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    Re: Sights with just azimuth
    From: David Pike
    Date: 2020 May 23, 01:45 -0700

    Hello Bill Lionheart. I hope you're feeling better.  You wrote:  "Is there a known formula for the intersection of two isoazimuthal curves in the navigation literature"? 

    I believe you would have to look long and hard to find one.  If you do, it will be from an academic or within the classified archives of a government agency or avionics company who’ve worked on plans concerning constantly operating self-monitoring integrated navigation systems involving an astro-tracker.  You probably wouldn’t need to read very far before the name Kalman croped up.  The system would probably have been more for use above the tropopause than on the surface. Therefore, I don’t see such a system being within the realm of all but a tiny band of working human navigators.  The reasons are as much practical as mathematical.   Zvonimir Lušić talks about 0.1 degree, or 6 minutes of arc, azimuth measuring accuracy being possible in a well-found ship.  3 minutes of arc might be a cautious estimate of the working errors in Ho for a vertical sextant angle.  However, whereas 3 minute’s error in a vertical sextant angle will always produce a 3nm error on the ground irrespective of how far away the star’s sub stellar-point is, a 6 minute error in measured azimuth will produce an increasing error on the ground depending upon how far the observer is from the sub stellar point.  This can be seen in Weems diagram of lines of constant bearing for the North Atlantic posted by Dave Walden http://fer3.com/arc/m2.aspx/Position-from-altitude-azimuth-Walden-may-2020-g47878 .  For high altitude stars the error might be less than using a sextant, but for low altitude stars it will be greater.

    Then you would have to be able to identify two suitable stars and take azimuths simultaneously, or add a correction for MOO and MOB, and this correction would have to be in azimuth not altitude.  Next, the true azimuth taken would depend upon the accuracy of the ship or vehicles compass system, and any value of magnetic variation applied.  Magnetic monitoring would depend upon the accuracy of the last compass swing, updated en-route by celestial heading checks on current course, remembering that hard iron magnetism can change with time and soft iron with latitude.  Any gyro input would be subject to hang-off error, and any inertial system heading would be subject to drift.  Therefore, integrating a solution to all these problems would probably be far more complicated than putting up with the vertical sextant relatively complicated procedure of altitude measurement and taking into account related corrections” mentioned by Lušić in his 2018 JoN paper.  DaveP 

       
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