From:scf@w0x0f.com (Steve Fenwick)Organization:Best Internet CommunicationsDate:13 Oct 95 01:30:22References:1 2

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In article <airliners.1995.1582@ohare.Chicago.COM>, kls@ohare.Chicago.COM (Karl Swartz) wrote: > >I wonder if anyone can provide me with the formulae to calculate great > >circle course and distance given the latitude and longitude of the > >departure point and destination. > > Distance itself is pretty easy. Given latitude and longitude in > radians, compute the angle (theta) between the initial and destination > longitudes and normalize it to the range -PI .. PI. The distance as > an angle is then > > acos( sin(lat1) * sin(lat2) + cos(lat1) * cos(lat2) * cos(theta) ) > > Multiply that by the radius of the earth (i.e., 6371.2 kilometers) to > get a reasonable approximation of the great circle distance. Another formula, slightly more accurate for short distances, but also more complicated, is: 2*asin( sqrt( (sin( (lat2-lat1)/2) )^2 + cos(lat2) * cos(lat1) * (sin( (lon2-lon1)/2) )^2 ) ) Course along a great circle varies constantly, of course, except along lines of longitude, but the departure direction from any point to any other is also relatively easy: atan( cos(lat2) * sin(lon2-lon1) / ( ( cos(lat1) * sin(lat2) ) - ( sin(lat1) * cos(lat2) * cos(lon2-lon1) ) ) ) Note that you need to use an arctan function equivalent to FORTRAN's ATAN2 for the atan in the second equation, or you need to handle the case of the numerator and/or denominator going to 0. One way to plot this is to use the forward and inverse course equations to plot a series of very short rhumb lines by calculating intermediate lat/lons based on the starting point of the rhumb line and an arbitrarily short distance (short relative to map scale.) Iterate until done. Again, this is all for Earth as a sphere. Caveat lector for flight planning based on these estimates (flattening is about 1/300.) (Taken from "Map Projections--A Working Manual", U.S.G.S., p.30.) Does the FMS in your DiamondJet fly great circles directly, or do you break it into a series of rhumb lines for it? Steve -- Steve Fenwick scf@w0x0f.com http://www.w0x0f.com