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    Re: Fw: Advancing COPs Revisited
    From: Jeremy C
    Date: 2010 May 7, 20:29 EDT
    If I were navigating using traditional methods (ie no electronic fixes) in  the deep ocean with celestial, any LOP over 3 hours old would be used sparingly and with the full understanding that it is a fairly low confidence LOP and resulting running fix.  On a nice day, i would take hourly sunline fixes crossed with the moon if available to keep track but I probably wouldn't adjust course for any sunline running fixes.  Full confidence fixes would be reserved for twilight star fixes and only then would I change course.
    The reasons for this mentality is that I have no objective method to determine course and speed over ground over short spans of time.  The best I have is heading from a compass and speed through the water from a Log.  Given my observations between the data provided by my gyro compass and log, I have seen large variations between these inputs and fix data and can find myself several miles off of the track line in a 4-hour watch. (for example I've seen leeway as much as 10 degrees in mid ocean). I have also noted that charted areas of current are often inaccurate and only general set and drift corrections can be applied.  For Byron's sake,  I will mention that we calculate gyro error often so that is accounted for as well.
    Before we can get too particular in mathematical methodology to advance LOP's, we have to understand the limits in precision of the math often far exceed the accuracy of our base assumptions. GIGO is the name of the game here.
    In a message dated 5/5/2010 11:21:39 A.M. Bangladesh Standard Time, pmh099@yahoo.com writes:
    If I had to do a rigorous (assuming spherical Earth but otherwise exact) advancement of a celestial LOP, this is what comes to my mind:

    1) Calculate the original circular LOP, which is a 1-parameter set of points.

    2) At each LOP point construct a rhumb line using the appropriate course (track).  Each rhumb line is yet another 1-D parametric curve.  Distance along the curve from the point of origin (on our LOP) would be the most suitable choice of parameter for our purposes.

    3) Use the distance traveled to construct the advanced LOP using the rhumb lines of step 2).  Its one parameter (enumerating all its points) would be the same one used in step 1) for the original LOP.

    This is really a straightforward, brute-force approach without much finesse.  However, if one wants to be really very rigorous about running fixes, then it should be possible to encode this procedure into a computer and run it with whatever accuracy is desired.

    Running fixes are typically only extended over a few hours, during which the vessel covers a distance that is tiny compared Earth's circumference, and remains far away from either Pole.  In that case the standard running fix with (usually) straight LOP sections near an AP should be adequate.

    Just my $0.02.

    Peter Hakel

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