S ielding or T ransmission Lines
C. F. WAGNER
MEMBER AIEE
G. D. McCANN
ASSOCIATE AIEE
A ODERN theories of direct-stroke
m protection premise that the ground
wires are so located as to intercept the
stroke and provide perfect shielding. In
spite of the fundamental importance of
this question there still exists considerable
doubt as to the correct position of the
ground wires relative to the transmission
conductors. Two avenues of approach
are suggested for the attack of this question; first, the collection of statistical
information regarding actual line performance, and second, the use of laboratory models. Line performance is, after
all, the final criterion. However, it is
difficult to isolate the shielding effect
from other factors which may produce
outage due to lightning. Studies with
models eliminate this difficulty but always contain the element of doubt as to
whether the laboratory conditions are
sufficiently representative of actuality
as to justify general conclusions. Perhaps the best course, that which is attempted in this paper, is to try both and
co-ordinate the results so obtained.
Previous Investigations
Models have previously been used for
investigating both the protective value
of horizontal ground wires and vertical
masts1- for shielding transmission lines
and other vulnerable objects such as substations, buildings, and oil storage tanks.
In one of the earliest investigations with
ground wires, Peek3 states that "for a
single wire, the ground is never hit nearer
the projection of the wire than about
four times its height above ground."
Peek4 further expands upon this point
by stating that from model tests upon
rods any object is protected if it lies between ground and within the surface
generated by a segment of a circle whose
center is the cloud height and is tangent
to the ground and passes through the
tip of the rod. This assumes that all the
Paper 40-107, recommended by the AIEE cornmittee on power transmission and distribution, and
presented at the AIEE summer convention, Swamp-
G. L. MacLANE, JR.
ASSOCIATE AIEE
strokes occur to the object nearest to the
origin of the stroke.10 Upon this assumption a set of curves can be constructed as shown in figure 1 for guidance
in the location of the ground wires with
respect to the conductors. In this
figure their relative location is specified
in terms of the protective angle, the
angle between the vertical and a line
through the conductor and ground wire.
The consideration of minimum sparkover distance just enunciated according
to figure 1 indicates, for a cloud height
of 1,000 feet and a ground wire height Of
100 feet, a protective angle of about 65
degrees which is essentially constant
over the practical range of conductor and
ground-wire separations.
No data of any consequence such as
tests on models of different scales have
been presented in an attempt to show
that model work is applicable to actual
size systems although Peek in a reply to
the discussion of his 1926 paper stated
1 1.however,
.
over a
that "tests were made,
wide range of scales with substantially
the same results. In other words, for a
given arrangement and ratio of rod and
cloud height the results were independent
of the scale." No data to substantiate
this statement have been published,
Zalesski,5 using impulse waves and
continuous voltages, concluded that a
positive cloud represented by a horizontal cylindrical electrode should be
used for test work since it gave more
pessimistic results. He determined the
worst position of the electrode and with
this position studied the necessary protective rod configuration to give complete protection to transmission lines
Akopian6 likewise
and substations.
limited his investigations mostly to
vertical rods and agrees with Zalesski
that positive impulse waves should be
used in model tests. He departed from
previous investigators by representing
the cloud by means of a point electrode.
Schwaiger7 in 1937 followed the phi-
ratory sparks of corresponding polarity.
They used only one model scale which
gave a reduction of 100:1. An argument was presented to justify the state-
ment that for model work the protective
value of a ground wire is not altered as
the ratio of the cloud height to ground
wire height is increased beyond a certain value. The effect of ground was
represented by dry sand. They presented data which indicate a protective
angle of the order of 23 degrees for a
positive stroke and 31 degrees for a
negative stroke.
from pracFortescue and
tical considerations gained from experience on actual systems, advocated a protective angle of not more than 20 degrees.
Additional work appeared to be desirable to reconcile, if possible, the divergent views of different investigators.
Inathe presentmnecsiangIamon t la thors
Conwellon
havestudiedthemechanism oflaboratory
sparks and have shown that the propagation of leader streamers is quite
closely simulated by positive waves of
slow rates of rise. Arguments are presented to show that for practical purposes model investigations can be carried out with 1 1/2x40-microsecond
positive impulses. Other points investiof overvoltage,
are the effects of
overodlt ,
gatmedre
thnfetis,
atmospheric conditions, scale of models,
and height of cloud. After establishing
the fundamentals of model investiga-
. ~~~~~~~gated
losophy that the conductors, if they are
tions considerations affecting construc-
tion practice such as the location of
ground wires, topography of terrain,
and soil resistivity, were studied. These
questions were then co-ordinated with
the results of actual system performance.
Mechanism of Natural Lightning
A knowledge of the characteristics of
natural lightning is a prerequisite to an
attempt to simulate its effect in the
laboratory on a model scale. The present theories of charge formation are
still controversial; suffice it for the present purpose to observe that it is concerned in some manner with the reactions between an upward movement of
air, usually in the head of the storm, and
a downward motion of water droplets.
The droplets in the lower portion of the
cloud are usually charged negatively and
scott, Mass., June 24-28, 1940, and at the Pacific
to be protected, must lie within the
shaded areas shown in figure 2.
those in the upper portion, positively.
made available for preprinting May 16, 1940.
C. F. WAGNER is consulting transmission engineer,
0.D
is
house Electric and Manufacturing Company, East
Pittsburgh, Pa.
In 1939 Matthias and Burkhardtsmaier8>9 presented results of investigaof transmission
tions reaigto
lines and other objects. They, however,
premised that natural lightning of both
polarities iS adequately simulated by labo-
This is borne out by the fact that 90 to 95
per cent of the strokes to transmission
lines lower
b the measurement of electrical gradient at the
ground in the vicinity of charged cloudsli
and by Simpson and Scrace's13 measure-
Coast convention, Los Angeles, Calif., August
MCCIiAcNN elntraol-station engnineer,asnd 0.-
1ae.Fralnmeereeec,selitaenof
1941, VOL. 60
shieldingr
neaiecharge,
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313
Figure 1. Protective angle based
0'°'-'
0
60
- - |
From figure 4 it can be seen that as
N arc', the leader streamer proceeds it lowers
\ e2 lg( a I
I
negative charge from the cloud and distributes it throughout the antenna-like
system of streamers. This lowering of
negative charge may consume a time of
the order of 10,000 microseconds. As
/PROTECTIVEthe stepped leader strikes the earth this
lt )
0.{
IV0
_
- }- } <
-1
-
upon the clearance
l
rO
//
/r
]
X0.'9
50-
hT0ty
h
E
4
6
S
I10
12
14
H/h
16
9OTECTIVE
PR
AllNGLE
Xt
is
20
come to be associated popularly with
lightning.
22
same charge is lowered to earth at a rate
77XzUJdependent
<
l | < upon the rate of40~~~~~~~~~~~~~~~~
propagation
W
24
26
28
of the return streamers, a process which
requires a time of the order of 50 microseconds to reach the cloud. Thus the
same charge which had been lowered
and distributed over the streamer network in a time of the order of 10,000
m icrosecnds
then .dir
to
groundi im the dercofr50 m o
seonds. tis ounts or the large
dence betwe nth pot strelame
and the return streamer currents.
anthreunsemrcret.
30
oi
ments of electrical gradients within
storm clouds by means of free balloons.
In addition, it appears that the charge
made up of a number of separate discharges or strokes which, for the region
that can be photographed between
density is nonhomogeneous and is dis- cloud and earth, travel along the same
tributed in zones or charge centers.
path. The time interval between suecessive strokes may. vary between 0.0005
RATE OF CHARGE ACCUMULATION
Only a portion of the cloud charge is
to 0.5 setond and the total duration may
AND GROUND GRADIENTS
be a second, and in a fewdases even involved in this part of the mechanism.
After the lapse of 50 or 100 microseconds
The rate at which the charge accumu- longer. Infrequently the number con- t c
lates is relatively slow as evidenced by stituting a single flash might be as high . cl and gn is dischargen the
the measurements of ground gradients as 40.
stoke cnt groundidereases to
Each stroke when resolved presents a a relatirely small value. Thereafter the
by Wilsoni2 and others. Figure 3 is a
c
i
typical record obtained by Wilson which rather complicated picture. During the s
shows both the magnitude and manner process of charge formation or as a result sthrae atwis ldestreamers p a
te into the lo ad tamore char
of variation of this quantity. The di- of some local condition, such as vertical
vision between the solid black and shaded air convection currents, the electric field gate into thecloud and tap more rharge
areas indicates the magnitude of the near the base of the cloud may rise to
After some time one of the leader
gradient according to the scale on the such an extent as to exceed the value streamers propagating into the interior
left-hand side. Sudden discontinuities which air can withstand. The discharge may meet a similar leader emanating
such as that at A and B represent the is then initiated at that point and propa- from another charge center. In this
destruction of a portion of the gradient gates earthward at a velocity of the case the charge from the second charge
as the result of a lightning stroke. Im- order of 1/20 of one per cent of that of center is discharged through the original
mediately after the occurrence of a light. The current associated with this lightning channel as shown in figure 4
stroke the regenerative processes within so-called pilot streamer is small, of the and the same process is repeated except
the cloud begin to re-establish the field order of a few hundred amperes and its fr the fact that the leader streamer is
at the rate indicated by the rate of change luminosity is very low. As it proceeds,
not branched and stepped. After the
of the gradient. It can be seen that in the pilot or leader streamer is accomgeneral the curve is exponential in char- panied by points of luminescence which
acter and requires a time of the order of move in steps or jumps, which give rise
-----several seconds before the charging to the term "stepped leader". Each
process attains a substantially constant of these steps is about 50 yards in
value. The prominence at 14 hours length with fairly regular pauses. This
12 minutes 30 seconds was produced by process usually involves a fresh direction
the measuring device to establish the of travel after each pause, and these
zero line and is not a record of change in changes in direction are responsible for
GW.
gradient due to a stroke. The fine the well-known zigzag nature of lightrweather gradient"5 at the surface of the ning. Branching of the leader streamer
earth is of the order of one volt per centi- also occurs, the branching being outward
meter but during thunderstorms it toward the earth.i
may reach several hundred volts per
When one of these stepped streamers _
_
centimeter.
strikes the ground an intense streamer ofGW
GW
W
luminosity is observed to
MECHNIS
MECHAISM
OOFLIGHNIN
LIGHNING STOKEvery
TROKEtravel great
from the ground to the cloud.
r
The
knowledge
regarding
the
mecha-
nism of the actual discharge is due almost
entirely to the work of Schonland'4 and
his associates in South Africa. Approximately half of all lightning flashes are
314
The
velocity
of the
"return"
streamer is
Li~
quite high, being of the order of 10 per
cent of that of light. Its current is also
vrery high, being of the order of 10,000 to
200,000 amperes, values which have
2
Figure 2. Protective zones of one or more
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ground wires7
AJEE TRANSACTIONS
charge from the second center has been
dissipated, the same process may be repeated for the third and subsequent
charge centers.
McEachron"6
Figure 4. Propagation of natural light.
ingJ
has shown that in the
--
discharge of lightning to a very tall
building, the initial streamer usually
from the building in
the form of a stepped leader. This
stepped leader then develops into what
he terms a continuing stroke-a stroke
of long duration and relatively small
current. The subsequent strokes are
similar to those which follow the first
stroke of discharges that propagate from
cloud to earth. From the published
evidence and some small evidence obtained by the authors, the phenomenon
of leader streanmers from the earth appears to be characteristic, in the main,
only of discharges to tall structures.
Discharges to lower structures seem to
lack ground streamers of any great length
which rise to meet the pilot leader descending from the clouds. Schonland
in a letter to the authors regarding his
lightning investigations states that "it
must be remembered that the country in
which we work consists of rolling hills
and valleys, so that the base of the discharge is often obscured, there must,
however, be a large number of cases in
which the full length of the discharge was
recorded by the cameras and we have
seen no evidence of any extensive leader
*i)
proceeds upward
discharge from ground. Such ground
leaders as do occur are comparatively
short, for otherwise we should have de-
tected them."
Small streamers may and probably do
exist which in the case of strokes to
transmission structures rise from the
tower or conductors. In general, hewever, the evidence available seem., to
point to the fact that in most cases the
streamers, if any, are small.
The factors which control the path of
the initial leader determine the point at
which it strikes the line and therefore
the shielding characteristics of an overhead ground wire. Upon completing
Figure 3. Measurement by C. T. R. Wilson12
of ground gradient during thunderstorms
-E
.
4
...ft+......
(fo"'
=
(
4(4i
.....:*_, s .... s.
_
0
v
the initial streamer the path is determined thereafter even to the extent of
multiple strokes, all of which follow the
same path blazed by the first discharge.
CHARGE
According to Schonland,16 the quantity
of electricity conveyed by a lightning
discharge varies between 2 and 100 coulombs with an average value of about 20,
but McEachror "
his continu-ng
strokes has measured a value as high as
164 coulombs.
CLOUD HEIGHTS
A search of the literature reveals very
little definite data regarding the height
at which the stroke may be said to origi-
nate. Simpson and Scrace13 from a
hmited number of cases obtained in
England estimate charge centers as occurring as low as 1,500 feet and as high
as 30,000 feet Of course, the origin of
the stroke may not coincide with the
charge center but may lie between the
charge center and the base. E. J.
Minser, chief meteorologist of the Transcontinental and Western Air, may be
quoted as authority that in his experience the altitude of the base of low-level
thunderclouds frequently lies between
500 and 1,000 feet. He further states17
that his studies show that the majority
of lightning discharges were found to
have occurred in the cumulus clouds of
the shower type and that strokes to
ground occur most frequently from
.,;
I
...
clouds having the lower altitudes. Data
in possession of the United States
Weather Bureau indicate cumulonimbus
clouds as having a mean ceiling of 5,500
feet with some of them as low as 600 to
700 ieet. Thunderstorms for which the
ceiling is practically zero are also reported at times. Cases for which the
storm clouds actually envelop mountains
rising from a plain are quite common.
In view of such data as the authors
have been able to obtain it is believed
that an altitude of 1,000 feet for the
origin of the stroke is sufficiently representative and pessimistic for use in this
paper.
Fundamentals of Model Tests
Allibone and Meek'8'1' have demonstrated certain similarities between the
mechanism of natural lightning and that
of long arcs obtained in the laboratory.
It was considered advisable to extend
the study of the mechanism of such
laboratory arcs to determine the effects
of their characteristics upon the protective performance of transmission line
ground wires and diverters.
DEscRIPTIoN OF APPARATus
A3,000-ot.0-mcfadsug
generator was used as a voltage source
for the experiments. Various types of
electrodes were used to represent the
cloud, andfor most of the
conducting plane represented the earth's
presenmoth
surface upon which was placed the model
to be tested.
In order to vary the wave shape of the
voltage over a wide range, two different
types of circuits were employed. The
conventional surge-generator circuit with
a resistance in parallel with the gap was
used for waves with relatively steep
fronts such as the 1 '/2x4O wave. As was
done by previous investigators," for
1941, VOL. 60
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315
L_
I
A
-4
GROUND WIRE
PROTECTIVE ANGLE H
4T4 FAONDUCTOR
h Ix
plane was used as a reference and that
of the electrode specified with respect to
6ROUND I PLANE
////
it.
A high-speed camera was constructed
for the study of the visual characteristics
of the laboratory stroke. It consists of
a drum 13 inches in diameter which ro-
l
TO
GROUND
PLANE
STROKES
TO
GROUND WIRE
AREA
ITROES\\
SO
tates at 3,600 rpm and is enclosed in a
STROKES
GO
V40
an antenna. The voltage of the ground
I
7
boo
I /.Jrcapacity of this circuit has a very pro;R¢7'
ELECTRODE
nounced effect upon the voltage wave
t
shape its capacity had to be as small as
possible. For this reason a short length
I
of wire, about two feet long, was used as
on
NOUCT.9 N\\\
O__________________________
0
2
(b)
3
the high speed of propagation of the
leaders but also to the great luminosity
of the return stroke. For this reason
high-speed camera studies were restricted
to the slower waves.
Still photography was also employed
for studying the visual characteristics of
the arcs. Such pictures not only show
the shape of the path of the arcs but also
light-tight case. thisThirty-five-millimeter
something of the character of the leader
film is placed
drum and rotates mechanism. For this reason they are
20X//
to
path for measuring the progress of the
initial leaders. The camera will not photograph satisfactorily the leader mechanism of arcs produced with the standard
1l/2x4O wave. This is due not only to
4
/h
Figure 5. Symbols utilized with stroke distribution curves
waves of much smaller rates of rise this
parallel resistance was removed and a
high resistance placed in series with the
gap. It was then necessary to use a
capacity divider with the cathode-ray
oscillograph for measuring the voltage.
Since, as will be shown later, the shunt
past a stationary lens in a direction perpendicular to the direction of propagation of the stroke. It was found that
satisfactory photographs could be obtained of the leader mechanism of arcs
produced by voltages of slow rates of
rise with an ordinary f/1.8 lens and
Eastman Super XX film. Typical photographs of arcs made with this camera
are shown in figure 6. The rotational
speed of the film is such that time intervals as small as one microsecond can
be measured. Since in all cases the time
for the return stroke of the arc is much
less than this, the image of the return
stroke can be taken as the reference
Figure 6. High-speed-camera
photographs oF arc mechanism
using slow waves
particularly valuable for arcs which can-
by the rotating camera.
In figure 8 are shown still photographs of
strokes taken with the conductor and
ground wire in place. They were taken
in a direction parallel to the wires and
not be recorded
thus, as nearly as possible, perpendicular
to the arc path. Those showing more
than one arc were taken by exposing the
same film to a number of strokes taken
in succession under the same conditions
in order to show the variable character
of the paths.
DISTRIBUTION CURVES
In this paper the lightning protection
performance of a particular model configuration is based primarily upon distribution curves of the type shown in
figure 5. The fundamental tests on
ground-wire protection were made with
one ground wire and one conductor as
shown. The positions are specified by
following dimensions: h, the height
of the ground wire above the ground
plane; y, the vertical distance of the
ground wire above the conductor; and x,
its horizontal distance from the conductor. II specifies the vertical distance of
the electrode representing the cloud
source of the stroke above the plane
(or cloud height) and A its horizontal
distance from the ground wire, from the
same side as that upon which the conductor is located. All dimensions are
specified in inches. For a given configuration (value of h, x, y, and HI) it is
desired to deterline the terminating
point of strokes for various positions of
the electrode corresponding to various
values of A.
When the cloud electrode is directly
above the ground wire all strokes terminate on the ground wire. As A is increased a position will be reached, if the
conductor is not fully protected, for
which the strokes divide between the
ground wire and the conductor. Since
this is a statistical phenomenon sufficient
the
316
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AIEE TRANSACTIONS
strokes should be observed, 50 is usually
enough, so that a percentage division of
the strokes between the ground wire and
conductor can be determined. As A is
further increased some of the strokes go
to the plane and finally a position will be
reached where all of the strokes go to the
plane. The distribution curve of figure
5b is obtained in this manner. A//h is
used as the abscissa in these curves instead of A so that models of different
scale dimensions are directly comparable.
Frecquently cases occurred for which
strokes terminated at more thani one
place as shown in figures 8d and 8e.
Any strokes of this type which termninated on the conductor were counted as
strokes to the conductor.
Because of the slow rate of charge
formation in nature a better representation of the conditions of natural lightning
is obtained if the minimum flashover
voltage is used. Unless stated otherwise, all distribution curves were obtained by readjusting the voltage as A
was varied to obtain the minimum sparkover value.
GAP AND PLANE
The slowest waves used were obtained
with a series resistance of two mcgohms,
which gave a wave rising to crest of the
order of 50 microseconds. For this case
it was not possible to obtain spark-over
between point and plane for values of H
greater than about 50 inches for positive
polarity and 30 inches for negative polarity. However, when using the 11/2x4O
wave spark-over could be obtained for
spacings as high as 160 inches. For
such a spacing a ground plane at least 20
feet square is necessary to eliminate edge
effects. The difficulty of obtaining a
smooth surface of such size was solved by
the formation of a salt-water plane on
the laboratory floor. Tests made with a
dry metal plane, then with a metal plane
covered with water, and lastly, with a
water plane alone in which a network of
wires was laid below the water surface to
further improve its conductivity, showed
no essential difference. The salt-water
plane was employed for most of the tests,
MECHANISM OF SPARK
The first tests on arc mechanism consisted of determining the characteristics
of arcs of both polarities for a point-toplane gap. Some of the results of these
tests confirm the previous work of Allibone and Meek and will be discussed
here primarily from the standpoint of
lightning protection. High-speed camera
records obtained with a minimum flashover voltage and a very flow front using
1941, VOL. 60
the surge generator circuit with a twoFigure 7. Laboratory multiple strokes
megohm series resistance, are shown in
figures 6a and 6b. Examination of
these two figures shows that in the case decreases rapidly and it moves over the
of negative polarity, leaders start from final portion of its path at a fairly uniboth the cloud and ground and meet form speed, of the order of i/looth of a
about midway in the gap. However, per cent of the speed of light. The posiwith positive polarity there is only a tive leader which rises from the plane
positive downward leader. This char- moves continuously at a fairly uniform
acteristic difference has been pointed velocity of the same low order of magniout by Allibone and Meek"8 and others tude.
to be due to the fact that a positive leader
For the case of positive polarity the
will propagate at a lower gradient than a downward positive leader is sometimes
negative leader. For this same reason also stepped and exhibits the same charthe voltage required to cause spark-over acteristics as the negative leader. Quite
of the positive point-to-plane gap is frequently, however, cases are found
much lower than for the negative point- where it moves continuously, starting
to-plane gap.
at a relatively slow velocity from the
The negative downward leader for the point electrode and increasing its velocity
case of the negative-polarity point elec- until it reaches a critical point in the gap,
trode was found in most cases to be then proceeding for the rest of its disstepped in character as shown in figure tance at a uniform velocity of the order
6b. The negative leader starts from of
of 1/looth of a per cent of
the electrode at a very high velocity, too themagnitude
speed of light.
high to be measured with the high-speed
Similar tests made with the ground
camera, but dies out after progressing a wire and conductor in place are shown
short distance. Before the occurrence in figures 6c and 6d. In this case it is
of the final streamer there may be several seen that for negative polarity the upleaders of this incomplete character, ward positive leader is the more preeach progressing further than the pre- dominant one, there being only a short
vious one. The final leader also moves negative downward leader. For posiat this relatively high speed until it has tive polarity the reverse is the case,
reached a point somewhat farther than there is only a very short upward leader.
the previous leader, then its velocity The character of the positive leaders for
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317
Figure 8. Still
g r a ph S
showing charac-
photo
ter oF arc paths
by the character of the wave shape is the
duration of the luminosity of the leaders
and the current which flows from the
electrode into the leader. The capacity
of the point-to-plane gap is relatively
small so that if no additional capacity is
in parallel with it the regulation of the
voltage at the gap is very poor when a
large series resistance is used. At the
instant the leader starts from the electrode enough current is drawn through
the series resistance to cause the voltage
to drop. Under such conditions of
regulation the current flows into the
leader only a very short time after its
start from the electrode. The leader
propagates at a relatively low velocity
and its luminosity dies out rapidly behind the leader tip. Thus the leader
photographs on the rotating camera film
as a nartow line. This is shown in figure
6d. In the case of natural lightning it is
thought probable that a considerable
voltage drop may exist in the lightning
channel during the propagation of the
downward leader. This is caused by the
recombination of free charges behind the
the two polarities are similar to those for
the point-to-plane gap.
The relative development of the two
initial leaders is thought to play a dominant part in determining the distribution
curves and it is felt that this is one of the
most important characteristics which
must be correctly simulated in the model.
As will be recalled, the discharge of natural lightning, which is usually negative,
is accompanied by very little streamer
formation from the earth. Peculiarly,
this is more closely represented in the
laboratory by a positive discharge which
likewise has relatively small leaders
emanating from the ground plane. Negative strokes in the laboratory, on the
other hand, have quite large streamers
from the plane. The difference between
the character of the negative stroke in
the laboratory and in natural lightning
in this regard is probably due to the relative difference in the field gradients at
the ground in the two cases. It is
thought that these gradients are much
higher in the model due to the fact that
it is not possible to get breakdown of a
point-to-plane gap without a certain
amount of corona streamer formation
from the point electrode. This increases
the effective size of the electrode and thus
the field gradient at the ground for a
given voltage. Further, this tends to
decrease the field at the upper electrode
and increase the voltage necessary to
318
cause the leaders to progress downward,
Due to this fact it is thought that the
ratio of the cloud potentials in the case
of natural lightning to the model pOtentials is considerably less than the
ratio of their dimensions. These differences may be increased further by the
lower breakdown strength of air at the
high altitudes at which the stroke originates in natural lightning as compared to
that at the earth.
One factor which is influenced greatly
100
d
z
leader tip. For the laboratory arcs this
condition is greatest for the above type
of discharge due not only to the fact that
a negligible amount of current flows into
the leader to re-establish its conducttvity
but also due to the drop in the series
resistor.
As the regulation of the voltage is improved by the addition of a parallel capacitor the current flowing into the leader
and the luminosity of the leader persists
for a longer time. The record shown in
figure 6a was taken with a sphere gap in
parallel with the point-to-plane gap.
By varying the spacing of the sphere gap
7.,
I
1
I
X
2 6so
20
20
- 0
|
|
| | -20
2
o
/0
3
100
1l
80
N\
a. _
40
x
W
Effet f:x
Eec o
9
Fi
Figure 9
wav sIIha
(a)-1 '/2x40
(b)-Slow rate of
rise
- l
|
-
-
l
I
3
I
3
(a)
4
4
0!
0
Wagner, McCann, MacLane-Transmission Lines
Authorized licensed use limited to: UNIVERSIDADE DO PORTO. Downloaded on October 13, 2009 at 14:02 from IEEE Xplore. Restrictions apply.
1
2
b 3
(b)
-
4
5
AIEE TRANSACTIONS
it served as a variable capacitor. The
increased duration of the leader luminosity is evidenced by the wide band of
lower
to the
the rer
luminositytothi
lowern luminosity
recdright
asofofshos
turn stroke. This record also shows a
greater amount of branching of the leader
than in the case shown in figure 6c.
By
the
addition
of
such
capacitance
it is also possible to produce multi strokes
having many of the characteristics of
those occurring in natural lightning.
Allibone and Meek produced such strokes
Table 1. Outages Due to Lightning for Lines Without Ground Wires
Length
Outages Per
of Covered
Years Outages
Total Line
Line
of
Kv
Lie
Ki
100 Miles
Line
Per Year
Reference
_____________________________________
Interstate Power
Company Clinton-Dubuque....... 66...
54
...
6... 277.
87
......
Pennsylvania Water
wood-York.
16-A
.
20-A.
23-BB ....
ence With Protector Tubes",
Electric Journal, August 1938
and Power Holt-
in this way. In figure 7a iS shown a
series of repetitive strokes produced in
Wisco and Monteith" Experi-
66 ...
ii....
..
11.213.
23
...
79.4...
140... 148.0...
132... 39.8 ...
6..
Above 100 kv-steel ........ 673
560
...
1929
1930
.
current can be varied over a wide range.
60 to 100 kv-wood.......
...
1929
.......
31B32...
......
37.2
394
.21
14
Lightning-
EEI Publication No. F6
Sporn, "Lightning Performance
111.0 ... 1.
0
14.853... 10.. 61
...
Design, Construction,
Hansson,"
and Operation of a
Proof Transmission Line,"
...............2
10 .5.6
8.
this manner. By varying the magnitude
and wave shape of the applied voltage
and the parallel capacity the number of
repetitive strokes, the time between
and the magmtude
them, and the them,
magnitude
of the stroke
34 0......
84
of 10 to 165 KY Transmission
Lines", AIEE TRANSACTIONS,
1939, page 294
Lakes Division of NELA,
1929-30 report of overhead
committee
...... Great
26.6 .
~~~~~~~~~~~~systems
1930-31 report of engineering
By this method it is possible to study the
erating records 1930
1929
recovery characteristics of air. In figure
60 to 100
.
23.5
30
7b is shown
case in which there
60 kv-wood.
73
...19........5........34.6
30.4
30to
60...9
.........k2 .193
only
two
microseconds
strokes
565
.
two
apart.
only
... 1929 .........17.6
~ ~ ~ ~ ~~~~~~0 o6 k-tel......165
This record is of interest because it
128 ... 1930 ............... 14.2
shows the presence of a stepped leader
for the second stroke.
As stated previously, the process of speed of propagation of the leader in- wire when a series resistance of one
charge generation in actual clouds is creases. The velocity of positive leaders megohm is used. This shows a negative
relatively slow. One would expect that of continuous character increases uni- leader bridging about one-third of the
the laboratory representation of this formly. For leaders of stepped char- gap as compared with the much shorter
condition would be most closely simu- acter the number of stepped leaders de- leader of figure 6d.
lated by a continuous voltage. This creases rapidly. The effective velocity
The effect of waves of very steep fronts
condition is difficult of attainment but of the negative leader increases some- such as those of standard 11/2x40 waves,
can be approximated by the use of waves what faster than that for the positive. can be studied by still photographs.
of very slow rates of rise. As will be High-speed camera records, obtained The direction of branching of leaders of
shown subsequently, this is not a very when the rate of rise of voltage is gradu- both polarities is always in the direction
important factor. As the time to crest ally increased by decreasing the series of its propagation. By this means it is
of the wave is decreased or the crest resistance, show this effect. Figure 6e is known that a particular leader progressed
magnitude of the voltage is increased the a record of a negative stroke to the ground at least as far as the last branching point.
As the leaders approach each other they
07-/O
branch out, and frequently several meet
- simultaneously, the return strokes ocsoe
I I < H Acurring along all of them. This forms
i
/ \several parallel paths over a short dis06
-tance of the arc at the junction point of
- ..
40
-m
the two leaders and
another
for
method
the
.
determlining
meeting
-topoint of the leaders. Both of these
--t -w z ' /|
-4
2
3
I1
4
5
2
3
characteristics can be seen on the photoA/h
A/h
graphs of figure 8.
MINIMUM FLASHOVER VOLTAGE
50% OVER M. F. 0.
The examination of many such still
21X40 NEGATIVE WAVE
pictures shows that for the 11/2x40 wave
the essential characteristics of the point-oo- - -L l | i | J L1 1\1 l |
to-plane gap alone and with the ground
°l 2 | / 1\ 1 1 1 | T\ I\ l |
~~~~~~wireand conductor in place:are the same
as with the slower waves. However,
60_W +/ \
| | t\\ _
relative development of the negative
~~~~~~~~~~~~~the
40 _ / t t
I I I \ _
although rather variable, is usu20-ally somewhat greater. This is most
the case
positive polarity
0i
I
2
3 ol fL1 1 0 | Lj | | 1 X1
2
forinwhich
theofnegative
ky-steel.....481
are
a
to
-1
provides
~~~~~~~~~~~~leader,
~~~~~~~~~~~noticeable
3strokes
I§X4O POSITIVE WAVE
HaSO h-lo Xa2 hal
MlNMU
FLSiVRVOTG
1941, VOL. 60
0% VRMF0
Wagner, MlcCann,
Figr 10. on disovervoltage
Effect of
tribution curves
ulpward
leader is found to have maximum lengths
as high as one-sixth the gap spacing for
point-to-plane gaps and one-fifth for
M71acLcne-Transmission Lines
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319
point-to-wire gaps for a ratio of H/h of
five to one. The corona streamer formation at the cloud electrode was found
to be considerably greater for the 1 1/2x40
wave than for the very slow one. This
additional effect tends to increase the
field gradient at the plane and thus the
relative development of upward leaders.
Table 11. Experience of Pennsylvania Water and Power Company
Mile-Years
for Data
Line
10
sO
s0
40y
s0
0
0.03 IN. Mg.
LOI
@r 0°°
-
-I--1X 40 NEG. WAVE
Hs20
h 20
--
60
40
Conductor
for positive-polarity sparks than for
negative ones. This is due to the fact
that the positive-polarity spark is initiated by a positive downward leader
traveling practically all the way across
the gap for both gap configurations.
The time lag and the voltage required
for spark-over are more nearly the same
for positive polarity and little affected by
the character of the voltage. The somewhat larger upward leader in the case of
the 1 '/2x40 wave has no appreciable effect on the distribution curves. However, for negative-polarity strokes the
point-to-wire gap is initiated by an up-
WEATHER CONDITIONS
All tests were made in the natural
atmosphere of the high-voltage laboratory
a-nd it was found that data taken under
0000
co
0
Per Year
Strokes to
Conductor
Per Year
°7-t,
6008
000 00
y/h
Strokes
ward positive leader which progresses
most of the gap length, while for a pointto-plane gap the leaders progress simul_
taneously from both electrodes toward the
P09. WAVE
1IX40
center of the gap. For this reason the
Ho .3
h*lO
time lag of the point-to-plane gap is less
XSUSIO
than that for the point-to-wire gap.
However, the point-to-plane gap requires
a higher voltage for spark-over for the
2 ~~~ 3A/h I ~~~~~" 3A/h ~~~same spacing. Thus voltages of slower
rates of rise will break down the point-towire gap more readily.
WINTER
%00
00
0
(Degrees)
between the wires and the ground plane.
The slower the rate of rise of voltage the
larger the value of A/h before strokes
start to go to the plane. Thus a greater
proportion of strokes will go to both the
ground wire and the conductor and the
conductor is less protected for this type
of wave.
The effect of voltage upon the character of the distribution curves can be explained by the nature of their leader
mechanism. The spark-over characteristics of the point-to-plane gap and the
point-to-wire gap are more nearly equal
ac
ASS. HUMID. 0.566
Per Cent
Line Per
Safe Harbor-Riverside ... 230 . 837.
16 ... 0.29 . 106 . .
0
0
Safe Harbor-Perryville ... 132 ...... 158.
17 ...... 0.18 .. 153 .
0.4 ..
0. 6*
Holtwood-Coatesville .... 69......
52and71..
0.11
.
59
.
192
1.75.
3.4**
_______________________________
* One flashover in five years. ** Two flaghovers in two years.
Results of studies to detei mine the
effect of the character of the applied
voltage upon the distribution curves for
both positive and negative strokes are
shown in figures 9 and 10. Figure 9
shows the effect of wave shape and figure
10 that of overvoltage. From these results it is seen that the nature of the
stroke voltage influences greatly the
curves for negative polarity strokes and
has little effect on those for positive
strokes. The greatest discrepancy caused
by varying voltage conditions for negative strokes is in the variation of the position of the portion of the distribution
curve formed by the division of strokes
REL. AIR DEN. 0.992
Strokes to
Safe Harbor-Westport
and
WAVE, SHAPE, AND DISTRIBUTION CUR~VES
SUMMER
Ky Considered
Angle
--
|
variou4
conditions did not
vroscniin
check in the case of the negative-polarity
atmospheric
X.yz4
strokes. The predominant change in
the atmosphere is in the humidity which
may vary from an absolute value as low
AXlA
3
001 r
31
2
Vh
2
as 0.01 inch of mercury in the winter to
ABS. HUMID. 0.679
0.001 IN. Hg.
as high as 0.6 inch in the summer. The
REL. AIR DEN. 0.985
1.01
effect of this factor is shown in figure 11.
Data published by Y. Ishiguro20 show
that
for point-to-plane gaps increasing
0
000
o
i
o
l
the
increases the breakdown
0=
humidity
" V 10 9)
100
XX vv
-. -_-uW W1 - }
1\ 1 |
in approximately the same pro60
portion for positive polarity. For negaA0 - |IXNGWV
O
tive
polarity, increasing humidity dezoLg 4
|
\ |
0 NE.WAVE
60 ~
- 7
hs20
creases
the breakdown voltage for point40||
X. 4
|\
....to-plane gaps
and has little effect for
l
~~~~~~~~~~~~point-to-point gaps. In referring to the
to F tt 1 1 1 1
r J &1|
11.
distribution curves for negative polarity
O~~~' AI, 2 ! 3
4 A/h
of atmospheric con- of figure 11 it will be seen that in that
ABS. HUMID. 0.627
0.106 IN. Hg.
ditions on distribu- part of the distribution curve for which
REL. AIR DEN. 0.97
1.00
-tion curves the strokes divide between the ground
~0=I
~~~~~~~~~~~~~voltage
~~~~Figure
320
Wagner,
EKfect
MIcCann, MacLane-Transmission Lines
Authorized licensed use limited to: UNIVERSIDADE DO PORTO. Downloaded on October 13, 2009 at 14:02 from IEEE Xplore. Restrictions apply.
AIBE TRANSACTIONS
,0n
0oo
O~e4
3
,oT 7
Ex
*o40
h
4
I
2
[
|3 t
_
60 __ + _ _
~2
1
3
xX.
l
t 11 1 | h.20t
tSt A
t
40
go
s
I40
20-
4 i
Ll
AU
r
e7L +7_-
_
r
E-
loo
SO
ever, a very definite effect for negative
4° | < 4
< | L| hs10
1 t S L2
2 3
too
0
00L
2
.O
ro7-i
m
CL WJ h5LH
_A
>1 L 1;1R1 I
2
;
40
r
4
|
I
k{
I
*1X40 NEGATIVE WAVE
1i4,.3
~
nLii
'
[
I
t
2
i1iiil
3
1
I
\ I
A
oL--,P
^
%
*1(40 POSITIVE WAVE
1 b4
I
%.4 *~0.2
Figure 12. Effect of changing scale
wire and conductor the breakdown voltage is not influenced to any considerable
extent by humidity but where the strokes
divide between the'wires and plane increasing humidity decreases the breakdown voltage. Applying Ishiguro's data
indicates that there should be no substantial change when the distribution
occurs between wires but where the distribution occurs between wires and plane
a greater proportion of the strokes should
go to the plane at higher humidity.
This has the effect of moving the distribution curve to the left in this region.
In the case of positive polarity the breakdown voltage of both point-to-wire and
point-to-plane gaps are affected only
slightly and therefore one would expect
little effect upon the distribution curves
as is borne out by the results of figure 11
and a considerable amount of other unpresented data.
GEOMETRIC SIMILITUDE
Tests were made to determine the effect
of geometric similitude. In figure 12 is
shown some of the data in which the
scale dimensions were varied over a
range of eight to one. The results of
these tests indicate that the range of
scales considered has no very great effect upon the distribution curves for
positive strokes. The very small effect
that may be present is in a direction to
make the protective value less for small
scales, which would produce pessimistic
results in model work. There is, how-
1941, VOL. 60
3
point; thus the division of strokes in
strokes.
As the scale is increased, and
thus the spacing
between the cloud electrode and ground, the range of A/h for
Awhich shots go to the wires decreases and
distribution
curves. The first component
of the field has,
however, a very definite
directive effect in influencing the ionization process at the leader tip and an apapproaches the results obtained with preciable
upward leader influences the
positive strokes.
downward one.
X
_The greater irregularity of arcs proFAC ORS A]?FECT G ARK PATHduced
by slow waves is probably due to
Exsamination of the still pictures of the fact that since the breakdown voltfigure 8 show how variable the path of age is less the directi've field is weaker
the arc is even though conditions are and has less directive effect. It thus
maintained as nearly constant as pos- approaches more closely the case of
sible. As the leader tip progresses it is natural lightning. By taking a large
apparently very unstable and easily number of shots in obtaining the disaffected by its own irregularities. For tribution curves a statistical average is
this reason it follows a tortuous path. obtained of the effect of the factors which
The paths of the negative polarity strokes influence the path of the arc. The fact
are much straighter and more closely
that wave shape has no effect upon the
grouped than those of positive strokes, distribution curves for positive polarity
while the paths of the arcs of slow volt- indicates that on the average the actual
age
J11!IEwaves are more spread' out and more magnitude of the directive field is not
irregular than those of the 11/2x40 waves. important. It is merely its relative
In considering these factors it is con-
value throughout the region in which the
venient to segregate the field at the tip
of the leader into two parts: that produced by charges remote from the tip including the effect of the leader from the
opposite electrode; which will be called
the directive field; and that produced by
the ionization phenomena taking place
in the region of the leader tip. The irregularities at the tip cause one arc to
have a totally different path from another and possibly a different terminating
arc might progress that determines the
average result.
The greater upward leaders in the
tests with the I1/2x40 waves over those
in the tests with slow waves had no effect
upon the distribution curves. Arguing
from these results, the extremely small
upward leaders that may occur with
natural lightning should be insignificant
in determining the terminating point of
the stroke.
O7-
.
IA
s1o
1oI
I
-
4
20
lo
r,,,,T0T2
4
- -
-
o
i3 i
-
I
FA-fAj
so
60
I
--
-
40
20
17 I I 7
\>r^/h
7
(b)
2
toe --
Figure 13. Effect of the presence of other conductors on
the protection of the most exposed conductor
1 '/2x40 positive wave, H/h =3,
y/h =2
3
- -v
p181 1.1/|q
[A
> |
S C-6C - - - -8 - <41
t °z
14 1
0
7rTT77T,,,TT
,,77TTll7
77 7
(c)2
Wagner, McCann, Maclane-Transmission Lines
Authorized licensed use limited to: UNIVERSIDADE DO PORTO. Downloaded on October 13, 2009 at 14:02 from IEEE Xplore. Restrictions apply.
|/
|^/
l
|X|
l
321
So far leader development and distribution curves have been considered
for a rod electrode only. It was felt
that perhaps the shape of the electrode
might have a certain directive effect
upon the leader in its vicinity and thus
influence the distribution curves. To
test this point a special electrode was
made by soldering a small wire one-half
inch long to a ten-inch sphere. With
the wire directed downward from a
height of 30 inches a distribution curve
was obtained for hh=10, x=4, and y=2.
This electrode gave the same distribution curve as a rod electrode and
,
643:=01
640
_
__ _
- -
h_o.I
HA=20
2,-.N
_
1.,-
-4_ 5
6
7 A/,
64*
°°I__I
H=13
|
It must be remembered, however, that
any results which can be deduced with
models can only be of a statistical nature. The distribution of charge within
a thundercloud is likely to be unsymmetrical about the point of origin of the
discharge and will influence to some extent the shielding value of the ground
wires. In open, level country this dissymmetry should, however, be eliminated by the statistical averaging of a
large number of strokes. Where the
prevailing storms in a locality originate
from the same direction this may be
true but, in general, any effect of this
oo107-
=0.2
L{ [t
ttXi
2
3
4
5
@°°1 11 > 111 11110l11 X1\11
I II
1 1 V 1\1 1 1
01 2
°3
6=5 ||
t /||\|
4
S
. 100r|
XE
p61
0 \ {
_ F}
This consideration would
tion for the prevalence of negative strokes
%=O.2
to transmission lines.
1
2
3
4%
27°Y0.
mHResults of Model Tests
Correct proportioning of the model
to those in actual practice resulted
EtELwires
in destruction of the wire for each shot.
1 12\
I1
was therefore had to larger
1\1 III
1
HRecourse
conductors. Distribution curves made
jjjjIS\
eoo
2 3 4
2
s
lWl\m
3%h
with wires of diameters varying from
~~~~~0.008 inch to 0.09 inch showed that wire
~~~~~~sizehas negligible effect for positive
H/;=3 1 } 1 A I I I ~~~polarity. Tests made with
however as may be
t1 I
F f 1\
~polarity
not so consistent.
0U I I i \I
1A/ 01
Figure 14. Effect of varying H/h for diffe ent
configurations
I~
~ H/h~ =20,~ all ~other curves
~ ~~h=10 ~rz
visual observation indicated that the
discharge was initiated from the wire of
the sphere in all cases. The proportion
of sphere diameter to electrode height
corresponded to proportions that might
be expected in thundercloud formations.
FINAL CHOICE OF LABORATORY MODEL
Consideration of the above results
leads to the conclusion that a good representation of natural lightning for
studying ground wire shielding on model
scales is obtained by using the minimum
flashover value of a l'l/2x40 positive
wave with a rod as the cloud electrode.
322
laboratory by positive
appear to throw doubt upon this explana-
f II I iX
1AX A/h
0I1 IY 2I183
electrode attracted a larger proportion of
negative than positive strokes. This
was used as a basis to explain the greater
prevalence of negative strokes to transmission lines. However, since the relative leader development is all controlling
in determining the point struck and since
the relative leader development is the
same for both positive and negative
lightning strokes they should be reprewaves.
t
1
ATTRACTIvE EFFECT OF POLARITY
Allibone'9fromlaboratory testsshowed
that a small projection from a plane
sented in the
LA
450
1 2 35 4
closely approach the laboratory negative polarity stroke in their relative
leader development. Since it is found
that strokes with a predominate upward
leader give entirely different shielding
results conclusions drawn from data obtained from such tall buildings cannot
be applied to lower structures for which
the leader development is different.
R
i
I
A/hare
negative
expected
IT'F
GRUDN OF CoNDucToRns
l
i|||
l lllThe speed of leader development is so
slow that it is thought that both the
'/x4 poitv poaiy h = o uv
A
2 3 A/h
ground wire and conductor, except for
°
1
3/h
the dynamic voltage, remain at essentially
ground potential during the development
nature should be very small.
of the leaders. However, to verify this
A distribution curve obtained for any point the effect of having both the ground
configuration which shows no area for wire and conductor grounded was comstrokes to a conductor does not mean pared with the case for which the ground
that no strokes will ever terminate on wire was grounded but the conductor
the conductor. If enough shots are oh- connected to ground at each end through
served it will be found that eventually 500-ohm resistors to represent the surge
in most practical configurations a stroke impedance of the line. Little difference
will finally strike the conductor. For was found for these two cases. Other
this reason isolated records of natural tests in which the conductor was insulightning which show strokes terminating lated gave somewhat better protection.
within certain regions of protective The most pessimistic results are ohspace should not be overemphasized,
tamned by grounding the conductor, a
Another important consideration is condition under which all subsequent
that strokes to very tall buildings more tests were made.
H/h=2
2IIil
Wagner, McCann, MacLane-Transmission Lines
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AIEE TRANSACTIONS
Figure 15. Effect of changing protective angle
ously as H/h is increased.
1 '/2x40
sult is in direct variance with that obtained by Matthias8'9 who concluded
450
positive
h =20 for curve
y/h=0.05,allothercurvesh=10; H/h=5
y4io.05
640
2IIWII
00
4o,
2
%
560 _
EITIII
JLLL
L
Y/h=02 ||1\\1
Llt Ll-
100
°LiIfl
2
that above a value of Il/h of 7 the proportion of strokes which strike the conductor is constant. Figure 17 is interest-0/07ing in showing the general effect of chang720
ing y/h while keeping the protective
IIIjII1I1I
Tangle and H/h constant. Figure 18
_ e L__ t_
444
shows how the strokes to conductor vary
as the protective angle is altered for
different values of y/h.
The curves of figure 1 were plotted on
2
3 /
~~~~~~~~~the
theory that the stroke strikes the
68°
nearest object, that is, either all the
terminate on the ground wire,
all on the conductor, or all on the plane.
1zl
< 4
~~~~For_H/h equal to 5 the protective angle
t1 4 4 =1 + d<t i 9!¢ 1 is 55 degrees and is essentially independent of y/h. Figure 18 emphasizes that
3
h
the desired configuration is dependent
444i4i,{
Y/h0o. [II11
0/h3.4
polarity;
3
h
2
1
2
3
X W1\X W-;
-
3
<
2
Xl I Istrokes
>
3
I<
2
k
to a very great extent upon the degree of
shielding to be expected. Thus for 99
per cent shielding the protective angle
varies between 46 degrees and 60 degrees
effect for particular locations in laying
out the entire line.
01
\l I
2
PRESENCE OF OTHER CONDUCTORS
Actual transmission-line construction
involves more complicated conductor
configurations than the simple ground
wire and single-conductor arrangement
so far discussed. To determine the effect of the presence of other conductors
upon the general problem of shielding,
tests were made upon several arrangements of ground wire and conductor.
Figure 13 shows a portion of the results
of these tests in the form of distribution
curves. It was found that the added
conductors of b and c which are indicated
by x's were not stricken as the electrode
was moved to the right of the ground
wire. In addition, the distribution
curves are not influenced by the presence
of the added conductors. Additional
ground wires likewise had little effect.
The following data are, therefore, confined to the single-ground-wire and
single-conductor configurations.
EFFECT OF CHANGING H/h, y/h,
AND
ANGLE
%The PROTECTIvE
effet of varying H/h, y/h, and
the protective angle are shown by the
distribution curves of figures 14 and 15.
In figure 5 areas G and C are proportional
to the total strokes to the ground wire
and total strokes to the conductor, respectively. The ratio area C/(area C+
area G) then represents the proportion of the total strokes to the structure
which strike the conductor. Data of
the character shown in figures 14 and 15
supplied information from which the
curves shown in figures 16, 17, and 18
were plotted. Figure 16 shows that the
strokes to conductor decrease continu-
effective is unimportant in level terrain.
In mountainous conditions particular
°
l
figure 2 by Schwaiger. However, the
curves by Schwaiger result in protective
angles which are entirely too small.
In order to orient one's self with regard to the nature of these parameters it
is necessary to consider their magnitudes
in actual transmission systems. The
height of the ground wire above ground
in fiat terrain varies from about 40 to
140 feet and y/h from 0.1 to 0.2. Using
a ground wire height of 100 feet and a
.10
l l
4 -5
-
U
30
y/h varies between 0.05 and 0.2 and if
tween 51 degrees and 72 degrees as the
shielding varies between 99 per cent and
95 per cent.
The safe location of a conductor has
frequently been described as any position within a volume enclosed by two
plane surfaces intersecting the ground
wire and making an angle of 45 degrees
with the vertical. The curves of figures
17 and 18 show that these surfaces should
not be plane but curved concave upward
in a manner similar to that shown in
50
-
to conductor as a function
zz
\tFigure
W T of16.H/h,Strokes
y/h, and protective
8
angle
W.U
,, ,,,
O
J
°
0 z
zy>
\ IPROT.ANGLE64°
}- °
0.2
I\
15l\j\
| 45*i
64-*
|
IC02
XvoX
I27i \S;450 |\
o
towers supporting spans having large sc°|{ x<|1|11sags might prove to be advantageous X )o1i_Sc
from this viewpoint. It would be runwise, howevrer, to take advantage of this
as
y/h is 0.1 the protective angle varies be-
60
°
o X|
g °
z ac
0
X
x
TOWERS
The point from which insulators are
supported on steel suspension towers is
directly above the conductor and naturally tends to protect it. Tests show,
however, that the extent to which this is
1941, VOL. 60
This re-
1
2
6 -8
~~~~4
-
x10v+Ir--_ 14
12
16
IB
20
H/h
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22
24
26
28
30
/
8
323
modelwrktaserntivo41607ofthedisrlbuncvewhi r
cloud height of 1,000 feet, gives a value
of H/h equal to 10. Examination of
figure 16 indicates that for these conditions and y/h equal to 0.2, and a protective angle of 64 degrees, 5 per cent of the
strokes strike the conductor. It must
be understood, however, that these conditions are not met in practice except in
flat country with very low soil resistivity.
In rough, rugged, and hilly country advantage is usually made of locating towers
on prominences so that the effective
height of the ground wire above ground
is considerably in excess of that at the
tower. This fact prompts the use of a
smaller value of H/h and y/h than just
mentioned, both of which decrease the
protection afforded by the ground wire.
For example, if h is doubled the corresponding values of H/h and y/h would
then become 5.0 and 0.1, respectively,
and from figure 16 it can be seen that 30
per cent of the strokes would strike the
conductor.
SOIL RESISTIVITY AND COUNTERPOISE
Soil resistivity might likewise affect
the appropriate value of h to use. The
propagation of the initial leader of natural lightning is so slow that for ordinary
soil conductivity the surface of the earth
is probably maintained at essentially the
same potential. For dry, sandy, or
rocky soil this consideration does not
apply and the equivalent depth of earth
plane should be lower than the actual
surface of the earth. Matthias9 in his
model work took as a representative
case a layer of dry sand of approximately
the same depth as that of the groundwire height. While this may be typical
in so far as resistivity of the soil and
geometric similitude is concerned it
does not follow that the voltage gradients in the earth are in proportion. In
order to show the general nature of this
phenomenon the tests illustrated in
figure 19 were made in which high earth
resistivity was simulated by simply
lowering the ground plane by a depth
equal to the ground-wire height. A
comparison of figure 19a and b indicates
quite conclusively that lowering the effective ground plane decreases the shield-
ing of the ground wire.
A buried counterpoise might be thought
of as raising the effective height of the
true water plane. However, a comparison of figure 19b and c shows that this is
not the case, the counterpoise having
practically no effect. The rather impractical condition of buried counterpoises at a distance from the tower equal
to several times the tower height would
in all probability have a beneficial effect.
TRANSVERSECONTOUR
The transverse contour of the topography likewise has an important bearing
on the shielding value of a ground wire.
Figure 20a shows a tower of a line running along the side of a hill. It is apparent that the effective earth plane is
inclined and that the protective angle
should be measured with respect to the
perpendicular to this plane. Thus the
--7-/
_ _ o
6 -
0
-i
- - - - - l
b
41
a
l0
3
g
- --
0
z
o
-
-
! 0.05
~_40
50
60
V
l
70
PROTECTIVE ANGLE
Figure 18. Strokes to conductor as a function
of protective angle for H/h= 5
protective angle measured with respect
to the vertical of the tower should, for
perfect protection, be increased by the
angle of inclination of the earth's surface. Naturally this is additive on the
downward side and substractive on the
upward side. But if the particular configuration provided adequate shielding
-on level terrain the decrease in shielding
*Z7
' -o _ illiiijii __4 on the lower side is not counteracted by
an increase in shielding on the upward
I| .5
o~~~~~~~~~~~~~~~~~~~~~~
- 45*
- - side. For the case shown in figre 2Gb
which represents a tower on a hillock,
8
F6A
_
R 8 4 \l
ll
_l both sides are additive. To further
this fact tests
I- - I
-o erfl:l
- SL
in figre 21 were made. Comparison of
_ -X
- _~ 0.1
_ 0.3
,_
the two
distribution
curves
shows
0.2
Q
that
the upper
dropping
away of the
earth
dethe
protection
considerably
h
Figure 17. Strokes to conductor as a function whereas the comparison of the two lower
of y/h
distribution curves shows a marked gain
-/o7
_-
~~mphasize
~~~~creased
824
thLe
illustraLted
in protection by the presence of the
neighboring hillside.
CONDUCTOR MIDWAY BETWEEN Two
GROUND WIRES
In order to determine the shielding
characteristics of conductors between two
ground wires, tests were made with
such a configuration that the distance
between ground wires was one-half the
ground wire height. This is representative of the maximum spacing for construction employing conventional ground
wires. A pessimistic cloud height corresponding to H/h equal to five was
chosen for the test. It was found that
for the conductor to be perfectly shielded
it was necessary to lower the conductor
at least 15 per cent of the spacing between the ground wires. By increasing
the spacing of the ground wires to a
value equal to that of the ground wire
height it was necessary to lower the conductor at least 10 per cent of the spacing.
The latter spacing is typical of the requirement for diverter construction.
STROKE DENSITY AND STROKES TO LINE
In an effort to apply a quantitative
measure to the effectiveness of groundwire protection a knowledge of the number of strokes to the line, S, per hundred
miles per yea is required. A shown n
l appendix his qu ntity
the
in terms if
the stroke density, D, in number per
square mile per year, i equal
o Dh/26.4
square
equa
G+
G +
ar
a
towdhge
C). From a knowledge
oibi
ves hi were
and y, the quantity S/Dh may be plotted
(rea
area
as shown in figure 22a. The strokes S
are thus proportional to D and are a
function of H and h. In figure 22b these
data are replotted with S/D as the ordinate and H as the abscissa for h equal
to 50, 75, and 100 feet. It is interesting
to observe that for a given stroke density
the strokes to .the line increase with the
height.
Tests with two ground wires separated
varying distances up to one-half the
ground-wire height showed little difference in the total area representing strokes
to the structure. Thus there should be
little difference between the total strokes
to a line with a single or double ground
wire or between a single- or double-circuit line. In what follows strokes or
outages will be based on a line rather
than acircuit basis.
Operating Experience
To correlate the laboratory data with
the performance of actual systems some
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AIFE TRANSACTIONS
o,0o07-/9
- - -
§°°0i07
^A
oJEPNICLR007- 20
Figure 1 9 (left).
Effect of high soil
G.L
--resistivity upon pro-
s
tective value of
-@^19.r.aX
._50
41--
CONDUCTOR
0
wires
01ground
'/2x 40 positive
0--
I
EFFECTIVE PROTECTIVE
-2-0polarityq
I
.
|
I3__'S
,
4 5 A/h Figure 20 (right).
(9
Cases for which lat-
H-8sSO
| 401
h io
7716,.,::77,,.,.,,,.,,,,,,,,,,,
GW
40
1{
nlCONDUCTOR
i
|
>
F
EFFECTIVE PROTECTIVE
ANGLE
---
20---(b)
-i- *
2
3
4
R5 /h
40 - - 20 - - -
halo
7'.0- COUNJERP,OISE
'O.,,,,, , , ,,c:
-i2
(C)
-published data are available and, in
addition, a number of utilities have
.made available to the authors certain
unpublished data.
STROKES TO LINE
E. Hansson and S. K. Waldorf, from
data obtained with magnetic links between 1935 and 1938 upon 703 mile-years of operation of lines of the Pennsylvania Water and Power Company,
-indicate an average of 116 strokes per
100 miles per year. Bell2' from data
.accumulated between 1926 and 1933 on
the portion of the Wallenpaupack-Sieg-fried line (without ground wires), ob-tained a value of 82.8 flashed towers per
100 miles per year. This figure is probably lower than the actual number of
strokes to the line as some of the strokes
-may not have left their markings. In
the same period data for the same line
-indicated an average of 25 tripouts per
100 miles per year. A comparison be-tween these figures shows that the fre-quency of lightning strokes should be
considerably in excess, something of the
order of three times, the number of outages. Table I is a compilation of outage data for a number of high-voltage
lines without ground wires. The
weighted average of these lines lies between 30 and 35. Applying the factor
-three to these values results in an esti-
4941, VOL. 60
angle
60
X *o
PROTECTIVE ANGLE
eral contour requires
smaller protective/
oo---~10-
A
NORMAL.
h-i
CI)
PETO GROUND PLANE
34
"
mated value of 100 strokes per 100 tites
per year. It must, of course, be remembered that this value is very much
of an approximation and will vary with
location and other factors. The ordinate of figure 16 which expresses the per
cent of strokes which strike the protected
conductor can also express numerically
the number of strokes to the conductor
on a basis of 100 strokes to line per 100
miles per year.
STROKES TO CONDUCTOR AND
OUTAGE DATA
The next step is to verify to what extent the data of figure 16 represent the
performance of actual system operation.
Before this is attempted it is well to
point out some of the difficulties encountered in this task. It will be observed first that the performance to be
expected of any configuration will depend
to an enormous extent upon the particular assumption of cloud height or
H/h. As pointed out previously, vrery
little data are available upon this point,
Cloud heights may and do vrary with
geographical location and local topography. Along with the variation of
storm numbers per year at different locations there also exists variations in range
of these heights. Two similar lines at
different locations might therefore have
entirely different performance records.
(b)
The variation of shielding with H/h as
shown in figure 16 therefore anticipates
that difficulties might be present in the
comparison of system performance.
In forming an opinion of what is adequate protection the criterion will be
adopted that the strokes to conductor
should be less than one per 100 miles per
year. For a value of H/h equal to 10
the curves of figure 16 indicate that a
protective angle of 60 degrees is adequate for a value of y/h equal to 0.2 and
50 degrees for y/h equal to 0.1.
Further obstacles are encountered when
an attempt is made to verify the extent
to which these data represent the performance of actual systems. It is difficult to isolate the effect of shielding alone.
Even for systems of very low tower-footing resistance the question still arises as
to whether flashovers might not be due
to currents of high rates of rise for which
the tower surge impedance and strokes to
midspan become important. Thunderstorms are usually accompanied by wind
and since the phase conductors and
ground wires are usually of different type
and sagged differently the protective
angle may be considerably greater at
midspan than at the tower. Of course,
on one side of the line the increment of
angle would be additive and on the other
side subtractive. The outage function
is not linear with respect to angle and,
therefore, the increased angle will cause a
much greater outage increase than the
decreased angle a decrease. However,
in some cases the smaller sag of the
ground wire may completely annul this
condition and even give the line a
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325
Figure 21 (left).
Effect of uneven()
ground plane
0007-2'
2 er 2
~
A
t
LLl
I.-A -
~
m2
T
50
o _
t
i
_
so0
112/x40
1
~~~~~~~
77,7mz1111 S
100
\L t |
60
0.31 ---
positive
~
- -
~ ~~~polarity.
- q///;///////Figure 22 (right).
Strokes to transmis_> line
< - as influ-°.
sion
enced
by cloud and
\ 1-
_
X
0/07-
l
ao
- I_
8
0
s
ground-wire height
0l|
Hl
[
10
P.0
a//,/''//
A
A
5
2
3
//j
/h/
i
5
h5
/h
i
100-
40
30
40
50
%/
40 |_
0
l
-
4
5
1
15~~~~~Jii_
11;
1
t~~~~~~~~~~~~~~A H~~~~~~~~~~~ ~
IN FEE
60
40
I
2
3
/h
4
A/h
5
0
1
smaller protective angle at midspan.
Hansson and Waldorf have supplied
the authors with the data tabulated in
table II. It will be observed that the
Safe Harbor lines to Westport, Riverside,
and Perryville, all have protective angles
well within the values set by the curves
as being adequate and the operating
experience verifies this result. The Holtwood-Coatesville line, being nearer the
limits set above, offers a better opportunity to check the laboratory results.
Inspection of the curves in figure 16 for
H/h equal to 10 and y/h equal to 0.1
shows that the per cent of strokes whicb
strike the conductor is of the correct
order of magnitude, the curves being
somewhat pessimistic.
The Fort Wayne-Marion-Muncie line
of the American Gas and Electric Corporation is interesting in that it has very
low tower-footing resistances, the average being about 2.5 ohms. The protective angle is 50 degrees and y/h is 0.11.
Data obtained from I. W. Gross giving
operating results over a five-year period,
representing 400 mile-years of operation,
shows 23 flashovers which is equivalent
to 5.7 per 100 miles of line per year. As
stated previously, the curves of figure 16
for H/Is equal to 10, y/h equal to 0.1,
and protective angle of 50 degrees give
326
2
one stroke per 100 miles per year, a
value which is somewhat low with respect
to the actual performance. It is probable that the change in angular position
occasioned by wind conditions is an important factor in this case since the line
is so close to the critical angle.
A number of utilities have maintained
rather accurate records of the resistance
of each individual tower and the particular ones upon which flashovers occurred.
By dividing the towers into classes according to their resistances and sorting
the flashovers into the same classes it is
possible, by weighting the flashovers according to the number of towers in the
class, to plot a curve of flashovers as a
function of tower-footing resistances.
This has been done for data relating to
flashovers and outages for several companies. The intercept with the ordinate
for resistance equal to zero should represent the effect of lack of shielding, tower
impedance drop, and possibly the effect
of ground-wire impedance for strokes to
midspan. Figure 23 represents data of
this type obtained for a 132-ky system
in flat country of low soil resistivity,
Data of this nature are of necessity somewhat random in character and it is difficult to determine the curve to be drawn
through the plotted points. The signi-
1000
2000
3000
4000
1*~~~~~~~~~~~~~~~~~~
5000
IN FEET
ficant fact is that the ordinate intercept
for resistance zero is zero or very small.
This would indicate not only satisfactory
shielding but also that the effect of tower
surge impedance is negligible. Published data22 for the Victoria Falls-Transvaal Power Company, plotted in figure
24, shows a similar result. This line also
transverses relatively flat country. The
results of these two systems check the
data from the model work.
Similar data supplied by I. W. Gross
applies to the system of the American
Gas and Electric Corporation and is
plotted in figure 25. Accepting the result of the two previous curves that the
effect of tower surge impedance is not of
any great importance, the y-intercept of
12 flashovers per 100 miles per year must
be attributed to poor shielding. This
number contrasts with about one per 100'
miles per year for y/h equal to 0.1 and a
protective angle of 45 degrees as dictated
by figure 16. For the same time for
which these curves were obtained the
total fiashovers of 521 corresponded to
371 tripouts. Applying this same ratio
to those due to lack of shielding provides
a value equal to nine tripouts per 100
miles per year. A large portion of the
lines involved in this group traversed
mountainous country in which the effect
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AIEE TRANSACTIONS.
Sc -
r
2 j
---IJ
_
2 t
III
16
14
I
-
--
o107-23
Figure 23. Lightning out-
n
- - --- - || t
7
132-kY system in flatcoun-
1,470 mile-yedrs
single
>
X Xx/h 0.093
y/h=0.152
- - - - protective angle=31.5 de-1 1
grees
11
-.--,
, 4
of
dnd double circuit
o0
-
10
a
age record of lines of
try
9
i l5.5
A
<
-
CO0
5_ _
10
IS
IN
of ten times the ground wire height a
25
20
FOOTING RESISTANCE
TOWER
ditions.
The results of model tests indicate
that to limit the strokes to one per cent
-of the strokes to the line for a cloud height
-
- - -
0
respect to a plane upon which is located
the model transmission line to be tested.
Positive-polarity discharges in the laboratory are more consistent in reproducing the same distribution curves and in
obeying the laws of geometric similitude
and also are less affected by weather con-
30
*
S
of transverse slope, the decrease of y/h
across valleys and canyons, and the
lowering of the equivalent ground plane
might be of considerable importance.
It is also possible that because of the
mountainous terrain, the cloud heights,
and thus H/h, are lower. In general,
the height of the ground wires on these
,
90l
-
Wo
- s
/ J3
-i5
93.8 - - -
H/ t
O
0T
2
60
-
50
-
>
° 40
W
U,
|
20-
- - - - 1 1
Z I
- - - - - - - - - - I
I |grees
1
0
record of lines of
Victoria
Falls-Transvaal
Power Company
132 kv, 444 mile-yedrs of
double circuit
age
.x/h=0.12,
.protective
-
4
8
12
TOWER
16
20
FOOTING
24
25
36
40
y/h=0.15,
dngle=40
de-
chairmanship of Philip Sporn submitted
a report23 in 1938 relating to the lightning
performance of lines between 110 kv and
165 kv. A number of the lines tabulated
in that report were selected for which the
avrerage tower-footing resistance was less
than ten ohms. Figure 26 shows the
outage data of these lines plotted ,against
their protective angles. Some of the
towers in this group must havre had a
52
apolis Power and Light Company. The
maximum tower-footing resistance for
this system is 11 ohms. The curve indicates that satisfactory shielding is obtamned for angles less than about 35
degrees. If an allowance of 10 or 20 degrees were provided for soil resistivity,
lowering of effective ground plane across
canyons and swinging of ground wires and
phase conductors, a substantial check
with laboratory results would be indicated.
Resume and Conclusion
The relative development of the leaders
preceding the actual discharge of the
lightning stroke is the most important
part of the mechanism which must be
correctly simulated in model work when
studying the shielding problem. In this
regard natural lightning, both from positive and negative charge sources, is most
closely simulated in the laboratory by
making a point electrode positive with
Wagner, M-ccann,
Z
70
-
us
60
-
7
0
96
7
5o -
Z~~~~~
C -
-
:
,
>
0
8
-
-
°-
- - -
7 o_
_
10
O
10
20
30
40
50
60
70
80
90
00
TOWER FOOTING RESISTANCE IN OHMS
Figure 25. Lightning flashover record of lines
of American Gas and Electric Company
132 kv, 2,426 mile-yedrs of double circuit
x/h=0.12, y/h=0.12, protective dngle=45
degrees
protective angle of 50 degrees is necessary
for y/h equal to 0.1 and 60 degrees for
y/h equal to 0.2. These values have been
checked substantially by operating experience upon lines in level count.
RESISTANCE IN OHMS
lines is larger than for the lines previously
considered, so that for a given cloud
height H/h is smaller which likewise
tends to decrease the shielding. Perhaps in view of these factors the agreement is not as bad as might first appear.
If the disagreement is to be attributed to
these causes, then it follows that the
nominal protective angle and y/h at the
towers must be corrected in some manner
to take these factors into consideration.
The lightning and insulator subcommittee of the AIEE power transmission
and distribution committee under the
1941, VOL. 60
44 46
L
yriri-<
sot
Figure 24. Lightning out-
- - - - l l-l
- - ll
- ll
IC0
72+
- -
40
6rTO
footing resistance considerably in excess
of 10 ohms which might explain some of
the outages. In drawing this curve
weight was given to the points which represented the largest circuit-years of experience. Information to plot the point
marked by an x was furnished by W.
Cronin, for the system of the Indian-
0107-29
T
9 l
OHMS
Other factors enter the problem, chief of
which are:
1. Cloud height. Strokes to the protected
conductor
decrease
with 16.
increasing H in the
manner
in figure
shown
resistivity and topography between
2.spans.Soil The
effect of high soil resistivity is
to lower the effective ground plane. A depression between spans such as a canyon or
valley has a similar effect. In lowering the
effective plane both y/h and H/h decrease
which tend to increase the outages.
3. Transverse contour. The slope of the
surface of the earth perpendicular to the
transmission decreases the effective protec-
tive angle by the angle of the slope.
4. Wind. The relative deflection of
ground wires and phase conductors under
the wind conditions prevailing at the time
of a storm may produce a very significant
increase in the protective angle.
If a 20-degree tolerance is allowed for
such uncertain factors as the above, a
recommended value of protective angle
at the tower of 30 degrees is obtained.
This should prove adequate for all practical values ofy/h.
MacLane~Transrnissia Lfines
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327
7
(
|.|
- -
_
H
#51
ZJ
0'0 7- 26
outage
Za . CIGRE2SeFigure 26.a Lightnsinog
_ - _
O
_ I
/
O
8
/
e
_.
3
-
-
a
-
0
-
I
-
-_ -L-_
-
-
-
I
-
- ~. ~~
0
-1D
t
10
record as function of protec_ _angle
_
tive
for a number of lines
whose average tower-footing
/ resistance is less than ten ohms
Supporting data are given in
the tabulation below
-
-
20o
40
0
50
PROTECTIVEANGLE
IN DEGREES
IN
PROTECTIVE ANGLE
DEGREES
Mile-Years
of Records
Lines
Averase
Resistance
Protective
Ansle
Distdnce Between
y/h
Ground Wire and Conductor
at Zero Swing
Outages
Per 100
Miles Per
Year
8A,8B ...
13.0
3.8
1,016 ......... 3.8 ..... -13 .. 0.12 ..
..
258 .......
840 .....
6.9 ......... 19. 0.23 .21.7
0.07
..
15F ........ 216 ......... 10.0 ......... 28
.11 ......... ... 11.7 .... 5.2
15G, H, . .... ....
32.
.10.10.6..
0
........
1A ........ 656 .
7.9
37. 0.13 .
14 .8.
0.9
P
23J, K,
0.12
45
15.4
7.2
R, U, 11. 287
3428
23GG......... 144 .
.......
6.9 ........ 45 ...0.0.13 .17.......
11.7
..7
1.2
23LL .
148 .......... 5.0 ........ 46 .. 0.13
.17.2
.5.9
372 ..
50..... ... -13 . 0.11 .11.3.
0.8
CONTREB LBS DEsCEiARGBS
DE LA FOUDRE, A. M.
CGESessn 1935, bulletin number
ZalE
317.
6. RECHERCHES DE
LABORATORIB SUR LES ZONES
PROTEGEES PAR DES PARADOUDRES A LIGNES
A. Akopian.
MULTIPLES,
CIGRE, Session 1937,
number
328.
~~~~~~~~~~~bulletin
7. UBER DEN SCHUTZWERT
ERDSIELE, A.
Schwaiger. ETZ, May 13, 1937.
8.
DBBR
MODELL vERSUCHE UBER BLITZEINSCHLAGE,
Adolph Matthias. ETZ, 58 Jahrg, Heft 32, August
12, 1937, page 881; August 26, 1937, page 928;
September 9, 1937, page 973.
9. DER SCHUTZRAUM VON BLITZFENG-VORRICHT-
ERMITTLUNG DUB MODELL
oUNGEN UNDA.SEINE
Matthias and Burkhardtsmaier.
VERSUCEE,
June 8, 1939, page 681; June 15, 1939, page
~~~~~~~ETZ,
720.
10. PROTECTION OF TRANSMISSION LINES AGAINST
LIGHTNING; THEORY AND CALCULATIONS, L. V.
Bewley. G. E. Review, April 1937, page 180.
11. LIGHTNING DISCHARGES AND LINE PROTECTIVE
MEASURES, C. L. Fortescue and R. N. Conwell.
AIEE TRANSACTIONS, volume 50, September 1931,
page 1090.
Also Lightning Reference Book, page
801.
12. INVESTIGATIONS ON LIGHTNING DISCARGES
AND ON THE ELECTRICAL FILD oF THUNDER-
STORMS, C. T. R. Wilson.
Phil. Trans. Roy. Soc.,
Sec. A, volume 221, 1920, page 73.
13. THE DISTRIBUTION OF ELECTRICITY ON
THUNDERCLOUDS, Sir George Simpson and F. J.
Scrace. Proceedings of Royal Society, Sec. A, No.
906, volume 161, August 1937, page 309.
14. THE LIGHTNING DISCHARGE (a book), B. F.
Schonland. The Clarendon Press, Oxford, England.
Appendix
Reduced to strokes per 100 miles this becomes
extentuand ufoatearmh
Assume aa flat earth surface of infinite
strokedensity.
densi. IfD
extent and a uniform stroke
If D
4
represents the density of *strokes
per square
mile per year, then from figure 5b it can be
seen that the strokes that emanate from an
element of cloud, dA in width and one mile
in length is DdA. However, if A is measured in feet, this quantity becomes D/5,280
dA, or Dh/5,280
=
328
Dh r+
Dh
{A
nd
280
hnd-1/
5,5,280_,
2Dh
+
I
nd
+
A
-1
5,28Oj h-
A\
The integral is simply the area under the
distribution upon one side of the line.
Bibliography
d(A/h), where h is in feet.
If n represents the fraction (not the percentage) of total strokes, as obtained from a
distibuioncure
curve fr
for aparicuaronfgua particular configudistribution
ration and cloud height, that strike both
conductors and ground wires, then the total
strokes from element dA which strike the
line is Dh/5,280 or d(A/h). The total
strokes to the line is then
S9
Dh
S= 26.4 jnd
h
*~~~~~2 4,,j0o
1. LIGHTNING AND OTHER TRANSIENTS ON TRANSMISSION
LINES, F. W. Peek, Jr. ATEE TRANSACTIONS, volume 43, October 1924, page 1205.
2. LIGHTNING PROTECTION FOR OIL STORAGE
TANKS AND RESERVOIRS, Sorensen, Hamilton, and
Hayward. AIEE TRANSACTIONS, volume 47,
January 1928, pages 164-80.
3. A STUDY OF LIGHTNING RODS AND CAGES WITH
SPECIAL REFERENCE TO OIL TANKS, F. S. Peek, Jr.
AIEE TRANSACTIONS, volume 45, 1926, pages 113144.
4. DIELECTRIC PHENOM§ENA IN HIGH-VOLTAGE
ENGINEERING (a book), F. W. Peek, Jr. McGrawHill Book Company, Inc., 1929.
5. RECHERCHES SUR MODELES RELATIVES A LA
PROTECTION DES LIGNES ET DES SOUSSTATIONS
Wagner, McCann,
15. ATMOSPHERIC ELECTRICITY (a book), B. F.
Schonland. Methuen & Co., Ltd., London.
16. LIGHTNING TO THE EMPIRE STATE BUILDING.
K. B. McEachron. Journal of the Franklin Institute,
volume 277, No. 2, February 1939.
ASSOCIATE3D
WITHMECTE;OROLOGICAL
AIRCRAFT, LIGHTNING DISCHARGES
AND
17.
17
CONDITIONS
EERLGCLCODTOsAsCAE
ATMOSPHERICS, E. J. Minser. Journal Aeronautical
Science, volume 7, No. 2, December 1939.
18. THE DEVELOPMENT OF THE SPARK DISCHARGE,
T. E. Allibone and J. M. Meek. Proceedings of
Royal Society, Sec. A, 1938, volume 166, page 97.
19. MECHANISM OF
THE
LONG SPARK, T.
E. Alli-
bone. Journal of the Institute of Electrical
Engi-
neers, 1938, volume 82, page 513.
20. EFFE3CT OPFHumIDITY ON IMPULSE FLASHOVIER
VOLTAGES OFRO GAPS AND INSULATORS, Y. Ishiguro. Institute of Electrical Engineers, of Japan,
volume 3, Number 7, July 1939, page 144.
21. LIGHTNING INVESTIGATION ON A 220-Kr
SYSTEM, Edgar Bell. ELECTRICAL ENGINEERING
(AIEE TRANSACTIONS), 1934, pages 1184-94.
22. AN ANALYSIS OF THE LIGHTNING FAULTING
CHARACTERISTICS OF THE 132-KV LINES OF THE
FALLS AND TRANSVAAL POWER COMVICTORIA
PANY, LIMI.TEr,D, M. C. Rendell and H. D. Goff ..
South African Institute of Elec. Engr.,
Trans. of24,thePart
volume
XI.
23. LIGHTNING PERFORMANCE OF 110 TO 165 Kv
TRANSMISSION LINES, AIEE Lightning and InsuAIEE TRANSACTIONS, vol-.
ume 58, 1939 (June section), page 294.
lator Subcommittee.
MacLane-Transmission Lines
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