Mapping Toolbox

Reckoning Positions

A common problem in geographic applications is the determination of a destination given a starting point, an initial azimuth, and a distance. In the Mapping Toolbox, this process is called reckoning. A new position may 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.

Measuring Azimuth and Elevation

Small Circles