290 BELL SYSTEM TECHNICAL JOURNAL 



per limit / may be replaced by infinity, and it is also seen that the first 

 term in (94) then vanishes. 



The lightning trouble expectancy as calculated from (92) is shown in 

 Fig. 12 as a function of the earth resistivity for various sheath resistances. 

 The curves are based on 2.4 strokes to ground per square mile, which is 

 approximately the number of strokes per square mile during 10 thunder- 

 storm clays. The number of thunderstorm days per year along a given route 

 is obtained from Fig. 8 and thus the number of times lightning failures would 

 be expected during one year. 



2.6 Expectancy of Direct Strokes 



The incidence of direct strokes to the cable may be obtained from (96) 

 with 7*0 = kiloamperes. 



The number of strokes arcing to the cable is thus 



Ua = 2Nsp^qH{0) (98) 



The cable will thus attract strokes within an effective distance. • 



y = p^qH(0) (99) 



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



y = .365 p' meters y = .22 p' meters 



= 1.2 p" feet = .7 p* feet 



2.7 Crest Current Distribution for Direct Strokes 



The fraction of the strokes to the cable having crest values in excess 

 of i is given by: 



P{i) = H{i)/H(0) 



(100) 



©^ 



♦ = 2 ( - 1 e-'' + erfc (iky 



and is shown by curve 2 in Fig. 1. It will be noticed that a buried cable 

 attracts a greater proportion of heavy currents than a transmission line, 

 because of the circumstance that heavy currents to ground arc for greater 

 distances. 



2.8 Lightning Trouble Experience 



As mentioned before, lightning damage may be due to denting or to 

 fusing of holes in the sheath, or to excessive voltages between the sheath 

 and the cable conductors. Only the latter form of lightning failures have 

 been considered here, since they predominate for cable of the size now being 

 used, particularly in high-resistivity areas, and are likely to extend for a 

 considerable distance to both sides of the point struck by lightning and are 



