[OSRS-PROJ] problem with azimuth and distance

Gerald I. Evenden gevenden at capecod.net
Mon Jun 5 13:08:06 EDT 2000

Answer: very simple, you have a great circle route and except for
N-S lines and E-W lines on the equator, none of these will follow
a parallel or meridian.  Think of the inverse problem.  Take two
points on a parallel and not on the equator.  The line will bow away
from the parallel, reaching a maximum N-S deviation from the parallel
midway between the points.  The forward and back azimuth will
be less than 90 degrees (northern hemisphere) and opposite in sign.
As the two points become more widely separated---still on the
same parallel, the |azimuth| decreases and eventuall will become
zero when the two points are separated by 180 degrees in longitude.

Its why you fly over Greenland getting from LA to Europe.

You are dealing with a geodesic line or great circle route not a
rhumb line or loxodrome represented by straight lines on a Mercator

Jerry Evenden and the Low Riders, Katie and  Daisy May
gevenden at capecod.net  http://www.capecod.net/~gevenden
----- Original Message -----
From: Pedro Morón Macías <pmoron at sainsel.es>
To: <osrs-proj at remotesensing.org>
Sent: Monday, June 05, 2000 12:01 PM
Subject: [OSRS-PROJ] problem with azimuth and distance

> Here's a little problem I have with the PROJ4 library, and since I've
> found no answer in the documentation nor in several sources, I'm trying
> this list.
> I have to determine latitude and longitude of a point given and initial
> point latitude and longitude, and an azimuth and a distance from this
> point.
> I'm using the "geod" program to test the library and these are the
> results:
> csp1.pmm:~/csp98/swb/proj.4/src > geod +units=kmi +ellps=WGS84 <<EOF
> > 80dN 10dE 90d 100
> > EOF
> 79d51'53.25"N   19d27'54.76"E   -80d40'47.564"
> In the example I want to determine the point at 90degrees azimuth and
> 100 nautic miles away from 80degrees North, 10degrees East.
> The given azimuth equals to 90 degrees, then, why the resulting latitude
> doesn't equal to 80 degrees North, like the starting point does?
> Why the back azimuth doesn't equal to -90 degrees?
> I'm sure this problem is not a bug of the PROJ4 library, and I want to
> know where am I misusing the library...
> Thanks a lot.

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