Table 160 (continued) 455 



HORIZONTAL VISIBILITY 



Thus if R becomes V , the visual range of a black object viewed against the horizon 

 sky, the contrast of luminance is expressed by 



B b (A) u; 



From equation (7) 



V = - loge jj- (8) 



Although' equation (8) was derived on the assumption that the object is black and 

 is viewed against the horizon sky, the equation is also valid to a close degree of approxi- 

 mation for the case in which an intrinsically dark object is viewed against an intrin- 

 sically dark, terrestrial background, provided that the background is at a distance at 

 least twice as great as the visual range of the object. 



The actual value of the threshold of luminance contrast, e, in practice depends on a 

 number of factors such as angular dimensions of object, degree of confidence of the 

 observer that he has detected the object, and the pattern of luminance in the visual field 

 surrounding the object. The value of e is greater if the observer endeavors to recognize 

 the object rather than merely to detect it with some definite degree of confidence. At 

 low levels of illuminance, the adaptation of the observer's vision to the existing condi- 

 tions also plays a role in determining e. 7 



The value of e may possibly range from about 0.006 for large objects and almost cer- 

 tain detection to a value of the order of 0.1 for small objects. Koschmicder 2 has used 

 the value 0.02 for e, apparently following Helmholtz, while another value sometimes 

 used is 0.055, 8 although we shall employ 0.05 in round numbers, as well as 0.02. 



Let V 2 = visual range as defined by equation (8) when e = 0.02 

 and ^5 = visual range as defined by equation (8) when € = 0.05; 



then since log 8 1/0.02 = 3.912 



and loge 1/0.05 = 2.996, 



y,= 3 -™, (9) 



a 



V> = 2 -^- (10) 



a 



Description: 



Tables 160-B1 and 160-B2 give values of <r as functions of V2 and Vs in accord with 

 equations (9) and (10), respectively. 



Tables 160— CI and 160-C2. — Visual range of point sources of light 

 Assumptions and Computations: 



Tables 160-C1 and 160-C2 based on equation (11), below, relate to the visual range 

 of light perceived as a point source ; that is, this equation is valid under the condi- 

 tion that the particles of the atmospheric aerosol are small; namely, of the sizes not 

 exceeding those found in haze or thin fog. 



Equation (11) must be used with reservation if the light is not far enough away from 

 the observer to appear as a point source. When fog, cloud, or other light-scattering 

 particles are present in the neighborhood of light sources, the particles will give rise to 



' Blackwell, H. R., Contrast thresholds of the human eye, Journ. Opt. Soc. Amer., vol. 36, pp. 

 624-643, 1946. 



8 Douglas, C. A., and Young, L. L., Development of a transmissometer for determining visual 

 range, Civil Aeronautics Administration, Technical Development Report No. 47, February 1945. 



Note: These investigators used principally 4-foot-square black boards as visibility marks at 

 distances between 0.15 and 1.0 kilometer, corresponding to angles subtended at the eye between 0.46° 

 and 0.07°. 



(continued) 



SMITHSONIAN METEOROLOGICAL TABLES 



