7
$\begingroup$

Take a look at these images:

enter image description here

enter image description here

enter image description here

As you can see, in all the images, the flight paths are curved. As far as I know, the shortest path between two points is a straight line. Planes usually would take the shortest path so that they can save fuel, money and time. Then why are the flight paths curved? Why don't planes fly straight to their destination?

$\endgroup$
7
  • 3
  • 24
    $\begingroup$ Because the straight path between two points on a globe leads through the globe. $\endgroup$ Dec 12, 2021 at 15:36
  • 5
    $\begingroup$ I voted to leave open; it's time this got a direct Q&A here. $\endgroup$
    – user14897
    Dec 12, 2021 at 16:01
  • 2
    $\begingroup$ Regardless of the optimal "most direct" route, planes also fly not-directly because there are other airplanes in the sky. ATC will route aircraft in ways that are most efficient for most users while preserving some sense of regularity and order that allows for safety. For example, see this question about arrival and departure gates at busier airports. $\endgroup$
    – randomhead
    Dec 12, 2021 at 16:11
  • 6
    $\begingroup$ It's because the massive nation of Greenland. All that landmass (larger than Africa) houses a secret technological society, which secretly controls the world. By their edicts, all airplanes must fly curved routes. $\endgroup$ Dec 12, 2021 at 22:43

3 Answers 3

50
$\begingroup$

Short answer

The routes on the screenshots are actually mostly straight.

It's true aircraft routes are not always the shortest paths, because other considerations count too, e.g. weather and the possibility of landing in case of a problem. Wind is a prime parameter, because it conditions fuel quantity and has a direct impact on airline profitability. Winds found at cruise altitudes are commonly about 200 km/h.

But the curves you show greatly exaggerate the curvature of actual routes. This problem is a map projection issue when converting the 3D spherical surface into a 2D flat representation. Nearly all maps used on websites use the web Mercator model, which is a standard Mercator projection, a projection on a cylinder tangent at the equator. So the only place the map is accurate is at the equator. As latitude increases, distortion increases too. It's nonsense near the poles where the meridians never converge, giving Greenland the size of Africa:

diagram showing Mercator projection rolled into a cylinder round a spherical Earth

Mercator projection, source: Encyclopedia Britannica

Details

  1. What you call straight path is a great circle.

  2. Most maps don't show a great circle as a straight line. Below is a portion of the great circle from Los Angeles to Grozny, which is approximately the route shown on your last screenshot:

    Great circle diagram on sphere and on Mercator map

    On the right hand the Mercator map shows it curved. This is the kind of map used by flight tracking sites. Note how parallels and meridians which are circles have been converted into straight lines on the Mercator projection. Due to this conversion, Greenland is now the size of Africa. Unfortunately this kind of projection curves all great circles except for the equator and meridians.

    The flight on your last screenshot (UAE37V) was ultimately heading to Dubai. The shortest path would have put it further North than the path it actually used. This is the great circle from LA to Dubai:

    Diagram showing route on sphere and on Mercator projection map

    Great circle from LA to Dubai, the shortest route for UAE37V

    The projection problem is manifest: the aircraft is following the 120°W meridian then the 60°E meridian. These meridians are (180°) opposite on the globe and form a continuous circle. However, on the Mercator map, this circle is folded at the pole and the two meridians are made parallel lines. So the aircraft seems to turn near the pole, while it actually continues flying straight ahead.

  3. Most flights take advantage of winds. On routes in the Northern hemisphere there are strong winds from West to East at cruise altitude, known as jet streams. Today's jet streams, from Null Earth:

    Image showing jet stream speeds around Earth using colours

    So flights going eastward change their route to join these winds, and flights going westward will avoid them. This has been already explained in:

    Why are westbound transatlantic routes located hundreds of km away from eastbound routes?

    Aircraft crossing the North Atlantic use predetermined tracks which are based on the location of current jet streams, recalculated twice a day. So two of the same flights may not use the same route, just because the North Atlantic tracks have moved.

$\endgroup$
7
  • 2
    $\begingroup$ A Mercator projection is not simply 'a projection on a cylinder tangent at equator', because it requires further mathematical elaboration. A simple cylindrical projection tangent to the equator is not conformal, as the Mercator is. math.stackexchange.com/questions/42838/… $\endgroup$
    – xxavier
    Dec 12, 2021 at 18:42
  • 7
    $\begingroup$ @xxavier, for someone just trying grasp the concept of a great circle the question you linked to is frankly a bit much. Because the earth isn't a perfect sphere either. $\endgroup$ Dec 12, 2021 at 22:29
  • 4
    $\begingroup$ @MichaelHall It's close enough to a perfect sphere that you need a very specialist situation for the difference to matter. The difference is about a third of a percent. Coincidentally that's exactly the size of a dimple on a basketball relative to the size of the ball. $\endgroup$
    – Graham
    Dec 13, 2021 at 0:57
  • 1
    $\begingroup$ @Graham, is the difference of a similar magnitude to the Mercator projection not being a "cylindrical projection tangent to the equator"? Because that was my point... $\endgroup$ Dec 13, 2021 at 1:02
  • $\begingroup$ The difference between a Mercator projection and a central cylindrical projection is very important. Pls compare this en.wikipedia.org/wiki/Central_cylindrical_projection and this en.wikipedia.org/wiki/Mercator_projection $\endgroup$
    – xxavier
    Dec 13, 2021 at 7:37
18
$\begingroup$

That is a straight path. It is the map projection being used that is curved.

This is because Earth is a round planet, not a flat surface, and creating accurate maps have always been a problem.

Take a globe and stretch a string between those two points and you will see that it follows the same path as the “curved” lines you have shown.

$\endgroup$
1
  • 5
    $\begingroup$ BREAKING: NORTH AMERICA DEVASTATED BY GIANT STRING, ORIGIN UNKNOWN $\endgroup$
    – Vikki
    Dec 13, 2021 at 5:42
7
$\begingroup$

As you know, Earth is not flat, but is rather close to a sphere.

So "the shortest path between two points is a straight line" does not actually work. The straight line between those two points would go through the Earth, which is quite challenging for most aircraft (!).

The shortest path between two points on a sphere is called the "great circle route". It's the intersection of a plane going through the centre of the sphere and the two points with the surface of the sphere.

Now, mapping a sphere to a flat surface is quite a challenge. Take a soccer ball, cut it in half, and try to lay it fully flat. Good luck. Or try to wrap a basketball with a sheet of paper without any wrinkles or tears. Not going to happen.

There are many different ways of doing that (called projections), which all have different properties, usually trying to conserve either distances or areas or angles, but never all of them at the same time (even though lots of people have tried and some maps are really funky. Just think about the poles: meridians on a sphere all converge to a single point (the pole), while meridians on many maps (and definitely on those you are used to, which use the Mercator or Web Mercator projections like the ones in your exemples) are parallel.

This distorts the representation of the route on the map.

Here's an example, generated with the Great circle mapper.

Your first route is roughly LAX to KEF. If you use an orthographic projection it does look like a straight line:

The exact same route, drawn using a rectangular projection, does look curved:

If you look at the points it goes through (e.g. intersections with state or US/CA boundaries or coastlines), you'll see that it's the exact same route, just viewed differently. You'll also see that it's quite close to the route on FR24. The remaining differences may come from:

  • Trying to take advantage of the jet stream (a high-altitude wind which flows west-to-east around those latitudes, which changes a bit all the time, and which can save a lot of time and fuel if you manage to get "pushed" by it as much as possible), or, the other way around, trying to avoid it.
  • Following navigation routes: like you follow roads to go from one place to another, aircraft follow pre-established routes from one waypoint to the next).
  • Avoiding other aircraft (this is actually one of the main goals of the navigation routes above).
  • Avoiding bad weather.
  • In some cases, especially transoceanic routes, making sure the aircraft is never too far from a diversion airport, though nowadays even a twin-engine aircraft can fly quite far from one, see ETOPS.
  • For some routes, avoiding the airpace of some countries, due to local conflicts (aircraft usually don't like flying over war zones which have a risk of stray missiles), or other geopolitical reasons.

A few more examples of routes which are straight but don't like they are:

  • JFK-SYD: Note how it looks like it curves one way then the other. The inflexion point is over the equator.

  • KEF-SYD: Yes, it is straight, going over the pole:

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.