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Who would have thought there was more mileage to be got from discussing 
latitude at noon, the oldest and simplest trick in the navigator's book? But 
so it seems to be...

Let me start by apologising for the long delay in responding to Henry's 
thoughtful and perceptive posting, back on 14 Jan, which is copied below. I 
have changed the threadname to suit the topic better.

Particularly, these words should be noted-
"IMHO postings to this List frequently seem to consist of “sound bites” 
which do not take into consideration the whole picture. It should be 
recognized that a Navigator’s Day’s Work at sea was not a series of isolated 
sight takings, but rather an integration of sights, positions, speed checks, 
course checks, and compass error checks, as well as a carefully advanced 
Dead Reckoning continuously upgraded as evaluated astronomical data 
dictated."

That's all too true. Ocean navigation involves a continuous process, linking 
together position lines by means of dead reckoning, with the occasional 
fix.when the opportunity arose. On the other hand, in textbook questions, 
and often here on Navlist, position-finding is often presented as an 
isolated "problem", to be solved on its own, in isolation from real-life.

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

My own comments here, and some of Henry's, respond to the posting from 
Jeremy "Anabasis" of 11 Jan, about his latitude observations, also copied 
below. It was a bit of a surprise from such a careful celestial navigator, 
to discover that he doesn't really distinguish, when observing for latitude, 
between observing at Local Apparent Noon (LAN) and observing at maximum 
altitude. Indeed, what he calls a LAN observation is actually a measurement 
of the maximum, not the value at LAN.

I will try to give some notion of the errors that occur, in observing for 
longitude and latitude, when the measurement is made around the moment of 
maximum altitude from a moving vessel. But first, let's consider the 
familiar longitude errors, as have been discussed at length here, in 
postings with subject "longitude around noon", or similar.

If longitude is obtained directly from the moment of maximum Sun altitude 
from a moving vessel, rather than from LAN, large errors arise, which must 
be corrected for.

The simplest explanation I'm aware of is contained in a paper by List Member 
Jim Wilson, in "Position from Observation of a Single Body", Navigation, Vol 
32 No 1 (Spring 1986), pages 85 - 95.

From this, we can deduce that the Easterly error in deriving longitude from 
max altitude, in arc-minutes, is

(12 / pi) (Northing - d) (tan lat - tan dec)

where Northing is the northerly component of vessel's speed, in knots 
(negative if Southerly)
d = rate of change of  declination, in arc-min per hour (+ if Northerly). d 
is zero at the solstices, ranging between  about +1 knot at the spring 
equinox, and -1 knot in Autumn.
lat and dec are positive when North.

These errors are plotted against latitude, in the upper graph of the 
attached diagram. Four ship speeds are shown, 10 and 20 knots Northing, and 
10 and 20 knots Southing, Two curves are shown for each speed, at the June 
and December solstices. At other dates, intermediate values apply.

A correction, with opposite value to the error, must be applied, to get true 
longitude. It's clear, from the sixe of those errors, particularly for a 
fast vessel at high latitudes, how important it is to make that correction, 
and how precisely that component of speed must be known.

So much for the longitude errors. Next, consider the corresponding errors in 
latitude, from measuring Sun altitude at its moment of maximum value, rather 
than at LAN.

Now, the errors involved, shown in the lower plot, are much, much less.  In 
this case,
latitude error = (Northing / (75 pi)) (Northing - d)  (tan lat - tan dec).

Because d is usually much smaller than the Northing (and zero at the 
solstices) this error varies roughly with the SQUARE of the ship speed, so 
it becomes important for fast vessels, and rather negligible for slow ones. 
As a result, the latitude error shown on the plot for a 10 knot vessel is 
only one quarter of that for one doing 20 knots. And for the same reason, 
the latitude error shown on the plot is exactly the same, whether the vessel 
is travelling Northward or Southward.

For an ordinary sailing yacht, or a historic sailing vessel, the upshot is 
that it matters little whether the latitude is measured from the altitude at 
LAN or at its maximum value; unless a navigator is being particularly 
pernickety: the resulting error won't usually exceed a minute of arc. But 
for the modern fast vessels on which Jeremy is likely to find himself, care 
needs to be taken, or latitudes can be out by a few minutes, especially in 
high latitudes.

This is intended to reinforce Henry's message, by putting some numbers on 
it.

How should one go about getting latitudes exactly right, from a fast ship? 
Well, you could simply measure altitude at LAN, not maximum; for which you 
would need a timepiece and a rough knowledge of longitude. Or you could 
correct an observed maximum altitude as an ex-meridian observation, for 
which the same knowledge would be needed. Or, without knowing longitude or 
time, you could correct a latitude, derived from max altitude, according to 
the formula provided above, or the lower graph: for which approximate ship 
speed needs to be known.

George.

contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.


----- Original Message ----- 
From: "hch" 
To: 
Sent: Thursday, January 14, 2010 6:53 AM
Subject: [NavList] Re: QMOW Days work in Navigation

Hi all,

Latitude at Noon, or thereabouts,

This matter has again raised its head. Jeremy has put his
oar in, and George has come forth with his usual number of insightful
questions. Yet it seems that we go further astray with each posting. Let’s 
for
the moment, forget about the various Lunar methods of determining GMT, or
Longitude, and allow ourselves the luxury of a well equipped ship, vessel,
boat, yacht, or whatever you can afford, possessing a well rated 
chronometer,
as well as the other appurtenances of modern Celestial Navigation. We can 
now
look into the Noon, or any Meridian Transit, observation as it was dealt 
with
at sea, utilizing the sea horizon, before the advent of universally 
available
electronic means.



The body to be observed, whether Sun, Moon, Planet, or Star,
will be on your meridian at such time as its GHA is equal to your Longitude. 
By
reference to a Nautical Almanac, or other appropriate publication, you may
readily deduce the corresponding GCT of transit, or if you like you can use 
the
old style LAT +/- EqT +/- Long method for the same result. Regardless of any
other consideration, this is the time to observe any body for the most 
accurate
determination of Latitude by the traditional Meridian Altitude method. It 
will
be the time of the body’s highest altitude for a specific location on the
surface of the earth. At this point in time the body appears at rest – for a
short time neither rising nor falling before the altitude begins to 
decrease, i.e. it "hangs".




You may, if you wish and as some textbooks do advocate, wait
until the body has “dipped” to insure having read its greatest altitude – 
this
constitutes more of a “security blanket” as assurance against having made a
mistake in calculation of the time than any sort of technical exercise; it 
is,
however, essentially incorrect and representative of the “good enough 
attitude”
which crept into the teaching of celestial navigation with the advent of
electronic methods. I can well remember articles on the various electronic
methods denigrating the position finding accuracy of celestial navigation, 
as
practiced at sea, to the order of 15 to 20 miles – a premise with which most
experienced navigators, then or now, would hardly agree.



Waiting for the “dip” has no great effect on the ultimate
outcome of the solution IF YOU ARE STATIONARY, or even moving slowly. If,
however, you are moving at any significant rate of speed there is a 
different
tale attached to the horse. With any ship movement, other than due East or
West, the observer will be either approaching or receding from the body –
neglecting possible declination change of the Sun or Moon, in approaching 
the
altitude will be raised and in receding lowered commensurate with the ship’s
motion, and the body will appear at rest when its rate of change due to the
earth’s rotation is equal and opposite to the apparent rate of change due to
the vessel’s motion. Therefore, at upper transit, in moving toward the body 
it
will appear to be at rest when its true altitude is really diminishing, 
i.e.,
after its actual meridian transit – conversely, in moving away from the body 
it
will appear at rest while its true altitude is increasing, i.e., before its
true meridian passage. It should be readily apparent from the foregoing that
the maximum altitude of a body is not always the true altitude at meridian
transit and, when such is desired, the altitude should be taken at the
predicted time of the phenomena to attain maximum accuracy of result –
otherwise, in either case meridian angle will have developed and, when
observing the Sun or Moon, there will be declination change.



Conventional wisdom and teaching allows that vessel movement
is not as significant factor in East/West ship movement at meridian transit, 
as
respects waiting for the “dip”.

This appears to be essentially true; East/West movement at
high speed may affect the actual time of the phenomena, however, will not
affect the altitude, thus making no difference in the Latitude ultimately
deduced, except as may be occasioned by declination change of the Sun or 
Moon.



Traditionally speaking, a relatively close off-meridian
observation, or a declination change, should theoretically be dealt with by
ex-meridian technology, i.e., utilizing the altitude at dip and the
corresponding time, calculate the correction to the meridian, as well as the
declination, for the time of observation by the methods described in vintage
texts, and therefrom determine the Latitude at the TIME OF OBSERVATION, 
which
reduced to the time of LAN will agree favorably with a Latitude as if then
determined. This all may sound complicated, but is really quite simple in
practice – it becomes of more relevance as the ship’s speed increases and a
greater north/south direction of movement becomes involved, and is of less
significance in east/west movement.



The ex-meridian, or Reduction to the Meridian, observation
was a standard and traditional method of obtaining the Latitude when, for
whatever reason, the altitude of the body observed, and particularly the 
Sun,
could not be obtained at LAN – even for the simple reason of the 
interference
with the lunch or dinner hour. Later teaching emphasizes the traditional 
sight
for Latitude at Meridian Transit to be but a special solution for a LOP and
suggests, even recommends, that conventional sight reduction methods be 
employed
in its place to determine a LOP running E/W, or nearly so, to be crossed 
with
an earlier or later LOP in the determination of a conventional running fix. 
As
the older methods disappear and celestial navigation is streamlined to suit
solely back-up requirements, as well as educational simplicity, I feel sure
that this latter methodology will ultimately prevail, more or less as one
solution to fit all purposes. This latter concept has just about done away 
with
the use of the Reduction methodology. Actually, what the MM does will be 
largely governed by USCG License examination requirements, a matter on which 
I diplomatically decline comment.




IMHO postings to this List frequently seem to consist of “sound bites” which 
do not take into consideration the whole picture.
It should be recognized that a Navigator’s Day’s Work at sea was not a 
series
of isolated sight takings, but rather an integration of sights, positions,
speed checks, course checks, and compass error checks, as well as a 
carefully
advanced Dead Reckoning continuously upgraded as evaluated astronomical data
dictated. It was seldom, indeed, that the Noon Position was not well known 
long
before LAN. Given:- a reasonably good
AM star fix, indicating an overnight speed from the previous PM star fix:
hourly Sun lines during the AM, serving both as speed and/or course checks 
and
for advancement to Noon; and, when available, a simultaneous Sun/Venus or
Sun/Moon cross - it becomes readily apparent that the Latitude sight at noon
was often largely anticlimactic and an acquiescence to tradition. Please don’t
misunderstand, it wasn’t always this way – there were times when position
finding became a struggle; when it became necessary to use every trick in 
the
book. Regardless, as Jeremy indicates, the Noon position, i.e., the LAN
position reduced to 1200 hours Standard Time, had and probably has, in the 
MM
become more of an Administrative Position, used for the standardized
calculation of a vessel’s performance in various categories. Yet, I feel 
obliged to ask what he, or
anyone else, did or would do if AM and PM star fixes were not available, as
North Atlantic winter conditions so frequently dictate – assuming of course 
the
absence of electronic equipment, i.e., GPS, et al.



Lastly, I would briefly address the matter of Longitude
determination at Noon by equal altitudes – recently rediscovered by this 
List
and considerably expanded upon by the graphing methods discussed at length.
While I am unable to historically comment on graphing methodology, it is
possible to cite excellent documentation on equal altitude use, including 
all
relevant corrections for course and speed between observations – for 
whatever
reason, it just died a natural death, apparently by simple neglect or 
misuse.

Suffice it to say, I occasionally used the method at sea and
found it to be quite practical; those interested may find further 
information
in Chauvenet’s , Vol. I of Spherical and Practical Astronomy or, if a less
“land bound” authority is desired, in a small volume entitled Ex-Meridian
Altitude Tables, Declination 0 – 70 degrees, authored by Captain Charles 
Brent,
RN, and others, published by George Philip & Son, Ltd., London, in 1914.
Regards,

Henry

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

On 11 Jan, Jeremy (Anabasis) wrote-

You are entirely correct George, they are not the same thing at all, but 
that is how it is taught, and that is how it is practiced in my experience. 
The motion of the vessel is only taken into account to acquire a DR to 
calculate the time of LAN and then a second estimate.  Observations at the 
time of LAN are not taught due to the possible error in the DR, but the 
maximum altitude is used.  Considering my last cadet didn't know how to 
shoot or reduce LAN observations, there is little hope in the USMM that this 
will change for the better in the near future.

In my earlier years,  I often wondered why my LAN observations were so much 
worse than my star fixes.  In the last few years, I have discovered that the 
distinction between LAN and maximum altitude is most likely the reason. 
Still, the error because of the lack of this distinction is small enough 
that it is accepted at sea.  A mile or two of error in Latitude for the 
slight increase in accuracy of the day's run was not worth dealing with. 
The noon fix was not used to correct the day's DR, only to find the day's 
run.  It is not correct, but that is the way it is taught, and before this 
list, no navigator in my experience has ever brought it up.

If Henry or Byron or any like experienced individual can tell us that I am 
incorrect with how LAN was taught to be observed, I will accept that my 
education in the 1990's and 2000's was degraded from the teaching of the 
past, but talking to Masters who started sailing in the 1960's shows no 
difference, unless they were deliberately not telling the students these 
things.

I can't interpret the time question completely accurately.  Are you asking 
time spread, or time spent in observation/reduction?  If it is spread, it 
can be any reasonable amount.  I have done 30+ observations, and then I've 
done 5.  The 30 sight was a bit over the top to be honest and not efficient 
for the observer.  The 5 sight fix was shot over 18 minutes and, with a 
computer, took about 3 minutes to get a fix with an error of 0.3 nm (32N and 
at a speed of 7.6 kts Crs 305T).  This is much more accurate than most of 
the 1200 R fixes I've ever shot and plotted.

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

This was in reply to a question of mine, on 10 Jan, which read in part-

This is a bit odd. Jeremy calls it a LAN (Local Apparent Noon) observation,
but what he describes is a maximum altitude observation.

Those are not the same thing. They do not occur at the same time, and they
do not produce the same result. The LAN observation gives the latitude at
LAN. directly. The maximum altitude is dependent on the North-South
component of the vessel's speed, and needs correcting for it. The faster the
vessel, the bigger the difference. Can Jeremy explain, please?

============================
and that question was prompted by an earlier posting from Jeremy on 10 Jan 
which read-


What Byron speaks of is what I was traditionally taught about observing LAN. 
Multiple altitudes ARE NOT RECORDED, but a frequent observation of the sun 
was taken and the sextant adjusted to keep the limb on the horison.  You 
start 10 minutes before calculated LAN in order to insure that you are ready 
for the observation in the case that the DR or calculations were in error. 
We were taught, as I have mentioned before, to watch until the sun "hung" in 
the sky (no apparent changes in altitude, and then the maximum altitude was 
recorded and the Latitude then calculated.  This Latitude was 
advanced/retarted along with the AM sunline where a 1200 LT Running fix was 
determined.

What is interesting to note, is that the DR plot was not changed at noon, 
but only "reset" when a more reliable star fix was obtained.  DR's in my 
training, were changed only at the two star times.

File:

   

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