From a height of six feet above sea level, looking out onto a clear sea, how far away is the horizon?

mutchisman

According to this web-page the calculation is made by finding the square root of the height of your eyes (in feet) and multiplying that value by 1.17. The square root of 6 is 2.45; multiply that by 1.17 and you get an answer of 2.86 nautical miles. http://www.boatsafe.com/kids/distance.htm Jun 06 07, 11:31 PM

davejacobs

Or 3.29 real miles! Jun 07 07, 8:18 AM

gmackematix

The situation involves a right angled triangle involving the distances from the eyes to the centre of the Earth (R+h), from the horizon to the centre of the earth (R) and the required distance to the horizon x. Suppose all distances are in feet. By Pythagoras, x = Sq rt ((R+h)^2 - R^2) = Sq rt (2Rh + h^2) Given that R is the radius of the Earth, then h^2 is so small compared to 2Rh ignoring it won't affect our approximate result. So x ~ Sq rt (2Rh) = Sq rt (2R) * Sq rt h The radius of the Earth is about 3,960 miles or 3,960 * 5,280 = 20,908,800 feet. So Sq rt (2R) ~ 6,467. So x in miles ~ 6,467/5,280 * Sq rt h ~ 1.22 * Sq rt h. For h = 6 ft, I make x to be as near as dammit 3 miles. I guess what I'm trying to say is yay, Mutch! Jun 07 07, 7:50 PM