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Subject: Re: Timing Noon
From: Peter Fogg (ffive@XXX.XXX)
Date: Thu Apr 11 2002 - 17:55:12 EDT
First of all I forgot, earlier, to thank George for checking the time of my
hypothetical meridian sight. 'gives me the same answer, within a second' sounds
pretty good to me.
'I hope Peter doesn't mind being treated as a "whipping-boy" example in this
matter'
No, not at all, its all part of the learning process. No more humiliating than
exposing my ignorance in public, the reward being the potential growth in my own
understanding, and perhaps that of others who tune in.
Know of two methods to determine the precise moment of the Sun's meridian passage
by observation.
Firstly, to plot any number of sights up to and after LAN, then draw a curve that
fits them. Apart from the difficulty of drawing smooth curves at any time, and
especially on a moving boat, the resulting parabolic (?) shape has a fairly flat
top, defying the choosing of an exact moment. As George says.
Secondly, making a timed observation of altitude before LAN, then noting the time
when the Sun's altitude again reaches this level. The next step is to divide this
time equally, giving, in theory, the exact moment of LAN. I don't understand
George's objection that using this method has 'already conceded the principle'.
Celestial navigation in general uses a series of convoluted steps to arrive at a
LOP, compared to coastal nav. where you take a bearing on an object on shore and
there is your LOP. This process seems fairly straightforward and accurate enough.
George has, if I understand correctly, pointed out that the Sun's seasonal
north/south movement and/or the vessel's own north/south motion may conspire to
rob this moment of its validity, although it seems the difference is too small to
worry about. So much for robustness.
There is a small advantage to using noon (or close to) as a time for Fix, in that
calculations for an ongoing DR are simplified so that they can often be done in
one's head in the cockpit, without going below, compared to using some other
complicated starting point for time. Remember reading in a cruising guide to a
part of the Queensland coast (Great Barrier Reef) words to the effect of that one
loses half of one's brain while on a boat. So true. Perhaps its the constant
motion, the loss of normal sleep patterns, but while on board I like to have a set
routine to follow for nav, using pre-printed forms and as little thinking as
possible.
'Has that helped?' Yes, greatly. Am still puzzling over just how knowing in
advance the exact moment of the Sun's meridian passage (from my nav. calculator)
can be of practical benefit. Its turning out to be the most detailed and
enlightening lesson on meridian sights, and the Time/Longitude problem, that I've
come across.
Harking back to taking sights of the Sun at 90° and 270°, how can one be sure of
measuring the altitude of the Sun at the precise moment of this Azimuth? Since
the Sun is not hovering about at these moments, but zooming across the sky.
(For the moment I'll pass over how to know in advance when this will happen - but
am happy to expand on this if anybody is wondering)
The answer is to start taking sights 2/3 minutes before this moment, and to
continue for 2/3 minutes after. Then plot these sights graphically, and compare
them to a calculated line representing the change in altitude of the body over 5
minutes of time (this technique was explained in detail in an earlier posting).
Then any point along this line which best fits the multiple sights can be used, in
this case the moment of exact azimuth, leading to a precise north/south LOP, which
is the line of Longitude.
As with any single LOP, the disadvantage is that one has no check on the accuracy
of this line. This is where I disagree (provisionally!) with George who says:
'In practice, only two bodies are required, not three. Two bodies will give
two position circles, which cross at two places. One of these crossings
will be the position of the observer, and the other can be ignored as
irrelevant. As long as the two bodies are well separated in the sky, it is
obvious which of the two is the relevant crossing because they are so far
apart on the Earth's surface.'
The problem is that we are assuming that we don't have a DR - lost amidst the
watery wastes! - so how will we know which of the intersections is the right one?
Three circles lead to a single (?) triangle, traditionally known as a 'cocked
hat', the centre of which is our Fix position. An important exception to the
centre (as in 'the doctrine of least squares' - more info available on request)
being the Fix is where there is a known danger - lee shore, reef, whatever - in
which case the Fix position becomes the closest point to the danger. This will be
along one of the LOPs, so could well be the real position.
It seems to me that three sights, with well separated azimuths, are always
preferable to two for this reason - two give an exact point of intersection, but
no indication about how accurate it may be. In general terms (and there are
specific qualifications) the size of the 'cocked hat' triangle is a good
indication of the accuracy of the observations: the smaller it is, the better - if
the three LOPs met at a single point then that would be perfection - and about as
unlikely as any perfection in this life. Which reminds me that I did once see
someone (an amateur) get a 'hole-in-one' playing golf - she was very pleased.
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