The U.S. Coast Guard Light List usually lists a light’s nominal range. Use the Luminous Range Diagram shown in the Light List to convert this nominal range to luminous range. Remember that the luminous ranges obtained are approximate because of atmospheric or background lighting conditions. To use the Luminous Range Diagram, first estimate the meteorological visibility by the Meteorological Optical Range Table. Next, enter the Luminous Range Diagram with the nominal range on the horizontal nominal range scale. Follow a vertical line until it intersects the curve or reaches the region on the diagram representing the meteorological visibility. Finally, follow a horizontal line from this point or region until it intersects the vertical luminous range scale.

**Example 1**

The nominal range of a light as extracted from the Light List is 15 nautical miles.

Required: The luminous range when the meteorological visibility is (1) 11 nautical miles and (2) 1 nautical mile.

Solution: To find the luminous range when the meteorological visibility is 11 nautical miles, enter the Luminous Range Diagram with nominal range 15 nautical miles on the horizontal nominal range scale, follow a vertical line upward until it intersects the curve on the diagram representing a meteorological visibility of 11 nautical miles, from this point follow a horizontal line to the right until it intersects the vertical luminous range scale at 16 nautical miles. A similar procedure is followed to find the luminous range when the meteorological visibility is 1 nautical mile.

Answers: (1) 16 nautical miles, (2) 3 nautical miles.

To predict the bearing and range at which a vessel will initially sight a light first determine the light’s geographic range. Compare the geographic range with the light’s luminous range. The lesser of the two ranges is the range at which the light will first be sighted. Plot a visibility arc centered on the light and with a radius equal to the lesser of the geographic or luminous ranges. Extend the vessel’s track until it intersects the visibility arc. The bearing from the intersection point to the light is the light’s predicted bearing at first sighting.

If the extended track crosses the visibility arc at a small angle, a small lateral track error can result in large bearing and time prediction errors. This is apparent if the vessel is farther from the light than predicted, the vessel may pass the light without sighting it. However, not sighting a light when predicted does not always indicate the vessel is farther from the light than expected. It could also mean that atmospheric conditions are affecting visibility.

**Example 2**

The nominal range of a navigational light 120 feet above the chart datum is 20 nautical miles. The meteorological visibility is 27 nautical miles.

Required: The distance at which an observer at a height of eye of 50 feet can expect to see the light.

Solution: The maximum range at which the light may be seen is the lesser of the luminous or geographic ranges. At 120 feet the distance to the horizon, by table or formula, is 12.8 miles. Add 8.3 miles, the distance to the horizon for a height of eye of 50 feet to determine the geographic range. The geographic range, 21.1 miles, is less than the luminous range, 40 miles.

Answer: 21 nautical miles. Because of various uncertainties, the range is rounded off to the nearest whole mile.

When first sighting a light, an observer can determine if it is on the horizon by immediately reducing his height of eye. If the light disappears and then reappears when the observer returns to his original height, the light is on the horizon. This process is called bobbing a light.

If a vessel has considerable vertical motion due to rough seas, a light sighted on the horizon may alternately appear and disappear. Wave tops may also obstruct the light periodically. This may cause the characteristic to appear different than expected. The light’s true characteristics can be found either by closing the range to the light or by increasing the observer’s height of eye.

If a light’s range given in a foreign publication approximates the light’s geographic range for a 15 foot observer’s height of eye, you can assume that the printed range is the light’s geographic range. Also assume that publication has listed the lesser of the geographic and nominal ranges. If the light’s listed range approximates the geographic range for an observer with a height of eye of 15 feet, then assume that the light’s limiting range is the geographic range. Then, calculate the light’s true geographic range using the actual observer’s height of eye, not the assumed height of eye of 15 feet. This calculated true geographic range is the range at which the light will first be sighted.

**Example 3**

The range of a light as printed on a foreign chart is 17 miles. The light is 120 feet above chart datum. The meteorological visibility is 10 nautical miles.

Required: The distance at which an observer at a height of eye of 50 feet can expect to see the light.

Solution: Calculate the geographic range of the light assuming a 15 foot observer’s height of eye. At 120 feet the distance to the horizon is 12.8 miles. Add 4.5 miles (the distance to the horizon at a height of 15 feet) to 12.8 miles, this range is 17.3 miles. This approximates the range listed on the chart. Then assuming that the charted range is the geographic range for a 15 foot observer height of eye and that the nominal range is the greater than this charted range, the predicted range is found by calculating the true geographic range with a 50 foot height of eye for the observer.

Answer: The predicted range = 12.8 mi. + 8.3 mi. = 21.1 mi. The distance in excess of the charted range depends on the luminous intensity of the light and the meteorological visibility.

The formula for the Geographic Range Table is based on: √ = square root key

Distance to the horizon = √ height x 1.17

By knowing the formula it will save you time in having to look the distance up in the tables. Since the table does not tabulate distance for each foot. I would recommend using a calculator and the formula to get the distances.

**Example 4**

Ht of Lt. = √ 65 ft = (8.0622577) x 1.17 = 9.43 or 9.4 miles

Ht of Eye = √ 35 ft = (5.9160797) x 1.17 = 6.92 or 6.9 miles

Geographic Range (GR) = 16.3 miles