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    Re: Meridional Distances
    From: Lu Abel
    Date: 2006 Jun 28, 08:36 -0700

    Gentlemen:
    
    Would someone please refresh my memory on why we're having this debate?
    
    Any skilled navigator applies techniques appropriate to the situation at
    hand.
    
    A skilled and competent navigator would therefore know that a Meridional
    Parts calculation would likely blow up for courses nearly east-west.
    
    But at the same time he/she would recognize that because there is very
    little if any change in latitude, mid-lat course calculations would
    provide excellent answers.
    
    Somewhere in this thread (not necessarily Peter and George's
    sub-thread), there has also been nit-picking about accuracy due to the
    earth's shape, table accuracy, etc, etc.  While these may be of great
    interest to an astronomer or geodesist working to centimeter accuracy
    across long distances I can't see how one can raise them in the context
    of practical navigation where one's vessel is subject to windage,
    current, and steering errors (most experts say that a small craft
    helmsman is lucky to steer a course within +/- 3 degrees of desired).
    
    Lu Abel
    
    Peter Fogg wrote:
    > George also wrote:
    >
    >
    >>Calculating difference of longitude, using meridional parts, gets
    >>imprecise for rhumb-line courses very near to 90 or 270 degrees, due
    >>East or West, and becomes impossible if the course is exactly East or
    >>West. The problem is that with such courses, the difference of
    >>latitude (and so the difference of Meridional Parts) approaches zero,
    >>which is compensated for by the way (tan course) increases towards
    >>infinity for courses near due East and West. So the result is a
    >>decreasing precision, for courses near East and West, and an
    >>meaninglessness, multiplying zero by infinity, for due East and West.
    >
    >
    > Fascinating. Let's see how Meridional Parts and Distances handles this.
    >
    > Q3) We're off again, heading due west this time (TC 270d) over 2751nm from
    > S11d 33.8'  E153d 14.7'. Just where will we end up?
    >
    > A3) S11d 33.8'  E106d 31.2.
    >
    > Is there a problem with this, I wonder? Incidentally, taking a Great Circle
    > route would have saved a comparatively trivial 7nm or so at that low
    > latitude.
    >
    > Hey, I've thought of a neat way of checking the accuracy of the method:
    >
    > Q4) We start from a nice round set of numbers: N/S 0d  E/W 0d. We go east
    > for 21638.9nm. Where do we arrive?
    >
    > This time I won't supply my answer just yet. Will look forward to seeing
    > YOUR solution, ladies and gentlemen - with workings; methodology attached,
    > please.
    >
    > Frank, you're barred until you supply the answer to your earlier puzzle
    > posed about the latitude that gets the most sun.
    >
    >
    
    
    

       
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