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Sight Reduction Tables for Celestial Navigation

Sight Reduction is the process of solving the navigational triangle for an assumed position and measured Altitude to obtain a Line-of-Position. The Sight Reduction Tables available here are very similar to the tables issued by the (former) "Defence Mapping Agency of the Hydrographic/Topographic Center" as publication "H.O. 229". Alternatively, the navigational triangle can be solved according to the "Ageton Method".

The difference between the "H.O. 229" Tables and the Tables presented here, is that the range for the Declination is limited to 0° to 29°. This is compliant with the Nautical Almanac available from this site, which does not include star data. The Declination of the Sun, the Moon and the planets is always below 30°.
Omitting the Declination range above 30° reduces the number of pages (and the weight!) of the Sight Reduction Tables by 60%!

Purpose and Scope

The main purpose of these tables is to facilitate the practice of celestial navigation at sea. The tables have been designed for use with the "Marcq Saint Hilaire" or "Altitude-Intercept" method of Sight Reduction, utilizing a position assumed or chosen such that interpolation for Latitude and Local Hour Angle is not required.

For each of the entry combination of integral degrees of Latitude, Declination and Local Hour Angle, the corresponding values for Altitude and Azimuth are tabulated. The Altitudes and their increments are tabulated to the nearest tenth of a minute. The results for the Azimuth Angles are tabulated to the nearest tenth of a degree. The tables are designed for a linear interpolation of the Altitude for Declination only. This interpolation can be performed by means of the interpolation tables also used for interpolating the Nautical Almanac data.


Each page of the table contains the Altitude (H) and Azimuth Angle (Z) values for the following ranges of arguments:

  • Latitude: one (integral) value
  • Local-Hour_Angle: 10 successive (integral) values
  • Declination: from 0° to 29° in integral values
    (Declination same as OR contrary to Latitude: NN/SS or NS/SN )
Also the increment or decrement of the Altitude for the Declination interval of 1° is tabulated (dH). This value can be used for linear interpolation to obtain the correct Altitude value (Hc) for the fractional (Degree/Minute) Declination value.


Interactive Tables


With the links on the left, a specific page of the Sight-Reduction Tables can be generated. The required entries are the integral values of Latitude and Local Hour Angle (LHA) as well as whether Declination and Latitude have the same or contrary signs. The range of Declination is from 0° to 29°, which is valid for the Sun, Moon and Planets as well as for most Stars that can be used for celestial navigation.

Pre-compiled Tables

The pre-compiled Sight Reduction Tables are available in PDF format. The complete Tables for 0° to 79° of Latitude (about 1000 pages) are divided over 16 Volumes, which can be selected from the table below. Each Volume has a Latitude range of 10°.

Latitude Declination SAME Name as Latitude Declination CONTRARY Name to Latitude
00°-09° SiRed00s.pdf (430 Kbyte) SiRed00c.pdf (420 Kbyte)
10°-10° SiRed10s.pdf (460 Kbyte) SiRed10c.pdf (420 Kbyte)
20°-29° SiRed20s.pdf (490 Kbyte) SiRed20c.pdf (410 Kbyte)
30°-39° SiRed30s.pdf (500 Kbyte) SiRed30c.pdf (400 Kbyte)
40°-49° SiRed40s.pdf (530 Kbyte) SiRed40c.pdf (390 Kbyte)
50°-59° SiRed50s.pdf (580 Kbyte) SiRed50c.pdf (360 Kbyte)
60°-69° SiRed60s.pdf (660 Kbyte) SiRed60c.pdf (330 Kbyte)
70°-79° SiRed70s.pdf (670 Kbyte) SiRed70c.pdf (270 Kbyte)

A worksheet for this table-based method of Sight Reduction is available as printer ready pdf file: worksheet for Sight Reduction using compiled Tables.

Background Information

The Sight Reduction Tables as produced for the above scripts and files contain tabulated values for the solutions of a spherical triangle of which two sides (90°-Latitude and 90°-Declination) and the including angle (Local Hour Angle) are known and the values of the third side (Altitude Hc) and adjacent angle (Azimuth Angle Zc) are required.

The solution can be analytically described by the following Sight Reduction equations: Altitude Hc is calculated by:

  Hc = asin[ sin(Lat) * sin(Dec) + cos(Lat) * cos(Dec) * cos(LHA) ]      
And the Azimuth Angle Z is:

  Z  = atan[ sin(LHA) / ( sin(Lat) * cos(LHA) - tan(Dec) * cos(Lat) ) ]  

The arguments for these formulas are Latitude (Lat), Declination (Dec) and Local Hour Angle (LHA). The values of the interactive tables are calculated with a JavaScript script using the build-in "Math"-trigonometric functions. I have compared at random about 100 sets of values from different argument combinations with the corresponding values from the "H.O. 229" publications and found no significant deviations other than "rounding errors".

The values from the "H.O. 229" were calculated (anno 1981) with 9 significant figures to obtain an accuracy of 0.1' for the Altitude and 0.1° for the Azimuth Angle. To my knowledge, the "Number" class and the "Math" class the JavaScript interpreter allow a number representation and processing, which is considerable better than the ones used for the "H.O. 229" publications.
The "rounding errors" mentioned above are ±0.1' for the Altitude and ±0.1° for the Azimuth Angle values.

The pre-compiled Sight Reduction Tables from the section above, have been generated with a C-program using double-precision number representation and processing for all intermediate variables. The accuracy of these calculations is much higher that the accuracy of the calculations used for the "H.O. 229" publications. Since for both calculations, the results are rounded to 0.1' for the Altitude and 0.1° for the Azimuth, differences in the results of the two methods of calculation, are due to "rounding effects".

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