LIGHTNING PROTECTION OF BURIED TOLL CABLE 283 



breakdown occurs until eo = 14000 volts/cm. On the other hand it is 

 known that arcing between two conductors a considerable distance apart 

 will occur when the average gradient is about 10,000 volts/cm. For air the 

 ratio fo/fi is thus about 1.4. For breakdown in the air, the ionization need 

 not be very dense in order that the corona envelope may be regarded as 

 conducting as regards displacement currents. For breakdown in the earth, 

 however, the ionization must be much more complete in order to provide 

 substantially better conductivity than the soil. The ratio eo/ci is, therefore, 

 likely to be greater, and has been taken as 2 in the following. 



If the latter ratio is assumed for soil, it is seen by comparison of (76) and 

 (79) that the presence of a cable may increase the arcing distance as much 

 as 50%. 



The arcing distance may be written in the form 



ri = (JpY'qi, ro = (Jp)"q, (80) 



where : 



9i 



\2-Keo} ei' ^ \27rgo/ \ ej 



With fo/^i = 2 the following values are obtained 



eo = 250,000 500,000 volts/meter 



qi = 1.6-10"' 1.13-10"' 



qo = 2.4-10"' 1.7-10"' 



Values of ^i and 92 about 25% greater than those given above are ob- 

 tained by assuming that breakdown does not take place in the soil, but that 

 a conducting plane of radius ro is formed by ionization of the air near the 

 ground. Expression (71) is in this case replaced by E(r) = Jp/-ir^ and the 

 expressions for q become 



91 



an 



. (82) 



In the following q = 2.5-10 has been taken as representative for low- 

 resistivity soil and q ^ 1.5 • 10"' for high-resistivity soil. When the current 

 is expressed in kiloamperes, the corresponding values are .08 and .047. 

 The distance to which a stroke may arc is accordingly taken as: 

 p < 100 meter-ohms p > 1000 meter-ohms 



r = .08 (Jp)^ meter r = .047 (Jp)' meter 



= .26 (/p)4eet = .15 (JpY ieet 



where / is in kiloamperes. 



