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The formula given below is for a spherical earth model.

Sam Chan
----- Original Message -----
From: "Dan Allen" 
To: 
Sent: Tuesday, September 17, 2002 4:51 PM
Subject: Re: Meridional Distances


> 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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