Santa Catalina and the horizon.

The question, “How far is the horizon,” has come up from time to time ever since I first raised it to myself many years ago. In those pre-Internet days, there were no readily available, googleable answers, so I did my own calculation using the Pythagorean theorem and came up with the formula: horizon distance in miles = sqrt(1.5h), where h is the height of your eyes in feet. (Hence the concept of the six-foot-eyed man.)

Of course, this formula is only good in Kansas (the flattest state) or over still water. It also does not take refraction into account, which can allow you to see farther because vertical variation in air density causes light to curve over the horizon. A good explanation of how various formulas may be derived is found here.

The question of how far you can see came up most recently when Dan called me from (I guess) Hermosa beach to describe how well he could see Catalina Island, known to be 26 miles off the coast. (I know this because of a 50s song by one of those ubiquitous quartets like the Four Lads, the Four Freshmen, the Four Preppies, the Four Seasons, the Crew Cuts, etc. that went, “26 miles across the sea, Santa Catalina is awaitin’ for me, Santa Catalina, the island of romance, romance, romance, romance.” Boy, those were the days.) He remembered my statement that a six-foot-eyed man could see only 3 miles across the sea, assuming the weather was clear enough. He estimated that his eyes might be as much as 15 feet above sea level from where he stood, but this would increase the horizon distance to only about 5 miles, give or take. To see 26 miles, one would have to position one’s eyes about 450 feet above sea level. Or, you could be looking at something that is sticking up more than 450 feet above the horizon. Actually, from 15 feet, you could see anything more then about 300 feet above sea level at a distance of 26 miles.

As this link indicates, most of Santa Catalina Island is above 300 feet in elevation. Mystery solved! On a clear day, you can see Catalina, the island of romance, even if you are prone on a surf board, with your eyes scant inches above the water. However, you could not wave to that cute little sweetie on the Catalina beach.

DadExplanations06/07/09 1 comments


Dad • 06/07/09 1:33 PM:

It was the Four Preps

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