Distance to horizon & Collision Avoidance:
From a height of eye of 6 feet, the distance to the horizon is 2.6 miles in calm conditions . This means that, another man in another similar vessel could be seen 5.2 miles away. An approaching ship with a superstructure height of typically 60 feet might be seen (if you are keeping a good lookout) about 11.5 miles away.
If you are doing 5 knots, and he is doing 10 - 15 knots - your closing speed could be 20 knots, leaving you less than 35 minutes before you meet (collide)
If you wish to avoid a close quarters situation, you need to take "early and substantial action" as required by the International Rule
of the Road
(you knew about that didnít you )
The reality of all this is that you actually have about 15 minutes to decide on, and take, the necessary action to avoid coming into close quarters. Of course if there is a swell running, or if there is reduced visibility, or you didnít immediately
spot the other vessel (at 11.5 mi distance) this warning time can be reduced even further.
How Far is the Horizon?
Due to the curvature of the earth, the higher the height of your eye (above sea level) the farther you can see, and vice versa.
If you want to know the distance to the visible horizon, you simply have to know the height of your eye above water
level. If you're in a sailboat, that might be less than 9 feet.
Distance to the horizon (nautical miles) = 1.17 x square root of your eye-height
For an eye height of 9 Feet
Dist. to Visible Horizon = 1.17 x Root 9 = 1.17 x 3 = 3.51 Nautical Miles
For an eye height of 7.5 Feet
Dist. to Visible Horizon = 1.17 x Root 7.5 = 1.17 x 2.7386 = 3.20 Nautical Miles
If you want to calculate the distance at which an object becomes visible, you must know your height of eye - AND the height of the object. You then do the same calculation for your distance to the horizon and for the object's distance to the horizon - and add the distances together.
You have the same height of eye of 9 feet so your distance to the horizon is still 3.51 nautical miles.
You're approaching a port that has a lighthouse that is shown on your chart to have a height of 81 feet. Using the same formula, you would find that 1.17 times the square root of 81 (1.17 x 9) = 10.53 nautical miles (the light houseís horizon is 10.53 nautical miles)
Add the two together: 3.51 + 10.53 = 14.04 nautical miles - you will first be able (theoretically*) to see the top of the lighthouse from 14.04 nautical miles away.
Of course these calculated distances could be reduced (in the real world) by atmospheric conditions (Darkness, Fog
, Rain, Dust, etc) and/or poor eyesight.