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Wouldnt that be the line it would fly actually? If you go from one side of the earth to the other its fastest over the poles or something no? Or because of map projections? Idk that much about maps.
Ignoring the fact that you would go east to reach Hawaii from Japan, because it’s in the northern hemisphere, it would actually curve up not down, and because both japan and Hawaii are close-ish to the equator the curve would be relatively flat.
Fun fact because every country charges you for every nautical mile flown in their airspace, you will actually get lines that zigzag and are less fuel efficient because they are paying less for airspace miles. Example. If you fly from Chicago to Paris or Dubai, you don’t actually head east first, you first head northeast into Canadian airspace and bypass the New England area because Canadian airspace is cheaper than U.S. airspace.
Isn’t that also the shorter route, because you’re circling the Earth where it has less circumference?
Also the North Atlantic Tracks are there. Might also play a role.
it’s mathematically provable that the shortest path between any two points on a sphere will be given by a so-called “great circle”. (a great circle is basically something like the equator: one of the biggest (greatest) circles that you can draw on the surface of a sphere.) i think this is pretty unintuitive, especially because this sort of non-euclidean geometry doesn’t really come up very frequently in day to day life. but one way to think about this that on the sphere, “great circles” are the analogues of straight lines, although you’d need a bit more mathematical machinery to make that more precise.
although in practice, some airlines might choose flight paths that aren’t great circles because of various real world factors, like wind patterns and temperature changes, etc.
You can't fly directly in a commercial aircraft. The airspace has routes and points you have to follow. Smaller planes don't always have to, but big planes almost always do. Altitude is one of the determining factors.
I haven't seen many toll booths in the air. A lot of weird routing comes down to stuff like "there's a military base there, they get big mad if anything goes near them", or noise abatement over populations, or not stranding a single-engine plane out over the water. Plenty of "air highways" to implicitly deconflict traffic without the need for ground control. Lots of technical and political considerations, not so many billing based ones.
Just go east?
You're a genius. An evil genius who could figure out the most efficient way to kamikaze Hawaii from Japan.
Judging by eye on the map projection OpenStreetMap uses, the direct line between Japan and Hawaii is about one quarter of the westbound straight line between Japan and Hawaii.