Welcome to the NavList Message Boards.


A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

Compose Your Message

Add Images & Files
    Latitude at noon. was: Re: QMOW Days work in Navigation
    From: George Huxtable
    Date: 2010 Jan 24, 21:10 -0000

    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 
    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 
    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.
    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" 
    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 
    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 
    as well as the other appurtenances of modern Celestial Navigation. We can 
    look into the Noon, or any Meridian Transit, observation as it was dealt 
    at sea, utilizing the sea horizon, before the advent of universally 
    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. 
    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 
    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 
    determination of Latitude by the traditional Meridian Altitude method. It 
    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 – 
    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 
    however, essentially incorrect and representative of the “good enough 
    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, 
    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 
    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 
    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 
    will appear to be at rest when its true altitude is really diminishing, 
    after its actual meridian transit – conversely, in moving away from the body 
    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, 
    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 
    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, 
    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 
    could not be obtained at LAN – even for the simple reason of the 
    with the lunch or dinner hour. Later teaching emphasizes the traditional 
    for Latitude at Meridian Transit to be but a special solution for a LOP and
    suggests, even recommends, that conventional sight reduction methods be 
    in its place to determine a LOP running E/W, or nearly so, to be crossed 
    an earlier or later LOP in the determination of a conventional running fix. 
    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 
    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 
    of isolated sight takings, but rather an integration of sights, positions,
    speed checks, course checks, and compass error checks, as well as a 
    advanced Dead Reckoning continuously upgraded as evaluated astronomical data
    dictated. It was seldom, indeed, that the Noon Position was not well known 
    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 
    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 
    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 
    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 
    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 
    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 
    relevant corrections for course and speed between observations – for 
    reason, it just died a natural death, apparently by simple neglect or 
    Suffice it to say, I occasionally used the method at sea and
    found it to be quite practical; those interested may find further 
    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 
    RN, and others, published by George Philip & Son, Ltd., London, in 1914.
    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 
    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 
    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.


    Browse Files

    Drop Files


    What is NavList?

    Join NavList

    (please, no nicknames or handles)
    Do you want to receive all group messages by email?
    Yes No

    You can also join by posting. Your first on-topic post automatically makes you a member.

    Posting Code

    Enter the email address associated with your NavList messages. Your posting code will be emailed to you immediately.

    Email Settings

    Posting Code:

    Custom Index

    Start date: (yyyymm dd)
    End date: (yyyymm dd)

    Visit this site
    Visit this site
    Visit this site
    Visit this site
    Visit this site
    Visit this site