Re: spherical geometry

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 8:56 AM -0500 8/19/04, RAUBER, JOEL wrote:
> As a side note, the airlines and mariners have long been interested in the
> solution to this problem.  And certain map projections have been designed to
> facilitate the solution.
If memory of my days doing navigation while in the Navy serves, There
is not a single heading one can take to follow a great circle route
from point A to point B, since the great circle route crosses each
meridian at a different angle, and it is that angle that determines
the compass heading one takes at that point. The straight line path
on a Mercator projection map (called a "rhumb line") does have a
constant heading, but it is not the great circle path.

Given that, I don't think that ships or aircraft would be interested
in a single heading to follow for an extended trip--one for which a
great circle path is significantly different from the rhumb-line
path. As a practical matter, on a trans-oceanic trip, a ship's
navigator will calculate the great circle path (and I have forgotten
the method used to do that on a Mercator projection), and then
approximate that path with a series of rhumb-line segments, so that
the ship's heading will change periodically during the trip. I recall
vaguely that the rhumb-line segments typically were about 5 degrees
of longitude, each, or some 300 nautical miles or less--roughly one
day's steaming.

Things may have changed dramatically with the advent of GPS
navigation, which occurred long after I got out of the navigation
business. I would expect that computerized nagivation systems will
automatically calculate the heading on a great circle route, leaving
the navigator with precious little to do, once a chip is clear of
harbor restrictions.

Hugh
--

Hugh Haskell
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<mailto:hhaskell@mindspring.com>

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