Great circle formulae, True cource and actual heading

Sims wrote:

flight headings.
If i use 2 lat/lon i can get a "true course"
but due to magnetic variations ...
actual heading varies a lot depending on my position along the
course. ...formula to calculate my actual heading at a certain
point along the course?

As Steve has noted there are two things happening:
(1) The bearing to point B along a great circle/ellipsoid path
from Point A to B varies along the path. (A computer/autopilot
can be set to follow the ever varying bearing.)

(2) The Earth's magnetic variation (a.k.a. declination) that affects
a magnetic compass heading varies with latitude and longitude
and also with time. This magnetic field offsets the
true great circle bearing at a given point along the path.

If one follows a rhumb line course instead of a great circle path,
the rhumb line bearing is constant. This is easier for a human
to follow at the expense of having a longer path.
One can find this on a Mercator projection map.
Again the magnetic variation offsets the rhumb line bearing
at a given point.

As Dave notes, Ed Williams' site discusses these issues.

http://williams.best.vwh.net/avform.htm


The World Magnetic Model (WMM) maintained by the U.S. DoD
and others

http://www.ngdc.noaa.gov/seg/WMM/DoDWMM.shtml

predicts the components of the Earth's steady state magnetic field
for a given latitude and longitude for a given date.
The horizontal component direction corresponds to the magnetic
variation. The target accuracy is one degree over a 5-year period.

My freeware DOS command line program GCGC* calculates the great circle
bearings between two points (WGS-84 default) and then uses
the WMM to also calculate the magnetic bearings at the end points.
If one needs the true and magnetic bearings along the flight path
(certainly a reasonable thing to need in flying), one would recalculate
the great circle path to point B from the position at the moment.
One can use the included Direct function (Lat1/Long1, Bearing 1-2,
and distance 1-2 to get Lat2/Long2) to calculate positions
along the great circle path by splitting it into pieces.

I also have a program (gcb12) that does rhumb lines at my web site,
but I haven't gotten around to adding the magnetic bearings.

Cheers, 73,

Ron McConnell
w2iol

N 40º 46' 57.9" W 74º 41' 21.9"
Magnetic Variation = 13.0º W in October 2003
FN20ps77GU46 [FN20ps77GV75]

* GCGC executable and source at

http://home.earthlink.net/~rcmcc