The Shortest Distance is…

The time-old adage is that “The shortest distance between two points is a straight line.” Most of what we see day-to-day would confirm that. On paper, you use a ruler, sometimes called a “straight edge,” to connect two dots. In a field, it’s easy to apply the same principle and cut straight across. But then why do the network maps for the airlines always have those funny looking arcs? What happened to those straight lines?

Well, it turns out there’s at least a couple of things at play. The first is that the earth is a globe, so things are a little different than that piece of paper you put the ruler across. This is called map projections, or how to turn something round (the earth) to something flat (a map). It is something that cartographers (map makers) have struggled with since navigators first started seriously exploring the globe. Depending on the purpose, maps are drawn using different projections. Some are set up to keep the longitude lines (the ones that run north - south) straight, others to preserve relative land mass area proportional, others to keep ocean shipping lines obvious. So, depending on how you draw the map, a “straight” line might not be drawn straight.

Another property of a sphere, is as you go towards the top (or bottom for the matter), the distance to go around the globe greatly decrease, until you get to the very top and you can just turn around on the spot. The Russians and the Americans were well aware of this during the Cold War. That’s why NORAD was set up - basically an early warning system for Russian bombers coming over the North Pole heading for American cities.

When you take to the skies, the concept of “airspeed”, which is not the same as “ground speed,” can become important. If you’ve been out on a really windy day, you can feel the difference of walking with or against the wind. A little further up, where airplanes fly, there’s a constant wind that’s determined by the jet stream. As the article in the Chicago Tribune points out, these winds can vary greatly between latitudes.

Add these things all up, and find, as the Chicago Tribune reports, that the fastest way to go from Chicago to Hong Kong is over Northern Canada, and the pole and then down across China (which takes about 15 hours), rather than across the Pacific (about 16 ½ hours flying time), as your straight edge might suggest, or even east across Russia (about 16 hours flying time). As well, as the flights get shorter, the planes need less fuel, which means that that weight can be used instead to haul passenger.

I remember running into this when I flew from Paris to Dallas - we flew over Labrador. Labrador, by the way, was just as they describe the Canadian Shield - lots of little lakes in the creases in the rocks and not much else.

So next time you hop a flight across the ocean, now you have a clue why all the flights “go north.” Happy flying!

Reference

• Chicago Tribune. United take polar express on flights to China, Japan. Published April 7, 2006. Available on-line at http://www.chicagotribune.com/business/chi-0604040271apr04,1,1640385.story?ctrack=1&cset=true Accessed May 2, 2006.
• For further reading on Map Projections, try Wikipedia.