LIGHTNING PROTKCriON OF BURIED TOLL CABLE 111 



conditions, in the same manner as before, the total sheath current may be 

 written in the form: 



/(.v) ^ c-/„(.v) + (1 - c)I-Sx) (68) 



where I,, is the current for a grounded sheath, /,• the current entering a 

 j^erfectlv insulated sheath by virtue of its capacity to ground and c is given 

 by: 



c = TVT'" = ro/T\.(0) (69) 



where T' is the potential ditTerence between sheath and adjacent ground 

 without breakdown at .v — 0, which is substantially equal to the earth po- 

 tential. The above relationship for the constant c is obtained by applying 

 equation (57) at .v = to the general solution for I\ , V being given by: 



r = 



G + icoc 



^ [ £u(-v)e~''^' dx (70) 



iwc Jo 



The voltage between core and sheath of an insulated cable may be written 

 in a similar manner when Ig is replaced by Vg , the voltage for a cable in 

 direct contact with the ground, and /^ replaced by F,- , the voltage for a cable 

 insulated from ground. 



From (68) and (69) it will be seen that wdien F(,(0) is much greater than 

 the breakdown voltage of the insulation, the current entering the sheath is 

 nearly the same as for a sheath in direct contact with the ground. Thus, 

 when the earth resistivity is 1000 meter-ohms, and the stroke current 30,000 

 amperes, the earth-potential at a distance of 30 meters (100 feet) is 160,000 

 volts. The impulse breakdown of the insulation may be in the order of 

 30,000 volts, so that the current entering the sheath will be substantially the 

 same as for a cable in direct contact with the soil. When the earth-potential 

 at .V = is only slightly larger than the breakdown voltage of the insulation, 

 however, the current entering the sheath through punctures in the insula- 

 tion is fairly small. 



In the above derivation the voltages and currents were assumed to vary 

 sinusoidally which, of course, is a rather rough approximation in a phenome- 

 non where breakdown occurs after the voltage reaches a certain instan- 

 taneous value. While the derivation is not accurate, it does indicate under 

 what conditions an insulated cable behaves like a cable in direct contact 

 with the ground. 



1.11 Oscillographic Observations of Lightning Voltages 



To obtain data on the characteristics of lightning voltages in buried 

 cable, five magnetic string oscillographs were installed for one lightning 



