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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: longitude around noon (a twist)
From: Gary LaPook
Date: 2008 Jun 20, 22:52 -0700
From: Gary LaPook
Date: 2008 Jun 20, 22:52 -0700
I found this listing on ebay, any comments? http://cgi.ebay.com/Latitude-and-Longitude-by-the-Noon-Sight-Using-Sextant_W0QQitemZ380037632231QQihZ025QQcategoryZ37971QQssPageNameZWDVWQQrdZ1QQcmdZViewItem gl On Jun 4, 9:06 am, "George Huxtable"wrote: > Frank Reed wrote- > > I chatted in my email a bit about longitude around noon > | and asked him this: > | "Which leads to a question: is there an established name in the > literature, > | or even in your own jargon, for a fix resulting from a series of ten or > | twelve sights taken over a relatively short period of time? I've been > | calling it a "rapid-fire fix". Do you know another name?" > | > | His reply: > | "I don't know of a special name. You're correct, of course, if you can > get > | a bunch of sights on either side of noon, you can get good enough geometry > | to get a 2-D position. It works with the LOPs, too, in that they provide > a > | good spread of azimuth around then. There is a slight catch, however, and > | that is, the higher the Sun is in the sky (and therefore the more rapid > the > | altitude and azimuth change near noon) the more you have to worry about > the > | curvature of the LOPs. In some near-degenerate cases (sun within several > | degrees of the zenith), the usual straight-line plotting -- or math that > | assumes straight-line LOPs -- may not provide the right fix." > > ================= > > There appears to be some misunderstanding in that dialogue. How does that > difficulty arise? I think it is quite illusory. > > Indeed, the higher the Sun is at noon, the simpler the picture gets, the > easier it becomes to determine the moment of noon, and the less is the > influence of any North-South velocity. It's because the whole process > DEPENDS on that curvature, and the sharper the curvature, the easier it > gets. > > As long as the Sun is within a few degrees of the vertical at noon, you can > plot the whole event on a Mercator projection, in plane geometry. The Sun is > travelling around a line of latitude at 900 knots or a bit less, the ship is > travelling (say) South at 10 knots along a line of longitude, and the zenith > distance in minutes is simply the distance between them in miles. > > Indeed, simplest case of all is if the so-called "degenerate" case where the > ship crosses the Equator at the same moment that the Sun, travelling round > the equator at 900 knots, passes that same spot. From the ship, it's a > zenith noon. Until that moment the ship and the Sun have been approaching at > a speed of 900 knots and 10 knots, which combine (quadratically) to 900.06, > so the ship speed is having no effect. Sun altitude increases steadily at 15 > degrees per hour, until that moment. Then, instantly, after they pass, they > separate at the same rate, so the altitude falls, again at 15 degrees per > hour. The observer's difficult task is to about-face, from East to West, at > that moment. But otherwise, determining the moment of noon becomes a doddle. > > That's because the plot of altitude against time has developed a sharp > corner at noon. Its curvature is infinite. And the maximum occurs AT noon, > whatever the ship speed was. > > For noons where the Sun is close to, but not at the vertical, the curve > becomes less sharp near the top, and ship speed starts to need correcting > for, but these high Suns are just the sort of observation for which Frank's > procedure of longitude around noon is, indeed, completely appropriate. > > Frank continued- > > | That's a good point about sights very close to the zenith. I had mentioned > | previously on the list that there may be a special case when the Sun is > | close to the zenith. I still haven't thought through whether it really > | screws up the graphical technique or merely requires more stringent rules > | for its application. > > Neither. Quite the reverse, in fact. > > George. > > contact George Huxtable at geo...@huxtable.u-net.com > or at +44 1865 820222 (from UK, 01865 820222) > or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---