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    Re: Azimuth determination (ad nauseum)
    From: Geoffrey Kolbe
    Date: 2007 Oct 07, 08:00 +0100
    Peter Fogg wrote (Navlist 3361)

    A statistical study has been carried out to analyse and quantify this potential problem. The results have never been challenged.  When 121,677,000 random combinations of possible values were tested, an azimuth correct to within 2 degrees was generated in 98.8% of the cases. "Very large errors i.e. greater than ten degrees occur in only 0.005% of the sample. An error in excess of ten degrees up to a maximum of less than 18 degrees is extremely rare.

    This is the second time Peter has brought this statistical survey to our attention.

    I would like to point out that there are times when one might CHOOSE to take sightings of celestial objects on the prime vertical. For example, when finding my position in the Sahara desert, I was plagued by problems of unknown index error with my bubble sextant. The solution I eventually arrived at was to take pairs of sightings of objects to the North and South, and also to the East and West. In this way, any systematic index error was cancelled out. It turns out that this is pretty standard methodology when finding one's position on land, where the index error in a bubble sextant or the level error in a theodolite is ill defined.

    In the case where one chooses to take sightings on objects which are close to the Prime Vertical, the implied assumption of Bennett's statistical sample - that the azimuths of celestial objects which are sighted are random - is no longer valid. The statistical weighting is no longer equal for objects of any azimuth, but becomes heavily weighted for azimuths close to 90 degrees and 270 degrees. In those circumstances, the "very large errors" might well start to become significant.

    I would agree with George that it might be appropriate for Bennett to warn users of his azimuth tables of the possibility of large errors for objects near the Prime Vertical. He does, after all, go to some lengths to explain how users can determine if celestial objects near the Prime vertical are in the Northern or Southern azimuth hemisphere - a tacit acceptance that the probability of users taking sightings of objects near the Prime Vertical is high enough to make it worth the column inches.

    I would also like to point out, Peter, that your acidic comments and continued personal attacks on George do nothing to further the discussion. The fact that George has or has not published books or tables on navigation does not affect the validity of his comments one iota. I, for one, would be grateful if you would keep your comments on an objective level and leave out the personal invective.

    Geoffrey Kolbe
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