Mapping Toolbox

Small Circles

In addition to rhumb lines and great circles, one other geographic construction is significant in geography and the Mapping Toolbox: the small circle. The precise definition of a small circle is the intersection of a plane with the surface of the planet. In the Mapping Toolbox, this definition includes planes passing through the center of the planet, so the set of all small circles includes all great circles as limiting cases. This usage is not universal.

Small circles are most easily defined by distance. All points 45 nm (nautical miles) distant from (45°N,60°E) would be the description of one small circle. If degrees of arc length are used as a distance measurement, then a great circle is the set of all points 90° distant from a particular center point.

For true small circles, the distance must be defined in a great circle sense, the shortest distance between two points on the surface of a sphere. However, the Mapping Toolbox also allows the calculation of a pseudo small circle, for which distances are measured in a rhumb line sense (along lines of constant azimuth). These should not be confused with true small circles.

Reckoning Positions

Measuring Area