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

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 radionavigation 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, operated on frequencies between 30 MHz and 80 MHz and employed master and “slave” transmitters spaced approximately 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 covering 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. Serving both the marine and aviation communities, Loran C boasts the highest number of users of any precise radionavigation 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 favor 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 transferring 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 determination 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 navigation. 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 station and the others as secondary stations. There must be at least two secondary stations for one master station; therefore, every Loran transmitting chain will contain at least three transmitting stations. The master and secondary stations transmit radio pulses at precise time intervals. A Loran receiver measures the time difference (TD) in reception 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 distance between the receiving vessel and the two stations. The locus of points having the same time difference from a specific 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 convert 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 latitude and longitude for display. Early receiver conversion algorithms were imprecise; however, modern receivers employ more precise algorithms. 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 vessel’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 reference. 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 received 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 instances, 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 sophistication; however, their signal processing is similar. The first processing stage consists of search and acquisition, during which the receiver searches for the signal from a particular Loran chain, establishing the approximate location in time of the master and secondaries with sufficient accuracy to permit subsequent settling and tracking. After search and acquisition, the receiver enters the settling 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 signals. 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 secondary 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 requirements, better signal identification properties, and more precise timing of the signals. After the time delays discussed below, secondary stations transmit a series of eight pulses, each spaced 1000 µsec apart. The master and secondary 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 secondary 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 secondary 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 transmits again, and the cycle is repeated. The time to complete this cycle of transmission defines an important characteristic 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 master 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 secondary 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 extension of this line beyond the stations to encompass the points along this great circle not lying between the two stations defines the baseline extension. The importance of these two concepts will become apparent during the discussion 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, transmitted, 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 hyperbola. Second, assuming a constant speed of propagation of electromagnetic radiation in the atmosphere, the time difference in the arrival of electromagnetic radiation from the two transmitter sites to the vessel is proportional to the distance between the transmitting sites and the vessel. The following equations demonstrating this proportionality between 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 directly proportional to the time delay detected at the vessel

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 secondary 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 station (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 difference 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 position, 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 determined, and the observer can fix his position in the plane at a discrete position in time. The above example was evaluated in terms of differences in distance; as discussed previously, an analogous situation exists with respect to differences in signal reception 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 transmits 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 observer 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 reception 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 master 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 hyperbolic 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 assumption; 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 correction 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 system, and it requires no operator action. A Secondary Phase Factor (SF) accounts for the effect 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 nonuniform speed of electromagnetic radiation is termed the Additional Secondary Phase Factor (ASF). Of the three corrections mentioned in this section, this is the most important one to understand because its correct application is crucial to obtaining the most accurate results from the system. 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 measured 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, navigators must use prudence and caution when operating with