Sight reduction

In astronavigation, sight reduction is the process of deriving from a sight (in celestial navigation usually obtained using a sextant) the information needed for establishing a line of position, generally by intercept method.

Sight is defined as the observation of the altitude, and sometimes also the azimuth, of a celestial body for a line of position; or the data obtained by such observation.

The mathematical basis of sight reduction is the circle of equal altitude. The calculation can be done by computer, or by hand via tabular methods and longhand methods.

Algorithm

Given:
* $Lat$, the latitude (North - positive, South - negative), $Lon$ the longitude (East - positive, West - negative), both approximate (assumed);
* $Dec$, the declination of the body observed;
* $GHA$, the Greenwich hour angle of the body observed;
* $LHA = GHA + Lon$, the local hour angle of the body observed.

First calculate the altitude of the celestial body $Hc$ using the equation of circle of equal altitude:

$\sin(Hc) = \sin(Lat) \cdot \sin(Dec) + \cos(Lat) \cdot \cos(Dec) \cdot \cos(LHA).$

The azimuth $Z$ or $Zn$ (Zn=0 at North, measured eastward) is then calculated by:

$\cos(Z) = \frac = \frac - \tan(Hc) \cdot \tan(Lat).$

These values are contrasted with the observed altitude $Ho$. $Ho$, $Z$, and $Hc$ are the three inputs to the intercept method (Marcq St Hilaire method), which uses the difference in observed and calculated altitudes to ascertain one's relative location to the assumed point.

Tabular sight reduction

The methods included are:
* The Nautical Almanac Sight Reduction (NASR, originally known as Concise Tables for Sight Reduction or Davies, 1984, 22pg)
* Pub. 249 (formerly H.O. 249, Sight Reduction Tables for Air Navigation, A.P. 3270 in the UK, 1947–53, 1+2 volumes)
* Pub. 229 (formerly H.O. 229, Sight Reduction Tables for Marine Navigation, H.D. 605/NP 401 in the UK, 1970, 6 volumes.
*The variant of HO-229: Sight Reduction Tables for Small Boat Navigation, known as Schlereth, 1983, 1 volume)
* H.O. 214 (Tables of Computed Altitude and Azimuth, H.D. 486 in the UK, 1936–46, 9 vol.)
* H.O. 211 (Dead Reckoning Altitude and Azimuth Table, known as Ageton, 1931, 36pg. And 2 variants of H.O. 211: Compact Sight Reduction Table, also known as Ageton–Bayless, 1980, 9+ pg. S-Table, also known as Pepperday, 1992, 9+ pg.)
* H.O. 208 (Navigation Tables for Mariners and Aviators, known as Dreisonstok, 1928, 113pg.)

Longhand haversine sight reduction

This method is a practical procedure to reduce celestial sights with the needed accuracy, without using electronic tools such as calculator or a computer. And it could serve as a backup in case of malfunction of the positioning system aboard.

Doniol

The first approach of a compact and concise method was published by R. Doniol in 1955 and involved haversine