# NavList:

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

**Re: Interpolation of Meridional Part Table**

**From:**Eddie C. Dost

**Date:**2009 Mar 26, 16:08 +0100

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 --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To unsubscribe, email NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---