A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Assumed positions, WAS: IN HONOR OF JEREMY...
From: Antoine Cou�tte
Date: 2009 Sep 25, 04:10 -0700
From: Antoine Cou�tte
Date: 2009 Sep 25, 04:10 -0700
Dear Peter, You are raising a very interesting subject : astronomical fixes without prior knowledge of assumed position. The "Assumed position" method - actually some kind of "regula falsi" approach . - led to the then revolutionary approach (mid XIX th Century) of the so-called Marc-Saint Hilaire Method, which apparently was pioneered by one (or two ?) different French Astronomer(s?), as we could learn in a most instructive recent thread in Navlist. When have "Astronomical-fixes-without-prior-knowledge-of-Assumed-position" first ever ever been devised ? I really do not know ... and maybe George or Frank may know better. ******* In France both in the Military Navy and Civilian Merchant Navy (most of the Merchant Navy Instructors come from the Military) , such problem has long been known as Douwes's problem. To the best of my memories, M. Douwe was a Dutch Navigator of the XIX (?) th century who reportedly had already spent a lot of thoughts about tackling this subject. I do not think he did find the exact solution. The exact mathematical solution for a steady course/speed moving vessel (i.e. immediately obtained from a one shot mathematical computation : no successive computation/approximation loops) has been recently found, not even by a Seaman, but by M. G. HOUNEAU who as I can recall, is a ... (French?) Air Force Colonel who published it there in 1991, see : http://cat.inist.fr/?aModele=afficheN&cpsidt=19474690. I am not aware that other people might have found this very same solution independently, or at least published it before. But other people did work and publish on this before as you mention it (1981 James van Allen). I would also think that in one of his papers - the third one unfortunately no longer available on the web (who has it, please ??? ) - Dr George Kaplan from the USNO did address this very same subject in depth a little over 10 years ago (see http://www.usno.navy.mil/USNO/astronomical-applications/publications/reports) . ******* To my sense - and to my burning memories (see the story below) - the reason why so few results have apparently been published before the early 80's is because only by such times has the sufficient computational power been more and more widely available. By 1980 I had devised on my own 3 independent methods of dealing with this, and I did have to wait until then to successfully run them on my (third type of) calculator. One of these methods had I already "invented" some 6 or 7 years earlier when at the French Naval Academy. I had painstakingly but eventually and successfully run only one example then in early 1974 but it had taken me over 10 hours of "manual" computation. I even made a (quite proud) presentation about my method and results to my fellows and instructors who found it ... "interesting indeed, but maybe (or "hopefully" would say the nicest ones in the audience) of some practical interest the future " ... Why such unexpected reaction and feelings ? Simply because WE DID NOT HAVE ANY PRACTICAL COMPUTATIONAL POWER AT HAND THEN ! I doubt whether I was the first and only one to do achieve such result then in 1974, but at that time, such methods were TOTALLY UNPRACTICABLE AT SEA ! Such computations can now be carried out (and with no error at all !) in less than once second on a laptop to-day. ******* Just a quick note : you also mentionned the Earth oblateness/ellipticity and might wonder whether it is difficult to fully take it in account in Celestial Navigation. My view point would be "NOT AT ALL". If you deal with local coordinates - which by chance are one the sets we use in Celnav - and if youy compare with results computed for a fully spherical Earth, the ONLY effects of oblateness are : - a different parallax value in Height which can be accounted for quite easily at any required accuracy, and - a parallax in Azimuth. Mathematically speaking, this one can even reach 180�, but only in exceptional cases almost totally ruled out by conventional observations. Parallax in Azimuth could be significant only when altitudes are almost equal to 90�, a case when a conventional sextant is almost totally useless, since above 85�-87� heights, swinging around is becoming a quite impracticable maneuver. True, there could be cases with (somewhat) appreciable horizontal parallax, but you can get rid of such (undesirable) effects just trough running one more iteration if required since it will reduce your intercepts lengths. Accordingly any position inaccuracy due to ignoring the parallax in azimuth can then be downgraded to almost any low value you would require : in other words, horizontal parallax effects on an ellipsoid can be minimized to well below one tenth of arc minute on observed coordinates which constitutes the VERY BEST conventional Celnav can EVER achieve. ******* Best Regards from Antoine M. "Kermit" Couette --~--~---------~--~----~------------~-------~--~----~ NavList message boards: www.fer3.com/arc Or post by email to: NavList@fer3.com To unsubscribe, email NavListemail@example.com -~----------~----~----~----~------~----~------~--~---