How far away is the hoizon when your onboard a ship in the middle of the ocean?

Answer 1

i've heard anecdotally it is about 40 miles

Answer 2

With the following assumptions, the calculation is a fairly straightforward pythagoras.
Assumption1. the earth is spherical (it's actually an oblate spheroid, but for a normal ship, the difference is negligible).
Assumption 2. the sea is calm, this can make a big difference, if the wave height is of the same order of magnitude as your eye level above the mean sea level.

Draw a circle, with one line going through its centre to the circumference and another at about 30 degrees to it but extending slightly beyond the circumference. Draw a tangent from the 1st line to the point where it crosses the extended line. This intersection represents your eye height (h) above sea level, and the distance from the intersection to the tangent point is the distance (d) to the horizon. If R is the radius of the earth, then by Pythagoras d^2 + R^2 = (R + h)^2, or the distance d is the square root of (R + h)^2 - R^2.
By the original definition of the metre, 10 million metres is the distance from the North Pole to the equator, so the circumference of the Earth is 40 million metres. The radius is therefore 40 Mm divided by 2 π which is approx 6366198 m.

So if, for example the height of your eye above sea level is 30m (the lookout cage of the Titanic), then the distance d to the horizon will be the square root of :-
(6366198+30)^2 - 6366198^2
which is 19544 m or about 19.5 km.

Answer 3

There is a simple formula derivable via Pythagoras' theorem which holds provided you are not too high up. It is similar in derivation to the one above but a simplification must be used to eradicate errors caused by subtracting similar numbers using a calculator or computer.

It is: distance to horizon = square root(2 x radius of earth x height above sea) so say you are on deck 30m high and a planet of radius of 6380 km (like the earth) this equates to: horizon ~ 19.5km - double it for every 4x increase in height - this will hold upto a height of 60km to an accuracy of 1%, so also applies in an aircraft.

But there are other effects to take into account, if the air at the sea surface is cooler & denser that higher up, which will be the case if there is a breeze, light will be lensed around the curve of the earth increasing the distance to the horizon.

If there is a swell, the horizon will come and go as you go up and down, but the waves of the swell will block your view. On the equator you will see a tiny tad farther east west than north south due to the slight elipsoid shape of the earth. You would have the longest view at the north pole if the ice were flat.

Answer 4

It's further away than on land (am I stating the obvious).
It's just that when I saw the 1999 total eclipse from a ship in the English Channel you could see outside the path of totality during totality, producing a bright golden sunset like horizon all around below the deep blue/black eclipsed sky.

Answer 5

How tall is the ship? I was on the eleventh deck of a cruise ship and I could see Freeport, Bahamas 19 miles away. I had a GPS and I am sure I could see further from this lofty perch.

In a single deck sailboat on fairly calm seas, you can see about 12 miles.

Answer 6

An average sized man see the horizon at a distance of about 22 miles on a flat surface.

Answer 7

It all depend on how high above the water you are - it could be 3 miles, say, at 6 feet up. But if there is a lot of swell, the horizon could be only 20 feet away!

Answer 8

7 miles standing on the ground; 10 miles 6 feet higher.

Answer 9

It is 27.97miles for a 6ft man standing at sea level with a calm ocean.
For anyone who said less than 20 miles.
Stand at Dover and look towards france,can you see it?
I say no more

Answer 10

It varies with the height of your eye above the sea, and tables are available for use of seamen. Examples:
Eye height 10m (33ft), horizon 6.6 nautical miles
Eye height 40m (131ft - you're on top deck of a big liner!), horizon 13.3 miles.

Answer 11

from six feet above the water the horizon is 3.2 miles. For other numbers use one more times excellent link.....

for the people who said 20 or 30 or 40 miles.........geeeeeez!
Optimistic thinking.......