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.

[1] 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.

Given: First calculate the altitude of the celestial body

using the equation of circle of equal altitude:

{\displaystyle \sin(Hc)=\sin(Lat)\cdot \sin(Dec)+\cos(Lat)\cdot \cos(Dec)\cdot \cos(LHA).}

(Zn=0 at North, measured eastward) is then calculated by:

{\displaystyle \cos(Z)={\frac {\sin(Dec)-\sin(Hc)\cdot \sin(Lat)}{\cos(Hc)\cdot \cos(Lat)}}={\frac {\sin(Dec)}{\cos(Hc)\cdot \cos(Lat)}}-\tan(Hc)\cdot \tan(Lat).}

These values are contrasted with the observed altitude

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.

The methods included are: 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.

The first approach of a compact and concise method was published by R. Doniol in 1955[4] and involved haversines.

The altitude is derived from

{\displaystyle a=\operatorname {hav} (LHA)}

The calculation is: A practical and friendly method using only haversines was developed between 2014 and 2015,[5] and published in NavList.

A compact expression for the altitude was derived[6] using haversines,

, for all the terms of the equation:

The algorithm if absolute values are used is: For the azimuth a diagram[7] was developed for a faster solution without calculation, and with an accuracy of 1°.

This diagram could be used also for star identification.

[8] An ambiguity in the value of azimuth may arise since in the diagram

is E↔W as the name of the meridian angle, but the N↕S name is not determined.

In most situations azimuth ambiguities are resolved simply by observation.

When there are reasons for doubt or for the purpose of checking the following formula[9] should be used:

The algorithm if absolute values are used is: This computation of the altitude and the azimuth needs a haversine table.

For a precision of 1 minute of arc, a four figure table is enough.