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    Re: Interpolation of Meridional Part Table
    From: Andrés Ruiz
    Date: 2009 Mar 26, 16:54 +0100

    Yes because Bowditch uses the sphere for a, and the WGS72 for f

     

    The different values for the Earth models gives:

    Ellipsoid

    a

     

    f

    BOWDITCH

    3437.746771

    nm

    0.003352779

    WGS84

    3443.918467

    nm

    0.003352811

    WGS72

    3443.917387

    nm

    0.003352779

    ESFERA

    3437.746771

    nm

    0

    NAD83

    3443.918467

    nm

    0.003352811

    EUROPE1950

    3444.053996

    nm

    0.003367003

     

    And the value for lat = 45º

     

    WGS84       MP( 45.000000 ) = 3019.058271

    WGS72       MP( 45.000000 ) = 3019.057477

    NAD83       MP( 45.000000 ) = 3019.058271

    EUROPE1950  MP( 45.000000 ) = 3019.108031

    E7784 WGS84 MP( 45.000000 ) = 3019.058271357112100000 [NavList 7784] equation

    E7784 BWD   MP( 45.000000 ) = 3013.648100569424100000 [NavList 7784] equation for BOWDITCH model

    BOWDITCH    MP( 45.000000 ) = 3013.648101

    ESFERA      MP( 45.000000 ) = 3029.939203

     

    -----Mensaje original-----
    De: NavList@fer3.com [mailto:NavList@fer3.com] En nombre de Ark Shvetsky
    Enviado el: jueves, 26 de marzo de 2009 16:35
    Para: NavList@fer3.com
    Asunto: [NavList 7791] Re: Interpolation of Meridional Part Table

     

     

     

    Quite interesting. I got 3015.6145.

     

    e=0.08181919

    a=3437.7468

     

    Bowditch 1968 gives a-3437.68,  e=0.082271854

     

     

     

     

     

     

    ----- Original Message ----

    From: George Huxtable <george@hux.me.uk>

    To: NavList@fer3.com

    Sent: Thursday, March 26, 2009 7:47:15 AM

    Subject: [NavList 7788] Re: Interpolation of Meridional Part Table

     

     

    The plot thickens-

     

    Andres calculates, from the expression he gives in [7784]

     

    WGS84

     

    a = 6378137 [m] = = 6378137/1852 [nm]

     

    f = 1.0/298.257223563

     

    The result is:

     

    MP( 45.000000 ) = 3019.058271357112100000

     

    The expression Andres quoted used eccentricity (epsilon) rather than the

    flattening f that he tells us is f = 1.0/298.257223563 for WGS84. However,

    we can deduce one from the other using the expression given in Meeus, in

    which

    eccentricity = square root of ((2 * f)  - (f * f)) for which I have taken

    the result to be 0.08181919, exactly in keeping with Earle's figure.

     

    ===========================

     

    On the other hand, I have tried to do exactly the same thing with my pocket

    calculator and with the following values, taken from Earle-

    E= 0.08181919

    A = 3437.7468, the Earth's equatorial radius in geodetic miles.

    Latitude L= 45

     

    and here's a transcription of the equation I've used, now corrected, which

    runs on a 20-year-old Casio programmable calculator-

    M=A*LN(TAN(45+.5*ABSL)*((1-E*SINABSL)/(1+E*SINABSL))^(E/2))

     

    and that gives me M(45º) = 3013.648, which conforms with Bowditch, and not

    (quite) with Andres..

     

    Why do Andres and I differ (slightly), and why do I agree with Bowditch,

    when Andres and I are trying to calculate the same thing with the same

    quantities, using what appears to be the same expression?

     

    You can see that I've rejoined the nit-picking purists, as my natural home.

     

    George.

     

    contact George Huxtable, at  george@hux.me.uk

    or at +44 1865 820222 (from UK, 01865 820222)

    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

     

     

     

     

     

         

     

     


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