456 Table 160 (continued) 



HORIZONTAL VISIBILITY 



a diffuse luminance of the atmosphere. In general, this will affect the threshold of 

 illuminance for detection of the lights. 8 



The basic equation, due to Allard, commonly used in regard to the visual range of 

 point sources is 



E=zhD-*e- aD (11) 



where D — visual range of point-source light, 



7o = luminous intensity (candlepower) of light in direction of observer, 

 a = atmospheric extinction coefficient, 



E = threshold of illuminance (luminous flux incident per unit area just de- 

 tectable) at the observer's eye, owing to luminous flux emitted by the light. 



The appropriate value of E depends greatly on the degree of dark adaptation of the 

 observer. Among the controlling factors are the time history of illuminance to which 

 the observer's eyes have been exposed prior to the observation, the luminance of the 

 horizon sky and background in the direction of observed lights, and the illuminance on 

 a horizontal plane at the point of observation. Presence of other light sources in 

 vicinity of the target light, intermittency of the light, and color of the light also effect 

 the value of E 3 . 



As a guide regarding choice of the proper value of E, the following data are provided: 



E (threshold illuminance) „ ,. . 



-. r. ; Condition 



lumens/km. a 



1 Twilight, or appreciable light from artificial sources. 



2 X 10" 1 Average illuminance on surface and background luminance 



during night at typical airport. 



3 X 10" a (about 10~ 1S ) Observer's eyes fairly well dark-adapted. No light other than 

 starlight. Foveal threshold against dark background. 



To permit evaluation of equation (11) by means of tables, it is rewritten 



(log./o-log.£) = (oD+2\og e D) (12) 



Description: 



Table 160-C1 gives values of the left-hand member (log./o — log.Zj) as a function 

 of E and h, while Table 160-C2 gives values of the right-hand member, (oD + 2 loge D), 

 as a function of <r and D. 



These tables permit the computation of any one of the four variables as a function 

 of the other three, provided that equation (12) is satisfied. 



Examples : 



Given : E = 2 X 10" 1 lumens/km. 2 

 Io = 30 candles 

 D = 5.0 km. 



To find : a. 



From Table 160-C1, we find 



(loge 7o- log. E) =5.011. 



Referring to Table 160-C2, which gives (crD -J- 2 log. D), and running along the line 

 for D = 5.0 km., we find by interpolation for a that the tabular value 5.011 occurs when 

 a = 0.358, which is the required result. 

 Given: Assuming e = 0.02, the daytime visual range of a black object viewed against 



the horizon sky is V% = 3.2 km. 

 To find: a; then, to find D or a light observed at night for this value of «r under the 

 condition that 



E = 1 lumen/km. a and h = 100 candles. 



From Table 160-B1, we find a = 1.222 km. -1 corresponding to Vi = 3.2 km. 

 From Table 160-C1, (log./o — log.£) =4.605. 



Referring to Table 160-C2, with this tabular value 4.605 = {a D -f 21og.D) in accord 

 with equation (12), and a = 1.222 km." 1 , we find by double interpolation that D = 2.36 km. 



{continued) 



SMITHSONIAN METEOROLOGICAL TAELES 



