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Subject: Re: Great Circle Charts
From: Lu Abel (lunav@XXX.XXX)
Date: Thu Sep 06 2001 - 00:25:59 EDT
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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