interception rate is given for an assumed building in the 

Cleveland area. 

A brief description is given of the lightning phenomena, 

as well as of the basic concepts which need to be understood for 

effective application of protective techniques. Prevention of 

direct effects, that is, the effects associated with current flow 

in the system, to be avoided, is first discussed. Indirect 

effects are also mentioned, and the document is completed by a 

bibliography for further reading by interested designers, and 

an Appendix discussing in more detail the history and rationale 

of the cone of protection concept. 
The phenomenon of lightning has been the subject of 

intensive study by many workers (see bibliography) and its 

behavior is fairly predictable in general terms, although 

the exact description of specific incidents is not predictable. Protection against lightning effects includes two 

categories: direct effects concerned with the energy, 

heating, flash, ignition of the lightning current, and indirect 

effects concerned with induced overvoltages in nearly electrical 

and electronic systems. 

Claims to the contrary notwithstanding, there is no conclusive evidence that lightning can be prevented. Consequently, 

one has to design and implement a facility to recognize the 

possibility of a lightning strike, and take appropriate 

measures to make this strike harmless. Lightning protection 

is then an approach where one can make theproper moves if the 

characteristics of the enemy are anticipated. 

Two concepts must be understood to apply effective lightning protection devices : the "cone of protection" and the 

"striking distance." These will be discussed with some detail 

in the following pages. Other fundamentals of electricity 

such as the impedance of a circuit to fast-changing currents 

impulses are assumed familiar to the reader. 

We will first review current theories on the formation 

of lightning, then go on to the concept of the cone of protection and striking distance. The following descriptions 

are based on the work and papers of Fisher, Cianos 6 Pierce, 

and Golde. 

2.1 Generation of the lightning flash 

The energy that produces lightning is provided by warm 

air rising upward into a developing cloud. In detail, 

several theories vary, but all are based on the observed 

evidence that the cloud, except for the top, is negative, with 
METERS 

8000 

Figure 2-1 

General ized diagram showing distribution of air currents 

and electrical charge distribution in a typical cumulonimbus 

a small body of positive charge near the front base of the 

cloud. Figure 2.1 shows a typical cloud distribution of 

charges; the solid lines represent the direction of the air 

movement in the cloud, with the cloud moving from right to 

left. As the cloud passes over a point on the ground, an 

electrical charge is attracted under the cloud on the ground. 

The average electric field at the surface of the ground will 

change from its fair-weather value of about 300 volts/meter 

to several thousand volts/meter. The gradient will be concentrated around sharp protruding points on the ground, and can 

exceed the breakdown strength of air, typically 30 kV/cm. 

However, the first significant event toward formation of 

a lightning flash occurs at the cloud. A slow-moving column 

of ionized air forms at the cloud, called pilot streamer, 

moving by steps of 30 to 50 meters, and followed by a more 

intense discharge called step-leader, because of the discontinuous process of ionization and filling of the column with 

charged particles. 
The step-leader does not move in straight line towards 

the ground, but seeks out the path with least electrical resistance, producing the familiar zig-zag pattern of the final stroke, 

with branches as several paths may be formed in the process of 

searching a weak path. The interval between the successive 

steps is about 50 microseconds, allowing progressive build-up 

of charges on the ground as the charged column advances toward 

the ground. Finally, a stage is reached with the step-leader 

being one step only away from the ground, when the last step 

is completed, either by continuation of the process, or by meeting 

a leader of positive charges originating from the ground. We 

will discuss the implications of this in some detail in the 

section dealing with the striking distance concept. 

With the path now completed, a positive charge then flows 

upward from the ground into the negative channel left in the 

wake of the step-leader, neutralizing the charge in this channel 

and moving at roughly one third of the speed of light. This is 

what constitutes the lightning stroke, carrying the current at 

peaks of 1000 to 100,000 amperes, with a decrement to halfvalue in the order of 50 microseconds. The first one of these 

which occurs in a flash is called the return stroke. 

The first return stroke neutralizes the ionized column as 

well as a small pocket of changes in the cloud; a second or more 

return strokes, sometimes called re-strikes or subsequent 

strokes, can take place, using the same ionized channel, but 

moving much faster. Thus, a series of strokes, such as 

shown in Figure 2.2, can occur in an interval in the order of 

a second. Each of these strokes increases from a very low quiescent value to a very high amplitude in a very short time, 

resulting in rates of current change up to 1 x 1011 amperes/second. 

When very tall objects are present, a step-leader can 

actually originate from this object, and travel upward to the 

cloud, rather than the more general case of downward-moving 

leader. Subsequent charges, however, will be similar, that is, 

move in the ionized channel left by the first discharge. 
Figure 2-2 

Diagram of the development of a lightning flash 

(a) Recording by conventional fixed camera 

(b) Recording by camera with moving f i lm 

resolving the progress of the leaders 

(After ~chonl and) 

In addition to the short (tens of microseconds) discharges 

just described, a low amplitude current can exist between the 

individual strokes. Although low in amplitude (a few hundred 

amperes), the long duration of this continuing current (tens 

to hundreds of milliseconds) is significant because of its 

total charge, resulting in most of the burning and metal-melting 

effects of a lightning flash. 

The wave form and amplitude of lightning stroke and continu 

ing currents vary over such a wide range that information has 

to be presented in statistical form; Cianos G Pierce have 

published a comprehensive set of statistics, from which the 

data of Figures 2-3 through 2-8 are derived, giving the reader 

a feel for the orders of magnitude involved. 
STROKE 

Figure 2-3 

Distribution of peak currents 

for first return stroke and 

subsequent strokes 

% > ORDINATE 

Figure 2-4 

Distribution of the number 

of return strokes per flash 

h01 a1 1 2 6 10 20 30 40 50 60 70 80 80 85 88 89 08.0 09.08 

X > ORDINATE 

Figure 2-6 

Distribution of rates of rise 

1 I 11 11 I IIIII I If 1, I 

001 0.1 1 2 5 10 20 30 40 50 60 70 80 90 95 88 98 89.9 89.89 

% > ORDINATE 
11 I I1 I I llj111 I 1 111 I I 0.01 0:l 1 2 5 10 20 30 40 50 60 70 80 80 85 98 BO 90.0 0O.m 

% > ORDINATE 

0.01 0.1 1 2 5 10 20 3040506070 80 80 85 88 99 99.9 8888 

% > ORDINATE 

Distribution of charges in 

continuing current 

Figure 2-7 

Distribution of charge/fl 

Figure 2-8 

Distribution of duration 

flashes to earth 

ash 

% > ORDINATE 
2.2 Frequency of occurrence 

One of the major factors to consider in determining the 

probability of lightning damage, and thus the need for strong 

protection, is the number of lightning flashes to earth in a 

given area for a given time. This is not generally available, 

and instead the number of "thunderstorm days" is quoted. However, this does also include the cloud-to-cloud discharges, 

and does not represent an accurate parameter, since it does not 

include the duration and intensity of each storm. Progress is 

being made in improved statistics, but these are not yet available, and therefore the "isokeraunic level" maps, showing the 

number of storm-days per year, is still the most widely used 

description of the occurrence distribution. An empirical 

equation has been derived, relating the density of flashes to 

ground and the number of storms per year, as follows: 

density in flashes per km2 per year: D 

thunderstorm-days per year: T 

D = 0.02 ~1.6 

This corresponds to approximately 1 flash per year per km2 at 

an isokeraunic level of 10, and 10 flashes per year per km2 at 

a level of 40. 

The significance of this situation is that, contrary to 

some popular beliefs, the density of lightning flashes, on the 

average, is independant of terrain. However, detail of the 

ground objects (trees, buildings, hills) will produce a bias 

in the local distribution of this average. 

2.3 Striking distance 

This distribution at the local scale is determined by the 

final stages of the step-leader coming from the cloud, so to 

speak, without knowing what it will find on the ground. Thus 

the actual pointof termination can be somewhat controlled, 

while the probability of a given area to receive a lightning 

stroke cannot. This is where the concept of the striking distance, as explained by Golde, becomes very useful. 
As the step-leader has approached the ground in the 

haphazard path described above, the point is reached where 

one more strike in the discontinuous process will close the 

path. The distance between the top of the leader and the 

object about to be struck (or about to emit the meeting leader) 

is called striking distance. The length of this distance is 

affected by the field established by the leader, which in 

turn is determined by the amount of charges existing in the 

ionized channel coming from the cloud. With large charges in 

the channel, the field is more intense, so that breakdown can 

for longer distances, while a shorter distance is necessary 

to produce breakdown for the weaker fields established by 

smaller charges. Figure 2-9 shows the relationship between 

the stroke current (which reflects the charge existing in the 

ionized channel) and the striking distance, as computed by Golde. 

STROKE CURRENT, KILOAMPERES 

Striking distance vs current amp1 i tude 

For instance, an average lightning current of 25 kA would 

correspond to a striking distance of 40 meters. Thus, for an 

average stroke, details of the terrain do not affect the point 

of termination of the stroke beyond this distance, but only 

within this distance will there be a race, or a competition, as 

to which point will receive the flash, or invite it by sending 

a meeting streamer. Conversely, very low amplitude flashes 
have an even shorter striking distance, meaning that they will 

ignore "attractive" points of termination, explaining some of 

the more puzzling exceptions to the generally assumed effect 

of tall.structures, rods, etc. In other words, once a lightning 

step-leader has approached the ground within just short of the 

striking distance, no amount of devices beyond the striking distance will have any effect on the occurrence of the stroke, just 

the details of the area within the striking distance will 

determine the point of termination; the area is committed to 

receive the stroke, and it is now up to the humans controlling 

the shape of the objects on the ground to provide a least harmful point of termination, and make it most attractive to the 

approaching leader ("take me to your leader" ...) 

A number of photographs have been collected, and reported 

in the literature, showing a lightning flash approaching the 

ground in a somewhat wandering but generally downward direction, 

but with a sharp "turn" near the lower part of the path. This, 

according to the striking distance just described, can be readily 

explained as being the point where the downcoming step-leader 

met the upcoming leader from the ground. A photograph of a 

particularly clear occurrence of this will be found in the 

Appendix. 

We are now ready to tackle the concept of the "cone of 

protection," having understood how the striking distance concept 

can explain some of the otherwise unexplained exceptions to the 

generally accepted and verified protection afforded by projecting 

objects, natural or artificial. 

2.4 Cone of ~rotection 

From the days of Benjamin Franklin, the concept of a cone 

of protection has been used to provide effective protection of 

objects within the cone. Briefly, this concept states that objects contained within a cone of 1:l or 1:2 ratio of height to 

radius (Figure 2-10) will not receive the lightning stroke, but 

that the object at the apex of the cone will. In the elementary 
GROUNDED CONOUCTOR 

Figure A. 

Cone of Protection Frovided by a Vertical Grounded Conductor. 

SUPPORT MAST 

Figure B. HM = Height of Mast. 

Zone of Protection Provided by a Horizontal Aerial Ground Wire. 

Figure 2-10 

Cones of protect ion (from NFPA 78- 1975) 

concept, only one projecting object above a ground plane is 

being considered; in most practical situations involving 

buildings, multiple cones will be or should be considered. 

Historically, a 1:2 cone was considered acceptable. However, some exceptions to the "rulett of protection (as if Zeus 

should abide by "rulestt) have recently led to a more conservatime use of a 1:l cone of protection; the exceptions can be 

explained by the striking distance concept, as we shall now see. 
Low-charged step leader - High-charged step leader 

-- Upward streamer from ground - - Upward streamer from ground 

Figure 2-11 Figure 2-12 

Termination of stroke with short Termination of stroke with long 

striking distance striking distance 

Classical "cone of protection" rule for the building 

shown in Figure 2-11 would assure that the lightning mast 

shown provides dependable protection for the building against 

an approaching step-leader. However, if we consider the 

striking distance shown by the circles, at each step of the 

leader advance, we can see that the leader will have ignored 

the lightning mast, and that at the fateful last decision 

point D, the shortest distance is to the corner of the building 

within the "cone of protection," rather than to ground, even 

less to the lightning mast. The path drawn here also exhibits 

3.0 DIRECT EFFECTS 

3.1 Conduction of current to ground 

We have now reached the state where lightning has struck, 

and have seen that it may strike in some rather unexpected (and 

unprotected) locations, and are faced next with an evaluation 

of the effects of the stroke and continuing current flow. In 

the case of a roof-top array of voltage-sensitive cells, the 

real story begins with the flow of current below the first 

metallic termination point. Therefore, lightning protection 

in this context will mean making sure that the lightning does 

terminate where we want it to terminate, and that from there 

it is led to earth in an acceptable manner, along a safe, 

controlled path. 

The most important consideration is then what happens to 

the potential drop along the current path to ground. We have 

seen that the current increases very rapidly on the front of 

the wave. Therefore the inductive drop L di/dt over the current 

path will be extremely large, in other words, during initial 

phase of the discharge, the "grounded" lightning rods and downcomers of a building network will be elevated to substantial 

potentials above earth ground, in the order of tens or hundreds 

of kilovolts. Any circuitous path in the downcomer will increase 

this voltage drop, with the attendant risk that a flashover may 

occur to bridge and shorten this path, defeating the intent of 

carrying the current directly to earth, away from the array. 

Another consideration is the difference of potential established during the initial phase, when the current increases 

at extremely fast rates, between the lightning system and the 

cell array. The upper portions of the downcomers are elevated 

at very high potential because of the inductive drop, while 

the upper metallic parts of the array remain uninvolved in the 

current path, and therefore remain at "gound" potential. We 

are writing "ground" in quotes as this is an arbitrary definition 

in the context of potential distribution during a lightning stroke. 
represented as the common point "G" at which the electric power 

system of the house is tied to the downcomer conductors; any 

further impedance below point "G" and "true" earth is not relevant to the difference of potential V established across the 

wall of the building at point A. If the length (inductance) 

between points B and G is large, and the distance between A and 

B small, the voltage V will exceed the dielectric strength of 

the AB gap, and a "side flash" will occur between A and B, with 

possible disastrous effect. 

LIGHTNING 

STROKE 

ENTRANCE 

11-1, 

Figure 3-1 

Side flash problem on lightning conductors 
from the protection to be provided, if any, for future mass

produced arrays. In the case of the experimental system, the 

high cost of a lightning strike should prevail over aesthetic 

considerations, so that the objective will be to maximize 

protection. Once the cost of the roof array is established as 

a commercial product, the trade off between economics and aesthetics will be quite different. In this discussion, however, we 

are addressing the case of the experimental house. 

There are two basic approaches to providing sufficient 

protection: lightning masts, at some distance from the house, 

with sufficient height to provide an effective cone of protection, and lightning conductors above the roof. Neither can 

provide absolute protection against all possible strikes; 

however, the likelihood of a strike attaching to the roof-mounted 

array will be decreased by several orders of magnitude if a 

properly designed system is installed. 

3.2.1 Lightning masts 

The discussion of paragraph 2.4 above, and the possible 

exception to the protection expected for 2 strict interpretation 

of the cone of protection formula, give some guidance on the 

design of a mast system. For the experimental model, two masts 

at minimum are recommended, with four being even more effective. 

(In the case of a project involving a group of closely spaced. 

houses, it may be possible to provide a common mast at each lot 

boundary. Figure 3-2 shows how such a mast system can be implemented. One of the advantages would be complete independence 

of the power system and lightning system at all but one point. 
BURIED 

CABLE, 

/ 

ALL ROOF LINE WITHIN 

EITHER OF THE CONES 

Figure 3-2. Lightning protection using two masts 

3.2.2 Lightning conductors 

A possibly more effective protection can be expected from 

a lattice of lightning conductors strung some distance abovee 

the roof. The number of conductors, and the distance from the 

roof are in inverse proportions. Therefore, there is a possible 

trade-off between a few conductors high above the roof, and many 

conductors close to the roof. The boundaries of the trade-off 

correspond to the situation where the many conductors would be 

so close to the roof that side-flash becomes a problem, or where 

only a few, very distant conductors would allow a low-amplitude 

stroke, with attendent short striking distance, travel around 

the theoretical cone of protection, as discussed in paragraph 2.4. 

In any case, the down conductors for the cable lattice have 

to be routed far enough away from the roof to prevent any side 

flash. Figure 3.3 shows a possible arrangement for a cable 

lattice system. 
MAST POWER SYSTEM 

BURIED 

CABLE 

Figure 3-3. Lightning protect ion using overhead cables 
changing magnetic flux associated with the high di/dt of the 

lightning current. A less important but still significant effect would be the voltage produced by electrostatic coupling 

between the roof array and the charges associated with atmospheric electricity. 

Typical lightning strokes involve currents of 50 kA reaching crest in 1 microsecond. Thus, the db/dt near the lightning 

conductors will be quite high and capable of inducing destructive 

voltages in any loop which would link a substantial flux from 

the lightning current. Therefore, the power system, cell array 

and control circuits must be designed to minimize intrinsic 

coupling, or be suitably shielded. 

4.2 Effect on incoming power system 

There is a certain amount of information available from 

various sources on the magnitude of transient overvoltage 

entering a house wiring system by the route of the utility 

service. While not exhaustive, the data collected so far have 

indicated that transients up to 6 kV can occur, infrequently, 

but still often enough to cause concern for sensitive electronics. 

This problem of course is not unique to photo-voltaic systems, 

but is faced by every applicance manufacturer. 

In the present case, recognition of the problem is all 

that is necessary since there is a wide variety of commercial 

devices available to suppress these surges. 
p y

flash density has been defined by empirical formul~ and 

plotted by Cianos G Pierce. Table 5-1 shows the computed 

ground flash density, obtained by multiplying the flash density 

by a factor relating the ground flashes to the total flashes. 

This factor depends on the latitude, as suggested by Cianos 

6 Pierce. 

Table 5-1 

FLASHES/~~~/YEAR 

Thunderstorm Days Flash Density Ground Flash Density 

per year (total) at 40" latitude 

Using the cone of protection concept in reverse, we can 

estimate that the effective area of an object protruding over 

the ground surface, in attracting a strike, increases as its 

height increases. For a height h, a circle of radius 2h can 

be considered as candidate for flash interception. Thus, 

assuming a building of 45 feet (15m) x 30 ft (lorn), with a 

height of 30 ft (lorn), the effective area is indicated by the 

sketch of Figure 5-1. The area corresponding to an elongated 

double cone originating from a roof antenna one one side and 

the peak of the roof on the other side, at a 2:l angle, is 

approximately 50mx 50m = 2500m2 = 0.0025 km2. 

Applying the ground flash density of Table 5-1 for an 

isokeraunic level of 40 (see map of Figure 5-2), we obtain 

an estimated interception rate of 0.0025 x 2.1 = 0.005 flashes 

per year on the area covered by the house and its associated 

cones. 
Figure 5-1. Interception area of a typical house 

F i gure 5- 2. Annual isokeraunic map (after Alexander) 
protection from other buildings, trees or structures, the house 

and its cones can be treated as completely independant from the 

surroundings. On the other hand, hill tops and elevated details 

of the terrain can affect the local isokeraunic level upward, 

while depressed locations will affect it downward. 

A simple trade-off based on economics would then consist 

in stating that for an estimated repair cost of say, $200000, 

and a project life of two years, the break-even value of a lightning protection system is 200 000 x 0.005 x 2 = $ 2000. However, 

this trade-off undoubtedly would be modified to take into consideration the "utility" concept in a game plan. This concept 

introduces subjective factors which tend to magnify the perceived 

cost of a failure, but decrease the perceived cost of a desired 

event. Stated in other terms, a trade-off in this project must 

also take into consideration intangible factors such as delays 

in the study and the embarrassing situation of a major failure 

caused by a single lightning strike. 

Therefore we submit that a well designed lightning protection 

system, at this time divorced from aesthetic considerations, would 

be a sound investment. This situation may change when the cost of 

the arrays will be lower, giving greater weight to aesthetics. 
6.0 BIBLIOGRAPHY 

Cavendish, H., Watson, W., Franklin, B., and Robertson, J., 

"Report of the Committee Appointed by the Royal Society to 

Consider a Method of Securing the Powder Magazines at Purfleet, " 

Philosophical Transactions of the Royal Society (London, England), 

vol. 63, 1773, and vol. 68, 1777. 

Walter, B, , "Uber die Schutzwirkung von Fernblitzableitern und 

die Blitzchlaghaufigbeit in einigen Grosstadten, " Deutsche 

offentlichrechtliche Versicherung, no. 18, 1935. 

Mc Cann, G. D. , "The Measurement of Lightning Currents in Direct 

Strokes, " AIEE Transactions, vol. 63, 1944. 

Golde, R. H., "The Frequency of Occurence and the Distribution of 

Lightning Flashes to Transmission Lines, " .4IEE Trmsactions, vol. 

64, 1945. 

Lewis, W, W. , The Protection of Transmission Lines Against Lightning. 

John Wiley, New York, 1950. 

Westinghouse Electric Corp., Electrical Transmission and Distribution 

Reference Book, Chapter 16, East Pittsburgh, Pa., 1950. 

Hagenguth, J. H, and Anderson, J. G. , "Lightning to the Empire State 

Building - Part Ill, "AIEE Transactions, vol. 71, Part I11 (Power 

Apparatus and Systems), August 1952. 

British Standard Code of Practice CP 326:1965, "The Protection of 

Structures Against Lightning, " British Standards Institution, British 

Standards House, 2 Park Street, London, W. I. 
Cianos, N. and Pierce, E. T., "A Ground-Lightning Environment for 

Engineering Usage, " Stanford Research Institute Technical Report 1, 

August 1972. 

Golde, R. H., "Lightning Protection, l' Edward Arnold Pub. , London, 

1973. 

Lightning Protection Code, 1975, NFPA-78, National Fire Protection 

Association, 60 Batterymarch St. , Boston, Mass. 021 10.