NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Lindy Line
From: Bill Noyce
Date: 2002 Dec 5, 13:14 -0500
From: Bill Noyce
Date: 2002 Dec 5, 13:14 -0500
I think Aubrey and Rodney are correct. For another way to approach the problem, consider a gnomonic chart, where great-circle courses are straight lines, and lines of latitude are curves. The original problem postulates that the GC course hits one of the curves (twice), and suggests an alternative course using the original GC course wherever it is not too far north, and the line of latitude where the GC is too far north. George's intuition that this is not the shortest path sounds right to me. But his suggested alternative doesn't work. If the GC course from origin to destination would travel north of the line of latitude, then the GC from some point on the line of latitude to either the origin or the destination must still travel too far north (and perhaps both of them). This is true because the GC course is a straight line, and the line of latitude is a convex curve. On the gnomonic chart it's easy to draw the ideal course: draw a line from the origin that is tangent to the desired latitude, and repeat from the destination. Follow the latitude line between these two tangents. I'm sure you can work it out numerically too, using formulas for GC's with a given "vertex" or highest latitude. I don't remember those formulas offhand (but they would be handy to know). -- Bill