The Amount of Curvature that Appears in Photographs of the Horizon

The amount of horizon curvature that appears in a photograph of the horizon depends on several factors:

  1. The altitude of the observer.
  2. The field of view of the camera.
  3. Lens distortions of the camera.

Some flat-Earthers assume that we should see the same amount of Earth’s curvature everywhere. And when they see the different amount of curvature in the different picture of Earth’s curvature, they wrongly took it as “proof” of some sort of misconduct.

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“Behind the Curve”: the Earth’s Curvature Experiment

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“Behind the Curve” is a documentary showing behind the scenes on what is happening in the flat-Earth community in the United States just before a flat-Earth conference. In a section, the film shows us how a flat-Earther tried to disprove curvature using a series of visual experiments. The result clearly indicates the surface curves, but he was unwilling to accept the fact.

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Variability of Atmospheric Refraction

In most situations, atmospheric refraction bends light downwards and causes objects to appear higher than they actually are. The strength of atmospheric refraction is not constant. It depends on weather condition and varies on the different seasons, different days, and even different times of the day.

Because of the variability of atmospheric refraction, a distant object that is usually obstructed by Earth’s curvature can sometimes be visible. Some flat-Earthers would cherry-pick moments when the object is visible. They would show such specific moments to everyone and use them to “disprove” Earth’s curvature; happily ignoring the cases where Earth’s curvature partly or entirely obstructs the object.

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Auguste Piccard, Another Scientist Falsely Claimed by Flat-Earthers

Auguste Piccard was a Swiss-Belgian physicist, inventor, and explorer, known for his record-breaking balloon flights to the stratosphere, as well as the invention for bathyscaphe to allow for deep ocean exploration.

Unfortunately for him, flat-Earthers are claiming him as their own these days. It started from a Popular Science article from 1931, saying:

Through portholes, the observers saw the earth through copper-colored then bluish, haze. It seemed a flat disk with upturned edge.

But, no. In reality, Auguste Piccard was not even close to being a flat-Earther.

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Football Field and ‘Flat-Earth Convergence Experiments’

A properly designed football field does not lie perfectly flat. Its middle portion is slightly raised to promote runoff of excess water. Without it, the field can become muddy & uncomfortable.

Some flat-Earthers conducted the perspective convergence ‘experiment’. They put a camera on the surface of a football field, and record a person walking away across the field. The person started to disappear from his feet first. Because they felt the football field is flat, they took the wrong conclusion that the person disappeared due to ‘perspective’. They were wrong. The field is, in fact, not perfectly flat. If it is perfectly flat, the person would appear fully at the end of the field.

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Earth’s Curvature Calculation

The amount of obstruction of a distant object that is caused by Earth’s curvature depends on:

  1. The distance of the object.
  2. The height of the observer.
  3. The height of the object.
  4. The magnitude of atmospheric refraction.

Flat-Earthers like to use the visibility of a distant object to prove Earth’s curvature does not exist. Very often, they failed to account for observer’s height and atmospheric refraction, or make other mistakes, like unit conversions errors, distance calculation errors, etc. Once all are considered for, and mistakes are fixed, everything will be consistent with spherical Earth.

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Salar de Uyuni and Other Salt Flats

Salt flats are flat expanses of ground covered with salt and other minerals. Salar de Uyuni in Bolivia is the world’s largest salt flat. Salt flats are visibly very flat, but like every other geology features, they all follow the curvature of the Earth.

Flat-Earthers take the flatness of Salar de Uyuni and other salt flats as ‘evidence’ of a flat Earth. They are wrong. While most salt flats appear flat, they still gradually curve and follow the curvature of the Earth.

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The Curvature Fitting Game

The amount of curvature that appears in a photograph of a sphere depends on 1. The radius of the sphere, 2. Camera distance from the sphere, 3. Field of view of the camera, and 4. The distortion characteristic of the camera being used.

The ‘curvature fitting game’ has been flat-Earthers’ favorite pastime. They would try to fit a photograph of Earth’s curvature with another. If they find the result is not proportionally correct, they will make fun of it. They are wrong. Two different photos of a sphere can be taken differently and would show a different curve, even if the object being photographed is the same object.

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Airborne Early Warning & Control (AEW&C): Mitigating Limited Radar Range Due to Earth’s Curvature

An AEW&C (airborne early warning and control) system is a radar system attached to an aircraft. It can detect objects at a very long range compared to any surface mounted radar system.

The reason is that Earth’s curvature limits the range of a surface-based radar. An airborne radar system mitigates this problem.

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Crow’s Nest on Ships

A crow’s nest is a structure in the upper part of the ship, especially old-fashioned ones. It is used as a lookout point and positioned high above to increase visibility over the curvature of the Earth.

On the deck of a ship 4 m (13 ft) above the surface of the ocean, an observer can spot a 20 m (66 ft) high ship from at most ±25 km (16 mi). On the other hand, from a 35 m (115 ft) high crow’s nest, an observer will be able to spot the same ship from ±40 km (25 mi) away.

On modern ships, the role of a lookout is replaced by radars. And for the same reason, a radar is positioned in the upper part of a ship.

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A Glass of Water

The surface of the water in a glass of water is practically flat. Some flat-Earthers claim this is ‘evidence’ that the surface of the water is flat, and it will always be flat no matter how wide the container. They are wrong.

If the Earth is a sphere with the radius of 6371 km (3960 miles), then the surface of the water in a 10 cm (4 in) wide glass will have a bulge of 0.00000002 cm as the result of gravity, excluding other effects like the surface tension.

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Grid Corrections — How the Spherical Figure of the Earth Affects Land Partitioning

Some countries decided to partition their territories into a rectangular or square grid. But the Earth is spherical, and it is not possible to divide a spherical surface into a perfect rectangular grid while maintaining the perfect angles, distances, and areas.

To solve this problem, land surveyors implemented grid corrections. Every certain distance, parts of the grid are shifted away from each other. Therefore, an equal area in each division is maintained as much as possible by giving up an entirely lined up grid.

If the Earth is flat, it is not necessary to have this compromise. It would be possible to divide the land into a perfect square grid system.

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Evidence of Curvature: Turning Torso Building, Malmö, Sweden

Turning Torso is a 190 m (623 ft) high building in Malmö, Sweden. It is situated near the strait of Øresund. At the other side of the channel lies the city of Copenhagen, Denmark, only 15 km (9 miles) away from Malmö. Turning Torso has a distinctive segmented shape that is easy to recognize from far. And more importantly for our purposes, the segmented form is making it easy to judge its height from far.

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The Reason We Cannot See Earth’s Curvature When Standing on a Beach

We can’t directly observe and subjectively perceive the curvature of the Earth from a position close to the surface. And this matches the expectations in the spherical Earth model.

Flat-Earthers often take the fact we can see the curvature by standing on a beach as ‘evidence’ the curve doesn’t exist. They are, once again, wrong.

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Curvature Calculators and Atmospheric Refraction

Atmospheric refraction causes a distant object to appear higher than its actual position. As a result, the object can be physically behind Earth’s curvature but is still visible because the light coming from it is refracted by the atmosphere.

There are many curvature calculators and simulation tools that don’t account for refraction. They would give us the correct results indicating the object’s physical positions but fail to show us the correct apparent position of the object when visually observed.

Flat-Earthers are often too happy with the calculator showing them the results they want to see and fail to see the reason for the discrepancy.

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Water Level Demonstrates The Dip of the Horizon and Proves Earth’s Curvature

As the Earth is spherical, the horizon is below the eye-level (or the astronomical horizon). The angle between the eye-level and the horizon is the dip of the horizon. The angle becomes larger as we go higher.

Flat-Earthers often claim that “the horizon always rises to eye-level”, and thus ‘proving’ the flat Earth claim. Despite their insistence to use a water level to ‘prove’ water is flat, the same device can be used to demonstrate the dip of the horizon, proving the water surface has curvature, and consistent with the spherical Earth model.

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Perspective Compression: Determining If a Curvature Exists

Soundly’s pictures and videos of Lake Pontchartrain power lines and causeway stirred up the flat-Earthers’ nests. They clearly show the curvature of the Earth, where it is usually hard to discern. For the rest of us, those pictures are just the consequence of the fact that the Earth is a globe.

Flat-Earthers can’t take this, and they invented various excuses to attack the credibility of these pictures and videos. Some of them look for specific vantage point where it is impossible or very hard to discern the curvature.  They would conclude if the curve is not seen from these vantage points, then it should not be visible from Soundly’s viewpoints.

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