I recently heard about the existence of a flight between Los Angeles and Dubai, so it prompted me to look up the longest flights in terms of distance.
The Los Angeles-Dubai route is the fourth longest (13420km in 16.5 hrs). In number one comes the 18 hour, 50 minute beast from Newark (New Jersey) to Singapore, at 15345km (9535 mi), or 38% across the globe! You might be wondering whether this flies via Europe or the Pacific Ocean and the answer is… neither! As seen below (ref) it goes north of Greenland, across the Arctic, within 150km of the north pole, then south through Russia, Mongolia, China and South East Asia.
It should be pointed out that the flight is not always so polar, since it often takes advantage of favourable winds in the Atlantic. This unexpected path (being used to seeing flat 2-D maps all the time) made me check out a few more counter-intuitive paths around the globe, courtesy of Wolfram Alpha.
Los Angeles to Dubai is another one that flies north of Greenland and then over the boundary between Europe and Asia.
From Melbourne to Dakar, Senegal, the shortest path is to go way south first (to more than 60 degrees south latitude) and the path is almost entirely oceanic.
To go from Melbourne to Recife in northeastern Brazil, you would pretty much traverse the south pole.
Finally, let us look at a few near-antipodal paths. Antipodes are points on the globe that are diametrically opposite. It is intriguing that less than 4% of the earth’s land is antipodal to land, with Australia antipodal to the Atlantic, North America antipodal to the Indian Ocean, and Africa and most of Eurasia antipodal to the Pacific (see this image). There are infinitely many shortest paths between antipodes (I am assuming the world is spherical now), and slightly perturbing one or both of these endpoints can change the shortest path drastically.
As an example, we take the paths between Buenos Aires and near-antipodal points of east Asia: Shanghai, Seoul and Beijing (distances from Buenos Aires between 19250 and 19650km). The true antipode is somewhere in the ocean within the triangle formed by this trio of big cities.
As you can see, three very different directions!