Why Are Great Circles the Shortest Flight Path?

Great Circles (Geodesic) vs Small Circles

great circle sphere

Last Updated: Feb 1, 2017

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 3-dimensional 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.
  • In other words, 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

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.

3 Comments

  1. Every airline in the world has a business route. This route determines where the aircraft can and cannot fly. For example certain routes over the Atlantic are more costly to make but much faster, the final determination is down to the pilot, in regards to how much fuel he has on board, how delayed the aircraft is, in respect to flying faster than he normally would. This is a very significant thing when determining which transatlantic route to take, because there are at least a dozen of which only 3 of those routes are the fastest and most economical, the rest vary with flight cost.
    In respect to flying over Greenland, there was a very valid reason to do so especially during the winter and early spring months. As the air gets colder, it gets thinner, and the air thins it gets more and more difficult for an aircraft to stay in the sky. This meant under aviation rules, those aircraft with only 2 Jet Engines had to make the shortest distance between land masses, incase an engine stopped working. This way the pilot could make an emergency landing. Aircraft such as the 747 had no such problems, and could easily fly the quickest transatlantic routes. However over the decades Jet Engines have become increasingly reliable, so much so, that they too can now fly over the Arctic to whatever destination.
    There are very few airlines who actually use Arctic routes, because these routes are extremely expensive to use.
    An example of a flight from Helsinki (EHFK; HEL) to Barcelona (LEBL, BCN) does not use a Great Circle nor a Small circle, it uses a direct path from point A to B.

    Small circles are not always used for short distances, infact they are seldom used in Europe. Instead most short distances are literally from A->B.

  2. Let me correct you. As the air gets colder, it gets denser, not thinner. However, as you increase in altitude, the air gets thinner and colder. Pilots will always want to fly higher as the low density of the air reduces drag and thus increases the efficiency of the fuel.

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