A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2018 Feb 7, 12:55 -0800
Those are great results! On your Moon-Sun lunars, that's very roughly a 1 s.d. of about a third of a minute of arc and on the Moon-Aldebaran lunars it's about a quarter of a minute of arc. And with small samples like this, those are basically indistinguishable. I usually claim that one should expect a quarter of a minute error if you're doing everything right and using a scope with 5x or better magnification (in the 1 s.d. sense, implying that about two-thirds of observations are within a quarter of a minute of arc). Your Moon-Sun lunars really are not significantly worse given the small sample size. It's really impressive that both sets average to very nearly zero error. They should, of course, mathematically: if you have a quarter of a minute random error in a set of four, then averaging sets should reduce the error by a factor of two (sqrt(N) generally) on "average". But this assumes no systematic error. So the fact that you are seeing the expected 0.1' error after averaging lets you know that you have a really good lock on your sextant's index error --an issue of absolute importance in lunars that's not emphasized enough.
You marked one of your observations as "could have rejected". An interesting thing about sextant observations, especially high-sensitivity observations like lunars, is that it may be possible to construct an objective rationale for rejecting outliers or for managing them since a "split-level" error pattern seems to be the norm. Any set of observations seems to have a tightly bunched set of errors and then some "wild" sights mixed in. One technique that was mentioned with respect to altitudes sometime in the past year was to use the "median" observation rather than the average. This is effective and fast --worth experimenting with. Another approach is to decide on a "kurtosis" level and reject observations based on the spread of the sights. And really that's why the median method works as well as it does.
Trying the median method: Take your Moon-Sun lunars... Clear them relative to some baseline (a DR position, e.g.), then order them by error relative to that baseline. You have errors of -0.4, -0.2, -0.1, 0.0, 0.2, 0.6. And sure enough the median is -0.05' corresponding to a GMT error of a mere six seconds of time, essentially perfect. This isn't circular reasoning since it would have worked to select the right value if you had used a DR position that was somewhat different from your actual location. The same trick with your Moon-Aldebaran lunars yields a median of +0.15' corresponding to a GMT difference of 18 seconds, also excellent.
For those of you who haven't visited Mystic recently, my two-day class "Lunars: Finding Longitude by Lunar Distances" is scheduled for April 21-22 this Spring. The class can travel, and I can teach it at any location with something resembling a classroom if we can get enough people signed up to pay my way. Please contact me if you have any ideas.