How far can a person see at sea level? A friend tells me 13 miles. Is that correct?
Dan Dickison responds:
Thanks for getting in touch with your question about visibility. The short answer is that a person of average height can see almost three miles at sea level, actually 2.8 miles to be exact. However, that answer assumes that the person's eyes are at six feet above sea level and the conditions are near perfect.
For a more thorough, you might want to look at what John Rousmaniere has written in his very useful tome, The Annapolis Book of Seamanship, but I'll summarize that here. In his chapter on navigation aids, he explains two ranges of visibility. One he terms the "nominal range of visibility," and the other the "geographic range of visibility." The former, says Rousmaniere, relates to the visibility of the light from a lighthouse, for instance. A light from a lighthouse may be bright enough to have a nominal range of visibility that measures 13 miles, but its geographic range of visibility—the distance at which you can actually see the lighthouse—would be much smaller. You can find a standard table of distances listed in Rousmaniere's book on page 214, with references to the height off the water required to see those distances.
The kind of visibility that you're asking about—geographical visibility—refers to the distance at which any object can be seen. This distance is limited by the curvature of the earth, and it's greatly influenced by height. Of course atmospheric conditions will also influence this distance, but for the purposes of this explanation let's just assume they are perfectly clear: no clouds, no haze, no smog. Let's say same the same hypothetical lighthouse is 50 feet tall. According to Rousmaniere's table, it would only be visible for 8.1 miles. Now, if you were standing on deck aboard a medium-sized sailboat and you were of average height, that would put your eyes about 10 feet off the water. From that vantage point, you should be able see 3.6 nautical miles, but you could see the light house at a distance of 11.7 n.m. (According to Rousmaniere's table, the 50-foot-high lighthouse is visible for 8.1 n.m. Combine that with your geographic range of visibility at 10 feet above sea level [3.6 n.m.] and you get a distance of 11.7 n.m.)
So whoever told you that you should be able to see the horizon from the shore 13 miles away was mistaken. If you could climb a 130-foot tower, then yes, you could see 13.1 miles out to sea. Or if the object at sea was 125 feet off the water, then you should be able to see it from a shoreline 13 miles away (125 feet added to your own five-or-so feet of height). I hope that this helps you understand the concepts at work here. If it doesn't, I'd recommend you get a copy of Rousmaniere's book and study that section more closely. Or just get the book anyway because It's a great resource for sailors.