A common problem in geographic applications is the determination of a destination given a starting point, an initial azimuth, and a distance. In the toolbox, this process is called reckoning. A new position can be reckoned in a great circle or a rhumb line sense (great circle or rhumb line track).
As an example, an airplane takes off from La Guardia Airport in New York (40.75°N, 73.9°W) and follows a northwestern rhumb line flight path at 200 knots (nautical miles per hour). Where would it be after 1 hour?
[rhlat,rhlong] = reckon('rh',40.75,-73.9,nm2deg(200),315) rhlat = 43.1054 rhlong = -77.0665
Notice that the distance, 200 nautical miles, must be converted to degrees of arc length
nm2deg conversion function to match the latitude and longitude
inputs. If the airplane had a flight computer that allowed it to follow an exact great circle
path, what would the aircraft's new location be?
[gclat,gclong] = reckon('gc',40.75,-73.9,nm2deg(200),315) gclat = 43.0615 gclong = -77.1238
Notice also that for short distances at these latitudes, the result hardly differs between great circle and rhumb line. The two destination points are less than 4 nautical miles apart. Incidentally, after 1 hour, the airplane would be just north of New York's Finger Lakes.