The Great circle
Perhaps you've noticed this before. You're on a plan and, either through boredom or curiosity, you keep track of your flight path. Or, you track a flight online. In either case, you might notice that the path being taken, when viewed on a map, does not follow a straight line. Is this a conspiracy? Are the airlines, like cliche crooked taxi cab drivers, going an extra distance to rack up the expense?
Actually no, they are following an old navigational route called the great circle. And yes, it is a shorter route.
How can this be?
Getting from here to there
OK, class.
Suppose you want to go from point A to point B, going the shortest distance, what path would you take?
Simple, a straight line.
Congratulations, you are correct – sort of.
Your answer is correct as long you are working on a flat surface; a chalkboard, a piece of paper or a computer screen. But move to a curved surface such as a beach ball or, better still, the Earth
things are different.
It's the great circle, Charlie Brown
So, what is the most direct route along the curved surface of the Earth?
Imagine taking the Earth and, utilizing a really big knife, slice it into two halves.
Diagram by Jhbdel*
The red circle above is called the “Great Circle.” To travel the shortest distance between any to points while staying on the circle (not digging a tunnel) requires one to travel along this circle.
So how would the path along the great circle look on a map? Going along this path one would, of course, go around the world, but also notice in the above diagram that one could spend half of the trip moving north, and the other half south.
To see it plainer, consider the path taken by a satellite in its orbit. It is the nature of orbits that they must follow the great circle. So consider the map below showing the path of the International Space Station.
Due to the rotation of the Earth, the path of satellites generally does not return directly to its original location. Still, one sees the general path made by the Great Circle on a map.
OK, you may say, but I'm not planning to go into orbit anytime soon, just on a holiday. Ah, but here is the punchline. You may not need the full circle, just the segment that takes you where you want to go. Suppose you are going from New York to Paris, the appropriate segment would look something like the below.
It is a strange conclusion, since we tend to be used to viewing the Earth as depicted on a map. But remember, maps take the round Earth we live on and place it on a flat picture. Distortions are inevitable. For times like these, it's good to think 3-dimensionally and view the Earth with its actual shape.
Fun for the family
Explore the great circle as it applies to navigation with a simple experiment. All you need are the following:
A globe.
A strip of paper, cut straight.
A “normal” map.
Choose two places on the globe, the further away and greater east/west change in position the better. Place the paper on the globe and touching the two points. This is the shortest distance.
Go along the paper from one point to another and notice different locations (cities, land features, longitude, and latitude, etc.) and find them on the regular map. Notice the curve.
On the web
This site appears to be geared to determining flight paths, but it is a fun way to generate flight paths between different destinations – maybe dream that perfect getaway.
Enter the airports to fly between (This site requires the standard airport abbreviations, there is a site with a searchable list of airports here.) separated by a dash in the paths field; you can select more than two stops. Click display map to see the path. It has several other features:
The distance is calculated and displayed.
If you select a ground speed, a time of flight will be shown.
Normally the map is displayed with the Earth shown in its round shape. However, under map style select topo for a more standard map that allows for the curved path to be more obvious.
Great books
Around the World in Eighty Days
Jules Verne classic. Phileas Fogg makes a boast that with modern technology (1872) it is possible for somebody to go around the world in 80 days. And so the adventure began. The story is told from the vantage point of his valet Jean Passepartout.
*License for Jhbdel drawing under creative commons license 3.0.
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