How come when a plane flys halfway around the world, it goes way up into the arctic and back then in a arc?

Wouldnt it be faster and a shorter distance if it went in a straight line? When I was on a flight from New York to Beijing, the plane went way up into northern Canada through the northern tip of Alaska and through Russia and went back down south to Beijing. Why dont the planes just fly straight west in a shorter straight line instead of making a huge detour?How come when a plane flys halfway around the world, it goes way up into the arctic and back then in a arc?The straight line on a map sometimes represents a curve on the Earth's surface according to which map projection you're using, (eg Mercator projection).



A simple way to show the shortest distance between two points is to take a globe and stretch a piece of string between those points. You'll find it always arcs towards the nearest pole, thus proving this to be the shortest track. (Part of a "great circle").



On trans-Atlantic flights tin twin engined aircraft his curve is sometimes a little accentuated in order that the aircraft can stay within a certain flying time of a usable airfield, while flying on one engine should one fail. (eg airfields in Iceland and Greenland).



Hope this helps.How come when a plane flys halfway around the world, it goes way up into the arctic and back then in a arc?Ahh an interesting question. You would think that a straight line would be the best course of action. But the truth is a little bit deceptive I assure you. On a flat, 2D surface yes a straight line is the shortest path between two points. But on a spherical object the shortest distance is actually an arc and what appears to be a long and drawn out course actually is the shortest path between two cities. Once you go 3D a lot of geometry changes, for instance in planar trigonometry the angles in a triangle will add up to 180 degrees. But is spherical trigonometry it will add up to 270, essentially three right angles. It's all crazy when you go up to higher dimensions.

I've also heard that it's a little shorter due to the oblateness of the Earth but I'm a little unsure of that, the difference between the equatorial radius and polar are only about 20 km. But the simple answer is because you're living on a spherical surface :)