NavList:

Interesting discussion indeed. Thanks Frank for the exercise.

I agree with all the numbers published so far (in particular from Lars Bergman, including Vincenty's formulae), with one exception being the RL course initially published by Martins Caminos at 53°18.6' unless it is actually published for WGS84, and not for a spherical Earth as is the case for the immediately preceeding GC course.

As also indicated elsewhere, in this specific exercise there are very small courses differences on a Sphere between GC, RL and Meridional Parts RL (Loxodromie Latitude moyenne as we have it in French) as they all differ by less than 0.1'. 

On the other hand, what is TRULY interesting here happens when you start considering WGS84 vs. a Spherical Earth. Again the respective GC and RL courses are almost identical in such WGS84 reference, but - so close from the Equator and for such small distances involved - they already do differ from their spherical counterparts by over 10' : 53°18.9' vs. 53°07.8'

I had never figured this out, because that is almost the first time I have been carefully comparing results on WGS84 against their spherical results counterparts for surface navigation, while I have always used WGS84 for Astronomical computations, and in particular for 3D parallax computation. Thanks again Frank.

If we are to address this drill more in depth, then we need to work on the Geoid. EGM 08 gives us our missing data : the geoid is very close from 26.5 meters under WGS84. We then should proceed with actual altitudes about 15 meters under WGS84 because this is where we are actually assumed to observe from as per our initial set up. And in addition to what Lars rightly suggests for such 10 meter high poles "diverging" effect - or better: "converging effect" since we are under WGS84 - for any meaningful accurate computations, i.e. geodesic surveying reliable results, this EGM08 correction should be taken in account.

One last word : Vincenty's formulae enable computing both minimum distance between 2 points on an Ellipsoid (here WGS84) as well as departure/arrival courses. Such geodesic curves are NOT plane curves, although in this specific example they differ by negligible amounts (less than 5 millimeters at midpoint) from the WGS84 intersection of the departure fix vertical plan containing the arrival fix and conversely (not the same WGS84 intersections though - except at both ends - and the geodesic curve falls in between). Likewise the geodesic initial/arrival courses differ from the geometric directions given by the vertical plans defined here-above by less than 0.001" in this specific example.

Kermit