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    Re: Gnomonic Charts - Usable Zones
    From: Stan K
    Date: 2018 Jan 19, 11:28 -0500
    Bob,

    I forgot to mention that Celestial Tools will also do two forms of composite great circle sailing.  Here is a brief description from the Celestial Tools Help:

    Great circle sailing provides the shortest distance between two points, but since it is more difficult to follow a great circle route than a rhumb line, it is 
    most practical when traveling long distances at high latitudes.  A frequently used rule of thumb is that for latitudes less than 40° and distances less than 
    1000 nautical miles, the distance saving in a great circle route is usually not significant.

    A great circle route can reach latitudes higher than that of the point of departure or destination.  To avoid high latitudes where ice or gales might be 
    encountered, a modification of great circle sailing called "composite sailing" may be used.  There are two methods used to accomplish this.  In Method 1, 
    a great circle route is plotted from the point of departure to the destination and is followed from the point of departure until it crosses the limiting 
    latitude, then the parallel of the limiting latitude is followed until the great circle again crosses it, then the great circle route is followed to the 
    destination.  In Method 2, one great circle is plotted from the point of departure tangent to the limiting parallel, and a second from the destination 
    tangent to the limiting parallel.  The first is followed from the point of departure to the limiting latitude, then the parallel of the limiting latitude is followed 
    until the second great circle reaches it, then the second great circle is sailed to the destination.  Method 1 is easier to plot, but Method 2 results in a 
    shorter course.  (In both methods, plotting is done on a gnomonic projection.)

    Stan


    -----Original Message-----
    From: Bob Goethe <NoReply_Goethe@fer3.com>
    To: slk1000 <slk1000---.com>
    Sent: Fri, Jan 19, 2018 2:45 am
    Subject: [NavList] Re: Gnomonic Charts - Usable Zones

    Thank you for this, Frank.
    Let me post a followup question not just to Frank but to whoever would like to respond:  I can use the Bygrave equations to calculate my initial great circle course and the distance from my current location to my destination.
    Is there another equation (or set of equations) that will let me say, "If I start from a certain latitude and longitude, and travel 200 nm on a course of θ°, what will be my latitude and longitude at the end of my journey?"  In a sense, I think my question is "Can I plan ahead my waypoints for a great circle route WITHOUT using a gnomonic chart?"
    If a mathematical solution to this is straightforward, that would be great. 
    If a table-driven approach is easier, I own a Volume 2 of Bowditch (1975 edition), as well as - of course - a downloaded Bowditch 2017.  If there is a table in one or both of these editions of Bowditch that will answer my question, I lack the skill to recognize that table for what it is.
    Thank you all for your assistance to me.
    Bob
       
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