NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Lunars without calculator
From: Herbert Prinz
Date: 2001 Jul 10, 10:15 AM
From: Herbert Prinz
Date: 2001 Jul 10, 10:15 AM
nigel_gardner wrote: > In the absence of tabulated LD's, is it possible to establish longitude by > means of currently available ephemeris (Nautical or Astronomical Almanacs), > log. tables and a sextant? And of course without the use of calculators or > computers. Dear Nigel, It was not fair of you to send us on a wild goose chase looking for all kinds of algorithms, when what you really wanted was a procedure without calculator. To most of us, this restriction is not so "of course" as it appears to be to you. But, OF COURSE, there is a way of finding longitude at sea without tabulated lunar distances and without calculator. All you need is the regular tables, plotting tools, etc. that you normally use when working your favorite flavor of intercept method. Latitude, longitude and time can be found simultaneously from the observation of 3 bodies, one of them being the moon. In order to avoid the need for lunar distance tables, we confine ourselves to altitude observations. One should be aware though that this works best when the moon changes altitude the fastest. I.e. the moon should be near the prime vertical and it should rise vertically, such as is the case in low latitudes. Even then the method is inherently less accurate than the lunar distance method, because an observation error in the altitude of the moon caused by abnormal refraction will have full impact on the result (unlike the LD method, where the detrimental effect of abnormal refraction is subtler, but certainly not non-existent, as was claimed elsewhere). The principal method is described in Chauvenet (see R. van Ghents earlier reference), pp382-386, including a worked example. It goes without saying that the method requires no calculator or computer, since Chauvenet wrote the book in 1863. It was Sir Francis Chichester's merit to find an elegant way of solving the same problem with the tools that every sailor has on his boat. It is documented in Francis Chichester, Along the Clipper Way, New York, 1967 (There may be an earlier English edition). I am quoting from pp.170-171: "Make a simultaneous observation of moon and sun [...]. Compute a sun-moon fix in the ordinary way, using a guessed-at GMT. Now compute a second fix from the same observation but using a GMT which differs from the first by half anhour or an hour. Now establish the latitude by meridian altitude of the sun [or any other way]. [...] Join the two sun-moon fixes and the point where the line joining them, produced if necessary, cuts the known latitude must be the correct longitude at the time of the observation. Knowing the longitude enables you also to know what the correct GMT was at the time of the sun-moon fix." I don't recommend the exercise in an unsettled sea. Your plotting has to be rather accurate... Herbert Prinz (from 1368950/-4603950/4182550 ECEF)