Reckoning

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 with the 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.

Related Topics

• Rhumb Lines
• Great Circles