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# Water's Edge: Newsletter Challenge (03/15/05)

Posted March 21, 2005 8:03 AM

The question posed in the March 15th edition of Specs & Techs from GlobalSpec:

"When standing at the water's edge, looking out over the ocean, how far away is the horizon? Is there an equation to figure it out?"

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Anonymous Poster
#1

03/24/2005 10:23 AM

You can find the answer to the March 15 newsletter Challenge Question by reading it in the March 22 issue. All answers can be found in the following issue.

Because of the curvature of the Earth, the distance to the horizon depends on the height of your eyes above the water. Here's a rough formula you can use to calculate the distance between yourself and the horizon:

sqrt(height in feet above surface / 0.5736) = number of miles

For instance, if you were 6 ft. tall, your eyes would be approximately 5.5 ft. above the surface, and the answer would be roughly 3 miles.

(For those whose browsers may not be displaying some of the symbols correctly, you would divide the height above the surface by 0.5736, and then take the square root of that answer to know the number of miles. For the metric equivalent, the "height above the surface" would be in centimeters, you would divide by 6.752, take the square root of that answer, and the final distance to the horizon would be in kilometers.)

Anonymous Poster
#2

### Re: Water's Edge: Newsletter Challenge (03/15/05)

03/15/2007 7:56 AM

Actually, I believe the correct formula (for nautical miles) is 1.17 tiimes the square root of the height of eye in feet.

Denny

Participant

Join Date: Mar 2007
Posts: 1
#3

### Re: Water's Edge: Newsletter Challenge (03/15/05)

03/15/2007 2:03 PM

d = [h(2R + h)]^0.5

d: the far away distance

h: the person's tall looking out over the ocean

But 2R >> h, so

d = [2Rh]^0.5

Simply use Pythagora's Theorem.