One of the most common rebuttals to people who believe the Earth is flat (aside from the countless experiments, equations of gravitation, camera and satellite footage, Einstein’s theory of relativity and time dilation, insert pretty much endless evidence here) is that one can observe the curvature of the planet from a passenger airplane at cruising altitude. But is that true?

Well, sort of. Here’s what that means.

Starting On The Ground

One of the ways the ancient Greeks concluded the Earth is spherical was by observing ships on a horizon. Boats moving away from an observer on the beach disappear – with the appearance that they are sinking into the sea. This illusion happens because the ship is moving further along the curve of the Earth. (Tape a box of matches to a beach ball, put it close to your face, then rotate it for a miniature version.)

We have several components of an equation, courtesy astrophysicist David Lynch, that can be used to calculate the curvature of the Earth. By measuring how much of the boat falls below the horizon based on the distance from the observer at sea level, the radius of our planet can be calculated. Alternatively, if we take the radius of Earth for granted (and trust what’s already been proven) we can also determine the Earth’s radius.

• The entire formula can be seen here.

In short, the higher in altitude you are, the further you can see – a direct result of you moving up and the horizon of the Earth being lower in relation to you.

As DrGC describes the following image:

“Cartoon defining the variables used above. d is the distance of visibility, h is the elevation of the observer O above the sea level.”

Plug in the numbers and at 10,000 meters (~35,000 feet) the horizon of the Earth will appear 3 degrees lower than at sea level (remember the ship falling below the horizon above).

Seeing any observable curvature from a plane is difficult for several reasons:

1. Airplane windows distort light coming into the plane, in other words, they add a curvature effect not too unlike a wide-angle lens.
2. Using the formulas above, you would need a roughly 60 degree field of view to see any curvature –  a standard passenger window doesn’t isn’t enough.
3. A clear sky over the ocean is a must. The figure below illustrates why a plane just isn’t high enough for a clear curved view.

Relative to the Earth’s size, you’re not really all that high up. Fortunately there are lots of experiments you can do from the ground to prove the Earth is round shown in the video below.

Or just send up a camera on a weather balloon.

Finally, if you want to do more aerial mathematics, here’s how to calculate the angle at which your plane turns on its side or the angle up during takeoff.