I'm told that the sailors of old always knew that the hulls disappeared from view first, and the mast tops and crows nest's last, so they knew the earth was curved rather than flat when, for example, Christopher Columbus sailed away.
https://www.quora.com/What-is-the-di...-level?share=1
Originally Answered:
How far is the horizon at sea level?As mentioned by others,
the distance to the horizon at sea level (assuming you mean looking out over calm water) depends on what elevation you are viewing from. A good approximation for this when your observing height is relatively small compared to the radius of the Earth (in effect, not from the ISS!) is 𝑑=2𝑅ℎ‾‾‾‾√d=2Rh, where d is the distance to the horizon, R is the radius of the Earth, and h is the observation height.
As
Chris Spencer wrote, this can be approximated as 𝑑=3.57ℎ‾‾√d=3.57h where h is in meters and d is in kilometers, or 𝑑=1.22ℎ‾‾√d=1.22h where h is in feet and d is in miles.
This would be great if we were on an airless planet, but in fact the distance to the horizon changes depending on the amount of atmospheric refraction, a function of temperature and pressure. In most cases, the atmosphere bends light rays downward, moving the horizon farther out. The equation is quite complicated and depends on knowing the atmospheric conditions quite precisely. However a reasonable approximation is either to increase the distance by 8%, or to replace the Earth’s radius by its effective radius, approximated to be 7/6 R. In which case the formulas become 𝑑=3.86ℎ‾‾√d=3.86h and 𝑑=1.32ℎ‾‾√d=1.32h.
Assuming an average overall height in the US, this would mean that
the horizon IS 2.87 miles away, but appears to be 3.11 miles away.