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    Re: The Noon Fix
    From: James N Wilson
    Date: 2009 Jul 10, 20:29 -0700
    In reviewing the posts on this subject, everything has been said, at least once. But explaining a graphical approach with words may not be totally adequate.
    I recently described my method at a Los Angeles Yacht Club Wednesday luncheon, and knowing that there would be non-navigators there, I prepared an introduction to help them understand. I still got a lot of blank looks, but I'll show what I did, in case everyone on the list doesn't completely understand the method.
    I introduced the double altitude method, showing the slide Myth, noting that it is very simple and often quoted. But it doesn't work on a moving vessel, and if you're standing on a rock during one of the solstices when it does work, it really isn't needed.
    I followed with the slide, Problem, showing the effect of vessel motion. This is taken from my Navigation paper. It shows that north-south motion affects the time of highest altitude. In that paper, I concentrated on determining Dt so as to correct for this effect. I noted that the change in maximum altitude Dh is insignificant.
    I then showed the slide, Solution, which illustrates the principle, and shows how to determine when to commence taking the last run of sights. That method is to calculate the time between the last sight of the first run and meridian transit, DT, and then adding it to that time. I explained that DH is the consequence of north-south movement (and declination change). As such, it is directly related to the time between observations, 2xDT.
    I then worked the example to demonstrate the method.
    For this group, I'll add two more slides. To properly bracket actual observations, another value of  DH is needed. Solution1 adds a second determination of it based on the first observation of the initial run of sights. From these two values, the corrected (solid) curve can be obtained.
    Now all of this is based on having a robot working the problem. He knows exactly where he is, and his sights are taken precisely at the theoretical time and need no correction. So, he doesn't need the data, but is working just to please us. But he does illustrate the principle, and one could imagine working backwards with a set of real and imperfect data.
    The next slide, Solution2, has translated the right hand portion of Solution1 to where it overlaps the left part, allowing the lines to intersect. This is for the convenience of the user, and I make DWT a whole number of minutes as a plotting convenience. No error is introduced here, and DWT consequently falls somewhere in the middle ranges of the sight data. I further calculate only one value of Dhs as a simplification. This does introduce some error, but since DWT has already been shown to be close to the intersection of the ascending altitude line and the adjusted descending line, the resultant error is small. This slide will be recognized as the example plot, with only one value of Dhs calculated.
    Hopefully, this will make the method more understandable.
    Jim Wilson

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