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I usually enjoy Doug Royer's contributions, as coming from a practical
professional with many years of sight-taking experience at sea, with good
hard-headed advice.

But his latest contribution (sent via Dick Savage) was a real
disappointment. He has described a method for finding latitude, as also
suitable for finding longitude. But it's so inaccurate for that purpose
that it doesn't really work. It's a popular fallacy that one can determine
useful longitudes from timing the maximum altitude of the Sun at noon, and
we have discussed it on Nav-l before. To assess it properly, it needs an
explanation of how big those errors are, but Doug doesn't provide that.  I
will do my best to fill that gap, in a (futile) attempt to lay this "old
wive's tale" finally to rest.

====================
Doug said-

>This is a slick trick to use in certain conditions to find your lat. and
>long. on a moveing vessel at sea.Although the resulting long. won't be as
>accurate as the lat. taken at LAN it does have its' uses for reduceing a
>fix at LAN instead of just a Lat at LAN.It's a decent technique when
>conditions are such after LAN that no sights can be taken.It can be used
>in conjuction with a running fix from a previos LOP to improve the results
>of the LAN sight.
>This is posted mainly to show those unaware or interested and its'
>accuracy or dependability can be debated ad nuesium but it is a good way
>to find a pos. when conditions in the real world conspire against you.
>Use the techniques associated with finding zt of LAN and takeing the noon
>sight.If the sight taker timed the noon sight within a few secounds of
>LAN(the Sun appears to hang for 20-30 sec at LAN but still moves in that
>time frame to greater than 180* or less than 360*)the sight taker has the
>vessel's longitude.When reduceing the sight to find Lat. at LAN go into
>the N.A. find the whole degree,min. and sec. of the GHA of the Sun at
>LAN.At LAN the Sun is 180 or 360* depending on the dec. of the Sun and
>hemisphere the vessel is in.The GHA of the Sun within a few secounds of
>time from LAN will equal the vessel's longitude.
>So if conditions are such that you then or in the future need a fix and
>not just a lat. line and can't obtain one this will give a passable
>result.

=================

There are two problems.

1. Accuracy in determining the time of maximum altitude.

Doug said-
>If the sight taker timed the noon sight within a few secounds of LAN(the
>Sun appears to >hang for 20-30 sec at LAN but still moves in that time
>frame to greater than 180* or less >than 360*)the sight taker has the
>vessel's longitude.

But the Sun doesn't simply "hang for 20-30 seconds", it hangs near its
unchanging maximum altitude for MUCH longer than that. Take, as an example.
a winter-solstice Sun observation from my own latitude of 51deg North.
Local Apparent Noon (LAN) is at 11h 57m 53sec GMT, when the Sun altitude is
at 15deg 33.7'. The Sun doesn't drop by 0.5' from that value until it is  5
minutes away from LAN, before or after. How little a change of altitude can
Doug reliably detect before he can say, with confidence, that it's past the
maximum and has started to descend again? Perhaps, as an experienced
observer, he might claim to detect that 0.5' change, but it would require a
crystal-sharp horizon to do so, I suspect. Perhaps he can do even better,
but it takes about two minutes before or after LAN for the Sun to drop by a
mere 0.1', and nobody is going to claim to improve on that.

So there's no way for an observer to time the noon sight within a few
seconds, as Doug claims. If the time of LAN could be determined within 5
minutes, then it would establish longitude within about 20 arc-minutes. Not
a great result. In the unlikely event of a timing precision to 2 minutes, a
longitude determination to 8 arc-minutes would result.

An observer can do much better by timing an altitude sometime before noon,
and timing the same altitude after noon, and splitting the difference
between those times. This is the age-old method of determining LAN by
equal-altitudes. And the more widespread that these two times depart from
Noon, the more accurate such a measurement will be. At noon itself is the
very worst moment to try to determine when LAN occurs. If the Sun appears
only at the moment of noon, and no other, it would be best to rely on
whatever DR information exists, rather than fool yourself by presuming you
can determine longitude at noon.

2. Time difference between moment of maximum altitude and LAN on a moving ship.

This second problem affects Doug's big-ships more than it does the small
vessels that most of us sail. I don't know the speed of Doug's ships, but
let's choose 20 knots as a round number. Let's say that he is steaming
South at 20 knots, toward the Sun, from 51deg N, at the exact LAN of 11 h
57m 53s GMT. A stationary observer with a sextant, in a raft that he
passes, will indeed see the Sun "hanging" with a constant maximum altitude
at that time. On his bridge, however, Doug WON'T see the Sun's altitude as
stationary, he will see it as increasing at 20' per hour, because he is
steaming toward the Sun at 20 knots, or 20' per hour. To him, the Sun won't
appear to "hang" in the sky until somewhat later, when it's real altitude
(to the man in the raft) is falling by 20' per hour, and just matches the
rise that's caused by his own speed. So his LAN will appear to be too late.
By how much?

The moment of LAN is delayed by 15.3 (tan lat - tan dec) * v where v is the
Southerly component of the speed in knots. If lat = +51deg and dec = -
23.5deg, this works out at 511 sec, or all of 8.5 minutes late. Unless
corrected for, this will give rise to an error (not an uncertainty this
time, but an actual error) of 34' in the longitude!

============

With those difficulties, will the method provide a "passable" result for
longitude as doug describes? I doubt it. It's unlikely to improve on the
latest DR.

I think Doug has anticipated the reaction that his posting will attract, in
saying-

>This is posted mainly to show those unaware or interested and its'
>accuracy or dependability can be debated ad nuesium but it is a good way
>to find a pos. when conditions in the real world conspire against you.

I think it's dangerous to encourage novice navigators to presume that they
can deduce a longitude from their LAN, when that just ain't so, with any
accuracy that's worthwhile.

George.


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contact George Huxtable by email at george@huxtable.u-net.com, by phone at
01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
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