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    Great circle vs. ellipsoidal geodesic
    From: Paul Hirose
    Date: 2002 Sep 23, 15:49 -0700

    Vic Fraenckel wrote:
    >
    > passing thru the two points. I believe the azimuth calculated on the ellipse
    > between the two points is the direction you would sail (neglecting the
    > variation etc.) passing from A to B. The methods you describe make an
    
    To be precise, azimuth from A to B equals your true course *departing*
    A. However, if the vessel holds that course it will miss B. To stay on
    the shortest route it must change course continuously. A good
    compromise is plot a few points and connect them with rhumb lines.
    
    
    > attempt to approximate the geodesic but you cannot deny that the earth is an
    > ellipsoid. (I guess you can, but it flies in face of the facts). You also
    > cannot deny that the great circle route is a fiction and the shortest
    > distance between A and B is the elliptical geodesic (by definition the
    > shortest distance).
    
    
    Saying Earth is an ellipsoid, period, is incorrect. Earth's irregular
    surface deviates from even the best geodetic ellipsoids by thousands
    of meters. In my neighborhood ground level is about 700 meters above
    the WGS84 ellipsoid. Even sea level (neglecting tide, waves, etc.)
    departs from the ellipsoid by plus or minus tens of meters.
    
    However, an ellipsoid does fit Earth better than a sphere. To see how
    much difference that makes for calculating courses, I did it both
    ways. Great circle distances and initial courses came from HO 229.
    I've also tabulated the errors of those figures with respect to
    geodetic distance and direction on the WGS84 ellipsoid. (Computed by
    the National Geodetic Survey's FORWARD program.) My great circle
    distances are based on 1' = 1 mile exactly. For simplicity I used
    estimated whole degrees for all city coordinates.
    
    from San Francisco (38N 122W)
    
     miles  error       TC  err.   destination
    
    4448.9  -.30%    303.6   .0    Tokyo (36N 140E)
    6483.9   .04%    240.6  -.1    Sydney (34S 151E)
    8858.5  -.04%     95.3   .2    Cape Town (34S 18E)
    3328.2   .05%    122.5   .1    Quito (0S 78W)
    5068.3  -.33%     11.1   .0    Moscow (56N 38E)
    
    
    from Manila (15N 121E)
    
    8938.7  -.14%     43.5   .4    Panama Canal (8N 80W)
    8312.6  -.06%    173.2  -.1    Cape Horn
    4423.0  -.15%    324.7   .1    Moscow
    4577.2  -.21%     70.5   .0    Honolulu
    
    
    The biggest course errors occur on routes which are more than 80% of
    the maximum possible distance. That's no surprise. As route length
    approaches 180 degrees the solution starts to become indeterminate. On
    the other hand it matters less and less what initial course you use.
    The extreme example is when your destination is the opposite side of
    the world.
    
    
    

       
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