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    Re: Lat/Lon by "Noon Sun"
    From: George Huxtable
    Date: 2009 Apr 13, 17:40 +0100

    My heart sank, somewhat, on reading Frank Reed's resending of a 
    four-year-old post, on a familiar topic.
    That topic was what I referred to recently as his "hobby-horse", which has 
    emerged from the toybox yet again. That original posting presented a 
    completely one-sided view of a proposed method of teaching navigation, 
    without the slightest acknowledgment of any drawbacks. Some of those defects 
    were discussed in detail at the time, and since, but it seems nothing has 
    changed. We have been presented with "the mixture as before". Those that 
    fail to learn from history are destined to relive it.
    We have had several new members, I'm pleased to see, recently, to whom all 
    this may well be new, and they should be aware that Frank has presented an 
    incomplete picture, painting in only the virtues of his proposal. I will 
    remedy that, for them, by providing yet again some of the warts in the 
    picture. There's nothing new in any of this, and old-hands will sigh, 
    gently, and click on to the next posting.
    We need to put it in perspective, though. "Longitude around noon", has been 
    presented in various forms for years, for example by list member Jim Wilson 
    in the journal "Navigation" in 1985. It's sometimes proposed as a form of 
    "emergency navigation", a way that will get-you-home if you know no better. 
    But from his words, "You can cross oceans safely and reliably for years on 
    end using this technique if it suits you to do so", Frank Reed appears to be 
    advocating it as The Way to teach Celestial Navigation to students, and it's 
    this that I regard as dangerous.
    I have not yet met a graduate of the Frank Reed school of Celestial 
    Navigation, and if I am misjudging Frank's notions, no doubt he will tell me 
    so. If students emerge from such courses with a rounded understanding of 
    position lines and sight reduction, how to read a nautical almanac, how to 
    use the Moon or take a twilight round of star observations, well and good. 
    But if students are led to believe they have learned Celestial Navigation, 
    from the handling of Sun noon sights alone, avoiding any trig., then a 
    generation of navigational incompetents will arise; "one-club golfers" who 
    will quickly become lost at sea, if the Sun doesn't shine for the requisite 
    hour around noon. It would be the dumbing-down of a skill, delivering 
    instant gratification without the necessary groundwork.
    Now for a bit of detail about that posting.
    The claim is made that it will get you "latitude and longitude to about +/-2 
    miles and +/-5 miles respectively". Certainly, there are many situations 
    where that will indeed be the case, but Frank has been asked about more 
    difficult environments, with a low Sun at noon, at higher latitudes and 
    rough weather conditions affecting the precision of sextant sights, but has 
    not responded by conceding any worsening. If we ask what assumptions have 
    been made about the various uncertainties, in course and speed, and 
    altitude, and how they combine, in such difficult cases, such questions have 
    been evaded.
    First, for comparison, lets consider what a navigator using position-lines 
    has to do, to get a precise position by the Sun. That calls for one 
    observation sometime mid-morning, and another in the afternoon, at 
    any-old-time, whenever the Sun happens to shine. He has to correct those 
    altitudes, get Sun positions from his almanac, work two sight-reductions to 
    get azimuth and intercept, draw two position lines, shift one according to 
    his DR, and plot where they cross.
    Compare that with the task that faces the man who wants to get a "fix around 
    noon". The suggested sequence requires the navigator to be taking and noting 
    timed Sun sights over a period of 40 to 60 minutes, resulting in 5 to 13 
    observations. To achieve any sort of accuracy, in most conditions the longer 
    time and the greater number will be called for, as I will assume. This must 
    be done at predefined times, irrespective of other urgent jobs arising on 
    board, such as attending to sails. If the Sun fails to shine over that whole 
    period, there's no position-finding that day.
    He has to estimate his speed over that period, as best he can, and his true 
    course, by correcting the compass. Then get the Northerly component, which 
    to most of us would be simply
    speed x cos (true course),
    though Frank explains it otherwise, as he can't bring himself to mention a 
    trig function in this context.
    Than a small correction, due to Sun's changing declination, must be summed 
    with that speed.
    Next, for each of 13 observations, he has to multiply that speed by the time 
    interval of the observation from noon, changing sign according to whether 
    it's before or after noon, and sum that with the observed altitude.
    At this point, we hit a snag. I hear the student ask, "just when is this 
    noon, then?" Well, that's Local Apparent Noon, which is Greenwich noon, 
    corrected for the Equation of Time, and for the longitude. Unfortunately, 
    the longitude is as yet unknown; until the final result is obtained. So how 
    does the poor student follow those instructions?
    Well, Frank knows, and I know (though the student hasn't been informed) that 
    any old time can be presumed for local apparent noon, at this stage, just 
    for the purpose of correcting the timing of the peak altitude. It can simply 
    be guessed, and the correction worked accordingly (just as long as the 
    peak-altitude of that plot isn't used later, for finding latitude). Having 
    done that, plotted the 13 corrected points, and folded the paper, the centre 
    of symmetry gives the watch time of local apparent noon.
    After allowing for the Equation of Time, the result, at 15� per hour, will 
    provide his longitude.
    Now the navigator has to go back to his original uncorrected altitude 
    observations, and interpolate between them to the now-known time of LAT. 
    Then correct as usual for index error, dip, refraction, semidiameter, and 
    allow for declination to get latitude. All familiar stuff.
    However, compared with the two-position-line option, the proposed procedure 
    can hardly be described as a saving of effort.
    Frank tells us that the job can be done without need of a nautical almanac 
    "you don't need one at all --only a short table of declination and equation 
    of time, possibly graphed as an "analemma" perhaps (he says). He doesn't 
    tell us what precision is available in the use of such a tool, and to what 
    extent his claimed precision of 2 miles in lat, 5 miles in long, would be 
    degraded by it. I would like to know. He doesn't even mention that without a 
    full almanac, both declination and equation of time need to be interpolated 
    between given values for two Greenwich noons, according to the observer's 
    All the difficulties described above have been ignored or glossed over in 
    Frank's (repeated) posting. These things need to be said.
    According to previous form, this posting will be followed by an indignant 
    response from Frank Reed, objecting to the denigration of his favourite 
    contact George Huxtable, at  george{at}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 ----- 
    Sent: Sunday, April 12, 2009 11:19 PM
    Subject: [NavList 7927] Lat/Lon by "Noon Sun"
    From the archives for June 4, 2005:
    "Latitude and Longitude by "Noon Sun"
    From: FrankReedCT---COM
    Date: 4 Jun 2005 19:54
    First things first: I've put the phrase "Noon Sun" in quotes here because 
    the set of sights required for this system goes a little beyond the standard 
    procedure for shooting the Noon Sun for latitude only.
    This short method of celestial navigation will get you latitude and 
    longitude to about +/-2 miles and +/-5 miles respectively --more than 
    adequate for any conceivable modern practical purpose. You can cross oceans 
    safely and reliably for years on end using this technique if it suits you to 
    do so. Its enormous advantage is simplicity. It's easy to teach, easy to 
    demonstrate, easy to learn, and also easy to re-learn if necessary. I 
    mention this because most people who are learning celestial navigation today 
    will quickly forget it. What's the point of learning something if you can't 
    reconstruct your knowledge of it quickly when and if the need actually 
    arises to use it? It's tough to resurrect an understanding of the tools of 
    standard celestial navigation on short notice, but easy with this lat/lon at 
    noon method. Additionally, this method does not require learning all the 
    details of using a Nautical Almanac (you don't need one at all --only a 
    short table of declination and equation of time, possibly graphed as an 
    "analemma") and it needs no cumbersome sight reduction tables.
    Here's how it's done:
    Start 20 or 30 minutes before estimated local noon. Shoot the Sun's altitude 
    with your sextant every five or ten minutes (or more often if you're so 
    inclined) and record the altitudes and times by your watch (true GMT). 
    Continue shooting until 20 or 30 minutes after local noon. [note the 
    difference from a noon latitude sight --we're recording sights leading up to 
    and following noon-- usually these are thrown away]
    Next you need to correct for your speed towards or away from the Sun. For 
    example, if we're sailing south and the Sun is to the south of us, then each 
    altitude that we have measured will be a little higher as we get closer to 
    the latitude where the Sun is straight up. We need to 'back out' this effect 
    so that the data can be used to get a fix at a specific point and time. This 
    isn't hard. First, we need the fraction of our speed that is in the 
    north-south direction. If I'm sailing SW at 10 knots, then the portion 
    southbound (in the Sun's direction) is about 7.1 knots. You can get this 
    fraction by simple plotting or an easy calculation. Next we need the Sun's 
    speed. The position where the Sun is straight overhead is moving north in 
    spring, stops around June 21, then heads south in fall, bottoming out around 
    December 21 (season names are northern hemisphere biased here). It is 
    sufficient for the purposes of this method to say that the Sun's speed is 1 
    knot northbound in late winter through mid spring, 1 knot southbound from 
    late summer through mid autumn, and 0 for a month or two around both 
    solstices (it's easy to prepare a monthly table if you want a little more 
    accuracy). Add these speeds up to find out how much you're moving towards or 
    away from the Sun. If you're moving towards the Sun, then for every six 
    minutes away from noon, add 0.1 minutes of arc for every knot of speed to 
    the altitudes before noon and subtract 0.1 minutes of arc for every knot of 
    speed to the altitudes after noon. Reverse the rules if you're moving away 
    from the Sun. Spelled out verbally like this, this speed correction can 
    sound tedious but the concept is really very simple and it's very easy to 
    do. [Incidentally, George Huxtable deserves credit for emphasizing the 
    importance of dealing with this issue (although I don't think he ever 
    spelled out how to do it)]
    Now graph the altitudes (use proper graph paper here if at all possible): 
    Sun's altitude on the y-axis versus GMT on the x-axis. The size of the graph 
    should be roughly square, maybe 6 inches by 6 inches so that you can clearly 
    see the rise and fall of altitude. For longitude, you will need to determine 
    the axis of symmetry of the parabolic arch of points that you've plotted. 
    There is a simple way to do this: make an eyeball estimate of the center and 
    lightly fold the graph paper in half along this vertical (don't "hard 
    crease" the fold yet). Now hold it up to the light. You can see the data 
    points preceding noon superimposed over the data points following noon which 
    are visible through the paper. Slide the paper back and forth until all of 
    the points, before and after, make the best possible smooth arch (half a 
    parabola). Now crease the paper. Unfold and the crease line will mark the 
    center of symmetry of the measured points with considerable accuracy. 
    Reading down along this crease to the x-axis, you can now read off the GMT 
    of Local Apparent Noon. Reading back up the crease to the data, you can pick 
    off the Sun's maximum noon altitude (which is probably already recorded but 
    if you missed the exact moment of LAN you can get it this way).
    Next we need two pieces of almanac data: the Sun's declination for this 
    approximate GMT on this date and the Equation of Time for the same date and 
    time. You do NOT need a current Nautical Almanac for this. The exact value 
    of declination and Equation of Time varies in a four-year cycle depending on 
    whether this year is a leap year or the first, second, or third year after. 
    So we don't need an almanac for this. A simple table will do (where to get 
    one? Today, they're very easy to generate on-the-fly... or you could use an 
    old Nautical Almanac... or you could also use an analemma drawn on a 
    sufficiently large scale).
    Apply the Equation of Time to the GMT of Local Apparent Noon that you found 
    above. You now have the Local Mean Time at LAN, and you already know the 
    Greenwich Mean Time. The difference between those two times is your 
    longitude. Convert this to degrees at the rate of 1 degree of longitude for 
    every four minutes of time difference. Done. We've got our longitude.
    Now for latitude. Notice that we didn't correct any of our altitudes for 
    index correction or dip or refraction or the Sun's semi-diameter. These 
    corrections are totally unnecessary for the longitude determination. But we 
    need them for latitude. Take the Sun's altitude at the time of LAN (read off 
    the "crease" or actually observed by watching the Sun "hang" at the moment 
    of LAN). Correct it for index correction, dip, refraction and semi-diameter 
    as usual. This gives you the Sun's corrected observed altitude. Subtract 
    from 90 degrees. This "noon zenith distance" tells us how many degrees and 
    minutes we are away from the latitude where the Sun is straight up. The 
    latitude where the Sun is straight is, by definition, the "declination" that 
    we have looked up previously from our tables. So if the Sun is north of us 
    at noon, then we are south of the Sun's declination (latitude) by exactly 
    the number of degrees and minutes in the noon zenith distance. If the Sun is 
    south of us at noon, then we are north of the Sun's declination by the same 
    amount. A simple addition or subtraction yields the required latitude. Done.
    We've spent about ten minutes making and recording observations of the Sun's 
    altitude over the course of 45 minutes to an hour, and reduced those 
    observations to get our latitude and longitude at noon with about five 
    minutes of paperwork. Not bad!
    Again, the overwhelming advantage of this "short celestial" is that it can 
    be taught easily, learned quickly, and RE-learned quickly on the spot if 
    necessary. An additional advantage is that it requires an absolute minimum 
    of materials. You need a sextant (metal if at all possible, but plastic will 
    do), a decent, cheap watch or small clock, tables of refraction and dip (one 
    sheet of paper), a four-year revolving almanac of the Sun's declination and 
    equation of time (another sheet or two of paper), and some graph paper and a 
    pencil. You could even print out these (or equivalent) instructions and 
    throw everything in the case with your sextant.
    As for disadvantages, they really depend on the student and his or her 
    expectations. What is it that we want to do with celestial navigation? Why 
    study any method? And for a thousand students, you will get a thousand 
    answers. The days are gone when celestial navigation was essential and fixed 
    curricula could be dictated for students to either take in their entirety or 
    leave. This field has moved on to the stage of "a la carte" learning. It can 
    be a pain in the neck for instructors accustomed to doing things the same 
    way year after year but it's a real liberation for students and possibly 
    also for more creative teachers and "information publishers".
    42.0N 87.7W, or 41.4N 72.1W.
    Navigation List archive: www.fer3.com/arc
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