Shortest distances

Have you ever wondered about the strange route followed by the plane when looking on the screens during the journey? This is especially the case for long flights like flying between Europe and the USA:

Amsterdam - Seattle (shortest distance)
Amsterdam – Seattle (shortest distance)

As you can see, for a flight from Amsterdam Schiphol to Seattle-Tacoma, the plane takes first a route full to the North and then curves southwards to the destination. Why not flying a straight line from origin to destination airport like depicted in the following map?

Amsterdam - Seattle (loxodrome)
Amsterdam – Seattle (loxodrome)

Well, the weird thing here comes simply from the map projection used in the previous examples. A map, which is flat, is the result of the projection from a 3D sphere to a 2D map. We are loosing one dimension in this process and hence, information. Technically speaking, the projection the most commonly used in the world, and which I used in my previous maps here, is the Mercator projection map. The shapes are well preserved but the areas and distances are NOT!

Take a look, for example, at the relative sizes of Greenland and Africa. They look similar:

Greenland/Africa comparison
Greenland/Africa comparison

Actually, they’re not of the same size:

  • Africa: 30 221 532 km²
  • Greenland: 2 166 086 km²

So Africa is 14 times bigger than Greenland!

As said, distances are also not preserved. The lines pictured on the following map seem to be the same size but are in reality 2000 km long near the Equator and 345 km near the Pole:

Distance Equator/Pole
Distance Equator/Pole

On Earth, the longitudes narrow as approaching the poles. On the Mercator map however, the “widths” of the longitudes stay the same, that causes the distances to stretch in some ways, and consequently to appear larger at the Poles.

Let’s take another presentation to better understand why the previous curved route is the shortest. Take Google Earth for instance, which has as 3D background:

Amsterdam - Seattle (Google Earth)
Amsterdam – Seattle (Google Earth)

Seen from space, the shortest route looks more obvious. Straight lines are the shortest route on, for example, a gnomonic map projection:

Amsterdam - Seattle (Gnomonic Projection)
Amsterdam – Seattle (Gnomonic Projection)

Actually, the shortest route on Earth is a part of a great circle. A Great Circle is the intersection of a sphere and a plane going through the center of the circle. The shortest route is also called geodesic or orthodrome (here it is A-B):

geodesic (source:
geodesic (source:

The Mercator map has this characteristic to preserve shapes and all the straight lines are in fact rhumb lines (also called loxodromes). A rhumb line is a line which bearing direction stays the same all along it. In other words, when flying from Amsterdam to Seattle by following a rhumb line, the pilot fixes a bearing direction and never changes it. The shortest route, in opposition, needs a permanent change in the bearing direction:

Amsterdam - Seattle (geodesic + loxodrome)
Amsterdam – Seattle (geodesic + loxodrome)

Here are the length for the shortest route and the rhumb line

  • Shortest route: 7865 km
  • Rhumb line: 9140 km
  • Difference: 1275 km

Here are other example to illustrate the concept of shortest route VS loxodromes

London – Seoul:

London - Seoul
London – Seoul
  • Shortest route: 8890 km
  • Rhumb line: 10161 km
  • Difference: 1271 km

Notice that a plane flying from London to Seoul MUST NOT enter the North Korean airspace. So the final part of the journey will present a workaround.

Sydney – Santiago

Sydney - Santiago
Sydney – Santiago
  • Shortest route: 11 363 km
  • Rhumb line: 12 802 km
  • Difference: 1439 km

London – Sydney (notice how the bearing direction is first to North before taking the South direction)

London - Sydney
London – Sydney
  • Shortest route: 16 921 km
  • Rhumb line: 17 708 km
  • Difference: 787 km

Notice that planes does not radically take the shortest route from origin to destination. Other parameters come also into account such as the global wind directions, like the jet stream, airspace usage restrictions (eg: North Korea), etc.

8 thoughts on “Shortest distances

  1. Daniel,
    I’ve had the same fascination with air routes since taking trips from Australia to Europe in the last couple of years. I have since used the FlightRadar24 App and find it equally fascinating. Most air routes follow fixed paths at present, but this will be changing when the new air traffic control systems are implemented using the latest technology where the aircraft will be able to decide their own routes. Your discussion on map projections is also spot on. I worked recently at a company where the maps were mostly produced without a projection. I of course used the appropriate projection for the purpose on my maps.

    1. Thank you very much for your useful comment Bill!

      I have not a lot knowledge in air routes honestly but your comment enlightens especially that point. I checked the FlightRadar website but unfortunately the acquisition of data is not for free so abandoned the idea to write an article on a specific topic.

      The little part on map projection was intended to show the distortion of distances and one has to know that there are three main kinds of map properties: conformal, equidistant and compromise projections. Depending on the purpose of the map, it is very important to know which property to preserve.

      Best Regards,


  2. Great work! This is the kind of information that are supposed to be shared across the net.

    Shame on the search engines for not positioning this post upper!
    Come on over and visit my website . Thank you =)

Leave a Reply

Your email address will not be published.

Proove you're not a robot * Time limit is exhausted. Please reload CAPTCHA.