At 100 feet above sea level, how far out to sea can I see?

Answer 1

According to BoatSafe, the standard rule for navigators is that the horizon is 1.17 times the square root of your height of eye in nautical miles. So at 100 feet above sea level, you can see 11.7 nautical miles, or 13.46 miles or 21.67 kilometers. [boatsafe]

According to the National Oceanic and Atmospheric Administration, iIf you are high enough, when the air is very clear, you can see objects as much as 90 miles away. [noaa]

Answer 2

Twelve and a quarter miles.

This is an easy geometry problem using the Pythagorean Theorem. Let O be the center of the earth, and draw an arc of the earth's circumference, using radius r.

Draw a radius to where you're standing, 100 feet above sea level. Draw a tangent line from where you're standing to the horizon, far out to sea, and then draw another radius from that horizon point back to the earth's center.

Your tangent line forms a right angle with the earth's radius at the horizon. Let the distance you can see be x, and your height above sea level (100 feet) be h. The two legs of the right triangle are x and r, and the hypoteneuse is x+h.

By the Pythagorean Theorem,

x^2 + r^2 = (r+h)^2 = r^2 + 2rh + h^2
x^2 = 2rh + h^2

You can delete the h^2 term here, because your 100 feet above sea level is nothing when compared with r, the radius of the earth. So that equation becomes

x^2 = 2rh, or x = sqrt(2rh)

The radius of the earth, r, is 3960 miles, so we can rewrite the above equation as

x = sqrt(2*3960) sqrt h = 88.994 sqrt h

which is very nearly equal to

x = 89 sqrt h (Answer One)

Here, h is your height above sea level . Since there are 5280 feet per mile, that formula becomes

x = 89 sqrt(h/5280) = 1.225 sqrt h miles, where h is in feet
(Answer Two).

So for h = 100 feet, your horizon is

x = 1.225 sqrt 100 = 12 1/4 miles away (Answer Three)

Answer Three is what you're looking for -- 12 1/4 miles.

Answer 3

Suppose you are on the beach in a very clear day and you are 100 feet above the sea level. Your question is related with optical resolution of our sight. Eyes are separated about 3 inches, using trigonometry, you maybe can see about 2-3 miles ahead in the point sea and horizont get in touch.

Answer 4

That depends on how close to the sea you are, how clear of a day it is, as well as a variety of other factors. People in Denver, which is a mile above sea level, wouldn't see the ocean. If there is a dense fog, it would be really hard to see regardless of how high you are. So, there probably isn't a definitive answer. There are too many unknowns to determine first.

Answer 5

11-12 miles.
The same as looking at a 100' tower from sea level, which is where I am, and the Owers lightbuoy is 11.4 miles away.

Answer 6

All the way to the horizon