Hello Thibaud and Robert Great thanks for your information. Unfortuantely I do not have direct acces to Astronomical Almanach.
I will still complicate the matter further. In 1999 edition of the Nautical Almanach (commercial edition) the formula still has coefficient 1.76 if meters are used for height of eye. Certainly the difference for dialing is not important. In navigation however minutes of arc of altitude (and other great circles) correspond directly to nautical miles and every precaution was taken to reduce the error in tables which are calculated ashore. At sea there are many sources of errors, sometimes much bigger than few tenths of a minute, but still introduction of another error is unwelcome even if on special occasions errors may cancel out. General accuracy of Almanach based calculations is 0.1' and they were really at pains to achieve this. Is it possible that formulae cited by Robert and Thibaud take into account pollution of the atmosphere certainly bigger now than in XIX century :-) On the other hand another well known formula for distance to the visible horizon is d[NM] = 2.08 * sqrt( a[m] ), (*) NM - nautical miles that is minutes of arc of great circles on Earth. If there were no refraction then both the dip (in minutes of arc) and distance to the visible horizon expressed in NM (that is again minutes of arc) would be the same. But because of refraction they are different. The distance d is really the distance at which we may spot a lighthouse light just on the horizon, while dip is the angle between the tangent to bent light ray and true level at observer's position. BTW, 1999 edition of the Nautical Almanach is solely on the authority of US Naval Observatory in Washington D.C. Previous editions, up to 1998 were joint publications of USNO and Her Majesties Nautical Almanach Office in London. Is this because of formal closing of the Royal Greenwhich Observatory last year? It looks like some epoch has come to an end. Slawek At 10:51 PM 1/31/99 +0100, you wrote: >Slawomir K. Grzechnik wrote: > >> Where did you get these formulae from? I have used for ages another one >> >> dip['] = 1.76 * sqrt( a[m] ) or its older equivalent >> dip['] = 0.97 * sqrt( a[ft] ) >> >> where a is height of eye and units are given in bracket angles and ' stands >> for minute of arc rather than foot. The formulae include Earth curvature and >> mean terrestrial refraction for standard pressure 760 mm Hg (1013.2 mb or hP) >> air temp. +10 C water temp. +10 C (guess formulae may be used on land as >> well) >> >> The result should be corrected for temperatures and pressure if you are able >> to measure those, not that hard after all. "My" formulae are cited in manuals >> of navigation and Alamanachs together with tables and correction tables for >> temperatures and pressure. So where did you get "yours" from? > >To complicate matters even further, the revised edition of the _Explanatory >Supplement to the Astronomical Almanac_ (1992) in fact recommends the following >correction for computing the true altitude of a celestial body near the horizon >(cf. p. 484): > > - 2.12 * sqrt(a[m]) or > - 1.17 * sqrt(a[ft]) > >As explained on pp. 488-489, when calculating the true altitude of a celestial >body near the horizon, in addition to ordinary dip (for which the constants >1.76 [m] or 0.97 [ft] are cited) an additional correction of 0.37 * sqrt >(a[m]), or 0.20 sqrt(a[ft]), has to be applied. > >================================================================ >* Robert H. van Gent * Tel/Fax: 00-31-30-2720269 * >* Zaagmolenkade 50 * E-mail: [EMAIL PROTECTED] * >* 3515 AE Utrecht * Home page (under construction): * >* The Netherlands * http://www.fys.ruu.nl/~vgent/ * >================================================================ Slawek Grzechnik 32 57.4'N 117 08.8'W http://home.san.rr.com/slawek
