I am going to take AC031 from Toronto to Beijing in a couple of weeks, I searched its flight path, most of the time it will fly westbound after taking off from Toronto and continue west across the north pole area and land in Beijing, but yesterday it flew eastbound, across the Atlantic, this is very strange since the distance is a little bit more than flying westbound.

Why? flying eastbound

normal flight path

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    $\begingroup$ Very weird definition of "the Atlantic" you have there. It clearly flies over the north pole, not the Atlantic. $\endgroup$
    – jwenting
    Aug 1 '18 at 5:49
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    $\begingroup$ I don't think it's really going east or west much, either way. It flies north, then south :-) $\endgroup$
    – jamesqf
    Aug 1 '18 at 15:45
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    $\begingroup$ Very weird definition of "clearly" you have there. The problem is the map. Mercator projections are exceptionally poor for anything within a few thousand miles of a pole. $\endgroup$ Aug 2 '18 at 15:46
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    $\begingroup$ Spheres are weird. $\endgroup$ Aug 3 '18 at 10:51
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    $\begingroup$ Never use a flat map when thinking about a globe. The routes are straight, it's the map what's curved. $\endgroup$
    – Agent_L
    Aug 3 '18 at 11:34

Those routes are extremely similar.

They're basically two almost-a-straight-line routes over the arctic ocean, except that the second one has deviated a bit to the right, so that it's gone just on the right of the North Pole instead of passing by the left. At the pole itself, there's no such thing as "East" or "West", and if you pass very close to it, there is a discontinuous jump between passing it "going East" and "going West".

You can see this explicitly by going to FlightAware, asking to View track log, and downloading the flight tracking data to be viewed on Google Earth:

Actual tracking data in white. Interpolations for the missing-data parts in green.

As you can see, there is indeed a nontrivial deviation of what's probably several hundred kilometers in clipping Nunavut vs the northeast corner of Greenland, but that deviation is within the normal ranges of what you'd get in your standard transatlantic flight, say. The only change here is that the variation now includes the North Pole itself.

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    $\begingroup$ Credit obviously due to the three answers posted previously to this one, which contain very similar content - I just thought I could provide a slightly clearer version and pull in the actual flight tracks. $\endgroup$
    – E.P.
    Aug 1 '18 at 18:10
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    $\begingroup$ Unrelated to the OP's question: is it possible one or the other of those (similar) routes is chosen due to eg. airstream etc ?? $\endgroup$
    – Fattie
    Aug 1 '18 at 18:13
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    $\begingroup$ @Fattie There are many factors that go into planning flight paths; wind conditions are obviously one of the most important ones. $\endgroup$
    – E.P.
    Aug 1 '18 at 18:34
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    $\begingroup$ It makes sense when you put it that way @E.P. :) $\endgroup$
    – Fattie
    Aug 1 '18 at 18:58
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    $\begingroup$ Is there any way to overlay the two routes onto the same image? $\endgroup$
    – jpmc26
    Aug 3 '18 at 0:19

I took Hewgill's picture and added the routes in the OP (I just eyeballed this, so I won't guarantee accuracy).

Flight paths from over the north pole

With the FlightAware maps it looks like drastically different routes, but from this angle you can see that both routes are not that far off the ideal route.

  • 14
    $\begingroup$ This is actually the most useful answer as it shows visually how little difference there is between the flight tracks. Not that any of the others are wrong... $\endgroup$
    – FreeMan
    Aug 1 '18 at 16:09

The direct route from YYZ to PEK flies almost over the north pole:

enter image description here

Sometimes, routes need to deviate a bit from the "direct" route, due to prevailing winds or other traffic. If your route from YYZ needs to deviate a bit to the right, then it will cross over to the other side of the north pole (which is the very centre of the map above), and your projected map from Flightaware would show it flying "over" the Atlantic. But really, it's just gone slightly to the right of the pole.

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    $\begingroup$ Showing the right picture can make a big difference. +1. $\endgroup$ Aug 1 '18 at 11:22
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    $\begingroup$ The aircraft must remain within 180 mins of a suitable landing airports at all times. There are very few airports along that Polar route so weather conditions may dictate a more easterly route over Greenland on some days. $\endgroup$ Aug 1 '18 at 11:30
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    $\begingroup$ 180 minutes - wouldn't that be about 1500 miles? With airports in Alaska, Iceland, and Norway that doesn't look like it would be too difficult. $\endgroup$
    – nasch
    Aug 1 '18 at 15:27
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    $\begingroup$ Not sure which is the relevant regulatory body here, but the Boeing 777-300ER has been certified by FAA in the US to fly as far as 330 minutes from airports aviationweek.com/awin/faa-extends-777-etops-approval $\endgroup$ Aug 1 '18 at 23:25
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    $\begingroup$ IDK what the A330's certification is, but the similar route DTW-PEK/PEK-DTW used to be flown by an A332 by Delta (Now they have A350 on it) and it followed approx the same route, basically over the pole. $\endgroup$ Aug 2 '18 at 5:54

The flight did not fly across the Atlantic. Rather, you're seeing the results of stereographic projection.

More specifically, the Earth is Spherical. Navigation needs to be thought of on the basis of a sphere. It is 3-dimensional, and if you have studied sphere geometry, you will know that it defies the rules of geometry we know in 2D - for example it is possible to construct a triangle with three 90-degree angles.

The problem is that 3-dimensional objects cannot be displayed on a map, which is 2-dimensional. Therefore a mathematical formula is used to make a sphere look like a rectangle. The conversion is really skewed for regions near the poles. As a result, you cannot compare distances by measuring them on the projected map.

The route merely deviated slightly to the left in the second picture. However it is still flying over the North Pole, not the Atlantic. The deviation may be due to changes in winds aloft and/or traffic.

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    $\begingroup$ @Cloud That's a byproduct of the map projection used by FlightAware. The Earth isn't flat, so the shortest distance between two points won't show up as a straight line on that map (the actual shortest distance for flight planning purposes also takes winds into account). The ideal path isn't anything remotely close to a straight line. $\endgroup$ Aug 1 '18 at 7:13
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    $\begingroup$ @Cloud It only looks like a big curve due to the limitations of drawing that type of projection. It isn't nearly as bad as it looks. $\endgroup$
    – Mast
    Aug 1 '18 at 8:30
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    $\begingroup$ @Cloud This great circle visualization of the ideal route might help you understand. Look at the 3D view to see how the route looks on a globe, then switch to the 2D view with the button in the top right and see how different it looks on a flat map. $\endgroup$
    – kwc
    Aug 1 '18 at 9:02
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    $\begingroup$ Some years ago, talking with a friend, I did a demonstration with a small ball and a tape measure. (He worked in a custom tailor shop in Bangkok.) The look on his face as he realized that the curved path really meant was PRICELESS. $\endgroup$ Aug 1 '18 at 17:54
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    $\begingroup$ Wait, wait, wait! You mean the earth is ROUND?! So, why would NBA players mislead us? $\endgroup$
    – TomMcW
    Aug 1 '18 at 18:14

ALL flight paths on the earth are curved, cause the earth is a sphere! Which way that curve appears depends on which side of the curve you are observing it from. If you observe it frm south of the flight path it will appear to curve northwards and then south. If you observe it from East of the flight path it will appear to curve West and then East, etc.


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