# Scope (light)

Scope is a nautical term and indicates how far a light, for example a beacon , can be seen.

## scope

The range is the distance at which a beacon is barely perceptible to the naked eye at night, provided the observer is high enough to theoretically see it directly because it is not shadowed by the horizon, for example.

The range depends on the light intensity of the light source measured in candela on the one hand, and the visibility or cloudiness of the atmosphere on the other hand ( absorption and scattering by rain, snow, fog or other). The luminous intensity of the light source results from its luminous flux and the bundling of rays ( lens , headlight ).

## Nominal range

The nominal range is the value given in the beacon list. The nominal range is independent of the weather. It is the scope under specified standard conditions of the atmosphere. The nominal range applies to a visibility of 0.74 and an atmospheric visibility of 10 nautical miles in daylight, measured with a contrast threshold of 0.05 and 5%, respectively.

For example, a fire with a nominal range of 25 nautical miles is only visible 1.2 to 2.2 nautical miles in light fog. Red coloring reduces the range to about 80%, green coloring to 90% compared to the white light.

## Nautical visibility

Eye height h, fire height H

The nautical visibility describes the distance at which a fire becomes visible, which may initially still be behind the horizon . In addition to the scope, it is also dependent on the eye level (h) of the observer and the fire height (H) of the observed object. It is made up of the distance from the beacon to the horizon, and the distance from the observer to the horizon ( chiming distance ). The straight line between the beacon and the observer touches the horizon as a tangent:

${\ displaystyle {\ text {Visibility}} = 1 {,} 93 \ cdot \ left ({\ sqrt {\ frac {h _ {\ text {Beacon}}} {\ mathrm {m}}}} + {\ sqrt {\ frac {h _ {\ text {eye level}}} {\ mathrm {m}}}} \ right) \, {\ text {nautical miles}}}$

or

${\ displaystyle {\ text {Visibility}} = 3 {,} 57 \ cdot \ left ({\ sqrt {\ frac {h _ {\ text {Beacon}}} {\ mathrm {m}}}} + {\ sqrt {\ frac {h _ {\ text {eye level}}} {\ mathrm {m}}}} \ right) \, \ mathrm {km}}$

Decisive for the visibility of a beacon is the smaller value of range or visibility, reduced by poor visibility (fog, rain), brightness on board, on land or in the sky (moon), or by obscuration by the coast or high waves. With good atmospheric visibility and a suitable nominal range, the visibility is often even greater because, although not the beacon itself, you can see its scattered light over the horizon or its reflection on low-hanging clouds.

${\ displaystyle {\ text {Visibility}} = {\ text {Visibility}} _ {\ text {left table}} + {\ text {Visibility}} _ {\ text {right table}}}$
Eye level Visibility
01 m 03.6 km
02 m 05.0 km
03 m 06.1 km
04 m 07.1 km
05 m 08.0 km
06 m 08.7 km
07 m 09.4 km
08 m 10.0 km
09 m 10.7 km
10 m 11.3 km
+
Tower height Visibility
010 m 011 km
020 m 016 km
030 m 019 km
040 m 022 km
050 m 025 km
060 m 027 km
070 m 029 km
080 m 031 km
090 m 033 km
100 m 035 km
200 m 050 km

In most cases, however, the actual range of vision to the horizon is increased by approx. 10% through refraction from the earth's atmosphere. This results in the formula, which is more common in shipping:

${\ displaystyle {\ text {Visibility}} = 2 {,} 1 \ cdot \ left ({\ sqrt {\ frac {h _ {\ text {Beacon}}} {\ mathrm {m}}}} + {\ sqrt {\ frac {h _ {\ text {eye level}}} {\ mathrm {m}}}} \ right) \, {\ text {nautical miles}}}$

or

${\ displaystyle {\ text {Visibility}} = 3 {,} 9 \ cdot \ left ({\ sqrt {\ frac {h _ {\ text {Beacon}}} {\ mathrm {m}}}} + {\ sqrt {\ frac {h _ {\ text {eye level}}} {\ mathrm {m}}}} \ right) \, \ mathrm {km}}$

A precise derivation of these formulas can be found in the article Geodetic Visibility