Line of Sight: Determining if an Object is Straight or Flat

Light travels in a practically straight line over a short distance. We often use this property of light to determine if an object is flat or straight from visual observation.

Some flat-Earthers start with the wrong assumption that a specific object is flat, then attempt to redefine how our vision works from that. They are wrong. From visual observation, we can determine if an object is flat, not the other way around.

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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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Leveling is the process of determining the elevation of a point relative to another point. The curvature of the Earth and atmospheric refraction affect the result of leveling. There are techniques and formulas to correct the effect of Earth’s curvature and atmospheric refraction.

Flat-Earthers assume that construction works like roads, bridges, railways, etc. are built without accounting for Earth’s curvature. They are wrong. The leveling in such works are done in such a way it minimizes the errors due to Earth’s curvature and atmospheric refraction.

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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 curvature itself. We can only directly see the curvature from a significant 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. Witnessing such an effect of Earth’s curvature is different from witnessing the curvature itself.

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A railgun is an experimental weapon that uses electromagnetic force to launch high-velocity projectiles. Some railguns are expected to have a range of more than 200 miles.

Flat-Earthers claim that a railgun round always travels straight. And because it can hit targets beyond 200 miles, they use it as “proof” Earth’s curvature does not exist. They are wrong. In reality, railgun rounds are projectiles. The same law of physics that applies to bullets, arrows, or thrown rocks also applies to them. The rounds are affected by air resistance and Earth’s gravity, and will not travel straight for very long. Railguns are capable of hitting targets obstructed by Earth’s curvature and are not proof that Earth’s curvature does not exist.

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Laser Guidance

Laser guidance is used by the military to guide a missile toward a target.  A laser designator marked a target by pointing a laser beam at it. The signals bounce off the target into the sky, where they are detected by laser-guided munition, which steers itself toward the center of the reflected signal.

A laser-guided missile can be launched toward a target behind Earth’s curvature. Flat-Earthers claim it proves a flat Earth as it would have been impossible for the launcher to point a laser beam at the target. They are wrong. The laser designator does not have to be the launcher itself. It can be another unit closer to the target, such as infantry or an aircraft.

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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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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.


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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