A nomogram is presented for predicting the sighting range for white, steady-burning signal lights. The theoretical and experimental bases are explained and instructions are provided for its use for a variety of practical problems concerning the visibility of signal lights. The nomogram is appropriate for slant path as well as horizontal sightings, and the gain of range achieved by utilizing binoculars can be predicted by use of it.
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Full Moon, or no moon with solar depression angle of 10°
3.4 × 10−3
Half Moon, or no moon with solar depression angle of 13°
3.4 × 10−4
Starlight or solar depression angle ≥ 18°
3.4 × 10−5
Overcast starlight
These values are consistent with full daylight, twilight, and starlight data of Hulburt and co-workers, Ref. 18. Full-moon-light values were scaled down from full sunlight by the ratio of sun illuminance from Johnson, Ref. 19, to moon illuminance from Sytinskaya, Ref. 20. The moon phase ratio came from Russel, Ref. 21.
Where sunset is defined as a sun depression angle of 0.8°.
TABLE III
International visibility code.
Code number
Daylight visual range VV
Weather fog, mist, haze
Attenuation length Ξ (km)
Attenuation coefficient (km−1)
0
<50 m
dense fog
<0.017
>60
1
50–200 m
thick fog
0.017–0.067
60–15
2
200–500 m
moderate fog
0.067–0.17
15–6.0
3
500–1000 m
light fog
0.17–0.33
6.0–3.0
4
1–2 km
thin fog
0.33–0.67
3.0–1.5
5
2–4 km
haze
0.67–1.3
1.5–0.75
6
4–10 km
light haze
1.3–3.3
0.75–0.30
7
10–20 km
clear
3.3–6.7
0.30–0.15
8
20–50 km
very clear
6.7–17
0.15–0.06
9
> 50 km
exceptionally clear
>17
<0.06
TABLE IV
Equivalent attenuation length at altitude divided by attenuation length at ground level and
for the optical standard atmosphere.
Altitude (km)
Altitude (km)
0
1.0
0
7
1.43
4.89
0.5
1.03
0.487
8
1.50
5.33
1.0
1.06
0.947
9
1.57
5.73
1.5
1.08
1.38
10
1.64
6.08
2.0
1.11
1.80
12
1.80
6.68
2.5
1.14
2.19
14
1.95
7.16
3.0
1.17
2.56
16
2.12
7.55
3.5
1.20
2.91
18
2.29
7.86
4.0
1.23
3.24
20
2.46
8.12
4.5
1.27
3.55
25
2.92
8.55
5
1.30
3.85
30
3.41
8.80
6
1.36
4.40
60
6.57
9.13
TABLE V
Pupil diameter as a function of background luminance.
Adaptation luminance (cd m−2)
Diameter of pupil of eye (mm)
340
2.7
34
3.6
3.4
4.4
3.4 × 10−1
5.1
3.4 × 10−2
5.8
3.4 × 10−3
6.3
3.4 × 10−4
6.7
3.4 × 10−5
7.0
Tables (5)
TABLE I
Critical visual angles for point-source Tiffany data.
Full Moon, or no moon with solar depression angle of 10°
3.4 × 10−3
Half Moon, or no moon with solar depression angle of 13°
3.4 × 10−4
Starlight or solar depression angle ≥ 18°
3.4 × 10−5
Overcast starlight
These values are consistent with full daylight, twilight, and starlight data of Hulburt and co-workers, Ref. 18. Full-moon-light values were scaled down from full sunlight by the ratio of sun illuminance from Johnson, Ref. 19, to moon illuminance from Sytinskaya, Ref. 20. The moon phase ratio came from Russel, Ref. 21.
Where sunset is defined as a sun depression angle of 0.8°.
TABLE III
International visibility code.
Code number
Daylight visual range VV
Weather fog, mist, haze
Attenuation length Ξ (km)
Attenuation coefficient (km−1)
0
<50 m
dense fog
<0.017
>60
1
50–200 m
thick fog
0.017–0.067
60–15
2
200–500 m
moderate fog
0.067–0.17
15–6.0
3
500–1000 m
light fog
0.17–0.33
6.0–3.0
4
1–2 km
thin fog
0.33–0.67
3.0–1.5
5
2–4 km
haze
0.67–1.3
1.5–0.75
6
4–10 km
light haze
1.3–3.3
0.75–0.30
7
10–20 km
clear
3.3–6.7
0.30–0.15
8
20–50 km
very clear
6.7–17
0.15–0.06
9
> 50 km
exceptionally clear
>17
<0.06
TABLE IV
Equivalent attenuation length at altitude divided by attenuation length at ground level and
for the optical standard atmosphere.
Altitude (km)
Altitude (km)
0
1.0
0
7
1.43
4.89
0.5
1.03
0.487
8
1.50
5.33
1.0
1.06
0.947
9
1.57
5.73
1.5
1.08
1.38
10
1.64
6.08
2.0
1.11
1.80
12
1.80
6.68
2.5
1.14
2.19
14
1.95
7.16
3.0
1.17
2.56
16
2.12
7.55
3.5
1.20
2.91
18
2.29
7.86
4.0
1.23
3.24
20
2.46
8.12
4.5
1.27
3.55
25
2.92
8.55
5
1.30
3.85
30
3.41
8.80
6
1.36
4.40
60
6.57
9.13
TABLE V
Pupil diameter as a function of background luminance.