A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2017 Oct 3, 11:08 -0700
Tony Zao, you wrote:
"I am not sure (yet?) that a star pair optimal for St.Hilair intercept method (i.e. the one suggested by vol.I H.O.249) is also optimal for the direct position computation."
I don't think you're coming at this the right way. In your earlier post, you said something about not getting an accurate longitude when the stars were separated by 20° in GHA. But if these were textbook cases -- cases with precomputed observational data, then any proper method for getting a fix should yield reasonable results when applied properly. If you input perfect observations into your algorithms, then they should yield a perfect fix (within very minor calculational limits) even with differences in azimuth that would be well below recommended limits in practical navigation. You should only be worrying about optimal azimuth selection when you try out these methods with practical observations. And when you have plenty of time for the observations, you can easily select stars just by looking at the sky. If you're standing in your backyard, you can do this with the toe of your shoe in the dirt. When you see Capella, for example, in the northeast, scrape a line on the ground perpendicular to that direction. Then turn to Aldebaran... scrape a line on the ground perpendicular to its direction. The angle between the lines you have drawn in the dirt is the angle between the lines of position that you would plot. Is it enough of an angle? You can see it, right on the ground at your feet.
Also the circles of position "exist" no matter how you calculate points along them. They are not a property of a specific algorithm. And if there is an error in either observed altitude in a pair, then you can understand its impact on position accuracy by thinking in terms of the circles of position: if the circles (lines at a local scale) cross at a low angle then you get a large impact from a small error; if the circles cross near 90°, then you minimize the impact on the position from a small error in either altitude. These phenomena are not a result of, or an element of, the intercept method. Lines of position are a fundamental description of the geometry of celestial altitude observations, above and beyond any specific mathematical procedures and algorithms.