How far to that horizon over there?

February 24, 2010 6:24 AM

Imagine I'm standing on a boat in the middle of the ocean with clear skies all around and good eyesight: how far is the surrounding horizon? And, bonus question, when I look up, how far away are the furthest clouds? (I assume it would depend on how high the clouds are but I'm still completely ignorant of how much difference that would make so any help would be great.)
posted by HopStopDon'tShop to science & nature (9 answers total)

According to this math site 3 miles.
posted by maxpower at 6:29 AM on February 24, 2010

About 3 miles according to Wikipedia.
posted by vacapinta at 6:30 AM on February 24, 2010

The horizon is about 2.9 miles away. See here for more details.
posted by rongorongo at 6:31 AM on February 24, 2010

If you're 3m above the water, the horizon is approximately 3.8 miles away.
It's about 3 miles away if you're actually standing on the water.

Clouds tend to be in a range from 6,500 feet to anything up to 60,000 feet.
posted by le morte de bea arthur at 6:32 AM on February 24, 2010

About clouds: you can kind of tell how high they are by what kind they are. Cumulus clouds, which are the stereotypical cotton-ball clouds, are pretty low, generally starting around 6500 feet. Stratus clouds, which are sheet-like affairs you see when the sky is completely overcast, can get so low they turn into fog. But cirrus clouds, the wispy things some people call Mare's Tails, rarely get below 23,000 feet.

You can also use the clouds to predict the weather over the next day or two. Which is a pretty useful thing to do when you're dealing with the ocean.
posted by valkyryn at 6:41 AM on February 24, 2010

To find the distance to the horizon: Take your height above the water in meters, and multiply by the diameter of the earth, 12,750,000 meters. Take the square root.
So if you are about 2 meters tall, you get 5000 meters, about 3 miles. To double the distance, you'll have to climb to 4 times the height.
If you know the height of the clouds, you can multiply this by the diameter of the earth and again take the square root. Add this to the distance you just calculated, and that gives the distance to the clouds. Using le morte de bea arthur's heights, you get a range of from about 160 km to about 480 km.
All of this is assuming that light travels in straight lines, which isn't really true when there is a temperature gradient as a function of height. But it is good for a rough approximation.
posted by Killick at 6:58 AM on February 24, 2010 [1 favorite]

If there are "clear skies all around," there's no way to tell how far away the furthest clouds are using eyesight.
posted by torquemaniac at 7:10 AM on February 24, 2010 [1 favorite]

related previous question

"According to wikipedia, the formula for distance to the horizon is: sqrt(13h) where h - height above sea level in meters. "


So if you're on a cruise ship and are, say, 15m above sea level, then the answer is roughly 14 km, or 8.67 miles

If you're in a rowboat then the answer is closer to 3.
posted by chrisamiller at 8:09 AM on February 24, 2010

And in all of the above, "height above sea level" means the distance from the water to your eyes.
posted by exphysicist345 at 5:47 PM on February 28, 2010