# Sight reduction

**Sight reduction** is the process of deriving from a sight the information needed for establishing a line of position.

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]}

Nowadays sight reduction uses the equation of the circle of equal altitude to calculate the altitude of the celestial body,

and the azimuth *Zn* is obtained from *Z* by:

With the observed altitude *Ho*, *Hc* and *Zn* are the parameters of the Marcq St Hilaire intercept for the line of position:

With *B* the latitude (+N/S), *L* the longitude (+E/-W), *LHA* = *GHA* + *L* is the local hour angle, *Dec* and *GHA* are the declination and Greenwich hour angle of the star observed, and *Hc* the calculated altitude. *Z* is the calculated azimuth of the body.

Basic procedures involved computer sight reduction or longhand tabular methods.

## Tabular sight reduction

The methods included are:

- The Nautical Almanac Concise method (NASR)
- Pub. 249 (formerly H.O. 249, Sight Reduction Tables for Air Navigation, A.P. 3270 in the UK)
- Pub. 229 (formerly H.O. 229, Sight Reduction Tables for Marine Navigation
- H.D. 486 (in the United Kingdom)
- H.O. 214 (Tables of Computed Altitude and Azimuth)
- H.O. 211 (Dead Reckoning Altitude and Azimuth Table, Third Edition, known as Ageton, and the Modified H.O. 211 Compact Sight Reduction Table, known as Ageton-Bayless)
- H.O. 208 (Navigation Tables for Mariners and Aviators, Sixth Edition, known as Dreisonstok)
- S-Table

## 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^{[2]} The altitude is derived from sin(*Hc*) = *n* − *a* (*m* + *n*), in which *n* = cos(*B* − *Dec*), *m* = cos(*B* + *Dec*), *a* = hav(*LHA*).

The calculation is:

n= cos(B-Dec)m= cos(B+Dec)a= hav(LHA)sin_Hc=n-a(m+n)Hc= arcsin(sin_Hc)

### Ultra compact sight reduction

A practical and friendly method using haversines was developed between 2014 and 2015,^{[3]} and published in NavList.

A compact expression for the altitude was derived^{[4]} using haversines, hav, for all the terms of the equation:

hav(*ZD*) = hav(*B* - *Dec*) + (1 - hav(*B* - *Dec*) − hav(*B* + *Dec*)) hav(*LHA*)

where *ZD* is the zenith distance

*Hc* = (90 - *ZD*) the calculated altitude

The algorithm if absolute values are used is:

if same name for latitude and declinationn= hav(|B| - |Dec|)m= hav(|B| + |Dec|) if contrary namen= hav(|B| + |Dec|)m= hav(|B| - |Dec|)q=n+ma= hav(LHA) hav(ZD) =n+ (1 -q)aZD= invhav -> look at the haversine tablesHc= 90° -ZD

For the azimuth a diagram^{[5]} was developed for a faster solution without calculation, and with an accuracy of 1°.

This diagram could be used also for star identification.^{[6]}

An ambiguity in the value of azimuth may arise since in the diagram 0 ≤ *Z* ≤ 90°. *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^{[7]} should be used.

hav(*Z*) = [hav(90° - *Dec*) - hav(*B* - *Hc*)] / (1 - hav(*B* - *Hc*) - hav(*B* + *Hc*))

The algorithm if absolute values are used is:

if same namea= hav(90° - |Dec|) if contrary namea= hav(90° + |Dec|)m= hav(B+Hc)n= hav(B-Hc)q=n+mhav(Z) = (a-n) / (1 -q)Z= invhav -> look at the haversine tables if LatitudeN: ifLHA> 180°,Zn=ZifLHA< 180°,Zn= 360° −Zif LatitudeS: ifLHA> 180°,Zn= 180° −ZifLHA< 180°,Zn= 180° +Z

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.^{[8]}

#### An example

Data:B= 34° 10.0′ N (+)Dec= 21° 11.0′ S (-)LHA= 302° 43.0′ AltitudeHc:a= 0.2298m= 0.0128n= 0.2157 hav(ZD) = 0.3930 -> table ->ZD= 77° 39′Hc= 12° 21′ AzimuthZn:a= 0.6807m= 0.1560n= 0.0358 hav(Z) = 0.7979Zn= 126.6°

## See also

## References

- ↑
*The American Practical Navigator*(2002) - ↑ . Table de point miniature (Hauteur et azimut), by R. Doniol, Navigation IFN Vol. III Nº 10, Avril 1955 Paper
- ↑ Rudzinski, Greg (July 2015). Ix, Hanno. "Ultra compact sight reduction".
*Ocean Navigator*. Portland, ME, USA: Navigator Publishing LLC (227): 42–43. ISSN 0886-0149. Retrieved 2015-11-07. - ↑ Altitude haversine formula by Hanno Ix http://fer3.com/arc/m2.aspx/Longhand-Sight-Reduction-HannoIx-nov-2014-g29121
- ↑ Azimuth diagram by Hanno Ix. http://fer3.com/arc/m2.aspx/Gregs-article-havDoniol-Ocean-Navigator-HannoIx-jun-2015-g31689
- ↑ Hc by Azimuth Diagram http://fer3.com/arc/m2.aspx/Hc-Azimuth-Diagram-finally-HannoIx-aug-2013-g24772
- ↑ Azimuth haversine formula by Lars Bergman http://fer3.com/arc/m2.aspx/Longhand-Sight-Reduction-Bergman-nov-2014-g29441
- ↑ http://fer3.com/arc/m2.aspx/Longhand-Sight-Reduction-HannoIx-nov-2014-g29172

## External links

- 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