NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Meridional Distances
From: Peter Fogg
Date: 2002 Sep 18, 10:09 +1000
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 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