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

“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.

## 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.

## General Information

• Claimed by: GARY IS RIGHT! (YouTube)
• Object 1:
• Name: CN Tower
• Height: 1815 ft (553 m)
• Distance: 30 miles (48.3 km)
• Object 2:
• Name: First Canadian Place
• Height: 951 ft (290 m) (top floor)
• Distance: 30 miles (48.3 km)
• Observer:
• Location: Niagara-on-the-Lake pier
• Elevation: unspecified, assumed to be 2 m

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## Fisheye Lenses Can Make Curved Lines Appear Flat

A fisheye lens distorts images. It results in images having barrel distortions. In a fisheye lens, a straight line can appear curved. But some flat-Earthers don’t realize that the opposite is also true, a fisheye lens can easily make a curved line look straight.

## 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.

## 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.

## Curvature of the Horizon in High-Altitude Balloon Footage

High-altitude balloon footage is often abused by flat-Earthers to show us that the Earth is flat when seen from a high altitude.

We analyzed more than two dozens of footage taken from high-altitude balloons on YouTube, and we can easily conclude the curvature is there and usually easy to spot, including in the cases where flat-Earthers use the video as ‘proof’ of a flat Earth.

## Equipotential: a Property of the Surface of Water

Gravity causes water to seek the lowest potential, which can be simplified as the position as close as possible to the Earth’s center of gravity. As a result, the surface of the water will have equipotential surface and form an approximately spherical surface which has the same center as the Earth. Every location along the surface has the same potential.

## Long-Range Wi-Fi and the Curvature of the Earth

Wi-Fi is one of the most common ways of getting connected to the Internet. Practically all short-range wireless network use WiFi. Using specialized equipment, Wi-Fi is usable over a very long distance, even over hundreds of miles.

When designing a long-range Wi-Fi link, we must account for the curvature of the Earth.

## Lake Pontchartrain Power Transmission Lines: Evidence of Earth’s Curvature

Lake Pontchartrain is a lake in Louisiana, United States. There are power transmission lines about 24.27 km (15 mi) across this lake. They are practically straight, and each tower is uniform and has the same height, making these towers ideal for observing the curvature of the Earth.

They were first popularized by Soundly who presented evidence of Earth’s curvature using a series of photos and videos of the power lines in June 2017. As of now, the towers and other objects on the lake are probably the most popular Earth curvature tourism spot in the world.

## Surface of Water and Communicating Vessels

Gravity is not the result of a particular shape of an object. It is caused by mass. All objects with mass exert gravity to each other. The larger the mass of an object, the greater the force of gravity.

On Earth, water forms a spherical surface which has the same center as the Earth. It applies to every surface of fluid which is under influence by Earth’s gravity, unaffected by another force. In a 10 cm wide container, the amount of curvature is only 0.0000002 mm. It is the reason the surface appears flat in small containers.

## The Little Piggy Balloon Footage Proves Earth is a Sphere, not Flat

Little Piggy is the nickname of a helium balloon launched by IndianaCaver. It reached the altitude of almost 37 km before it finally ruptured and fell to the Earth. Before that, it took several hours of video, and IndianaCaver made these video available on YouTube.

Then, some flat-Earthers cherry-picked bits of the video where the horizon looked flat and presented it as ‘proof’ of flat-Earth. These are widely circulated in various memes and forms, even years after the originals were published.

But, can we use these videos as ‘proof’ of flat-Earth?

## Sunset at Burj Khalifa

Having the total height of about 830m, Burj Khalifa is the tallest building in the world. It is so tall that we can observe the sunset at the base of the building, then rush to the upper floors and watch the same sunset again for the second time on the same day.

This phenomenon can only happen if the Earth is a sphere. On a higher position, we will observe the sunset later than when we are closer to the ground.