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    Re: Latitude by Noon Sun for Beginners
    From: Gary LaPook
    Date: 2009 Apr 30, 00:20 +0200

    
    JPK wrote:
    
    "As an aside, you asked why I thought there was a 12-minute time span between 
    the time of the shot and LAN for the DR longitude.  I converted his DR 
    longitude of 68d 25' to time, and got 4h + 32m + 100s, or 16:33:40.  I 
    figured that meant that the sun would be over his meridian at that time.  The 
    shot was made at 16:46:20, which is 12m and 40s later.  Did I go wrong on 
    that reasoning? Did the navigator make his shot when he did, rather than when 
    I would have advised him to had he asked me, simply because he recognized 
    that his DR was not likely to be close enough to make the difference 
    significant?  "
    
    That is one way to do it but then you have to apply the equation of time which 
    is listed at the bottom of each Nautical Almanac page. As Jean-Philippe 
    Planas points out, the sun was 3� 03.1' slow meaning that it didn't cross the 
    Greenwich meridian until 12 minutes and 12 seconds after noon Z. The equation 
    of time shows the minutes and seconds that the sun is fast or slow compared 
    to mean time and the almanac also lists the time of meridian passage, just 
    another way of expressing the equation of time. The sun can be up to 16 
    minutes off form mean time during the year. 
    
    A different way to accomplish the same thing is to calculate the time when the 
    GHA of the sun equals the longitude. Take out the GHA for the hour when it is 
    east of the DR and subtract the GHA from the longitude to find the 
    difference. Then flip through the Increments and corrections section of the 
    almanac to find our how many minutes and seconds it takes for the sun to move 
    that additional distance. To get a start on the right page of the increments 
    section remember that the sun moves one degree every four minutes and one 
    minute of GHA for every four seconds of time. 
    
    That said, I think that you still don't get it. You are looking through the 
    wrong end of the telescope. For a LAN sight you do not use your DR longitude 
    to try to predict the exact time of LAN in advance, you just get an 
    approximate idea so you can get your sextant into operation prior to LAN. The 
    navigator does not take the shot when advised that he should based on DR, he 
    starts taking sights sometime prior to the approximate time of LAN and 
    follows the sun as it increases in altitude. Then when he notices it starting 
    down he says mark and you note the time at that point. Note, the time of LAN 
    is determined by seeing the sun start to descend not the other way around, as 
    you suggested, by a calculation of the time the sun should be at the DR. You 
    then use the observed time of LAN to enter the almanac to take out the sun's 
    declination for the calculation of latitude. 
    
    To some level of accuracy you can also use the time of observed LAN to 
    determine your longitude and the level of accuracy that can be achieved this 
    way has been the subject of the recent threads. If you can be sure that you 
    did not miss LAN by more than a minute then the longitude should be accurate 
    within plus or minus 15'. If you can be certain that your possible error in 
    noting LAN is less than one minute then your level of accuracy will be 
    better. 
    
    Even with the one minute level of uncertainty in the time of LAN the 30' range 
    of longitudes may be completely adequate for emergency or backup navigation. 
    In fact this level of accuracy is twice the level required to have won the 
    top prize of 20,000 pounds from the Board of Longitude in the 18th century. 
    Prior to the development of the chronometer navigators routinely sailed 
    around the world with little idea of their longitude relying on latitude 
    sailing to find their destination.
    
    The LAN sight is a special case in which the navigational triangle collapses 
    to a line making the computation of latitude one of simple arithmetic. In the 
    olden days, doing trig using trig tables was a major chore so navigators 
    liked special cases like this one. Similar is the use of Polaris for 
    latitude, just simple arithmetic. Ex- meridian was a more complicated 
    procedure in which you made a correction of a non-LAN sight using some 
    assumptions (so some sources of error) so that it could be treated as a LAN 
    sight and so would still be easier that the full course press using trig.  
    
    Now  a days, with calculators and inspection tables and better educated 
    navigators, I don't see any reason to continue these special cases, just 
    treat them all as normal sights, calculate Hc and Az and plot the LOP as I 
    pointed out in my previous post. 
    
    gl
    
    
    
    
    
    JKP{at}obec.com wrote:
    > Gary,
    > Thanks very much for your in-depth explanation. I find that it was the 
    declination giving me trouble, and I finally realized I was subtractng 30' 
    for the "d" correction, not 0.5' as I should have. (Half a degeree instead of 
    half a minute!) So for the time of the sight I (eventually) got a declination 
    of 18d 59.8'S and the correct latitude of 55d 37.8'S.  Whew!
    >
    > As an aside, you asked why I thought there was a 12-minute time span between 
    the time of the shot and LAN for the DR longitude.  I converted his DR 
    longitude of 68d 25' to time, and got 4h + 32m + 100s, or 16:33:40.  I 
    figured that meant that the sun would be over his meridian at that time.  The 
    shot was made at 16:46:20, which is 12m and 40s later.  Did I go wrong on 
    that reasoning? Did the navigator make his shot when he did, rather than when 
    I would have advised him to had he asked me, simply because he recognized 
    that his DR was not likely to be close enough to make the difference 
    significant?   
    >
    > Or, as another reader suggested, was this perhaps meant to be an 
    "ex-meridian" sight?  In that case, as I eventually found in Jeff Toghill's 
    "Celestial Navigation," the observed altitude should be corrected for the 
    time difference by factors found in Bowditch.  (The tables referred to were 
    29 and 30, though in the 2002 Bowditch they are now 24 and 25.)  I plan to 
    rework the problem from that perspective and see what I get.
    >
    > Thanks again for your patience and thoroughness.  This list is like having 
    dozens of expert tutors on call!
    >
    > John
    >
    >
    > >
    >
    >   
    
    
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