《航海学》课程参考文献（地文资料）CHAPTER 12 HYPERBOLIC SYSTEMS

CHAPTER 12HYPERBOLICSYSTEMSINTRODUCTIONTOLORANC1200.Historyboasts the highest number ofusers of any precise radionav-igation system in use. It has been designated the primaryThetheorybehind the operation of hyperbolic radion-federally provided marine navigation system for theU.S.avigation systems was known in thelate1930's,but ittookCoastal Confluence Zone(CCZ), southern Alaska,and thethe urgency of World War II to speed development of theGreat Lakes.Themaritime community comprises thevastmajorityofLoran C users (87%),followed by civil aviationsystem into practical use. By early 1942, the British had anusers (14%).Thenumberof Loran users is projected tooperating hyperbolic system in use designed to aid in longgrow until well into the next centuryrangebomber navigation.This system,named Gee,operat-edon frequencies between30MHzand80MHzandNotwithstandingthepopularity ofthe system,theU.Semployedmaster and"slave"transmitters spacedapproxi-Department of Defenseis phasing out useof LoranCinfa-mately100 milesapart.TheAmericans were not farbehindvor ofthe highly accurate, space-based Global PositioningtheBritishindevelopmentoftheirownsystemBy1943.System (GPS). This phase out has resulted in closing thethe U.S.Coast Guard was operating a chain of hyperbolicHawaii-basedCentralPacificLoranCchainandtransfer-navigation transmitters thatbecame Loran A.By the end ofring several overseas Loran Cstations to hostgovernments.the war,thenetwork consisted of over70transmitterscov-The use of Loran C in the United States'radionavigationeringover30%of the earth's surface.plan will undergo continuous evaluation until a final deter-In the late1940's and early 1950's, experiments in lowminationofthefutureofthesystem ismadein1996.Atthatfrequency Loran produced a longer range,more accuratepoint, a decision will be made to either continue operationssystem,Using the90-110kHz band, Loran developed intoor tobegin tophase out the system infavor of satellitenav-a 24-hour-a-day,all-weather radionavigation system.Serv-igation.Nomatter what decision is reached, Loran C ising both the marine and aviation communities,Loran Cexpected to remain operational until at least 2015.LORANCDESCRIPTION1201.Basic TheoryOf OperationTherearetwomethodsbywhichthenavigatorcancon-vert these time differences to geographic positions.Thefirst involves the use of a chart overprinted with a LoranThe Loran C system consists ofa chainoftransmittingtime delay lattice consisting of time delay lines spaced atstations, each separated by several hundred miles.Withinconvenient intervals.Thenavigator plots the displayed timethe Loran chain, one station is designatedas themaster sta-differencebyinterpolatingbetweenthelatticelinesprintedtionandtheothersassecondarvstations.Theremustbeaton thechart.In the second method computeralgorithms inleast two secondary stationsfor one master station; there-the receiver'ssoftware convertthe timedelay signals to lat-fore, every Loran transmitting chain will contain at leastitudeand longitudefor display.threetransmitting stations.Themasterand secondarysta-Earlyreceiver conversion algorithmswere imprecise;tions transmit radio pulses at precise time intervals. ALoran receiver measures the time difference (TD)in recep-however, modem receivers employ more precise algo-tion atthe vessel between thesepulses; it then displaysrithms.TheirpositionoutputisusuallywellwithintheO.25either this difference or a computed latitude and longitudeNM accuracy specification for Loran C.Modern receiverscanalso navigateby employing waypoints,directing a ves-totheoperator.sel's course between twooperator-selected points.SectionThe signal arrival time difference between a given1207,section1208,andsection1209morefullyexploremaster-secondary pair corresponds tothedifference in dis-questions ofsystem employment.tance between the receiving vessel and the two stations.Thelocusofpointshavingthesametimedifferencefromaspe1202.ComponentsOfTheLoranSystemcific master-secondary pair forms a hyperbolic line ofposition (LOP).The intersection of two or more of theseLOP's produces a fix of the vessel's position.The components of the Loran system consist of the land-189

189 CHAPTER 12 HYPERBOLIC SYSTEMS INTRODUCTION TO LORAN C 1200. History The theory behind the operation of hyperbolic radion￾avigation systems was known in the late 1930’s, but it took the urgency of World War II to speed development of the system into practical use. By early 1942, the British had an operating hyperbolic system in use designed to aid in long range bomber navigation. This system, named Gee, operat￾ed on frequencies between 30 MHz and 80 MHz and employed master and “slave” transmitters spaced approxi￾mately 100 miles apart. The Americans were not far behind the British in development of their own system. By 1943, the U. S. Coast Guard was operating a chain of hyperbolic navigation transmitters that became Loran A. By the end of the war, the network consisted of over 70 transmitters cov￾ering over 30% of the earth’s surface. In the late 1940’s and early 1950’s, experiments in low frequency Loran produced a longer range, more accurate system. Using the 90-110 kHz band, Loran developed into a 24-hour-a-day, all-weather radionavigation system. Serv￾ing both the marine and aviation communities, Loran C boasts the highest number of users of any precise radionav￾igation system in use. It has been designated the primary federally provided marine navigation system for the U. S. Coastal Confluence Zone (CCZ), southern Alaska, and the Great Lakes. The maritime community comprises the vast majority of Loran C users (87%), followed by civil aviation users (14%). The number of Loran users is projected to grow until well into the next century. Notwithstanding the popularity of the system, the U. S. Department of Defense is phasing out use of Loran C in fa￾vor of the highly accurate, space-based Global Positioning System (GPS). This phase out has resulted in closing the Hawaii-based Central Pacific Loran C chain and transfer￾ring several overseas Loran C stations to host governments. The use of Loran C in the United States’ radionavigation plan will undergo continuous evaluation until a final deter￾mination of the future of the system is made in 1996. At that point, a decision will be made to either continue operations or to begin to phase out the system in favor of satellite nav￾igation. No matter what decision is reached, Loran C is expected to remain operational until at least 2015. LORAN C DESCRIPTION 1201. Basic Theory Of Operation The Loran C system consists of a chain of transmitting stations, each separated by several hundred miles. Within the Loran chain, one station is designated as the master sta￾tion and the others as secondary stations. There must be at least two secondary stations for one master station; there￾fore, every Loran transmitting chain will contain at least three transmitting stations. The master and secondary sta￾tions transmit radio pulses at precise time intervals. A Loran receiver measures the time difference (TD) in recep￾tion at the vessel between these pulses; it then displays either this difference or a computed latitude and longitude to the operator. The signal arrival time difference between a given master-secondary pair corresponds to the difference in dis￾tance between the receiving vessel and the two stations. The locus of points having the same time difference from a spe￾cific master-secondary pair forms a hyperbolic line of position (LOP). The intersection of two or more of these LOP’s produces a fix of the vessel’s position. There are two methods by which the navigator can con￾vert these time differences to geographic positions. The first involves the use of a chart overprinted with a Loran time delay lattice consisting of time delay lines spaced at convenient intervals. The navigator plots the displayed time difference by interpolating between the lattice lines printed on the chart. In the second method computer algorithms in the receiver’s software convert the time delay signals to lat￾itude and longitude for display. Early receiver conversion algorithms were imprecise; however, modern receivers employ more precise algo￾rithms. Their position output is usually well within the 0. 25 NM accuracy specification for Loran C. Modern receivers can also navigate by employing waypoints, directing a ves￾sel’s course between two operator-selected points. Section 1207, section 1208, and section 1209 more fully explore questions of system employment. 1202. Components Of The Loran System The components of the Loran system consist of the land-

190HYPERBOLICSYSTEMSbased transmitting stations, the Loran receiver and antennasecondary and the CD.The time required for the master toand the Loran charts. Land-based facilities include mastertravel to the secondaryis defined asthe baselinetraveltransmittingstations,atleasttwosecondarytransmittersforeachtime(BTT)orbaselinelength(BLL).Afterthefirstsec-mastertransmitter,controlstations,monitorsites,andatimereondarytransmits,theremaining secondaries transmitinerence.Thetransmitters transmittheLoran signals atpreciseorder.Eachof thesesecondarieshas itsownCD/EDvalue.intervalsintime.ThecontrolstationandassociatedmonitorsitesOncethelastsecondaryhastransmitted,themastertrans-continuallymeasurethecharacteristicsoftheLoransignals re-mits again,and the cycle is repeated.The time to completeceived to detect any anomalies or any out-of-specificationthis cycleoftransmission defines an important characteris-conditionSometransmittersserveonlyonefunctionwithinaticforthechain:thegrouprepetitioninterval(GRI).Thechain (i.e., either master or secondary); however, in several ingroup repetition interval divided by ten yields the chain'sstances,onetransmittercanserveasthemasterofonechainanddesignator.For example,the interval between successivesecondary inanother.This dual function lowerstheoverallcoststransmissions of themasterpulsegroupforthenortheastand operatingexpenseforthesystem.USchainis99.600usec.Fromthedefinitionabove.theGRI designator for this chain isdefined as 9960.The GRILoran receivers exhibitvarying degrees of sophisticamustbe sufficiently largetoallowthesignalsfromthemas-tion, however, their signal processing is similar.The firstter and secondary stations in the chain to propagate fullyprocessing stage consists of search and acquisition, dur-throughout the region covered by the chain before the nexting which thereceiver searches for the signal from acycle of pulses begins.particular Loran chain,establishing the approximate loca-Other concepts important to the understanding of thetion in time of the master and secondaries with sufficientoperationof Loran arethebaselineand baselineextensionaccuracytopermitsubsequent settlingandtracking.Thegeographic line connecting amasterto a particular sec-After search and acquisition, the receiver enters the set-ondary station is defined as the station pair baseline.Thetling phase.In thisphase,thereceiver searchesforand detectsbaseline is, in other words, that part of a great circle onthefrontedgeoftheLoranpulse.Afterdetectingthefrontedgewhichlieall thepoints connecting thetwo stations.The ex-ofthepulse,itselectsthecorrectcycleofthepulsetotracktensionof this line beyond the stationsto encompass theHaving selected the correcttrackingcycle,the receiverpoints along this great circle not lying between the two stabegins the tracking and lock phase, in which the receivertions defines the baseline extension.The importance ofmaintains synchronization with the selected received sigthesetwo concepts will becomeapparentduringthediscus-nals.Once this phase is reached, the receiver displays eithersion of Loran accuracy considerationsbelow.the time difference of the signals or the computed latitudeAsdiscussed above,LoranCreliesontimedifferencesand longitudeasdiscussedabove.betweentwoormorereceivedsignalstodevelopLOP'susedtofix the ship's position.This section will examine in greater1203.DescriptionOfOperationdetail the process by which the signals are developed,trans-mitted, and ultimately interpreted by the navigator.TheLoransignal consistsofa seriesof100kHzpulsesThebasic theory behind theoperation of a hyperbolicsentfirstby the master station and then, in turn, by the sec-system is straightforward.First,thelocus of pointsdefiningondary stations.For the master signal, a series of ninea constant difference in distancebetweena vessel and twopulses istransmitted,the firsteight spaced 1000μusec apartseparate stations is described by a mathematical functionfollowed by a ninthtransmitted 2000μsec after the eighththat,when plotted in twodimensional space,yields a hyper-Pulsed transmission results in lower power output require-bola. Second, assuming a constant speed of propagation ofments,better signal identificationproperties, andmoreelectromagneticradiationintheatmosphere,thetimedifprecise timing of the signals. After the time delays dis-ference in thearrival of electromagnetic radiation from thecussed below, secondary stations transmit a series ofeighttwotransmitter sitestothevessel is proportional tothedis-pulses, each spaced 1000 μsec apart.The master and sec-tance between the transmitting sites and the vessel.Theondary stations ina chaintransmitat precisely determinedfollowing equations demonstrating this proportionalitybe-intervals.First, the master station transmits; then, after atween distance and time apply:specified interval, the first secondary station transmits.Then the second secondarytransmits,and so on.SecondaryDistance=VelocityxTimestations are given letter designations of W,X,Y,and Z; thisletterdesignation indicates the order in which they transmitor, using algebraic symbolsfollowing the master.When the master signal reaches thenext secondary in sequence,this secondary station waits and=c xtinterval, defined as the secondary coding delay,(SCD)orsimply coding delay (CD), and then transmits.The totalTherefore, if the velocity (c) is constant, the distanceelapsed timefromthemastertransmissionuntil the second-ary emission is termed the emissions delay (ED).The EDbetween a vessel and two transmitting stations will be di-is the sum of thetimeforthemaster signal totravel to therectlyproportional tothetimedelaydetected atthevessel

190 HYPERBOLIC SYSTEMS based transmitting stations, the Loran receiver and antenna, and the Loran charts. Land-based facilities include master transmitting stations, at least two secondary transmitters for each master transmitter, control stations, monitor sites, and a time ref￾erence. The transmitters transmit the Loran signals at precise intervals in time. The control station and associated monitor sites continually measure the characteristics of the Loran signals re￾ceived to detect any anomalies or any out-of-specification condition. Some transmitters serve only one function within a chain (i.e., either master or secondary); however, in several in￾stances, one transmitter can serve as the master of one chain and secondary in another. This dual function lowers the overall costs and operating expense for the system. Loran receivers exhibit varying degrees of sophistica￾tion; however, their signal processing is similar. The first processing stage consists of search and acquisition, dur￾ing which the receiver searches for the signal from a particular Loran chain, establishing the approximate loca￾tion in time of the master and secondaries with sufficient accuracy to permit subsequent settling and tracking. After search and acquisition, the receiver enters the set￾tling phase. In this phase, the receiver searches for and detects the front edge of the Loran pulse. After detecting the front edge of the pulse, it selects the correct cycle of the pulse to track. Having selected the correct tracking cycle, the receiver begins the tracking and lock phase, in which the receiver maintains synchronization with the selected received sig￾nals. Once this phase is reached, the receiver displays either the time difference of the signals or the computed latitude and longitude as discussed above. 1203. Description Of Operation The Loran signal consists of a series of 100 kHz pulses sent first by the master station and then, in turn, by the sec￾ondary stations. For the master signal, a series of nine pulses is transmitted, the first eight spaced 1000 µsec apart followed by a ninth transmitted 2000 µsec after the eighth. Pulsed transmission results in lower power output require￾ments, better signal identification properties, and more precise timing of the signals. After the time delays dis￾cussed below, secondary stations transmit a series of eight pulses, each spaced 1000 µsec apart. The master and sec￾ondary stations in a chain transmit at precisely determined intervals. First, the master station transmits; then, after a specified interval, the first secondary station transmits. Then the second secondary transmits, and so on. Secondary stations are given letter designations of W, X, Y, and Z; this letter designation indicates the order in which they transmit following the master. When the master signal reaches the next secondary in sequence, this secondary station waits an interval, defined as the secondary coding delay, (SCD) or simply coding delay (CD), and then transmits. The total elapsed time from the master transmission until the second￾ary emission is termed the emissions delay (ED). The ED is the sum of the time for the master signal to travel to the secondary and the CD. The time required for the master to travel to the secondary is defined as the baseline travel time (BTT) or baseline length (BLL). After the first sec￾ondary transmits, the remaining secondaries transmit in order. Each of these secondaries has its own CD/ED value. Once the last secondary has transmitted, the master trans￾mits again, and the cycle is repeated. The time to complete this cycle of transmission defines an important characteris￾tic for the chain: the group repetition interval (GRI). The group repetition interval divided by ten yields the chain’s designator. For example, the interval between successive transmissions of the master pulse group for the northeast US chain is 99,600 µsec. From the definition above, the GRI designator for this chain is defined as 9960. The GRI must be sufficiently large to allow the signals from the mas￾ter and secondary stations in the chain to propagate fully throughout the region covered by the chain before the next cycle of pulses begins. Other concepts important to the understanding of the operation of Loran are the baseline and baseline extension. The geographic line connecting a master to a particular sec￾ondary station is defined as the station pair baseline. The baseline is, in other words, that part of a great circle on which lie all the points connecting the two stations. The ex￾tension of this line beyond the stations to encompass the points along this great circle not lying between the two sta￾tions defines the baseline extension. The importance of these two concepts will become apparent during the discus￾sion of Loran accuracy considerations below. As discussed above, Loran C relies on time differences between two or more received signals to develop LOP’s used to fix the ship’s position. This section will examine in greater detail the process by which the signals are developed, trans￾mitted, and ultimately interpreted by the navigator. The basic theory behind the operation of a hyperbolic system is straightforward. First, the locus of points defining a constant difference in distance between a vessel and two separate stations is described by a mathematical function that, when plotted in two dimensional space, yields a hyper￾bola. Second, assuming a constant speed of propagation of electromagnetic radiation in the atmosphere, the time dif￾ference in the arrival of electromagnetic radiation from the two transmitter sites to the vessel is proportional to the dis￾tance between the transmitting sites and the vessel. The following equations demonstrating this proportionality be￾tween distance and time apply: Distance=Velocity x Time or, using algebraic symbols d=c x t Therefore, if the velocity (c) is constant, the distance between a vessel and two transmitting stations will be di￾rectly proportional to the time delay detected at the vessel

191HYPERBOLICSYSTEMSbetween pulses of electromagnetic radiation transmittedmiles.Assume further that the master station is located atco-fromthetwostations.ordinates (x,y)=(-200,0)and the secondary is located at (x.y)Anexamplewillbetter illustratetheconcept.SeeFig=(+200,0).Designate this secondary station as station Xrayure1203a.Assumethat twoLoran transmitting stations,aAnobserverwithareceivercapableofdetectingelectromagmaster anda secondary,arelocated along withan observernetic radiation is positioned at any point A whose coordinatesin a Cartesian coordinate system whose units are in nauticalare defined as x()and y(°).The Pythagorean theorem can beused to determine the distance between the observer and themasterstation,similarly,onecanobtainthedistancebetweenthe observer and the secondary station.This methodologyCENTERLINE600yields thefollowingresult for thegiven example:E400 disanceam= [(xa + 200) +ye j0.5BASELINE200REXTENSIONdistanceas=[(xa200)°+y j0MX?0上BASELINEFinally,the differencebetween thesedistances(Z)isEXTENSION-200BASELINEgiven by the following:2-400Z= dam(-das)-600Afteralgebraicmanipulation,-800-400-200o200400600XCOORDINATE(NAUTICALMILES)2,0.5z-[(a+200)2+]10-5[(xa-200] +Figure1203a.DepictionofLoranLOPsWithagiven positionofthe master and secondary stations,therefore,thefunction describing the difference in distance isre-duced to onevariable,i.e.,theposition ofthe observer.VESSELVESSELRECEIVESRECEIVESMASTERSECONDARYSECONDARYMASTERRECEIVESSECONDARYTRANSMITSMASTERTRANSMITS中BASELINESECONDARYCODINGDELAY(CD)-TRAVELTIMEEMISSIONDELAY(ED)MEASUREDTIMEDIFFERENCE(TD)ATVESSEL--11o2.0004.0006,0008.00010,00014,00016.00012,000TIMEINMICROSECONDSFigure1203b.Thetimeaxis forLoranCTDfor point"A

HYPERBOLIC SYSTEMS 191 between pulses of electromagnetic radiation transmitted from the two stations. An example will better illustrate the concept. See Fig￾ure 1203a. Assume that two Loran transmitting stations, a master and a secondary, are located along with an observer in a Cartesian coordinate system whose units are in nautical miles. Assume further that the master station is located at co￾ordinates (x,y) = (-200,0) and the secondary is located at (x,y) = (+200,0). Designate this secondary station as station Xray. An observer with a receiver capable of detecting electromag￾netic radiation is positioned at any point A whose coordinates are defined as x(a ) and y(a ). The Pythagorean theorem can be used to determine the distance between the observer and the master station; similarly, one can obtain the distance between the observer and the secondary station. This methodology yields the following result for the given example: Finally, the difference between these distances (Z) is given by the following: After algebraic manipulation, With a given position of the master and secondary stations, therefore, the function describing the difference in distance is re￾duced to one variable; i.e., the position of the observer. Figure 1203a. Depiction of Loran LOPs. distanceam xa ( ) + 200 2 ya 2 [ ] + 0.5 = distanceas xa ( ) – 200 2 ya 2 [ ] + 0.5 = Z dam das = ( ) – Z xa ( ) + 200 2 ya 2 )]0.5 xa ( ) – 200 2 ya 2 ] 0.5 = + – + Figure 1203b. The time axis for Loran C TD for point “A

192HYPERBOLICSYSTEMSFigure 1203a is a conventional graphical representation ofsignal to thereception ofthe secondary signal.Therefore,thethedataobtainedfrom solving for the value (Z)usingvaryingtime quantity above must be corrected by subtracting thepositions of A in the example above.The hyperbolic lines ofamountoftimerequiredforthesignaltotravelfromthemas-position inthefigurerepresentthe locus ofpoints alongwhichtertransmitterto theobserverat pointA.This amountof timetheobserver's simultaneous distancesfromthemasterand sec-was3,167 usec.Therefore,thetime delay observed at pointondarystationsareegual:heisonthecenterline.Forexample.A in this hypothetical example is (14.785-3,167) usec orif the observer above were located at the point (271.9,200)11.618 μsec.Once again,this timedelay is a function of thethen the distance between thatobserver and the secondary sta-simultaneousdifferencesindistancebetweentheobservertion (in this case,designatedx)would be212.5NM.Inandthetwotransmittingstations,anditgivesrisetoahyper-turn,the observer'sdistancefromthe master station wouldbebolic lineof positionwhichcanbecrossed withanother LOP512.5nauticalmiles.ThefunctionZwouldsimplybethedif-tofix theobserver's position at a discreteposition.ference of the tw0, or 300 NM Refer again to Figure 1203a.Thehyperbolamarkedby"300"representsthelocusofpoints1204.AllowancesForNon-UniformPropagationRatesalongwhichtheobserverissimultaneously300NMclosertothe secondary transmitter than to the master.To fix his posi-Theproportionalityofthetimeand distancedifferencestion, the observer must obtain a similar hyperbolic line ofassumes aconstantspeedofpropagationofelectromagneticposition generated by another master-secondary pair. Onceradiation.To a first approximation,this is a valid assumpthis is done, the intersection of the two LOP's can be deter-tion; however, in practice,Loran's accuracy criteria requiremined,and the observer can fix his position in the plane ataa refinementof this approximation.Theinitial calculationsdiscretepositionintime.above assumedthespeedof light in a vacuum,however,theThe above example was evaluated in terms ofdifferenc-actual speed at which electromagnetic radiation propagateses in distance, as discussed previously, an analogousthrough the atmosphere is affected by both the mediumsituation exists with respectto differences in signal recep-through which ittravels and theterrain over which it passes.tion time. All that is required is the assumption that theThefirst of these concerns, the nature of the atmospheresignal propagates atconstant speed.Oncethis assumption isthrough whichthe signal passes,gives riseto thefirstcorrec-made,thehyperbolicLOP'sinFigure1203aabovecanbetion term: the Primary PhaseFactor (PF).This correctionre-labeledtoindicatetimedifferencesinsteadofdistances.is transparent to theoperator ofa Loran system because it isThis principle isgraphicallydemonstrated inFigure1203b.incorporated into thecharts and receivers usedwith the sys-tem,and itrequires no operatoraction.Assume that electromagnetic radiation travels at theASecondaryPhaseFactor(SF)accountsfortheef-speed of light (one nautical mile traveled in 6.18 usec)andfecttraveling over seawater has on the propagated signal.reconsiderpointA fromtheexampleabove.The distanceThis correction, like the primary phase factor above, isfromthemasterstationtopointAwas512.5NM.Fromtherelationship between distance andtime defined above,ittransparenttotheoperator since it is incorporated intowouldtakeasignal (6.18usec/NM)×512.5NM=3,167chartsandsvstemreceivers.μsectotravelfromthemaster stationtotheobserveratpointThethird and final correction required becauseof non-A.At the arrival of this signal, the observer's Loran receiveruniform speed of electromagneticradiation istermed thewouldstartthetimedelay(TD)measurement.RecallfromAdditional SecondaryPhaseFactor (ASF).Ofthe threethegeneral discussionabovethata secondary station trans-correctionsmentionedinthissection,thisisthemostim-mits afteran emissionsdelayequalto the sumofthebaselineportant one to understand because its correct application istraveltimeandthesecondarycodingdelay.Inthisexample.crucialtoobtainingthemostaccurateresultsfromthesys-themasterand the secondary are400NMapart,therefore,tem.ThiscorrectionisrequiredbecausetheSFdescribedthebaselinetravel time is(6.18usec/NM)×400NM=aboveassumes that the signal travels onlyover water when2,472 μsec. Assuming a secondary coding delay of 11,000thesignaltravelsoverterraincomposedofwaterandlandusec,the secondary station in this examplewould transmitTheASF canbedeterminedfromeitheramathematical(2,472+11,000)usecor13,472usecafterthemasterstation.model oratableconstructedfromempiricalmeasurement.Thesignalmustthenreachthereceiverlocatedwiththeob-The lattermethod tends to yield more accurate results.Toserver at point A.Recall from above that this distance wascomplicatemattersfurther,theAsFvaries seasonally212.5NM.Therefore,thetimeassociated with signal travelTheASF correction is important because it is requiredis: (6. 18 μsec/NM) × 212. 5 NM = 1,313 μsec. Therefore,toconvertLorantimedelaymeasurements intogeographicthetotaltimefromtransmissionof themaster signaltothecoordinates.ASFcorrections must beusedwithcare.Somereception of thesecondary signal bytheobserverat point ALoran charts incorporate ASF corrections while others dois (13,472 + 1,313) μusec = 14,785 μsec.not.One cannot manually apply ASF correction to mea-Recall, however,that the Loran receiver measures thesured time delays when using a chart that has already beentime delay between reception ofthe master signal and there-corrected.In addition, theaccuracy of AsF's is muchlessception of the secondary signal.The quantity determinedaccurate within 10NM ofthe coastline.Therefore,naviga-abovewasthetotaltimefromthetransmissionofthemastertorsmust use prudence and caution whenoperating with

192 HYPERBOLIC SYSTEMS Figure 1203a is a conventional graphical representation of the data obtained from solving for the value (Z) using varying positions of A in the example above. The hyperbolic lines of position in the figure represent the locus of points along which the observer’s simultaneous distances from the master and sec￾ondary stations are equal; he is on the centerline. For example, if the observer above were located at the point (271. 9, 200) then the distance between that observer and the secondary sta￾tion (in this case, designated “X”) would be 212. 5 NM. In turn, the observer’s distance from the master station would be 512. 5 nautical miles. The function Z would simply be the dif￾ference of the two, or 300 NM. Refer again to Figure 1203a. The hyperbola marked by “300” represents the locus of points along which the observer is simultaneously 300 NM closer to the secondary transmitter than to the master. To fix his posi￾tion, the observer must obtain a similar hyperbolic line of position generated by another master-secondary pair. Once this is done, the intersection of the two LOP’s can be deter￾mined, and the observer can fix his position in the plane at a discrete position in time. The above example was evaluated in terms of differenc￾es in distance; as discussed previously, an analogous situation exists with respect to differences in signal recep￾tion time. All that is required is the assumption that the signal propagates at constant speed. Once this assumption is made, the hyperbolic LOP’s in Figure 1203a above can be re-labeled to indicate time differences instead of distances. This principle is graphically demonstrated in Figure 1203b. Assume that electromagnetic radiation travels at the speed of light (one nautical mile traveled in 6. 18 µsec) and reconsider point A from the example above. The distance from the master station to point A was 512. 5 NM. From the relationship between distance and time defined above, it would take a signal (6.18 µsec/NM) × 512. 5 NM = 3,167 µsec to travel from the master station to the observer at point A. At the arrival of this signal, the observer’s Loran receiver would start the time delay (TD) measurement. Recall from the general discussion above that a secondary station trans￾mits after an emissions delay equal to the sum of the baseline travel time and the secondary coding delay. In this example, the master and the secondary are 400 NM apart; therefore, the baseline travel time is (6.18 µsec/NM) × 400 NM = 2,472 µsec. Assuming a secondary coding delay of 11,000 µsec, the secondary station in this example would transmit (2,472 + 11,000)µsec or 13,472 µsec after the master station. The signal must then reach the receiver located with the ob￾server at point A. Recall from above that this distance was 212. 5 NM. Therefore, the time associated with signal travel is: (6. 18 µsec/NM) × 212. 5 NM = 1,313 µsec. Therefore, the total time from transmission of the master signal to the reception of the secondary signal by the observer at point A is (13,472 + 1,313) µsec = 14,785 µsec. Recall, however, that the Loran receiver measures the time delay between reception of the master signal and the re￾ception of the secondary signal. The quantity determined above was the total time from the transmission of the master signal to the reception of the secondary signal. Therefore, the time quantity above must be corrected by subtracting the amount of time required for the signal to travel from the mas￾ter transmitter to the observer at point A. This amount of time was 3,167 µsec. Therefore, the time delay observed at point A in this hypothetical example is (14,785 - 3,167) µsec or 11,618 µsec. Once again, this time delay is a function of the simultaneous differences in distance between the observer and the two transmitting stations, and it gives rise to a hyper￾bolic line of position which can be crossed with another LOP to fix the observer’s position at a discrete position. 1204. Allowances For Non-Uniform Propagation Rates The proportionality of the time and distance differences assumes a constant speed of propagation of electromagnetic radiation. To a first approximation, this is a valid assump￾tion; however, in practice, Loran’s accuracy criteria require a refinement of this approximation. The initial calculations above assumed the speed of light in a vacuum; however, the actual speed at which electromagnetic radiation propagates through the atmosphere is affected by both the medium through which it travels and the terrain over which it passes. The first of these concerns, the nature of the atmosphere through which the signal passes, gives rise to the first correc￾tion term: the Primary Phase Factor (PF). This correction is transparent to the operator of a Loran system because it is incorporated into the charts and receivers used with the sys￾tem, and it requires no operator action. A Secondary Phase Factor (SF) accounts for the ef￾fect traveling over seawater has on the propagated signal. This correction, like the primary phase factor above, is transparent to the operator since it is incorporated into charts and system receivers. The third and final correction required because of non￾uniform speed of electromagnetic radiation is termed the Additional Secondary Phase Factor (ASF). Of the three corrections mentioned in this section, this is the most im￾portant one to understand because its correct application is crucial to obtaining the most accurate results from the sys￾tem. This correction is required because the SF described above assumes that the signal travels only over water when the signal travels over terrain composed of water and land. The ASF can be determined from either a mathematical model or a table constructed from empirical measurement. The latter method tends to yield more accurate results. To complicate matters further, the ASF varies seasonally. The ASF correction is important because it is required to convert Loran time delay measurements into geographic coordinates. ASF corrections must be used with care. Some Loran charts incorporate ASF corrections while others do not. One cannot manually apply ASF correction to mea￾sured time delays when using a chart that has already been corrected. In addition, the accuracy of ASF’s is much less accurate within 10 NM of the coastline. Therefore, naviga￾tors must use prudence and caution when operating with

193HYPERBOLICSYSTEMSASFcorrectionsinthisarea.the Loran system,he should use and plot the TD's generat-OneotherpointmustbemadeaboutASFcorrections.edbythereceiver,not the convertedlatitudeand longitudeSome commerciallyavailableLoran receiverscontainpre-When precision navigation is not required,converted lati-programmed ASF corrections for the conversion oftudeand longitudemaybeused.measured time delays into latitude and longitude printouts1205.LoranPulseArchitectureThe internal values for ASF corrections used by these re-ceivers may or may not be accurate, thus leading to thepossibility ofnavigational error.Periodically,the navigatorAs mentioned above, Loran uses a pulsed signal rathershouldcomparehisreceiver'slatitudeandlongituderead-thanacontinuouswavesignal.ThissectionwillanalvzetheLoran pulse signal architecture,emphasizing design andoutwitheitherapositionplottedonachartincorporatingASF corrections for observed TD's or a position deter-operationalconsiderations.mined from manual TD correction using official ASFFigure1205represents the Loran signal.Nine ofpublished values.This procedure can actas a check on histhese signals aretransmitted by the master station andreceiver's ASF correction accuracy.When the navigatoreight are transmitted by the secondary stations everywantstotakefull advantageofthenavigationalaccuracyoftransmission cycle.Thepulseexhibitsa steepriseto itsLORAN-CCHAINGRISECONDARYSECONDARYSECONDARYMASTEROVERALLMASTERYPULSESZPULSESPULSESPULSESXPULSESPULSE1PATTERNTDX卡NOTE:TIMEAXIS1000ASECTDYNOTTOSCALETDZPULSEENVELOPESHAPE=2-2V/65tINMICROSECONDS.CYCLEZEROCROSSINGTOBEIDENTIFIEDANDTRACKEDDETAILEDVIEWOFINDIVIDUALPULSESHAPEFigure1205.PulsepatternandshapeforLoranCtransmission

HYPERBOLIC SYSTEMS 193 ASF corrections in this area. One other point must be made about ASF corrections. Some commercially available Loran receivers contain pre￾programmed ASF corrections for the conversion of measured time delays into latitude and longitude printouts. The internal values for ASF corrections used by these re￾ceivers may or may not be accurate, thus leading to the possibility of navigational error. Periodically, the navigator should compare his receiver’s latitude and longitude read￾out with either a position plotted on a chart incorporating ASF corrections for observed TD’s or a position deter￾mined from manual TD correction using official ASF published values. This procedure can act as a check on his receiver’s ASF correction accuracy. When the navigator wants to take full advantage of the navigational accuracy of the Loran system, he should use and plot the TD’s generat￾ed by the receiver, not the converted latitude and longitude. When precision navigation is not required, converted lati￾tude and longitude may be used. 1205. Loran Pulse Architecture As mentioned above, Loran uses a pulsed signal rather than a continuous wave signal. This section will analyze the Loran pulse signal architecture, emphasizing design and operational considerations. Figure 1205 represents the Loran signal. Nine of these signals are transmitted by the master station and eight are transmitted by the secondary stations every transmission cycle. The pulse exhibits a steep rise to its Figure 1205. Pulse pattern and shape for Loran C transmission

194HYPERBOLICSYSTEMSmaximumamplitudewithin65usecofemissionandanex-contamination isknown asphasecoding.Withphasecod-ponential decay to zero within 200 to 300μsec.The signaling, the phase of the carrier signal (i.e., the 100 kHz signal)frequency is nominally defined as 100 kHz, in actuality,theischangedsystematicallyfrompulsetopulse.Uponreach-signal is designed such that 99% of the radiated power ising the receiver, skywaves will be out of phasewith thecontainedina20kHzbandcenteredon100kHzsimultaneously received ground waves and,thus, they willnot be recognized by the receiver.Althoughthis phase cod-The Loran receiver is programmed to detect the signaling offers several technical advantages,the one moston thecycle correspondingtothe carrierfrequency'sthirdimportanttotheoperator is this increasein accuracyduetopositive crossing of the x axis. This occurrence, termed thetherejection of sky wavesignals.third positive zero crossing, is chosen for two reasons.First, it is late enough for the pulse to have built up suffi-The final aspect of pulse architecture that is importantcient signal strength for the receiver to detect it. Secondly,to the operator is blink coding.When a signal from a sec-it is earlyenough inthepulsetoensurethatthereceiverisondary station is unreliable and should not be used fordetectingthetransmitting station'sground wavepulseandnavigation,the affected secondary station will blink,that is,not its sky wave pulse.Sky wave pulses are affected by at-the first two pulses of the affected secondary station aremosphericrefraction and induce large errors into positionsturnedofffor3.6secondsandonfor0.4seconds.Thisdetermined by the Loran system. Pulse architecture is de-blink is detected by the Loran receiver and displayed to thesigned to eliminate this major source of erroroperator.When the blink indication isreceived,theopera-Anotherpulsefeaturedesigned to eliminateskywavetor should not use the affected secondary stationLORANCACCURACYCONSIDERATIONS1206.Position UncertaintyWithLoranCLoranCLOP'sforvarious chains and secondaries (thehyperbolic latticeformed bythefamiliesof hyperbolaeforseveral master-secondary pairs) are printed on special nauti-As discussed above, theTD'sfroma given master-sec-cal charts.Each ofthe sets ofLOP's isgiven a separate colorondary pairform a family of hyperbolae.Each hyperbola inand is denoted bya characteristic set of symbols.For exam-thisfamilycanbeconsideredalineofposition,thevesselmustple,anLOP might bedesignated 9960-X-25750.Thebe somewhere along that locus of points whichform the hyper-bola.Atypicalfamily ofhyperbolae is shown inFigure1206a.designation is read as follows: the chain GRI designator is9960, the TD is for the Master-Xray pair (M-X),and thetimeNow, suppose thehyperbolic familyfrom the master-differencealong this LOP is 25750usec.Thechart onlyXray stationpair shown inFigure1203awere superimposedshowsalimitednumberof LOP'storeduceclutterontheupon thefamily shown in Figure1206a.The results wouldbethehyperbolic latticeshown inFigure1206b.chart.Therefore,iftheobservedtimedelayfallsbetweentwo600600400400A2002000oM200200400-400>6008000200800600=400-200400-600-400-200o200400600XCOORDINATE(NAUTICALMILES)XCOORDINATE(NAUTICALMILES)Figure1206a.Afamily of hyperbolic linesgenerated byFigure1206b.AhyperboliclatticeformedbystationpairsM-X and M-Y.Loransignals

194 HYPERBOLIC SYSTEMS maximum amplitude within 65 µsec of emission and an ex￾ponential decay to zero within 200 to 300 µsec. The signal frequency is nominally defined as 100 kHz; in actuality, the signal is designed such that 99% of the radiated power is contained in a 20 kHz band centered on 100 kHz. The Loran receiver is programmed to detect the signal on the cycle corresponding to the carrier frequency’s third positive crossing of the x axis. This occurrence, termed the third positive zero crossing, is chosen for two reasons. First, it is late enough for the pulse to have built up suffi￾cient signal strength for the receiver to detect it. Secondly, it is early enough in the pulse to ensure that the receiver is detecting the transmitting station’s ground wave pulse and not its sky wave pulse. Sky wave pulses are affected by at￾mospheric refraction and induce large errors into positions determined by the Loran system. Pulse architecture is de￾signed to eliminate this major source of error. Another pulse feature designed to eliminate sky wave contamination is known as phase coding. With phase cod￾ing, the phase of the carrier signal (i.e. , the 100 kHz signal) is changed systematically from pulse to pulse. Upon reach￾ing the receiver, sky waves will be out of phase with the simultaneously received ground waves and, thus, they will not be recognized by the receiver. Although this phase cod￾ing offers several technical advantages, the one most important to the operator is this increase in accuracy due to the rejection of sky wave signals. The final aspect of pulse architecture that is important to the operator is blink coding. When a signal from a sec￾ondary station is unreliable and should not be used for navigation, the affected secondary station will blink; that is, the first two pulses of the affected secondary station are turned off for 3. 6 seconds and on for 0. 4 seconds. This blink is detected by the Loran receiver and displayed to the operator. When the blink indication is received, the opera￾tor should not use the affected secondary station. LORAN C ACCURACY CONSIDERATIONS 1206. Position Uncertainty With Loran C As discussed above, the TD’s from a given master-sec￾ondary pair form a family of hyperbolae. Each hyperbola in this family can be considered a line of position; the vessel must be somewhere along that locus of points which form the hyper￾bola. A typical family of hyperbolae is shown in Figure 1206a. Now, suppose the hyperbolic family from the master￾Xray station pair shown in Figure 1203a were superimposed upon the family shown in Figure 1206a. The results would be the hyperbolic lattice shown in Figure 1206b. Loran C LOP’s for various chains and secondaries (the hyperbolic lattice formed by the families of hyperbolae for several master-secondary pairs) are printed on special nauti￾cal charts. Each of the sets of LOP’s is given a separate color and is denoted by a characteristic set of symbols. For exam￾ple, an LOP might be designated 9960-X-25750. The designation is read as follows: the chain GRI designator is 9960, the TD is for the Master-Xray pair (M-X), and the time difference along this LOP is 25750 µsec. The chart only shows a limited number of LOP’s to reduce clutter on the chart. Therefore, if the observed time delay falls between two Figure 1206a. A family of hyperbolic lines generated by Loran signals. Figure 1206b. A hyperbolic lattice formed by station pairs M-X and M-Y

195HYPERBOLICSYSTEMScharted LOP's, interpolate between them to obtain the pre-LOP errorfix uncertainty=cise LOP. After having interpolated (if necessary) betweensinxtwoTDmeasurements andplottedtheresultingLOP'son thechart,thenavigator marks the intersection of the LOP's andAssuming that LOP error is constant, then position un-labels that intersection as his Loran fix.certainty is inversely proportional to the sineofthecrossingangle. As the crossing angle increases from 0° to 90°, theAcloserexamination ofFigure 1206breveals two pos-sin of the crossing angle increases from 0 to 1. Therefore,siblesourcesof Loranfixerror.Thefirstoftheseerrors isthe error is at a minimum when the crossing angle is 900,a function of the LOP crossing angle. The second is a phe-and it increases thereafter as thecrossing angledecreases.nomenonknownasfixambiguity.Letusexaminebothofthese in turn.Fix ambiguity can also cause the navigator to plot aner-Figure 1206c shows graphically how error magnituderoneous position.Fix ambiguity results when one Loranvaries as a function of crossing angle. Assume that LOP 1LOPcrossesanotherLOPintwoseparateplaces.Most Lo-isknown to containnoeror,whileLOP2has an uncertain-ran receivers havean ambiguity alarmto alert the navigatorly as shown.As the crossing angle (i.e.,the angle ofto this occurrence.Absent other information,the navigatorintersection of the two LOP's)approaches 900,rangeofis unsure as to which intersectionmarks his true position.possible positions along LOP1 (i.e., the position uncertain-Again,refer to Figure 1206b for an example.The-350 dif-tyor fix error)approaches a minimum; conversely,as theference line from the master-Xray station pair crosses thecrossingangledecreases,theposition uncertaintyincreas--500difference line fromthe master-Yankeestation pair ines;the linedefining the range ofuncertaintygrows longer.two separate places.Absent a third LOP from either anotherThis illustrationdemonstrates the desirability of choosingstation pair or a separate source, the navigator would notLOP's for which the crossing angle is as close to 90°as pos-knowwhichoftheseLOPintersectionsmarkedhisposition.sible. The relationship between crossing angle and accuracyFix ambiguity occurs in thearea known as the master-canbeexpressedmathematicallysecondary baseline extension, defined above in section1203.Therefore,do not use a master-secondarypairwhileLOP errorsinx =operating in the vicinity of that pair's baseline extension iffix uncertaintyotherstationpairsareavailablewherex is the crossing angle.Rearranging algebraicallyThe large gradient ofthe LOP when operating in the vi-OVERALLERRORASMULTIPLEOFLOP2ERRORLOP2UNCERTAINTY-INLOP2INSETGRAPHSHOWSDANGERSOFSMALL-CROSSINGANGLESAPPARENTPOSITION602940c1CROSSINGANGLE(DEGREES)RANGEOFPOSSIBLEPOSITIONS WITHLOP1ERRORINLOP2Figure 1206c.Error in Loran LOPs is magnified if the crossing angle is less than 900

HYPERBOLIC SYSTEMS 195 charted LOP’s, interpolate between them to obtain the pre￾cise LOP. After having interpolated (if necessary) between two TD measurements and plotted the resulting LOP’s on the chart, the navigator marks the intersection of the LOP’s and labels that intersection as his Loran fix. A closer examination of Figure 1206b reveals two pos￾sible sources of Loran fix error. The first of these errors is a function of the LOP crossing angle. The second is a phe￾nomenon known as fix ambiguity. Let us examine both of these in turn. Figure 1206c shows graphically how error magnitude varies as a function of crossing angle. Assume that LOP 1 is known to contain no error, while LOP 2 has an uncertain￾ly as shown. As the crossing angle (i.e. , the angle of intersection of the two LOP’s) approaches 90°, range of possible positions along LOP 1 (i.e., the position uncertain￾ty or fix error) approaches a minimum; conversely, as the crossing angle decreases, the position uncertainty increas￾es; the line defining the range of uncertainty grows longer. This illustration demonstrates the desirability of choosing LOP’s for which the crossing angle is as close to 90° as pos￾sible. The relationship between crossing angle and accuracy can be expressed mathematically: where x is the crossing angle. Rearranging algebraically, Assuming that LOP error is constant, then position un￾certainty is inversely proportional to the sine of the crossing angle. As the crossing angle increases from 0° to 90°, the sin of the crossing angle increases from 0 to 1. Therefore, the error is at a minimum when the crossing angle is 90°, and it increases thereafter as the crossing angle decreases. Fix ambiguity can also cause the navigator to plot an er￾roneous position. Fix ambiguity results when one Loran LOP crosses another LOP in two separate places. Most Lo￾ran receivers have an ambiguity alarm to alert the navigator to this occurrence. Absent other information, the navigator is unsure as to which intersection marks his true position. Again, refer to Figure 1206b for an example. The -350 dif￾ference line from the master-Xray station pair crosses the -500 difference line from the master-Yankee station pair in two separate places. Absent a third LOP from either another station pair or a separate source, the navigator would not know which of these LOP intersections marked his position. Fix ambiguity occurs in the area known as the master￾secondary baseline extension, defined above in section 1203. Therefore, do not use a master-secondary pair while operating in the vicinity of that pair’s baseline extension if other station pairs are available. The large gradient of the LOP when operating in the vi￾sinx LOP error fix uncertainty = - fix uncertainty LOP error sinx = -. Figure 1206c. Error in Loran LOPs is magnified if the crossing angle is less than 90°

196HYPERBOLICSYSTEMScinity of a baseline extension is another reason to avoidandincreasestoitsmaximumvalue inthevicinityoftheusing stations in the vicinity of their baseline extensions.baseline extension.The navigator,therefore, has several factors to consid-Uncertainty error is directlyproportional to thegradient oftheLOP's used todetermine thefix.Therefore,tominimizeer in maximizing fix accuracy.Do not use a station pairpossible error, the gradient of the LOP's used should be aswhen operatingalong itbaselineextensionbecauseboththeLOP gradient and crossing angle are unfavorable. In addi-small as possible.Refer again to Figure 1206b.Note thatthe gradient is at a minimum along the station pair baselinetion, fix ambiguity is more likely here.LORANC OPERATIONS1207.Waypoint Navigationworking definition of three types of accuracy: absolute ac-curacy, repeatable accuracy, and relative accuracy.A Loran receiver's major advantage is its ability to ac-Absolute accuracy is the accuracy of a position with re-ceptand store waypoints.Waypoints are sets of coordinatesspect to the geographic coordinates of the earth. Forexample,ifthenavigatorplots aposition basedontheLo-thatdescribea locationofnavigational interest.Anavigatorcan enter waypoints into a receiver in one of two ways.HeranClatitudeand longitude(orbasedonLoranCTD's)thedifferencebetween the Loran Cpositionand theactual po-can either visit the area and press the appropriate receivercontrol key,or he can enter thewaypoint coordinates man-sition is a measure of the system's absolute accuracy.ually.When manually entering the waypoint,he canRepeatable accuracyis the accuracywith which theexpress iteither as aTD,a latitude and longitude,or a dis-navigator can return to a position whose coordinates havetance andbearing from another waypoint.been measured previously with the same navigational sys-Typically,waypoints mark either points along atem.Forexample,supposeanavigatorweretotraveltoaplanned route or locations of interest. The navigator canbuoy and note the TD's at that position, Later, suppose theplan his voyage as a series of waypoints,and the receivernavigator, wanting to return to thebuoy,returns to the pre-will keep track of the vessel's progress in relationto theviously-measured TD's. The resulting position differencetrack between them.In keeping track of the vessel'sbetween the vessel and the buoy is a measure of the sys-progress, most receivers display the following parameterstem'srepeatableaccuracyto the operator.Relative accuracy is the accuracy with which a userCross Track Error (XTE): XTE is the perpendicularcan measureposition relativeto that of another userofthedistance from the user's presentposition to the intendedsamenavigationsystematthesametime.Ifonevesselweretrack between waypoints.Steering to maintainXTE nearto travel to the TD's determined by another vessel, the dif-zerocorrectsfor crosstrack current,crosstrackwind,andference inposition between thetwo vessels would beacompasserror.measure ofthe system's relative accuracyBearing (BRG): The BRG display, Sometimes calledThe distinctionbetween absolute and repeatableaccu-theCourseto Steerdisplay,indicatesthebearingfromtheracy is the most important one to understand. With thevessel tothedestination waypoint.correct application of ASF's, the absolute accuracy oftheDistancetoGo(DTG):TheDTGdisplay indicatestheLoran systemvariesfrombetween0.1and0.25nauticalgreat circle distance between the vessel's present locationmiles.However,the repeatable accuracy of the system isand thedestination waypoint.much greater.If the navigator has been to an area previous-Course and Speed Over Ground (COG and SOG):lyand noted theTD'scorrespondingtodifferentTheCOG and the SOGrefertomotionoverground rathernavigationalaids(abuoymarkingaharborentrance,forex-than motion relative to thewater.Thus, COG and SOG re-ample),the highrepeatableaccuracyofthe system enablesflectthe combined effects ofthevessel's progress throughhimto locate thebuoy in under adverse weather.Similarlythe water and the set and drift to which it is subject. Theselected TD data forvarious harbor navigational aids hasnavigator may steer to maintain the COG equal to the in-been collected and recorded.These tables, if available totended track.the navigator,provide an excellent backup navigationalLoran navigation using waypointswasan importantsource to conventional harbor approach navigation. Tomaximize a Loran system's utility, exploit its high repeatdevelopment because it showed the navigator his positionin relation tohis intended destination.Though this methodable accuracy by using previously-determined TDof navigation is notasubstituteforplotting a vessel'sposi-measurements thatlocatepositions criticaltoavessel'ssafetion on a chart to check for navigation hazards, it does givepassage.This statement raises an important question:Whythe navigator a second check on his plot.use measured TD's and not a receiver's latitude and longi-tude output? If the navigator seeks to use the repeatable1208.Using Loran's High Repeatable Accuracyaccuracy of the system,whydoes it matter if TD's or coor-dinates are used? The following section discusses thisIn discussing Loran employment, one must develop aquestion

196 HYPERBOLIC SYSTEMS cinity of a baseline extension is another reason to avoid using stations in the vicinity of their baseline extensions. Uncertainty error is directly proportional to the gradient of the LOP’s used to determine the fix. Therefore, to minimize possible error, the gradient of the LOP’s used should be as small as possible. Refer again to Figure 1206b. Note that the gradient is at a minimum along the station pair baseline and increases to its maximum value in the vicinity of the baseline extension. The navigator, therefore, has several factors to consid￾er in maximizing fix accuracy. Do not use a station pair when operating along it baseline extension because both the LOP gradient and crossing angle are unfavorable. In addi￾tion, fix ambiguity is more likely here. LORAN C OPERATIONS 1207. Waypoint Navigation A Loran receiver’s major advantage is its ability to ac￾cept and store waypoints. Waypoints are sets of coordinates that describe a location of navigational interest. A navigator can enter waypoints into a receiver in one of two ways. He can either visit the area and press the appropriate receiver control key, or he can enter the waypoint coordinates man￾ually. When manually entering the waypoint, he can express it either as a TD, a latitude and longitude, or a dis￾tance and bearing from another waypoint. Typically, waypoints mark either points along a planned route or locations of interest. The navigator can plan his voyage as a series of waypoints, and the receiver will keep track of the vessel’s progress in relation to the track between them. In keeping track of the vessel’s progress, most receivers display the following parameters to the operator: Cross Track Error (XTE): XTE is the perpendicular distance from the user’s present position to the intended track between waypoints. Steering to maintain XTE near zero corrects for cross track current, cross track wind, and compass error. Bearing (BRG): The BRG display, sometimes called the Course to Steer display, indicates the bearing from the vessel to the destination waypoint. Distance to Go (DTG): The DTG display indicates the great circle distance between the vessel’s present location and the destination waypoint. Course and Speed Over Ground (COG and SOG): The COG and the SOG refer to motion over ground rather than motion relative to the water. Thus, COG and SOG re￾flect the combined effects of the vessel’s progress through the water and the set and drift to which it is subject. The navigator may steer to maintain the COG equal to the in￾tended track. Loran navigation using waypoints was an important development because it showed the navigator his position in relation to his intended destination. Though this method of navigation is not a substitute for plotting a vessel’s posi￾tion on a chart to check for navigation hazards, it does give the navigator a second check on his plot. 1208. Using Loran’s High Repeatable Accuracy In discussing Loran employment, one must develop a working definition of three types of accuracy: absolute ac￾curacy, repeatable accuracy, and relative accuracy. Absolute accuracy is the accuracy of a position with re￾spect to the geographic coordinates of the earth. For example, if the navigator plots a position based on the Lo￾ran C latitude and longitude (or based on Loran C TD’s) the difference between the Loran C position and the actual po￾sition is a measure of the system’s absolute accuracy. Repeatable accuracy is the accuracy with which the navigator can return to a position whose coordinates have been measured previously with the same navigational sys￾tem. For example, suppose a navigator were to travel to a buoy and note the TD’s at that position. Later, suppose the navigator, wanting to return to the buoy, returns to the pre￾viously-measured TD’s. The resulting position difference between the vessel and the buoy is a measure of the sys￾tem’s repeatable accuracy. Relative accuracy is the accuracy with which a user can measure position relative to that of another user of the same navigation system at the same time. If one vessel were to travel to the TD’s determined by another vessel, the dif￾ference in position between the two vessels would be a measure of the system’s relative accuracy. The distinction between absolute and repeatable accu￾racy is the most important one to understand. With the correct application of ASF’s, the absolute accuracy of the Loran system varies from between 0. 1 and 0. 25 nautical miles. However, the repeatable accuracy of the system is much greater. If the navigator has been to an area previous￾ly and noted the TD’s corresponding to different navigational aids (a buoy marking a harbor entrance, for ex￾ample), the high repeatable accuracy of the system enables him to locate the buoy in under adverse weather. Similarly, selected TD data for various harbor navigational aids has been collected and recorded. These tables, if available to the navigator, provide an excellent backup navigational source to conventional harbor approach navigation. To maximize a Loran system’s utility, exploit its high repeat￾able accuracy by using previously-determined TD measurements that locate positions critical to a vessel’s safe passage. This statement raises an important question: Why use measured TD’s and not a receiver’s latitude and longi￾tude output? If the navigator seeks to use the repeatable accuracy of the system, why does it matter if TD’s or coor￾dinates are used? The following section discusses this question

197HYPERBOLICSYSTEMS1209.TimeDelayMeasurementsAndRepeatablefrom the different pairs must travel over different terrain toAccuracyreach the receiver. A Loran receiver does not always use thesame pairs of stations to calculate afix. Suppose a navigatorThe ASF conversion process is the reason for usingmarks the position of a channel buoy by recording its lati-TD's and not Latitude/Longitude readings.tude and longitude as determine by his Loran receiver.If,on the return trip, the receiver tracks different station pairs,Recall that Loran receivers use ASF conversion factorsthe latitude and longitudereadings forthe exact same buoyto convertmeasured TD's into coordinates.Recall also thattheASFcorrections areafunctionoftheterrainover whichwould bedifferent becausethe new stationpair would beusing a different ASF correction.The same effect would oc-thesignalmustpasstoreachthereceiver.Therefore,theASF correctionsforonestationpairaredifferentfromthecur if the navigator attempted to find the buoy with anotherreceiver.By using previously-measured TD's and notASF correctionsforanotherstationpairbecausethe signals9960-W33WLONGITUDEWEST75°74°553555045403025 2015100'0"39°0-0.9-1.0-0.9-0.90.8-0.7-0.6-0.6-0.60.555-1.4-1.2-0.9-0.9-0.9-0.70.7-0.6-0.5-1.1-0.80.6-0.650-1.3-1.1-1.0-0.9-0.8-0.80.7-0.7-0.6-0.60.6-0.5-0.645-1.3-1.0-1.0-0.9-0.9-0.7-0.7-0.6-0.6-0.5-0.60.60.640-0.9-1.3-1.1-1.0-0.8-0.7-0.6-0.7-0.7-0.60.6-0.5-0.635-0.9-1.1-1.0-1.0-0.8-0.6-0.6-0.6-0.6-0.60.6-0.6-0.6L30-1.0-1.0-1.0-0.8-0.7-0.6-0.7-0.7-0.6-0.6-0.6-0.6-0.6A25-1.0-1.1-0.9-0.8-0.7-0.7-0.7-0.6-0.6-0.6-0.6-0.6-0.6T20-0.9-0.9-0.8-0.70.70.7-0.6-0.6-0.6-0.6-0.6-0.6-0.615-0.8-0.8-0.8-0.70.7-0.7-0.6-0.6-0.60.6-0.6-0.61-0.610-0.6-0.6-0.7-0.7-0.7-0.7-0.6-0.6-0.6-0.6-0.6-0.6-0.6T5-0.5-0.6-0.7-0.7-0.7-0.7-0.60.6-0.6-0.6-0.6-0.6-0.6U38°0-0.3-0.6-0.7-0.7-0.7-.06-0.6-0.6-0.6-0.6-0.6-0.60.6D55-0.4-0.5-0.7-0.7-0.6-0.6-0.6-0.60.6-0.6-0.6-0.6E50-0.3-0.3-0.6-0.7-0.7-0.7-0.7-0.6-0.6-0.6-0.645-0.3-0.4-0.6-0.6-0.6-0.6-0.7-0.6-0.6-0.6-0.640-0.3-0.3-0.4-0.5-0.6-0.7-0.7-0.6-0.6-0.635-0.2-0.5-0.3-0.3-0.7-0.6-0.7-0.6-0.630-0.2-0.4-0.2-0.3-0.6-0.6-0.7-0.6N25-0.2-0.2-0.3-0.4-0.6-0.5-0.720-0.2-0.2-0.3-0.4-0.60.5-0.6015-0.2-0.20.3-0.3-0.50.4-0.6R10-0.2-0.2-0.3-0.2-0.4-0.4T5-0.2-0.3-0.2-0.3-0.4-0.4AreaOutsideofCCZ37°0*-0.2-0.2-0.2-0.2-0.4H55-0.2-0.2-0.2-0.3-0.250-0.2-0.2-0.2-0.2-0.245-0.2-0.2-0.2-0.240-0.2-0.2-0.2-0.235-0.2-0.2-0.2-0.230-0.2-0.2-0.2-0.1250.2-0.20.2-0.0200.2-0.2-0.2-0.0150.2-0.2-0.1-0.00.0050.10.2-0.1-0.1-0.00.0-0.1-0.00.1-0.0-0.00.10.336°0"-0.1-0.0-0.0-0.10.20.1Figure 1210.Excerpt from Loran C correction tables

HYPERBOLIC SYSTEMS 197 1209. Time Delay Measurements And Repeatable Accuracy The ASF conversion process is the reason for using TD’s and not Latitude/Longitude readings. Recall that Loran receivers use ASF conversion factors to convert measured TD’s into coordinates. Recall also that the ASF corrections are a function of the terrain over which the signal must pass to reach the receiver. Therefore, the ASF corrections for one station pair are different from the ASF corrections for another station pair because the signals from the different pairs must travel over different terrain to reach the receiver. A Loran receiver does not always use the same pairs of stations to calculate a fix. Suppose a navigator marks the position of a channel buoy by recording its lati￾tude and longitude as determine by his Loran receiver. If, on the return trip, the receiver tracks different station pairs, the latitude and longitude readings for the exact same buoy would be different because the new station pair would be using a different ASF correction. The same effect would oc￾cur if the navigator attempted to find the buoy with another receiver. By using previously-measured TD’s and not 9960-W 33W LONGITUDE WEST 75° 74° 0' 55 50 45 40 35 30 25 20 15 10 5 0' 39°0' -0.9 -1.0 -0.9 -0.9 -0.8 -0.7 -0.6 -0.6 -0.6 -0.5 55 -1.4 -1.2 -1.1 -0.9 -0.9 -0.9 -0.8 -0.7 -0.7 -0.6 -0.6 -0.6 -0.5 50 -1.3 -1.1 -1.0 -0.9 -0.8 -0.8 -0.7 -0.7 -0.6 -0.6 -0.6 -0.6 -0.5 45 -1.3 -1.0 -1.0 -0.9 -0.9 -0.7 -0.6 -0.7 -0.6 -0.6 -0.6 -0.6 -0.5 40 -1.3 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.7 -0.7 -0.6 -0.6 -0.5 -0.6 35 -1.1 -1.0 -1.0 -0.9 -0.8 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 L A T I T U D E 30 -1.0 -1.0 -1.0 -0.8 -0.7 -0.6 -0.7 -0.7 -0.6 -0.6 -0.6 -0.6 -0.6 25 -1.0 -1.1 -0.9 -0.8 -0.7 -0.7 -0.7 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 20 -0.9 -0.9 -0.8 -0.7 -0.7 -0.7 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 15 -0.8 -0.8 -0.8 -0.7 -0.7 -0.7 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 10 -0.6 -0.6 -0.7 -0.7 -0.7 -0.7 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 5 -0.5 -0.6 -0.7 -0.7 -0.7 -0.7 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 38°0' -0.3 -0.6 -0.7 -0.7 -0.7 -.06 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 55 -0.4 -0.5 -0.6 -0.7 -0.7 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 50 -0.3 -0.3 -0.6 -0.7 -0.7 -0.7 -0.7 -0.6 -0.6 -0.6 -0.6 45 -0.3 -0.4 -0.6 -0.6 -0.6 -0.6 -0.7 -0.6 -0.6 -0.6 -0.6 40 -0.3 -0.3 -0.4 -0.5 -0.6 -0.7 -0.7 -0.6 -0.6 -0.6 35 -0.2 -0.3 -0.3 -0.5 -0.7 -0.6 -0.7 -0.6 -0.6 30 -0.2 -0.2 -0.3 -0.4 -0.6 -0.6 -0.7 -0.6 N O R T H 25 -0.2 -0.2 -0.3 -0.4 -0.6 -0.5 -0.7 20 -0.2 -0.2 -0.3 -0.4 -0.6 -0.5 -0.6 15 -0.2 -0.2 -0.3 -0.3 -0.5 -0.4 -0.6 10 -0.2 -0.2 -0.2 -0.3 -0.4 -0.4 5 -0.2 -0.3 -0.2 -0.3 -0.4 -0.4 Area Outside of CCZ 37°0' -0.2 -0.2 -0.2 -0.2 -0.4 55 -0.2 -0.2 -0.2 -0.2 -0.3 50 -0.2 -0.2 -0.2 -0.2 -0.2 45 -0.2 -0.2 -0.2 -0.2 40 -0.2 -0.2 -0.2 -0.2 35 -0.2 -0.2 -0.2 -0.2 30 -0.2 -0.2 -0.2 -0.1 25 -0.2 -0.2 -0.2 -0.0 20 -0.2 -0.2 -0.2 -0.0 15 -0.2 -0.2 -0.1 -0.0 0.0 10 -0.2 -0.1 -0.1 -0.0 0.0 0.1 5 -0.1 -0.0 -0.0 -0.0 0.1 0.1 36°0' -0.1 -0.0 -0.0 -0.1 0.1 0.2 0.3 Figure 1210. Excerpt from Loran C correction tables

198HYPERBOLICSYSTEMSwaypoints. If, on the return visit, the same ASF's are ap-previously-measured latitudes and longitudes, this ASF in-troduced error is eliminated.plied to the sameTD's, the latitudeand longitude will alsoEnvisiontheprocess thisway.Areceivermeasuresbethesame.Butaproblemsimilartotheonediscussedbetween measuring these TD's and displaying a latitudeabove will occur if different secondaries are used.Avoidand longitude,the receiver accomplishes an intermediatethis problembyrecordingall theTD's of waypoints of in-step:applying the ASF corrections.This intermediate stepterest,notjusttheonesusedbythereceiveratthetime.is fraught with potential error. The accuracy of the correc-Then, when returning to the waypoint, other secondariestions is afunction of the stations received, the quality ofthewill be available ifthepreviously used secondaries are notASFcorrection softwareused,andthetypeofreceiver em-ASF correction tables were designed for first genera-ployed. Measuring and using TD's eliminates this step, thustion Loran receivers. The use of advanced propagationincreasing the system's repeatable accuracycorrectionalgorithmsinmodernreceivershaseliminatedMany Loran receivers store waypoints as latitude andtheneedformostmarinerstorefertoASFCorrectiontableslongitude coordinates regardless of theform in which theUsethesetables onlywhen navigating on a chartwhoseTDoperator entered them into the receiver's memory.That is,LOP'shave notbeenverified by actualmeasurement withathereceiver applies AsF correctionspriorto storingthereceiver whose ASF correction function has been disabledINFREQUENTLORANOPERATIONS1210.UseofASFCorrectionTables740 30'W,the ASF value for the Whiskey station pair ofchain9960.The following is an example of the proper use of ASFSolution: Enter the Whiskey station pair table with theCorrectionTables.correct latitude and longitude. See Figure 1210.Extracta val-ue of-0.9μsec.This value would thenbeadded to the observedExample: Given an estimated ship's position of 39°NtimedifferencetocomputethecorrectedtimedifferenceINTRODUCTIONTOOMEGA1211.SystemDescriptiontransmitters.Figure 1211 gives the location ofthese stations.There is no master-secondary relationshipbetween theOmega isa worldwide,internationally operated radioOmega stations as there is between Loran C stations.Thenavigation system.It operates in the VeryLowFrequencynavigator is freeto useany station pairthatprovides the(VLF)band between 10and14kHz.Itprovides an allmost accurate lineof position.Additionally,Omega mea-weather,medium-accuracy navigation service to marinesures phase differences between the two signals whereasnavigators.The system consists of eight widely-spacedLoranCmeasurestimedelaysbetween signal receptionsCommon Frequencies:11.05 kHz11-1/3 kHz10.2 kHz13.6 kHzUnique Frequencies:StationErequency (kHz)12.1A:Norway12.0B: Liberia11.8C: Hawaii13.1D: North Dakota12.3E: La Reunion12.9F:Argentina13.0G: Australia12.8H:JapanFigure1211.Omega stations andfrequencies

198 HYPERBOLIC SYSTEMS previously-measured latitudes and longitudes, this ASF in￾troduced error is eliminated. Envision the process this way. A receiver measures between measuring these TD’s and displaying a latitude and longitude, the receiver accomplishes an intermediate step: applying the ASF corrections. This intermediate step is fraught with potential error. The accuracy of the correc￾tions is a function of the stations received, the quality of the ASF correction software used, and the type of receiver em￾ployed. Measuring and using TD’s eliminates this step, thus increasing the system’s repeatable accuracy. Many Loran receivers store waypoints as latitude and longitude coordinates regardless of the form in which the operator entered them into the receiver’s memory. That is, the receiver applies ASF corrections prior to storing the waypoints. If, on the return visit, the same ASF’s are ap￾plied to the same TD’s, the latitude and longitude will also be the same. But a problem similar to the one discussed above will occur if different secondaries are used. Avoid this problem by recording all the TD’s of waypoints of in￾terest, not just the ones used by the receiver at the time. Then, when returning to the waypoint, other secondaries will be available if the previously used secondaries are not. ASF correction tables were designed for first genera￾tion Loran receivers. The use of advanced propagation correction algorithms in modern receivers has eliminated the need for most mariners to refer to ASF Correction tables. Use these tables only when navigating on a chart whose TD LOP’s have not been verified by actual measurement with a receiver whose ASF correction function has been disabled. INFREQUENT LORAN OPERATIONS 1210. Use of ASF Correction Tables The following is an example of the proper use of ASF Correction Tables. Example: Given an estimated ship’s position of 39°N 74° 30'W, the ASF value for the Whiskey station pair of chain 9960. Solution: Enter the Whiskey station pair table with the correct latitude and longitude. See Figure 1210. Extract a val￾ue of -0.9 µsec. This value would then be added to the observed time difference to compute the corrected time difference. INTRODUCTION TO OMEGA 1211. System Description Omega is a worldwide, internationally operated radio navigation system. It operates in the Very Low Frequency (VLF) band between 10 and 14 kHz. It provides an all weather, medium-accuracy navigation service to marine navigators. The system consists of eight widely-spaced transmitters. Figure 1211 gives the location of these stations. There is no master-secondary relationship between the Omega stations as there is between Loran C stations. The navigator is free to use any station pair that provides the most accurate line of position. Additionally, Omega mea￾sures phase differences between the two signals whereas Loran C measures time delays between signal receptions. Common Frequencies: 10.2 kHz 11.05 kHz 11-1/3 kHz 13.6 kHz Unique Frequencies: Station Frequency (kHz) A: Norway 12.1 B: Liberia 12.0 C: Hawaii 11.8 D: North Dakota 13.1 E: La Reunion 12.3 F: Argentina 12.9 G: Australia 13.0 H: Japan 12.8 Figure 1211. Omega stations and frequencies