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Subject: Re: Meridional Distances
From: Sam Chan (schan@XXX.XXX)
Date: Wed Sep 18 2002 - 00:51:24 EDT
The formula in Bowditch uses a series expansion. A closed form derived in
Williams is
M(psi) = a * Ln (Tan(pi/4 +abs(psi)/2)) - (a
e)/2*Ln{(1+e*sin(abs(psi)))/(1-e*sin(abs(psi)))}
where
psi is the Geodetic Latitude
a is the length of the semi-major axis
e is eccentricity.
For those who really want to know, the equation for the Meridional Distance
(Distance along the arc of a meridian on the surface of an ellipsoid) as
given by Williams is:
L(psi) = integral from 0 to psi of (a[1-e^2])/sqrt([1-e^2 sin^2(psi)]^3)
d(psi)
No closed form solution to this integral can be had so a numerical solution
must be used.
Sam Chan
----- Original Message -----
From: "Chuck Taylor" <ctaylor@XXX.XXX>
To: <NAVIGATION-L@XXX.XXX>
Sent: Tuesday, September 17, 2002 9:20 AM
Subject: Re: Meridional Distances
> >
> > Although I have tables accurate to 2 decimal places for the Meridional
> > Parts, the Meridional Distances come only in whole degrees, so need to
> > be interpelated for in-between values.
>
> Peter,
>
> Bowditch has tables of Meridional Parts to quite a number of decimal
places.
> The method for computing distances using Meridional Parts is called
"Mercator
> Sailing" and is also described in Bowditch.
>
> The introduction to the tables in Bowditch gives a formula for computing
> Meridional Parts. I have programmed this into a calculator. One could
also
> program it into a spreadsheet. If memory serves me correctly (I'm away
from my
> home library) there is a typo in the formula in Bowditch 95, but Bowditch
80/84
> Volume 2 has it right.
>
> Best regards,
>
> Chuck Taylor
> Everett, WA, USA
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