Great Circle and Rhumb Line

Wing Commander Rajagopal

Great Circle and Rhumb Lines

A Great Circle is the shortest distance between two points on the Earth’s surface. Its direction (bearing) changes continuously during the flight, making it the most fuel-efficient route for long-distance travel. A Rhumb Line (Loxodrome) is a path that crosses all meridians at the same angle, so the aircraft maintains a constant heading. It is longer than a Great Circle route but is easier to navigate, especially for shorter distances.

Vertex of a Great Circle

  • Great circle vertices are the northernmost and southernmost points of a great circle.
  • The Northern Vertex is the point on the great circle closest to the North Pole.
  • The Southern Vertex is the point on the great circle closest to the South Pole.

Properties of Great Circle Vertices

  • The northern and southern vertices are antipodal points.
  • Antipodal means diametrically opposite points.
  • The shortest distance between the vertices is 10,800 NM.
  • Flight along a great circle results in a continuous change in direction.
  • At either vertex, the great circle direction is due East or West.

Latitudes and Longitudes of a Great Circle

  • The numerical value of the latitudes of both vertices is the same but in opposite hemispheres.
  • The longitudes of the vertices lie on a meridian and its anti-meridian.
  • An anti-meridian is the meridian located 180° from a given meridian.

Equator Crossing of Great Circles

  • Great circles intersect the Equator at two points.
  • Each intersection occurs at a longitude 90° from the vertex.
  • The angle between the Equator and the great circle equals the latitude of the vertex.
  • This relationship allows calculation of the great circle track at the Equator crossing.

Equator Crossing on an Easterly Track

  • North-to-South Equator crossing = 90° + Vertex Latitude.
  • South-to-North Equator crossing = 90° − Vertex Latitude.

Equator Crossing on a Westerly Track

  • North-to-South Equator crossing = 270° − Vertex Latitude.
  • South-to-North Equator crossing = 270° + Vertex Latitude.

Properties of Rhumb Line

  • Rhumb lines are uniformly curved lines joining two points on the Earth’s surface.
  • Meridians converge toward the poles.
  • A rhumb line intersects every meridian at the same angle.
  • Rhumb lines maintain a constant track direction with respect to True North.
  • The track angle between True North and a rhumb line remains constant.
  • Only one rhumb line can be drawn between any two points.
  • Infinite rhumb lines can be drawn between diametrically opposite points.

Equator is a Special Line

  • The Equator is both a rhumb line and a great circle.
  • As a great circle, it represents the shortest distance.
  • As a rhumb line, it has a constant direction.
  • The Equator is a great circle with vertices at 0° latitude.
  • It has infinite vertices pointing due East or West.
  • All points on the Equator have a constant direction of 090° or 270°.

Meridians are Special Lines

  • Meridians are both rhumb lines and great circles.
  • As great circles, they represent the shortest distance.
  • As rhumb lines, they maintain a constant direction.
  • Meridians have vertices at 90° North and 90° South.
  • Meridians intersect all latitudes in northerly and southerly directions.
  • All points on a meridian have a constant direction of 000° or 180°.

Rhumb Line and Great Circle Directions

  • Rhumb lines maintain a constant track direction.
  • Great circles do not maintain a constant track direction.

Rhumb Line and Great Circle Distances

  • Great circle routes provide the shortest distance between two points.
  • Rhumb line distances are always greater than or equal to great circle distances.

Appearance of Rhumb Lines and Great Circles

Great Circle

  • Great circle tracks are convex toward the nearer pole.
  • Great circle tracks are concave toward the Equator.

Rhumb Line

  • Rhumb lines are convex toward the Equator.
  • Rhumb lines are concave toward the nearer pole.

Great Circle vs Rhumb Line

  • A rhumb line is a regularly curved line with constant direction.
  • A great circle track changes direction continuously.
  • Up to the midpoint, a great circle moves toward the nearer pole.
  • At the midpoint, its direction matches the rhumb line track.
  • After the midpoint, it gradually moves toward the Equator.

Value of Great Circle Track in the Northern Hemisphere

  • The numerical value of a great circle track depends on the hemisphere and direction of flight.
  • For easterly tracks, the track value increases while moving toward the North Pole (clockwise).
  • For westerly tracks, the track value decreases while moving toward the North Pole (anti-clockwise).

Value of Great Circle Track in the Southern Hemisphere

  • The numerical value of a great circle track depends on the hemisphere and direction of flight.
  • For easterly tracks, the track value decreases while moving toward the South Pole (anti-clockwise).
  • For westerly tracks, the track value increases while moving toward the South Pole (clockwise).