Straight Talk on Great Circles

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Pondering my next great circle route.

Why do airplane routes look funny on world maps?

The shortest distance between two points is a straight line, right? If you want to fly, boat, bike, or drive, following a straight line saves time and money. When you look at aircraft routes on flight tracking sites, does it look like airliners take the long way home? Why do they fly those curvy routes across the oceans and continents?

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Spherical Globes and Flat Maps

The earth, as we know, is a sphere (more accurately, a spheroid). Maps are flat. Imagine trying to cut and stretch a globe into a flat rectangle. Tough job! Cartographers need to distort the shapes of land masses in order to fit the entire planet on flat paper. The maps pilots use, like road maps, only display a small portion of the planet so the distortion is minimal. This distortion is what causes straight lines to look curved on maps.

AirlineGreatCircle

Typical route for Trans-Pacific flights. Shortest distance?

What’s a great circle route?

Using a globe and some string is easier.

The shortest route between any two points on the earth’s surface is called a great circle. Although air routes look curved on flat maps, airliners do try to fly straight lines between cities. Exact routes vary due to winds, flight rules, and political borders (we don’t fly over certain countries).  There are trig formulas for doing great circle calculations, but it’s more fun to find them with a globe (or other spheroid, like a basketball) and a piece of string.

Pick two cities on the globe, like Tokyo and Los Angeles. Stretch the string between the two cities and wiggle it around until you’ve found the shortest distance. That’s it! You’ve found the great circle route (and preferred airline or ship route) for those two cities. If you were to slice the earth along your great circle line, the earth would be cut into two equal halves. Try different cities around the planet. You might be surprised at the routes you discover. The above map shows a typical route between Tokyo and Los Angeles. If you try the string trick, you’ll see that the route displayed on the map is pretty close to where your string falls.

LAX - NRT

String stretched between LA & Tokyo:  Curved.

Tilt globe to look directly over route:  Straight!

Polar Routes – Over The Top of The World!

Cathay Pacific’s ultra long-haul New York to Hong Kong flight looks really strange on a flat map. It appears to head north, turn west for several thousand miles then south to Hong Kong.

AirlineGreatCircle-PACpolar

RollingGlobe

Great circle route: New York to Hong Kong. Beach balls are not approved for navigation.

Is this really the route the airplane flies? You bet! The area near the top of the map is extremely distorted. The straight course represents the short portion of the flight that transits the north pole. Yep, this flight flies over the Arctic Circle near Santa’s Workshop. The total flight distance is 7000 nautical miles (nm). The segment over the pole (that looks really long on the flat map) is only 1200nm, or less than 3 hours of this 15 ½ hour flight. When you look at the route on a sphere, it makes more sense. Try stretching a string on a globe between New York and Hong Kong. Sure enough, the shortest distance passes close to the North Pole.

CathayPacific747

Cathay Pacific Boeing 747  © Lasse Fuss

Polar trivia: Russia opened four cross-polar routes in 1998. Prior to this, polar flights were difficult to arrange due to poor communications in Siberia. Cathay Pacific flew the first cross-polar passenger flight in July of 1998 from New York to Hong Kong. This was also the first flight to land at Hong Kong’s new Chek Lap Kok Airport.

 

Great Circle Resources Need more knowledge?  Look no further…

Great Circle Mapper: This online resource does all the work for you. Enter two cities and Great Circle Mapper displays the great circle route on the most appropriate style of map. Plenty of customization options for Map Geeks.

Wolfram MathWorld Great Circle page: If you want to work the formulas, Wolfram MathWorld is the place for you! I’m a product of the public education system, so I’ll stick with my beach ball and string… and my Flight Management System.

Wikipedia Great Circle Navigation Page:  Nice overview of the great circle navigation and a few formulas to play with.

AeroSavvy is written by Ken Hoke. Since 1984, Ken has loitered the skies in many vehicles, most notably the classic Douglas DC-8. He currently frustrates air traffic controllers in the US, Asia, and Europe as a Boeing 767 captain for a package express airline.
Ken can be reached here or any of these fine social media outlets:   

15 thoughts on “Straight Talk on Great Circles

    1. Ken H. Post author

      Hello, Sandaru. Thanks for the comment!

      The countries we avoid often change, sometimes month to month, based on current security and safety concerns. The list also varies by airline. Currently, my company avoids Syria and Crimea overflights due to recent political unrest. All U.S. carriers must avoid Iraq overflights, but carriers based in other countries can still overfly it. Both Lufthansa and Emirates regularly fly routes over Iraq. Last year, we avoided North Korean airspace for about a month.

      The world is always changing. This is part of what makes international flying challenging and fun!

      Reply
  1. Jake Houston

    This is great…I’ll have to use the “tilting” method to explain the great circle routes to the students here at Vance AFB. Never thought of explaining it like that. Well written article.

    Reply
    1. Ken H. Post author

      Jake,
      Thanks for the nice comments! Glad I was able to give you another way to look at great circles. Thanks for reading!

      Reply
  2. georgesimard

    A follow-up question: When following a great circle route, is the magnetic bearing constantly changing in the cockpit or do they stay on one heading for a period of time?

    Reply
    1. Ken H. Post author

      Great question!
      When flying a great circle route, our track across the ground appears straight on our map display, but the magnetic course we fly is always changing. If we fly a great circle from New York to LA, we start out heading northwest and arrive in LA heading southwest. From our point-of-view in the cockpit, we have flown a perfectly straight line and we haven’t turned (other than to correct for changing winds). It’s pretty cool to watch.

      Thanks for reading!

      Reply
  3. BS

    Hello Ken,
    Nice explanation in a very interesting way. I have few questions.

    1. Has any pilot tried taking a route that maps a straight line instead of Great Circle path ? Has anyone tried flying from Asia to the U.S. on a straight line path ?

    2. In one of the comments you have mentioned: ” From our point-of-view in the cockpit, we have flown a perfectly straight line and we haven’t turned “. How is it possible that though you head North-West while starting NewYork, you end up heading South-East while landing at LA, though you do not turn ?

    Thank you

    Reply
    1. Ken H. Post author

      Hello,

      Question 1: “Has anyone tried flying from Aisa to the U.S. on a straight line path?”

      YES! Every day. Remember that a great circle path is the ONLY straight line between two points on the planet.

      Forget about paper maps. There are several different types (projections) and they all provide a distorted view of the earth. Take a look at the globe illustrations above. The “curved” line only looks curved when you looking at it from an angle. When you look at the route from directly above, the line is straight. When flying this line in an aircraft, the nose of the jet (assuming no wind) points straight down the line, pointing at the destination. The aircraft never turns. As you pointed out, the compass and our heading move significantly as we scoot across the globe, but the aircraft remains flying the straight line. The reason for heading changes is that we are using magnetic or true north as our heading reference point. If it were possible to move magnetic north to Hong Kong and use Hong Kong as our “North” reference, we would maintain the same heading all the way Hong Kong.

      You can prove this for yourself using a globe and a piece of string as I did in the article. Play with it a bit. Stretch the string in a straight line between New York and Hong Kong (or anywhere else). Looking directly above it, it should appear straight.

      Great questions! I hope I answered them in a way that makes sense.
      Thanks for reading!
      Ken

      Reply
  4. Stephen Kosciesza

    A comment, if I may, rather than a question. It’s sort of a corollary to all that you’ve said, and it looks at the picture sort of the other way round. I’ve looked at some of the questions asked; I’m not sure if this will confuse or clarify.

    If you start flying exactly north or south anywhere in the world, and you keep flying straight, you’ll continue to fly north or south (at least until you get to the North or South Pole).
    If you start ON THE EQUATOR, and fly exactly east or west, and you keep flying straight, you’ll continue to fly east or west.

    Begin flying in any other direction–or begin flying east or west, somewhere away from the Equator–and you will have to turn gradually if you want to keep the same geographical heading (I deliberately avoid calling it the same “direction”).

    So as a broad example, if you’re in the northern hemisphere and you set out flying east (or, for that matter, northeast or southeast), you have to keep bearing left in order to maintain east (or northeast or southeast).

    I think a good way to picture this, in your mind or on a globe (NOT a paper map!) is to consider a trip going always east at a high latitude–i.e., one of the circles very near the North Pole. It’s easy, then, to see that from the plane’s point of view, it’s flying in a circle going left.

    As another exercise, imagine that you are 50 feet from the North Pole. You face east, and start walking–always east. You’ll have to walk in a circle roughly 300 feet (more exactly, 314.15926… feet) around, constantly turning left. If you do not, you will walk east for ONE INSTANT, and then you’ll be going more and more south of east. Walk/swim the same way for long enough, and you will pass a point 50 feet from the South Pole–walking east for one instant before heading more more north.

    Reply
    1. Ken H. Post author

      Hi Stephen,

      Very nice explanation! It might help someone who is struggling with the concept of navigating on a sphere.

      Thanks for the comment!
      Ken

      Reply

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