A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: David Pike
Date: 2016 Jan 17, 08:50 -0800
I’ve been unable to resist the temptation to scan the internet and my and my dad’s navigation books, at least a little bit, for a mathematical explanation of the course calculating ‘hyperbolae’ provided with the North Atlantic Great Circle Sailing Chart. I’ve not had any luck so far. Most books are happy say “Take the 10 degree meridian crossing latitudes off the gnomonic chart and transfer the points to a Mercator or Lambert’s Chart. Then measure the doglegs”. I’ll continue to search when time’s available. In the meantime, I came across a couple of gems. This link takes you to an earlier North Atlantic GC Chart, (which even has Charles Lindbergh’s writing on it) which is much more enlargeable than photographs of the current version of the chart https://www.wdl.org/en/item/6778/ .
I also found a neat explanation of why great circles must be straight lines on a gnomonic chart. It runs as follows:
1. A gnomonic projection is a projection of the Earths Surface from the Earth’s centre onto a plane touching the Earth at a point of tangency.
2. A great circle is a line generated where a plane passing though the Earth’s centre crosses the Earth’s surface.
3. When two planes intercept, a straight line is generated.
4. Therefore, great circles must appear on a gnomic chart as straight lines.
To tie in with the current mails on U-boat navigation and detection, with shore-based allied listening stations all around the Atlantic, might such a chart be the ideal chart for pin-pointing U-boat HF transmissions? It was, I believe, possible to generate a squashed/stretched compass rose for a fixed position on a gnomonic chart, but not for a ship, of course, which would be moving around. DaveP