On Friday 14 May 2004 22:13, Andy Ross wrote:
> Durk Talsma wrote:
> > I want to calculate the current position of the aircraft , sssuming
> > that it travels along a great circle route between these two points
> > and also assuming that the current time is somewhere between arrival
> > and departure.
> Probably the simplest approximation is to convert both locations to
> cartesian coordinates, interpolate a path between them, back-convert
> the interpolated to a lat/lon pair. The altitude will be wrong, of
> course, but you probably don't care. Remember to do the interpolation
> in angle-space: make a triangle with the origin and the two points and
> sweep a vector across the triangle by angle; don't just linearly
> interpolalte along the line.
> That approximation assumes a spherical earth (for non-spheres, the
> constant-angular-speed interpolation isn't quite right). If you
> really want to use a ellipsoid earth model, then the problem becomes
> hard to solve analytically. One way to handle this would be to chop
> up the interpolated path into a large number of smaller segments, back
> convert them to lat/lon/alt as above, *re-convert* to cartesian values
> to compute a distance table, and then linearly interpolate them
> between the points.
That's cool, the interpolation procedure you're suggesting is conceptually
very similar to the solution I had in mind, the only difference being that I
was going to try and do the whole solutions using polar coordinates. Using
cartesian coordinates probably simplifies the procedure quite a bit.
After sending my mail, I realized that doing these calculations in WGS84
coordinates is probably not even necessary: all I want to do is get a rough
approximation of the position of an aircraft, and the assumption that is
flies a perfect great circle nav route, instead of a real world flight plan
already introduces an estimation error that is probably far greater than the
one introduced by assuming a sperical model. I was playing a lot with WGS84
code yesterday, so that was what my state of mind was in, I guess.
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