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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Humber Bridge and Earth’s Curvature

The Humber Bridge, near Kingston upon Hull, East Riding of Yorkshire, England, is a 2.22-kilometer (1.38 mi) single-span road suspension bridge, which opened to traffic on 24 June 1981. When it opened, the bridge was the longest of its type in the world.

The towers, although both vertical, are 36 mm (1.4 inches) farther apart at the top than the bottom due to the curvature of the earth.

References

Flat-Earth “Perspective” is not Real-World Perspective

To an observer, the law of perspective will cause objects moving away in a straight line to:

  1. appear to approach the vanishing point but never quite reach it,
  2. never appear to go across the vanishing point,
  3. appear to shrink in size,
  4. never appear to be cut in half unless when it is obstructed by another object.

If the Earth were flat, sunsets, sunrises, and other general phenomena where objects are not visible due to Earth’s curvature should not occur. To “fix the problem,” flat-Earthers invented the explanation that the apparent obstruction of a distant object can occur on a flat Earth due to “perspective.” Their “perspective” is simply a baseless ad-hoc explanation that does not resemble how the real-world perspective works.

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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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Climbing Higher Reveals Distant Objects

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Because the Earth is a sphere, the surface of Earth obstructs distant enough objects. Climbing to a higher altitude allows us to see farther and more of the previously obstructed objects will become visible, starting from the tops first.

This phenomenon would not occur if the Earth were flat. In a flat Earth, it would not be possible for Earth’s surface to obstruct more of an object —starting from the bottom portions first— if the observer is closer to the surface.

The same thing also happens for objects nearby a large body of water. The surface of the water —which is obviously lower than the object— can obscure the object if the viewer is far enough. Flat-Earthers often invent the “explanation” that Earth’s contour causes the obstruction. This phenomenon can easily prove them wrong.

“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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White Alice and the Troposcatter Propagation

Troposcatter is a signal propagation method using the scattering phenomenon in the upper troposphere. As the signal pass through the upper troposphere, some of the energy is scattered back toward Earth, allowing the receiver station at the correct location to pick up the signal.

White Alice is a decommissioned troposcatter network in North America. Some flat-Earthers invented the “explanation” that the various satellite-based services we enjoy today are using White Alice. They are wrong. White Alice and other troposcatter networks cannot possibly replace all the services provided by satellites.

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Range Estimation Using the Distance to the Horizon

Sailors sometimes need to estimate the range of a distant contact. Without radars, the only readily available reference point for estimating ranges is the horizon.

By knowing the height of the observer from the waterline, it is possible to calculate the distance to the horizon, and thus, it is possible to determine the distance to a remote contact, relative to the horizon. It is possible to do this only because the Earth is spherical.

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Level, Higher and Lower

A higher position is farther up, away from the center of the Earth, relative to sea level. Conversely, a lower position is closer toward Earth’s center, relative to sea level. Two positions are level if they are at the same height from sea level.

Some flat-Earthers are unable to understand this. To them, ‘level’ means straight. They are wrong. In Earth sciences, height is measured from a plane of reference, usually the sea level.

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Ships Disappearing Over the Horizon and the Various “Explanations” Invented by Flat-Earthers

Due to Earth’s curvature, ships traveling over an ocean disappear from the bottom up. This fact is one of the first evidence to confirm the Earth is a sphere, and one of the first facts of which flat-Earthers had to invent various “explanations” for.

Some of the popular “explanations” are: refraction, perspective, zooming reveal distant ships and visibility limitations. None can explain away the fact.

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Suez Canal

The Suez Canal is a waterway connecting the Mediterranean Sea to the Red Sea. The level of water on both seas is practically the same, and the Suez Canal contains no locks system.

Flat-Earthers are claiming that the Suez Canal was constructed without accounting for curvature. They said if the Earth were spherical, then the middle of the canal should have been 1666 ft deep. This is merely a misconception. The surface of the water is equipotential. It has roughly the same distance to the Earth’s center of gravity. It is not necessary to dig 1666 ft in the middle of the Suez Canal. The engineers only need to ensure the base of the canal is below sea level for sea water to flow.

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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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Infrared Vision

When we are unable to see a distant object, then it is due to one of these reasons:

  • Our eyes lack the sufficient angular resolution to recognize the object.
  • Atmospheric condition limits visibility.
  • The object is far enough and obscured by Earth’s curvature.

Some flat-Earthers like to show that a previously unseen distant object can be brought into view using infrared vision. They would take that as ‘evidence’ of the non-existence of Earth’s curvature. They are wrong. Infrared vision can reveal hidden objects caused by visibility limitations, but not ones obscured by Earth’s curvature.

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Sunset, Camera Zooming, and Autoexposure

There are videos showing the sun to appear to set, but after the camera is zoomed in, the sun is still above the horizon. The reason is that the camera’s autoexposure system is constantly adjusting the exposure, and in such scenes, there’s a difference in overall brightness before and after zooming in.

Flat-Earthers are taking such videos as ‘evidence’ of a receding sun. They are wrong. This is merely a matter of photography. In reality, the sun is not receding, and it has the same angular size throughout the day.

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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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Magnetic Dip

Magnetic dip is the angle between the horizontal and Earth’s magnetic field. A compass needle, for example, will not point north and south, but will also have a dip. It tends to dip at an angle toward the Earth (and to the sky). The dip is generally greater toward the pole.  At various locations close to the equator (but not exactly at the equator), the dip is zero.

Magnetic dip as observed on various locations on Earth can only happen if the Earth is spherical.

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