Rhumb Lines

We are now aware of great circles, which are circles drawn on the surface of earth with their centre and radius same as that of earth. Equator and Meridians are perfect examples of a great circle. Both would cut the earth into two equal halves. Their difference lies in the fact that equatorial plane is perpendicular to the axis of rotation of earth. Whereas, the plane of any meridian is parallel to the axis of rotation of earth.

If we draw circles on the earth with their planes parallel to the equator, they would obviously be smaller than the equator. Small circles are circles on surface of earth whose centre & radius are not the same as that of earth. To be more exact the radius of a small circle would be smaller than the circumference of earth. That is the reason they are named as small circles.

A circle with radius smaller than the circumference of earth would obviously cut the earth into two unequal halves. Therefore, The plane of the small circle cuts earth into two unequal halves

Properties of a rhumb line

Rhumb lines are regularly curved line between two points on the surface of earth. Rhumb line cuts all meridians at same angle. Due to this reason, Rhumb lines are constant direction lines. Since Rhumb lines maintain constant direction, there is no problem of change in headings while flying a rhumb line track. In other words, you can fly a constant heading along a rhumb line track.

To summarise in a few words, firstly rhumb lines are not the shortest distance between two places on earth. Only one rhumb line can be drawn between any two points on earth. The only exception to this rule is when the two points are diametrically opposite to each other. Infinite rhumb lines can be drawn in the case of two diametrically opposite points. Rhumb line is always near to the equator than a great circle. Rhumb lines are convex to equator or concave to nearer pole.

Special rhumb lines

There are a few special rhumb lines which possess the properties of both the great circle as well as rhumb lines. Equator and Meridians are Rhumb lines which are also Great circles. That means to say that when you fly along the equator of along a meridian, you would have the benefit of both constant direction as well as the shortest distance.

In contrast, small circles are only rhumb lines. That means to say that, they have constant direction but will not be the shortest distance between two points.

A rhumb line is a path that maintains a constant compass bearing or direction throughout the journey. This means that if you were to follow a rhumb line on a globe, you would be constantly steering along the same angle relative to the compass. This results in the path appearing as a spiral of small circles around the globe, intersecting each meridian at the same angle.

Comparison with Great Circles

A great circle is a circle formed by the intersection of a plane that passes through the centre of the sphere. It divides the sphere into two equal halves. Examples of great circles on earth are the equator or the lines of longitude known as meridians.

The shortest distance between two points on a sphere is always along a great circle. However, a great circle path does not maintain a constant compass bearing unless the two points are directly opposite each other. This means that to follow a great circle, you would need to make constant adjustments to your compass bearing.

While the rhumb line offers a relatively simple navigation method, it is important to note that it is not the shortest distance between two points on a curved surface. The reason for this is that the earth is a sphere (or more accurately an oblate spheroid), and the shortest path between two points on a sphere is known as a great circle.

In summary, while small circles (rhumb lines) are useful for maintaining a constant compass bearing, they are not the shortest distance between two points on a curved surface like the earth. The shortest distance is achieved by following a great circle path, which requires continuous adjustments to the compass bearing.