A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Bill Lionheart
Date: 2020 May 22, 12:06 -0700
Well since the thread from Dave Walden's question on a fix from altitude and azimuth ran for a while I thought this maybe deserved a new thread, although I take it we now know ALL about isoazmuthal curves.
I came across this paper
Lušić, Zvonimir. "Astronomical position without observed altitude of the celestial body." The journal of navigation 71.2 (2018): 454-466. DOI
in which the idea of position fixing with just azimuth measurements is suggested, and he gives formulae for the isoazimuthal lines, and uses our favourite Napier's analogies.
So my question is "Is there a known formula for the intersection of two isoazimuthal curves in the navigation literature"? Of course we now know this is the intersection of two quartic curves in Cartesian coordinates, or in a sereographic projection the intersection of two cubic curves. But it may be simpler than the general case.
It relates of course Dave Walden's other post on Position from two azimuths but digressing a little bit in to algebra. Lušić approximates with straight lines and I am sure that is reasonable on a small scale just as we do with small circles and azimuth sights.
Best wishes Bill
(ps I wonder if Zvonimir Lušić is a member of NavList?)