The loxodrome and two projections of the sphere Resize


Meridians and parallels

In general, a path along a loxodrome is not the shortest path between two points, except when the loxodrome's arc is contained in the Equatorial line or a meridian, because the Equatorial line is a great circle and meridians are half great circles.

If a traveller followed a route always defined by a loxodrome different from a meridian and a parallel, then their journey would continue indefinitely in a spiral around the poles. Fortunately, for navigation purposes, only part of the curve is relevant.

The meridians (without the poles) are loxodromes of zero angle. The Equatorial line or the geographical parallels are loxodromes orthogonal to the meridians.

Any other loxodrome takes the shape of a spiral around the poles.

If one would follow the route determined by a loxodrome orthogonal to the meridians (a geographical parallel), it is possible to return to the starting point. However, in the case of a loxodrome that is not a geographical parallel, such behaviour does not occur.