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    Re: Meridional Distances
    From: George Huxtable
    Date: 2006 Jun 28, 00:12 +0100

    Peter Fogg seems keen to get a response to his questions, so I am
    happy to humour him.
    
    He wrote-
    
    | 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.
    
    As I have explained, a meridian-parts table will not cope with courses
    of, or near, 90 or 270 deg. But it's just in that situation that plane
    sailing becomes precise. So, taking a simple spherical-Earth model, I
    would divide the distance by cos (11 deg 33.8'), convert to degrees,
    subtract from 153d 14.7', and end up with a long of E 106 d 26.7'.
    
    But we can do a bit better, knowing that because of the Earth's
    ellipsoidal shape, the length of a degree at the Equator is not 60
    miles, but approx 60.07 miles. And at a lat of S 11 d 33.8', that
    length won't have reduced much from its equatorial value. In which
    case, a closer result will be 106 d 30.0'. Peter's result, at 106 d
    31.2', is a reasonably good answer.
    
    | 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?
    
    Back on the equator, having gone right round-and a bit. For a
    spherical Earth, we would end up at 38' E, but more accurately, with
    an ellipsoidal model, I would put it at 12.8'E.
    
    All that's been needed is a bit of simple trig and some knowledge of
    the Earth's shape as a fine-correction. No call for any tables in
    those simple cases.
    
    However, if that "Meridional Parts and Distances" table handles such
    examples seamlessly, where the ordinary Meridian Parts table will not,
    I am interested in finding out more about it. So far, Peter has been
    coy about supplying any information. In response to my request-
    
    "I ask Peter to inform us about this "Table of meridional distances",
    that he regards as so essential. Where are we to find it, and what is
    done with it, under what circumstances?"
    
    he has responded, so far, in this guarded manner-
    
    "I'll have to think about this. Can supply the formulas, and scan the
    tables.
    I'm not the best person, unfortunately, to explain the mathematical
    (or
    other) theory behind its effectiveness. My understanding is that it is
    better because M. Parts only does part of the necessary job. Since it
    involves extra work and tables it would indeed be disappointing to
    find that
    it is less accurate than M. Parts alone."
    
    I didn't ask him to scan the tables, or explain them; just to tell us
    where to find them, and how to use them. Until he does so, we are left
    guessing (or I am, anyway). I have found no references to "meridional
    distance tables" on my bookshelf. Perhaps others can help, if Peter
    will not. But he can hardly complain about being misunderstood, if he
    doesn't give us some clue to what he is on about.
    
    George.
    
    contact George Huxtable at george@huxtable.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    
    

       
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