A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Position-Finding
From: Michael Bradley
Date: 2017 Mar 17, 03:56 -0700
By happenstance I've recently been running an intermittent study of Hav/Doniol using Hanno's 4 figure haversine table.
The comparison is against the same data used with the StarPilot app, which has a long standing reputation for reliability.
The criterion of acceptability I've chosen is to perform the reduction within 1' of the StarPilot result for the same data.
I don't throw any information away early in the process, so use Lat, Long and ephemeral data with a 0.1' precision, then round the data for t, Lat, Dec to the nearest minute. I interpolate the haversine on the downside for angles up to 90 degrees, on the upside above 90 degrees.
It all works fine in 4 figures until the navigational triangle gets smaller - Lat and Dec near the nearest pole, or meridian angle small so the the triangle is obtuse. I had to use 5 figure haversines to meet my accuracy criterion for a twighlight sight of Pollux on the 15th, meridian angle 14 degrees, my Lat 55 degrees. That's the first time I've hit trouble. I guess any small fixed length numerical approach would struggle dealing with the same triangle.
One solution is to stop the boat and wait an hour for a Mer Pass ....