NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Meridional Distances
From: Dan Allen
Date: 2002 Sep 17, 16:51 -0700
From: Dan Allen
Date: 2002 Sep 17, 16:51 -0700
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
