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.

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. 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{\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 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. The first approach of a compact and concise method was published by R. Doniol in 1955 and involved haversines. The altitude is derived from \sin (Hc) = n - a \cdot (m + n) , in which n = \cos (Lat - Dec) , m = \cos (Lat + Dec) , a = \operatorname{hav}(LHA) . The calculation is: n = cos(Lat − Dec) m = cos(Lat + Dec) a = hav(LHA) Hc = arcsin(n − a ⋅ (m + n)) \operatorname{hav}(ZD) = \operatorname{hav}(Lat - Dec) + \left( 1 - \operatorname{hav}(Lat - Dec) - \operatorname{hav}(Lat + Dec) \right) \cdot \operatorname{hav}(LHA) where ZD is the zenith distance, Hc = (90^\circ - ZD) is the calculated altitude. The algorithm if absolute values are used is: For the azimuth a diagram was developed for a faster solution without calculation, and with an accuracy of 1°. This diagram could be used also for star identification. An ambiguity in the value of azimuth may arise since in the diagram 0^\circ \leqslant Z \leqslant 90^\circ . Z 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 should be used: \operatorname{hav}(Z) = \frac{\operatorname{hav}(90^\circ \pm \vert Dec\vert) - \operatorname{hav}(\vert Lat\vert - Hc)}{1 - \operatorname{hav}(\vert Lat\vert - Hc) - \operatorname{hav}(\vert Lat \vert + Hc)} 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.

External links

Navigational Algorithms: AstroNavigation - Free App for Windows Navigational Algorithms: resources for Longhand Haversine Sight Reduction NavList A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Position-Finding Celestial Tools for the USPS/CPS JN/N Student Graphical all-haversine Hc reduction Sight Reduction - free App for android Vector Solution for the intersection of two Circles of Equal Altitude - free App for android

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