NavList:

Gary J. LaPook writes:
"Anyway, I  think this shows that there are many texts that state the position is found within the triangle so I think I have proved my point. "

 

Congratulations Gary, on building an argument you find entirely convincing. While this research was going on the argument has taken another track.

 

Remember that the basis for the contention that there is only a one in four chance of the position lying within an enclosing shape of LOPs is a narrow statistical one, and relies on error being entirely random. Specifically, the argument relies on NO systematic error.

 

But how can this assumption be safely made? What supports it? That error is involved is clear, or all LOPs would meet at a single point. How can one decide in advance that this error is only random and in no way systematic, whether involving time or altitude?

 

Presumably a round of sights could contain both systematic and random error, with the proportion of each unknown.

 

Systematic error can be resolved, as I have attempted to recently show and explain, leading to an improved fix free of systematic error. This improved fix will lie at the centre of the shape in the case of azimuths that span more than 180 degrees of azimuth, and outside a triangle with a spread of azimuths of less than 180 degrees, again at a determinable point.

 

The practical approach of surveyors, who used astronomical position finding methods we find familiar, was to eliminate random error as much as possible at source. One practical means of doing this is the analysis of successive sights as compared with the slope of the body's apparent rise or fall, an independent fact. Having done what they could to eliminate random error, a practical approach was to consider remaining error as systematic. As they preferred to use observations from the whole sky (ie; >180d) this led to a fix at the centre of the shape.

 

Was this a reliable method? Well, they aimed to establish a fix to within one arc second (about 30 metres) of the position, so it doesn't seem too shabby.

 

And so we come full circle, back to your contention that texts emphasise that a fix is located at the centre of enclosing LOPs. To the extent that this is so, perhaps they got it right. To the extent that error is systematic and a spread of azimuths of more than 180 degrees is involved, in your own words: "the position is found within the triangle". More than that, the fix free of this error is found at the centre of the triangle. Right where you say that you were taught that it lies.

 

However, it would be interesting to see whether the computer models that only tested for random error could be adapted or redesigned to consider the effects of differing proportions of random AND systematic error.