Comparison of Rhumb Lines and Great Circles - MATLAB & Simulink (2024)

FAQs

Comparison of Rhumb Lines and Great Circles - MATLAB & Simulink? ›

Rhumb lines are useful for navigation because the bearing (azimuth) does not change along the route. While rhumb line paths are longer than great circle paths, the constant bearing makes rhumb line paths easier to navigate.

A great circle is the shortest path between two points along the surface of a sphere, a geodesic is the shortest path between two points on a curved surface, and a rhumb line is a curve that crosses each meridian at the same angle.

While the great circle route offers the shortest and most direct path between two points, taking advantage of the Earth's sphericity, the rhumb line adheres to a constant course, simplifying navigation but extending the total distance of the journey.

The rhumb-line track is very convenient, because the ship keeps to the same course through the whole trip. Its disadvantage is that the straight line on a Mercator map may not be the shortest path between its endpoints, when measured back on the earth's surface.

Although a great circle is the shortest path, it is difficult to navigate because the bearing continuously changes as you proceed. In contrast, a rhumb line is an arc crossing all meridians of longitude at the same angle, a path with constant bearing as measured relative to true or magnetic north.

Any diameter of any great circle coincides with a diameter of the sphere, and therefore every great circle is concentric with the sphere and shares the same radius. Any other circle of the sphere is called a small circle, and is the intersection of the sphere with a plane not passing through its center.

Meridians of longitude and parallels of latitude provide special cases of the rhumb line, where their angles of intersection are respectively 0° and 90°. On a north–south passage the rhumb line course coincides with a great circle, as it does on an east–west passage along the equator.

Great circle routes, which require constantly changing headings, are most useful beyond the equatorial regions and for distances greater than several hundred miles. Long-distance air traffic uses great circle routes routinely, saving time and fuel. Navigational radio signals also follow great circle paths.

The advantage of a great circle is obvious, the shorter distance. The disadvantages, depending on latitude, could be quite a few. Colder weather, stronger winds, higher seas and perhaps even icebergs.

(Remember: any circle that passes through two points opposite each other on a sphere is a great circle.) Why are great circles important in navigation? Because they show us the shortest routes between two points on a sphere.

Do ships follow great circle routes? ›

For many shipping routes, sailing along the shortest great circle route can yield the earliest time of arrival. This is often true during summer months, when seas are more tranquil, or when ships are sailing in the same direction as winds and seas.

Simply, when plotting a course over a distance of 500 miles or more it usually makes sense to travel a 'Great Circle' route between origin and destination as it will be a shorter distance over the surface of the planet than the straight route - also known as the Rhumb Line.

Radio bearings are great circle azimuths (the bearing is the angle between the meridian of the ship or station taking the bearing and the great circle, not the rhumb line).

If a line on a sphere has constant slope (constant azimuth), then the line follows a rhumb line path. If a line on a sphere represents the shortest path between two points, then the line follows a great circle path.

A great circle is the largest circle that divides a sphere into two halves. The equator is the only great circle of the Earth. It shows the shortest path between two points on the Earth. Thus, sailors and pilots use great circles to adjust their routes while travelling over long distances.

Since the earth is a sphere, the shortest path between two points is expressed by the great circle distance, corresponding to an arc linking two points on a sphere. The circumference inferred from these two points divides the earth into two equal parts, thus the great circle.

Great circle routes (GC) are often compared to rhumb line routes (RL) in navigation planning, so recall the basics that a RL is the direct straight line between the two points and it will have a constant true heading at every point on the route, whereas the GC route will always be shorter but it will curve toward the ...

A great circle always divides the Earth in half, thus the Equator is a great circle (but no other latitudes) and all lines of longitude are great circles. The shortest distance between any two points on the Earth lies along a great circle. Great circles intersect the center of the Earth and divide the Earth in half.

Very few cruising boats need to use Great Circles, but it's certainly an important consideration for commercial vessels across the North Atlantic and North Pacific. The advantage of a great circle is obvious, the shorter distance.

great circle route, the shortest course between two points on the surface of a sphere. It lies in a plane that intersects the sphere's centre and was known by mathematicians before the time of Columbus.