< The American Practical Navigator
- Sight Reduction Tables 2018
- Sight Reduction Tables For Marine Navigation
- Sight Reduction Tables Vol 1 Pdf
The American Practical Navigator
by the United States government
Chapter 20
by the United States government
Chapter 20
- 1CHAPTER 20 - SIGHT REDUCTION
- 1.1BASIC PROCEDURES
- 1.2SIGHT REDUCTION
- 1.3MERIDIAN PASSAGE
- 1.4LATITUDE BY POLARIS
- 1.5THE DAY’S WORK IN CELESTIAL NAVIGATION
BASIC PROCEDURES[edit]
2000. Computer Sight Reduction[edit]
The purely mathematical process of sight reduction isan ideal candidate for computerization, and a number ofdifferent hand-held calculators and computer programshave been developed to relieve the tedium of working outsights by tabular or mathematical methods. The civiliannavigator can choose from a wide variety of hand-heldcalculators and computer programs which require only theentry of the DR position, altitude and azimuth of the body,and GMT. It is not even necessary to know the name of thebody because the computer can figure out what it must bebased on the entered data. Calculators and computersprovide more accurate solutions than tabular andmathematical methods because they can be based on actualvalues rather than theoretical assumptions and do not haveinherent rounding errors.
U.S. Naval navigators have access to a program calledSTELLA (System To Estimate Latitude and Longitude Astronomically;do not confuse with a commercial astronomyprogram with the same name). STELLA was developed bythe Astronomical Applications Department of the U.S. NavalObservatory based on a Navy requirement. Thealgorithms used in STELLA provide an accuracy of onearc-second on the Earth’s surface, a distance of about 30meters. While this accuracy is far better than can be obtainedusing a sextant, it does support possible naval needsfor automated navigation systems based on celestial objects.These algorithms take into account the oblateness ofthe Earth, movement of the vessel during sight-taking, andother factors not fully addressed by traditional methods.
STELLA can perform almanac functions, position updating/DR estimations, celestial body rise/set/transitcalculations, compass error calculations, sight planning,and sight reduction. On-line help and user’s guide are included,and it is a component of the Block III NAVSSI.Because STELLA logs all entered data for future reference,it is authorized to replace the Navy Navigation Workbook.STELLA is now an allowance list requirement for Navalships, and is available from:
Superintendent
U.S. Naval Observatory
Code: AA/STELLA
3450 Massachusetts Ave. NW
Washington, DC, 20392-5420
U.S. Naval Observatory
Code: AA/STELLA
3450 Massachusetts Ave. NW
Washington, DC, 20392-5420
or on the Navigator of the Navy Web site at
- http://www.navigator.navy.mil/navigator/surface.html.
2001. Tabular Sight Reduction[edit]
The remainder of this chapter concentrates on sight reductionusing the Nautical Almanac and Pub. No. 229, Sight Reduction Tables for Marine Navigation. The methodexplained here is only one of many methods of reducing asight. The Nautical Almanac contains directions for solvingsights using its own concise sight reduction tables or calculators,along with examples for the current year.
Reducing a celestial sight to obtain a line of positionusing the tables consists of six steps:
1. Correct the sextant altitude (hs) to obtain observedaltitude (ho).
2. Determine the body’s GHA and declination (dec.).
3. Select an assumed position (AP) and find its localhour angle (LHA).
4. Compute altitude and azimuth for the AP.
5. Compare the computed and observed altitudes.
6. Plot the line of position.
2. Determine the body’s GHA and declination (dec.).
3. Select an assumed position (AP) and find its localhour angle (LHA).
4. Compute altitude and azimuth for the AP.
5. Compare the computed and observed altitudes.
6. Plot the line of position.
The introduction to each volume of Pub. 229 containsinformation: (1) discussing use of the publication for a varietyof special celestial navigation techniques; (2)discussing interpolation, explaining the double second differenceinterpolation required in some sight reductions, andproviding tables to facilitate the interpolation process; and(3) discussing the publication’s use in solving problems ofgreat circle sailings. Prior to using Pub. 229, carefully readthis introductory material.
Celestial navigation involves determining a circularline of position based on an observer’s distance from a celestialbody’s geographic position (GP). Should theobserver determine both a body’s GP and his distance fromthe GP, he would have enough information to plot a line ofposition; he would be somewhere on a circle whose centerwas the GP and whose radius equaled his distance from thatGP. That circle, from all points on which a body’s measuredaltitude would be equal, is a circle of equal altitude. Thereis a direct proportionality between a body’s altitude as measuredby an observer and the distance of its GP from thatobserver; the lower the altitude, the farther away the GP.Therefore, when an observer measures a body’s altitude heobtains an indirect measure of the distance between himselfand the body’s GP. Sight reduction is the process of convertingthat indirect measurement into a line of position.
Sight reduction reduces the problem of scale to manageablesize. Depending on a body’s altitude, its GP couldbe thousands of miles from the observer’s position. Thesize of a chart required to plot this large distance would beimpractical. To eliminate this problem, the navigator doesnot plot this line of position directly. Indeed, he does notplot the GP at all. Rather, he chooses an assumed position(AP) near, but usually not coincident with, his DR position.The navigator chooses the AP’s latitude and longitude tocorrespond to the entering arguments of LHA and latitudeused in Pub. 229. From Pub. 229, the navigator computeswhat the body’s altitude would have been had it been measuredfrom 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 observed altitudes is directlyproportional to the distance between the circles of equal altitudefor the assumed position and the actual position. Pub. 229 also gives the direction from the GP to the AP. Having selected the assumed position, calculated the distance betweenthe circles of equal altitude for that AP and his actualposition, and determined the direction from the assumedposition to the body’s GP, the navigator has enough informationto plot a line of position (LOP).
To plot an LOP, plot the assumed position on either achart or a plotting sheet. From the Sight Reduction Tables,determine: 1) the altitude of the body for a sight taken at theAP and 2) the direction from the AP to the GP. Then, determinethe difference between the body’s calculated altitudeat this AP and the body’s measured altitude. This differencerepresents the difference in radii between the equal altitudecircle passing through the AP and the equal altitude circlepassing through the actual position. Plot this differencefrom the AP either towards or away from the GP along theaxis between the AP and the GP. Finally, draw the circle ofequal altitude representing the circle with the body’s GP atthe center and with a radius equal to the distance betweenthe GP and the navigator’s actual position.
One final consideration simplifies the plotting of the equalaltitude circle. Recall that the GP is usually thousands of milesaway from the navigator’s position. The equal altitude circle’sradius, therefore, can be extremely large. Since this radius is solarge, the navigator can approximate the section close to his positionwith a straight line drawn perpendicular to the lineconnecting the AP and the GP. This straight line approximationis good only for sights at relatively low altitudes. The higher thealtitude, the shorter the distance between the GP and the actualposition, and the smaller the circle of equal altitude. The shorterthis distance, the greater the inaccuracy introduced by thisapproximation.
2002. Selection of the Assumed Position (AP)[edit]
Use the following arguments when entering Pub. 229to compute altitude (hc) and azimuth:
1. Latitude (L)
2. Declination (d or Dec.)
3. Local hour angle (LHA)
2. Declination (d or Dec.)
3. Local hour angle (LHA)
Latitude and LHA are functions of the assumedposition. Select an AP longitude resulting in a whole degreeof LHA and an AP latitude equal to that whole degree oflatitude closest to the DR position. Selecting the AP in thismanner eliminates interpolation for LHA and latitude inPub. 229.
2003. Comparison of Computed and Observed Altitudes[edit]
The difference between the computed altitude (hc) andthe observed altitude (ho) is the altitude intercept (a).
The altitude intercept is the difference in the length ofthe radii of the circles of equal altitude passing through theAP and the observer’s actual position. The position havingthe greater altitude is on the circle of smaller radius and iscloser to the observed body’s GP. In Figure 2004, the AP isshown on the inner circle. Therefore, hc is greater than ho.
Express the altitude intercept in nautical miles andlabel it T or A to indicate whether the line of position istoward 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 HoMoreToward. Another is C-G-A: Computed Greater Away,remembered as Coast Guard Academy. In other words, if hois greater than hc, the line of position intersects a pointmeasured from the AP towards the GP a distance equal tothe altitude intercept. Draw the LOP through thisintersection point perpendicular to the axis between the APand GP.
2004. Plotting the Line of Position[edit]
Plot the line of position as shown in Figure 2004. Plotthe AP first; then plot the azimuth line from the AP towardor away from the GP. Then, measure the altitude interceptalong this line. At the point on the azimuth line equal to theintercept distance, draw a line perpendicular to the azimuthline. This perpendicular represents that section of the circleof equal altitude passing through the navigator’s actualposition. This is the line of position.
A navigator often takes sights of more than onecelestial body when determining a celestial fix. Afterplotting the lines of position from these several sights,advance the resulting LOP’s along the track to the time ofthe last sight and label the resulting fix with the time of thislast sight.
2005. Sight Reduction Procedures[edit]
Just as it is important to understand the theory of sightreduction, it is also important to develop a practicalprocedure to reduce celestial sights consistently andaccurately. Sight reduction involves several consecutivesteps, the accuracy of each completely dependent on theaccuracy of the steps that went before. Sight reduction tableshave, for the most part, reduced the mathematicsinvolved to simple addition and subtraction. However,careless errors will render even the most skillfullymeasured sights inaccurate. The navigator using tabular ormathematical techniques must work methodically to reducecareless errors.
Naval navigators will most likely use OPNAV 3530, U.S.Navy Navigation Workbook, which contains pre-formattedpages with “strip forms” to guide the navigator through sightreduction. A variety of commercially-produced forms are alsoavailable. Pick a form and learn its method thoroughly. Withfamiliarity will come increasing understanding, speed andaccuracy.
Figure 2005 represents a functional and complete worksheetdesigned to ensure a methodical approach to any sight reductionproblem. The recommended procedure discussed below is notthe only one available; however, the navigator who uses it can beassured that he has considered every correction required to obtainan accurate fix.
SECTION ONE consists of two parts: (1) Correctingsextant altitude to obtain apparent altitude; and (2)Correcting the apparent altitude to obtain the observedaltitude.
Body: Enter the name of the body whose altitude youhave measured. If using the Sun or the Moon, indicatewhich limb was measured.
Index Correction: This is determined by the characteristicsof the individual sextant used. Chapter 16 discussesdetermining its magnitude and algebraic sign.
Dip: The dip correction is a function of the height ofeye of the observer. It is always negative; its magnitude isdetermined from the Dip Table on the inside front cover ofthe Nautical Almanac.
Sum: Enter the algebraic sum of the dip correction andthe index correction.
Sextant Altitude: Enter the altitude of the bodymeasured by the sextant.
Apparent Altitude: Apply the correction determinedabove to the measured altitude and enter the result as theapparent altitude.
Altitude Correction: Every observation requires an altitudecorrection. This correction is a function of the apparentaltitude of the body. The Almanac contains tables for determiningthese corrections. For the Sun, planets, and stars, these tablesare 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 nameimplies, this correction is applied to sights of Mars and Venus.The correction is a function of the planet measured, thetime of year, and the apparent altitude. The inside front coverof the Almanac lists these corrections.
Additional Correction: Enter this additional correctionfrom Table A-4 located at the front of the Nautical Almanacwhen obtaining a sight under non-standard atmospheric temperatureand pressure conditions. This correction is afunction of atmospheric pressure, temperature, and apparentaltitude.
Horizontal Parallax Correction: This correction is uniqueto reducing Moon sights. Obtain the H.P. correction value fromthe daily pages of the Almanac. Enter the H.P correction table atthe back of the Almanac with this value. The H.P correction is afunction of the limb of the Moon used (upper or lower), the apparentaltitude, and the H.P. correction factor. The H.P.correction is always added to the apparent altitude.
Moon Upper Limb Correction: Enter -30' for thiscorrection if the sight was of the upper limb of the Moon.
Correction to Apparent Altitude: Sum the altitudecorrection, the Mars or Venus additional correction, theadditional correction, the horizontal parallax correction, and theMoon’s upper limb correction. Be careful to determine and carrythe algebraic sign of the corrections and their sum correctly.Enter this sum as the correction to the apparent altitude.
Observed Altitude: Apply the Correction to ApparentAltitude algebraically to the apparent altitude. The result is theobserved altitude.
SECTION ONE: OBSERVED ALTITUDE | ||
Body | _________________ | _________________ |
Index Correction | _________________ | _________________ |
Dip (height of eye) | _________________ | _________________ |
Sum | _________________ | _________________ |
Sextant Altitude (hs) | _________________ | _________________ |
Apparent Altitude (ha) | _________________ | _________________ |
Altitude Correction | _________________ | _________________ |
Mars or Venus Additional Correction | _________________ | _________________ |
Additional Correction | _________________ | _________________ |
Horizontal Parallax Correction | _________________ | _________________ |
Moon Upper Limb Correction | _________________ | _________________ |
Correction to Apparent Altitude (ha) | _________________ | _________________ |
Observed Altitude (ho) | _________________ | _________________ |
SECTION TWO: GMT TIME AND DATE | ||
Date | _________________ | _________________ |
DR Latitude | _________________ | _________________ |
DR Longitude | _________________ | _________________ |
Observation Time | _________________ | _________________ |
Watch Error | _________________ | _________________ |
Zone Time | _________________ | _________________ |
Zone Description | _________________ | _________________ |
Greenwich Mean Time | _________________ | _________________ |
Date GMT | _________________ | _________________ |
SECTION THREE: LOCAL HOUR ANGLE AND DECLINATION | ||
Tabulated GHA and v Correction Factor | _________________ | _________________ |
GHA Increment | _________________ | _________________ |
Sidereal Hour Angle (SHA) or v Correction | _________________ | _________________ |
GHA | _________________ | _________________ |
+ or - 360° if needed | _________________ | _________________ |
Assumed Longitude (-W, +E) | _________________ | _________________ |
Local Hour Angle (LHA) | _________________ | _________________ |
Tabulated Declination and d Correction Factor | _________________ | _________________ |
d Correction | _________________ | _________________ |
True Declination | _________________ | _________________ |
Assumed Latitude | _________________ | _________________ |
SECTION FOUR: ALTITUDE INTERCEPT AND AZIMUTH | ||
Declination Increment and d Interpolation Factor | _________________ | _________________ |
Computed Altitude (Tabulated) | _________________ | _________________ |
Double Second Difference Correction | _________________ | _________________ |
Total Correction | _________________ | _________________ |
Computed Altitude (hc) | _________________ | _________________ |
Observed Altitude (ho) | _________________ | _________________ |
Altitude Intercept | _________________ | _________________ |
Azimuth Angle | _________________ | _________________ |
True Azimuth | _________________ | _________________ |
Figure 2005. Complete sight reduction form.
SECTION TWO determines the Greenwich Mean Time(GMT; referred to in the Almanacs as Universal time or UT) andGMT date of the sight.
Date: Enter the local time zone date of the sight.
DR Latitude: Enter the dead reckoning latitude of thevessel.
DR Longitude: Enter the dead reckoning longitude of thevessel.
Observation Time: Enter the local time of the sight asrecorded on the ship’s chronometer or other timepiece.
Watch Error: Enter a correction for any known watcherror.
Zone Time: Correct the observation time with watcherror to determine zone time.
Zone Description: Enter the zone description of the timezone indicated by the DR longitude. If the longitude is west of theGreenwich Meridian, the zone description is positive.Conversely, if the longitude is east of the Greenwich Meridian,the zone description is negative. The zone description representsthe correction necessary to convert local time to GreenwichMean Time.
Greenwich Mean Time: Add to the zone description thezone time to determine Greenwich Mean Time.
Date: Carefully evaluate the time correction applied aboveand determine if the correction has changed the date. Enter theGMT date.
SECTION THREE determines two of the three argumentsrequired to enter Pub. 229 Zar x serial key. : Local Hour Angle (LHA)and Declination. This section employs the principle that a celestialbody’s LHA is the algebraic sum of its GreenwichHour Angle (GHA) and the observer’s longitude. Therefore,the basic method employed in this section is: (1) Determinethe body’s GHA; (2) Determine an assumed longitude; (3)Algebraically combine the two quantities, remembering tosubtract a western assumed longitude from GHA and to addan eastern longitude to GHA; and (4) Extract the declinationof the body from the appropriate Almanac table, correctingthe tabular value if required.
Tabulated GHA and v Correction Factor:For the Sun, the Moon, or a planet, extract the value forthe whole hour of GHA corresponding to the sight. Forexample, if the sight was obtained at 13-50-45 GMT, extractthe GHA value for 1300. For a star sight reduction, extract thevalue of the GHA of Aries (GHA ♈), again using the valuecorresponding to the whole hour of the time of the sight.For a planet or Moon sight reduction, enter the vcorrection value. This quantity is not applicable to a Sun orstar sight. The v correction for a planet sight is found at thebottom of the column for each particular planet. The vcorrection factor for the Moon is located directly beside thetabulated hourly GHA values. The v correction factor forthe Moon is always positive. If a planet’s v correction factoris listed without sign, it is positive. If listed with a negativesign, the planet’s v correction factor is negative. This vcorrection factor is not the magnitude of the v correction; itis used later to enter the Increments and Correction table todetermine the magnitude of the correction.
GHA Increment: The GHA increment serves as aninterpolation factor, correcting for the time that the sightdiffered from the whole hour. For example, in the sight at13-50-45 discussed above, this increment correctionaccounts for the 50 minutes and 45 seconds after the wholehour at which the sight was taken. Obtain this correctionvalue from the Increments and Corrections tables in theAlmanac. The entering arguments for these tables are theminutes and seconds after the hour at which the sight wastaken and the body sighted. Extract the proper correctionfrom the applicable table and enter the correction.
Sidereal Hour Angle or v Correction: If reducing astar sight, enter the star’s Sidereal Hour Angle (SHA). TheSHA is found in the star column of the daily pages of theAlmanac. The SHA combined with the GHA of Ariesresults in the star’s GHA. The SHA entry is applicable onlyto a star. If reducing a planet or Moon sight, obtain the vcorrection from the Increments and Corrections Table. Thecorrection is a function of only the v correction factor; itsmagnitude is the same for both the Moon and the planets.
GHA: A star’s GHA equals the sum of the TabulatedGHA of Aries, the GHA Increment, and the star’s SHA.The Sun’s GHA equals the sum of the Tabulated GHA andthe GHA Increment. The GHA of the Moon or a planetequals the sum of the Tabulated GHA, the GHA Increment,and the v correction.
+ or – 360° (if needed): Since the LHA will bedetermined from subtracting or adding the assumedlongitude to the GHA, adjust the GHA by 360° if needed tofacilitate the addition or subtraction.
Assumed Longitude: If the vessel is west of the primemeridian, the assumed longitude will be subtracted from theGHA to determine LHA. If the vessel is east of the primemeridian, the assumed longitude will be added to the GHAto determine the LHA. Select the assumed longitude tomeet the following two criteria: (1) When added orsubtracted (as applicable) to the GHA determined above, awhole degree of LHA will result; and (2) It is the longitudeclosest to that DR longitude that meets criterion (1).
Local Hour Angle (LHA): Combine the body’s GHAwith the assumed longitude as discussed above todetermine the body’s LHA.
Tabulated Declination and d Correction factor: (1)Obtain the tabulated declination for the Sun, the Moon, thestars, or the planets from the daily pages of the Almanac.The declination values for the stars are given for the entirethree day period covered by the daily page of the Almanac.The values for the Sun, Moon, and planets are listed inhourly increments. For these bodies, enter the declinationvalue for the whole hour of the sight. For example, if thesight is at 12-58-40, enter the tabulated declination for 1200.(2) There is no d correction factor for a star sight. There ared correction factors for Sun, Moon, and planet sights.Similar to the v correction factor discussed above, the dcorrection factor does not equal the magnitude of the dcorrection; it provides the argument to enter the Incrementsand Corrections tables in the Almanac. The sign of the dcorrection factor, which determines the sign of the dcorrection, is determined by the trend of declination values,not the trend of d values. The d correction factor is simplyan interpolation factor; therefore, to determine its sign, lookat the declination values for the hours that frame the time ofthe sight. For example, suppose the sight was taken on acertain date at 12-30-00. Compare the declination value for1200 and 1300 and determine if the declination hasincreased or decreased. If it has increased, the d correctionfactor is positive. If it has decreased, the d correction factoris negative.
d correction: Enter the Increments and Correctionstable with the d correction factor discussed above. Extractthe proper correction, being careful to retain the propersign.
True Declination: Combine the tabulated declinationand the d correction to obtain the true declination.
Assumed Latitude: Choose as the assumed latitudethat whole value of latitude closest to the vessel’s DRlatitude. If the assumed latitude and declination are bothnorth or both south, label the assumed latitude “Same.” Ifone is north and the other is south, label the assumedlatitude “Contrary.”
SECTION FOUR uses the arguments of assumedlatitude, LHA, and declination determined in Section Three toenter Pub. 229 to determine azimuth and computed altitude.Then, Section Four compares computed and observed altitudesto calculate the altitude intercept. From this the LOP is plotted.
Declination Increment and d Interpolation Factor:Note that two of the three arguments used to enter Pub. 229,LHA and latitude, are whole degree values. Section Three doesnot determine the third argument, declination, as a wholedegree. Therefore, the navigator must interpolate in Pub. 229for declination, given whole degrees of LHA and latitude. Thefirst steps of Section Four involve this interpolation fordeclination. Since declination values are tabulated every wholedegree in Pub. 229, the declination increment is the minutes andtenths of the true declination. For example, if the true declinationis 13° 15.6', then the declination increment is 15.6'.
Pub. 229 also lists a d Interpolation Factor. This is the magnitudeof the difference between the two successive tabulatedvalues for declination that frame the true declination. Therefore,for the hypothetical declination listed above, the tabulated d interpolationfactor listed in the table would be the differencebetween declination values given for 13° and 14°. If the declinationincreases between these two values, d is positive. If thedeclination decreases between these two values, d is negative.
Computed Altitude (Tabulated): Enter Pub. 229with the following arguments: (1) LHA from SectionThree; (2) assumed latitude from Section Three; (3) thewhole degree value of the true declination. For example, ifthe true declination were 13° 15.6', then enter Pub. 229 with13° as the value for declination. Record the tabulatedcomputed altitude.
Double Second Difference Correction: Use thiscorrection when linear interpolation of declination forcomputed altitude is not sufficiently accurate due to the nonlinearchange in the computed altitude as a function ofdeclination. The need for double second difference interpolationis indicated by the d interpolation factor appearing initalic type followed by a small dot. When this procedure mustbe employed, refer to detailed instructions in the introductionto Pub. 229.
Total Correction: The total correction is the sum ofthe double second difference (if required) and the interpolationcorrections. Calculate the interpolation correction bydividing the declination increment by 60' and multiply theresulting quotient by the d interpolation factor.
Computed Altitude (hc): Apply the total correction,being careful to carry the correct sign, to the tabulatedcomputed altitude. This yields the computed altitude.
Observed Altitude (ho): Enter the observed altitudefrom Section One.
Altitude Intercept: Compare hc and ho. Subtract thesmaller from the larger. The resulting difference is themagnitude 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) fromPub. 229, using the same arguments which determined tabulatedcomputed altitude. Visual interpolation is sufficiently accurate.
True Azimuth: Calculate the true azimuth (Zn) fromthe azimuth angle (Z) as follows:
a) If in northern latitudes:
LHA > 180°, then Zn = Z
LHA < 180°, then Zn = 360° - Z In sentimental mood sheet music.
LHA > 180°, then Zn = Z
LHA < 180°, then Zn = 360° - Z In sentimental mood sheet music.
b) If in southern latitudes:
LHA > 180°, then Zn = 180° - Z
LHA < 180°, then Zn = 180° + Z
LHA > 180°, then Zn = 180° - Z
LHA < 180°, then Zn = 180° + Z
SIGHT REDUCTION[edit]
The section above discussed the basic theory of sightreduction and presented a method to be followed whenreducing sights. This section puts that method into practicein reducing sights of a star, the Sun, the Moon, and planets.
2006. Reducing Star Sights to a Fix[edit]
On May 16, 1995, at the times indicated, the navigatortakes and records the following sights:
Star | Sextant Altitude | Zone Time |
---|---|---|
Kochab | 47° 19.1' | 20-07-43 |
Spica | 32° 34.8' | 20-11-26 |
Height of eye is 48 feet and index correction (IC) is+2.1'. The DR latitude for both sights is 39° N. The DRlongitude for the Spica sight is 157° 10'W. The DRlongitude for the Kochab sight is 157° 08.0'W. Determinethe intercept and azimuth for both sights. See Figure 2006.
First, convert the sextant altitudes to observedaltitudes. Reduce the Spica sight first:
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 |
Correction to ha | -1.5' |
Observed Altitude (ho) | 32° 28.7' |
Determine the sum of the index correction and the dipcorrection. Go to the inside front cover of the Nautical Almanacto the table entitled “DIP.” This table lists dipcorrections as a function of height of eye measured in eitherfeet or meters. In the above problem, the observer’s height ofeye is 48 feet. The heights of eye are tabulated in intervals,with the correction corresponding to each interval listedbetween the interval’s endpoints. In this case, 48 feet liesbetween the tabulated 46.9 to 48.4 feet interval; thecorresponding correction for this interval is -6.7'. Add the ICand the dip correction, being careful to carry the correct sign.The sum of the corrections here is -4.6'. Apply this correctionto the sextant altitude to obtain the apparent altitude (ha).
Next, apply the altitude correction. Find the altitudecorrection table on the inside front cover of the Nautical Almanacnext to the dip table. The altitude correction variesas a function of both the type of body sighted (Sun, star, orplanet) and the body’s apparent altitude. For the problemabove, enter the star altitude correction table. Again, thecorrection is given within an altitude interval; ha in this casewas 32° 30.2'. This value lies between the tabulatedendpoints 32° 00.0' and 33° 45.0'. The correctioncorresponding to this interval is -1.5'. Applying thiscorrection to ha yields an observed altitude of 32° 28.7'.
Having calculated the observed altitude, determine thetime and date of the sight in Greenwich Mean Time:
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 |
Record the observation time and then apply any watcherror to determine zone time. Then, use the DR longitude atthe time of the sight to determine time zone description. Inthis case, the DR longitude indicates a zone description of+10 hours. Add the zone description to the zone time toobtain GMT. It is important to carry the correct date whenapplying this correction. In this case, the +10 correctionmade it 06-11-26 GMT on May 17, when the date in thelocal time zone was May 16.
After calculating both the observed altitude and the GMTtime, enter the daily pages of the Nautical Almanac tocalculate the star’s Greenwich Hour Angle (GHA) anddeclination.
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 |
First, record the GHA of Aries from the May 17, 1995daily page: 324° 28.4'.
Next, determine the incremental addition for theminutes and seconds after 0600 from the Increments andCorrections table in the back of the Nautical Almanac. Theincrement for 11 minutes and 26 seconds is 2° 52'.
Then, calculate the GHA of the star. Remember:
The Nautical Almanac lists the SHA of selected stars oneach daily page. The SHA of Spica on May17, 1995: 158° 45.3'.
Pub. 229’s entering arguments are whole degrees ofLHA and assumed latitude. Remember that LHA = GHA -west longitude or GHA + east longitude. Since in thisexample the vessel is in west longitude, subtract itsassumed longitude from the GHA of the body to obtain theLHA. Assume a longitude meeting the criteria listed inArticle 2005.
From those criteria, the assumed longitude must end in05.7 minutes so that, when subtracted from the calculatedGHA, a whole degree of LHA will result. Since the DRlongitude was 157° 10.0', then the assumed longitudeending in 05.7' closest to the DR longitude is 157° 05.7'.Subtracting this assumed longitude from the calculatedGHA 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 thestar’s SHA. Spica’s declination is S 11° 08.4'. There is no dcorrection for a star sight, so the star’s true declinationequals its tabulated declination. The assumed latitude isdetermined from the whole degree of latitude closest to theDR latitude at the time of the sight. In this case, the assumedlatitude is N 39°. It is marked “contrary” because the DRlatitude is north while the star’s declination is south.
The following information is known: (1) the assumedposition’s LHA (329°) and assumed latitude (39°Ncontrary name); and (2) the body’s declination (S11° 08.4').
Find the page in the Sight Reduction Tablecorresponding to an LHA of 329° and an assumed latitudeof N 39°, with latitude contrary to declination. Enter thistable with the body’s whole degree of declination. In thiscase, the body’s whole degree of declination is 11°. Thisdeclination corresponds to a tabulated altitude of 32° 15.9'.This value is for a declination of 11°; the true declination is11° 08.4'. Therefore, interpolate to determine the correctionto add to the tabulated altitude to obtain the computedaltitude.
The difference between the tabulated altitudes for 11°and 12° is given in Pub. 229 as the value d; in this case, d =-53.0. Express as a ratio the declination increment (in thiscase, 8.4') and the total interval between the tabulated declinationvalues (in this case, 60') to obtain the percentage ofthe distance between the tabulated declination values representedby the declination increment. Next, multiply thatpercentage by the increment between the two values forcomputed altitude. In this case:
Subtract 7.4' from the tabulated altitude to obtain thefinal computed altitude: Hc = 32° 08.5'.
Dec Inc / + or − d | 8.4' / -53.0 |
hc (tabulated) | 32° 15.9' |
Correction (+ or −) | −7.4' |
hc (computed) | 32° 08.5' |
It will be valuable here to review exactly what hoand hc represent. Recall the methodology of thealtitude-intercept method. The navigator first measuresand corrects an altitude for a celestial body. Thiscorrected altitude, ho, corresponds to a circle of equalaltitude passing through the navigator’s actual positionwhose center is the geographic position (GP) of thebody. The navigator then determines an assumedposition (AP) near, but not coincident with, his actualposition; he then calculates an altitude for an observerat that assumed position (AP). The circle of equalaltitude passing through this assumed position isconcentric with the circle of equal altitude passingthrough the navigator’s actual position. The differencebetween the body’s altitude at the assumed position (hc)and the body’s observed altitude (ho) is equal to thedifferences in radii length of the two correspondingcircles of equal altitude. In the above problem,therefore, the navigator knows that the equal altitudecircle passing through his actual position is:
ho = 32°28.7' |
−hc = 32°08.5' |
20.2 NM |
away from the equal altitude circle passing through hisassumed position. Since ho is greater than hc, thenavigator knows that the radius of the equal altitudecircle passing through his actual position is less thanthe radius of the equal altitude circle passing throughthe assumed position.
The only remaining question is: inwhat direction from the assumed position is the body’sactual GP. Pub. 229 also provides this final piece ofinformation. This is the value for Z tabulated with the hcand d values discussed above. In this case, enter Pub. 229as before, with LHA, assumed latitude, 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: |
LHA > 180°, then Zn = Z |
LHA < 180°, then Zn = 360°–Z |
In southern latitudes: |
LHA > 180°, then Zn = 180° – Z |
LHA < 180°, then Zn = 180°+Z |
In this case, LHA > 180° and the vessel is in northern latitude.Therefore, Zn = Z = 143.3°T. The navigator now hasenough information to plot a line of position.
The values for the reduction of the Kochab sight follow:
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 |
T Date | 17 May 1995 |
Tab GHA ♈ | 324° 28.4' |
GHA Increment | 1° 56.1' |
SHA | 137° 18.5' |
GHA | 463° 43.0' |
+/- 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' |
hc (computed) | 47° 08.4' |
ho | 47° 13.6' |
a (intercept) | 5.2 towards |
Z | 018.9° |
Zn | 018.9° |
2007. Reducing a Sun Sight[edit]
The example below points out the similarities betweenreducing a Sun sight and reducing a star sight. It also demonstratesthe additional corrections required for low altitude(<10°) sights and sights taken during non-standard temperatureand pressure conditions.
On June 16, 1994, at 05-15-23 local time, at DR positionL 30°N λ 45°W, a navigator takes a sight of the Sun’supper limb. The navigator has a height of eye of 18 feet, thetemperature is 88° F, and the atmospheric pressure is 982mb. The sextant altitude is 3° 20.2'. There is no index error.Determine the observed altitude. See Figure 2007.
Apply the index and dip corrections to hs to obtain ha.Because ha is less than 10°, use the special altitude correctiontable for sights between 0° and 10° located on the right insidefront page of the Nautical Almanac.
Enter the table with the apparent altitude, the limb ofthe Sun used for the sight, and the period of the year. Interpolationfor the apparent altitude is not required. In thiscase, the table yields a correction of −29.4'. The correction’salgebraic sign is found at the head of each group of entriesand at every change of sign.
The additional correction is required because of thenon-standard temperature and atmospheric pressure underwhich the sight was taken. The correction for these nonstandardconditions is found in the Additional Correctionstable located on page A4 in the front of the Nautical Almanac.
First, enter the Additional Corrections table with thetemperature and pressure to determine the correct zoneletter: in this case, zone L. Then, locate the correction in theL column corresponding to the apparent altitude of 3° 16.1'.Interpolate between the table arguments of 3° 00.0' and 3°30.0' to determine the additional correction: +1.4'. The totalcorrection to the apparent altitude is the sum of the altitudeand additional corrections: −28.0'. This results in an ho of2° 48.1'.
Next, determine the Sun’s GHA and declination.
Body | Sun UL |
Index Correction | 0 |
Dip Correction (18 ft) | −4.1' |
Sum | −4.1' |
hs | 3° 20.2' |
ha | 3° 16.1' |
Altitude Correction | −29.4' |
Additional Correction | +1.4' |
Horizontal Parallax | 0 |
Correction to ha | −28.0' |
ho | 2° 48.1' |
Date | June 16, 1994 |
DR Latitude | N30° 00.0' |
DR Longitude | W045° 00.0' |
Observation Time | 05-15-23 |
Watch Error | 0 |
Zone Time | 05-15-23 |
Zone Description | +03 |
GMT | 08-15-23 |
Date GMT | June 16, 1994 |
Tab GHA / v | 299° 51.3' / n.a. |
GHA Increment | 3° 50.8' |
SHA or v correction | not applicable |
GHA | 303°42.1' |
Assumed Longitude | 44° 42.1' W |
LHA | 259° |
Tab Declination / d | N23° 20.5' / +0.1' |
d Correction | 0.0 |
True Declination | N23° 20.5' |
Assumed Latitude | N30° (same) |
Again, this process is similar to the star sights reducedabove. Notice, however, that SHA, a quantity unique to starsight reduction, is not used in Sun sight reduction.
Determining the Sun’s GHA is less complicated thandetermining a star’s GHA. The Nautical Almanac’s dailypages list the Sun’s GHA in hourly increments. In this case,the Sun’s GHA at 0800 GMT on June 16, 1994 is 299°51.3'. The v correction is not applicable for a Sun sight;therefore, applying the increment correction yields theSun’s GHA. In this case, the GHA is 303° 42.1'.
Determining the Sun’s LHA is similar to determininga star’s LHA. In determining the Sun’s declination, however,an additional correction not encountered in the starsight, the d correction, must be considered. The bottom ofthe Sun column on the daily pages of the Nautical Almanaclists the d value. This is an interpolation factor for theSun’s declination. The sign of the d factor is not given; itmust be determined by noting from the Almanac if theSun’s declination is increasing or decreasing throughoutthe day. If it is increasing, the factor is positive; if it is decreasing,the factor is negative. In the above problem, theSun’s declination is increasing throughout the day. Therefore,the d factor is +0.1.
Having obtained the d factor, enter the 15 minuteincrement and correction table. Under the column labeled“v or d corrn,” find the value for d in the left hand column.The corresponding number in the right hand column is thecorrection; apply it to the tabulated declination. In thiscase, the correction corresponding to a d value of +0.1 is0.0'.
Correction (+ or −) | +10.8' |
Computed Altitude (hc) | 2° 39.6' |
Observed Altitude (ho) | 2° 48.1' |
Intercept | 8.5 NM (towards) |
Z | 064.7° |
Zn | 064.7° |
The final step will be to determine hc and Zn.Enter Pub. 229 with an LHA of 259°, a declination of N23° 20.5', and anassumed latitude of 30°N.
Declination Increment / + or − d | 20.5' / +31.5 |
Tabulated Altitude | 2° 28.8' |
2008. Reducing a Moon Sight[edit]
The Moon is easy to identify and is often visible duringthe day. However, the Moon’s proximity to the Earth requiresapplying additional corrections to ha to obtain ho. This articlewill cover Moon sight reduction.
At 10-00-00 GMT, June 16, 1994, the navigator obtains asight of the Moon’s upper limb. Hs is 26° 06.7'. Height of eyeis 18 feet; there is no index error. Determine ho, the Moon’sGHA, and the Moon’s declination. See Figure 2008.
This example demonstrates the extra correctionsrequired for obtaining ho for a Moon sight. Apply the indexand dip corrections in the same manner as for star and Sunsights. The altitude correction comes from tables located onthe inside back covers of the Nautical Almanac.
In this case, the apparent altitude was 26° 02.6'. Enter thealtitude correction table for the Moon with the aboveapparent altitude. Interpolation is not required. Thecorrection is +60.5'. The additional correction in this case isnot applicable because the sight was taken under standardtemperature and pressure conditions.
The horizontal parallax correction is unique to Moonsights. The table for determining this HP correction is on theback inside cover of the Nautical Almanac. First, go to thedaily page for June 16 at 10-00-00 GMT. In the column forthe Moon, find the HP correction factor corresponding to10-00-00. Its value is 58.4. Take this value to the HPcorrection table on the inside back cover of the Almanac.Notice that the HP correction columns line up verticallywith the Moon altitude correction table columns. Find theHP correction column directly under the altitude correctiontable heading corresponding to the apparent altitude. Enterthat column with the HP correction factor from the dailypages. The column has two sets of figures listed under “U”and “L” for upper and lower limb, respectively. In this case,trace down the “U” column until it intersects with the HPcorrection factor of 58.4. Interpolating between 58.2 and58.5 yields a value of +4.0' for the horizontal parallaxcorrection.
Body | Moon (UL) |
Index Correction | 0.0' |
Dip (18 feet) | −4.1' |
Sum | −4.1' |
Sextant Altitude (hs) | 26° 06.7' |
Apparent Altitude (ha) | 26° 02.6' |
Altitude Correction | +60.5' |
Additional Correction | 0.0' |
Horizontal Parallax (58.4) | +4.0' |
Moon Upper Limb Correction | −30.0' |
Correction to ha | +34.5' |
Observed Altitude (ho) | 26° 37.1' |
The final correction is a constant -30.0' correction to haapplied only to sights of the Moon’s upper limb. This correctionis always negative; apply it only to sights of the Moon’s upperlimb, not its lower limb. The total correction to ha is the sum ofall the corrections; in this case, this total correction is +34.5minutes.
To obtain the Moon’s GHA, enter the daily pages in theMoon column and extract the applicable data just as for a star orSun sight. Determining the Moon’s GHA requires an additionalcorrection, the v correction.
GHA Moon and v | 245° 45.1' and +11.3 |
GHA Increment | 0° 00.0' |
v Correction | +0.1' |
GHA | 245° 45.2' |
First, record the GHA of the Moon for 10-00-00 onJune 16, 1994, from the daily pages of the Nautical Almanac.Record also the v correction factor; in this case, it is+11.3. The v correction factor for the Moon is always positive.The increment correction is, in this case, zero becausethe sight was recorded on the even hour. To obtain the vcorrection, go to the tables of increments and corrections. Inthe 0 minute table in the v or d correction columns, find thecorrection that corresponds to a v = 11.3. The table yields acorrection of +0.1'. Adding this correction to the tabulatedGHA gives the final GHA as 245° 45.2'.
Finding the Moon’s declination is similar to finding thedeclination for the Sun or stars. Go to the daily pages forJune 16, 1994; extract the Moon’s declination and d factor.
Tabulated Declination / d | S 00° 13.7' / +12.1 |
d Correction | +0.1' |
True Declination | S 00° 13.8' |
The tabulated declination and the d factor come fromthe Nautical Almanac’s daily pages. Record the declinationand d correction and go to the increment and correctionpages to extract the proper correction for the given d factor.In this case, go to the correction page for 0 minutes. Thecorrection corresponding to a d factor of +12.1 is +0.1. It isimportant to extract the correction with the correctalgebraic sign. The d correction may be positive or negativedepending on whether the Moon’s declination is increasingor decreasing in the interval covered by the d factor. In thiscase, the Moon’s declination at 10-00-00 GMT on 16 Junewas S 00° 13.7'; at 11-00-00 on the same date the Moon’sdeclination was S 00° 25.8'. Therefore, since thedeclination was increasing over this period, the d correctionis positive. Do not determine the sign of this correction bynoting the trend in the d factor. In other words, had the dfactor for 11-00-00 been a value less than 12.1, that wouldnot indicate that the d correction should be negative.Remember that the d factor is analogous to an interpolationfactor; it provides a correction to declination. Therefore, thetrend in declination values, not the trend in d values,controls the sign of the d correction. Combine the tabulateddeclination and the d correction factor to determine the truedeclination. In this case, the Moon’s true declination is S00° 13.8'.
Having obtained the Moon’s GHA and declination,calculate LHA and determine the assumed latitude. Enter theSight Reduction Table with the LHA, assumed latitude, andcalculated declination. Calculate the intercept and azimuth inthe same manner used for star and Sun sights.
2009. Reducing a Planet Sight[edit]
There are four navigational planets: Venus, Mars,Jupiter, and Saturn. Reducing a planet sight is similar toreducing a Sun or star sight, but there are a few importantdifferences. This Article will cover the procedure fordetermining ho, the GHA and the declination for a planetsight.
On July 27, 1995, at 09-45-20 GMT, you take a sightof Mars. Hs is 33° 20.5'. The height of eye is 25 feet, and theindex correction is +0.2'. Determine ho, GHA, and declination.See Figure 2009.
The table below XX demonstrates the similarity betweenreducing planet sights and reducing sights of the Sun andstars. Calculate and apply the index and dip corrections exactlyas for any other sight. Take the resulting apparentaltitude and enter the altitude correction table for the starsand planets on the inside front cover of the Nautical Almanac.
Body | Mars |
Index Correction | +0.2' |
Dip Correction (25 feet) | −4.9' |
Sum | −4.7' |
hs | 33° 20.5' |
ha | 33° 15.8' |
Altitude Correction | −1.5' |
Additional Correction | Not applicable |
Horizontal Parallax | Not applicable |
Additional Correction for Mars | +0.1' |
Correction to ha | −1.4' |
ho | 33° 14.4' |
In this case, the altitude correction for 33° 15.8' results ina correction of -1.5'. The additional correction is not applicablebecause the sight was taken at standard temperature and pressure;the horizontal parallax correction is not applicable to aplanet sight. All that remains is the correction specific to Marsor Venus. The altitude correction table in the Nautical Almanacalso contains this correction. Its magnitude is a function ofthe body sighted (Mars or Venus), the time of year, and thebody’s apparent altitude. Entering this table with the data forthis problem yields a correction of +0.1'. Applying thesecorrections to ha results in an ho of 33° 14.4'.
Tabulated GHA / v | 256°10.6' / 1.1 |
GHA Increment | 11° 20.0' |
v correction | +0.8' |
GHA | 267°31.4' |
The only difference between determining the Sun’s GHAand a planet’s GHA lies in applying the v correction. Calculatethis correction from the v or d correction section of the Incrementsand Correction table in the Nautical Almanac.Find the v factor at the bottom of the planets’ GHA columnson the daily pages of the Nautical Almanac. For Mars onJuly 27, 1995, the v factor is 1.1. If no algebraic signprecedes the v factor, add the resulting correction to thetabulated GHA. Subtract the resulting correction only whena negative sign precedes the v factor. Entering the v or dcorrection table corresponding to 45 minutes yields acorrection of 0.8'. Remember, because no sign preceded thev factor on the daily pages, add this correction to thetabulated GHA. The final GHA is 267°31.4'.
Tabulated Declination / d | S 01° 06.1' / 0.6 |
d Correction | +0.5' |
True Declination | S 01° 06.6' |
Read the tabulated declination directly from the dailypages of the Nautical Almanac. The d correction factor islisted at the bottom of the planet column; in this case, thefactor is 0.6. Note the trend in the declination values for theplanet; if they are increasing during the day, the correctionfactor is positive. If the planet’s declination is decreasingduring the day, the correction factor is negative. Next, enterthe v or d correction table corresponding to 45 minutes andextract the correction for a d factor of 0.6. The correction inthis case is +0.5'.
From this point, reducing a planet sight is exactly thesame as reducing a Sun sight.
MERIDIAN PASSAGE[edit]
This section covers determining both latitude andlongitude at the meridian passage of the Sun, or LocalApparent Noon (LAN). Determining a vessel’s latitude atLAN requires calculating the Sun’s zenith distance anddeclination and combining them according to the rulesdiscussed below.
Latitude at LAN is a special case of the navigationaltriangle where the Sun is on the observer’s meridian and thetriangle becomes a straight north/south line. No “solution” isnecessary, except to combine the Sun’s zenith distance andits declination according to the rules discussed below.Longitude at LAN is a function of the time elapsed since theSun passed the Greenwich meridian. The navigator mustdetermine the time of LAN and calculate the GHA of the Sun atthat time. The following examples demonstrates these processes.
2010. Latitude at Meridian Passage[edit]
At 1056 ZT, May 16, 1995, a vessel’s DR position is L40° 04.3'N and λ 157° 18.5' W. The ship is on course 200°Tat a speed of ten knots. (1) Calculate the first and second estimatesof Local Apparent Noon. (2) The navigator actuallyobserves LAN at 12-23-30 zone time. The sextant altitudeat LAN is 69° 16.0'. The index correction is +2.1' and theheight of eye is 45 feet. Determine the vessel’s latitude.
First, determine the time of meridian passage from the dailypages of the Nautical Almanac. In this case, the meridianpassage for May 16, 1995, is 1156. That is, the Sun crosses thecentral meridian of the time zone at 1156 ZT and the observer’slocal meridian at 1156 local time. Next, determine the vessel’sDR longitude for the time of meridian passage. In this case, thevessel’s 1156 DR longitude is 157° 23.0' W. Determine the timezone in which this DR longitude falls and record the longitudeof that time zone’s central meridian. In this case, the centralmeridian is 150° W. Enter the Conversion of Arc to Time tablein the Nautical Almanac with the difference between the DRlongitude and the central meridian longitude. The conversion for7° of arc is 28m of time, and the conversion for 23' of arc is1m32s of time. Sum these two times. If the DR position is westof the central meridian (as it is in this case), add this time to thetime of tabulated meridian passage. If the longitude difference isto the east of the central meridian, subtract this time from thetabulated meridian passage. In this case, the DR position is westof the central meridian. Therefore, add 29 minutes and 32seconds to 1156, the tabulated time of meridian passage. Theestimated time of LAN is 12-25-32 ZT.
This first estimate for LAN does not take into account thevessel’s movement. To calculate the second estimate of LAN,first determine the DR longitude for the time of first estimate ofLAN (12-25-32 ZT). In this case, that longitude would be 157°25.2' W. Then, calculate the difference between the longitude ofthe 12-25-32 DR position and the central meridian longitude.This would be 7° 25.2'. Again, enter the arc to time conversiontable and calculate the time difference corresponding to thislongitude difference. The correction for 7° of arc is 28' of time,and the correction for 25.2' of arc is 1'41' of time. Finally, applythis time correction to the original tabulated time of meridianpassage (1156 ZT). The resulting time, 12-25-41 ZT, is thesecond estimate of LAN.
Solving for latitude requires that the navigator calculatetwo quantities: the Sun’s declination and the Sun’s zenithdistance. First, calculate the Sun’s true declination at LAN. Theproblem states that LAN is 12-28-30. (Determining the exacttime of LAN is covered in Article 2011.) Enter the time ofobserved LAN and add the correct zone description todetermine GMT. Determine the Sun’s declination in the samemanner as in the sight reduction problem in Article 2006. In thiscase, the tabulated declination was N 19° 19.1', and the dcorrection +0.2'. The true declination, therefore, is N 19° 19.3'.
Next, calculate zenith distance. Recall from NavigationalAstronomy that zenith distance is simply 90° - observed altitude.Therefore, correct hs to obtain ha; then correct ha to obtain ho.Then, subtract ho from 90° to determine the zenith distance.Name the zenith distance North or South depending on therelative position of the observer and the Sun’s declination. If theobserver is to the north of the Sun’s declination, name the zenithdistance north. Conversely, if the observer is to the south of theSun’s declination, name the zenith distance south. In this case,the DR latitude is N 39° 55.0' and the Sun’s declination is N 19°19.3'. The observer is to the north of the Sun’s declination;therefore, name the zenith distance north. Next, compare thenames of the zenith distance and the declination. If their namesare the same (i.e., both are north or both are south), add the twovalues together to obtain the latitude. This was the case in thisproblem. Both the Sun’s declination and zenith distance werenorth; therefore, the observer’s latitude is the sum of the two.
Date | 16 May 1995 |
DR Latitude (1156 ZT) | 39° 55.0' N |
DR Longitude (1156 ZT) | 157° 23.0' W |
Central Meridian | 150° W |
d Longitude (arc) | 7° 23' W |
d Longitude (time) | +29 min. 32 sec |
Meridian Passage (LMT) | 1156 |
ZT (first estimate) | 12-25-32 |
DR Longitude (12-25-32) | 157° 25.2' |
d Longitude (arc) | 7° 25.2' |
d Longitude (time) | +29 min. 41 sec |
Meridian Passage | 1156 |
ZT (second estimate) | 12-25-41 |
ZT (actual transit) | 12-23-30 local |
Zone Description | +10 |
GMT | 22-23-30 |
Date (GMT) | 16 May 1995 |
Tabulated Declination / d | N 19° 09.0' / +0.6 |
d correction | +0.2' |
True Declination | N 19° 09.2' |
Index Correction | +2.1' |
Dip (48 ft) | -6.7' |
Sum | -4.6' |
hs (at LAN) | 69° 16.0' |
ha 69° | 11.4' |
Altitude Correction | +15.6' |
89° 60' | 89° 60.0' |
ho 69° | 27.0' |
Zenith Distance | N 20° 33.0' |
True Declination | N 19° 09.2' |
Latitude | 39° 42.2' |
If the name of the body’s zenith distance is contrary tothe name of the Sun’s declination, then subtract the smallerof the two quantities from the larger, carrying for the nameof the difference the name of the larger of the twoquantities. The result is the observer’s latitude. Thefollowing examples illustrate this process.
Zenith Distance | N 25° |
True Declination | S 15° |
Latitude | N 10° |
Zenith Distance | S 50° |
True Declination | N 10° |
Latitude | S 40° |
2011. Longitude at Meridian Passage[edit]
Determining a vessel’s longitude at LAN is straightforward.In the western hemisphere, the Sun’s GHA atLAN equals the vessel’s longitude. In the easternhemisphere, subtract the Sun’s GHA from 360° todetermine longitude. The difficult part lies in determiningthe precise moment of meridian passage.
Determining the time of meridian passage presents aproblem because the Sun appears to hang for a finite timeat its local maximum altitude. Therefore, noting the timeof maximum sextant altitude is not sufficient fordetermining the precise time of LAN. Two methods areavailable to obtain LAN with a precision sufficient fordetermining longitude: (1) the graphical method and (2)the calculation method. The graphical method isdiscussed first below.
See Figure 2011. For about 30 minutes before theestimated time of LAN, measure and record several sextantaltitudes and their corresponding times. Continue takingsights for about 30 minutes after the Sun has descendedfrom the maximum recorded altitude. Increase the sightingfrequency near the meridian passage. One sight every 20-30seconds should yield good results near meridian passage;less frequent sights are required before and after.Plot the resulting data on a graph of sextant altitudeversus time and draw a fair curve through the plotteddata. Next, draw a series of horizontal lines across thecurve formed by the data points. These lines willintersect the faired curve at two different points. The xcoordinates of the points where these lines intersect thefaired curve represent the two different times when theSun’s altitude was equal (one time when the Sun wasascending; the other time when the Sun was descending).Draw three such lines, and ensure the lines havesufficient vertical separation. For each line, average thetwo times where it intersects the faired curve. Finally,average the three resulting times to obtain a final value
for the time of LAN. From the Nautical Almanac,determine the Sun’s GHA at that time; this is yourlongitude in the western hemisphere. In the easternhemisphere, subtract the Sun’s GHA from 360° todetermine longitude. For a quicker but less exact time,simply drop a perpendicular from the apex of the curveand read the time along the time scale.The second method of determining LAN is similar tothe first. Estimate the time of LAN as discussed above,Measure and record the Sun’s altitude as the Sunapproaches its maximum altitude. As the Sun begins todescend, set the sextant to correspond to the altituderecorded just before the Sun’s reaching its maximumaltitude. Note the time when the Sun is again at thataltitude. Average the two times. Repeat this procedurewith two other altitudes recorded before LAN, each timepresetting the sextant to those altitudes and recording thecorresponding times that the Sun, now on its descent,passes through those altitudes. Average thesecorresponding times. Take a final average among thethree averaged times; the result will be the time ofmeridian passage. Determine the vessel’s longitude bydetermining the Sun’s GHA at the exact time of LAN.
LATITUDE BY POLARIS[edit]
2012. Latitude by Polaris[edit]
Since Polaris is always within about 1° of the NorthPole, the altitude of Polaris, with a few minor corrections,equals the latitude of the observer. This relationship makesPolaris an extremely important navigational star in thenorthern hemisphere.
The corrections are necessary because Polaris orbits ina small circle around the pole. When Polaris is at the exactsame altitude as the pole, the correction is zero. At twopoints in its orbit it is in a direct line with the observer andthe pole, either nearer than or beyond the pole. At thesepoints the corrections are maximum. The followingexample illustrates converting a Polaris sight to latitude.
At 23-18-56 GMT, on April 21, 1994, at DR Lat. 50°23.8' N, λ=37° 14.0' W, the observed altitude of Polaris (ho) is 49° 31.6'. Find the vessel’s latitude.
To solve this problem, use the equation:
where ho is the sextant altitude (hs) corrected asin any other star sight; 1° is a constant; and A0, A1, and A2 arecorrection factors from the Polaris tables found in theNautical Almanac. These three correction factors arealways positive. One needs the following information toenter the tables: LHA of Aries, DR latitude, and the monthof the year. Therefore:
Enter the Polaris table with the calculated LHA of Aries(162° 03.5'). See Figure 2012. The first correction, A0, is afunction solely of the LHA of Aries. Enter the table columnindicating the proper range of LHA of Aries; in this case,enter the 160°-169° column. The numbers on the left handside of the A0 correction table represent the whole degrees ofLHA ♈; interpolate to determine the proper A0 correction.In this case, LHA ♈ was 162° 03.5'. The A0 correction forLHA = 162° is 1° 25.4' and the A0 correction for LHA = 163°is 1° 26.1'. The A0 correction for 162° 03.5' is 1° 25.4'.
To calculate the A1 correction, enter the A1 correctiontable with the DR latitude, being careful to stay in the 160°-169° LHA column. There is no need to interpolate here; simplychoose the latitude that is closest to the vessel’s DR latitude. Inthis case, L is 50°N. The A1 correction corresponding to anLHA range of 160°-169° and a latitude of 50°N is + 0.6'.
Finally, to calculate the A2 correction factor, stay in the160°-169° LHA column and enter the A2 correctiontable. Follow the column down to the month of the year; inthis case, it is April. The correction for April is + 0.9'.
Sum the corrections, remembering that all three arealways positive. Subtract 1° from the sum to determine thetotal correction; then apply the resulting value to theobserved altitude of Polaris. This is the vessel’s latitude.
Tabulated GHA ♈ (2300 hrs.) | 194° 32.7' |
Increment (18-56) | 4° 44.8' |
GHA ♈ | 199° 17.5' |
DR Longitude (-W +E) | 37° 14.0' |
LHA ♈ | 162° 03.5' |
A0 (162° 03.5') | +1° 25.4' |
A1 (L = 50°N) | +0.6' |
A2 (April) | +0.9' |
Sum | 1° 26.9' |
Constant | −1° 00.0' |
Observed Altitude | 49° 31.6' |
Total Correction | +26.9' |
Latitude | N 49° 58.5' |
THE DAY’S WORK IN CELESTIAL NAVIGATION[edit]
2013. Celestial Navigation Daily Routine[edit]
The navigator need not follow the entire celestial routineif celestial navigation is not the primary navigationmethod. It is appropriate to use only the steps of the celestialday’s work that are necessary to provide a meaningfulcheck on the primary fix source and maintain competencyin celestial techniques.
The list of procedures below provides a complete dailycelestial routine to follow. This sequence works equallywell for all sight reduction methods, whether tabular, mathematical,computer program, or celestial navigationcalculator. See Figure 2013 for an example of a typicalday’s celestial plot.
1. Before dawn, compute the time of morning twilightand plot the dead reckoning position for that time.
2. At morning twilight, take and reduce celestial observationsfor a fix. At sunrise take an amplitude of theSun for a compass check.
3. Mid-morning, wind the chronometer and determinechronometer error with a radio time tick.
4. Mid-morning, reduce a Sun sight for a morning Sunline.
5. Calculate an azimuth of the Sun for a compasscheck, if no amplitude was taken at sunrise.
6. At LAN, obtain a Sun line and advance the morningSun line for the noon fix. Compute a longitude determinedat LAN for an additional LOP.
7. Mid afternoon, again take and reduce a Sun sight.This is primarily for use with an advanced noon Sunline, or with a Moon or Venus line if the skies are overcastduring evening twilight.
8. Calculate an azimuth of the Sun for a compass checkat about the same time as the afternoon Sun observation.The navigator may replace this azimuth with anamplitude observation at sunset.
9. During evening twilight, reduce celestial observationsfor a fix.
10. Be alert at all times for the moon or brighter planetswhich may be visible during daylight hours for additionalLOP’s, and Polaris at twilight for a latitude line.
Chapter 7, Chapter 17, and Chapter 20 contain detailed explanationsof the procedures required to carry out the variousfunctions of this routine.
Retrieved from 'https://en.wikisource.org/w/index.php?title=The_American_Practical_Navigator/Chapter_20&oldid=6944521'
Download Book Marine Navigation in PDF format. You can Read Online Marine Navigation here in PDF, EPUB, Mobi or Docx formats.Draft Marine Navigation Bill
Author :Great Britain. Parliament House of Commons. Transport CommitteeISBN :0215522230
Genre :
File Size : 30.36 MB
Format :PDF, ePub
Download :347
Read :1001
The Draft Marine Navigation Bill was published on 6 May 2008. (Cm. 7370, ISBN 9780101737029 ). A supplementary consultation on the ratification of the Nairobi Convention on the Removal of Wrecks, for which the draft Bill includes the necessary statutory provisions, was published at the same time by the Department for Transport. The Bill covers four main areas: (a) port safety, including measures relating to pilotage, National Occupational Standards for Harbour Masters and pilots, and extending powers of general direction to more harbour authorities; (b) the closure of harbours, and the subsequent relinquishing of the legal rights and duties of the harbour authority; (c) the role of the General Lighthouse Authorities, including their powers of enforcement, the territorial extent of their operations, their commercial work and their pension schemes; and (d) the ratification and implementation of the Nairobi Convention. The introduction of new powers to issue directions to port and harbour authorities and to specify minimum standards of competence for harbour masters and pilots is supported. The provisions relating to General Lighthouse Authorities are a sensible package intended to clarify their powers and put beyond doubt the legal validity of much of the essential work which they have been carrying out for centuries. The provision in the draft Bill to give statutory effect Nairobi International Convention on the Removal of Wrecks will remove from the UK taxpayer a significant potential liability in respect of wrecks in UK waters.
Marine Navigation And Safety Of Sea Transportation
Author :Adam WeintritISBN :9781315882987
Genre :Mathematics
File Size : 70.9 MB
Format :PDF, ePub
Download :787
Read :1116
The TransNav 2013 Symposium held at the Gdynia Maritime University, Poland in June 2013 has brought together a wide range of participants from all over the world. The program has offered a variety of contributions, allowing to look at many aspects of the navigational safety from various different points of view. Topics presented and discussed at the Symposium were: navigation, safety at sea, sea transportation, education of navigators and simulator-based training, sea traffic engineering, ship's manoeuvrability, integrated systems, electronic charts systems, satellite, radio-navigation and anti-collision systems and many others. This book is part of a series of four volumes and provides an overview of Problems in Marine Navigation and is addressed to scientists and professionals involved in research and development of navigation, safety of navigation and sea transportation.
Marine Navigation 1 Piloting
Author :Richard R. HobbsISBN :9789401173704
Genre :Juvenile Nonfiction
File Size : 46.98 MB
Format :PDF, ePub, Mobi
Download :305
Read :1325
Throughout the history of warfare at sea, navigation has been an important basic determinant of victory. Occasionally, new members of the fraternity of the sea will look upon navigation as a chore to be tolerated only as long as it takes to find someone else to assume the responsibility. In my experience, such individuals never make good naval officers. Commander Hobbs has succeeded in bringing together the information and practical skills required for that individual who would take the first step down the road toward becoming a competent marine navigator. At the outset of this book, the author stresses the necessity for safe navigation, but there is another basic tenet of sea warfare that this book serves. The best weapons system man has ever devised cannot function effectively unless it knows where it is in relation to the real world, where it is in relation to the enemy, and where the enemy is in relation to the real world. Not all defeats can be attributed to this lack of information, but no victories have been won by those who did not know where they were.
Elementary Marine Navigation
Author :S. A. WallingISBN :9781107419414
Genre :Education
Sight Reduction Tables 2018
File Size : 41.84 MB
Format :PDF, ePub
Download :246
Read :296
Originally published in 1944, this book was originally intended as a continuation of the 1943 publication Nautical Mathematics, which is also reissued in this series. In it, the principles set out in Nautical Mathematics are given practical applications, and the text is supplied with exercises to test and clarify the lessons. This book will be of value to anyone with an interest in the history of education in the forces during WWII.
Pub229 Sight Reduction Tables For Marine Navigation
Author :NIMA StaffISBN :1577851935
Genre :
File Size : 62.22 MB
Format :PDF, Mobi
Download :880
Read :668
The Sight Reduction Tables for Marine Navigation (Pub 229) is published in six volumes, each of which contains two-eight degree zones of latitude with a one-degree overlap between volumes. They are designed to facilitate the practice of celestial navigation at sea. The tables are primarily used with the intercept method of sight reduction by entering arguments of latitude, declination, and local hour angle and obtaining tabulated altitudes and azimuth angles. The tables are prepared and published by NIMA on an as-needed basis.
Sight Reduction Tables For Marine Navigation
Author :ISBN :UCR:31210014700817
Genre :Navigation
File Size : 89.63 MB
Format :PDF
Download :679
Read :633
Marine Electronic Navigation
Author :Stephen F. AppleyardISBN :9781134963096
Genre :Business & Economics
File Size : 81.81 MB
Format :PDF, ePub
Download :409
Read :831
'This 600 page textbook must be a good candidate for being the authoritative reference on its subject..This book reveals all through a good, clear text amply illustrated.. The authors and publisher are to be congratulated on an excellent production.'--The Naval Review Well organized, clear and easy to read. The second edition has been enlarged with various items devoted to new electronic equipment now encountered by mariners, especially those concerned with navigational and radiocommunication equipment.'--International Hydrographic Bulletin 'A major and standard text, now much enlarged and revised with sections on radar, communications, the gyro compass and all navigation systems encountered in merchant ships. Full and expert treatment of all aspects of electronic navigation and communication systems making it one of the leading references on its subjects.'--Lloyds List
Basic Marine Navigation
Author :Bart Jan BokISBN :UCSD:31822012371910
Genre :Navigation
File Size :
Sight Reduction Tables For Marine Navigation
53.25 MBFormat :PDF, ePub
Download :269
Read :1206
Sight Reduction Tables For Marine Navigation Latitudes 750 900 Inclusive
Author :ISBN :MINN:31951D02598003C
Sight Reduction Tables Vol 1 Pdf
Genre :Nautical astronomy
File Size : 74.37 MB
Format :PDF, ePub, Docs
Download :719
Read :263
Marine Charts Unleashed
Author :Richard Fairman BA JPISBN :
Genre :
File Size : 83.73 MB
Format :PDF, ePub
Download :674
Read :376
Access to, or create fully calibrated Digital Marine Charts for all areas of the world We guarantee that wherever you are in the world you can have your own Digital Marine Chart. The Digital Marine Charts you can access, or create for your own use Compatible with computer based chartplotters including SeaClear, OpenCPN, Polar Navy, Coastal Explorer Fugawi Ozie Explorer and many others, Access many thousand of chart images including US Waters, Worldwide, NZ, Brazil etc. Create your own Satellite Image Charts. Create calibrated charts from your own paper charts for your own use Your first Marine Chart will already save you the price of this book The book includes free Chartplotter Comparison Guide
Top Download:
Items in search results
SIGHT REDUCTION TABLES FOR MARINE NAVIGATION: VOL. 3, LATITUDES 30 - 45, INCLUSI
Pre-owned- £11.99
- + £9.14 postage
- Customs services and international tracking provided
SIGHT REDUCTION TABLES FOR MARINE NAVIGATION: VOL. 3, LATITUDES 45 - 60, INCLUSI
Pre-owned- £16.75
- + £3.00 postage
Admiralty, Sight Reduction Tables for Marine Navigation Vol. 2
Pre-owned- £35.32
- + £32.03 postage
- From United States
- Customs services and international tracking provided
Admiralty, Sight Reduction Tables for Marine Navigation Vol. 1
Pre-owned- £78.53
- + £32.69 postage
- From United States
- Customs services and international tracking provided
Admiralty, Sight Reduction Tables for Marine Navigation Vol. 3
Pre-owned- £35.32
- + £32.03 postage
- From United States
- Customs services and international tracking provided
Sight Reduction Tables for Air Navigation by Nautical Almanac Office
Pre-owned- £22.29
- + £7.20 postage
PUB 229 SIGHT REDUCTION TABLES FOR MARINE NAVIGATION, VOLUME 4: By N.i.m.a. NEW
~ Brand New!! Free Shipping. Satisfaction Guaranteed! ~- £60.46
- + £17.18 postage
- From United States
- Customs services and international tracking provided
1981 Sight Reduction Tables For Marine Navigation Pub. No. 229 Vol. 3 Defense Ma
- £15.71
- + £74.06 postage
- From United States
Sight Reduction Tables for Marine Navigation Latitudes 15-30, Inclusive Vol..
by Editor | HC | Good- £23.57
- + £7.85 postage
- From United States
Sight Reduction Tables for Marine Navigation, Pub No 229, Vol 2 (1st Ed)
by Defense Mapping Agency | HC | Acceptable- £140.09
- + £7.85 postage
- From United States
Sight Reduction tables for Marine Navigation PUB. NO. Vol. 4
New (other)- £17.90
- + £4.47 postage
- From Germany
Sight Reduction Tables for Marine Navigation: Lat. 0-15, Inclusive Pub. No..
by U. S Government | HC | Good- £23.56
- + £7.85 postage
- From United States
SIGHT REDUCTION TABLES MARINE NAVIGATION PUB 229/VOL2/DEFENSE MAPPING AGENCY
New (other)- £27.50
- + £19.18 postage
- From United States
- Customs services and international tracking provided
Sight Reduction Tables For Marine Navigation, Latitudes 15-30, Inclusive
Pre-owned- £15.71
- + £11.30 postage
- From United States
- Customs services and international tracking provided
Sight Reduction Tables for Marine Navigation-Commercial Edition [Latitudes 15-
Pre-owned- £15.56
- + £15.71 postage
- From United States
PUB 229 SIGHT REDUCTION TABLES FOR MARINE NAVIGATION, VOLUME 2: By N.i.m.a. NEW
~ Brand New!! Free Shipping. Satisfaction Guaranteed! ~- £49.10
- + £18.11 postage
- From United States
- Customs services and international tracking provided
SIGHT REDUCTION TABLES FOR MARINE NAVIGATION 45-60, INCLUSIVE By National VG
~Excellent Condition! Quick &Free Shipping. US Seller~- £21.96
- + £12.35 postage
- From United States
- Customs services and international tracking provided
SIGHT REDUCTION TABLES FOR MARINE NAVIGATION LATITUDES 30 - 45 By National NEW
~ Brand New!! Free Shipping. Satisfaction Guaranteed! ~- £32.18
- + £12.51 postage
- From United States
- Customs services and international tracking provided
PUB 229 SIGHT REDUCTION TABLES FOR MARINE NAVIGATION, VOLUME 3: By N.i.m.a.
~Free Shipping! U.S. Seller. Satisfaction Guaranteed!~- £25.10
- + £12.40 postage
- From United States
- Customs services and international tracking provided
SIGHT REDUCTION TABLES FOR MARINE NAVIGATION (PUB 229) VOL. 1 By National NEW
~ Brand New!! Free Shipping. Satisfaction Guaranteed! ~- £32.18
- + £12.51 postage
- From United States
- Customs services and international tracking provided
SIGHT REDUCTION TABLES FOR MARIN NAVIGATION PUB. NO. 229 VOLUME 6 By NEW
~ Brand New!! Free Shipping. Satisfaction Guaranteed! ~- £29.03
- + £12.46 postage
- From United States
- Customs services and international tracking provided
Sight Reduction Tables for Marine Navigation Volume 3. by Nga (English) Paperbac
- £18.43
- + £14.14 postage
- 1 Watching
- From United States
Sight Reduction Tables for Marine Navigation Volume 2 by Nga (English) Paperback
- £18.76
- + £14.08 postage
- From United States
Sight Reduction Tables for Marine Navigation Volume 5. by Nga (English) Paperbac
Brand new- £19.60
- + £14.29 postage
- From United States
Sight Reduction Tables for Marine Navigation Volume 6. by Nga (English) Paperbac
Brand new- £18.76
- + £14.25 postage
- From United States
Sight Reduction Tables for Marine Navigation Volume 1. by N.G.A. (English) Paper
Brand new- £18.08
- + £14.08 postage
- From United States
Sight Reduction Tables for Marine Navigation Volume 4. by Nga (English) Paperbac
Brand new- £18.05
- + £14.08 postage
- From United States
SIGHT REDUCTION TABLES FOR MARINE NAVIGATION-COMMERCIAL EDITION By National NEW
~ Brand New!! Free Shipping. Satisfaction Guaranteed! ~- £35.32
- + £13.51 postage
- From United States
- Customs services and international tracking provided
Sight Reduction Tables for Air Navigation, Volume 3 (Unnamed - 1984) (ID:09248)
- £23.50
- + £4.00 postage
Sight Reduction Tables For Air Navigation V Anon 1967 Book 29667
- £10.32
- + £4.00 postage
Good - Sight Reduction Tables for Air Navigation Vol 1 1982 HMSO
Pre-owned- £12.90
- + £3.99 postage
Sight Reduction Tables for Air Navigation Volume 3 9781921936845
Brand new- £17.33
- + £2.46 postage
Sight Reduction Tables For Navigation
New (other)- £2.40
- 0 bids
- Postage not specified
Rapid Sight Reduction Tables for Navigation: United Kingdom Ed ,.9780118875561
Pre-owned- £5.68
- + £3.49 postage
- Buy 1, get 1 20% off
Sight Reduction Tables for Air Navigation Volume I SELECTED STARS EPOCH 1975.0
- £3.10Was: Previous price£4.43
- + £5.37 postage
- From Germany
- £3.10
Rapid Sight Reduction Tables for Navigation: United Kingdom Edition: United Ki,
Pre-owned- £13.82
- + £3.49 postage
- Buy 1, get 1 20% off
Sight Reduction Tables for Air Navigation Volume 2 9781921936838
Brand new- £15.02
- + £1.40 postage
Sight Reduction Tables for Air Navigation Volume 1 9781921936869
Brand new- £17.33
- + £2.35 postage
Sight Reduction Tables for Air Navigation (Selected Stars) 1951 U.S. Navy Publ.
Pre-owned- £29.06
- + £29.46 postage
- From United States
SIGHT REDUCTION TABLES #249 Volumes 1, 2 & 3 Book Lot Air Navigation DoD 1980
Pre-owned- £39.28
- + £32.51 postage
- From United States
- Customs services and international tracking provided
Sight Reduction Tables For Air Navigation 1980 Pub No 249 Vol 1
- £15.71Was: Previous price£31.42
- + £17.60 postage
- From United States
- Customs services and international tracking provided
- £15.71
Rapid Sight Reduction Tables for Navigation: United Kingdom Ed ,.9780118875554
Pre-owned- £25.89
- + £3.49 postage
- Buy 1, get 1 20% off
Rapid Sight Reduction Tables for Navigation: United Kingdom Edition Vol 3 by Na
Pre-owned- £63.36
- + £7.20 postage
Air Navigation Sight Reduction Tables
Pre-owned- £20.43
- + £9.43 postage
- From United States
- Customs services and international tracking provided
Altitude Tables 31 to 60 N or S by Frederick Ball 1910 . Marine Navigation
- £14.95
- + £10.08 postage
- Customs services and international tracking provided
Publications Nautical-Sight Reduction Tables For Air (US IMPORT) BOOK NEW
Brand new- £17.76
- + £3.00 postage
- From United States
Rapid Sight Reduction Tables for Navigation: United Kingdom Edition Vol 2 by Na
Pre-owned- £18.96
- + £7.20 postage
Sight Reduction Tables for Air Navigation: Volume 1 EPOCH 1980.0 Air Force Dept
Pre-owned- £29.99
- + £11.98 postage
Celestial Navigation Using the Sight Reduction Tables from 'Pub.. 97814602
Brand new- £15.85
- + £2.46 postage
Sight Reduction Tables for Air Navigation (A.P.3270), Volume One,
Pre-owned- £13.99
- + £1.50 postage
Vintage WWll era sight reduction tables air navigation US dept defense
Pre-owned- £19.64
- + £17.49 postage
- From United States
- Customs services and international tracking provided
Sight Reduction Tables Vol 3 US Navy Hydrographic Air Navigation MS37
Brand new- £70.71
- + £20.62 postage
- From United States
- Customs services and international tracking provided
1963 Reprint Naval Sight Reduction Tables Air Navigation #249 Vol 2 O-39 MS37
Brand new- £70.71
- + £20.62 postage
- From United States
- Customs services and international tracking provided
Sight reduction tables for small boat navigation: Latitudes 0⁰-58⁰, declinati..
Brand new- £65.62
- Postage not specified
- From United States
Astro Navigation Made Easy Using a Pocket Calculator 9780713662221
Brand new- £9.74
- + £1.51 postage
Astro Navigation Made Easy - 9780713662221
Brand new- £9.74
- Postage not specified
Sight Reduction Tables for Air Navigation: Selected Stars Epoch 1995.0 v. 1, Nau
Pre-owned- £16.49
- Postage not specified
The Nautical Almanac for the Year 1981: For Training Purposes Only by H M..
Brand new- £21.13
- + £1.40 postage
The Complete On-Board Celestial Navigator : Includes 2003-2007 Nautical Almanac
Brand new- £48.78
- Postage not specified
- From United States
Sight reduction tables for air navigation - United States - Good - Hardcover
Pre-owned- £37.49
- + £1.60 postage
sight reduction tables for air navigation vol 1 HMSO 1972 AP3270 epoch 1975
- £19.99
- 0 bidsor Best Offer
- + £9.42 postage
- Customs services and international tracking provided
Items in search results
SIGHT REDUCTION TABLES FOR MARINE NAVIGATION: VOL. 3, LATITUDES 30 - 45, INCLUSI
Pre-owned- £11.99
- + £9.14 postage
- Customs services and international tracking provided
SIGHT REDUCTION TABLES FOR MARINE NAVIGATION: VOL. 3, LATITUDES 45 - 60, INCLUSI
Pre-owned- £16.75
- + £3.00 postage
Admiralty, Sight Reduction Tables for Marine Navigation Vol. 2
Pre-owned- £35.32
- + £32.03 postage
- From United States
- Customs services and international tracking provided
Admiralty, Sight Reduction Tables for Marine Navigation Vol. 1
Pre-owned- £78.53
- + £32.69 postage
- From United States
- Customs services and international tracking provided
Admiralty, Sight Reduction Tables for Marine Navigation Vol. 3
Pre-owned- £35.32
- + £32.03 postage
- From United States
- Customs services and international tracking provided
Sight Reduction Tables for Air Navigation by Nautical Almanac Office
Pre-owned- £22.29
- + £7.20 postage
PUB 229 SIGHT REDUCTION TABLES FOR MARINE NAVIGATION, VOLUME 4: By N.i.m.a. NEW
~ Brand New!! Free Shipping. Satisfaction Guaranteed! ~- £60.46
- + £17.18 postage
- From United States
- Customs services and international tracking provided
1981 Sight Reduction Tables For Marine Navigation Pub. No. 229 Vol. 3 Defense Ma
- £15.71
- + £74.06 postage
- From United States
Sight Reduction Tables for Marine Navigation Latitudes 15-30, Inclusive Vol..
by Editor | HC | Good- £23.57
- + £7.85 postage
- From United States
Sight Reduction Tables for Marine Navigation, Pub No 229, Vol 2 (1st Ed)
by Defense Mapping Agency | HC | Acceptable- £140.09
- + £7.85 postage
- From United States
Sight Reduction tables for Marine Navigation PUB. NO. Vol. 4
New (other)- £17.90
- + £4.47 postage
- From Germany
Sight Reduction Tables for Marine Navigation: Lat. 0-15, Inclusive Pub. No..
by U. S Government | HC | Good- £23.56
- + £7.85 postage
- From United States
SIGHT REDUCTION TABLES MARINE NAVIGATION PUB 229/VOL2/DEFENSE MAPPING AGENCY
New (other)- £27.50
- + £19.18 postage
- From United States
- Customs services and international tracking provided
Sight Reduction Tables For Marine Navigation, Latitudes 15-30, Inclusive
Pre-owned- £15.71
- + £11.30 postage
- From United States
- Customs services and international tracking provided
Sight Reduction Tables for Marine Navigation-Commercial Edition [Latitudes 15-
Pre-owned- £15.56
- + £15.71 postage
- From United States
PUB 229 SIGHT REDUCTION TABLES FOR MARINE NAVIGATION, VOLUME 2: By N.i.m.a. NEW
~ Brand New!! Free Shipping. Satisfaction Guaranteed! ~- £49.10
- + £18.11 postage
- From United States
- Customs services and international tracking provided
SIGHT REDUCTION TABLES FOR MARINE NAVIGATION 45-60, INCLUSIVE By National VG
~Excellent Condition! Quick &Free Shipping. US Seller~- £21.96
- + £12.35 postage
- From United States
- Customs services and international tracking provided
SIGHT REDUCTION TABLES FOR MARINE NAVIGATION LATITUDES 30 - 45 By National NEW
~ Brand New!! Free Shipping. Satisfaction Guaranteed! ~- £32.18
- + £12.51 postage
- From United States
- Customs services and international tracking provided
PUB 229 SIGHT REDUCTION TABLES FOR MARINE NAVIGATION, VOLUME 3: By N.i.m.a.
~Free Shipping! U.S. Seller. Satisfaction Guaranteed!~- £25.10
- + £12.40 postage
- From United States
- Customs services and international tracking provided
SIGHT REDUCTION TABLES FOR MARINE NAVIGATION (PUB 229) VOL. 1 By National NEW
~ Brand New!! Free Shipping. Satisfaction Guaranteed! ~- £32.18
- + £12.51 postage
- From United States
- Customs services and international tracking provided
SIGHT REDUCTION TABLES FOR MARIN NAVIGATION PUB. NO. 229 VOLUME 6 By NEW
~ Brand New!! Free Shipping. Satisfaction Guaranteed! ~- £29.03
- + £12.46 postage
- From United States
- Customs services and international tracking provided
Sight Reduction Tables for Marine Navigation Volume 3. by Nga (English) Paperbac
- £18.43
- + £14.14 postage
- 1 Watching
- From United States
Sight Reduction Tables for Marine Navigation Volume 2 by Nga (English) Paperback
- £18.76
- + £14.08 postage
- From United States
Sight Reduction Tables for Marine Navigation Volume 5. by Nga (English) Paperbac
Brand new- £19.60
- + £14.29 postage
- From United States
Sight Reduction Tables for Marine Navigation Volume 6. by Nga (English) Paperbac
Brand new- £18.76
- + £14.25 postage
- From United States
Sight Reduction Tables for Marine Navigation Volume 1. by N.G.A. (English) Paper
Brand new- £18.08
- + £14.08 postage
- From United States
Sight Reduction Tables for Marine Navigation Volume 4. by Nga (English) Paperbac
Brand new- £18.05
- + £14.08 postage
- From United States
SIGHT REDUCTION TABLES FOR MARINE NAVIGATION-COMMERCIAL EDITION By National NEW
~ Brand New!! Free Shipping. Satisfaction Guaranteed! ~- £35.32
- + £13.51 postage
- From United States
- Customs services and international tracking provided
Sight Reduction Tables for Air Navigation, Volume 3 (Unnamed - 1984) (ID:09248)
- £23.50
- + £4.00 postage
Sight Reduction Tables For Air Navigation V Anon 1967 Book 29667
- £10.32
- + £4.00 postage
Good - Sight Reduction Tables for Air Navigation Vol 1 1982 HMSO
Pre-owned- £12.90
- + £3.99 postage
Sight Reduction Tables for Air Navigation Volume 3 9781921936845
Brand new- £17.33
- + £2.46 postage
Sight Reduction Tables For Navigation
New (other)- £2.40
- 0 bids
- Postage not specified
Rapid Sight Reduction Tables for Navigation: United Kingdom Ed ,.9780118875561
Pre-owned- £5.68
- + £3.49 postage
- Buy 1, get 1 20% off
Sight Reduction Tables for Air Navigation Volume I SELECTED STARS EPOCH 1975.0
- £3.10Was: Previous price£4.43
- + £5.37 postage
- From Germany
- £3.10
Rapid Sight Reduction Tables for Navigation: United Kingdom Edition: United Ki,
Pre-owned- £13.82
- + £3.49 postage
- Buy 1, get 1 20% off
Sight Reduction Tables for Air Navigation Volume 2 9781921936838
Brand new- £15.02
- + £1.40 postage
Sight Reduction Tables for Air Navigation Volume 1 9781921936869
Brand new- £17.33
- + £2.35 postage
Sight Reduction Tables for Air Navigation (Selected Stars) 1951 U.S. Navy Publ.
Pre-owned- £29.06
- + £29.46 postage
- From United States
SIGHT REDUCTION TABLES #249 Volumes 1, 2 & 3 Book Lot Air Navigation DoD 1980
Pre-owned- £39.28
- + £32.51 postage
- From United States
- Customs services and international tracking provided
Sight Reduction Tables For Air Navigation 1980 Pub No 249 Vol 1
- £15.71Was: Previous price£31.42
- + £17.60 postage
- From United States
- Customs services and international tracking provided
- £15.71
Rapid Sight Reduction Tables for Navigation: United Kingdom Ed ,.9780118875554
Pre-owned- £25.89
- + £3.49 postage
- Buy 1, get 1 20% off
Rapid Sight Reduction Tables for Navigation: United Kingdom Edition Vol 3 by Na
Pre-owned- £63.36
- + £7.20 postage
Air Navigation Sight Reduction Tables
Pre-owned- £20.43
- + £9.43 postage
- From United States
- Customs services and international tracking provided
Altitude Tables 31 to 60 N or S by Frederick Ball 1910 . Marine Navigation
- £14.95
- + £10.08 postage
- Customs services and international tracking provided
Publications Nautical-Sight Reduction Tables For Air (US IMPORT) BOOK NEW
Brand new- £17.76
- + £3.00 postage
- From United States
Rapid Sight Reduction Tables for Navigation: United Kingdom Edition Vol 2 by Na
Pre-owned- £18.96
- + £7.20 postage
Sight Reduction Tables for Air Navigation: Volume 1 EPOCH 1980.0 Air Force Dept
Pre-owned- £29.99
- + £11.98 postage
Celestial Navigation Using the Sight Reduction Tables from 'Pub.. 97814602
Brand new- £15.85
- + £2.46 postage
Sight Reduction Tables for Air Navigation (A.P.3270), Volume One,
Pre-owned- £13.99
- + £1.50 postage
Vintage WWll era sight reduction tables air navigation US dept defense
Pre-owned- £19.64
- + £17.49 postage
- From United States
- Customs services and international tracking provided
Sight Reduction Tables Vol 3 US Navy Hydrographic Air Navigation MS37
Brand new- £70.71
- + £20.62 postage
- From United States
- Customs services and international tracking provided
1963 Reprint Naval Sight Reduction Tables Air Navigation #249 Vol 2 O-39 MS37
Brand new- £70.71
- + £20.62 postage
- From United States
- Customs services and international tracking provided
Sight reduction tables for small boat navigation: Latitudes 0⁰-58⁰, declinati..
Brand new- £65.62
- Postage not specified
- From United States
Astro Navigation Made Easy Using a Pocket Calculator 9780713662221
Brand new- £9.74
- + £1.51 postage
Astro Navigation Made Easy - 9780713662221
Brand new- £9.74
- Postage not specified
Sight Reduction Tables for Air Navigation: Selected Stars Epoch 1995.0 v. 1, Nau
Pre-owned- £16.49
- Postage not specified
The Nautical Almanac for the Year 1981: For Training Purposes Only by H M..
Brand new- £21.13
- + £1.40 postage
The Complete On-Board Celestial Navigator : Includes 2003-2007 Nautical Almanac
Brand new- £48.78
- Postage not specified
- From United States
Sight reduction tables for air navigation - United States - Good - Hardcover
Pre-owned- £37.49
- + £1.60 postage
sight reduction tables for air navigation vol 1 HMSO 1972 AP3270 epoch 1975
- £19.99
- 0 bidsor Best Offer
- + £9.42 postage
- Customs services and international tracking provided
Price refinements - Carousel
Showing slide {CURRENT_SLIDE} of {TOTAL_SLIDES} - Price refinements
Brand New
From United States
Buy It Now
Customs services and international tracking provided5 Watching
Sight Reduction Tables for Air Navigation Volume 3 (Paperback or Softback)
Brand New
From United States
List price: Previous Price$28.10
+$8.50 shipping
Sight Reduction Tables for Air Navigation Volume 1 (Paperback or Softback)
Brand New
From United States
List price: Previous Price$28.10
+$8.50 shipping
Star Sight Reduction Tables for 42 Stars: The Assumed Altitude Method of Celest
by Thomas D. Davies | Paperback
From United States
Buy It Now
Sight Reduction Tables for Marine Navigation-Commercial Edition [Latitudes 15-
Pre-Owned
From United States
Buy It Now
by Allan E. Bayless | PB | Good
10% off 4+
Top Rated Plus+$9.99 shipping
From United StatesSIGHT REDUCTION TABLES #249 Volumes 1, 2 & 3 Book Lot Air Navigation DoD 1980
Pre-Owned
From United States
or Best Offer
Customs services and international tracking providedSight Reduction Tables for Air Navigation Volume 3 9781921936845
Brand New
From United Kingdom
Buy It Now
SIGHT REDUCTION TABLES FOR AIR NAVIGATION VOL. 2 (PUB 249) By Celestaire **NEW**
New (Other)
From United States
Was: Previous Price$39.99
Customs services and international tracking provided+$15.60 shipping
Sight Reduction Tables Vol 3 US Navy Hydrographic Air Navigation MS37
Brand New
From United States
or Best Offer
Customs services and international tracking providedSIGHT REDUCTION TABLES FOR AIR NAVIGATION VOL. 2 (PUB 249) By Celestaire
From United States
Was: Previous Price$34.99
Customs services and international tracking provided+$16.78 shipping
SIGHT REDUCTION TABLES FOR AIR NAVIGATION VOLUME 2&3 DEFENSE MAPPING AGENCY
Top Rated Plus
Buy It Now
From United StatesCustoms services and international tracking providedSight Reduction Tables For Air Navigation 1980 Pub No 249 Vol 1
From United States
Was: Previous Price$39.99
Customs services and international tracking provided+$22.40 shipping
SIGHT REDUCTION TABLES FOR AIR NAVIGATION VOL. 3 (PUB 249)
New (Other)
From United States
Was: Previous Price$39.99
Customs services and international tracking provided+$15.60 shipping
Sight Reduction Tables for Air Navigation, Volume 3 (Unnamed - 1984) (ID:09248)
From United States
Buy It Now
sight reduction tables for air navigation vol 1 HMSO 1972 AP3270 epoch 1975
Time left23h 24m left
0 bids
From United KingdomCustoms services and international tracking provided+$11.99 shipping
Sight Reduction Tables For Air Navigation Vol.3 (Anon - 1967) (ID:29667)
From United States
Buy It Now
Sight Reduction Tables for Air Navigation Vol. 2 (pub 249) by Celestaire
by Celestaire | PB | Good
10% off 4+
Top Rated Plus+$9.99 shipping
From United StatesSight Reduction Tables for Marine Navigation Latitudes 15-30, Inclusive Vol..
by Editor | HC | Good
10% off 4+
Top Rated Plus+$9.99 shipping
From United StatesSight Reduction Tables for Air Navigation Volumes 2 Early 80’s
Pre-Owned
Time left2d 4h left
0 bids
From United StatesCustoms services and international tracking providedBuy It Now
Sight Reduction Tables for Air Navigation (Selected Stars) 1951 U.S. Navy Publ.
Pre-Owned
From United States
or Best Offer
Sight Reduction Tables for Marine Navigation: Lat. 0-15, Inclusive Pub. No..
by U. S Government | HC | Good
10% off 4+
Top Rated Plus+$9.99 shipping
From United StatesAir Navigation Sight Reduction Tables
Pre-Owned
From United States
or Best Offer
Customs services and international tracking provided1963 Reprint Naval Sight Reduction Tables Air Navigation #249 Vol 2 O-39 MS37
Brand New
From United States
or Best Offer
Customs services and international tracking providedRapid Sight Reduction Tables for Navigation: United Kingdom Edition Vol 2 By Na
Pre-Owned
From United Kingdom
Buy It Now
Rapid Sight Reduction Tables for Navigation: United Kingdom Edition Vol 3 By Na
Pre-Owned
From United Kingdom
Buy It Now
Rapid Sight Reduction Tables for Navigation: United Kingdom Edition Vol 1 By Na
Pre-Owned
From United Kingdom
Buy It Now
Sight Reduction Tables for Air Navigation Vol. 3 (pub 249)
by Celestaire | Paperback
From United States
Buy It Now
Vintage WWll era sight reduction tables air navigation US dept defense
Pre-Owned
From United States
or Best Offer
Customs services and international tracking providedSight Reduction Tables for Marine Navigation, Pub No 229, Vol 2 (1st Ed)
by Defense Mapping Agency | HC | Acceptable
10% off 4+
Top Rated Plus+$9.99 shipping
From United States1981 Sight Reduction Tables For Marine Navigation Pub. No. 229 Vol. 3 Defense Ma
From United States
or Best Offer
PAIR OF SIGHT REDUCTION TABLES AIR NAVIGATION DEPARTMENT OF DEFENSE EPOCH 1975
Pre-Owned
From United States
or Best Offer
Admiralty, Sight Reduction Tables for Marine Navigation Vol. 2
Pre-Owned
From United States
or Best Offer
Customs services and international tracking providedAdmiralty, Sight Reduction Tables for Marine Navigation Vol. 3
Pre-Owned
From United States
or Best Offer
Customs services and international tracking providedAdmiralty, Sight Reduction Tables for Marine Navigation Vol. 1
Pre-Owned
From United States
or Best Offer
Customs services and international tracking provided1957 vintage 3vol SIGHT REDUCTION TABLES AIR NAVIGATION u.s. navy hydrographic
Top Rated Plus
Buy It Now
From United StatesSight Reduction Tables for Marine Navigation Volume 6 by Nga
Free US Delivery | ISBN: 1463622104
15% off 3+
From United States+$6.99 shipping
Sight Reduction Tables for Air Navigation Volume 1 by National Geospatial-Intell
Brand New
From United States
Buy It Now
Sight Reduction Tables for Air Navigation Vol 2 by National Geospatial-Intellige
Brand New
From United States
Buy It Now
Sight Reduction Tables for Air Navigation Volume 3 by National Geospatial-Intell
Brand New
From United States
Buy It Now
Rapid Sight Reduction Tables Volume 2. by Nga (English) Paperback Book Free Ship
Brand New
From United States
Buy It Now
Only 1 left!