A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Sean C
Date: 2018 Jan 19, 01:17 -0800
"Can I plan ahead my waypoints for a great circle route WITHOUT using a gnomonic chart?"
Sure. Any method which can be used for sight reduction can be used for G.C. route planning. They're essentially the same problem - finding spherical distances (intercepts) and directions (azimuths). I use the law of cosines formulae and sometimes Pub. 229. For waypoints along the G.C. track, just substitute 90 minus the distance in degrees for declination and the initial course angle for LHA. So for instance, if you want your waypoints to be 300 NM apart, use 5 degree increments. The results are the latitude of the waypoint (Hc), and the difference in longitude between the departure point and the waypoint (Z). All that's left is to add or subtract the difference in longitude to/from the departure and you have your coordinates.
So, for the first waypoint, one might use 90 - 5 = 85° for the declination. For the second waypoint, 90 - 10 = 80°, and so on. The same initial course angle is used for all waypoints.
Using Pub. 229 makes very quick work of the problem. Because of the way the book is laid out, you only need to open to one page and the latitude and difference in longitude for each waypoint is listed in order going up each column - all the way from the point of departure to the destination.