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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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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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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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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The so-called “Experiment” Done by Flat-Earthers

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We often see flat-Earthers create a ‘miniaturized physical model’ of a real object and present them as ‘proof’ in support of flat-Earth and against spherical Earth. Their M.O. is to observe if the model remotely resembles the actual object in a particular way. If it does, then it is enough for them to conclude the model describe how the real object works.

Conversely, if a real object cannot be miniaturized and still have the same behavior as the original object, they would conclude that the behavior of the original object doesn’t exist.

They would wrongly call creating such models “doing an experiment”.

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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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Atmospheric Refraction

Light waves are not always moving in a straight line. When it passes through a medium of a different refractive index, the waves will deviate. The phenomenon is called refraction and described according to Snell’s Law.

Earth’s atmosphere has variation in air density that depends on the altitude. As the refractive index changes with the density of the medium, light waves passing through Earth’s atmosphere also experience refraction.

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