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Old 01-07-2005, 13:40   #1
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Distance to Horizon & Collision Avoidance

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 didn’t 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 didn’t 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

Hence:
For an eye height of 9 Feet (above water level):
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.

Hence:
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 house’s 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.

HTH,
Gord May
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Old 18-06-2009, 17:59   #2
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Thanks Gord, I was vaguely aware of that formula but will have to crush it into my mind until it can't sneak out again. But does this pertain to a radar reflector? I thought that was the point of radar: it isn't line of sight, right?
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Old 18-06-2009, 18:48   #3
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Quote:
Originally Posted by unbusted67 View Post
I thought that was the point of radar: it isn't line of sight, right?
Sorry, Unbusted--radar is line of sight.
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Old 18-06-2009, 19:32   #4
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Ok so higher is better?
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Old 18-06-2009, 19:34   #5
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For distance off ,don't you have to allow for height of tide also,of shore object.Is the structure height measured at mean high or low water?
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Old 18-06-2009, 19:45   #6
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Radar waves refract a little more than light, so the radar horizon is a little further off - 1.23x (sq.rt of antenna height in ft) = range in NM
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Old 18-06-2009, 19:56   #7
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You can't see something over the horizon until enough of "it" is actually seeable. So to see a lighthouse light you'd want to know how high the light is above sea level and probably the bottom of the lens.

Same for a sailboat mast... you won't be seeing the top of a thin mast at those distances as you won't be able to resolve something that small. Perhaps the light at the top... Look at a sky scaper and try to resolve something 6" wide from 10 miles away. The entire sky scraper appears as a block!
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Old 19-06-2009, 01:18   #8
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Bowditch has a nice table for the visible range of lights.
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