《航海学》课程参考文献（地文资料）CHAPTER 20 SIGHT REDUCTION

CHAPTER 20SIGHTREDUCTIONBASICPRINCIPLES2000.Introductiona chart required to plot this large distance would be imprac-tical.To eliminatethisproblem, the navigator doesnot plotReducing a celestial sight to obtain a line of positionthis line of position directly.Indeed,hedoes notplotthe GPconsists of six steps:atall,Rather, he chooses an assumed position (AP)near,but usually not coincident with,his DR positionThe navi-1.Correcting sextant altitude (hs)to obtainobservedgatorchoosestheAPs latitude and longitude tocorrespondaltitude (ho)to the entering arguments of LHA and latitude used in theDetermining the body's GHA and declination.SightReductionTables,From the SightReduction Tables,23Selectingan assumedposition andfindingthatpo-thenavigator computeswhatthebody's altitudewould havesition's localhourangle.been had it been measured from the AP.This yields theComputing altitudeand azimuth fortheassumed4computed altitude(h.).Hethen comparesthiscomputedvalue withtheobserved altitude(h.)obtained at his actualposition.Comparingcomputed and observedaltitudes.5position.The difference between the computed and ob-6Plottingthe lineofposition.served altitudes is directly proportional to the distancebetween the circles of equal altitudeforthe assumed posi-This chapter concentrates on using theNautical Alma-tion and the actual position.The Sight Reduction Tablesnac andPub.No.229,SightReductionTablesforMarinealsogivethedirectionfrom theGPto theAP.Having se-lected the assumed position,calculated the distanceNavigationTheintroductiontoeachvolumeofthe SightReductionbetweenthecirclesofeqgualaltitudeforthatAPandhisacTablescontains information:()discussinguse ofthepubli-tual position, and determined the direction from thecation in a varietyofspecial celestial navigationtechniquesassumed position to the body's GP,the navigator has(2)discussing interpolation, explaining the double secondenough informationtoplota lineofposition (LOP)difference interpolation required in some sightreductions.Toplot an LOP,plot the assumedposition on eitherachart or a plotting sheet.From the Sight Reduction Tables,and providing tables to facilitate the interpolation process;and(3)discussingthepublication'suseinsolvingproblemsdetermine: I)the altitude ofthe bodyfor a sight taken at theof great circle sailings.Prior to using the Sight ReductionAPand2)thedirectionfrom theAPto theGP.Then,deter-Tables,carefully read this introductorymaterialmine the difference between the body's calculated altitudeCelestial navigation involves determining a circularat thisAPand the body'smeasured altitude.This differencelineof position based on an observer's distance froma ce-represents the difference in radii between the equal altitudecircle passing through the AP and the equal altitude circlelestial body's geographicposition (GP).Should theobserverdeterminebothabody'sGPandhisdistancefrompassing through the actual position. Plot this differencethe GP,he would haveenough information to plot a line offromtheAPeithertowardsoraway fromtheGPalongtheposition; he would be somewhere on a circle whose centeraxis between theAP andtheGP.Finally,drawthe circle ofwas the GP and whose radius equaled his distance from thatequal altituderepresentingthecirclewiththebodys GP atGP.Thatcircle.fromallpointsonwhichabody'smeasuredthe center and with a radius equal to the distance betweenaltitude would be equal, is a circle of equal altitude.Therethe GP and the navigator's actual position.isadirectproportionalitybetweena body'saltitudeasmea-Onefinal consideration simplifiestheplottingof thesured by an observer and the distance of its GP from thatequalaltitudecircle.RecallthattheGPisusuallythousandsobserver, the lower the altitude, the farther away the GPofmiles awayfrom thenavigator's position.Theequal alti-Therefore,when an observer measures a body's altitude hetude circle's radius, therefore,canbe extremelylarge.Sinceobtains an indirectmeasureof thedistance between himselfthisradius is solarge,the navigator can approximatethe sec-andthebody's GP.Sightreductionistheprocessof con-tion close to his position with a straight linedrawnperpendicularto the line connecting theAPand theGP.Thisverting that indirectmeasurement into a line ofposition.Sight reduction reduces theproblem scaleto manage-straight line approximation is good onlyfor sights of rela-ablesize.Dependingonabody's altitude,its GPcouldbetivelylowaltitudes.Thehigherthealtitude,theshorterthethousandsofmilesfromtheobserver'sposition.ThesizeofdistancebetweentheGP and the actual position, and the307

307 CHAPTER 20 SIGHT REDUCTION BASIC PRINCIPLES 2000. Introduction Reducing a celestial sight to obtain a line of position consists of six steps: 1. Correcting sextant altitude (hs) to obtain observed altitude (ho). 2. Determining the body’s GHA and declination. 3. Selecting an assumed position and finding that po￾sition’s local hour angle. 4. Computing altitude and azimuth for the assumed position. 5. Comparing computed and observed altitudes. 6. Plotting the line of position. This chapter concentrates on using the Nautical Alma￾nac and Pub. No. 229, Sight Reduction Tables for Marine Navigation. The introduction to each volume of the Sight Reduction Tables contains information: (1) discussing use of the publi￾cation in a variety of special celestial navigation techniques; (2) discussing interpolation, explaining the double second difference interpolation required in some sight reductions, and providing tables to facilitate the interpolation process; and (3) discussing the publication’s use in solving problems of great circle sailings. Prior to using the Sight Reduction Tables, carefully read this introductory material. Celestial navigation involves determining a circular line of position based on an observer’s distance from a ce￾lestial body’s geographic position (GP). Should the observer determine both a body’s GP and his distance from the GP, he would have enough information to plot a line of position; he would be somewhere on a circle whose center was the GP and whose radius equaled his distance from that GP. That circle, from all points on which a body’s measured altitude would be equal, is a circle of equal altitude. There is a direct proportionality between a body’s altitude as mea￾sured by an observer and the distance of its GP from that observer; the lower the altitude, the farther away the GP. Therefore, when an observer measures a body’s altitude he obtains an indirect measure of the distance between himself and the body’s GP. Sight reduction is the process of con￾verting that indirect measurement into a line of position. Sight reduction reduces the problem scale to manage￾able size. Depending on a body’s altitude, its GP could be thousands of miles from the observer’s position. The size of a chart required to plot this large distance would be imprac￾tical. To eliminate this problem, the navigator does not plot this line of position directly. Indeed, he does not plot the GP at all. Rather, he chooses an assumed position (AP) near, but usually not coincident with, his DR position. The navi￾gator chooses the AP’s latitude and longitude to correspond to the entering arguments of LHA and latitude used in the Sight Reduction Tables. From the Sight Reduction Tables, the navigator computes what the body’s altitude would have been had it been measured from the AP. This yields the computed altitude (hc). He then compares this computed value with the observed altitude (ho) obtained at his actual position. The difference between the computed and ob￾served altitudes is directly proportional to the distance between the circles of equal altitude for the assumed posi￾tion and the actual position. The Sight Reduction Tables also give the direction from the GP to the AP. Having se￾lected the assumed position, calculated the distance between the circles of equal altitude for that AP and his ac￾tual position, and determined the direction from the assumed position to the body’s GP, the navigator has enough information to plot a line of position (LOP). To plot an LOP, plot the assumed position on either a chart or a plotting sheet. From the Sight Reduction Tables, determine: 1) the altitude of the body for a sight taken at the AP and 2) the direction from the AP to the GP. Then, deter￾mine the difference between the body’s calculated altitude at this AP and the body’s measured altitude. This difference represents the difference in radii between the equal altitude circle passing through the AP and the equal altitude circle passing through the actual position. Plot this difference from the AP either towards or away from the GP along the axis between the AP and the GP. Finally, draw the circle of equal altitude representing the circle with the body’s GP at the center and with a radius equal to the distance between the GP and the navigator’s actual position. One final consideration simplifies the plotting of the equal altitude circle. Recall that the GP is usually thousands of miles away from the navigator’s position. The equal alti￾tude circle’s radius, therefore, can be extremely large. Since this radius is so large, the navigator can approximate the sec￾tion close to his position with a straight line drawn perpendicular to the line connecting the AP and the GP. This straight line approximation is good only for sights of rela￾tively low altitudes. The higher the altitude, the shorter the distance between the GP and the actual position, and the

308SIGHTREDUCTIONsmaller the circle ofequal altitude. The shorter this distance,theradii of the circles of equal altitudepassingthroughthethegreater the inaccuracy introduced bythis approximation.AP and the observers actual position.The position havingthe greater altitude is on the circle of smaller radius and is2001.SelectionOfTheAssumedPosition(AP)closerto the observed body'sGP.InFigure2003,theAP isshown on the inner circle. Therefore, h。 is greater than ho.Use the following arguments when entering the SightExpress thealtitude interceptin nautical miles and la-ReductionTablestocomputealtitude(h)andazimuthbel it T or A to indicate whether the line of position istoward orawayfromtheGP,asmeasuredfromtheAP.1. Latitude (L).A useful aid in remembering the relation between ho.he, and the altitude intercept is:H, M, I,for H,More o-2. Declination (d or Dec.)3.ward. Another is C-G-A:Computed Greater Away,Local hour angle (LHA)remembered as Coast Guard Academy. In other words,ifh。isgreaterthan h,theline ofposition intersects apointmea-Latitude and LHA are functions of the assumed posi-sured from the AP towards the GP a distance equal to thetion.SelectanAP longituderesulting in a wholedegreeofaltitudeintercept.DrawtheLOPthroughthis intersectionLHAand an AP latitude equal tothat whole degree of lati-pointperpendiculartotheaxisbetweentheAPandGPtude closest to the DR position. Selecting the AP in thismannereliminates interpolationforLHAand latitudeinthe2003.PlottingTheLineOfPositionSight Reduction Tables.Reducing the sight usinga computer or calculator sim-plifies this AP selection process. Simply choose anyPlotthelineof positionasshown inFigure2003.Plotconvenient position such as the vessel's DR position as thethe AP first; then plot the azimuth line from the AP towardassumedposition.Entertheinformationrequiredbythespe-orawayfromtheGP.Then, measurethe altitudeinterceptalong this line. At the point on the azimuth line equal to thecific celestial program in use.Usingacalculatorreduces themath and interpolation errors inherent in using the Sight Re-interceptdistance,drawa lineperpendicularto the azimuthduction tables.Enter the required calculatordata carefullyline.This perpendicularrepresentsthat sectionofthecircleofequal altitudepassing throughthe navigator'sactualpo-2002.Comparison Of Computed And Observedsition.This is theline of positionAltitudesA navigator often takes sights of more than one celes-tial body when determining a celestial fix.After plotting theThedifferencebetween the computedaltitude(h.)andlines of position from these several sights, advance there-the observed altitude (h)is the altitude intercept (a)sulting LOP's along the track to the time of the last sightThe altitude intercept is the difference in the length ofand label theresulting fixwith the time of this last sight.SEASEQUALTITDEFOR拉COMPUTEDofALCIRCLE0GPALDEINTERCEPTFigure2003.Thebasisforthe lineof positionfroma celestial observation

308 SIGHT REDUCTION smaller the circle of equal altitude. The shorter this distance, the greater the inaccuracy introduced by this approximation. 2001. Selection Of The Assumed Position (AP) Use the following arguments when entering the Sight Reduction Tables to compute altitude (hc) and azimuth: 1. Latitude (L). 2. Declination (d or Dec.). 3. Local hour angle (LHA). Latitude and LHA are functions of the assumed posi￾tion. Select an AP longitude resulting in a whole degree of LHA and an AP latitude equal to that whole degree of lati￾tude closest to the DR position. Selecting the AP in this manner eliminates interpolation for LHA and latitude in the Sight Reduction Tables. Reducing the sight using a computer or calculator sim￾plifies this AP selection process. Simply choose any convenient position such as the vessel’s DR position as the assumed position. Enter the information required by the spe￾cific celestial program in use. Using a calculator reduces the math and interpolation errors inherent in using the Sight Re￾duction tables. Enter the required calculator data carefully. 2002. Comparison Of Computed And Observed Altitudes The difference between the computed altitude (hc) and the observed altitude (ho) is the altitude intercept (a). The altitude intercept is the difference in the length of the radii of the circles of equal altitude passing through the AP and the observers actual position. The position having the greater altitude is on the circle of smaller radius and is closer to the observed body’s GP. In Figure 2003, the AP is shown on the inner circle. Therefore, hc is greater than ho. Express the altitude intercept in nautical miles and la￾bel it T or A to indicate whether the line of position is toward or away from the GP, as measured from the AP. A useful aid in remembering the relation between ho, hc, and the altitude intercept is: Ho Mo To for Ho More To￾ward. Another is C-G-A: Computed Greater Away, remembered as Coast Guard Academy. In other words, if ho is greater than hc, the line of position intersects a point mea￾sured from the AP towards the GP a distance equal to the altitude intercept. Draw the LOP through this intersection point perpendicular to the axis between the AP and GP. 2003. Plotting The Line Of Position Plot the line of position as shown in Figure 2003. Plot the AP first; then plot the azimuth line from the AP toward or away from the GP. Then, measure the altitude intercept along this line. At the point on the azimuth line equal to the intercept distance, draw a line perpendicular to the azimuth line. This perpendicular represents that section of the circle of equal altitude passing through the navigator’s actual po￾sition. This is the line of position. A navigator often takes sights of more than one celes￾tial body when determining a celestial fix. After plotting the lines of position from these several sights, advance the re￾sulting LOP’s along the track to the time of the last sight and label the resulting fix with the time of this last sight. Figure 2003. The basis for the line of position from a celestial observation

SIGHT REDUCTION3092004.Recommended SightReductionProcedureliststhesecorrections.Additional Correction: Enter this additional correctionJust as it is important to understand the theory of sightfromTableA4 located at thefront oftheAlmanac whenob-taining a sight under non-standard atmospheric temperaturereduction,itisalsoimportanttodevelopaworkingproce-dure to reduce celestial sights accurately,Sight reductionand pressure conditions.This correction is a function of atinvolves several consecutive steps, the accuracy of eachmosphericpressure,temperature,and apparentaltitudecompletelydependenton theaccuracyofthesteps that wentHorizontal Parallax Correction: This correction isbefore.Sight reduction tableshave,for the most part, re-uniqueto reducing moon sights.Obtain the HP.correction val-duced the mathematics involved to simple addition anduefromthedailypagesoftheAlmanac.EntertheH.Pcorrectionsubtraction.However,careless errors will render even thetableatthebackoftheAlmanacwiththisvalue.TheH.Pcorrecmost skillfully measured sights inaccurate.The navigatortion is a function ofthe limb of the moon used (upper or lower),mustworkmethodicallytoreducethesecarelesserrorsthe apparent altitude, and the H.P. correction factor.The H.PNavalnavigatorswillmost likelyuseOPNAV3530,U.Scorrection is always added totheapparentaltitudeNavy Navigation Workbook,which containspre-formattedMoonUpper Limb Correction:Enter-3o'forthispages with “strip forms"to guide the navigator through sightcorrection if the sight was of the upperlimb ofthemoon.reduction.Avarietyofcommercially-producedformsarealsoCorrection to Apparent Altitude: Sum the altitude coravailable.Pick a form and learn its method thoroughly.Withrection,theMarsor Venus additional correction,the additionalfamiliarity will comeincreasing understandingcorrection,thehorizontal parallax correction,and the moon'sFigure 2004 represents a functional and completeupperlimb correction.Be careful to determine and carry the al-worksheetdesignedtoensureamethodical approachtoanygebraic sign ofthe corrections and their sum correctly.Entersight reduction problem. The recommended procedure dis-thissumasthecorrectiontotheapparentaltitudecussed below is nottheonlyoneavailable;however,theObserved Altitude:Apply the Correction to Apparentnavigator who uses it can be assured that he has consideredAltitude algebraically to the apparent altitude.The resultiseverycorrectionrequiredtoobtainanaccuratefix.theobservedaltitudeSECTION ONE consists of two parts: (1) CorrectingSECTION TWO determines the Greenwich Meansextantaltitudetoobtainapparentaltitude,and(2)CorrectTime (GMT) and GMT date of the sight.ing theapparentaltitudetoobtain theobserved altitudeDate:Enter thelocal time zone date of the sight.Body:Enter the nameof the body whose altitude youDR Latitude:Enter the dead reckoning latitude ofthehave measured.Ifusing the sun or the moon,indicatewhichvessel.limb was measured.DR Longitude: Enter the dead reckoning longitude ofIndex Correction:This is determined by the charac-the vessel.teristics ofthe individual sextant used.Chapter 16discussesObservation Time: Enter the local time ofthe sight asdetermining its magnitude and algebraic sign.recorded on the ship's chronometer or othertimepiece.Dip: The dip correction is a function of the height ofWatchError:Enteracorrectionforanyknown watcheye ofthe observer.It is always negative, its magnitude iserror.determinedfromtheDipTableontheinsidefrontcovertofZone Time: Correct the observation time with watchthe Nautical Almanac.errortodeterminezonetime.Sum:Enter the algebraic sumofthedip correction andZone Description: Enter the zone description of thethe index correction.time zone indicated by the DR longitude. If the longitude isSextant Altitude: Enter the altitude of the body mea-west of the Greenwich Meridian, the zone description issured by the sextant.positive.Conversely, if the longitude is east of the Green-Apparent Altitude: Apply the sum correction deter-wich Meridian, the zone description is negative.The zonemined above to the measured altitude and enter the result asdescription represents the correction necessary to convertlocal timetoGreenwichMeanTime.the apparent altitude.Greenwich Mean Time:Add to the zonedescriptionAltitude Correction:Every observation requires analtitude correction.This correction is a function of the ap-thezonetimetodetermineGreenwichMeanTimeparentaltitudeofthebody.TheAlmanaccontainstablesforDate: Carefully evaluate the time correction applieddetermining these corrections. For the sun, planets, andaboveand determine ifthecorrection has changed thedatestars,thesetablesare located on theinsidefrontcoverandEnter theGMTdate.facing page.For the moon, these tables are located on theback inside cover and preceding page.SECTIONTHREE determines two of the threeargu-Mars or Venus Additional Correction: As the name im-mentsrequiredtoentertheSightReductionTables:Localplies, this correction is applied to sights ofMars and Venus.TheHour Angle (LHA)and Declination.This section employscorrection isafunctionofthe planetmeasured, the timeofyear,the principle that a celestial body's LHA is the algebraic sumandtheapparentaltitude.The insidefront coveroftheAlmanacofitsGreenwichHourAngle(GHA)andtheobserver'slon

SIGHT REDUCTION 309 2004. Recommended Sight Reduction Procedure Just as it is important to understand the theory of sight reduction, it is also important to develop a working proce￾dure to reduce celestial sights accurately. Sight reduction involves several consecutive steps, the accuracy of each completely dependent on the accuracy of the steps that went before. Sight reduction tables have, for the most part, re￾duced the mathematics involved to simple addition and subtraction. However, careless errors will render even the most skillfully measured sights inaccurate. The navigator must work methodically to reduce these careless errors. Naval navigators will most likely use OPNAV 3530, U.S. Navy Navigation Workbook, which contains pre-formatted pages with “strip forms” to guide the navigator through sight reduction. A variety of commercially-produced forms are also available. Pick a form and learn its method thoroughly. With familiarity will come increasing understanding. Figure 2004 represents a functional and complete worksheet designed to ensure a methodical approach to any sight reduction problem. The recommended procedure dis￾cussed below is not the only one available; however, the navigator who uses it can be assured that he has considered every correction required to obtain an accurate fix. SECTION ONE consists of two parts: (1) Correcting sextant altitude to obtain apparent altitude; and (2) Correct￾ing the apparent altitude to obtain the observed altitude. Body: Enter the name of the body whose altitude you have measured. If using the sun or the moon, indicate which limb was measured. Index Correction: This is determined by the charac￾teristics of the individual sextant used. Chapter 16 discusses determining its magnitude and algebraic sign. Dip: The dip correction is a function of the height of eye of the observer. It is always negative; its magnitude is determined from the Dip Table on the inside front covert of the Nautical Almanac. Sum: Enter the algebraic sum of the dip correction and the index correction. Sextant Altitude: Enter the altitude of the body mea￾sured by the sextant. Apparent Altitude: Apply the sum correction deter￾mined above to the measured altitude and enter the result as the apparent altitude. Altitude Correction: Every observation requires an altitude correction. This correction is a function of the ap￾parent altitude of the body. The Almanac contains tables for determining these corrections. For the sun, planets, and stars, these tables are located on the inside front cover and facing page. For the moon, these tables are located on the back inside cover and preceding page. Mars or Venus Additional Correction: As the name im￾plies, this correction is applied to sights of Mars and Venus. The correction is a function of the planet measured, the time of year, and the apparent altitude. The inside front cover of the Almanac lists these corrections. Additional Correction: Enter this additional correction from Table A 4 located at the front of the Almanac when ob￾taining a sight under non-standard atmospheric temperature and pressure conditions. This correction is a function of at￾mospheric pressure, temperature, and apparent altitude. Horizontal Parallax Correction: This correction is unique to reducing moon sights. Obtain the H.P. correction val￾ue from the daily pages of the Almanac. Enter the H.P correction table at the back of the Almanac with this value. The H.P correc￾tion is a function of the limb of the moon used (upper or lower), the apparent altitude, and the H.P. correction factor. The H.P. correction is always added to the apparent altitude. Moon Upper Limb Correction: Enter -30' for this correction if the sight was of the upper limb of the moon. Correction to Apparent Altitude: Sum the altitude cor￾rection, the Mars or Venus additional correction, the additional correction, the horizontal parallax correction, and the moon’s upper limb correction. Be careful to determine and carry the al￾gebraic sign of the corrections and their sum correctly. Enter this sum as the correction to the apparent altitude. Observed Altitude: Apply the Correction to Apparent Altitude algebraically to the apparent altitude. The result is the observed altitude. SECTION TWO determines the Greenwich Mean Time (GMT) and GMT date of the sight. Date: Enter the local time zone date of the sight. DR Latitude: Enter the dead reckoning latitude of the vessel. DR Longitude: Enter the dead reckoning longitude of the vessel. Observation Time: Enter the local time of the sight as recorded on the ship’s chronometer or other timepiece. Watch Error: Enter a correction for any known watch error. Zone Time: Correct the observation time with watch error to determine zone time. Zone Description: Enter the zone description of the time zone indicated by the DR longitude. If the longitude is west of the Greenwich Meridian, the zone description is positive. Conversely, if the longitude is east of the Green￾wich Meridian, the zone description is negative. The zone description represents the correction necessary to convert local time to Greenwich Mean Time. Greenwich Mean Time: Add to the zone description the zone time to determine Greenwich Mean Time. Date: Carefully evaluate the time correction applied above and determine if the correction has changed the date. Enter the GMT date. SECTION THREE determines two of the three argu￾ments required to enter the Sight Reduction Tables: Local Hour Angle (LHA) and Declination. This section employs the principle that a celestial body’s LHA is the algebraic sum of its Greenwich Hour Angle (GHA) and the observer’s lon-

310SIGHTREDUCTIONSECTIONONE:OBSERVEDALTITUDEBodyIndexCorrectionDip (height of eye)SumSextant Altitude (hs)Apparent Altitude (h)Altitude CorrectionMars orVenus Additional CorrectionAdditional CorrectionHorizontal ParallaxCorrectionMoon Upper Limb CorrectionCorrection to Apparent Altitude (ha)Observed Altitude (ha)SECTIONTWO:GMT TIMEANDDATEDateDR LatitudeDR LongitudeObservation TimeWatchErrorZone TimeZone DescriptionGreenwich Mean TimeDateGMTSECTIONTHREE:LOCALHOURANGLEANDDECLINATIONTabulated GHA andy CorrectionFactorGHA IncrementSidereal HourAngle (SHA) orvCorrectionGHA+or-360°if neededAssumed Longitude (-W,+E)Local HourAngle (LHA)Tabulated Declination anddCorrection FactordCorrectionTrue DeclinationAssumed LatitudeSECTIONFOUR:ALTITUDEINTERCEPTANDAZIMUTHDeclination Increment anddInterpolation FactorComputed Altitude (Tabulated)Double Second Difference CorrectionTotal CorrectionComputed Altitude (he)Observed Altitude (b)-Altitude InterceptAzimuthAngleTrue AzimuthFigure 2004. Complete sight reduction form

310 SIGHT REDUCTION Figure 2004. Complete sight reduction form

SIGHTREDUCTION311gitude.Therefore,thebasicmethod employed in this sectionaddition or subtraction.is:(I)Determine the body's GHA;(2)Determine an as-Assumed Longitude: Ifthe vessel is west of the primesumed longitude;(3)Algebraically combine the twomeridian,theassumed longitudewill be subtracted from thequantities,remembering to subtract a westem assumed lon-GHA to determine LHA.If the vessel is east of the primegitude from GHA and to add an eastern longitude to GHA;meridian, the assumed longitude will be added to the GHAand(4)Extractthedeclinationofthebodyfromtheappropri-to determine the LHA.Select the assumed longitude toateAlmanactable,correctingthetabularvalue ifrequired.meet the following two criteria: (1) When added or sub-tracted(asapplicable)totheGHA determined above,a() Tabulated GHA and (2) v Correction Factor:whole degree ofLHA will result, and (2) It is the longitudeclosesttothatDRlongitudethat meets criterion(1)above(1)Forthesun,themoon,or aplanet, extractthevalueforthewhole hourofGHAcorrespondingtothe sight.Forexam-Local Hour Angle(LHA):Combine the body's GHAple, if the sight was obtained at 13-50-45 GMT,extract thewith theassumedlongitudeasdiscussed abovetodetermineGHAvaluefor 1300.For a star sightreduction,extract theval-the body's LHA.ue of the GHA of Aries (GHA ),again using the value(I) Tabulated Declination and d Correction factor:corresponding to the wholehourofthetime ofthe sight.(1)Obtain the tabulated declination for the sun, the moon,(2)Fora planet ormoon sight reduction, enter theythestars,ortheplanetsfromthedailypagesoftheAlmanac.The declination values for the stars are given for the entirecorrectionvalue.Thisquantityisnotapplicabletoasunorstar sight.The v correction for a planet sight is found at thethreedayperiod coveredbythedailypageof theAlmanacbottom of thecolumnforeachparticularplanet.Thevcor-The values for the sun, moon, and planets are listed in hourlyrectionfactorforthemoonislocateddirectlybesidetheincrements.Forthesebodies,enterthedeclinationvaluefortabulated hourly GHA values.The y correction factor forthe whole hour ofthe sight. For example, if the sight is at 12-58-40,enter the tabulated declinationfor 1200.(2)There isthemoonisalwayspositive.Ifaplanet'svcorrectionfactoris listedwithout sign,it is positive.If listed witha negativenod correction factor for a star sight.There are d correctionsign, the planet's correction factor is negative.This vcor-factors for sun,moon,andplanetsights.Similarto the v cor-rectionfactorisnotthemagnitudeoftheycorrection:itisrectionfactordiscussedabove.thedcorrectionfactordoesused latertoentertheIncrementsand Correctiontabletonot equal the magnitude of the d correction, it provides theargumenttoenterthe Increments and Correctionstables indetermine themagnitude of the correction.theAlmanac.Thesignofthedcorrectionfactor.whichdeGHAIncrement:TheGHA incrementserves as an intermines the sign of the d correction, is determined by theterpolationfactor.correctingforthetimethatthe sighttrendofdeclinationvalues.notthetrend ofdvalues.Theddiffered fromthe wholehour.For example, in the sight at13-50-45 discussed above,this increment correction ac-correction factor is simply an interpolation factor;therefore,to determine its sign, look at the declination values for thecounts for the 50 minutes and 45 seconds after thewholehoursthatframethetimeofthesight.Forexample,supposehour at whichthe sightwas taken.Obtain this correctionthe sight was taken on a certain date at 12-30-00.ComparevaluefromtheIncrementsandCorrectionstablesintheAl-thedeclination valuefor1200and1300and determine if themanac.The entering arguments for thesetables are thedeclinationhasincreasedordecreased.Ifithasincreasedminutesandsecondsafterthehouratwhichthesightwasthe d correction factor is positive.If it has decreased, the dtaken and the body sighted Extract the proper correctioncorrectionfactorisnegative.fromtheapplicabletable andenterthecorrection hered correction:Enter the Increments and Correctionsta-Sidereal Hour Angle or v Correction: If reducing astar sight, enter the star's Sidereal Hour Angle (SHA).Theblewiththedcorrectionfactordiscussedabove.Extracttheproper correction, being careful to retain the proper sign.SHA is found in the star column ofthe daily pages of theTrue Declination: Combine the tabulated declinationAlmanac.TheSHAcombinedwiththeGHAofAriesre-Sults in the star's GHA, The SHA entry is applicable onlyand thed correctionto obtainthetrue declination.to a star.Ifreducing aplanetor moon sight,obtain the vcor-Assumed Latitude:Choose as the assumed latituderectionfrom theIncrements andCorrectionsTable.Thethat whole value of latitudeclosestto the vessel's DR lati-correctionisafunctionof onlytheycorrectionfactor:itstude.If the assumed latitude and declination are both northmagnitudeis the samefor boththemoon and theplanetsorboth south,label theassumed latitude same.If oneisGHA:A star's GHA equals the sum of the Tabulatednorth and the other is south, label the assumed latitudeGHAofAries, the GHAIncrement, and the star's SHAcontrary.Thesun'sGHAequalsthesumoftheTabulatedGHAandtheGHAIncrement.TheGHA of the moon or a planetSECTION FOUR uses the arguments of assumed lati-equals the sum of the Tabulated GHA, the GHA Increment,tude,LHA, and declination determined in Section Three to enterand the v correction.theSightReductionTablestodetermineazimuthandcomputed+ or-360° (if needed): Since the LHA will be deter-altitude.Then, Section Four compares computed and observedminedfromsubtractingoraddingtheassumedlongitudetoaltitudes to calculate the altitude intercept The navigator thentheGHA,adjusttheGHAby360°if needed tofacilitate thehasenoughinformationtoplotthelineofposition

SIGHT REDUCTION 311 gitude. Therefore, the basic method employed in this section is: (1) Determine the body’s GHA; (2) Determine an as￾sumed longitude; (3) Algebraically combine the two quantities, remembering to subtract a western assumed lon￾gitude from GHA and to add an eastern longitude to GHA; and (4) Extract the declination of the body from the appropri￾ate Almanac table, correcting the tabular value if required. (1) Tabulated GHA and (2) v Correction Factor: (1) For the sun, the moon, or a planet, extract the value for the whole hour of GHA corresponding to the sight. For exam￾ple, if the sight was obtained at 13-50-45 GMT, extract the GHA value for 1300. For a star sight reduction, extract the val￾ue of the GHA of Aries (GHA ), again using the value corresponding to the whole hour of the time of the sight. (2) For a planet or moon sight reduction, enter the v correction value. This quantity is not applicable to a sun or star sight. The v correction for a planet sight is found at the bottom of the column for each particular planet. The v cor￾rection factor for the moon is located directly beside the tabulated hourly GHA values. The v correction factor for the moon is always positive. If a planet’s v correction factor is listed without sign, it is positive. If listed with a negative sign, the planet’s v correction factor is negative. This v cor￾rection factor is not the magnitude of the v correction; it is used later to enter the Increments and Correction table to determine the magnitude of the correction. GHA Increment: The GHA increment serves as an in￾terpolation factor, correcting for the time that the sight differed from the whole hour. For example, in the sight at 13-50-45 discussed above, this increment correction ac￾counts for the 50 minutes and 45 seconds after the whole hour at which the sight was taken. Obtain this correction value from the Increments and Corrections tables in the Al￾manac. The entering arguments for these tables are the minutes and seconds after the hour at which the sight was taken and the body sighted. Extract the proper correction from the applicable table and enter the correction here. Sidereal Hour Angle or v Correction: If reducing a star sight, enter the star’s Sidereal Hour Angle (SHA). The SHA is found in the star column of the daily pages of the Almanac. The SHA combined with the GHA of Aries re￾sults in the star’s GHA. The SHA entry is applicable only to a star. If reducing a planet or moon sight, obtain the v cor￾rection from the Increments and Corrections Table. The correction is a function of only the v correction factor; its magnitude is the same for both the moon and the planets. GHA: A star’s GHA equals the sum of the Tabulated GHA of Aries, the GHA Increment, and the star’s SHA. The sun’s GHA equals the sum of the Tabulated GHA and the GHA Increment. The GHA of the moon or a planet equals the sum of the Tabulated GHA, the GHA Increment, and the v correction. + or – 360° (if needed): Since the LHA will be deter￾mined from subtracting or adding the assumed longitude to the GHA, adjust the GHA by 360° if needed to facilitate the addition or subtraction. Assumed Longitude: If the vessel is west of the prime meridian, the assumed longitude will be subtracted from the GHA to determine LHA. If the vessel is east of the prime meridian, the assumed longitude will be added to the GHA to determine the LHA. Select the assumed longitude to meet the following two criteria: (1) When added or sub￾tracted (as applicable) to the GHA determined above, a whole degree of LHA will result; and (2) It is the longitude closest to that DR longitude that meets criterion (1) above. Local Hour Angle (LHA): Combine the body’s GHA with the assumed longitude as discussed above to determine the body’s LHA. (1) Tabulated Declination and d Correction factor: (1) Obtain the tabulated declination for the sun, the moon, the stars, or the planets from the daily pages of the Almanac. The declination values for the stars are given for the entire three day period covered by the daily page of the Almanac. The values for the sun, moon, and planets are listed in hourly increments. For these bodies, enter the declination value for the whole hour of the sight. For example, if the sight is at 12- 58-40, enter the tabulated declination for 1200. (2) There is no d correction factor for a star sight. There are d correction factors for sun, moon, and planet sights. Similar to the v cor￾rection factor discussed above, the d correction factor does not equal the magnitude of the d correction; it provides the argument to enter the Increments and Corrections tables in the Almanac. The sign of the d correction factor, which de￾termines the sign of the d correction, is determined by the trend of declination values, not the trend of d values. The d correction factor is simply an interpolation factor; therefore, to determine its sign, look at the declination values for the hours that frame the time of the sight. For example, suppose the sight was taken on a certain date at 12-30-00. Compare the declination value for 1200 and 1300 and determine if the declination has increased or decreased. If it has increased, the d correction factor is positive. If it has decreased, the d correction factor is negative. d correction: Enter the Increments and Corrections ta￾ble with the d correction factor discussed above. Extract the proper correction, being careful to retain the proper sign. True Declination: Combine the tabulated declination and the d correction to obtain the true declination. Assumed Latitude: Choose as the assumed latitude that whole value of latitude closest to the vessel’s DR lati￾tude. If the assumed latitude and declination are both north or both south, label the assumed latitude same. If one is north and the other is south, label the assumed latitude contrary. SECTION FOUR uses the arguments of assumed lati￾tude, LHA, and declination determined in Section Three to enter the Sight Reduction Tables to determine azimuth and computed altitude. Then, Section Four compares computed and observed altitudes to calculate the altitude intercept. The navigator then has enough information to plot the line of position

312SIGHTREDUCTIONTotal Correction: The total correction is the sum of(1) Declination Increment and (2)d Interpolation Fac-tor: Note that two ofthe threearguments used to entertheSightthe double second difference (if required)and the interpo-Reduction Tables, LHA and latitude,are whole degree values.lationcorrections.Calculate the interpolationcorrectionbySection Three does not determine the third argument, declina-dividing thedeclination increment by 60'and multiply thetion, as a whole degree. Therefore, the navigator mustresulting quotient by thed interpolation factorinterpolateintheSightReductionTablesfordeclination,givenComputed Altitude(h):Apply the total correction,whole degrees of LHA and latitude.Thefirst steps of Sectionbeing careful to carry the correct sign, to the tabulated com-Four involve this interpolation for declination. Sincedeclinationputed altitude.This yields the computed altitudevalues are tabulated every whole degree in the Sight ReductionObserved Altitude (ho):Enter the observed altitudeTables,thedeclination increment is theminutes andtenthsofthefromSectionOnetrue declination.For example,ifthe true declination is 13°15.6,AltitudeIntercept:Compare h.and h.Subtract thethen thedeclination increment is15.6.(2)TheSightReductionsmallerfromthelarger.The resultingdifference is themagTables also list a d Interpolation Factor.This is the magnitude ofnitude of the altitude intercept.If h,is greater than h.,thenthedifferencebetweenthetwo successivetabulatedvaluesforlabel the altitude intercept toward.If heis greater than hodeclination that frame the true declination Therefore,for the hy-then label the altitude interceptawaypothetical declination listed above,thetabulated d interpolationAzimuth Angle: Obtain the azimuth angle(Z)fromfactor listed in the tablewould be the difference between decli-the Sight Reduction Tables, using the same argumentsnation values givenfor13°and140.Ifthe declination increaseswhich determined tabulated computed altitude. Visual in-between these two values, d is positive.If the declination de-terpolation is sufficientlyaccurate.creases between these two values,d is negative.True Azimuth:Calculatethe true azimuth (Z,)fromComputed Altitude (Tabulated):Enter the Sight Re-theazimuth angle (Z)as follows:duction Tableswith thefollowing arguments:(1)LHAa)If in northernlatitudes:from SectionThree;(2)assumedlatitude from SectionThree; (3) the whole degree value of the true declinationForexample,ifthe truedeclination were13°15.6,thenen-ter the Sight Reduction Tables with 13°as the value forLHA>180°,then Z,=Zdeclination.Record thetabulated computed altitude.LHA180°,thenZ,=180°-Zployed, refer to detailed instructions in the Sight Reduction=180°+ZLHA<180°, then ZTables introduction.SIGHTREDUCTIONThe section above discussed the basic theory of sight+2.1The DR latitudefor both sights is 39°N.The DR lon-reduction and proposed a method tobefollowed when re-gitude for the Spica sight is 157°10W.TheDR longitudefor theKochab sight is 15708.0W.Determine the inter-ducing sights.This section puts that method into practice inreducing sights of a star, the sun, the moon, and planets.ceptand azimuth forboth sights.SeeFigure2005First, convert the sextant altitudes to observed alti-tudes. Reduce the Spica sight first:2005.Reducing Star Sights ToAFixBodySpicaOnMay16,1995,at thetimes indicated,the navigator+2.1°IndexCorrectiontakes and records thefollowing sights:-6.7Dip (height 48 ft)-4.6'SumStarSextantAltitudeZoneTime32°34.8Sextant Altitude (hs)32°30.2'47°19.1"20-07-43Apparent Altitude (ha)Kochab32°34.8"20-11-26Spica-1.5'AltitudeCorrection0AdditionalCorrection0Height of eyeis48 feetand index correction(IC)isHorizontal Parallax

312 SIGHT REDUCTION (1) Declination Increment and (2) d Interpolation Fac￾tor: Note that two of the three arguments used to enter the Sight Reduction Tables, LHA and latitude, are whole degree values. Section Three does not determine the third argument, declina￾tion, as a whole degree. Therefore, the navigator must interpolate in the Sight Reduction Tables for declination, given whole degrees of LHA and latitude. The first steps of Section Four involve this interpolation for declination. Since declination values are tabulated every whole degree in the Sight Reduction Tables, the declination increment is the minutes and tenths of the true declination. For example, if the true declination is 13° 15.6’, then the declination increment is 15.6’. (2) The Sight Reduction Tables also list a d Interpolation Factor. This is the magnitude of the difference between the two successive tabulated values for declination that frame the true declination. Therefore, for the hy￾pothetical declination listed above, the tabulated d interpolation factor listed in the table would be the difference between decli￾nation values given for 13° and 14°. If the declination increases between these two values, d is positive. If the declination de￾creases between these two values, d is negative. Computed Altitude (Tabulated): Enter the Sight Re￾duction Tables with the following arguments: (1) LHA from Section Three; (2) assumed latitude from Section Three; (3) the whole degree value of the true declination. For example, if the true declination were 13° 15.6’, then en￾ter the Sight Reduction Tables with 13° as the value for declination. Record the tabulated computed altitude. Double Second Difference Correction: Use this cor￾rection when linear interpolation of declination for computed altitude is not sufficiently accurate due to the non linear change in the computed altitude as a function of declination. The need for double second difference interpolation is indi￾cated by the d interpolation factor appearing in italic type followed by a small dot. When this procedure must be em￾ployed, refer to detailed instructions in the Sight Reduction Tables introduction. Total Correction: The total correction is the sum of the double second difference (if required) and the interpo￾lation corrections. Calculate the interpolation correction by dividing the declination increment by 60’ and multiply the resulting quotient by the d interpolation factor. Computed Altitude (hc): Apply the total correction, being careful to carry the correct sign, to the tabulated com￾puted altitude. This yields the computed altitude. Observed Altitude (ho): Enter the observed altitude from Section One. Altitude Intercept: Compare hc and ho. Subtract the smaller from the larger. The resulting difference is the mag￾nitude of the altitude intercept. If ho is greater than hc, then label the altitude intercept toward. If hc is greater than ho, then label the altitude intercept away. Azimuth Angle: Obtain the azimuth angle (Z) from the Sight Reduction Tables, using the same arguments which determined tabulated computed altitude. Visual in￾terpolation is sufficiently accurate. True Azimuth: Calculate the true azimuth (Zn) from the azimuth angle (Z) as follows: a) If in northern latitudes: b) If in southern latitudes: SIGHT REDUCTION The section above discussed the basic theory of sight reduction and proposed a method to be followed when re￾ducing sights. This section puts that method into practice in reducing sights of a star, the sun, the moon, and planets. 2005. Reducing Star Sights To A Fix On May 16, 1995, at the times indicated, the navigator takes and records the following sights: Height of eye is 48 feet and index correction (IC) is +2.1’. The DR latitude for both sights is 39° N. The DR lon￾gitude for the Spica sight is 157° 10’W. The DR longitude for the Kochab sight is 157° 08.0’W. Determine the inter￾cept and azimuth for both sights. See Figure 2005. First, convert the sextant altitudes to observed alti￾tudes. Reduce the Spica sight first: LHA 180° then Zn > , = Z LHA 180° then Zn , = 180° – Z LHA 180° then Zn < , = 180°+Z Star Sextant Altitude Zone Time Kochab 47° 19.1’ 20-07-43 Spica 32° 34.8’ 20-11-26 Body Spica Index Correction +2.1’ Dip (height 48 ft) -6.7’ Sum -4.6’ Sextant Altitude (hs) 32° 34.8’ Apparent Altitude (ha) 32° 30.2’ Altitude Correction -1.5’ Additional Correction 0 Horizontal Parallax 0

313SIGHTREDUCTION-1.5SHA158°45.3Correction to haGHA486°05.7'32°28.7ObservedAltitude(h。)+/- 360°not requiredDetermine the sum of the index correction and the dip157°05.7Assumed Longitudecorrection.Gototheinsidefrontcoverof theNauticalAlma-3290LHAnactothetableentitledDIP.Thistable listsdipcorrectionsTabulatedDec/dS 11°08.4/n.a.as a function of height of eye measured in either feet ordCorrectionmeters. In the aboveproblem, the observer's height of eye isS 11°08.4True Declination48feetThe heights ofeyearetabulated in intervals,with theAssumed LatitudeN39°contrarycorrection correspondingtoeach interval listed between theinterval's endpoints.In this case,48feetlies between thetab-ulated46.9to48.4feet interval;thecorrespondingcorrectionforthisintervalis-6.7.AddtheICandthedipcorrection,beFirst,record theGHAofAriesfrom theMay17,1995ing careful to carry the correct sign The sum of thedaily page: 324°28.4.corrections here is -4.6. Apply this correction to the sextantaltitudetoobtain theapparentaltitude(h.)Next,determinethe incremental addition for themin-Next, apply the altitude correction. Find the altitudeutes and seconds after 0600 from theIncrements andcorrectiontableontheinsidefrontcoveroftheNauticalAlCorrections table in the back of the Nautical Almanac. Themanacnexttothediptable.Thealtitudecorrectionvariesasincrementfor11minutesand26seconds is252afunctionofboththetypeofbodysighted(sun,star,orplan-et)and thebody's apparent altitude.For theproblem above,Then,calculate the GHA of the star.Remember:enter the staraltitude correction table.Again,the correctionis given within an altitude interval; h, in this case was 320GHA (star)= GHA (P)+ SHA (star)30.2'.Thisvaluelies between thetabulated endpoints32000.0'and33°45.0.Thecorrectioncorrespondingtothisin-terval is -1.5'. Applying this correction to h, yields anThe Nautical Almanac lists the SHA of selected stars onobservedaltitudeof32°28.7each daily page.The SHA ofSpica on May 17,1995:158°45.3'Having calculated the observed altitude,determinetheThe Sight Reduction Tables entering arguments aretime and dateof the sight in Greenwich Mean Time:whole degrees of LHA and assumed latitude.Rememberthat LHA=GHA-west longitude or GHA +east longitude.Date16May1995Since in this example the vessel is in west longitude, sub-39°NDRLatitudetract its assumed longitudefrom theGHAof the body toDR Longitude157°10'Wobtain the LHA.Assume a longitude meeting the criteria20-11-26ObservationTimelisted in section 2004.0WatchErrorFromthosecriteriatheassumedlongitudemustendin20-11-26Zone Time05.7minutes sothat, when subtractedfromthecalculated+10Zone DescriptionGHA.awholedegreeofLHAwillresult.SincetheDRlon-GMT06-11-26gitude was157°10.0',then theassumed longitudeending inGMTDate17May199505.7' closest to the DR longitude is 157°05.7.SubtractingthisassumedlongitudefromthecalculatedGHAofthestarRecord the observation time and then apply any watchyields anLHAof3290errortodeterminezonetime.Then,usetheDRlongitudeatThe next value ofconcern is the star's true declination.the time of the sight to determine time zone description. InThis value is found on the May 17th daily page next to thethis case, the DR longitude indicatesa zone description ofstar's SHA.Spica's declination is S11o08.4'.There is nod+10 hours.Add the zone description to thezone time to ob-correction for a star sight, so the star's true declinationtainGMT.Itis importanttocarrythecorrectdatewhenequals its tabulated declination.The assumed latitude is de-applying this correction. In this case, the +10 correctiontermined from the whole degree of latitude closest to themade it 06-11-26GMT on May1Z,when the date in thelo-DR latitude at the time ofthe sight.In this case,the assumedcaltimezonewasMay16latitude is N39°It is markedcontrary"because theDRAfter calculating both the observed altitude and the GMTlatitude isnorth while the star's declination is south.time,enterthedailypagesoftheNautical Almanacto calcu-Thefollowing information is known: (1)the assumedlate the star's Greenwich Hour Angle (GHA)and declinationposition'sLHA(329°)andassumed latitude(39°Ncontraryname);and (2)the body's declination (S11°08.4)324°28.4'Tab GHA()Findthepagein theSight ReductionTablecorrespond-2°52.0GHAIncrementing to an LHA of 329° and an assumed latitude ofN 390

SIGHT REDUCTION 313 Determine the sum of the index correction and the dip correction. Go to the inside front cover of the Nautical Alma￾nac to the table entitled DIP. This table lists dip corrections as a function of height of eye measured in either feet or meters. In the above problem, the observer’s height of eye is 48 feet. The heights of eye are tabulated in intervals, with the correction corresponding to each interval listed between the interval’s endpoints. In this case, 48 feet lies between the tab￾ulated 46.9 to 48.4 feet interval; the corresponding correction for this interval is -6.7'. Add the IC and the dip correction, be￾ing careful to carry the correct sign. The sum of the corrections here is -4.6'. Apply this correction to the sextant altitude to obtain the apparent altitude (ha). Next, apply the altitude correction. Find the altitude correction table on the inside front cover of the Nautical Al￾manac next to the dip table. The altitude correction varies as a function of both the type of body sighted (sun, star, or plan￾et) and the body’s apparent altitude. For the problem above, enter the star altitude correction table. Again, the correction is given within an altitude interval; ha in this case was 32° 30.2'. This value lies between the tabulated endpoints 32° 00.0' and 33° 45.0'. The correction corresponding to this in￾terval is -1.5'. Applying this correction to ha yields an observed altitude of 32° 28.7'. Having calculated the observed altitude, determine the time and date of the sight in Greenwich Mean Time: Record the observation time and then apply any watch error to determine zone time. Then, use the DR longitude at the time of the sight to determine time zone description. In this case, the DR longitude indicates a zone description of +10 hours. Add the zone description to the zone time to ob￾tain GMT. It is important to carry the correct date when applying this correction. In this case, the +10 correction made it 06-11-26 GMT on May 17, when the date in the lo￾cal time zone was May 16. After calculating both the observed altitude and the GMT time, enter the daily pages of the Nautical Almanac to calcu￾late the star’s Greenwich Hour Angle (GHA) and declination. First, record the GHA of Aries from the May 17, 1995 daily page: 324° 28.4'. Next, determine the incremental addition for the min￾utes and seconds after 0600 from the Increments and Corrections table in the back of the Nautical Almanac. The increment for 11 minutes and 26 seconds is 2° 52'. Then, calculate the GHA of the star. Remember: GHA (star) = GHA ( ) + SHA (star) The Nautical Almanac lists the SHA of selected stars on each daily page. The SHA of Spica on May 17, 1995:158° 45.3'. The Sight Reduction Tables’ entering arguments are whole degrees of LHA and assumed latitude. Remember that LHA = GHA - west longitude or GHA + east longitude. Since in this example the vessel is in west longitude, sub￾tract its assumed longitude from the GHA of the body to obtain the LHA. Assume a longitude meeting the criteria listed in section 2004. From those criteria, the assumed longitude must end in 05.7 minutes so that, when subtracted from the calculated GHA, a whole degree of LHA will result. Since the DR lon￾gitude was 157° 10.0', then the assumed longitude ending in 05.7' closest to the DR longitude is 157° 05.7'. Subtracting this assumed longitude from the calculated GHA of the star yields an LHA of 329°. The next value of concern is the star’s true declination. This value is found on the May 17th daily page next to the star’s SHA. Spica’s declination is S 11° 08.4'. There is no d correction for a star sight, so the star’s true declination equals its tabulated declination. The assumed latitude is de￾termined from the whole degree of latitude closest to the DR latitude at the time of the sight. In this case, the assumed latitude is N 39°. It is marked “contrary” because the DR latitude is north while the star’s declination is south. The following information is known: (1) the assumed position’s LHA (329°) and assumed latitude (39°N contrary name); and (2) the body’s declination (S11° 08.4'). Find the page in the Sight Reduction Table correspond￾ing to an LHA of 329° and an assumed latitude of N 39°, Correction to ha -1.5' Observed Altitude (ho) 32° 28.7' Date 16 May 1995 DR Latitude 39° N DR Longitude 157° 10' W Observation Time 20-11-26 Watch Error 0 Zone Time 20-11-26 Zone Description +10 GMT 06-11-26 GMT Date 17 May 1995 Tab GHA ( ) 324° 28.4' GHA Increment 2° 52.0' SHA 158° 45.3' GHA 486° 05.7' +/- 360° not required Assumed Longitude 157° 05.7' LHA 329° Tabulated Dec/d S 11° 08.4'/n.a. d Correction — True Declination S 11° 08.4' Assumed Latitude N 39° contrary

314SIGHTREDUCTIONwithlatitude contraryto declination,Enterthis tablewithThe only remaining question is: in what direction from thethe body's whole degree of declination. In this case, theassumed andactual position is thebody'sgeographicposi-body's whole degree of declination is 11°.This declinationtion. The Sight Reduction Tables also provide this finalcorresponds to a tabulated altitude of 32°15.9'.This valuepiece of information.This is thevalue for Z tabulated withis for a declination of 11°the truedeclination is11°08.4the hand d values discussed above. In this case, enter theTherefore,interpolate to determine thecorrection to add toSight Reduction Tables as before,with LHA,assumed lati-thetabulated altitudetoobtain thecomputed altitude.tude, and declination. Visual interpolation is sufficient.Thedifferencebetween thetabulated altitudesfor 11oExtractthevalueZ=143.3°.TherelationbetweenZ andZn, the trueazimuth, is asfollows:and 12°isgiven in the Sight ReductionTablesas thevalued, in this case, d =-53.0. Express as a ratio the declinationIn northern latitudes:increment (in this case, 8.4)and thetotal interval betweenthe tabulated declination values (in this case,60')toobtainthe percentage ofthe distance between thetabulated decli-nation values represented by the declination increment.LHA>180°,thenZ,=ZNext, multiply that percentageby the increment betweenLHA180°, thenZ,= 180°-Znal computedaltitude:H。=32°08.5'LHA 180° and the vessel is in northern lati--7.4'Correction (+ or -)tude. Therefore, Z, = Z = 143.3°T. The navigator now has32°08.5'h。(computed)enoughinformationtoplotalineofpositionItwill bevaluablehere to review exactlywhat h。andThe values for the reduction of the Kochab sight follow:herepresent. Recall the methodology of the altitude-inter-cept method.The navigator first measures and corrects analtitude for a celestial body.This corrected altitude,ho, cor-BodyKochabresponds to a circle of equal altitude passing through the+2.1'IndexCorrectionnavigator's actual position whose center is the geographic-6.7'DipCorrectionposition (GP)ofthe body.The navigator then determines an-4.6'Sumassumed position (AP)near,but notcoincidentwith,his ac-hs47°19.1'tual position; he then calculates an altitude for an observer47°14.5haat that assumed position (AP).The circle of equal altitude-.9'AltitudeCorrectionpassing through this assumed position is concentric with thenot applicableAdditional Correctioncircle of equal altitudepassing through thenavigator's ac-Horizontal Parallaxnotapplicabletual position.The difference between the body's altitude at-9'Correction to hathe assumed position (h.)and the body's observed altitudeho47° 13.6(h.)is equal tothedifferences inradii lengthofthe two cor-Date16 May1995responding circles of equal altitude. In the above problem,39°NDRlatitudetherefore, the navigator knows that the equal altitude circle157°08.0'WDR longitudepassing through his actual position is:20-07-43ObservationTime0Watch Errorh。=32°28.7"Zone Time20-07-4332°08.5'-h。+10Zone Description20.2 NMGMT06-07-4317May1995GMT Dateaway from the equal altitude circle passing through his as-324°28.4Tab GHAYsumed position.Since his greater than he,the navigator1° 56.1'GHA Incrementknows that the radius of the equal altitude circle passingSHA137°18.5'through his actual position is less than the radius of theGHA463°43.0equal altitudecirclepassing through the assumed position

314 SIGHT REDUCTION with latitude contrary to declination. Enter this table with the body’s whole degree of declination. In this case, the body’s whole degree of declination is 11°. This declination corresponds to a tabulated altitude of 32° 15.9'. This value is for a declination of 11°; the true declination is 11° 08.4'. Therefore, interpolate to determine the correction to add to the tabulated altitude to obtain the computed altitude. The difference between the tabulated altitudes for 11° and 12° is given in the Sight Reduction Tables as the value d; in this case, d = -53.0. Express as a ratio the declination increment (in this case, 8.4') and the total interval between the tabulated declination values (in this case, 60') to obtain the percentage of the distance between the tabulated decli￾nation values represented by the declination increment. Next, multiply that percentage by the increment between the two values for computed altitude. In this case: Subtract 7.4' from the tabulated altitude to obtain the fi￾nal computed altitude: Hc = 32° 08.5'. It will be valuable here to review exactly what ho and hc represent. Recall the methodology of the altitude-inter￾cept method. The navigator first measures and corrects an altitude for a celestial body. This corrected altitude, ho, cor￾responds to a circle of equal altitude passing through the navigator’s actual position whose center is the geographic position (GP) of the body. The navigator then determines an assumed position (AP) near, but not coincident with, his ac￾tual position; he then calculates an altitude for an observer at that assumed position (AP).The circle of equal altitude passing through this assumed position is concentric with the circle of equal altitude passing through the navigator’s ac￾tual position. The difference between the body’s altitude at the assumed position (hc) and the body’s observed altitude (ho) is equal to the differences in radii length of the two cor￾responding circles of equal altitude. In the above problem, therefore, the navigator knows that the equal altitude circle passing through his actual position is: away from the equal altitude circle passing through his as￾sumed position. Since ho is greater than hc, the navigator knows that the radius of the equal altitude circle passing through his actual position is less than the radius of the equal altitude circle passing through the assumed position. The only remaining question is: in what direction from the assumed and actual position is the body’s geographic posi￾tion. The Sight Reduction Tables also provide this final piece of information. This is the value for Z tabulated with the hc and d values discussed above. In this case, enter the Sight Reduction Tables as before, with LHA, assumed lati￾tude, and declination. Visual interpolation is sufficient. Extract the value Z = 143.3°. The relation between Z and Zn, the true azimuth, is as follows: In northern latitudes: In southern latitudes: In this case, LHA > 180° and the vessel is in northern lati￾tude. Therefore, Zn = Z = 143.3°T. The navigator now has enough information to plot a line of position. The values for the reduction of the Kochab sight follow: Dec Inc / + or - d 8.4' / -53.0 hc (tabulated) 32° 15.9' Correction (+ or -) -7.4' hc (computed) 32° 08.5' 8.4 60 - × ( ) –53.0 = –7.4 ho = 32°28.7′ –hc 32°08.5′ 20.2 NM = - Body Kochab Index Correction +2.1' Dip Correction -6.7' Sum -4.6' hs 47° 19.1' ha 47° 14.5' Altitude Correction -.9' Additional Correction not applicable Horizontal Parallax not applicable Correction to ha -9' ho 47° 13.6' Date 16 May 1995 DR latitude 39°N DR longitude 157° 08.0' W Observation Time 20-07-43 Watch Error 0 Zone Time 20-07-43 Zone Description +10 GMT 06-07-43 GMT Date 17 May 1995 Tab GHA 324° 28.4' GHA Increment 1° 56.1' SHA 137° 18.5' GHA 463° 43.0' LHA 180° then Zn > , = Z LHA 180° then Zn , = 180° – Z LHA 180° then Zn < , = 180° + Z

315SIGHT REDUCTION+/-360°not applicable156°43.0"Assumed Longitude3070LHATabDec /dN74°10.6/n.a.dCorrectionnotapplicableN74°10.6True Declination39°N (same)Assumed LatitudeDec Inc / + or - d10.6/-24.8he47° 12.6′-4.2'Total Correction

SIGHT REDUCTION 315 +/- 360° not applicable Assumed Longitude 156° 43.0’ LHA 307° Tab Dec / d N74° 10.6’ / n.a. d Correction not applicable True Declination N74° 10.6’ Assumed Latitude 39°N (same) Dec Inc / + or - d 10.6’ / -24.8 hc 47° 12.6’ Total Correction -4.2’

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316 SIGHT REDUCTION Figure 2005. Left hand daily page of the Nautical Almanac for May 17, 1995