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    More formulae for mid-lat/Mercator sailing
    From: Aubrey O´Callaghan
    Date: 1998 Jun 19, 4:51 AM

    Recently Paul gave the formula below for calculating meridional parts.
    There is another formula in The Admiralty Manual of Navigation which gives
    an extra term for more accuracy (the formula is in fact a series), this
    formula also gives a different coefficient to Paul's for the sin L term any
    body have an explanation ?
    M= 7915.7045*Log {tan(45d + L/2)}-23.4285*sin L + 0.0133 sin 3L
    At 02:50 10-06-98 -0400, you wrote:
    >I've seen the distance formula, (lat diff) / (cos C), but that is a
    >plane sailing formula.  What I'd like to see is the formula for length
    >of a rhumb line.  Couldn't find one in Bowditch.
    >The meridional parts formula previously posted to the list is quite
    >        M=7915.7045*Log tan*(45d + L/2)-23.2689*sin L
    >I checked it at 10-degree multiples from latitude 10 to 70, and it
    >matched the tables in Bowditch within .2 or so.  However, the notation
    >is not correct where it says "Log tan*(45...".  There should be no
    >asterisk there.
    >To make clear the sequence of computation, suppose we want M for 30
    >degrees latitude, i.e., L = 30.  Begin by dividing 30 by 2, add 45 and
    >take the tangent of the resulting sum.  Display should read about
    >1.7 at this stage.  Then take the common logarithm (on calculators,
    >key marked "log") of the tangent.  (read about .24)  Multiply by 7915
    >etc. and from here the road should be clear.  For L = 30, M = 1876.74.
    Aubrey O'Callaghan
    Wandrin' Star of Dart
    Rival 38
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