Standing on a beach, watching a ship get smaller and smaller, how far are my eyes seeing as the ship disappears from view?
It depends on your [url-http://www.boatsafe.com/tools/horizon.htm]height above ground. About 2.8 miles for a 6-foot person standing on the ground.
Also depends on boat’s mast height.
For the mathematically inclined:
Distance to horizon = sqrt(2hr), where h = your height, and r = the Earth’s radius.
Distance to boat = sqrt(2hr) + sqrt(2Hr), where h and r are the same, and H = height of the mast.
These are fairly close approximations, not exact figures.
- Jeff
It ain’t that hard.
Bowditch gives a nice easy formula:
Distance to horizon in nautical miles = 1.1 x sqrt(h), where h is height in feet of observer.
Or, distance to horizon in statute miles = 1.3 x sqrt(h).
I tend to round these both off to "square root of height in feet is the distance to the horizon in miles. Tres simple…
Furthermore, the distance depends on the direction you look, to a very very small degree.
I disagree with the above calculations with regards to this specific question - when I used to go deep sea fishing we’d lose sight of the tops of buildings over 12 miles out (I think you could still barely see some at 20 miles). A ship that can be seen at the horizon sits pretty high on the water, and I think you can see it a lot further than 3 miles. My citeless answer (but verified by personal experience) is 12 miles.
I’m not sure how that disagrees, Bob55. Using the formulae posted by ElJeffe and MonkeyMensch (actually the same formula, in different units), a building about 150 feet high could be seen out to about 12 miles, and one about 400 feet high could be seen out to about 20 miles. If you’re looking at a big city, these seem like perfectly reasonable heights for buildings.
More personal experience - I can easily see the “Pink Palace” hotel (Don Cesar) in St. Pete Beach, FL up the shore at North Redginton Beach, which is ~10 miles away.