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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.
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