# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Interpolation of Meridional Part Table
From: Ark Shvetsky
Date: 2009 Mar 26, 16:23 -0700

```
e is different.� 0.08181919 and 0.082271854 (this one is from�
Bowditch-1968).� Mr. Earle formula requires to use WGS84 value of e, whatever
it is.

----- Original Message ----
From: "Christian "Eddie" Dost"
To: NavList@fer3.com
Sent: Thursday, March 26, 2009 8:08:45 AM
Subject: [NavList 7789] Re: Interpolation of Meridional Part Table

The difference is in the factor A used in both examples.

For WGS84 this is A = 6378137 / 1852 = 3443.9185
in the second example this is A = 3437.7468

The term inside the logarithm is the same for both examples.

/Eddie

George Huxtable wrote:
> 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(45�) = 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{at}hux.me.uk
> or at +44 1865 820222 (from UK, 01865 820222)
> or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
>
>
>
> >

--
___________________________________________________brainaid_____________
Eddie C. Dost� � � � � Rue de la Chapelle 51� � � phone +32 87 788817
� � � � � � � � � � � � B-4850 Moresnet� � � � � � fax� +32 87 788818
ecd{at}brainaid.de� � � � Belgium� � � � � � � � � � cell� +49 172 9312808

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