If I'm standing 50 feet above the Ocean, how far out can I see on a clear day?

Answer 1

d^2 = (R + h)^2 - R^2
d^2 = R^2 + 2hR + h^2 - R^2
d^2 = 2hR + h^2
d = √(2hR + h^2)
d = √h(2R + h)
but 2R = D, so
d = √h(D + h)
h = 50 ft.
D = 7,926.41 mi. = 41,851,444.8 ft. (equatorial)
41,851,444.8 >>> 50, so a good approximation is
d = √hD
Since we desire an answer in miles, using feet for input,
d = √h(7,926.41/5,280) ≈ √1.501214h ≈ √3h/2
d(50) ≈ √3(50)/2 ≈ 8.660254 mi. ≈ 8 2/3 mi.

In metric
d = √h(12,756.32/1,000) ≈ √12.75632h ≈ √13h, with input in meters and output in kilometers
50 ft = 50/3.2808399 = 15.24 m
d = √13*15.24 ≈ 13.94297 km ≈ 14 km

Answer 2

what ocean are you staring over, there are huge factors that will effect this... How good is your sight? i would say 30-40Miles...

(side note)plus you can see millions of miles... look at the sun... it just depends on the size... lol... but for earth the most distance that you can see is near the mountains were the water in the air makes the mountains disappear(you can see around the mountains..) and that is i think about 30 Miles...

Answer 3

distance to horizon:
d = sqrt (2Rh + h^2)
where h is the height of eye and R is the earth's radius.

The wiki page has some good shortcuts you can also use for h << R.

d (in km)= sqrt (13h (in meters))

So 50 feet is about 15 meters. sqrt (15*13) is about 14. 14 km is about 9 miles.

Answer 4

12 miles

Answer 5

according to the "distance to the horizon" calculator

(located at http://www.boatsafe.com/tools/horizon.htm)

standing at 50 feet, you'll be able to see 9.51 miles

Answer 6

8.27 nautical miles...

I used the formula 1.17 (sqrt of height of your eye in feet)
1.17 (sqrt 50)

This is a standard I learned in navigation class

Answer 7

I have heard that the farthest we can see is 25 miles, don't know how true that is though.

Answer 8

well abt 30 miles

Answer 9

To the horizon.