LIGHTXIXG PROTECTIOX OF BURIED TOLL CABLE 257 



^leasurements of current in the ground structure of transmission lines'*'" 

 indicate that a relationship as shown in Fig. 1 exists between the crest cur- 

 rents and the percentage of discharges in which they occur. In the same 

 iigure is shown the crest current distribution for strokes to buried structures, 

 which is derived in Part II from the curve for strokes to transmission line 

 ground structures. Although measurements of wave shape are not exten- 

 sive, they indicate that the current reaches its crest value in 5 to 10 micro- 

 seconds and that it decays to half its maximum in 25 to 100 microseconds, 

 the average being about 50 microseconds.'' An average wave shape is 

 assumed in this investigation. 



In some 80 per cent of all lightning discharges the cloud is negative, so 

 that the flow of current is from the earth toward the cloud. Further details 

 about lightning discharges are summarized in recent surveys**'' which also 

 contain an extensive list of references. 



1.2 Direct Strokes — Current Propagation Along Sheath 



As mentioned in the introduction and discussed further in Part II, a 

 lightning stroke to ground may arc to a buried cable in the vicinity, in which 

 case virtually all of the current will enter the sheath near the stroke point. 



When a sinusoidal current J enters the sheath at .v = and the sheath is 

 assumed to extend indehnitely in opposite directions from this point, the 

 sheath current at the distance .v is given by the following approximate ex- 

 pression 



I{x)=le-'' (2) 



where F is the propagation constant of the sheath-earth circuit and is given 

 by the following expression, derived in a previous paper. ^ 



r = - [/a;(/co + 1/p/v)]^ (3) 



V 



where: v — Velocity of propagation along sheath 

 = {I/vkY meters per second 



V — Inductivity of earth = 1.256-10^'' hy/meter 



K = Capacitivity of earth = e- 8.858 -Ur'- fd/meter 



e — Dielectric constant of earth 



p = Earth resistivity, meter-ohms 

 In deriving the above formula the resistance of the sheath is neglected in 

 comparison with its external reactance, which is permissible for frequencies 

 in the range of importance, and the sheath is assumed to be half buried, 

 that is, with its axis in the plane of the earth's surface. The latter assump- 

 tion gives rise to a comparatively small error when the formula is applied 



