A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2018 Jan 22, 11:35 -0800
Bob, you asked:
"if I draw a line on a gnomonic chart from Vancouver to London, can I measure half way along that line and say "That is indeed the half-way point in a journey that follows this course-line"?"
No. The easiest way to see this is to look at the distortion at the outer edges of the chart. Distant points on a great circle project to much more distant points on the gnomonic chart. Remember that the gnomonic projection can be understood very simply by thinking of a crystal globe with a lightbulb at the center. The lat/lon coordinate lines and continent lines are etched into the globe. We place that globe on a flat table with some point of tangency --for example, 30°N, 60°W. Now turn on the light. The coordinates and continent lines are all projected onto the flat table, and if we trace them, we have our gnomonic projection. Since every great circle on the globe is centered on the Earth's center, they naturally all project to straight lines on the globe. But you can see, I think, that points on those great circles farther from the point of tangency project to greater distances from the center of the chart in a non-linear fashion (which you can calculate as d=R·tanϑ where ϑ is the central angle). This guarantees that the center point on a great circle path on the globe will not project to the center of the straight line on the gnomonic chart, except in special cases.
Note also, as Andres said, "Nowadays practical use of gnomonic charts is nearly over..." And that's true. Except in antiquated exams, like the awful USCG exams, gnomonic charts are as rare as hens' teeth. Don't get me wrong: they're interesting to experiment with, and they're intriguing historical artifacts. But they are irrelevant to modern navigation. You want an analog method for getting great circles? Go buy a nice small globe and stretch a string across it! I bought a nice one in the gifts section at an office supply store a few years ago. It's about five inches in diameter, and I think it cost eight dollars. It's really very handy when Google Earth is too far away... :)