Great Circle Routes vs Rhumb Lines in Aviation

061-03-01Pablo Asensio Martínez2026-04-012 min

Air navigation is based on understanding how the spherical shape of the Earth affects direction and distance between two points. Below, we explain the fundamental concepts for understanding flight paths.

Great Circle and Rhumb Line

To navigate from one point to another, there are two main ways to trace a line on the Earth:

  • Great Circle: This is the line that represents the shortest distance between two points on the Earth's surface. It is formed by a plane that cuts through the Earth passing exactly through its center. Examples of Great Circles are the Equator and all meridians. A key property is that, although it is the shortest path, its direction changes constantly as we cross meridians.
  • Rhumb Line: This is a line of constant direction. It crosses all meridians at the same angle. Navigating a rhumb line is simpler (you maintain the same heading on the compass), but the distance traveled is greater than that of a great circle.

Convergence

Meridians are not parallel lines; they meet (converge) at the Poles. Because of this, a straight line drawn on the Earth (a Great Circle) will have different directions throughout its course. This change in direction is called Convergence.

Convergence expresses how much the track of a Great Circle changes between two points due to converging meridians.

  • Formula: $\text{Convergence} = \text{Change in Longitude} \times \sin(\text{Mean Latitude})$

The value of convergence depends on latitude: it is zero at the Equator (where meridians are parallel) and maximum at the Poles.

Conversion Angle

The angular difference between the direction of a Great Circle and a Rhumb Line between two points is called the Conversion Angle.

  • The Conversion Angle equals: $\text{Conversion Angle} = \frac{1}{2} \times \text{Convergence}$
  • This allows us to calculate the Great Circle heading if we know the Rhumb Line heading (and vice versa).

The Vertex

Every Great Circle has a point where it reaches its highest latitude; this point is called the Vertex.

  • At the Vertex, the direction of the Great Circle is exactly 090° (East) or 270° (West).
  • Each Great Circle has two vertices (one in the northern hemisphere and one in the south), which are opposite and separated by 180° of longitude.

Heading Behavior (Practical Rules)

Due to convergence, the true track of a flight varies depending on the hemisphere and flight direction:

  • Northern Hemisphere:
    • Flying East, the true track increases.
    • Flying West, the true track decreases.
  • Southern Hemisphere:
    • The opposite occurs: Flying East decreases and flying West increases.

A useful rule to remember the difference between Great Circle (GC) and Rhumb Line (RL) heading in the Northern Hemisphere is that the Great Circle path always curves toward the Pole. Therefore, the Great Circle is always "above" (further north) of the Rhumb Line.