《航海学》课程参考文献（地文资料）CHAPTER 07 DEAD RECKONING

CHAPTER 7DEADRECKONINGDEFINITIONANDPURPOSE700.The ImportanceOf Dead ReckoningDead reckoning helps in determining sunrise and sunsetin predicting landfall, sighting lights and predicting arrivalDead reckoning allows a navigator to determine histimes;and inevaluatingtheaccuracyofelectronicpositioningpresent position by projecting his past courses steered andinformation. It also helps in predicting which celestial bodiesspeeds overground from a known past position.He canalsowill beavailableforfutureobservation.determine his future position by projecting an orderedThe navigator should carefully tend his DRplot, up-course and speed of advance from aknown presentposi-date it when required, use it to evaluate external forcestion.TheDRposition is onlyanapproximatepositionacting on his ship,and consult itto avoidpotential naviga-because it does not allowfor the effect of leeway,current,helmsman error,or gyro error.tion hazards.CONSTRUCTINGTHEDEADRECKONINGPLOTMaintain the DR plot directly on the chart in use. DR atintroduces no significanterror.Since the Mercator's latitudeleast two fix intervals ahead while piloting.If transiting in thescale expands as latitude increases, measure distances on theopenocean,maintaintheDRatleastfourhoursaheadofthelastlatitudescaleclosesttotheareaof interestOnlargescalefixposition.Ifoperating inadefined,smalloperatingarea,therecharts,such as harbor charts,usethe distance scale providedisno needto extendtheDR outof theoperatingarea,extend itTomeasure longdistanceson small-scalecharts,breakthedistance into a number of segments andmeasure each segonlytotheoperatingareaboundary.MaintainingtheDRplotdi-rectly on the chart allows the navigator to evaluate a vessel'sment at its mid-latitude.futureposition inrelation to charted navigation hazards.It alsoNavigational computers canalso computedistancesbe-allowstheconningofficerandcaptaintoplancourseandspeedtween two points.Becauseofthe errors inherent in manuallychanges requiredtomeetanyoperational commitments.measuring track distances,use a navigation computer if oneThis section will discuss how to construct the DR plot.isavailable.702. Plotting And Labeling The Course Line And701.Measuring Courses And DistancesPositionsTo measure courses,use the chart's compass rose near.Drawa new course linewheneverrestarting theDR.Ex-esttothechart section currently inuse.Transfercourse linestend the course line from a fix in the direction of the orderedto and from the compass rose usingparallel rulers, rollingrulers,ortriangles.Ifusingaparallel motionplotter(PMP)course.Abovethecourselineplaceacapital Cfollowedbytheordered course.Below the course line,placea capital sfol-simplyset the plotter atthedesired course andplotthatcourse directly on the chartlowedbythe speed inknots.Label all course lines and fixessoon afterplottingthembecauseaconningofficerornavigatorThenavigator canmeasuredirection atany convenientcaneasilymisinterpretanunlabeledlineorpositionplaceon a Mercator chartbecausethemeridiansareparallelEncloseafixfromtwoormoreLOPsbyasmall circletoeachotherandalinemakingananglewithanyonemakesthe same angle with all others.Measure direction on a con-and label it with thetime to the nearestminute.Mark a DRformal chart having nonparallel meridians at themeridianposition with a semicircle and the time.Mark an estimatedclosest to the area of the chart in use.The only common non-position (EP)bya small square andthe time.Determining anEP is covered later in this chapter.conformal projection used is the gnomonic;a gnomonic chartusually contains instructions for measuringdirectionExpress thetimeusingfourdigitswithout punctuationUseeitherzonetimeorGMTCompass roses givebothtrueand magnetic directionsFor most purposes, use true directions.Label the plot neatly, succinctly, and clearlyMeasure distances using the chart's latitude scale.As.Figure 702 illustrates this process.The navigator plotsand labelstheO8oofix.Theconningofficerordersa coursesuming that one minute of latitude equals one nautical mile113

113 CHAPTER 7 DEAD RECKONING DEFINITION AND PURPOSE 700. The Importance Of Dead Reckoning Dead reckoning allows a navigator to determine his present position by projecting his past courses steered and speeds over ground from a known past position. He can also determine his future position by projecting an ordered course and speed of advance from a known present posi￾tion. The DR position is only an approximate position because it does not allow for the effect of leeway, current, helmsman error, or gyro error. Dead reckoning helps in determining sunrise and sunset; in predicting landfall, sighting lights and predicting arrival times; and in evaluating the accuracy of electronic positioning information. It also helps in predicting which celestial bodies will be available for future observation. The navigator should carefully tend his DR plot, up￾date it when required, use it to evaluate external forces acting on his ship, and consult it to avoid potential naviga￾tion hazards. CONSTRUCTING THE DEAD RECKONING PLOT Maintain the DR plot directly on the chart in use. DR at least two fix intervals ahead while piloting. If transiting in the open ocean, maintain the DR at least four hours ahead of the last fix position. If operating in a defined, small operating area, there is no need to extend the DR out of the operating area; extend it only to the operating area boundary. Maintaining the DR plot di￾rectly on the chart allows the navigator to evaluate a vessel’s future position in relation to charted navigation hazards. It also allows the conning officer and captain to plan course and speed changes required to meet any operational commitments. This section will discuss how to construct the DR plot. 701. Measuring Courses And Distances To measure courses, use the chart’s compass rose near￾est to the chart section currently in use. Transfer course lines to and from the compass rose using parallel rulers, rolling rulers, or triangles. If using a parallel motion plotter (PMP), simply set the plotter at the desired course and plot that course directly on the chart. The navigator can measure direction at any convenient place on a Mercator chart because the meridians are parallel to each other and a line making an angle with any one makes the same angle with all others. Measure direction on a con￾formal chart having nonparallel meridians at the meridian closest to the area of the chart in use. The only common non￾conformal projection used is the gnomonic; a gnomonic chart usually contains instructions for measuring direction. Compass roses give both true and magnetic directions. For most purposes, use true directions. Measure distances using the chart’s latitude scale. As￾suming that one minute of latitude equals one nautical mile introduces no significant error. Since the Mercator’s latitude scale expands as latitude increases, measure distances on the latitude scale closest to the area of interest. On large scale charts, such as harbor charts, use the distance scale provided. To measure long distances on small-scale charts, break the distance into a number of segments and measure each seg￾ment at its mid-latitude. Navigational computers can also compute distances be￾tween two points. Because of the errors inherent in manually measuring track distances, use a navigation computer if one is available. 702. Plotting And Labeling The Course Line And Positions Draw a new course line whenever restarting the DR. Ex￾tend the course line from a fix in the direction of the ordered course. Above the course line place a capital C followed by the ordered course. Below the course line, place a capital S fol￾lowed by the speed in knots. Label all course lines and fixes soon after plotting them because a conning officer or navigator can easily misinterpret an unlabeled line or position. Enclose a fix from two or more LOPs by a small circle and label it with the time to the nearest minute. Mark a DR position with a semicircle and the time. Mark an estimated position (EP) by a small square and the time. Determining an EP is covered later in this chapter. Express the time using four digits without punctuation. Use either zone time or GMT. Label the plot neatly, succinctly, and clearly. Figure 702 illustrates this process. The navigator plots and labels the 0800 fix. The conning officer orders a course

114DEADRECKONINGof095°T and a speed of15knots.The navigator extends theposition along the course line and marks that point on thecourse linefrom the 0800fix ina direction of 095°T.Hecourse line with a semicircle.He labels thisDR with thecalculates that in one hour at15knots he will travel 15 nau-time.Note that, by convention, he labels the fix time hori-tical miles.Hemeasures15nautical milesfromthe0800fixzontallyand theDRtimediagonallyGC 0950800$15dFigure 702. A course line with labels.THERULESOFDEADRECKONING703.PlottingTheDRchange to 060°T,The navigator plots the 1030 DR positioninaccordancewiththerulerequiringplottingaDRpositionPlot the vessel's DR position:at every course and speed change. Note that the course linechanges at1030 to 060°T to conformto thenewcourse.At1Atleasteveryhouronthehour.1100,theconningofficerchangescoursebackto090°T2.Thenavigator plotsan1100DRbecauseofthecourseAftereverychangeofcourseorspeed3.Aftereveryfix or running fix.change, Note that, regardess ofthe course change, an 11004.After plotting a single line of positionDR would have been required because of the“every houron the hour"rule.Figure703 illustratesapplyingtheserules.ClearingtheAt1200,theconningofficerchangescourseto180°Tharbor at 0900, the navigator obtains a last visual fix,Thisand speed to5knots.The navigatorplots the1200DR.Atis taking departure, and theposition determined is called1300, thenavigator obtains a fix.Note that the fix positionthe departure. At the 0900 departure, the conning officerisoffsettotheeastfromtheDRposition.Thenavigatorde-orders a course of 090°T and a speed of 10 knots. The nav-termines set and drift from this offset and applies this setigator laysoutthe090°TcourselinefromthedepartureanddrifttoanyDRpositionfrom1300until thenextfixtodeterminean estimated position.He also resets theDRtoAt1ooo,thenavigatorplotsaDRpositionaccordingtothe fix; that is, he draws the 180°T course line from thethe rule requiring plotting a DR position at least every houron thehour.At1030, the conning officer orders a course1300fix, not the 1300DR12001100C·0909S·1006010001030a10S0900C·090Sn?1805S-101300D@1300C.4005Figure703.Atypicaldeadreckoningplot

114 DEAD RECKONING of 095°T and a speed of 15 knots. The navigator extends the course line from the 0800 fix in a direction of 095°T. He calculates that in one hour at 15 knots he will travel 15 nau￾tical miles. He measures 15 nautical miles from the 0800 fix position along the course line and marks that point on the course line with a semicircle. He labels this DR with the time. Note that, by convention, he labels the fix time hori￾zontally and the DR time diagonally. THE RULES OF DEAD RECKONING 703. Plotting The DR Plot the vessel’s DR position: 1. At least every hour on the hour. 2. After every change of course or speed. 3. After every fix or running fix. 4. After plotting a single line of position. Figure 703 illustrates applying these rules. Clearing the harbor at 0900, the navigator obtains a last visual fix. This is taking departure, and the position determined is called the departure. At the 0900 departure, the conning officer orders a course of 090°T and a speed of 10 knots. The nav￾igator lays out the 090°T course line from the departure. At 1000, the navigator plots a DR position according to the rule requiring plotting a DR position at least every hour on the hour. At 1030, the conning officer orders a course change to 060°T. The navigator plots the 1030 DR position in accordance with the rule requiring plotting a DR position at every course and speed change. Note that the course line changes at 1030 to 060°T to conform to the new course. At 1100, the conning officer changes course back to 090°T. The navigator plots an 1100 DR because of the course change, Note that, regardless of the course change, an 1100 DR would have been required because of the “every hour on the hour” rule. At 1200, the conning officer changes course to 180°T and speed to 5 knots. The navigator plots the 1200 DR. At 1300, the navigator obtains a fix. Note that the fix position is offset to the east from the DR position. The navigator de￾termines set and drift from this offset and applies this set and drift to any DR position from 1300 until the next fix to determine an estimated position. He also resets the DR to the fix; that is, he draws the 180°T course line from the 1300 fix, not the 1300 DR. Figure 702. A course line with labels. Figure 703. A typical dead reckoning plot

115DEADRECKONING704. Resetting The DRple,a submerged submarine is operating in the GulfStream,fix information is availablebutoperational considerationsmaypreclude the submarinefromgoingtoperiscopedepthResettheDRplottothe ship's latestfix or running fixtoobtaina fix.Similarly,a surface ship with an inertial nav-Inaddition,consider resetting theDRtoan inertialestimat-igator may be in a dynamic currentand suffera temporaryedpositionasdiscussedbelow.loss ofelectronicfixequipment.In eithercase,thefix infor-Ifa navigator has not received a fixfora long time,themation will be available shortly but thedynamics of thesituationcall fora more accurate assessmentof thevessel'sDR plot,nothaving been resetto a fix,will accumulateposition.Plotting an inertial EP and resetting the DR to thattime-dependenterror.Soon thaterror may become so significantthattheDRwill nolonger showtheship'spositionEPmayprovidethenavigatorwithamoreaccurateassess-with sufficient accuracy.If his vessel is equipped with anmentof thenavigation situation.inertial navigator,the navigator should considerresetting(3)Reliability and accuracy ofthe fix source. Ifa sub-theDRtotheinertialestimatedposition.Somefactorstomarine is operating under the ice, for example, only theinertial EP and Omega fixes may be available for weeks atconsiderwhenmakingthisdeterminationare(1)Time sincethelastfixandavailabilityoffix infor-atime.Givenaknowninaccuracyof Omega,ahighpriormation. If it has been a short time since the last fix and fixcorrelation between the inertial EP and highly accurate fixinformation maysoon become available,it maybeadvis-systems suchas GPS, andthecontinued proper operation ofableto waitfor thenext fix to resettheDR.the inertial navigator,the navigator may well decideto reset(2)Dynamicsofthenavigationsituation.If,forexam-the DRto the inertial EP ratherthan the Omegafix.DEADRECKONINGANDSHIPSAFETYProperlymaintaininga DRplotis important for shipSome of themost importantfactors are current and windsafety.TheDRallows thenavigator toexamineafuturepo-compass orgyro error,and steeringerror.Anymethodsition in relation to a planned track. It allows him towhich attempts to determine an error circlemusttake theseanticipate charted hazards andplanappropriate actiontofactorsintoaccount.Thenavigatorcanusethemagnitudeof setand drift calculated from hisDRplot.See section707avoid them.Recall that the DR position is only approxi-mate.Usingaconceptcalledfix expansion compensatesbelow.He can obtain the current's magnitude from pilotfortheDR's inaccuracyand allows thenavigatortousethecharts or weather reports.He can determine wind speedDRmore effectivelytoanticipate and avoiddanger.fromweatherreportsordirectmeasurement.Hecandeterminecompass error by comparison with an accurate705.FixExpansionstandard or by obtaining an azimuth of the sun. The naviga-tor determines the effect each of these errors has on hisOftenashipsteams intheopenoceanforextendedpe-course and speed overground, and applies that errortotheriods without afix.This can result from of any number offixexpansioncalculationfactorsrangingfrom the inabilitytoobtain celestialfixestoAs noted above,theerror isa function oftime, itgrowsmalfunctioning electronicnavigation systems.Infrequentas the ship proceeds down the track without a obtaining afixes areparticularly common onsubmarines.Whatever thefix. Therefore, the navigator must incorporate his calculat-reason,in some instancesa navigator mayfind himself inederrors intoan error circlewhoseradiusgrowswithtimetheposition of havingto steam many hours on DR alone.For example, assume the navigator calculates that all theThe navigatormusttake precautions to ensure that allvarious sources oferrorcan createa cumulativepositioner-hazards to navigation along his path are accounted forbyror of no more than 2 nm.Then his fix expansion errortheapproximatenatureof aDRposition.Onemethodcircle would growat that rate; it would be2 nm afterthewhich can be used is fixexpansion.first hour, 4 nm after the second, and so on.Fixexpansiontakes into accountpossibleerrors intheAt what value should the navigator start this error cir-cle? Recall that a DR is laid out from every fix. All fixDR calculation caused byfactorswhichtendtoaffectthevessel's actual course and speed over ground.The naviga-sourceshaveafiniteabsoluteaccuracyandtheinitialerrortor considers all such factors and develops an expandingcircle should reflect that accuracy.Assume,for example."errorcircle"aroundtheDRplot.Oneof thebasicassump-thata satellite navigation system has an accuracy of0.5nmtions offix expansion is that the various individual effectsThen the initial error circle around that fix should be set atof current, leeway, and steering error combine to cause a0.5 nmConstructthe error circle as follows.When the navigatorcumulative error which increases overtime, hence, the con-obtains a fix, reset the DR to that fix.Then, enclose that DRceptofexpansionErrors considered in the calculation of the fix expan-position in a circle the radius of which is equal to the accura-sionencompass all errorsthatcanleadto DR inaccuracycy of the system used to obtain the fix.Layout the ordered

DEAD RECKONING 115 704. Resetting The DR Reset the DR plot to the ship’s latest fix or running fix. In addition, consider resetting the DR to an inertial estimat￾ed position as discussed below. If a navigator has not received a fix for a long time, the DR plot, not having been reset to a fix, will accumulate time-dependent error. Soon that error may become so sig￾nificant that the DR will no longer show the ship’s position with sufficient accuracy. If his vessel is equipped with an inertial navigator, the navigator should consider resetting the DR to the inertial estimated position. Some factors to consider when making this determination are: (1) Time since the last fix and availability of fix infor￾mation. If it has been a short time since the last fix and fix information may soon become available, it may be advis￾able to wait for the next fix to reset the DR. (2) Dynamics of the navigation situation. If, for exam￾ple, a submerged submarine is operating in the Gulf Stream, fix information is available but operational considerations may preclude the submarine from going to periscope depth to obtain a fix. Similarly, a surface ship with an inertial nav￾igator may be in a dynamic current and suffer a temporary loss of electronic fix equipment. In either case, the fix infor￾mation will be available shortly but the dynamics of the situation call for a more accurate assessment of the vessel’s position. Plotting an inertial EP and resetting the DR to that EP may provide the navigator with a more accurate assess￾ment of the navigation situation. (3) Reliability and accuracy of the fix source. If a sub￾marine is operating under the ice, for example, only the inertial EP and Omega fixes may be available for weeks at a time. Given a known inaccuracy of Omega, a high prior correlation between the inertial EP and highly accurate fix systems such as GPS, and the continued proper operation of the inertial navigator, the navigator may well decide to reset the DR to the inertial EP rather than the Omega fix. DEAD RECKONING AND SHIP SAFETY Properly maintaining a DR plot is important for ship safety. The DR allows the navigator to examine a future po￾sition in relation to a planned track. It allows him to anticipate charted hazards and plan appropriate action to avoid them. Recall that the DR position is only approxi￾mate. Using a concept called fix expansion compensates for the DR’s inaccuracy and allows the navigator to use the DR more effectively to anticipate and avoid danger. 705. Fix Expansion Often a ship steams in the open ocean for extended pe￾riods without a fix. This can result from of any number of factors ranging from the inability to obtain celestial fixes to malfunctioning electronic navigation systems. Infrequent fixes are particularly common on submarines. Whatever the reason, in some instances a navigator may find himself in the position of having to steam many hours on DR alone. The navigator must take precautions to ensure that all hazards to navigation along his path are accounted for by the approximate nature of a DR position. One method which can be used is fix expansion. Fix expansion takes into account possible errors in the DR calculation caused by factors which tend to affect the vessel’s actual course and speed over ground. The naviga￾tor considers all such factors and develops an expanding “error circle” around the DR plot. One of the basic assump￾tions of fix expansion is that the various individual effects of current, leeway, and steering error combine to cause a cumulative error which increases over time, hence, the con￾cept of expansion. Errors considered in the calculation of the fix expan￾sion encompass all errors that can lead to DR inaccuracy. Some of the most important factors are current and wind, compass or gyro error, and steering error. Any method which attempts to determine an error circle must take these factors into account. The navigator can use the magnitude of set and drift calculated from his DR plot. See section 707 below. He can obtain the current’s magnitude from pilot charts or weather reports. He can determine wind speed from weather reports or direct measurement. He can deter￾mine compass error by comparison with an accurate standard or by obtaining an azimuth of the sun. The naviga￾tor determines the effect each of these errors has on his course and speed over ground, and applies that error to the fix expansion calculation. As noted above, the error is a function of time; it grows as the ship proceeds down the track without a obtaining a fix. Therefore, the navigator must incorporate his calculat￾ed errors into an error circle whose radius grows with time. For example, assume the navigator calculates that all the various sources of error can create a cumulative position er￾ror of no more than 2 nm. Then his fix expansion error circle would grow at that rate; it would be 2 nm after the first hour, 4 nm after the second, and so on. At what value should the navigator start this error cir￾cle? Recall that a DR is laid out from every fix. All fix sources have a finite absolute accuracy, and the initial error circle should reflect that accuracy. Assume, for example, that a satellite navigation system has an accuracy of 0.5 nm. Then the initial error circle around that fix should be set at 0.5 nm. Construct the error circle as follows. When the navigator obtains a fix, reset the DR to that fix. Then, enclose that DR position in a circle the radius of which is equal to the accura￾cy of the system used to obtain the fix. Lay out the ordered

116DEADRECKONINGcourse and speed from the fix position. Then, apply the fixare considered).If anyhazards are indicated withintheexpansioncircletothehourlyDR's.Intheexamplegivencone,the navigator should be especially alertfor those dan-above, the DR after one hour would be enclosed bya circlegers. If, for example, the fix expansion indicates that theof radius2.5nm,aftertwohours 4.5nm,andsoon.Havingvesselmaybestanding into shoal water,continuouslymon-encircled the four hour DR positions with the error circles,itor thefathometer.Similarly,ifthefix expansion indicatedthe navigator then draws two lines originating tangent to thethat thevessel mightbe approaching a charted obstruction,original error circle and simultaneously tangent to the otherpostextra lookouts.error circles.The navigator then closelyexamines the areaThe fix expansion may grow at such a rate that it be-between the two tangent lines for hazards to navigation.Thiscomes unwieldy.Obviously,if thefix expansion grows totechniqueisillustratedinFigure705belowcover too large an area, it has lost its usefulness as a tool forThe fix expansion encompasses all the area in whichthe vessel could be located (as long as all sources of errorthe navigator, and he should obtain a new fix.0800C090CS12Figure 705.Fix expansion.All possible positions oftheship lie between the lines tangentto the expanding circlesExaminethisareafordangersDETERMININGANESTIMATEDPOSITIONAnestimated position isaDRposition corrected fortheLeeway and current effects combine to produce the mosteffects of leeway,steering error,and current.This sectionpronouncednaturaldynamiceffects ona transitingvessel.willbrieflydiscussthefactorsthatcausetheDRpositiontoInadditiontothesenaturalforces.helmsmanerroranddivergefrom the vessel's actual position.It will then discussgyro error combine to produce a steering error that causescalculating set and drift and applying these values to the DRadditional error in the DR.toobtainanestimatedposition.Finally,itwilldiscussdeter-707. Calculating Set And Drift And Plotting Anminingtheestimated courseand speedmadegood.EstimatedPosition706.FactorsAffectingDRPositionAccuracyItis difficult toquantifytheerrorsdiscussed aboveTidal current is the periodic horizontal movement ofindividually.However,thenavigator can easily quantifythe water's surface caused bythetide-affectinggravitation-their cumulative effect by comparing simultaneous fixal force of the moon,Current is the horizontal movementand DRpositions.Were thereno dynamic forces actingof the sea surface caused by meteorological, oceanograph-on the vessel and no steering error,the DR position andthe fixposition would coincide.However,they seldomic, or topographical effects.From whatever its source, thehorizontal motion of the sea's surfaceis an important dy-coincide.The fix is offset from theDRby a finitedis-namic force acting on a vessel moving through the water.tance.This offset is caused by the error factors discussedSet refers to the current's direction, and drift refers to theabove.current's speed.Note again thatthis methodology provides no meansLeeway is theleeward motion ofa vessel duetothattodeterminethemagnitudeof theindividual errors.Itcomponentofthewindvectorperpendiculartothevessel'ssimplyprovidesthenavigatorwithameasurablerepresen-track.tationoftheircombinedeffect

116 DEAD RECKONING course and speed from the fix position. Then, apply the fix expansion circle to the hourly DR’s. In the example given above, the DR after one hour would be enclosed by a circle of radius 2.5 nm, after two hours 4.5 nm, and so on. Having encircled the four hour DR positions with the error circles, the navigator then draws two lines originating tangent to the original error circle and simultaneously tangent to the other error circles. The navigator then closely examines the area between the two tangent lines for hazards to navigation. This technique is illustrated in Figure 705 below. The fix expansion encompasses all the area in which the vessel could be located (as long as all sources of error are considered). If any hazards are indicated within the cone, the navigator should be especially alert for those dan￾gers. If, for example, the fix expansion indicates that the vessel may be standing into shoal water, continuously mon￾itor the fathometer. Similarly, if the fix expansion indicated that the vessel might be approaching a charted obstruction, post extra lookouts. The fix expansion may grow at such a rate that it be￾comes unwieldy. Obviously, if the fix expansion grows to cover too large an area, it has lost its usefulness as a tool for the navigator, and he should obtain a new fix. DETERMINING AN ESTIMATED POSITION An estimated position is a DR position corrected for the effects of leeway, steering error, and current. This section will briefly discuss the factors that cause the DR position to diverge from the vessel’s actual position. It will then discuss calculating set and drift and applying these values to the DR to obtain an estimated position. Finally, it will discuss deter￾mining the estimated course and speed made good. 706. Factors Affecting DR Position Accuracy Tidal current is the periodic horizontal movement of the water’s surface caused by the tide-affecting gravitation￾al force of the moon. Current is the horizontal movement of the sea surface caused by meteorological, oceanograph￾ic, or topographical effects. From whatever its source, the horizontal motion of the sea’s surface is an important dy￾namic force acting on a vessel moving through the water. Set refers to the current’s direction, and drift refers to the current’s speed. Leeway is the leeward motion of a vessel due to that component of the wind vector perpendicular to the vessel’s track. Leeway and current effects combine to produce the most pronounced natural dynamic effects on a transiting vessel. In addition to these natural forces, helmsman error and gyro error combine to produce a steering error that causes additional error in the DR. 707. Calculating Set And Drift And Plotting An Estimated Position It is difficult to quantify the errors discussed above individually. However, the navigator can easily quantify their cumulative effect by comparing simultaneous fix and DR positions. Were there no dynamic forces acting on the vessel and no steering error, the DR position and the fix position would coincide. However, they seldom coincide. The fix is offset from the DR by a finite dis￾tance. This offset is caused by the error factors discussed above. Note again that this methodology provides no means to determine the magnitude of the individual errors. It simply provides the navigator with a measurable represen￾tation of their combined effect. Figure 705. Fix expansion. All possible positions of the ship lie between the lines tangent to the expanding circles. Examine this area for dangers

117DEADRECKONINGWhen thenavigatormeasuresthis combined effect,he708.Estimated CourseAnd Speed MadeGoodoftenreferstoitasthe"setanddrift."Recall fromabovethat these terms technically were restricted to describingThe direction of a straight line from the last fix to thecurrenteffects,However,eventhoughthefix-to-DRoffsetEP is the estimated track made good.The length of thisis caused by effects in addition to the current, this text willline divided by the time between the fix and the EP is thefollow the convention of referring to the offset as the setestimated speed madegood.and drift.Solvefortheestimatedtrack and speedbyusing a vectorThe set is the direction from the DR to the fix.The driftdiagram.Seetheexampleproblemsbelow.See.Figure708ais the distance in miles between the DR and thefix dividedby the number of hours since the DR was last reset.This isExample I:A ship on course 080,speed 10knots, istrueregardless ofthenumberofchanges of courseor speedsince the last fix.Calculate set and drift at every fixsteamingthroughacurrenthavinganestimatedsetof1400CalculateanEPbydrawingfromaDRpositionavecand drift of 2knots.tor whose direction equals the set and whose magnitudeRequired:Estimated track and speed madegood.equalstheproductofthedriftand thenumberofhourssinceSolution:See Figure 708a.From A, any convenientthe lastDRreset.SeeFigure707.Fromthe0900DRposipoint, drawAB,thecourse and speedofthe ship,in direction thenavigatordrawsa setand driftvector.Theend oftion080°,foradistanceof 10milesthat vectormarks the0900EP.Note that theEP is enclosedFrom B draw BC, the set and drift of the current,inin a squareand labeled horizontallywith thetime.Plot andevaluateanEPwitheveryDRpositiondirection140°fora distanceof2miles.Thedirection andGC.095080009000S15Figure 707. Determining an estimated position.BQSteered 080CourseSpeed Through Water 10toTrack Made Good089oCAGSpeedMadeGood112Figure708a.Findingtrackandspeedmadegoodthroughacurrent.ACourse To Make Good 095Speed Made Good 12.4第IDBCourse To Steer 083.5Speed Through Water 12cOFigure 7o8b.Finding the course to steer at agiven speed to make good a given course through a current

DEAD RECKONING 117 When the navigator measures this combined effect, he often refers to it as the “set and drift.” Recall from above that these terms technically were restricted to describing current effects. However, even though the fix-to-DR offset is caused by effects in addition to the current, this text will follow the convention of referring to the offset as the set and drift. The set is the direction from the DR to the fix. The drift is the distance in miles between the DR and the fix divided by the number of hours since the DR was last reset. This is true regardless of the number of changes of course or speed since the last fix. Calculate set and drift at every fix. Calculate an EP by drawing from a DR position a vec￾tor whose direction equals the set and whose magnitude equals the product of the drift and the number of hours since the last DR reset. See Figure 707. From the 0900 DR posi￾tion the navigator draws a set and drift vector. The end of that vector marks the 0900 EP. Note that the EP is enclosed in a square and labeled horizontally with the time. Plot and evaluate an EP with every DR position. 708. Estimated Course And Speed Made Good The direction of a straight line from the last fix to the EP is the estimated track made good. The length of this line divided by the time between the fix and the EP is the estimated speed made good. Solve for the estimated track and speed by using a vector diagram. See the example problems below. See. Figure 708a Example 1: A ship on course 080°, speed 10 knots, is steaming through a current having an estimated set of 140° and drift of 2 knots. Required: Estimated track and speed made good. Solution: See Figure 708a. From A, any convenient point, draw AB, the course and speed of the ship, in direc￾tion 080°, for a distance of 10 miles. From B draw BC, the set and drift of the current, in direction 140°, for a distance of 2 miles. The direction and Figure 707. Determining an estimated position. Figure 708a. Finding track and speed made good through a current. Figure 708b. Finding the course to steer at a given speed to make good a given course through a current

118DEADRECKONINGlengthofACaretheestimatedtrackandspeedmadeMeasurethelengthAD,12.4knots.Thisisthespeedgood.made good.Answers:Estimated track made good 089°,estimatedAnswers: Course to steer 083.5°, speed made good12.4knots.speed made good 11.2knots.To find the course to steer at a given speed to makeTofind the course to steer and the speed to use to makegood a desired course, plot the current vector from the ori-good a desired course and speed, proceed as follows:gin, A, instead of from B. See Figure 708b.SeeFigure708c.Example 2:The captain desires to make good a courseExample 3:Thecaptain desires to makegooda courseof095°througha current having a setof170°anda drift ofof 265°and a speed of 15knots through a current havinga2.5knots, usinga speed of 12 knots.setof185°and a driftof 3knots.Required:The courseto steer and the speed madegoodRequired:The course to steerandthe speed touseSolution:SeeFigure 708b.From A, any convenientSolution: See Figure 708c.From A, any comvenientpoint, draw line ABextending in the direction ofthe coursepoint,drawABinthedirectionofthecoursetobemadetobemadegood.0950good, 265° and for length equal to the speed to be madeFromA drawAC,thesetanddriff ofthecurrentgood, 15 knots.From A draw AC, the set and drift of the current.Using C as a center, swing an arc of radius CD, thespeedthroughthewater(12knots),intersectinglineABatDrawa straight linefrom Cto B.Thedirection of thisD.line,276,is the required course to steer; and thelength.Measurethedirectionof lineCD,083.5°Thisisthe14.8knots,isthe required speedAnswers:Coursetosteer276°,speedtouse14.8kn.course to steer.AGCourse To Make Good 265Speed To Make Good 15BGCourse To Steer 276Speed Through Water 14.8ecFigure708c.Findingcoursetosteerand speedto usetomakegood agiven course and speed through thecurrent

118 DEAD RECKONING length of AC are the estimated track and speed made good. Answers: Estimated track made good 089°, estimated speed made good 11.2 knots. To find the course to steer at a given speed to make good a desired course, plot the current vector from the ori￾gin, A, instead of from B. See Figure 708b. Example 2: The captain desires to make good a course of 095° through a current having a set of 170° and a drift of 2.5 knots, using a speed of 12 knots. Required: The course to steer and the speed made good. Solution: See Figure 708b. From A, any convenient point, draw line AB extending in the direction of the course to be made good, 095°. From A draw AC, the set and drift of the current. Using C as a center, swing an arc of radius CD, the speed through the water (12 knots), intersecting line AB at D. Measure the direction of line CD, 083.5°. This is the course to steer. Measure the length AD, 12.4 knots. This is the speed made good. Answers: Course to steer 083.5°, speed made good 12.4 knots. To find the course to steer and the speed to use to make good a desired course and speed, proceed as follows: See Figure 708c. Example 3: The captain desires to make good a course of 265° and a speed of 15 knots through a current having a set of 185° and a drift of 3 knots. Required: The course to steer and the speed to use. Solution: See Figure 708c. From A, any convenient point, draw AB in the direction of the course to be made good, 265° and for length equal to the speed to be made good, 15 knots. From A draw AC, the set and drift of the current. Draw a straight line from C to B. The direction of this line, 276°, is the required course to steer; and the length, 14.8 knots, is the required speed. Answers: Course to steer 276°, speed to use 14.8 kn. Figure 708c. Finding course to steer and speed to use to make good a given course and speed through the current