Mapping Hacks

Plot a Great Circle on a Flat Map #30

Chapter 3, Mapping Your World

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HACK

Boston; but, in fact, due to the curvature of the globe, the actual shortest

route runs nearer to the North Pole, passing over the south of Greenland.

This hack makes use of Generic Mapping Tools,orGMT

[Hack #28] to show

how to plot segments of a great circle on many different cartographic projec-

tions, including those designed for marine and aerial navigation. We’ll also

show you how you can try this yourself with a quick Perl script.

Great Circles on a Mercator Projection

The Mercator projection was historically useful because it preserved naviga-

tional direction along lines of constant bearing, known as rhumb lines. One

could draw a straight line to one’s destination on the map, set off in the

direction indicated by that line, and actually arrive at the intended destina-

tion sometime in the future. Navigating by a Mercator map therefore had

the great advantage of simplicity, but the disadvantage was that the rhumb

line between two points was often not the shortest path.

Instead, the shortest path between two points follows a line of variable bear-

ing, which turns out to be the arc of a great circle. This may seem counterin-

tuitive, because a great-circle arc will usually end up looking curved on a flat

map. Figure 3-31 depicts the great-circle arc connecting San Francisco and

London on a Mercator projection of the ...