NavList:

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.