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From: George Huxtable (no email)
Date: Sat Jun 04 2005 - 19:54:17 EDT
Lu Abel wrote-
>I don't know how many on this list have actually taken a noon sight. I
>have.
But from on-land, it seems, when he says later "I also freely confess this
sight was taken on dry land, so I wasn't dealing with trying to bring down
the sun on a heaving ship's deck."
It's quite a lot harder, and less accurate, when you observe a Sun altitude
in real-life, at sea, above a real sea-horizon. Is an observation from
on-land considered adequate by the US Power Squadron?
>A noon sight is part of the requirements for US Power Squadron's
>Navigation course (advanced celestial nav) which I have taken. I found
>(at ~40N Lat, sight taken during the early summer) that not only did I
>get a spot-on latitude value, but by graphing a series of sights over
>about 10 minutes (5 min on either side of LAN) I got quite an excellent
>value for longitude.
I would expect a "spot-on" latitude value, just as Lu claims. But notice,
he doesn't quote any actual figures for his "quite an excellent value" for
longitude. I hope he will dig out his observation log and give us some real
numbers.
I have recalculated what Lu's observations should have been, taking an
observer at 40 deg North, 0 deg West, and as an example of "early Summer",
today's date of 4 June 05. The following altitudes include no correction
for refraction, dip, semidiameter.
Noon-by-the Sun occurred at 11h 58m 18s, when Sun alt. was at its maximum
of 72deg 28.6'
5 minutes earlier, and also 5 minutes later, the Sun alt was 1.9' less, at
72deg 26.7'
At those two times, 10 minutes apart, for which Lu will have to split the
difference to find his moment-of-noon, the Sun is first rising, then
falling, at 0.75 arc-minutes for each minute of time.
How accurate are Lu's altitudes going to be, if measured in real-life at
sea? I wonder if any one of us can put his hand on his heart and claim to
be able to measure the altitude of a real Sun above a real horizon AT SEA
within a scatter of, say, ±1 arc-minute. Here, I am referring to the
small-craft situation; I accept that on a big-ship, in millpond conditions,
somewhat less scatter than that might perhaps be achievable.
If the altitude is changing at only 0.75 arc-minutes, each minute of time,
at the extremes of Lu's time-range, and with a presumed scatter of ± 1
minute in each observation, I really can't see how, with the most careful
graph-plotting over those 10 minutes, a navigator will find the
centre-of-symmetry of the resulting curve to better than, say ±1 minute of
time. Not a very precise result then, when he might expect his chronometer
to be good to a second. A scatter of ±1 minute of time corresponds to a
longitude error of ±15'.
Those error estimates seem fair to me, but I would be happy to argue the
matter out if anyone thinks otherwise.
Compare that with a time-sight measurement made several hours away from
noon. If the Sun is on a path to pass overhead, then its altitude will
change by 15 arc-minutes for every minute of time. From higher latitudes,
the rate of rise will be less, but a properly chosen moment for a
time-sight will normally involve the altitude changing by at least 7.5
arc-minutes per time-minute (except in arctic latitudes). This is ten times
faster than the rate-of-change that Lu observed, so given the same accuracy
in observing altitude, the scatter in deduced time will be reduced by a
factor of 10, to be 6 seconds of time. And that would correspond to a
longitude error of 1.5 miles, not 15 miles: a substantial improvement,
obtained by using the traditional time-sight technique.
So if Lu really did get his unspecified "quite excellent value for
longitude", I wonder if it was perhaps obtained by some sort of fluke.
I don't deny that a noon Sun longitude can be made to work, to some extent.
One distinct improvement would be to extend the period of observation, to
be significantly longer than the 10 minutes around noon that Lu allowed
himself. But if the time interval between the rising Sun and the falling
Sun becomes great enough, the question then arises: can you call it a "noon
observation" any more?
Of course, from a moving ship, with any Northing or Southing in her course,
there's another factor to consider, that didn't come into Lu's on-land
observations. That motion gives rise to a displacement in time between the
moment of maximum altitude (which is what's observed) and the moment of the
Sun's meridian passage (which is what's needed). It isn't hard to correct
for, but that correction should not be neglected. There's an additional,
smaller, correction to make to allow for the Sun's changing declination,
being greatest near the equinoxes, but that's usually small enough to
neglect.
George.
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contact George Huxtable by email at , by phone at
01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
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