Distance to the horizon

A while ago we posted a short video taken on board MSY Wind Surf in the middle of the Atlantic.  Actually, not really the middle, we were about 300 miles from the Azores, but not that far off.  We were part way through a 14 day Transatlantic crossing which started in Barbados and ended up in Lisbon.

The footage was taken outside the Compass Rose bar late morning.

One of the unusual things about the Windstar ships is that they operate an open bridge policy.  When not in port the bridge is open and guests are welcome to visit and ask questions.  On this day that proved useful.  Our conversation went something like this;

How far away is the horizon?  Umm, not sure.  A few miles … or so … maybe more … or perhaps less?

Thinking someone on the bridge should know the answer Ian wandered up there to ask.  As luck would have it the Chief Engineer was present and happy to help.  Such is the beauty of sailing with Windstar: have a question, well ask the Chief Engineer and he may just have half an hour spare.

Anyway, the answer was this: With normal visibility the distance to the horizon, in nautical miles, is 2.1 times the square root of the height, in meters, above sea level.

Distance to horizon = 2.1 * √(height, in meters, above sea level)

In that time we were about 12m above sea level so about 7¼ miles to the horizon.

Taking the maths one step further, if the distance to the horizon was just over 7 nm then the circle of sea that was visible to us was about 165 nm² … and not another ship in sight.  Actually, we hardly saw another ship the entire crossing.

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