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 exponential 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 sufficient 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 atmospheric refraction and induce large errors into positions determined by the Loran system. Pulse architecture is designed to eliminate this major source of error. Another pulse feature designed to eliminate sky wave contamination is known as phase coding. With phase coding, the phase of the carrier signal (i.e. , the 100 kHz signal) is changed systematically from pulse to pulse. Upon reaching 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 coding 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 secondary 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 operator 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-secondary 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 hyperbola. A typical family of hyperbolae is shown in Figure 1206a. Now, suppose the hyperbolic family from the masterXray 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 nautical charts. Each of the sets of LOP’s is given a separate color and is denoted by a characteristic set of symbols. For example, 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 precise 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 possible sources of Loran fix error. The first of these errors is a function of the LOP crossing angle. The second is a phenomenon 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 uncertainly 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 uncertainty or fix error) approaches a minimum; conversely, as the crossing angle decreases, the position uncertainty increases; 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 possible. 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 uncertainty 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 erroneous position. Fix ambiguity results when one Loran LOP crosses another LOP in two separate places. Most Loran 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 difference 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 mastersecondary 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 visinx 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°