There are complex structures for which the installation and positioning of the lightning protection system (LPS) cannot be done using the lightning protection standard guidelines. As a result, there are some "unprotected" or "exposed" areas. In an effort to quantify the lightning threat to these areas, a Monte Carlo statistical tool has been developed. This statistical tool uses two random number generators: a uniform distribution to generate origins of downward propagating leaders and a lognormal distribution to generate returns stroke peak currents. Downward leaders propagate vertically downward and their striking distances are defined by the polarity and peak current. Following the electrogeometrical concept, we assume that the leader attaches to the closest object within its striking distance. The statistical analysis is run for 10,000 years with an assumed ground flash density and peak current distributions, and the output of the program is the probability of direct attachment to objects of interest with its corresponding peak current distribution

Mata, Carlos T.

Rakov, V. A.

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https://ntrs.nasa.gov/search.jsp?R=20130011492 2019-08-31T00:41:21+00:00Z
GROU D '2008 International Conference on Grounding and Earthing 
&	 311 International Conference on 
3 rd Lightning Physics and Effects Florianopolis - Brazil
	 November, 2008 
EVALUATION OF LIGHTNING INCIDENCE TO ELEMENTS OF A COMPLEX STRUCTURE:

A MONTE CARLO APPROACH 
C. 1. Mata
ASRC Aerospace, KSC FL, 32899 
Abstract - There are complex structures for which the 
installation and positioning of the lightning protection 
system (LPS) cannot be done using the lightning protection 
standard guidelines. As a result, there are some 
"unprotected" or "exposed" areas. In an effort to quantify 
the lightning threat to these areas, a Monte Carlo statistical 
tool has been developed. This statistical tool uses two 
random number generators: a uniform distribution to 
generate origins of downward propagating leaders and a 
lognormal distribution to generate returns stroke peak 
currents. Downward leaders propagate vertically downward 
and their striking distances are defined by the polarity and 
peak current. Following the electrogeometrical concept, we 
assume that the leader attaches to the closest object within 
its striking distance. The statistical analysis is run for 
10,000 years with an assumed ground flash density and 
peak current distributions, and the output of the program is 
the probability of direct attachment to objects of interest 
with its corresponding peak current distribution. 
1 - INTRODUCTION 
It is not very often that an engineer is challenged to 
design a lightning protection system for a complex 
structure that does not resemble those represented in 
the lightning protection standards. Furthermore, some of 
these complex structures do not permit the use of air 
terminals (lightning rods or catenary wires) as 
recommended by the standards. This is the case for the 
new lightning protection system for Launch Complex 39B 
at the Kennedy Space Center, Florida, to be used for the 
Constellation Program. The design of this lightning 
protection system presented many challenges, such as 
minimizing the likelihood of a direct attachment to the 
space craft while providing enough clearance required by 
the expected drifts during launch. Spacecrafts require 
what is known as a flight out hole, which is an opening in 
the lightning protection system for the vehicle to go 
through. The problem is that providing this clearance 
increases the possibility of sneak through strikes 
(shielding failures) that could potentially impact the 
vehicle or ground support equipment. 
The problem becomes more complicated when the 
location of lightning protection towers and downlead 
anchoring points is dictated by existing infrastructure that 
cannot be removed or relocated, such as underground 
tunnels, utilities, etc. 
All these unique challenges prompted the refinement of a 
Monte Carlo statistical tool that was originally developed 
in 2006 by ASRC Aerospace to evaluate the lightning
V. A. Rakov
University of Florida, Gainesville, FL 32611 
protection system of the Space Shuttle. The first version 
of this tool had some limitations that were overcome by 
the new development used to design and evaluate the 
new lightning protection system for Launch Pad 3gB. The 
new version of this tool allows for the simulation of both 
negative and positive strikes, while providing the user 
with the probability of a direct attachment to any object of 
interest and the current distribution. With this tool, it is 
possible to quantify the exposure of certain objects or 
likelihood of direct lightning attachments. 
The assumptions of this tool are presented in Section 2. 
Two case studies, that of vertical conductors of different 
height and the Launch Complex 39B at the Kennedy 
Space Center, FL are presented in Section 3. The results 
are discussed in Section 4 and the conclusions are 
presented in Section 5. 
2— MONTE CARLO SIMULATION ASSUMPTIONS 
The following assumptions are made by the Monte Carlo 
procedure: 
• Peak current (I, in kiloamperes) and striking 
distance (d, in meters) are related by the 
following equations: d= lOx!° 65 [1] (negative 
strikes) and d=lOx!° 47
 [2,3] (positive strikes). 
• The leaders travel vertically downward with 
computational steps equal to 5% of their striking 
distance and with an imaginary sphere, whose 
radius is equal to the striking distance, centered 
at the leader tip. 
• The leader will attach to any point that first 
comes in contact with the surface of the sphere 
as it travels downward. So, the bottom section 
of the leader channel (whose length is equal to 
the striking distance) can be in any direction. 
• Ground flash density is assumed to be 10 
flasheslkm2/year with a correction factor of 1.7 
[1] (to account for multiple ground terminations 
that the existing KSC lightning detection system 
cannot detect), or 17 flasheslkm2/year. 
•	 Positive strikes are assumed to be 5% of all 
strikes (0.85 flashes/km2/year). 
• The peak current distributions for positive and 
negative strikes (first strokes in the absence of 
strike object) are defined by lognormal 
distributions with p =35 kA, =1.2 and p=31.1 
kA, o=0.484, respectively, where p and are 
the logarithmic mean and standard deviation, 
respectively. Strokes with peak currents less 
than 2 kA are not considered in the simulation.
The Monte Carlo simulation runs for a period of 
10,000 years, and the results are used to 
compute the annual lightning incidence. The 
number of years of simulation can be changed 
by the user. 
Only downward propagating leaders are 
considered regardless of the height of the 
structures. 
Structures and vehicles being protected are 
assumed to be at the pad for 365 days per year. 
In practice, they are at the pad for a fraction of 
that time. 
E 
0
Peak Current. kA 
Figure 1 - Striking distance as a function of stroke peak 
current. Note that the 5, 50, and 95% points are marked with 
circles and asterisks for negatives and positives strokes, 
respectively. 
The ground flash density and percent of positive strikes 
are based on actual data collected at KSC. The 
cumulative peak current distributions were obtained by 
performing a curve fit to 95%, 50%, and 5% values [1] 
(see Table 1 and Figure 2). Figure 2 shows the 
lognormal cumulative distribution function that indicates 
the probability of a stroke peak current of being less than 
the tabulated values. 
Peak Current (mm	 2 kA)
Percent of cases exceeding 
tabulated value 
95% 50% 5% 
_____________________ 
Negative	 Strokes (kA) 14 31 80 
(14) (31) (70) _____________________________ 
Positive l	 Strokes (kA) 4.6 35 250 
_____________________ (4.8) (35) (252)
Table 1 - Lightning peak current statistics [1]. The values in
parentheses are those that the lognormal distributions used by
the Monte Carto model yields (See Figure 1). 
100
I	 I — — 
	
80	 ._ ------------------
>. 60 
40 
20 
	
C	 I	 I	 I 
	
0	 50	 100	 150	 200	 250	 300
Current, kA 
Figure 2 - Lognormal cumulative distribution function of the 
first stroke peak current parameters in Table 1. Note that 
the 5, 50, and 95% values are shown with circle markers 
and asterisks for the negative and positive strokes, 
respectively.
	
0	 20	 40	 60	 80	 180	 120
HegI6. m 
Figure 3 - Geometric mean peak current as a function of 
the height of the vertical conductor. 
3—CASE STUDIES 
To demonstrate the capabilities of the presented method, 
two case studies are presented. The first case study is a 
vertical conductor in the open field (Section 3.1) and the 
second case is the new lightning protection system for 
Launch Complex 398 at the Kennedy Space Center 
(Section 3.2). Note that the estimation of the current 
distributions for both cases has been carried considering 
only the negative strokes. 
3.1 —VERTICAL CONDUCTORS 
A vertical conductor with a variable height varying from 5 
to 120 meters in increments of 5 meters was modeled 
and the Monte Carlo Statistical Tool was run for each 
one of the different heights to evaluate the peak current 
distributions as a function of the height of the vertical 
conductor. The results of the simulation seem to indicate 
that the current distribution geometric mean increases 
almost linearly with the height of the vertical conductor 
(See Figure 3). In this case, a least square curve fitting is 
given by(1): 
urrrO.O444xh+36.5 (1) 
The standard deviation of the current distributions of 
those strokes that attach to the vertical conductor is 
shown in Figure 3. 
0.475
I	 I	 I	 I	 I 
	
0.47	 + --------- - - - .L - - - - - - - - 
*	 I	 I	 I	 I 
16 
2
	
*	 I	 I	 I	 I	 I 
I	 *1	 I	 I 
*1	 I	 I 
r0.4C5
I	 4*	 I 
I	 *I	 I 
I	 I	 I	
* 0)
	
0.46	 I	 I	 I 
I	 I	 1*	 + 
	
0.455	 I	 I	 I	 I 
	
0	 20	 40	 60	 80	 180	 120
Hntgle, m 
Figure 4 - Standard Deviation as a function of the height of 
the vertical conductor. 
Note that the number of strikes to the vertical conductor 
increases as a function of height, therefore, the curve 
40 
39 
38 
fithng for the current distributions at higher heights is 
better resolved because of the increased samples or 
number of direct strikes to the vertical conductor (See 
Figure 5). The number of direct strikes to the vertical 
conductor seems to reach a plateau at about 120m. This 
is expected since the striking distances have finite values 
and are defined by the lognormal distribution of the peak 
currents.
t- - - -. - - - . .*t 
	
I	 I 
.1 -$- ------------
	
I	 I	 I	 I 
I	 I	 I 
-
	
I	 I	 I 
- - - - - - - - - - - - 
	
1	 I
---I- - - 
	
*1	 I 
*	 I	 I 
* 
0 1	 I 	 I 	 I 
0	 20	 40	 00	 80	 100	 120
Height, m 
Figure 5 - Normalized number of direct strikes to the 
vertical conductor per year for Ng=1 as a function of height 
(only negative strokes are considered). 
These results seem to indicate that as the height of the 
vertical conductor increases, so does the probability of 
larger peak currents. 
3.2 - LC39B LIGHTNING PROTECTION SYSTEM 
This lightning protection system consists of three towers 
and nine downleads, as shown on Figure 6. The towers 
are about 161 meters height with insulators of about 22 
meters mounted on top, for an overall height of about 
183 meters. A catenary wire system rests on top of the 
insulators. The outer triangle is formed by the catenary 
wires that connect towers 1, 2, and 3. The flight out hole 
has the shape of a pentagon and the space craft is 
centered underneath it. 
	
D2	 -.
D5
D6 
D7 
Os 
Figure 6. Plan view of the lightning protection system of 
LC39B at the Kennedy Space Center, FL.
An isometric view of the lightning protection system, 
showing the towers, the catenary wire system, and the 
downleads is shown in Figure 7. The model used by the 
Monte Carlo Simulation tool is derived from the CAD 
model of the system. Therefore, sag information is taken 
into consideration. 
/ 
Figure 7. Isometric view of the lightning protection system of 
LC39B at the Kennedy Space Center. 
Note that the openings in the catenary wire system will 
result in shielding failures (sneak through strikes) that 
may potentially impact equipment below the lightning 
protection system. In this particular case, the peak 
currents of negative and positive strokes for events that 
may result in shielding failures are shown in Figures 8 
and 9, respectively. 
When the Monte Carlo model is run for a period of 
10,000 years, the shielding failure occurs at the flight out 
hole about five times during this simulation period. This 
translates into a probability of a direct attachment to the 
vehicle of about 0.05% per year, assuming the vehicle is 
parked at the launch pad for 365 days per year. 
Figure 8. Sneak through peak currents for negative strikes 
The Monte Carlo model also allowed us to investigate 
the expected current distributions at each downlead and 
catenary wire section. This information was used for a 
flashover analysis that was performed using the ATP. 
This analysis will be presented on a future publication. 
0.035 
003 
0,025 
S
0.02 
0.015 
E
0.01 
0.
Figure 9. Sneak through peak currents for positive strikes. 
4 - RESULTS 
The results of the study case of the vertical conductors of 
different height seem to indicate that at least for the first 
120 meters, the peak current geometric mean increases 
linearly with the conductor height. Nevertheless, the 
number of direct strikes or incidence level to the vertical 
conductor seem to reach a plateau when the height is 
about 120 meters, which is expected given the 
relationship between the striking distance and the peak 
current. 
In the case of the lightning protection system of Launch 
Complex 39B, running the Monte Carlo simulation for a 
period of 10,000 years results on a total of five direct 
attachments of less than 10 kA (both positive and 
negative strikes) and one direct strike of more than 10 kA 
(a positive strike). This translates into a probability of a 
direct strike to the spacecraft of about O.O6% per year, 
assuming that the vehicle is parked at the Launch Pad 
365 days a year. In reality, the vehicle is expected to be 
at the Lunch Pad for a week or two with about four times 
per year. Also, the distribution of lightning activity varies 
per month, with the months from June through 
September being the months of greatest lightning 
activity. 
5- CONCLUSIONS 
A Monte Carlo approach to evaluate the lightning 
incidence to elements of complex structures and to 
estimate the current distributions has been presented. 
The approach was used to validate the design of the 
lightning protection system of Launch Complex 39B at 
the Kennedy Space Center, FL, for the Constellation 
program. The tool allowed the designers to move the 
position of the towers, within many constraints, and to 
design the catenary wire system to minimize the 
probability of direct strikes to the space craft. This tool 
can be used to evaluate, validate, and aid in the design 
of lighting protection systems, specially when the 
guidelines provided by lightning protection standards 
cannot be followed. 
7 - REFERENCES 
[1] RAKOV, V.A. and UMAN, M.A. "Lightning: Physics and 
Effects", Cambridge University Press, ISBN 0521583276, 2003
[21 MXA, C.J., "Paper Presentation Format", GROUND'98 
Proceedings, vol.1, pp. 84-87, Belo Honzonte, Brazil, April 1998 
[3] MXA, C.J., "Paper Presentation Format', GROUND'98 
Proceedings, vol.1, pp. 84-87, Belo Honzonte, Brazil, April 1998 
Main author 
Name: Carlos T. Mata 
Address: M/S ASRC-25, Kennedy Space Center, FL 32899 
Fax' (321) 867-6300 ; Phone' (321) 867-6964 
E-mail:


Evaluation of Lightning Incidence to Elements of a Complex Structure: A Monte Carlo Approach

There are complex structures for which the installation and positioning of the lightning protection system (LPS) cannot be done using the lightning protection standard guidelines. As a result, there are some "unprotected" or "exposed" areas. In an effort to quantify the lightning threat to these areas, a Monte Carlo statistical tool has been developed. This statistical tool uses two random number generators: a uniform distribution to generate the origin of downward propagating leaders and a lognormal distribution to generate the corresponding returns stroke peak currents. Downward leaders propagate vertically downward and their striking distances are defined by the polarity and peak current. Following the electrogeometrical concept, we assume that the leader attaches to the closest object within its striking distance. The statistical analysis is run for N number of years with an assumed ground flash density and the output of the program is the probability of direct attachment to objects of interest with its corresponding peak current distribution

	I	 Evaluation of Lightning Incidence to Elements of a Complex Structure: 
	
2	 A Monte Carlo Approach 
	
4	 By 
	
6	 C. T. Mata' and V. A. Rakov2 
7 
	
8	 1 ASRC Aerospace, Kennedy Space Center, FL 32899 
	
9	 2 Department of Electrical and Computer Engineering, University of Florida, 
	
10	 Gainesville, FL 32611 
11 
12 
	
13	 Abstract 
14 
	
15	 There are complex structures for which the installation and positioning of the lightning 
16 protection system (LPS) cannot be done using the lightning protection standard 
	
17	 guidelines. As a result, there are some "unprotected" or "exposed" areas. In an effort to 
	
18	 quantify the lightning threat to these areas, a Monte Carlo statistical tool has been 
19 developed. This statistical tool uses two random number generators: a uniform 
20 distribution to generate the origin of downward propagating leaders and a lognormal 
	
21	 distribution to generate the corresponding returns stroke peak currents. Downward 
22 leaders propagate vertically downward and their striking distances are defined by the 
	
23	 polarity and peak current. Following the electrogeometrical concept, we assume that the 
	
24	 leader attaches to the closest object within its striking distance. The statistical analysis is 
25 run for N number of years with an assumed ground flash density and the output of the 
	
26	 program is the probability of direct attachment to objects of interest with its 
	
27	 corresponding peak current distribution. 
28
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Evaluation of Lightning Incidence to Elements of a Complex Structure: A Monte Carlo Approach

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