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.LHA<180°, thenZ,=360°ZDouble Second Difference Correction:Use this cor-rectionwhenlinearinterpolationofdeclinationforcomputedaltitude is not sufficiently accurate due to the non linearchange in the computed altitude as a function of declinationThe need for double second difference interpolation is indi-cated bythed interpolationfactorappearing in italic typeb)If insouthernlatitudes:followed by a small dot When this procedure must be em-LHA>180°,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 Factor: 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, declination, 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 hypothetical declination listed above, the tabulated d interpolation factor listed in the table would be the difference between declination values given for 13° and 14°. If the declination increases between these two values, d is positive. If the declination decreases between these two values, d is negative. Computed Altitude (Tabulated): Enter the Sight Reduction 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 enter the Sight Reduction Tables with 13° as the value for declination. Record the tabulated computed altitude. Double Second Difference Correction: Use this correction 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 indicated by the d interpolation factor appearing in italic type followed by a small dot. When this procedure must be employed, 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 interpolation 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 computed 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 magnitude 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 interpolation 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 reducing 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 longitude for the Spica sight is 157° 10’W. The DR longitude for the Kochab sight is 157° 08.0’W. Determine the intercept and azimuth for both sights. See Figure 2005. First, convert the sextant altitudes to observed altitudes. Reduce the Spica sight first: LHA 180° then Zn > , = Z LHA 180° then Zn < , = 360°–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 Almanac 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 tabulated 46.9 to 48.4 feet interval; the corresponding correction for this interval is -6.7'. Add the IC and the dip correction, being 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 Almanac next to the dip table. The altitude correction varies as a function of both the type of body sighted (sun, star, or planet) 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 interval 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 obtain 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 local time zone was May 16. After calculating both the observed altitude and the GMT time, enter the daily pages of the Nautical Almanac to calculate 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 minutes 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, subtract 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 longitude 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 determined 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 corresponding 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