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    Latitude AND Longitude by Noon Sun
    From: Frank Reed CT
    Date: 2004 Jan 23, 18:57 EST
    The biggest advantage of knowing how to get Lat and Lon from a Noon Sun sight (really a series of sights) is that it requires no sight reduction tables and an absolute minimum of almanac data. If you have a sextant and any decent modern watch or clock, you can determine your position in a pinch with nothing more than a single page of information. You could easily store the required almanac data and dip/refraction data inside a sextant case.

    Celestial navigation today is nearly dead. If it is to survive, it will happen in one of two ways and maybe both. It will continue in a minor way as a hobby for enthusiasts and historians. It may also survive in a simplified form learned by real boaters for use in emergencies. As an emergency navigation tool, Noon Sun sights used for latitude *and* longitude, too, might be the last practical use for celestial navigation since the technique can be learned in an afternoon and requires no tables.

    Getting latitude by LAN sights is easy, and I won't bore anyone with details. Determining longitude is only slightly more difficult. You need to take a series of sights around the time of LAN recording both altitude and the time on your clock for each sight and then make a graph of those altitudes versus time. The altitude at the peak of the graph is the altitude to use to get latitude --that's easy enough. The TIME of the peak of the graph is the Greenwich Time (or other standard time on your clock) corresponding to local apparent noon at your location. A simple correction for equation of time converts apparent time to mean time. Then the difference between that corrected time and the Greenwich Time on the clock is directly proportional to your longitude at the rate of 4 minutes per degree of longitude. Fast and easy.

    In order for this method to work well, you need to take a series of sights over the course of 15 or 20 minutes that can be plotted to yield a clear curve. The shape of the curve is always the same --it's an upside-down parabola. It's essentially flat at the top, so the sight series has to run long enough to see the curvature. You need to see some of the rise to maximum altitude and then some of the decline from maximum altitude. The time of noon is right smack in the middle. How long do you have to wait? That depends on how well you can measure altitudes. If you have a bad sextant or a dicey horizon, you have to wait longer. To see a change in altitude of 0.5 minutes of arc in altitude, which is reasonable with a good sextant under good conditions, the amount of time you will need to wait is approximately as follows:
    Latitude        Wait Time
    0                   2-2.5 minutes
    15                 2-3.2 min.
    30                 2.2-3.9 min.
    45                 3-4.7 min.
    60                 4.5-5.8 min.

    The longer wait times occur when the Sun's maximum altitude is lower (for example, you have to wait longer in winter in the northern hemisphere).

    The amount of time tabulated above is the time you need to wait from true local apparent noon to see the Sun drop by 0.5 minutes in altitude after noon. I've ignored all cases where the maximum altitude is greater than 80 degrees --see below. In order to make a nice graph, you need to start before noon by the same number of minutes, so double the time above. OK so far? Now suppose your sextant isn't all that good, or suppose you simply want a better graph showing more of that parabola around noon. Do you have to wait twice as long to see twice the change in altitude? Nope. The change in altitude is quadratic in time so if you wait twice as long, you see FOUR times as much change in altitude. If you wait three times as long, you see NINE times as much change in altitude. Waiting that long and graphing the results will allow a navigator to read off the time of apparent noon to less than one minute of time accuracy. Converted to longitude, that's equivalent to getting your longitude to within 15 minutes of arc which would be useful, but not great, if all else fails. The LAN latitude would be more accurate of course.

    The declination of the Sun changes somewhat during a series of sights like this. Around the equinoxes, it's changing at the fastest possible rate at about 1 minute or arc per hour. This will skew the parabola's peak in time but in a completely predictable way. A simple table with a time offset for each month (and keyed to the rate of change of altitude) would eliminate any error from this issue.

    The LAN sight has an important disadvantage in the Tropics. If your latitude is within ten degrees of the Sun's declination, the maximum altitude of the Sun at LAN will be above eighty degrees, and it's very difficult to measure such high altitudes with a sextant. This means that there are large parts of the world where this method of navigation will be difficult for a month or more. In addition, as has been discussed already on the list, if your vessel is moving at any significant speed, both the time and max altitude at LAN will be thrown off. For emergency navigation, this is probably not a significant problem. If things are that bad, I think you could afford to slow down for twenty minutes around noon! This point would have to be included in the instructions for the method.

    Frank E. Reed
    [X] Mystic, Connecticut
    [ ] Chicago, Illinois
       
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