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Fromabovecalculations,itcanbederivedthatRMincreaseswithincreasedlatitude.Atequator,thecurvatureradiusofprimemeridianreachitsminimum,whichislessthanthelengthofsemi-minoraxis,b,whileinthepoles,thecurvatureradiusofprimemeridianreachitsmaximum,whichisgreaterthanthelengthofsemi-majoraxis,a.

Example:得到子午面內(nèi)一點(diǎn)（緯度?）的曲率半徑RM后，可以從載體的北向速度vN求出載體相對(duì)地球沿東向的轉(zhuǎn)動(dòng)角速度?E（即緯度的變化率）:

???vN/RM?E???ThecurvatureradiusofPrimeVerticalRN:

可以從數(shù)學(xué)上證明，卯酉圈曲率半徑的端點(diǎn)總是落在短軸上。于是有：

r?RNcos?RN??a(1?e2sin2?)1/2

when??0,RN0?awhen??90,RN90??a(1?e2)1/2?a?a?RM90bFromcalculations,itcanbederivedthatRNincreasesaswellwithincreasedlatitude.Atequator,thecurvatureradiusofPrimeVerticalreachitsminimum,whichisequaltothelengthofsemi-majoraxis,a,whileinthepoles,thecurvatureradiusofPrimeVerticalreachitsmaximum,whichisgreaterthanthelength

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ofsemi-majoraxis,a.And

aRNe2cos2?(1?e2sin2?)1/21?e2sin2????1?222RMa(1?e)1?e1?e(1?e2sin2?)3/2WecanknowthatRN>RMatanylatitudeunlessat??90,whereRN=RM.

Example:載體以東向速度vE沿緯度圈航行，產(chǎn)生極軸方向的角速度?e:

????e??vErvEvcos??ErRN北向角速度是極軸方向角速度的分量，即：

?N??e?cos??1.5.6Thearclengthof1’onmeridian

AssumingSisthearclengthof1‘onmeridian,wecanderivefromthefollowingequation:

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S?RM?1'?a(1?e2)22(1?esin?)

3?a(1?e2)(1?e2sin2?)?1'2?1852.2?9.3cos2?Sincreaseswithincreasedlatitude.(赤道最短，兩極最長(zhǎng))At

?1'??0?,S=1842.9m.At??45?,S=1852.2m.At??90?,the

lengthofSreachitsmaximum,S=1861.5m.

1nauticalmile(nm)=1852m.TheerrorsofSatequatorandpolesare9.1mand9.5m,respectively.（1929年國(guó)際水文物理學(xué)會(huì)制定）

1cable(cab)=0.1nmile=185m1foot(ft)=0.3048m1yard=3ft=0.9144m

1fathom(fm，拓)=6ft=1.8288m1.6DistanceOnTheEarth

Distance,asusedbythenavigator,isthelengthofrhumblineconnectingtwoplaces.Thisisalinemakingthesameanglewithallmeridians.Meridiansandparallelswhichalsomaintainconstanttruedirectionsmaybeconsideredspecialcasesofrhumbline.Anyotherrhumblinespiralstowardthepole,formingaloxodromiccurveorloxodrome.(Alinewhichmakesthesameanglewithallmeridians.Theoreticallynottheshortestroute,buta

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handystraightlineonaMercatorchart.)

Speed(S)israteofmotion,ordistanceperunitoftime.Aknot(kn.),theunitofspeedcommonlyusedinnavigation,isarateof1nauticalmileperhour.

Theexpressionspeedofadvance(SOA)isusedtoindicatethespeedtobemadealongtheintendedtrack.

Speedovertheground(SOG)istheactualspeedofvesseloverthesurfaceoftheearthatanygiventime.

Tocalculatethespeedmadegood(SMG)betweentwopositions,dividethedistancebetweentwopositionsbythetimeelapsedbetweenthetwopositions.

S(nm)=V(kn)?T(hr)S(nm)=V(kn)?T(min)/601.7DirectionOntheEarth

Directionisthepositionofonepointrelativetoanother.Navigatorsexpressdirectionastheangulardifferenceindegreesfromareferencedirection,usuallynorthortheship‘shead.TrueNorth:intersectionofObserverTrueHorizonandObserverMeridian.TheNorth,East,SouthandWestarecalledCardinalDirections.

Thedirectionscanbeexpressedinseveralmethods:(1)Circlemethod（圓周法）:000?-360?:005?.0,085?.7

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(2)Semi-Circlemethod（半圓法）:0?-180?：150?.0NE,125?.0SW

(3)Quadrantmethod(象限法):0?-90?：N60?.0E,S35?.0W(4)Compassmethod(羅經(jīng)點(diǎn)法):32等分圓周，每一等分稱作一個(gè)羅經(jīng)點(diǎn)（pointofthecompass）.1pointofcompass=360??32=11?.25

N,N/E,NNE,NE/N,NE,NE/E,ENE,E/N,E,E/SESE,SE/E,SE,SE/S,SSE,S/E,S,………….

Course(C,Cn)isthehorizontaldirectioninwhichavesselissteeredorintendedtobesteered,expressedasangulardistancefromnorthclockwisethrough360?.

Thecourseisoftendesignatedastrue,magnetic,orcompass,accordingtothereferencedirection.

Trackmadegood(TMG)isthesingleresultantdirectionfromthepointofdeparturetopointofarrivalatanygiventime.Courseofadvance(COA)isthedirectionintendedtobemadegoodovertheground.

Courseoverground(COG)isthedirectionbetweenavessel‘slastfixandanEP(EstimatedPosition).

Courselineisalinedrawnonachartextendinginthedirectionofacourse.

Track(TR)istheintendedhorizontaldirectionoftravelwithrespecttotheearth.

ForeandAftLine(艏艉線)

Heading(Hdg.,SH)isthedirectioninwhichavesselis

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pointed,expressedasangulardistancefrom000?(North)clockwisethrough360?.Donotconfuseheadingandcourse.Headingconstantlychangesasavesselyaws(偏航)backandforthacrossthecourseduetosea,wind,andsteeringerror.

Bearing(B,Brg.)isthedirectionofoneterrestrial(terrestrialglobe，地球儀)pointfromanother,expressedasangulardistancefrom000?clockwisethrough360?.Bearingandazimutharesometimesusedinterchangeably,butthelattermoreaccuratelyreferstothehorizontaldirectionofapointonthecelestialspherefromapointontheearth.

Arelativebearingismeasuredrelativetotheshipsheadingfrom000?clockwisethrough360?.However,itisconvenientlymeasuredrightorleftfrom0?attheship‘sheadthrough180?.

TrueBearing=RelativeBearing+TrueHeadingRelativeBearing=TrueBearing–TrueHeading

Note:右舷為正，左舷為負(fù)。

Part2TraditionalMarineNavigationchartedNAVAIDSarepreferred.

2.3CelestialNavigation

2.3.1PreliminaryConsiderations

Astronomy(天文學(xué))

Astronomypredictsthefuturepositionsandmotionsof

celestialbodiesandseekstounderstandandexplaintheirphysicalproperties.Navigationalastronomy,dealingprincipallywith

celestialcoordinates,time,andtheapparentmotions（視運(yùn)動(dòng)）ofcelestialbodies,isthebranchofastronomymostimportanttothenavigator.

TheCelestialSphere(天球)

Lookingattheskyonadarknight,imaginethatcelestialbodiesarelocatedontheinnersurfaceofavast（巨大的）,earth-centeredsphere.Thismodelisusefulsinceweareonlyinterestedintherelativepositionsandmotionsofcelestialbodiesonthisimaginarysurface.Understandingtheconceptofthecelestialsphereismostimportantwhendiscussingcelestialnavigation.

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2.3.2TheUniverse

TheSolarSystem(太陽系)

Thesun,themostconspicuous（顯著的）celestialobjectinthesky,isthecentralbodyofthesolarsystem.Associatedwithitareatleastnineprincipalplanets（行星）andthousandsofasteroids（小行星）,comets（彗星）,andmeteors（流星）.Someplanetslikeearthhavesatellites.

MotionsOfBodiesOfTheSolarSystem

Astronomersdistinguishbetweentwoprincipalmotionsofcelestialbodies.Rotation（自轉(zhuǎn)）isaspinningmotionaboutanaxiswithinthebody,whereasrevolution（公轉(zhuǎn)）isthemotionofabodyinitsorbitaroundanotherbody.Thebodyaroundwhichacelestialobjectrevolvesisknownasthatbody‘sprimary（源星）.Forthesatellites,theprimaryisaplanet.

Fortheplanetsandotherbodiesofthesolarsystem,theprimaryisthesun.Theentiresolarsystemisheldtogetherbythe

gravitationalforceofthesun.ThewholesystemrevolvesaroundthecenteroftheMilkyWaygalaxy(銀河系),andtheMilkyWayisinmotionrelativetoitsneighboringgalaxies.

Thereasonsofmotionsintheuniversearecausedbytheforceofgravity.Asaresultofgravity,bodiesattracteachotherinproportiontotheirmassesandtotheinversesquareofthe

distancesbetweenthem.Thisforcecausestheplanetstogoaroundthesuninnearlycircular,ellipticalorbits.

Ineachplanet‘sorbit,thepointnearestthesuniscalledtheperihelion(近日點(diǎn)).Thepointfarthestfromthesuniscalledtheaphelion（遠(yuǎn)日點(diǎn)）.Intheorbitofthemoon,thepointnearestthe

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issimilartoaparalleloflatitudeontheearth.

Apointonthecelestialspheremaybeidentifiedattheintersectionofitsparallelofdeclinationanditshourcircle.

Theparallelofdeclinationisidentifiedbythedeclination.

測(cè)者真地平圈：Aplaneperpendiculartothetrueverticalisahorizontalplane,anditsintersectionwiththecelestialsphereisahorizon.Itisthecelestialhorizoniftheplanepassesthroughthecenteroftheearth,thegeoidalhorizonifitistangenttotheearth,andthesensiblehorizonifitpassesthroughtheeyeofthe

observeratA.Sincetheradiusoftheearthisconsiderednegligiblewithrespecttothatofthecelestialsphere,thesehorizonsbecomesuperimposed,andmostmeasurementsarereferredonlytothe

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celestialhorizon.

Thisissometimescalledtherationalhorizon.

測(cè)者真地平圈與測(cè)者子午圈相交兩點(diǎn)——北、南；測(cè)者真地平圈與天赤道也相交兩點(diǎn)——東、西；天球區(qū)域的劃分：

北天半球和南天半球——以天赤道為基準(zhǔn)；東天半球和西天半球——以測(cè)者子午圓為基準(zhǔn)；上天半球和夏天半球——以測(cè)者真地平圈為基準(zhǔn)；高極與測(cè)者緯度之間的關(guān)系：

Oneofthesepoles(havingthesamenameasthelatitude)isabovethehorizonandiscalledtheelevatedpole.Theother,calledthedepressedpole,isbelowthehorizon.

在上天半球的天極叫做高極。在北半球，天北極是高極；在南半球，天南極是高極。

從測(cè)者真地平圈到高極的弧距，稱為高極的高度，所以，高極的高度=測(cè)者的緯度

2.3.4TwoEquatorialCoordinates

Twobasicmethodsoflocatingthehourcircleareinuse.Thefirstmethodoflocatingthehourcircleistoindicateitsangulardistancewestofacelestialmeridian.IftheGreenwichcelestialmeridianisusedasthereference,theangulardistanceiscalledGreenwichhourangle(GHA)(格林時(shí)角),andifthe

meridianoftheobserver,itiscalledlocalhourangle(LHA)(地方時(shí)角).

這種方法稱作第一赤道坐標(biāo)系，由天體地方時(shí)角和天體赤緯來決定。基準(zhǔn)大圓是天赤道和測(cè)者子午圓，輔助圓是天體時(shí)

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圓。

天體赤緯(declination)+天體極距(poledistance)=90?

Second,theangulardistancewestofareferencehourcirclethroughapointonthecelestialsphere,calledthevernalequinoxorfirstpointofAries(白羊座),iscalledsiderealhourangle(SHA)(恒星時(shí)角).

這種方法稱作其次赤道坐標(biāo)系，由天體赤經(jīng)和天體赤緯來決定。基準(zhǔn)大圓是天赤道和春分點(diǎn)時(shí)圓，輔助圓是天體時(shí)圓。

AnotherCoordinate,HorizontalCoordinate(地平坐標(biāo)系)天體方位圓：

天體高度+天體頂距=90?2.3.5TheNavigationalTriangle

Atriangleformedbyarcsofgreatcirclesofasphereiscalledasphericaltriangle.Asphericaltriangleonthecelestialsphereiscalledacelestialtriangle.Thesphericaltriangleofparticularsignificancetonavigatorsiscalledthenavigationaltriangle,formedbyarcsofacelestialmeridian,anhourcircle,anda

verticalcircle.Itsvertices(至高點(diǎn))aretheelevatedpole,thezenith,andapointonthecelestialsphere(usuallyacelestialbody).

Theterrestrialcounterpartisalsocalledanavigational

triangle,beingformedbyarcsoftwomeridiansandthegreatcircleconnectingtwoplacesontheearth,oneoneachmeridian.Theverticesarethetwoplacesandapole.

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2.4Radionavigation

Radionavigationistheprocessofdeterminingaship‘spositionbyapplyingradiowavepropagation,usingtheparameter(course,distance,etc)determinedbyitstransmittersonaknownpositionandreceiversonavessel.

Electromagneticspectrum.

2.4.1ClassifyofRadionavigation:

1.Shortrangeradionavigation-DME,VOR,TACAN,etc.2.Intermediaterangeradionavigation-Loran-A,Loran-D,etc.3.Longrangeradionavigation-Loran-C,etc.

4.Exceedlong-rangeradionavigation-Omega,etc.

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2.4.2AdvantagesandDisadvantagesofRadioNavigationAdvantages

1.noinfluenceforradionavigationwithweatherandrangeofvisibility.2.Fastmeasure3.Easytorealize4.Betterprecision5.BetterreliabilityDisadvantages:

1.Easytobedisturbedbynaturefactorsuchasmagneticstorm,macula,etc.

2.Easytobedestroyedbyenemy.

3.Complexsystem(Transmitter,receiver,etc).4.Cannotbeusedunderwater.

2.4.3Loran-CnavigationandpositioningsystemComponentsofLoran-C

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PositioningmethodsofLoran-CHyperbolamode:

Measurethedistancedifferencebetweenamasterstationandtwoslavestations,andgetthetwoHyperbolas.Wecangetthevessel‘spositionfromtheintersectionofthetwoHyperbolas.

Thepopularwaysincludeimpulsemethod,phasemethodandimpulsewithphasemethod.

Rangefindingmode:Actually,Loran-Cisarangefindingsystem.Becauseoftheunavoidablemeasuringerror,therangeisafake.It‘sfamiliarwithGPS.WecanintegrateLoran-CinthismodewithGPStogetahigh-poweredsystem.Principlechart:

SlMa

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PrincipleofHyperbolamodeSignalofMasterStationA:

Ua(t)?E(t)cos?tSignalofSlaveStationB:

Ub(t)?E(t?td??t)cos[?(t?td??t)]where

??2?f?2?/Tea(t)?tE(?t?ta/)*cos[?(t?ta)]dceb(t)?E(t?tb?td??t)*cos[?(t?tb?td??t)]ReceivedSignalsofA,BinthepositionofvehicleM:

dta?Ra/c;tb?Rb/c;??tn??(tb?ta?td??t)?n??a??bwhereTimedifferenceofSignalsofA,B:

PhasedifferenceofSignalsofA,B:

tn?tb?ta?td??tOr

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?tn??n/??T?n/2?(Ra?Rb)?(tn?td??t)C

LORANAccuracy:0.1to0.25NauticalMiles(183to458meters)LORANAccuracyisaffectedbyCrossingAngle(near90o)Gradient(low)(ratioofTDspacingtoTDdifference)LORANAccuracyisdegradedwithin10nmofShore.ClosetoBridges,PowerLinesandLargeStructuresLORANRepeatabilityiswithin60feet.ReceiverFeatures:?LaAtitude&Longitude?SpeedOvertheGround?CourseOvertheGround?CrossTrackError(XTE)

?SteerRightorLeft?Waypoints(Destinations,enroute&final)?CoursetoSteer(Bearing)toWaypoint?DistancetoGotoWaypoint

?TimetoGotoWaypoint?ManOverboardLocation?Bearing&DistancetoManOverboard?AlarmsforArrival,AnchorWatch

?CrossTrackError?LORANSignalAlarms2.5Radarnavigation

Objectives:1.Beabletodrawthebasicdiagramofthecomponentsofaradarset.

2.Outlinetheprinciplesandcharacteristicsofradar.

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3.Discussthelimitationsofradar.

4.Describetheuseofradarinnavigation.

5.GainanunderstandingofthefunctionalpositionsonatypicalshipboardpilotingteamandRadNavteam.2.5.1.RadarComponents

1.Transmitter

Consistsofanoscillatorthatproducesradio-frequency(RF)

waves.2.ModulatorEssentiallyatimingdevicethatregulatesthetransmittersothatitsendsoutrelativelyshortpulsesofenergyseparatedbyrelativelylongperiodsofrest.

3.Antenna-Controlledbythemodulatortoperformtwofunctions:formsoutgoingpulsesintobeamsandcollectsthereturningpulses.4.Receiver-Comprisedofthecircuitrythatamplifiestheweakreturningechoesfromacontactandconvertsthemintoaform,whichmaybepresentedonadisplay.

5.RadarRepeater-ACathodeRayTube(CRT)displaystheradarinformation.

Forsurfacenavigation,thePlanPositionIndicator(PPI)isused.Controls:VariableRangeRing(strobe)VariableBearingMarkerRangeRings

RangeScalescanbealtered

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2.5.2LimitationsandAdvantagesofRADAR

Limitations

1.BearingResolution

Theminimumdifferenceinbearingbetweentwoobjectsatthesamerange.RelatedtoBeamWidth2.RangeResolution

Theminimumdifferenceinrangebetweentwoobjectsonthesamebearingthatcanbeseparatedbyaradar.RelatedtoPulseWidth3.Frequency&Wavelength

DeterminingcharacteristicsofaRADAR.a.PropagationAffectedbytheprevailingmeteorologicalconditions.

b.AntennaSize-Higherfrequenciesrequiresmallerantennae.OperatorControls

Enablesoperatortoimprovethepicturebeingdisplayed.a.SensitivityTimeControl

Removesseaclutteratcloseinrangessothatnearbycontactscanbeseen.

b.FastTimeConstant

Reducestheeffectsofrainandotherunwantedechoes.c.PulseLength

Shorterthepulselength,thebettertheresolutioninrange.5.Range

a.MinimumRange-RADARcannotreceiveareturningechountilthetrailingedgeofthepulsehasclearedtheantennaandthetransmit/receiveswitchhasswitchedtoreceive.

b.MaximumRange-Determinedbytheheightoftheantenna,poweroutputandfrequency.

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1985

?Lastsatellitedecommissionedin1995

–BlockII/IIAlaunched1989-1997

?4atomicclocks

?Increasedsatellitelifetime?Moredatastoragecapabilities?Nucleardetonationdetector

–BlockIIR

?Abilitytooperateautonomouslyforlong

periods

?Upto5carriersignals

CurrentGPSCapabilities

?Thecurrentsystememploys24activesatellites,atleast6

backups?Costtomaintainsystem:$750millionperyear

–CombinationofBlockII,IIAandIIR

–1995useofGPSbecameavailabletothepublic,free

ofcharge

–Levelsofservice:

?SPSchannelL1

–Predictedaccuracy:13mhorizontal,

22mvertical,200ns

?PPSchannelL2

–Predictedaccuracy:8mhorizontal

andvertical,40ns

3.1.4OtherSystemsGLONASS

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?GlobalNavigationSystemdevelopedbyRussia?Nominallyconsistsof21satellitesplus3spares

?8satellitesarrangedin3orbitalplaneswithaninclination

of64.8o?Orbitsareapproximatelycircularwithaperiodof11h15m?????????

AlsotransmitsL1?TimingAccuracy:99.7%;?30satellites;Galileo

?ProposedandbeingplannedbyEurope

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?Itwillbecontrolledbycivilians

?Planscallfor30mediumEart