Curvature of Water Surface

If Earth is a sphere, why is the surface of water always flat?

Due to Earth’s gravity, water seeks the lowest potential or as close as possible to the center of Earth. It forms a practically spherical surface centered on Earth’s center. The width of the surface in everyday cases is tiny compared to Earth’s radius. Thus, the water surface looks practically flat but not perfectly flat.

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Where’s the Curvature?

A human eye can only visually perceive the curvature of the Earth if we are at a considerable altitude from the surface, which is still beyond the reach of most humans today. A commercial jet airliner is the highest position realistically attainable by most humans today. We can only perceive very slight curvature at such altitude and, even then, only in an ideal condition.

The basis of flat-Earthers’ belief is that the horizon appears flat. They would say if we cannot see the curvature, then there’s no curvature, and therefore, the Earth is flat. In reality, only a few people can travel high enough to see the curve.  The highest we can realistically go is by getting on a commercial jet airliner, which can only go about 11-15 km up, only a fraction of Earth’s radius.

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Curvature Dilemma

A ship disappearing from the bottom first is an effect of Earth’s curvature. It is not a direct observation of the curve itself. We can only directly see the curve from a high altitude, not from near the surface.

Flat-Earthers present this reality as if it is a dilemma: 1. Earth is too big for us to see the curvature, but 2. We can see ships go over the curvature. It is a false dilemma. Ships disappearing from the bottom first is an effect of Earth’s curvature. Such an observation is different from directly witnessing the curve itself.

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Curvature App

Curvature App is a web application we can use to create a simulation of the horizon’s shape and the visibility of distant objects on a flat and spherical Earth. Curvature App is available at walter.bislins.ch/Curve.

When determining a distant object’s visibility, flat-Earthers often use wrong calculators that fail to account for all the important variables and give them incorrect results. Curvature App accounts for all of these variables, and not only it gives us the numbers, but also the simulated view.

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Bonneville Salt Flat and Earth’s Curvature

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Interstate 80 traverses the Bonneville Salt Flat, Utah, in a practically straight segment. From the hilly terrain to the west of the highway, we can observe the highway’s curve following Earth’s curvature using a long-zoom camera.

Flat-Earthers incorrectly claim that salt flats are perfectly flat and use them to “prove” a flat Earth. In reality, salt flats form a curve following Earth’s curvature, like the ocean’s surface.

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Exalt’s Mediterranean Microwave Transmission Link

One of the longest microwave links is between Lebanon and Cyprus, spanning 235 km (146 miles). To clear Earth’s curvature, both transceivers need to be placed on high ground. In the illustration, we provide an example where we can install both transceivers to establish the link.

Flat-Earthers claim that the link can only be established if Earth is flat. In reality, it is trivial to find locations in Lebanon and Cyprus where we can set up a microwave link between them that clears Earth’s curvature without using any towers and still leaves us with plenty of wiggle room.

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“Stuff is Flat”: Incorrect Neil deGrasse Tyson’s Claim About the Observation of Earth’s Curvature

Neil deGrasse Tyson once incorrectly stated that it is still too close to the surface to see Earth’s curvature from the height of Felix Baumgartner’s jump. In reality, we should be able to see it using our eyes.

Flat-Earthers believe people take Neil’s remarks as gospel and use Neil’s incorrect statement to dismiss any observation of Earth’s curvature. However, we have no problem saying that Neil was wrong. It is OK to be wrong as long as we are willing to revise our views when faced with new facts, and we are certain Neil will.

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Avoiding Challenges and Ignoring Offers of Compensation

Flat-Earthers like to dismiss evidence of spherical Earth as fake. But if we challenge them to witness it themselves, they will avoid it. They will even turn a blind eye to offers to compensate them if their claim of fake evidence is right.

It is a form of willful ignorance. Deep inside, flat-Earthers are not even sure Earth is flat, or even subconsciously understand Earth is a sphere, but they emotionally believe a flat Earth anyway. Unwilling to let go of their belief, they purposefully ignore any evidence against flat Earth.

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Invalid Hypothesis for the Observation of a Distant Object

Flat-Earthers love to observe the visibility of a distant object. But the observation can never prove Earth is flat.

The observation of a distant object can only go as far as to disprove Earth is a sphere with a radius of 3959 miles. A flat Earth is merely one of the so many possibilities, but it is still possible the Earth is a sphere, only much larger.

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Earth’s Curvature and the Size of a Coronavirus SARS-CoV-2 Causing the COVID-19 Outbreak

The surface of the water in a container with a width of one meter (3 ft) will have a curvature of 0.000002 cm from Earth’s gravity. As a comparison, a single SARS-CoV-2 coronavirus is at least 0.000005 cm in diameter, or at least 2½ times larger.

If a SARS-CoV-2 coronavirus is not visible to the naked eye, then there is no reason to expect that we will be able to see the much smaller curvature of the surface of water.

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Dizzib’s Earth Curve Calculator

Dizzib’s Earth Curve Calculator is one of the most popular Earth’s curvature calculator on the Internet. However, it does not account for atmospheric refraction and, therefore, unsuitable for determining the visibility of a distant object.

Many flat-Earthers used Dizzib’s calculator to analyze the observation of the visibility of a distant object and led them to an erroneous conclusion. If we can spot the calculator being used in their images, we can easily rule out their conclusion.

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Magnifying Images Vertically to Reveal Earth’s Curvature

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The horizon appears flat because the curvature is too small when observed from near the Earth’s surface. However, in some cases, we can exaggerate the curve by taking photographs of the horizon and then magnifying the results vertically.

Magnifying in such a way will also magnify the distortions introduced by the camera lens. We will need to control these distortions using proper photography techniques, or by placing a known straight object as a control object in the frame, close to the horizon. If successful, then the remaining curvature in the photograph can only come from the curvature of the Earth.

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The Legendary AutoCAD Diagram Involving the Pythagorean Theorem from Flat-Earthers

There is a legendary diagram of spherical Earth from flat-Earthers that was made using AutoCAD involving the Pythagorean theorem, flaunting the fact that it is was created “using AutoCAD 2016 with 15-digit precision”™. The diagram is not wrong, but it does not account for the height of the observer and atmospheric refraction. And therefore, it is unsuitable for determining the obstruction of a distant object due to Earth’s curvature.

The numbers in the diagram will give us a much higher number than it should be. If a distant object is visible, but according to the diagram it should not, then flat-Earthers will incorrectly conclude that the Earth is flat.

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The Angle of a Distant Object Due to Earth’s Curvature

Due to Earth’s curvature, a distant but still visible object is slightly leaning away from an observer. However, the angle is minuscule and undetectable to any observer.

After being shown photos showing the obstruction of a distant object due to Earth’s curvature, flat Earthers would often shift the topic by pointing out that the tilt due to Earth’s curvature is not apparent in those photos. In reality, the tilt is too small and not visible to our eyes.

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Offshore Wind Farms and the Curvature of the Earth

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Offshore wind farms consist of a series of large turbines having a similar shape and size. In some cases, they are spread over a very large area of water. They are suitable landmarks where we can easily observe the effect of the curvature of the Earth.

If the turbines are far enough, the bottom parts will not be visible and the blades can look as if they are submerged. The phenomenon is only possible if Earth is a sphere.

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Lighthouses and the Loom of the Light

Lighthouses are equipped with powerful lights. In a dark night, even if Earth’s curvature obscures the entire structure of the lighthouse, the phenomenon of the loom of the light allows their lights to be visible beyond the horizon; not unlike how the beam of a green laser is visible to our eyes.

Flat-Earthers like to point out the cases where the light from a lighthouse is visible even if the lighthouse should be completely obscured by Earth’s curvature. They would claim it as “proof” that the Earth is flat. They are wrong. The loom of the light lets us see the light even when the lighthouse itself is below the horizon.

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Zooming In On Distant Boats Does Not Disprove Earth’s Curvature

If a distant boat is not visible, then it is because of at least one of these reasons:

  • Our eyes have limited angular resolution and are unable to resolve the ship at that distance.
  • The atmospheric condition is limiting our visibility.
  • The curvature of the Earth obscures the ship.

Flat-Earthers like to demonstrate that a previously invisible ship at a distance can be made visible by zooming in. They would use it to disprove Earth’s curvature. They are wrong. There are reasons other than Earth’s curvature that can obscure a distant boat.

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Railroads and Earth’s Curvature

Railways are built to follow Earth’s terrain, minimizing the grade/slope as much as possible. Consequently, they all follow Earth’s curvature. And many of them were built by explicitly accounting for the curve of the Earth.

Flat-Earthers claim that railroads are straight, and never built by accounting for Earth’s curvature. They are wrong. The leveling works were done in such a way to minimize the effect of Earth’s curvature. There are also multiple books describing railroad constructions where the curvature of the Earth is specifically accounted for.

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Observation of Earth’s Curvature from Near the Surface

Observing Earth’s curvature is more difficult when we are too close to Earth’s surface. The highest place within reach of the general public is a commercial passenger flight. Even then, it is still difficult to casually discern the curvature of the Earth from an airplane. With some effort, it is possible to observe the curve of the Earth from a location closer to the surface, as long as we are willing to do some planning and careful observation.

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Eight Inches Per Mile Squared

The “eight inches per mile squared” is a rule of thumb to determine the drop height due to the curvature of the Earth. It does not account for the observer’s height and atmospheric refraction. And therefore, the rule is unsuitable to determine the amount of obstruction of a distant object due to Earth’s curvature.

Many Flat-Earthers often use the “8 inches” rule to reach the conclusion similar to “X is visible, but at the distance of Y miles, X should be Z feet below the horizon, so the Earth is flat.” They are wrong. The “8 inches” rule is the wrong tool for the purpose as it does not account for the height of the observer and atmospheric refraction.

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