LIGHTNING CURRENTS IN BURIED CABLE 



283 



age current is therefore smaller the higher the soil resistivity. Thus the 

 current will travel farther the higher the earth resistivity. It has been 

 shown elsewhere'- ^ that a sinusoidal current would be propagated as 



I(x) = 7(0) e-"" (4) 



- 2 



cr 



2 K5 



5 1.0 

 o 0.9 

 2 0.8 

 (T 0.7 

 ^ 0.6 

 ^0.5 

 _l 0.4 



O 0.2 



300 500 1000 2000 3000 



EARTH RESISTIVITY IN METER-OHMS 



10,000 



Fig. 3 — Theoretical lightning trouble expectancy curves showing number of times 

 insulation failures due to excessive voltages would be expected per 100 miles for 10 thun- 

 derstorm days, for cables having sheath resistances as'indicated on curves and 2000 volts 

 insulation between core and sheath. Dashed line represents full size cable. 



where 7(0) is the current in the sheath in one direction from the stroke 

 point, I{x) the current at the distance x, and the propagation constant F 

 per meter is given by: 



r = y/ii>iv/2p (5) 



where w = lirf, v = inductivity of the earth = 1.257-10"^ henry/meter, 

 and p is the earth resistivity in meter-ohms. 



Let it be assumed that the current at the distance x has been evaluated 

 for a given earth resistivity p and radian frequenc}^ co. If the earth re- 



