A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Gary LaPook
Date: 2016 Oct 27, 03:19 -0700
I said before:
"From: Gary LaPook
Date: 2016 Oct 1, 16:14 +0000
To answer one of your questions, the number of waypoints you need for your great circle course (actually an approximation of it) depends on the latitude and on the amount of extra distance you can accept. "
We can look at this in more detail since I fired up my Casio PB-1000 calculator again. On another thread I calculated that for a 1426 nm route in latitudes about 50 north that the GC would save you 18 nm over the rhumb line course. It takes only three waypoints on an approximation of the GC save 15.2 of those miles so that the GC approximated with only three waypoints is almost as good as one with an infinite number of waypoints.
Using the progarm that I wrote for my calculator i worked several examples. For a westerly course at the equator a 1000 nm RL course will also be 1000 nm on a GC course, no saving with a GC the same for a 2000 nm RL course.
At 30 degrees latitude a 1000 nm RL course is only 998 nm on the GC, a savings of 2 nm, 0.2%. For a 2000 nm RL the GC will be 1989, saving 11 nm, 0.5%,
At 40 degrees latitude a 1000 nm RL course is only 997 nm on the GC, a savings of only 3 nm, 0.3%. For a 2000 nm RL the GC will be 1978, saving 22 nm, 1.1%.
At 60 degrees latitude a 1000 nm RL course is only 987 nm on the GC, a savings of only 13 nm, 1.3%. For a 2000 nm RL the GC will be 1909, saving 91 nm, 4.5%.
So is it worth it to try to sail a great circle, "you pays your money and you takes your choice."