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Subject: Re: Meridional Distances
From: Peter Fogg (ffive@XXX.XXX)
Date: Tue Sep 17 2002 - 20:09:17 EDT
I'm glad Dan thinks the Williams formula is pretty straightforward.
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
there is a separate, rather more complicated, formula for when the
course lies close to east or west.
Dan Allen wrote:
> On Tuesday, September 17, 2002, at 03:53 PM, Peter Fogg wrote:
>
> > Have recently come across a new (to me) method of calculating rhumb
> > line
> > courses and distances, and also traverse calculations, where the
> > starting position, course and distance are known, and the finishing
> > position needs to be calculated.
>
> The formula is pretty straightforward for this.
>
> From http://williams.best.vwh.net/avform.htm is this:
>
> To find the lat/lon of a point on true course tc, distance d from
> (lat1,lon1) along a rhumbline:
>
> lat = lat1+d*cos(tc)
> dphi = log(tan(lat/2+pi/4)/tan(lat1/2+pi/4))
> IF (abs(lat-lat1) < sqrt(TOL)) {
> q=cos(lat1)
> } ELSE {
> q= (lat-lat1)/dphi
> }
> dlon=-d*sin(tc)/q
> lon=mod(lon1+dlon+pi,2*pi)-pi
>
> (the initial point cannot be a pole!)
> (logs are "natural" logarithms to the base e.)
> (TOL is a small number of order machine precision- say 1e-15.)
> (The tests avoid 0/0 indeterminacies on E-W courses.)
>
> Dan Allen
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