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    Re: Meridional Distances
    From: Peter Fogg
    Date: 2002 Sep 18, 10:09 +1000

    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
    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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