## Correct Hidden Formula

Flat-Earthers like to use the erroneous “8 inches per mile squared” to calculate the height hidden by Earth’s curvature. The following is the correct equation for the purpose, accounting for the observer’s height & atmospheric refraction

$h_\mathrm{h} = { R \over \cos\left[ { s \over R } - \arccos\left( { R \over R + h_\mathrm{O} } \right) \right] } - R$

## Refraction Effect on the Lake Pontchartrain Power Transmission Line

The strength of atmospheric refraction is not constant but varies depending on the weather condition. As a result, a distant object usually obscured by Earth’s curvature can sometimes be visible if the refraction is strong enough.

Lake Pontchartrain transmission towers demonstrate Earth’s curvature. Flat-Earthers like to cherry-pick moments where the towers appear straight, ignoring other cases. In reality, they look straight only because the refraction was strong enough.

## Perspective and the Lake Pontchartrain Transmission Line

The Lake Pontchartrain power transmission pylons demonstrate Earth’s curvature. Flat-Earthers invented various excuses to dismiss the observation, including the excuse that it was just a perspective effect.

If it were just a perspective effect, the same parts of the pylons would line up in a straight line, converging into a distant point. In reality, they do not line up in a straight line but are visibly curving downward due to the curvature of the Earth.

## Lake Pontchartrain’s Horizon Curvature

The Lake Pontchartrain causeway and transmission lines demonstrate Earth’s curvature. Flat-Earthers attempt to dismiss it using aerial photos where it is more difficult to see the curved landmarks over water.

On the other hand, from these alternative vantage points, it becomes easier to reveal the horizontal curvature by magnifying vertically. Because of the possibility of lens distortions, some of the images are inadequate evidence of the curve. However, all of them are insufficient evidence of a flat Earth.

## Perspective Compression: Determining If a Curvature Exists

By utilizing perspective compression, it will be easier for us to observe the curvature of an object if the object is curved.

Flat-Earthers like to deliberately choose a vantage point where it is difficult to see Earth’s curvature, and they use it to “prove” the curvature does not exist. In reality, they only make it more difficult to see the curvature. It does not mean the curve is not there.

## 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.

## Objects Obscured by Earth’s Curvature and Zoom Factor

From an observer on a shore, the distance to the horizon is 5 km (3 miles), or more if the observer is higher. Therefore, Earth’s curvature obscures objects starting from that distance. If the objects are not large enough, we need an optical aid, like zooming in using a camera, to see them in the first place.

Flat-Earthers often show us wide-angle photos to demonstrate that objects are not obscured by Earth’s curvature. In reality, in such photos, objects far enough to be obscured by Earth’s curvature cannot be resolved. It is hard to see objects obscured by Earth’s curvature if the objects themselves are not visible in the picture.

## Misleading “Debunking” of the Lake Pontchartrain Power Lines Images

The various images of the Lake Pontchartrain power lines taken by Soundly and others easily demonstrate the curvature of the Earth. In a desperate attempt to “debunk” the images, a group of flat-Earthers made an “analysis”, but failed to locate the correct power lines. They incorrectly “analyzed” another power lines on the same lake, just not the ones being presented as a demonstration of Earth’s curvature.

The erroneous “analysis” spread in flat-Earth communities as a hoax, as though it “debunks” the actual power lines in the demonstration.

## Climbing Higher Reveals Distant Objects

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.

## 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.

## 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.