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When we see contrails in the sky, let's say traveling left/right in your vision, you are seeing across a sky that is easily a couple of hundred miles wide. I mean, we can see one side of space and then another, so we can see across a great distance in the sky depending on the height of an object. Am I wrong? I mean, we can see entire cities from a long distance away on the ground, so an unobstructed view of the sky would give us the ability to see something very long, right?

That being said, an airplane is following a curve, and when a plane makes a trail it is essentially tracing out the shape of the earth. Being that this trail is very high up, and following the curve, why don't the trails curve (left/right trail), and we see a giant arch across the sky? None of the lines in the sky look curved from any direction, they are straight lines, or at least appear to be.

Am I missing something? Maybe it's a dumb question, but I remain ignorant on the topic because I haven't been able to find the answer from anyone with a clue. This site seems legit, so I asked it here. Thanks, in advance.

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  1. Some contrails disperse and therefore end up being short to show any curvature.

enter image description here
(contrailscience.com)

  1. Long ones don't stay put because of the wind. They wiggle.

  2. It's for the same reason flying at 30,000 feet the Earth's curvature is not apparent. Earth is huge and it takes higher altitudes for the curvature to become noticeable to our eyes.

enter image description here
(californiacapitalairshow.com)

  1. Flying higher at or above 60,000 feet or so (where the Concorde cruised) the Earth curvature starts to become more noticeable.

To notice it from the ground, you need a very clear day, not the slightest haze on the horizon, calm winds, and the plane to come from the right angle, as the illustration below shows:

enter image description here
(metabunk.org) 5-mile grid at 35,000 feet seen from the surface.

Note that the lines are squashed together the farther they are, so it'll take a very long contrail at a low angle above the horizon (called an altitude in astronomical terms) for that curvature to be easily seen.

RE comments:

  • The horizontal lines aren't as curved:

That's a property of one-point perspective, you see more depth than breadth.

  • The contrails are at least a few hundred miles long:

Not when viewed moving side-to-side. Jetliners cruise at around 550 MPH. The grid above shows what 5 miles are like. A 250-mile long contrail would take a plane 30 minutes to draw. You can time the next plane you see for proof on how long it takes to pass side-to-side in your field of vision. A lot less than 30 minutes. Example below is from a time lapse video:

enter image description here
Click image to open the GIF.

The GIF duration is 1.29 seconds and the video is shot at 5-second intervals at 24 fps. The contrail moved right to left in ~2.5 minutes, or roughly 25 miles (5 squares).

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  • $\begingroup$ The horizontal lines are not curved and that can easily be a span of a few hundred miles that we are looking at. No matter how big the earth may be, we should see this curve represented by the trails. If you can see that kind of curve on the lines heading out to sea (because that is what the picture depicts), then why doesn't that apply to the horizontal lines across the same distance? Again, if we can see a boat go over a curve, then we are seeing curvature with the naked eye. There is a big difference to what we can see straight ahead and across the sky horizontally. Thanks for the respons $\endgroup$
    – Chris
    Apr 27, 2018 at 23:11
  • $\begingroup$ @Chris - see update. $\endgroup$
    – user14897
    Apr 27, 2018 at 23:18
  • $\begingroup$ @Chris: First, if you look closely you can see that the horizontal (left-right) lines are slightly curved. Second, the vertical lines are drawn brighter than the horizontal ones, thus it's very difficult to make out the distant ones, which would encompass enough distance to make the curvature obvious. $\endgroup$
    – jamesqf
    Apr 28, 2018 at 18:04
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See this link the second answer from the top.

Basically the answer is the curvature of the earth is too small to detect by the naked eye. From a point on the earth, the observed point on the horizon will only drop by 8 inches for every mile. This is why there are flat-earthers because they say they cannot see the curvature of the earth. Airplanes don't exactly fly in exact straight lines either and you cannot see the slight variations in flight path from the naked eye that far away.

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  • $\begingroup$ But, boats are going over a curve and you can see that with the naked eye. You can see the bottoms of building be cut off, which is supposed to happen because of the curve. That isn't far away. If the curve is that close, then why shouldn't you see this represented across several hundred miles up in the sky? I get how we couldn't see it on the ground, but the lines in the sky represent the shape of the earth, as if it's being traced. I don't understand how you couldn't see an arch spanning across several hundred miles in the sky. Again, maybe that is ignorant, so my bad. $\endgroup$
    – Chris
    Apr 27, 2018 at 21:38
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    $\begingroup$ The cases you described are where you are looking horizontally a building and ships that are tall compared with their surroundings and with a completely flat horizon. Contrails are vertical from your observation point. Your depth perception cannot discern a curve that subtle. $\endgroup$
    – DLH
    Apr 27, 2018 at 21:53
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    $\begingroup$ @Chris when you take plank, rise it to your eyes and look along it, it's very easy to say it's warped even by a single mm. But when you look at a even more warped plank from the side, it looks "straight enough". Looking along a horizon from a ship vs looking at a contrail up there is same thing. $\endgroup$
    – Agent_L
    Apr 28, 2018 at 6:43

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