Great Circles


The longest flight that Cathay Pacific flies is between New York (JFK) and Hong Kong (Chek Lap Kok). To be nit picky, flying to JFK is longer in mileage and flying back to Hong Kong is longer in flight time. Why is this? The answer lies in the understanding of great circle routes and jet stream winds.

Winds generally flow from West to East, so a flight leaving New York and headed for Hong Kong would be facing a headwind, whereas a flight leaving Hong Kong and flying to New York would have the wind at its back, helping push it along. Therefore, the flights into strong headwinds want to fly a route that covers the least amount of mileage across the ground because flying into headwinds slow planes down and costs money in extra fuel costs. When flights have a good tailwind helping push them along, an extra few miles added to the distance is negated by the help of the wind.

The next factor, beyond winds, is how to actually fly a route that takes the least amount of ground miles to go from point A to B, in this case, JFK and HKG. A great circle is a plot along the surface of a sphere that represents the shortest distance between those two points. Point A and B lie on a circle that cuts the Earth into two exact halves and represents the largest circle that could be drawn from the shape of a sphere – the Earth. The Equator is a great circle, cutting the sphere into equal halves and is the largest circle that can be derived from the spherical shape of the Earth. All other lines of latitude (think of rungs on a ladder) are not great circles, because lines of latitude don’t cut the Earth in half as they move toward the poles. However, lines of longitude (think of the long way down) are great circles, because they each can cut the Earth in half and go through the center of the Earth.

Now to twist the brain a little farther, imagine our two points on the Earth as being HKG and JFK. Any two points on a sphere (and even though the Earth is not a sphere, that goes beyond the scope of our discussion — read about a Geoid for more info) can be put on a great circle that cuts the Earth in half, or cuts through the center of the Earth. It might look something like this:

Using this method, we arrive at the path that is the shortest distance between two points on a sphere. If NYC and HKG are two points on a circle that cuts the sphere in to two equal halves, then that circle runs up near the North pole. Here is another view of JFK-HKG, looking at the Earth from above the North Pole:

You can see clearly that the “circle” this path creates, cuts right through the center of the Earth.

The airplane won’t fly this exact route due to weather, airspace air traffic control restrictions. Also, the flight has to remain within a certain safe distance of a suitable landing airport, incase of trouble. But, on the whole, this is about where the plane will fly. Because this is the shortest route possible, it seems strange to be heading almost due north out of New York to head for Hong Kong!

We get so used to the Mercator projection, where the map of the world is formed to wrap around a cylinder (instead of one that would wrap around a sphere) so that straight lines on those maps represent lines of a constant course.

The trouble is that it the farther from the equator one looks, the more “distortion” there is. No — Antarctica is not the same size as Russia and Greenland is not the same size as Africa! It’s not really a distortion, but the size of a landmass has to change so the goal of the map (all straight lines represent a constant course) remains true. When a great circle route is drawn on a map with Mercator projection, we get those familiar curving paths that are seen in the backs of airline magazines. The curve is accurate for the map, but the airplane is not constantly turning, like the map line would suggest. We are so used to viewing of the world through Mercator projection, that when we think of taking a flight from JFK to HKG, we would be passing overhead the Colorado rockies, then the Golden gate bridge, then the sunny beaches of Hawaii and the Philippines, and then descend into HKG.

However, this couldn’t be farther from the truth, because that would be so much father, and take so much longer than flying a great circle route. The Mercator map is lying to you! Put a string over a globe and see how much farther flying the “mercator method” is versus flying the great circle route. The shortest way across the globe from NYC to HKG would be close to crossing the north pole and then next map projection will show that to be true.

Another map projection is the Gnomonic projection, where all straight lines on it represent great circle routes. That might help a pilot get a general idea of what countries he will cross when flying a great circle route, but for the most part, isn’t much help because of it’s extreme distortion from the actual size and view of the continents. As you can see, it also isn’t much help to school kids to learn their countries.  It is similar to the Google Earth view from overtop the North pole. 

Flights that travel Easterly, like our example from Hong Kong to New York, don’t always travel the great circle route. This is because of the high tailwinds that can be achieved by following closer to the route of the Jet Stream. Even though deviating from the great circle route adds track miles to the route, the winds pushing the flight along more than make up the difference of flying a farther distance. In this case, the route of flight would head well south of North Pole. The flight would head out over Japan, over the North Pacific, and then make landfall around Anchorage or Vancouver, and then over the northern U.S. or Southern Canada, and then into NYC. A lot more miles, yes, but much faster and less fuel is burned, thanks to winds of up to 200 miles per hour, pushing the flight along.

The great circle route, though a simple concept, is much harder to explain than it is to understand. The flying of these routes has opened up a whole new era in air travel. Because airliners have navigational computers that can calculate these routes, greater and greater distances can be flown, connecting more and more cities. The next time you are headed overseas to a tropical paradise, especially over the Pacific, look out your window and look down. If you see ice and snow covered plains, you’ll understand why and have it make sense to you. It’s all about traveling the shortest distance and forgetting about the world as a flat map on the wall.

Just as an aside note, the four longest scheduled flights in the world are:

1) Singapore – New York (Newark) 9,500 miles (Singapore Airlines)
2) Singapore – Los Angeles 8,700 miles (Singapore Airlines)
3) Bangkok – New York 8,600 miles (Thai Airways)
4) Hong Kong – New York 8,100 miles (Cathay Pacific)

The flight times and distances are staggering and hard to comprehend. Remember, these are non-stop flights. Over three hours flight time separate flight number one from flight number four, and only the ultra long range Airbus A340-500 and Boeing 777-200LR can make the Singapore – New York run. Singapore to New York is over 18 hours flight time, so if one of these above flights are in your future, may I recommend that you save up enough money for business class? If not, at least bring some binoculars to look for Santa on your way “over the top.”

TobyLaura.com

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