Can You See This?

Explanation: What are we seeing here? We are on the beach of the Pacific Ocean in Waldport, Oregon, USA.

Here is a critical analysis of a story about the "round world" that you may have heard since childhood. But ... is it true? Can you really see this?

There is a myth that ancient people knew that the Earth is curved because they could see a sailing ship disappear over the curvature of the Earth.

Is this possible?

The Earth curves by approximately 8 inches per mile (20 cm per km).

Let's say that a sailing ship has 20-foot masts.

This means that to detect a ship on the ocean disappearing over the horizon, if at least, for example, 10 feet of the ship was to be over the horizon, the ship would have to be:

(10 ft) (12 inches/ft) / (8 inches/mile) = 15 miles away.
So to detect a 5 foot difference, the ship would have to be 7.5 miles away.

Is it possible for the human eye to detect this?

I photographed an apparently large cargo ship way out on the horizon. I don't know how far out it was (I will guess about 8-10 miles) but it was being blurred by atmospheric refraction, as with a mirage, yet I could still see what seemed to be all or most of the ship body. With the naked eye, the ship was but a dot, and with very a high-power lens it was so blurred that it still was not apparent that part of it was beyond the curvature of the Earth. (The digital camera lens was set at full 48x digital zoom with a 2.2x telephoto lens; the camera's 12x optical zoom was equivalent to a 432mm film camera lens, so the zoom I was using was equivalent to (432)(48)(2.2)/12 = 3802mm. This is a massive zoom.)

Another way to determine the validity of this story is to ask what the smallest angular resolution is of the human eye, and given that if it is possible to detect the curvature of the Earth.

The human eye has an angular resolution of 1-2' (about 0.02-0.03 degrees) of arc, which corresponds to 30-60 cm at a 1 km distance [http://www.answers.com/topic/naked-eye] (or 19-38 inches at a 1 mile distance). This means that the human eye simply can not see anything smaller than 19-38 inches at a mile's distance. Just this fact alone suggests that the naked eye cannot detect a curvature effect of only 8 inches per mile.

So at our "test" distance of 7.5 miles, the eye can detect a difference of height no smaller than (19-38 inches per mile)(7.5 miles) = 142.5-285 inches or about 12-24 feet. But at 7.5 miles, the Earth would curve only (8 inches per mile)(7.5 miles) = 60 inches or 5 feet. At 15 miles, the eye can detect only 24-48 feet but the Earth would curve only about 10 feet. And the confounding effects of atmospheric refraction and blurring along the horizon only complicate this further.

Conclusion: the human eye simply does not have the acuity to detect curvature across the surface of the ocean. Therefore, ancient peoples could not detect the loss of apparent height as a ship sailed away over the ocean's horizon.

Compare this to a hawk's visual acuity of 20/5, or 2.0 to 3.5 times better than a human's (Shlaer, R., An eagle's eye: quality of the retinal image, Science, 176:920-922, 1972).

EPOW - Ecology Picture of the Week