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    Lat/Lon by "Noon Sun"
    From: Frank Reed
    Date: 2009 Apr 12, 15:19 -0700

    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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