280 BELL SYSTEM TECHNICAL JOURNAL 



Based on laboratory observations on small-scale models ' ' ' , a line 

 above ground will attract lightning strokes within an average distance on 

 each side of the line which is about 3.5 times the height of the line when the 

 cloud is positive and about 5.5 times the height when the cloud is negative. 

 When the average height of a transmission line ground structure above 

 ground is taken as 70 feet, a 100-mile line will thus attract positive strokes 

 (i.e., strokes originating from a positive cloud) within an area of about 9.3 

 square miles and negative strokes within an area of approximately 14.5 

 square miles. 



About 15% of the strokes to transmission line ground structures have 

 positive polarity,*' " so that the average rate of positive strokes to ground 

 would be about 1.8 and that of negative strokes about 6.6 per square mile 

 per year. The rate of positive and negative strokes to ground would thus 

 be about 8.4 per square mile per year in areas where the yearly number of 

 thunderstorm days is about 35, corresponding to about 2.4 strokes per square 

 mile per 10 thunderstorm days. 



Based on the above date, the ratio of negative to positive strokes to 

 ground in open country would be 3.6. The ratio of negative to positive 

 strokes has been determined by various investigators in different ways. 

 The ratio derived from measurement of field changes during thunderstorms 

 varies between 2.1 and 6.5, that obtained from voltages observed in antennas 

 is about 2.9, while point discharge recorder measurements indicate a ratio 

 of 3.5 and the magnetization of basalt rocks struck by lightning indicates a 

 ratio of 2.25. The above data were obtained in the temperate zone; in the 

 tropics nearly all strokes have negative polarity. 



2.3 Arcing to Cable of Strokes to Ground 



As the stepped leader of a lightning discharge approaches the earth, 

 charges accumulate in the ground under the leader and the resulting flow of 

 current in the ground will give rise to a potential difference between points 

 in the ground under the leader and remote points. Thus, when the tip of 

 the leader has approached within 10 meters off the ground and the leader 

 current is assumed to be as high as 500 amperes and the earth resistivity to 

 be 1000 meter-ohms, a point directly under the leader will have a potential 

 of 8000 volts with respect to a remote ground. The potential gradient along 

 the surface of the ground would, of course, be affected by the presence of a 

 buried cable. The total potential involved is, however, so small that the 

 effect of a buried cable on the path of the leader would be entirely negligible 

 compared to the effect of irregularities in the surface of the earth. As the tip 

 of the leader contacts the ground, the potential may be large enough so that 

 the leader may arc to a cable located within 2 ft. or so of the leader. Only 



