does this photo show curvature of the earth, or something else?

[jjimm]

I saw the curvature of the earth from Concorde with my naked eye when I flew in it (~60,000 feet). Plenty of websites agree that this is indeed the case, but none of them look reputable. Anyone have an opinion if I actually did or not?

[ethansiegel]

Your photo shows a “curvature” of around 6 degrees worth of a circle. (About 1/9 of a radian.)

If your altitude is correct at 11 km, that would mean the radius of the Earth is just about 1800 km.

Since the radius of the Earth is more like 6370 km, I would definitely conclude there’s some sort of distortion, even knowing absolutely nothing about cameras.

[Freddy_the_Pig]

@jjimm

I saw the curvature of the earth from Concorde with my naked eye when I flew in it (~60,000 feet). Plenty of websites agree that this is indeed the case, but none of them look reputable. Anyone have an opinion if I actually did or not?

When someone asks this question, I feel the need to qualify the answer. If by “curvature of the earth” you mean that the horizon was round, then no, you didn’t see anything that I can’t see out my office window. If by “curvature of the earth” you mean that the horizon fell away so that the earth filled less than half of your field of vision, then maybe you saw something. From 18 kilometers the earth fills about 170 degrees of your field of vision, which is noticeably less than 180 if you’re looking closely.

[Irishman]

Freddy the Pig said:

Every time we do one of these threads on “curvature of the earth”, I’m completely baffled. What are people talking about?

[snip]

No, absolutely not. Curvature of the horizon is caused by the fact that the locus of points equidistant from an observer is a circle.

Ah, you’re talking about something completely different.

Here is a picture showing curvature of the Earth. See how the horizon bends? That is what we mean.

Also here for an extreme case. See how the Earth looks round?

[coremelt]

@ethansiegel

Since the radius of the Earth is more like 6370 km, I would definitely conclude there’s some sort of distortion, even knowing absolutely nothing about cameras.

ok well take a look at this picture, lens distortion is removed and I straightened it and overlaid a grid. To me there is still a visible curve… technical details below:

http://www.coremelt.com/private_downloads/misc/curve_lens_remove_with_grid.jpg

tech details, among other things I’m a feature film digital compositor. I shot a grid using the Tamron lens set to 17mm and then used the LensDistortion tool in NukeX compositing software to generate lens distortion removal for this Lens (see here: Nuke | VFX and Film Editing Software). I then straightened the image up with an 8 degree rotation and overlaid the grid. According to specs here this lens gives a 78 degree FOV when used on set to 17mm a crop sensor (EOS 7D) (Tamron SP AF17-50mm F/2.8 XR Di-II LD Aspherical [IF] Review)

Looks to me like 1 or 2 degrees of curve now which would give approx the right earth radius from 11 klicks high.

[Freddy_the_Pig]

@Irishman

Here is a picture showing curvature of the Earth. See how the horizon bends? That is what we mean.

The horizon also bends out of my office window. Where the plane of a window frame is superimposed in front of it, I can distinctly see the horizon “peaking” in the middle and curving lower toward the sides.

To be sure, from an airplane or from outer space, the curve is sharper because the earth is filling less and less of your field of vision. If you’re high enough to perceive this differential curvature, relative to what you see at ground level, then you’re seeing the “curvature of the earth”. Unfortunately, every time we do one of these threads, people interpret any kind of roundness as “the curvature of the earth”, and say, oh yeah, I saw the curvature of the earth from a beach.

[pulykamell]

@coremelt

Looks to me like 1 or 2 degrees of curve now which would give approx the right earth radius from 11 klicks high.

I can believe that. But it looks like we answered your main question: “Was this just an exceptionally clear view where the curvature is visible or is something else causing the apparent curve?” correctly. Most of what you see in your picture is lens distortion, not the curvature of the earth.

[CookingWithGas]

@Freddy_the_Pig

@CookingWithGas

Curvature of the horizon is due to the fact that the Earth is round.

No, absolutely not. Curvature of the horizon is caused by the fact that the locus of points equidistant from an observer is a circle. Imagine yourself standing on a boat in an infinite flat ocean. What would the horizon look like? Would it be square? Triangular? No, it would be round–you see the same distance in every direction (out to where the distant land merges into an indistinct blur), and perceive the shape as a circular curve.

I’m trying to work with you here but I’m having a hard time visualizing this. My intuition is that if I am standing on an infinite plane, I see a perfectly flat horizontal horizon in every direction. I might have the vague impression that I’m standing on a big circle, because I agree that the limit of the distance I can see is the same in every direction. But that’s different than curvature of the horizon. Let’s exaggerate the effect on Earth and imagine we’re standing on a relatively small sphere, say 1 km in diameter. Then it’s clear that we see curvature, because the curvature is certainly there.

Also, my subjective experience looking out my ofice window is completely different than what you describe looking out yours. I just see a flat horizon.

[CurtC]

@Freddy_the_Pig

The horizon also bends out of my office window. Where the plane of a window frame is superimposed in front of it, I can distinctly see the horizon “peaking” in the middle and curving lower toward the sides.

The way I see it, the window frame is the thing that’s going to be (apparently) curved to you, because of the fisheye effect of your eye, the window frame will appear to curve upwards at its ends. The horizon will be straight as well as you can tell, but will seem curved downwards only in relation to the upwards-curved window frame.

Unfortunately, every time we do one of these threads, people interpret any kind of roundness as “the curvature of the earth”, and say, oh yeah, I saw the curvature of the earth from a beach.

But that’s basically what you’re saying, and you’re the only one here saying it.

[CookingWithGas]

[quote=“CurtC, post:29, topic:553896”]

@Freddy_the_Pig

Unfortunately, every time we do one of these threads, people interpret any kind of roundness as “the curvature of the earth”, and say, oh yeah, I saw the curvature of the earth from a beach.

But that’s basically what you’re saying, and you’re the only one here saying it.

To be fair, that’s not what he’s saying. He’s claiming that you see curvature on the beach, but it is not due to curvature of the Earth.

[coremelt]

@pulykamell

I can believe that. But it looks like we answered your main question: “Was this just an exceptionally clear view where the curvature is visible or is something else causing the apparent curve?” correctly. Most of what you see in your picture is lens distortion, not the curvature of the earth.

sure, but correcting for lens distortion a clear curve of 1 or 2 degrees across 78 degree field of view is visible and that matches mathematically what you’d expect to see from 11 kms of height… So technically my photo DOES show the curvature of the earth… even when corrected for barrel distortion.

So for all the webpages that claim you can’t see the earths curve until 60,000 feet I say “bollocks” and I have the photo to prove it…

[Richard_Pearse]

@Freddy_the_Pig

@Irishman

Here is a picture showing curvature of the Earth. See how the horizon bends? That is what we mean.

The horizon also bends out of my office window. Where the plane of a window frame is superimposed in front of it, I can distinctly see the horizon “peaking” in the middle and curving lower toward the sides.

I don’t believe you’re seeing curvature there. Use a straight edge against an ocean horizon and measure the curvature (or take a photo) and I might believe you but what you’re saying is contrary to my experience.

What you’ve been describing has been the roundness of the horizon caused by it being a circle centred on the viewer, but something can be round without appearing curved. Imagine a halo, now put your eye in the centre of the halo, all around you can see the halo and deduce that it is round but there is no curvature because the edge of halo is level with your eye. Now lift your eye up above the halo, as you get higher the actual curve will become apparent. Get far enough above it and you can see the entire halo. When you are at low altitude on the Earth you are so close to being in the centre of the circle that is your horizon that you can’t see any curve, it is only when you get higher that the curve becomes apparent.

[Absolute]

I don’t see any curvature in your altered photo. The grid is not aligned with the horizon.

[matt_mcl]

So what exactly are you seeing, then, when you see an apparent curve? I remember standing on top of the campanile at San Giorgio Maggiore and looking down on Venice and its lagoon, and distinctly noticing that the line of the horizon appeared to be curved downward. This is a common enough sensation in other high (but not very high) places.

Now this is obviously not due to the curvature of the earth, for the reasons already described; but what is it due to?

[coremelt]

@Absolute

I don’t see any curvature in your altered photo. The grid is not aligned with the horizon.

I’m too lazy to post another image but if you take the grid picture into photoshop and draw another horizontal line directly through the horizon there is a clear rise in the middle.

[Quartz]

Never mind the issue of curvature; you do have an excellent photo of the ‘thin blue haze’.

[jackdavinci]

It’s not the curvature of the Earth, however, it is definitely possible that it’s not caused by lens distortion, etc. As others have mentioned, the point at which the horizon disappears is curved because it’s a circle. But the circle is just a tiny maybe 2 mile wide slice of the Earth’s surface at near ground level.

[FluffyBob]

Just found this browsing slashdot and thought of this thread.

Visual daytime observations show that the minimum altitude at which curvature of the horizon can be detected is at or slightly below 35,000 ft, providing that the field of view is wide (60°) and nearly cloud free. The high-elevation horizon is almost as sharp as the sea-level horizon, but its contrast is less than 10% that of the sea-level horizon. Photographs purporting to show the curvature of the Earth are always suspect because virtually all camera lenses project an image that suffers from barrel distortion. To accurately assess curvature from a photograph, the horizon must be placed precisely in the center of the image, i.e., on the optical axis.

David K. Lynch, “Visually discerning the curvature of the Earth,” Appl. Opt. 47, H39-H43 (2008)