How Far is the Horizon?

 

The distance to the horizon is dependant on the height of your eye above sea level. If you were standing at the water's edge, the height of your eye is the distance from your eye to your feet. From a cliff you need to know the height of the cliff and then add your eye to foot measurement.

 

Once you know your height of eye, use the following formula:

 

1.17 times the square root of your height of eye = Distance to the horizon in nautical miles

 

For example, let's say you are at the top of Walton-on-Naze Navigation Tower, which is 81 ft high, and the cliff at that point is 75 feet high, then you are 156 feet above sea level.

The formula to calculate distance to the horizon is:

 

1.17 times the square root of 156 = Distance to the horizon in nautical miles.

Therefore:

 

1.17 X 12.5 = 14.625 nautical miles

 

If you want to calculate the distance at which an object becomes visible, then you must know your height of eye and the height of the object. You can then carry out the same calculation for your distance to the horizon and the object's distance to the horizon and add the two distances together.

For example:

If you are standing 50 ft above the sea on a ships bridge and looking for the Walton Tower use the same formula for each to the horizon and add the two together.

Tower 1.17 X 12.5 = 14.625 nautical miles

Ship 1.17 X 7.1 = 8.3 nautical miles

 

By adding the two together: 14.625 + 8.3 = 22.9 nautical miles, If you are on board ship 50 ft from sea level you should be able to see the Naze Tower when you are 22.9 nautical miles away.(Assuming exceptional visibility)

 

Note: 1 Nautical Mile = approximately 1.15 Statute Miles