NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Sun sights by 13 year-olds
From: Charles Seitz
Date: 2004 Sep 27, 10:28 -0400
From: Charles Seitz
Date: 2004 Sep 27, 10:28 -0400
I was 13 years old 48 years ago but have always been intrigued with the mysteries of celestial navigation. So I finally got on the web and searched for some pertinent links (including this list). Surprise, it's very simple in concept. A fix is obtained from the intersection of the circles of equal altitude obtained from sextant sightings to several heavenly bodies. Well it seems no one really does it that way because of plotting scale problems. The solution requires a sight reduction procedure that refines a dead reckoning position. OK, I can't argue against that time proven methodology. With a computer, what's wrong with a direct calculation in the event that you don't have the 'foggiest' idea of where you are? Getting back to the intersection of circles of equal altitude, I had to convince myself of the validity of this concept with real world data. How accurate can a 'low tech' approach be? Looking at the Dec and GHA table values to 0.1 minute precision (about 600 Ft) suggests nautical mile accuracy is possible if the sight timing and measuring process is under control. That's not too bad. I found some useful equations for spherical earth calculations (Aviation Formulary by Ed Williams) and wrote a software program that calculates the locus of Lat-Lon points at 0.01 degree increments around the Geographical Position of a body. I borrowed a plastic Davis sextant and took it on vacation to Myrtle Beach, SC. On a clear morning, I trekked to the beach, checked sextant alignment per its instructions, measured a reference position with time by GPS and finally, took several sun sights timing them with an alarm chime from my watch. To my amazement, a point on a resulting equal altitude circle passes within 0.8 nm of the GPS position! Close enough? Obviously, the next step would be to rewrite the software to accept data from additional sightings and calculate the circle intersections. That's easier said than done. Many hours of web searching have failed to reveal any equations to do this. I can't believe that during several thousand years of spherical geometry study, someone has not solved this problem. It might be a horrendous problem but the solution is out there somewhere. GPS is based on a similar concept. I'm not a mathematician and will not attempt to derive the equations. I'll look into solving this problem numerically. But, that is a brute force approach that is not particularly satisfying from an aesthetic viewpoint. --- CHAS