedMountainPress.

Cutler,T.J.(2003).Dutton'sNauticalNavigation,15thed.Annapolis,MD:NavalInstitutePress.

Eaton,J.(Ed.).(2017).ChapmanPiloting&Seamanship,68thed.NewYork:Hearst.

Meeus,J.(1999).AstronomicalAlgorithms,2nded.Richmond,VA:Willmann-Bell.

NOAA.(2011).WanderingoftheGeomagneticPoles.NationalGeophysicalDataCenter.Retrievedfromhttp://www.ngdc.noaa.gov/geomag/GeomagneticPoles.shtml

Sobel,D.(1995).Longitude:TheTrueStoryofaLoneGeniusWhoSolvedtheGreatestScientificProblemofHisTime.NewYork:Walker&Co.

Sweet,R.J.(2011).GPSforMariners,2nded.Camden,ME:InternationalMarine/RaggedMountainPress.

Sweet,R.J.(2011).TheWeekendNavigator,2nded.Camden,ME:InternationalMarine/RaggedMountainPress.

U.S.CoastGuard.(n.d.).NavigationRules--InternationalandInlandWaters.Retrievedfromhttp://www.navcen.uscg.gov/pdf/navrules/navrules.pdf

U.S.CoastGuard.(2011,June).U.S.AidstoNavigationSystem.Retrievedfromhttp://uscgboating.org/images/486.PDF

U.S.CoastGuard.(2017).LightListdocumentseries.Washington,D.C.:U.S.GovernmentPrintingOffice.Retrievedfromhttp://www.navcen.uscg.gov/?pageName=lightlists

U.S.DepartmentofCommerce.(variousdates).UnitedStatesCoastPilot®documentseries.Washington,D.C.:U.S.DepartmentofCommerce,NationalOceanicandAtmosphericAgency,NationalOceanService.Retrievedfromhttp://www.nauticalcharts.noaa.gov/nsd/cpdownload.htm

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U.S.DepartmentofCommerceandU.S.DepartmentofDefense.(2013,April15).ChartNo.1:Symbols,AbbreviationsandTermsusedonPaperandElectronicNavigationalCharts,12thed.SilverSpring,MD:U.S.DepartmentofCommerce,NationalOceanicandAtmosphericAgency,NationalOceanService.Retrievedfromhttp://www.nauticalcharts.noaa.gov/mcd/chart1/ChartNo1.pdf

U.S.DepartmentofDefense.(1969,rev.2003).InternationalCodeofSignalsforVisual,Sound,andRadioCommunications(UnitedStatesEdition).Publication102.Washington,D.C.:U.S.DepartmentofDefense,NationalImageryandMappingAgency.Retrievedfromhttp://www.seasources.net/PDF/PUB102.pdf

Wing,C.(2015).GetYourCaptain'sLicense:TheCompleteStudyGuide,5thed.Camden,ME:InternationalMarine/RaggedMountainPress.

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AcknowledgementsMythankstoBillYoungoftheGreensboro(NC)PowerSquadronforhiscommentsaboutcoursemadegoodandnotingerrorsinAppendixCthatneededfixing.

AbouttheAuthorGaryC.KesslerwascertifiedasaSCUBAdiverasateenagerinsouthernCaliforniain1967.HewaslatercertifiedasanOpenWaterDiver,AdvancedOpenWaterDiver,andRescueDiverbytheProfessionalAssociationofDiveInstructors(PADI)aspartoftheColchester(Vermont)RescueDiveTeamin1991.In2009,GarybecameaPADIDivemasterandOpenWaterInstructor,becomingaMasterSCUBADiverTrainerin2011.LivingonLakeChamplain(thesixthlargestfreshwaterlakeintheU.S.)andwantingtodivewheneverhewanted,Garyboughthisfirstboatin1994andreceivedhisfirstUSCGCaptain'slicensein2012.Hecurrentlyholdsa50GTMasterInlandWater/OUPVNearCoastallicense,withaTowAssistendorsement.GarycurrentlylivesinOrmondBeach,Florida,andisontheICW(HalifaxRiverandIndianRiverLagoon)andwatersnearPonceInletatleastacoupleoftimesamonth.Healsodrivesaneco-tourboatonceortwiceaweekfortheMarineDiscoveryCenter(NewSmyrnaBeach).Inhisotherlife,GaryisaprofessorofcybersecurityatEmbry-RiddleAeronauticalUniversityinDaytonaBeach,wherehechairstheDepartmentofSecurityStudiesandInternationalAffairs.Heisalsoacybersecurityanddigitalforensicsconsultant,educator,andpractitioner,withaparticularinterestinmaritimecybersecurity.GaryholdsaB.A.inMathematics,M.S.inComputerScience,andPh.D.inComputingTechnologyinEducation.