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Subject: Re: Meridional Distances
From: Chuck Taylor (ctaylor@XXX.XXX)
Date: Tue Sep 17 2002 - 22:32:11 EDT
Peter,
In an earlier response I mentioned an error in the formula for Meridional
Parts as given in Bowditch 1995. I am happy to report that it (a missing
exponent) has been corrected in the online version at
http://164.214.12.145/pubs/, and presumably in later printings.
At 10:09 AM 9/18/2002 +1000, Peter wrote:
>My new (again, new to me) formula for rhumb line goes
>
>Arctan course = DLON/DMP
>
>Distance = DMD/cosCourse
>
>where:
>DLON means the difference in longitude expressed in minutes of arc
>DMP means the difference in Meridional Parts
>DMD means the difference in Meridional Distances
The standard formulas for Mercator Sailing, using your notation, are
Course = arctan( DLON/DMP )
Distance = DLAT / cos( Course)
where DLAT means the difference in latitude in minutes of arc.
These formulas are given in paragraph 2417 of Bowditch 1995 and paragraph
1007 of Bowditch 1981 Volume 2.
>there is a separate, rather more complicated, formula for when the
>course lies close to east or west.
The use of a separate formula for when the course lies close to east or
west is characteristic of Mid-Latitude Sailing. Like Michael Wescott, I
suspect that what you are looking at is some sort of hybrid method. Would
you mind giving us a reference that describes the method? I have never
heard of a table of Meridional Distances, only Meridional Parts.
Chuck Taylor
Everett, WA, USA
C
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