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    Re: Great Circle Charts
    From: Dave Weilacher
    Date: 2001 Sep 06, 10:56 AM

    Has anyone found or written a program for producing blank great circle charts?
    
    
    Original Message:
    -----------------
    From- Lu Abel lunav{at}ABELHOME.NET
    Date: Wed, 5 Sep 2001 21:25:59 -0700
    To: NAVIGATION-L{at}LISTSERV.WEBKAHUNA.COM
    Subject: Re: [NAV-L] Great Circle Charts
    
    
    At 04:26 PM 8/29/2001 +0200, Russel Sher wrote:
       I think it is a Gnomonic projection (conical projection ?)
    
    The great circle chart is indeed a gnomic projection (which is not the same
    as a conical).  One of the properties of the projection is that all
    straight lines are great circles.  The most common gnomic projections one
    sees are in the classic classroom map which has a Mercator of most of the
    world and then the two polar areas shown with gnomics.
    
    Quick lesson on projections.  The problem is to show the globe (a sphere)
    on a flat piece of paper.  Basically, possible only with distortion (hence
    the fact that Greenland appears bigger than Mexico in the classic Mercator map)
    
    While this is a technical oversimplification, one can think of a projection
    as mapping from the surface of the earth onto the sheet of paper by shining
    a light at the center of the earth through the earth's surface and thence
    tracing things onto the surface of the paper.
    
    You can make three geometrical shapes with a sheet of paper -- leave it
    flat, roll it into a cone, or roll it into a cylinder.   Which shape the
    paper has while doing the projection gives us the three types of projections.
    
    Flat sheet - gnomic projection
         The sheet touches the earth's surface at a single point,
         called the point of tangency.  On polar maps, it's the pole.
         On great circle charts, the point of tangency is indicated on
         the chart.  Distorts both sizes and directions, therefore not
         a very useful projection *except* for determining great circle
         courses.
    
    Cone - conic projection
         Not used a lot in navigation because parallels of latitude
         form arcs and meridians of longitude fan out from the nearer
         pole, so it's hard to determine courses.  But used a lot in
         mid-latitude land maps because it distorts sizes of features
         the least.  For example, with a Lambert projection where the
         cone isn't tangent to the earth's surface but actually briefly
         goes beneath it, the 48 contiguous states of the US can be
         mapped with less than 2% distortion in size.
    
    Cylinder - cylindrical projection
         The Mercator chart is the archetype of a cylindrical projection.
         Biggest advantage is that the parallels and meridians are
         parallel and perpendicular.  True direction is the same all
         across the chart.  Also while land masses grow in size as
         one gets away from the equator, their shape is shown correctly.
    
    There's a good summary of projections in Dutton's.
    
    Lu Abel
    
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