# 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

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