Hi there dwilliams - what a great (and tricky) question!
If you're standing on the beach and seeing 16 miles, it seems that
you're doing a lot better than the mathematicians would like! The
horizon at sea level is around three miles away.
It's difficult to give very accurate figures, for a number of reasons:
1) The earth is not a perfectly shaped sphere, so depending on where
you're standing, the numbers will differ slightly.
(See: http://regentsprep.org/Regents/earthsci/units/introduction/oblate.cfm
)
2) The atmosphere distorts light, allowing you to sometimes see "over"
the horizon - that is, it bends the light and carries it further - in
some cases, for tens of miles. This is also how the mirage effect
works.
(See: http://www.islandnet.com/~see/weather/elements/mirage1.htm )
3) In addition to the earth's odd shape, there are local contours like
hills, or seas which move tidally, and these make the measurement
harder still.
With those caveats in mind:
The commonly accepted way of measuring the distance to the horizon is
to assume the earth is a perfect sphere, and work out where the
horizon would be on that perfect sphere. A good formula I found to do
this is:
"Distance to horizon in miles = square root(height above surface in
feet / 0.5736)"
(See http://www.howstuffworks.com/question198.htm for more
information).
Therefore:
-- If you were six feet tall, standing at sea level, the horizon would
be 3.2 miles away.
-- If you were at 100 feet from sea level, you would see 13.2 miles to
the horizon.
-- And if you knew the horizon was 16 miles away, you'd be at 146 feet
above sea level (the rearranged formula is: height = distance squared
multiplied by 0.5736)
I hope this answers your question. If anything's unclear, or needs
further explanation, then please don't hesitate to use the "request
clarification" feature before rating this question.
Further information:
An online tool to calculate the distance (gives slightly different
results): http://www.boatsafe.com/tools/horizon.htm
A mathematical explanation of how to calculate this distance:
http://www.sailingissues.com/vier/mathproof2.html
Thanks,
--seizer-ga
Search strategy:
distance to horizon
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