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    Re: The Noon Fix
    From: Frank Reed
    Date: 2009 Apr 7, 18:08 -0700

    For anyone who does not have software that can read WordPerfect files, here is 
    the text from Jim's announcement of his book (note: I edited the text very 
    slightly, replacing italicized book titles by quoted titles).
    
    -FER
    
    Jim's text begins here:
    
    Authorhouse has just published my book, "The Noon Fix", and it is available 
    from them or Barnes and Noble. I hope no one is offended by this 
    announcement. My apologies if this comes across as advertising (and I checked 
    with Frank who said it's ok). But you don't have to buy the book to know what 
    it's about. The following is the gist of it:
    
    INTRODUCTION
    When I first tried the double altitude method to determine longitude, I 
    quickly found that north-south boat movement affected the time of maximum 
    altitude. I immediately started looking for a simple, direct method of 
    compensating for it. When none was forthcoming, I wrestled with the 
    mathematics to derive the equation for the time between maximum altitude and 
    meridian transit (Reference 1). That was a bit messy, but it worked. But 
    recently, the simple, direct method hit me. Like many others, I slapped my 
    head, muttering, "Why didn't I think of this before?"
    
    THE METHOD
    
    The double altitude approach averages the times for equal altitudes before and 
    after meridian passage. But north-south observer movement and declination 
    change need to be considered, since they affect the measured altitudes. From 
    reference 1, (Sn - d) is the rate of movement between the observer and the 
    body, where Sn is the northerly component of speed, and d is the rate of 
    change of declination, here positive if the change is northerly. Multiplying 
    this by the time between observations gives the resultant change in altitude.
    At meridian transit the navigational triangle has become a line. At this time, 
    the change in sextant altitude (Δhs) is (Sn - d)ΔWT, where ΔWT is the 
    difference in watch times between observations. It can be simply added to or 
    subtracted from the initially measured altitude hs. Averaging the times of 
    the initial hs and the adjusted second hs gives the time of meridian transit. 
    That's it!
    
    Relying on single observations is not recommended, but it does illustrate the 
    basic approach. Reference 1 describes a graphical method for determining the 
    time of maximum altitude. There the rising and setting altitudes are plotted 
    versus watch time. Adjusting the setting line determines the time of LAN at 
    their intersection.
    
    DISCUSSION
    
    The intent of this method was to simplify the approach. But three unexpected 
    bonuses resulted. The first is that the method is insensitive to the body 
    selected. The same approach can be used to get the time of meridian transit 
    for all bodies, including the moon. The second is that the asymmetry of the 
    altitude-time curve due to north-south motion is automatically considered. 
    The third is that changes in longitude are also automatically considered. 
    These benefits accrue because the method utilizes the data contained in the 
    slope of the altitude lines. Consider an observer with a westward component 
    of movement. His measured altitudes will rise and fall at a lesser rate than 
    an observer traveling along a meridian. Thus the hs versus WT lines will have 
    a flatter slope. This means that there will be a greater WT difference 
    between equal altitudes. Thus the resultant change in hs will be greater, and 
    the time difference between maximum altitude and meridian transit will also 
    be greater.
    
    CONCLUSION
    
    While the method was aimed at getting the simplest backup to GPS, other uses 
    may materialize. That it's more accurate than the equation in reference 1 
    (and its predecessor in the "Admiralty Navigation Manual" some fifty plus 
    years earlier) could be of benefit.
    
    
    
    
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