Great circle sailing is the method ships and submarines use to follow the shortest path between two points on Earth. Because Earth is nearly spherical, the shortest route lies along a great circle, which is a circle that cuts the planet into two equal halves. On a flat Mercator map, that route often looks like a curve, even though it is the straightest possible path on the globe.
This matters because shorter routes can save fuel, time, and mission resources across long ocean crossings.
A Mercator map preserves compass angles, so a constant compass course called a rhumb line appears straight on the map. A great-circle route usually requires changing heading along the journey, so it appears curved on the same map. Navigators often compare the two routes, then choose a practical path that balances distance, weather, currents, ice, restricted areas, and safety.
For example, a route from New York to London bends northward on a Mercator map because the shorter path crosses higher latitudes on the spherical Earth.
Key Facts
- A great circle is any circle on Earth whose plane passes through Earth’s center.
- The shortest surface path between two points on a sphere is an arc of a great circle.
- On a Mercator map, rhumb lines are straight but great-circle routes usually look curved.
- Central angle formula: cos c = sin φ1 sin φ2 + cos φ1 cos φ2 cos Δλ.
- Great-circle distance: d = R c, where R is Earth’s radius and c is in radians.
- Earth’s mean radius is about R = 6371 km, so 1 radian on Earth equals about 6371 km.
Vocabulary
- Great circle
- A circle on a sphere that has the same center as the sphere and divides it into two equal hemispheres.
- Great-circle route
- The shortest route along Earth’s surface between two locations, following part of a great circle.
- Rhumb line
- A path that crosses all meridians at the same angle, allowing a navigator to hold a constant compass heading.
- Mercator projection
- A flat map projection that preserves angles and compass bearings but greatly distorts size and distance near the poles.
- Central angle
- The angle at Earth’s center between two surface locations, used to calculate great-circle distance.
Common Mistakes to Avoid
- Assuming the straight line on a Mercator map is always shortest. This is wrong because the Mercator projection distorts distance, especially over long east-west ocean routes.
- Forgetting to convert degrees to radians before using d = R c. This is wrong because the distance formula requires the central angle c to be measured in radians.
- Thinking a curved path on a flat map means the ship is turning inefficiently. This is wrong because the curve is a map effect, and the route is closest to a straight path on the spherical Earth.
- Confusing a rhumb line with a great-circle route. This is wrong because a rhumb line keeps a constant compass bearing, while a great-circle route usually changes bearing to minimize distance.
Practice Questions
- 1 A ship follows a great-circle arc with central angle c = 0.82 radians. Using R = 6371 km, calculate the distance traveled.
- 2 Two possible ocean routes are 5580 km and 5840 km long. If a ship burns 0.12 metric tons of fuel per kilometer, how much fuel is saved by taking the shorter route?
- 3 On a Mercator map, the route from New York to London curves northward instead of appearing as a straight horizontal line. Explain why this curved map path can still be the shortest route on Earth.