How to Take a Photo of the Curve of the Horizon

Z.W. Wolf

Senior Member
Reminder: What we are seeing is the edge of a circle.

Stand in any one of the three circles on a basketball court. Turn around in place. From your perspective the edge of the circle in your line of sight will be the point farthest away from you. It will therefore appear to be the top of the circle. There will always be a top of the circle as you turn through 360 degrees.

The horizon on a sphere Earth is a circle all around you. The circle is defined by where your line of sight meets the surface. That's what creates the edge of the circle. There will always be a top of the circle.

As you turn 360 degrees, the edge of the circle in your line of sight will always be the part of the circle farthest away from you, and from your perspective that will always be the top of the circle.

So what does this mean?

On a huge plane surface there wouldn't be any circle. There wouldn't be anything to define the edge of the circle. (Unless someone painted one on, like the paint on the basketball court.) Therefore the horizon on a plane Earth wouldn't be a circle and wouldn't show any curve.
 
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Mechanik

Member
@Chris Rippel - Your thought experiment, or a variation of it, has tricked many globers as well as flat earthers. Stated a little differently, it almost seems to be a mathematical proof that the horizon can't be curved. i.e. A) Eye level is a flat plane through the eye of the observer B) eye level out in the distance appears as a straight line, as it is part of that flat plane. C) The horizon on a spherical ocean is a constant drop below the straight eye level line. D) A line a constant distance from another line is a parallel line. Conclusion: A line, such as the horizon, that is parallel to a straight line must also be a straight line.
This is presented as a logic problem, so let’s treat it as such. If A, B, C, and D are all true, then the conclusion must be true. However, the horizon on a spherical ocean is not a plane or a line parallel to a plane and the drop (as measured by the length of a line perpendicular to your eye level line or plane) is clearly not constant (i.e. equal) across your eye level flat plane. That makes C false and therefore the conclusion is also false.

A plane at eye level extends infinitely far to both left or right. For C to be true, the drop from your eye level plane to the surface of the water at the horizon must be constant (exactly 12 feet, or 12 inches, of 23 pixels, or whatever measurement you’re using) across your field of view or across the field of view of the camera. It’s clear from photos that placing a straight line across a photo, or across the field of vision, shows the drop is greater the farther you get from the center of your view. Therefore the drop varies from the center to right or left. The horizon on a spherical ocean is a curve and the distance of that horizon to the original plane is not constant and C is false.

We see these logic errors regularly in conspiracy theories. What seems to be a logical conclusion is reached, but one or more statements are untrue, making the conclusion false.
 

Rory

Senior Member
To try and combine all the above:

A) Eye level is a flat plane through the eye of the observer - true (could add MW's "and parallel to local down")

B) Eye level out in the distance appears as a straight line, as it is part of that flat plane - true

C) The horizon on a spherical ocean is a constant drop below the straight eye level line - true (for example, eye level always at zero degrees, and a 360 degree horizon at -0.7 degrees)

D) A line a constant distance from another line is a parallel line - kind of true (see below)

Conclusion: A line, such as the horizon, that is parallel to a straight line must also be a straight line - not true

ZWW points out that the horizon forms a circle, and I've said the horizon is akin to the curved edge of a flat coin: I think this is the key. The imaginary plane at eye level is not a circle, but rather an infinite plane. So perhaps imagine this: a large horizontal square (eye level) hovering above a much smaller flat circle, such as a coin. Every point on the circle is the same distance below the square ("a constant drop") and you could say that the edge of the circle and a similar circle traced on the plane would be parallel. But it doesn't stop the edge of the circle being curved, just as it doesn't stop "eye level in the distance" being a straight line.

An actual diagram may help that. It makes sense in my head. Though I'm sure there are better ways to visualise it.
 
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Trailblazer

Moderator
Staff member
As you turn 360 degrees, the edge of the circle in your line of sight will always be the part of the circle farthest away from you, and from your perspective that will always be the top of the circle.
Nitpick: the circle of the horizon, by definition, is equidistant from the observer all the way round. I assume you meant “furthest away in the direction you are looking at a given time”.
 

Z.W. Wolf

Senior Member
Yes, I need to fine tune that. I'm struggling to describe how it looks.

In a simple, real world example: Standing in a circle painted on the basketball court.

Along your line of sight there will always be a "top" of the circle. It's the point that separates "curving to my left" and "curving to my right. "

But if I spin in place there's always a NEW point that looks like that. There's no problem in that simple real world example.
 

Mick West

Administrator
Staff member
In a simple, real world example: Standing in a circle painted on the basketball court.
I prefer the example of standing in the middle of a circus ring. The edge of the ring, at the bottom of the barrier, is a flar circle, and yet you can see a curve.
Metabunk 2019-10-06 10-33-13.jpg
 

Mad Mac

New Member


This is a photo I took that I believe shows the curvature of the earth.

In 2018 I observed this phenomena while holding down a beer on the deck of our rental beach house. At that time I didn't say anything to anyone because I did not want to sound like a loon. In the meantime, I Googled around and found this scholarly thread on metabunk.

When we returned to Galveston this year, I used the panoramic feature on my new iPhone 8 to take this handheld picture. The railing in the foreground helps to see the curve. A lens can make a straight line appear to be curved, but I believe the railing in the foreground would have to be curved the same way and it is not.

Now I will confess that as I pivoted the camera it may have risen slightly in the middle. Position a piece of paper above the railing so that the edge rests on the corners of the railing. A tiny sliver of the gulf appears in the middle. Flip it over and position the paper so that the edge is under the corners of the railing and the gulf definitely has a bulge in it.

The picture is almost a 180 degree view, all the way northeast up the coast to Galveston and all the way southwest down the coast to the San Luis Pass. So it is not a small layout, but about 15 miles in each direction, about a 30 mile span.

But I could be wrong, I often am.
 

Jesse3959

New Member
I've actually thought about hiking up to a high place and tying a thick string between two trees really tight, parallel to the horizon - then hanging a few helium party balloons on it (enough to lift it if it were slack) to prove that it it's not sagging and causing an appearance of curve.
Then position the camera so the string lines up with the horizon - that way there's no argument about whether the curved horizon is from the lens or real because the string is known to be straight (or curved up from the helium balloons, but in any case not curved down..)

Why a string instead of an 8-foot straight edge? Because the string could be 50 feet long, and thus far away enough from the camera that it was in good focus along with the horizon.

I haven't had a chance to try it yet though.
 

Rory

Senior Member
The string could for sure work, but I suppose it's more difficult to verify that a string is perfectly straight than it is with a solid bar, as well as to set up. Plus the solid bar has shown to work really well - especially with the option of having one above and one below the horizon.

As far the deck shot, given the amount of visible curve from a low elevation - more than from much higher elevations, and more than the math would predict - it would appear that it's being caused by the camera. Perhaps lens, but probably more to do with the panoramic aspect of it. I would imagine that the ends of the balcony are further away than the center, so that probably has a lot to with it too. But others are much more au fait with the workings of cameras than I, so now doubt they will explain it better.
 

Mick West

Administrator
Staff member
As far the deck shot, given the amount of visible curve from a low elevation - more than from much higher elevations, and more than the math would predict - it would appear that it's being caused by the camera. Perhaps lens, but probably more to do with the panoramic aspect of it.
Yeah, it's the panorama. Look at the huge curve in the bottom rail. Unfortunately any curvature in this image is an illusion. There's about the same amount of ocean above the railing all the way across, relative to the height of the railing at that point.
Metabunk 2019-11-16 09-04-56.jpg
 

Jesse3959

New Member
The string could for sure work, but I suppose it's more difficult to verify that a string is perfectly straight than it is with a solid bar, as well as to set up. Plus the solid bar has shown to work really well - especially with the option of having one above and one below the horizon.
The string won't be perfectly straight. Because of the helium balloons, it will be ever so slightly curved up in the center, favoring the flat earthers. But I like your idea of two strings, one above and the other below the horizon.

The reason I'm interested in a string for this is because many cameras will not focus sharply at infinity and at 4 feet away at the same time. With a string, the straight edge can be much farther from the camera and still fill the horizontal field of view.

There are also some unexpected conditions relating to the effective aperture of the camera lens when especially close to an object. By moving the straight edge out these effects are reduced.

As to knowing that a straight edge is straight, I think for many people, doubters may say "Well your red stick wasn't straight." But everyone knows that a taut line has to be nearly straight - and it's buoyancy determines the direction of the curve.

(I'm not personally doubting your red ruler, but rather pointing out that a taut line is inherently straight (to the degree it is straight) while a stick can be any shape you like. It does not have an inherent straightness. A taut line does - and it is a function of it's buoyancy and tension and length.)
 

Rory

Senior Member
As to knowing that a straight edge is straight, I think for many people, doubters may say "Well your red stick wasn't straight."
That's true, and though I included ways to show that the red bars were straight - rotating them; showing along their length; and measuring the distance between them - it was always more a demonstration of what 'doubters' could do for themselves. But as far as I'm aware, no globe denier has yet repeated the observation. :)
 

Amber Robot

Member
What definition are you using? :)
I envision an “ideal” execution of a panoramic photograph would have very little horizontal field of view that sweeps across a large angle. That would minimize distortions, rather that stitching together multiple wide angle photographs.

if you expected curvature to show in a panoramic photograph what would you expect to happen in a 360 degree panorama?
 

Jesse3959

New Member
So we really would have to look at the method used to form the panorama.

The normal way we take a panorama is with a smart phone or an equally smart camera - it takes multiple photos as we rotate the camera then it tries its best to distort and stitch them together into a seamless scene. But the shape of the horizon is completely up to how the software distorts the pictures to make them all stitch. It's really completely useless for measuring the curve of the horizon without a known-straight reference bar in the field of view.

For a panorama to actually measure the curve, you would need a camera that records a single vertical column of pixels at a time, and the camera would be on a swivel which would allow it to turn and take in the next vertical column of pixels, one column at a time, eventually taking in the whole desired scenery.

If the swivel were perfectly level, no curve would be seen. The horizon would be a straight line, so many degrees down from level.

However, if the swivel axis were tilted slightly down so that it was exactly at right angles to the horizon in one direction, then it would produce a panorama which correctly showed the curve of the horizon.

This fellow built himself one using the guts of an old flatbed scanner: https://hackaday.com/2009/12/29/panoramic-scanner-camera/
 

Amber Robot

Member
However, if the swivel axis were tilted slightly down so that it was exactly at right angles to the horizon in one direction, then it would produce a panorama which correctly showed the curve of the horizon.
yes. If it were tilted down and spun in a plane it would be tilted up at 180.
 

Jesse3959

New Member
yes. If it were tilted down and spun in a plane it would be tilted up at 180.
So I guess in summary, all a panorama proves is that the horizon is a circle. And that if you are at some altitude and you point a tube at the horizon in one direction, it will be pointing above the horizon in the other direction.

(And obviously the earth has to be essentially spherical for the horizon to be close enough that there's a distinct boundary, because if the edge was the horizon then we couldn't see it at all unless we were at the edge of the disk..)
 

Amber Robot

Member
So I guess in summary, all a panorama proves is that the horizon is a circle. And that if you are at some altitude and you point a tube at the horizon in one direction, it will be pointing above the horizon in the other direction.
I saw a YouTube video in which a guy did exactly that. He was on a hill that had a view of water in both directions and set up a tube and pointed it at the horizon looking one way and showed that it was above the horizon looking the other way.
 

Priyadi

Member
My attempt at this. Taken from the third floor of the Hotel Santika Premiere Belitung:

Screenshot_20200115_233743.png


The situation at the balcony. There are glass railings that I used as a reference:

Screenshot_20200115_235108.png


The shot. Exposure is f/22, 1/160s, ISO 3200. Taken using Canon EOS R with EF 16-35 f/4 lens, at the widest setting. I aligned the horizon with the glass railing and focused on the horizon.

Screenshot_20200115_235643.png


Vertically stretched:

Screenshot_20200116_000127.png


I was surprised at how easy this was, considering this was taken less than 30 m (100 ft) above sea level and I was without any preparation. I brought the correct lens by chance & had only about 10 minutes before the fog came in.
 

Mick West

Administrator
Staff member
Vertically stretched:

Screenshot_20200116_000127.png


I was surprised at how easy this was, considering this was taken less than 30 m (100 ft) above sea level and I was without any preparation. I brought the correct lens by chance & had only about 10 minutes before the fog came in.
I'm not sure about this one. You are not really high enough, and the tops of the glass panels don't form a continuous verifiably straight line. So it's hard to tell what role lens distortion has.

Did you try correcting with the lens profile in Photoshop? If you email me the original photo I can give that a go. mick@mickwest.com
 

Priyadi

Member
I'm not sure about this one. You are not really high enough, and the tops of the glass panels don't form a continuous verifiably straight line. So it's hard to tell what role lens distortion has.

Did you try correcting with the lens profile in Photoshop? If you email me the original photo I can give that a go. mick@mickwest.com
I had "lens aberration correction - lens distortion correction" enabled in-camera, so the camera will correct barrel distortions. doing it again in PS will only 'correct' it for the second time and reintroduce the distortions. unfortunately, I did not take raw version of the pictures.

the pictures are here: https://priyadi.smugmug.com/Other/Flat-Earth-Debunking/Belitung-Pictures/n-jrggHN/i-344WLzt
 

Priyadi

Member
As a follow up to my attempt above, I have managed to get a simulated view of the scene using Walter Bislin's curvature app. The problem is that the observation is very close to the surface, and by default, the resolution of the output is too small to show the curvature. Here's a crude way I did to get a higher resolution simulation:
  • Go to Walter's curvature app
  • Input the height of the observation (25 m) and the focal length of my camera (16 mm)
  • Maximize the browser window across my triple monitor setup (6400 px of horizontal pixels)
  • Increase the zoom of the browser window to 500%
With these steps, the app gave me a simulated view with a resolution of 4530x3020.

Here is my photo & the result of Walter's simulation, vertically stretched together, side by side:

Screenshot_20200121_204110.png
 
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