Quantification of the probability of lightning strikes to structures using a fractal approach

Abstract

Recently fractal theory has been used to model the observed paths of lightning discharges. This paper extends previous work by using a fractal approach to describe the effects of tortuosity and branching of the lightning channel. In particular, we use the model to make predictions of the probability of lightning strikes to practical structures. Some of the specific estimates include the probability of strikes as a function of interception angle, predictions of the strike points on structures, and the probability of ''side strikes'' to tall structures. Significant polarity and geometric effects are shown. The shielding effects of nearby taller structures, shielding failure or '' breakthrough'' probabilities of so-called protected objects, and the effects of ground topography are also examined. The results are discussed in terms of the implications for the protection of structures against lightning.

Simulation of gigantic jets propagating from the top of thunderclouds to the ionosphere

“…Niemeyer et al (1984) have proposed that discharge patterns have fractal dimension. On the basis of this concept, many investigators have developed the fractal models to study streamer and leader discharges in gaseous dielectrics, cloud-to-ground (CG) lightning, lightning above thunderclouds, and so on (e.g., Niemeyer et al, 1989;Femia et al, 1993;Pasko et al, 2000Pasko et al, , 2001Pasko and George, 2002;Petrova, 1993, 1999;Petrov et al, 2003;Tong et al, 2005). Pasko and George (2002) have developed a streamer model to study blue jets and blue starters which are considered as positive streamer coronas expanding from the streamer zones of conventional lightning leaders.…”

La interdisciplinariedad en la ciencia del rayo

“…Algunos autores habían modelado la propagación y el camino del líder usando modelos probabilísticos basados en teoría de fractales (Petrov, 2003), (Agoris, et. al., 2004), (Lupo, 2000).…”

Study on the Effectiveness of Single Lightning Rods by a Fractal Approach

“…We randomly choose a point from the upper boundary of the 2-D configuration and generate a section of downward leaders to initiate our simulation. Since the approach of a lightning leader from the thundercloud does not depend on the existence of ground objects until it enters a "striking distance" of structures [4], we only need to make a cutoff at certain height H (in this paper we set H = 500 m). The horizontal scale W = 2 km is so chosen that the downward leaders initiating from places beyond the side boundary will not strike the grounded structures and therefore not contribute to the results in concern.…”

“…Numerical model of lightning leader process based on fractal growth named dielectric breakdown model (DBM) has been developed and verified in Ref. [3][4][5][6][7][8][9], which present more realistic lightning channels. Nevertheless, though its potential for practical applications has been demonstrated in Ref.…”

“…Nevertheless, though its potential for practical applications has been demonstrated in Ref. [4], the fractal simulation of lightning has mostly been used as a descriptive or visualization tool of lightning processes and channels rather than a predictor or analyzer in lightning protection engineering. As an attempt to convert this methodology to practical utility, in the present work we calculate the interception area, the strike distribution and the protection zone of single lightning rods of various heights using the *Address correspondence to this author at the State Key Lab of Power Systems, Department of Electrical Engineering, Tsinghua University, Beijing 100084, China; Tel: +86-10-62775585; E-mail: hejl@tsinghua.edu.cn fractal approach.…”