284 BELL SYSTEM TECHNICAL JOURNAL 



These values are, of course, of an approximate nature, and are only 

 indicative of what may be expected under average conditions. In some 

 cases the breakdown voltage of high-resistivity soil may be substantially 

 lower than assumed, while that of low-resistivity soil may be noticeably 

 higher. 



2.4 Crest Currenl Distribution for Strokes to Ground 



When the earth resistivity is taken as high as 5000 meter-ohms and the 

 breakdown voltage of the soil is taken as high as 5000 volts/cm, the re- 

 sistance encountered by the channel on the ground for a current of 25,000 

 amperes is about 250 ohms. If the lightning channel were a long conductor 

 already in existence at the initiation of the return stroke and capable of 

 carrying the stroke current without being fused, the current would be 

 propagated upward with the velocity of light and the surge impedance of 

 the channel would be in the order of 500 ohms. Due to the resistance in 

 the ground the current would then be some 30% smaller than for a stroke 

 to an object of zero resistance to ground. However, the lightning channel 

 may not be regarded in the above manner, but as a conductor which is 

 gradually prolonged at about 1/10 the velocity of light, and the impedance 

 of the channel is then much larger, perhaps 5000 ohms. The surge im- 

 pedance of a long insulated conductor having unit length capacitance C 

 is {\/Cv), V being the velocity of propagation. When energy is required 

 to create the conductor, so that the velocity of propagation is reduced, the 

 impedance is increased. Because of the high impedance of the channel, 

 the resistance encountered in the ground may, therefore, be neglected as 

 regards the effect on the crest current. The crest current distribution 

 curve for strokes to transmission line ground structures may thus be used 

 also in the case of strokes to ground, although a different distribution curve 

 is obtained for those of the strokes to ground which arc to buried cable 

 (Section 2.7). 



2.5 Failures Due to Direct Strokes and Strokes to Ground 



In calculating the number of failures due to direct strokes and strokes 

 to ground, the earth is assumed to be a plane surface. A tree placed at 

 random may attract a lightning stroke toward a cable or it may divert it 

 from the cable and the net effect of a large number of trees along a route 

 of substantial length is likely to be small. This is also true for variations 

 in the terrain. 



W^hen A^ is the number of lightning strokes to ground per unit of area, 

 and 5 the length of the cable, the number of lightning strokes on both sides 

 of the cable within y and y + dy is : 



dN = 2Ns dy (83) 



