Great Circle: Why are Geodesic Lines the Shortest Flight Path?

great circle sphere

Why do you fly over Greenland in an airplane flight?

Or why is it that when you see flight paths on a map they always take a curved route between 2 cities?

It’s because planes travel along the true shortest route in a 3-dimensional space.

This route is called a geodesic or great circle route. They are common in navigation, sailing and aviation.

But geodesics can be confusing when you’re looking at a 2-dimensional map as they follow quite the odd flight path. Let’s dig into this concept a bit deeper.

Great Circle Explained

In a flight path from New York to Madrid, if I asked you which line is shorter, you’d say the straight one, right?

great circle flight path

However, a straight line in a 2-dimensional map is not the same as a straight line on a spherical earth/globe. This is why flight paths take an arc route between an origin and a destination.

Now here’s how the same flight paths look like on a sphere. Remember that the straight line in the Mercator map above followed the 40° latitude line.

great circle new york madrid

This paints quite the different story, doesn’t it? It’s deceiving to the human eye.

The takeaway is this:

A route that looks longer on the map is because of the distortion created with map projections like the Mercator projection. In navigation, pilots often use great circles (geodesic) as the shortest distance flight.

Great Circles vs Small Circles

Now that you have a visual understanding of great circles. Here’s a definition of what a great circle is:

  • A great circle is a circle on the globe such that the plane passing through the sphere’s center is equal to the circumference of the Earth.
  • Alternatively, a great circle is where the radius is equal to that of the globe when taken at the center of globe representing the shortest distance between two points on the surface of the earth.

In basic terms, imagine you’re cutting into an orange. You can cut them at any angle – north-south, east-west, diagonally. As long as you cut two identical portions, then the circle where cut was made is a great circle.

For example, the equator is a great circle because it’s the maximum possible circle:

Equator

You could also cut it at the north and south pole. This longitudinal line also cuts two equal portions. Any meridian line is a great circle as well:

Longitude

From New York to Madrid, here’s how the plane create two equal segments.

A great circle generates two arcs with shorter one being the shortest path. Here is the shortest path and how the plane is angled to create the shortest path.

great circle new york madrid

How about when you follow along the 40° latitude line? Anywhere that it doesn’t cut two equal pieces is a small circle. While a rhumb line track is at a constant azimuth, a geodesic line changes direction all the time.

small circle

READ MORE: Rhumb Lines: Setting it Straight with Loxodromes

Final Takeaway – Great Circle

Planes travel along the true shortest route in 3-dimensional space.

This route is called a geodesic or great circle.

While map projections distort these routes confusing passengers, the great circle path is the shortest path between two far locations.

This is why pilots fly polar routes saving time and distance.

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