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4.--> %2-y
A Study of the
Dielectric Strength of Cables
B J
Y
al-f
ROBERT J: WISEMAN
ABSTRACT OF A THESIS
SUBMITTED TO THE FACULTY OF THE MASSACHUSETTS IN-
STITUTE OF TECHNOLOGY IN PARTIAL FULFILMENT
OF THE REQUIREMENTS FOR THE DEGREE
OF DOCTOR OF ENGINEERING
-º-
BOSTON, MASSACHUSETTS
I9 I 5
engineERİNG
t.AERARY
F $tanbope ſpregg
• H. G. I. LSO N C C M PANY
R O S TO N, U. S. A.
.
TABLE OF CONTENTS.
PART I. INTRODUCTORY:
. PAGE
A. Purpose of the Investigation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
B. Theoretical Development of the Breakdown Voltage for a
Cable. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
a. Mathematical Development. . . . . . . . . . . . . . . . . . . . . . . 8
b. Electrical Development. . . . . . . . . . . . . . . . . . . . . . . . . . . 9
c. Study of Formula. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
C. Previous Work Done. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
PART II. DESIGN of APPARATUS:
4. Proper Dielectric. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I2
B. Design of Cable. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I3
C. Size of Cable. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I3
D. Parallel Plates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I4.
PART III. METHODS OF TESTING:
A. Preparing the Sample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I5
B. Testing a Sample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I5
C. Chemical Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I6
PART IV. Discussion of Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I6
PART V. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
PART VI. Suggestions for Future Work. . . . . . . . . . . . . . . . . . . . . . . 25
PART VII. Relation to Previous Work. . . . . . . . . . . . . . . . . . . . . . . . . 26
PART VIII. Engineering Value of Investigation. . . . . . . . . . . . . . . . . . 26
§
(b
i
;
A STUDY OF THE
DIELECTRIC STRENGTH OF CABLES.
I. INTRODUCTORY.
A. PURPOSE OF THE INVESTIGATION.
In the design of a cable to be used for the transmission of
power, and where a high voltage is required, the necessary
thickness of insulation around the wire is dependent on the
kind of insulation to be used, the voltage to be applied to
the cable, and the size of the wire.
When a cable is tested to see if it meets requirements, it is
found that the breakdown voltage does not agree with the
value obtained theoretically. Especially is this true when the
ratio of the inside diameter of the sheath to the diameter of
the wire is greater than the Naperian base, “E = 2.72.”
It is the object of this investigation to determine experi-
mentally whether or not the theoretical law is correct and to
explain, if possible, any departure from this law: also to
observe if the dielectric strength of the insulation is constant;
if not, on what factors does it depend.
Although a factor of assurance is used when designing a
cable, it would be of value to cable manufacturers if they had
a clearer understanding of the manner in which cable acts when
the size of the wire or the size of the sheath is varied. If, by
proper designing, it were possible to reduce the factor of assur-
ance, then an economic gain would be made, which would
assist both the manufacturer and the user.
B. THEORETICAL DEVELOPMENT OF THE BREAKDOWN
VOLTAGE FOR A CABLE.
A cable may be considered as a condenser consisting of two
concentric cylinders, the medium between the cylinders being
the insulation.
The formula for the breakdown voltage of a condenser, con- A,
, & '
7 A
sisting of two concentric cylinders, may be obtained in two
ways, either from a pure mathematical point of view or from
an electrical point of view, both leading to the same result.
a. Mathematical Development. — In the mathematical de-
velopment Laplace's equation for cylindrical distribution of
potential is taken and solved for the conditions imposed.
In this case we have two con-
centric cylinders of radius ri and r2
centimeters, having a potential V1
Yº- and V, volts respectively. To find
the potential in volts at any point
Gº. between the two cylinders:
Laplace's equation for the poten-
tial in volts is
6°W 6°W
ax; it a 75 = 9
in Cartesian coördinates.
Expressing in polar coördinates and solving we get

W = Clog r + C volts,
where C and Ci are constants.
Substituting for V and r their values at the inner and outer
cylinders and taking the difference,
Vo = V2 — V1 = clogºvolts.
1
As C = ,07,
07:
tº-º- ô V 72
Wo = 37' log 71 volts.
ô V e
Let R = ar volts per centimeter,
then Vo = Kr logº volts.
1
That is, the potential between the cylinders is a function of
the radii of the two cylinders and is dependent on the space
rate of change of the potential. The space rate of change of
the potential is supposed to be constant between the two
cylinders.
8
b. Electrical Development. — In this case we take the stress
at any point between the two cylinders and express it in terms
of the potential and distance to the point, that is, if f is the
stress, then d V
f = dr. volts per cm.
That is, the stress at any point is equal to the space rate of
change of potential at that point, the rate being assumed
COnStant.
As the field is radial, f = ##.
2 T ºr
dV
dr T
d V = f. .#dr volts,
f, volts per cm. and
Y1
fr, 7. volts per cm.,
V = ſº f...; dr volts,
V = Kri logº volts, where K = frt.
1
c. Study of Formula. — If r1, the radius of the wire or inner
cylinder, is varied, the theoretical breakdown voltage has a
maximum value when the ratio of r2 to ri is equal to the Nape-
rian base “E = 2.72.”
If r2, the inner radius of the sheath or outer cylinder, is varied,
the voltage increases constantly although not in direct pro-
portion and reaches its maximum value when r2 = co.
These statements may be verified by differentiating the
voltage formula with respect to r1 and r2 separately, and equat-
ing the derivative to zero.
If we express K in terms of V, ri, and r2 and differentiate
with respect to ri, we find K will increase as ri decreases (the
ratio re/ri increases). When we differentiate with respect to
r2, K will decrease as rº increases (the ratio rº/ri increases).
C. PREVIOUS WORK DONE.
The formula expressing the voltage at which a cable will
puncture can be used for any medium –gas, liquid, or solid —
provided the medium does not change its properties when
stressed, for instance, the medium is not deformed or the
space rate of change of potential not varied.
9
In the experimental study of the formula, a departure from
theoretical values has been noted in all cases. For gases, this
has been satisfactorily explained by means of the ionization
theory of gases. One of the earliest investigators of the prob-
lem with gases is Gaugain." He shows that when r2 is large
compared to ri the stress at which the air begins to break is
independent of r2, consequently the formula will not hold.
Recent investigators, such as Townsend”, have studied the
affect of the pressure of the gas on its dielectric strength.
Whitehead” and Peek“ have conducted elaborate experimental
studies on the behavior of air between cylinders and around
wires. Each has developed an empirical formula, expressing
in terms of the radius of the wire the potential gradient
at which the air becomes conducting. Ryan" has written a
valuable paper on the subject of air and oil, giving an expla-
nation for the cause of corona in terms of ionization. Davis"
has offered a theory in terms of ionization in explanation of the
way air acts. He shows how his theory and the experimental
data of Whitehead and Peek agree.
When one comes to consider liquids and solids, experi-
mental verification is lacking and explanations are far from
convincing. Liquids are very good retainers of moisture and
impurities. Corona, such as occurs in gases, has been ob-
served at times in liquids, but absolute proof is wanting.
Discrepancies in the experimental data have been explained
by the presence of moisture and foreign matter in the liquid.
The moisture theory looks promising and further lines of
investigation in that direction will be valuable. A very com-
plete study of the affect of moisture on the dielectric strength
is given in the thesis of Ferris, conducted at the Massachusetts
Institute of Technology."
Solids have offered the greatest problem and although va-
* Gaugain, Annals de Chimie et de Physique, Vol. 8; 1866.
* Townsend, London Electrician, Vol. 71, p. 348; 1913.
* Whitehead, Trans. A.I.E.E., Vol. 30, Part II, June, 1911.
* Peek, Proc. A.I.E.E., Vol. 30, Part II, p. 1485; 1911.
* Ryan, Proc. A.I.E.E., Vol. 30, Part I, Jan. 1911.
* Davis, Proc. A.I.E.E., Vol. 33, April, 1914.
7
L. P. Ferris, “Dielectric Strength of Cables.” Electrical Engineering
Dept. Mass. Inst. Tech., 1911.
IO
rious theories have been advanced, proof of them is lacking.
Two important factors in solids are homogeneity and molec-
ular structure; i.e., is it an isotropic or an anisotropic medium.
Homogeneity is probably the greatest factor in determining
the dielectric strength of cables.
Many theories which have been advanced in explanation
of the departure of practice from theory are described briefly
below. -
Charring Theory. — Professor A. Russell' has advanced a
theory which is founded on suggestions of Jona” in a valuable
paper on the study of cables. Briefly, it states that when
the stress on the insulation is greater than the latter can
stand, the insulation is disrupted to a zone where the stress
is equal to what it is capable of standing. It assumes the
overstressed insulation becomes charred and the wire radius
increased to the point where the charring ends. Attempts
have been made to support this theory without success.”
Corona Theory. — A corona theory has also been advanced
by Professor Russell, which has been questioned in that no
visible effect has been observed to substantiate it. Is it
necessary to have a visible change in the dielectric when
Corona is formed? Is Corona of such a nature that a physical
or chemical change is a result of its presence? Such questions
when answered may lead to the solution of the mystery.
Needle-point Theory. — A theory advanced by Dr. H. S.
Osborne* considers the insulation whenever its strength is
exceeded, to breakdown not completely, rather in points. In
commercial dielectrics, which are not homogeneous and liable
to contain impurities, the dielectric is over-stressed in the
vicinity of the impurities and an incipient breakdown occurs
in the form of “needle-points thrust into the insulation.”
These needle-points are assumed to push their way into the
dielectric in enough places to keep the stress in the insulation
* A. Russell, “Theory of Electric Cables and Networks,” p. 163. Also
Journal of Institution of Electrical Engineers, Vol. 40, p. 6; 1908.
* Jona, International Electrical Congress, St. Louis, 1904; Vol. II,
p. 550. See also discussion of Osborne's paper.
* H. S. Osborne, “Potential Stresses in Dielectrics,” Mass. Inst. Tech.,
I9IO. Also Trans. A.I.E.E., Vol. 29; 1910, p. 1553, 1582.
II
down to its dielectric strength until the amount remaining
can no longer stand the stress and puncture will occur.
A test was made on a wire insulated with rubber, and placed
in a glass tube. The manner in which the rubber and glass
acted was such as to support this theory. More data along
this direction would be of extreme value.
Moisture Theory. — A moisture theory has been advanced
by Mr. Del Mar," based on the difference in the specific ca-
pacity of water and the dielectric. Briefly, it states that the
water collects around the wire, causing the insulation around
the wire to act as a conductor and bringing the potential of
the wire into the insulation. This will result in a new diameter
for the wire, and consequently a new voltage gradient.
It is not expected that the moisture around the wire will
give equipotential lines concentric with the wire. It is prob-
able that peaks will occur. If so, then the stress will follow
the path of these peaks and the resulting phenomena may be
similar to the “needle-point theory.”
Middleton’s Formula. — Mr. I. W. Middleton, an elec-
trical engineer connected with one of the cable manufacturing
companies in the East, has suggested an empirical formula
to use for radii ratios greater than 2.72. In this formula,
W = K de log D/d, volts, he takes de = D/2.72. That is, the
dielectric surrounding the wire up to the zone where the ratio
of D/d equals 2.72 plays no part in the insulating of the wire.
He does not regard the material as conducting, but that is
really what the formula involves.
As the various theories advanced have not conclusively
explained the departure of practice from theory, it was decided
to attack the problem anew with the hope that either some
definite explanation would be found, or a foundation laid for
its future solution.
II. DESIGN OF APPARATUS.
A. PROPER DIELECTRIC.
The primary requisite in a study of this nature is to get a
dielectric which will meet the requirements of a theoretical
* L. P. Ferris, “Dielectric Strength of Cable,” Mass. Inst. Tech., 1911.
I2
study. The first and most important requirement is its homo-
geneity. The dielectric should be free from impurities and
absorb no moisture. The dielectric strength must be high
enough so that it will be possible to work at voltages which
can be read with reasonable accuracy.
The dielectric chosen is known as “ceresine wax.” It is
obtained from a Russian “ozokerite.” Its melting point is
69°C. It is similar in appearance to paraffine and absorbs
no moisture. Its dielectric strength is about 15,000 volts
per millimeter. It may be purchased in either the pure or
the adulterated state. It is usually adulterated with paraffine.
All tests were made with pure wax.
B. DESIGN OF CABLE.
In designing the cable, the following essential features
were considered: reproducibility of the test sample, con-
venience and safety of operation, reliability, and compactness.
The method, which was a-
dopted after many trials, and
which met with good success,
consists in taking a brass cyl-
inder which represents the
sheath, and in placing a rod
at the axis to represent the
wire. The rod is held in
position by means of insulat-
ing cylindrical heads, made
of maple, which fit on the ends of the brass cylinder as shown
in Figs. I and 2.
Fig. I gives an end view of the cylinder (a) and is shown cut
away at the top for moulding purposes. Fig. 2 gives an idea
of the assembled cable. It will be noticed that the ends are
flared to reduce the terminal stresses.
%%
C. SIZE OF CABLE.
The size of the wire and sheath were determined by consider-
ing what values of the ratio D/d were necessary. It was
decided that one value at a ratio of 2.72, and three above and
below this value would show the phenomena likely to occur.



I3
It was also decided to keep the sizes near those used com-
mercially, as the study should follow conditions occurring in
practice and reproduce them as nearly as possible.
For the cable conditions, with the inside diameter of sheath
constant and the diameter of wire variable, the sheath was
taken at O.375 in. (O.953 cm.) diameter, and the wire from
O.313 in. (O.795 cm.) to O.O7OI in. (O.I.78 cm.) diameter.
For the cable conditions, with the diameter of sheath
variable and the diameter of wire constant, the wire had a
diameter of O.I.87 in. (O.475 cm.) and the sheath from O.250 in.
(0.635 cm.) to I in. (2.54 cm.). t
These gave a range of ratio D/d up to 5.35.
D. PARALLEL PLATES.
Parallel plates were also used to determine the affect of
thickness on the dielectric strength of the dielectric.
The method used consisted in supporting brass disks on
pieces of maple, and separating the


# #EFă plates by means of fiber blocks held
in position by bolts. The accom-
tºwns panying figures show how they are
constructed. -
#ssel Three different sizes of plates, 5.I
cm., 7.62 cm., and Io.2 cm. in diam-
E. #-F#-i eter, were used to show the affect
FIG. 3. Fro. 4 of electrode area on the dielectric
strength. The thickness of wax
tested covered a range from one millimeter to about seven
millimeters. This covers almost completely the thickness of
wax tested for the cable.
III. METHODS OF TESTING.
The results of tests depend, to a large degree, on the method
of preparing a sample, and on the manner in which a test has
been made.
1 When diameter of sheath is mentioned, the inside diameter is meant in
all cases. *
I4
A. PREPARING THE SAMPLE.
The method used consisted in assembling the cable with the
sheath and wire very hot. When it is placed in a pan, the
wax which has been melted is poured in slowly. This allows
the wax to rise gradually in the pan, and prevents the entrain-
ing of any air in the cable. By having the wire and sheath
hot, the wax is not cooled suddenly, but is allowed to run freely
over both conductors. This prevents the retention of any
air on either the wire or sheath. As the wax cools, it settles
into the cable, on account of the opening in the upper side.
The same method applies to the moulding of samples for
parallel plates.
Tests were also made with an impurity added to the wax.
The reason for doing so will be found under the discussion of
results. Two kinds of impurity were added. Emery flour
was used, as representing a physical impurity such as dirt,
sulphur, etc., likely to be introduced into a cable in the course
of manufacture. Stearine, which contains stearic acid, and
which is liable to be present in the wax, was also used as a
chemical impurity.
B. TESTING A SAMPLE.
When a sample is ready to test, the a-C. testing voltage is
raised until puncture occurs. The voltage was measured by
a voltmeter across the secondary terminals of a IOO,OOO-volt
transformer. This transformer has a secondary winding of
four coils, each capable of giving 25,000 volts. The coils
may be connected either in series or in parallel, as desired.
The voltage was raised by strengthening the field of the
generator supplying the transformer. The field rheostats
were near the transformer, so that control was possible while
the test was being conducted. The generator was of the
“Mordey” type, giving a close approximation to a sinusoidal
Wa We. •
The average of fifteen tests was taken in determining each
point of the breakdown voltage curves for the sample cables,
and the average of ten tests for the breakdown voltage curves
for the sample slabs between plates.
In the actual testing of a sample for puncture, it has been
I5
found that the time of application of the voltage is important.
Various investigators have suggested a standard rate of in-
crease in voltage of 1000 volts per second. This rate was used
in testing both the sample cable and the parallel plates. To
show the affect of the time of application, a 2000 volt per
second rate and also a constant time of application of ten
seconds were used for the 7.62-cm. plates in addition to the
tests with standard rate.
In the tests where the time of application was Io seconds,
the voltage was raised rapidly enough to cause the wax to
puncture Io seconds after the test was started. This meant
that for every new thickness of wax, a new rate of applying
the voltage was used.
The 1000 volt per second rate was used for the tests where
an impurity was added to the wax.
C. CHEMICAL TESTs.
Chemical tests were made on the wax after the conclusion
of the electrical tests to see if a change in the chemical proper-
ties due to electrical stresses had occurred. A sample taken
from between the plates was compared with a similar sample
taken from outside the plates and was tested for the amount
of free acid present. -
§
FIG. 5.
IV. DISCUSSION OF RESULTS.
Fig. 5 shows the curves obtained for the conditions, diameter
of sheath constant, and diameter of wire variable. The curve
of breakdown voltage is similar to the theoretical curve. The
I6 - w

voltage reaches a maximum at a ratio 2.72 and then decreases.
In developing the formula V = Kr log D/d volts, the dielec-
tric strength has been assumed constant; but from the curve
in the figure, its apparent value is seen to increase as the radius
ratio increases.” It has been possible to express this curve
by an empirical formula of the same type that Whitehead
obtained for the dielectric strength of air about a wire.
Fig. 6 gives the curves of voltage and dielectric strength for
the conditions, diameter of sheath variable, and diameter of
;
FIG. 6.
wire constant. The results obtained here are quite different
than what other investigators have obtained. According to
the theoretical formula, the voltage increases as the radius
ratio increases, assuming the dielectric strength to be constant.
This condition is seen to be considerably departed from in the
figure. If we examine the curve of dielectric strength, we see
that it remains constant up to a ratio of about 2 and then
decreases very rapidly, finally approaching a lower constant
value.
If we compare Figs. 5 and 6, we see that the voltage and
dielectric strength are respectively quite different in these two
* Dielectric strength, as used in this paper, is defined as the space rate
of change in potential expressed in root mean square volts per centimeter,
which causes breakdown. For cable tests it is 6V/ðr where V is the poten-
tial in volts between the wire and sheath, while r is the radius of the wire in
centimeters. Since the maximum potential gradient occurs at the wire, this
is the value accepted. For parallel plates, the dielectric strength is com-
puted from V/t, where V is the potential between the electrodes in volts
and t is the distance between the electrodes in centimeters.

I7
cases. This shows that the dielectric strength is not only
variable but that the formula must be in error. The question
arises as to the reason for this discrepancy. ---
Neither voltage curve corresponds to the voltage curve
computed by Middleton's formula. In the case of the diam-
FIG. 7. •-r
eter of sheath variable and diameter of wire constant, there is
a wide departure of the curve obtained from the curve using
the Middleton formula.
Fig. 7 shows the results of tests on flat plates of wax to see
if the dielectric strength is independent of the thickness. The
FIG. 8.
breakdown voltage curve corresponds very closely to a straight
line law. However, the dielectric strength is quite variable.
For small thicknesses, it is high, decreasing very rapidly as
the thickness increases, and less rapidly above a thickness of ***
six millimeters.


- I8
If the variation of dielectric strength computed for parallel
plates remains the same as for cable computed from the
V
r log D/d'
as it does is explained. This has been worked out, and the
result is shown in Fig. 8. It is seen that there is a considerable
difference between the dielectric strength for equal thicknesses.
In one case, there is a constantly increasing difference, while in
the other, the difference reaches a maximum, then decreases as
the thickness increases and finally approaches a constant value.
Further discussion of sample cable tests will be postponed
until an explanation can be obtained for the behavior of
dielectric strength of wax in different thicknesses of plates.
Other investigators have noted the deviation of the break-
down voltage curve from the law V = Kt; but have not tried
to explain the departure. One
found the curve to lie somewhere
between the first power and the
square root of the thickness."
The curve of voltage (V) obtained
in Fig. 7 does not follow either
law.
The other sizes of electrodes
give curves of the same shape.
The difference between the results
with the 5. I-cm. plates and the
IO.2-cm. plates is about IO per
cent. The results with 7.6-cm.
plates lie between the two. It
may be concluded from these re-
sults, that the area of the electrode has only a slight affect on
the dielectric strength.
Heating of the wax has been found to affect the dielectric
strength. If different rates of applying the test voltage are
used, the wax should stand a higher voltage for high rates
than for low rates. The results for the three rates used are
shown in Fig. 9. It is seen that the dielectric strength is
higher for all the thicknesses of wax.
* Hendrick, Trans. A.I.E.E., Vol. 30, Part I, p. 167, 1911.
formula K = then the reason for the cable acting
FIG. 9.

I9
The ratios of dielectric strength between thick and thin
plates changed with different rates of application of voltage,
as will be seen by examining the upper curves of Fig. Io.
Each of the three conditions of test has a curve distinct from
the others. These curves show very clearly the necessity of
standardizing the rate at which dielectrics are to be tested .
in order that various materials may be compared as to insulat-
ing value. - -
Chemical tests were made on the wax to see whether the
wax had undergone a change due to the electric stress. It
was not possible, however, to detect any change in the chem-
ical properties of the dielectric. s
FIG. Io. FIG. II.
Impurities in the dielectric offer a good opportunity for
varying the dielectric strength. They are liable to change
the distribution of the electrostatic flux, and, consequently,
the dielectric will not behave in the same way as in a uniform
field. The impure dielectric would be expected to break down
at a lower voltage than a pure dielectric. - -
Fig. II shows the results of adding different amounts of
emery flour to the wax (one-half gram per avoirdupois pound
and One gram per avoirdupois pound of wax). It is to be
noted that the curves intersect, and the dielectric strength is
apparently increased for small thicknesses and diminished for

2O
large thicknesses. If we compare the change in dielectric
strength with thickness, as was done in the case of the curves
showing time of application, the lower curves of Fig. IO are
obtained. These curves show very clearly how an impurity
may affect the dielectric strength.
In tests with a chemical impurity added to the wax, a sim-
ilar change was noted.
If tests are to be made on a dielectric, it is essential that the
dielectric be as pure as can possibly be obtained. -
Very fine shavings of the wax after testing were examined
under a microscope, to see if the wax had a crystalline struc-
ture, and whether any impurities could be detected. The
samples were pure wax, wax with stearine added, and wax
with emery flour added. No crystalline structure was ob-
served in any case. No difference in the samples of pure
wax and wax containing stearine impurity was observed. In
the case of the wax containing emery flour, a few very small
specks of dirt were observed. It is possible that they may have
been added to the wax while preparing the slide.
Taking all the factors which have been found to affect the
dielectric strength and giving them due consideration, it
seems possible that the dielectric strength may be unaffected
by the thickness of the insulating layer provided that the
manner in which the test is made and the degree of purity of
the dielectric are taken into account. The tests with impuri-
ties added would indicate the possibility of obtaining an abso-
lutely pure material which would have a constant dielectric
strength. -
'We have no present means of telling when we have an
absolutely pure dielectric material, or how much impurity
may exist in a material which we assume to be pure. A mere
trace of an impurity may affect the dielectric strength con-
siderably. If a straight line law of deviation from constant
dielectric strength is assumed to be caused by impurity, we
may estimate roughly the way in which wax would be able to
act if it could be purified to a greater extent. In the case of
emery flour added to the wax, if impurities to the extent of
I# grams per avoirdupois pound could be separated from the
pure wax, the dielectric strength might fall to about 90,000 to
2I
Ioo,000 volts per centimeter for all slab thicknesses. For the
case of stearine added to the wax, if I# grams of stearine or
chemical impurities per avoirdupois pound of wax were with-
drawn from the pure wax, the dielectric strength would fall to
between 90,000 and IOO,000 volts per centimeter. The wax
obtained is the purest that can be found commercially. It
does not seem likely that impurities are present to the extent
necessary to bring the dielectric strength to a constant value.
Furthermore, the straight line law assumed may be far from
true. Consequently, we cannot say that the impurities are
the real cause of the variation in dielectric strength, but the
suggestion offers a promising field for future research.
If we assume a straight line law of deviation from constant
dielectric strength to be caused by the time of application of
voltage, we may estimate roughly, as before, the dielectric
strength it may have at zero rate, i.e., the dielectric strength
the wax would have if the voltage were applied indefinitely.
Here, again, the dielectric strength approaches a value of
about 90,000 volts per centimeter.
The theory of ionization offers a very simple explanation
of the phenomena which have taken place. The theory of
corona, advanced by B. Davis' for air, may be extended to
solids, and his theory is applied here. This theory may be
applied provided ionization occurs in solids. We know there
are a few free electrons present, and that when subjected to an
electric field, they are set in motion. No visible effect has
been observed in the tests to support the theory that ioniza-
tion occurs. A slight glow has been noted, but apparently
it did not affect the strength of the material. It is doubtful
whether a visible change is necessary, however, in order to
support this theory. None of the tests have lasted longer
than one minute, and most of them have occupied only half a
minute. It is doubtful whether any change can take place
during so short a time, sufficient to be manifested physically.
To the writer, it does not seem likely that a visible change
could be produced by ionization in such a short test.
Let us start with a dielectric of any shape between two elec-
trodes and subjected to a difference of potential. Due to the
1 B. Davis, “Theory of Corona,” Proc. A.I.E.E., Vol. 33, Apr. 1914.
22
electrostatic field, any ions present will be set in motion, caus-
ing other ions to be formed by collision with neutral molecules.
These ions are moving toward the positive electrode to be
discharged. If the positive electrode is near the negative
electrode, the ions will be discharged, and a further increase
in voltage gradient is necessary in order to produce a sufficient
number of ions to cause the material to become conducting
by breakdown.
If the positive electrode is not close to the negative elec-
trode, the ions do not have time to reach the positive elec-
trode before a large number have been produced in the region
of the negative electrode. This may result in the dielectric
around the negative electrode exhibiting the properties of a
conductor and the electrode has been virtually extended into
the substance of the dielectric. This will result in a greater
increase in the number of ions and, finally, puncture will occur.
The voltage necessary to cause breakdown here will not be pro-
portional to the voltage required for small distances between
the electrodes. This will mean that the dielectric strength
computed for the two cases will not be the same. It will show a
higher value for small thicknesses than for large thicknesses.
In the case of alternating impressed voltages, there is the
additional consideration that the time phase is likely to change
before the ions have been able to discharge, so that they will
simply accumulate around the electrodes, and the dielectric
will become conducting at these electrodes with the result
previously stated.
In the case of the tests with parallel plates and with pure
wax, the dielectric strength decreases with increase in thick-
ness of the wax. This may be explained by the above theory.
In the case in which a chemical impurity was added to the
wax, we may consider the wax to acquire the properties of a
different dielectric, whereas when the physical impurity is
added, the particles may be considered as conductors embedded
in the wax, upon which charges are induced. These particles
may be assumed to bring the electrodes nearer together, so
that for small thicknesses, the dielectric strength will appear
to be increased, and, for the large thicknesses, there will be
only a slight change in the dielectric strength.
23
The difference in dielectric strength occurring with differ-
ent rates of application of the voltage may be considered as
due to the rate of production of the ions. For a high rate of in-
crease in voltage, more ions will be discharged than for a low
rate owing to the higher velocity of the ions. Consequently, a
higher voltage will be required to puncture the wax. For large
thicknesses the difference in dielectric strength for high and
low rates will not be great, as the distance between the elec-
trodes may be sufficient to prevent the discharge of any ions,
thus causing them to accumulate until puncture occurs.
In explaining the results with the cable samples, two things
must be considered, viz.: (1) the change in the thickness of
the insulation and (2) the change in the stress at the wire.
As the thickness increases, we have found the dielectric strength
to decrease. When the radius of the wire decreases, the stress
at the wire increases. This will result in an increase in the
velocity imparted to the ions. If the diameter of the wire
is kept constant, but the diameter of the sheath increased,
the stress at the wire becomes less and the velocity of the ions
will be less.
When the conditions of diameter of wire variable and diam-
eter of sheath constant are taken, the diameter of the wire
decreases. Since the ions are given a higher velocity, more
ions will be discharged as the diameter of the wire decreases,
and the increase in thickness will not be sufficient to offset
this discharge. Consequently, a higher voltage will be re-
quired to produce puncture. When the dielectric strength is
computed from the formula, it will show an increase due to
the increase in voltage. The empirical formula for the curve
of dielectric strength is an exact duplicate of the formula
obtained by Whitehead in his study of corona in air. Davis
has shown how his formula, based on ionization, may be
reduced to this empirical formula. A sufficient number of
points have been taken from the curve, obtained by the writer,
to get the necessary constants in Davis's formula and then,
when other points were computed, checking values were actu-
ally obtained. The agreement of the two empirical formulae,
one for air and the other for solids, strengthens the theory that
the phenomena are of an ionization nature.
24
When the diameter of sheath is variable and the diameter
of the wire constant, the decrease in dielectric strength due
to increase in thickness is sufficient to offset the increase
due to the increase of stress at the wire, so that the computed
value of the dielectric strength from the formula comes out
as a constant. For large thicknesses, however, the stress at
the wire decreases as the diameter of the sheath is increased.
The discharge of the ions is less than for small thicknesses,
and as the dielectric strength has decreased on account of this
increase in thickness, the dielectric strength as computed from
the formula will diminish.
From the results of tests with cable samples, it may be
concluded that the reason practice does not agree with theory
is due to a change in the dielectric strength of the insulator.
The dielectric strength for cable, instead of being Constant,
as was supposed, is a variable, depending on the thickness of
the insulation and on the shape of the electrodes.
V. CONCLUSIONS.
The results of the tests of dielectric between parallel plates
show that the dielectric strength is not a constant, but de-
creases with increase in thickness of the slab.
The purity of the dielectric and the time of application of
the voltage are factors upon which the dielectric strength is
dependent.
When cable samples are tested, the dielectric strength in-
creases when the diameter of the wire decreases, and the
diameter of the sheath is held constant. The dielectric
strength decreases when the diameter of the wire is kept
Constant and the diameter of the sheath increases beyond a
radius ratio of 2. -
The change in dielectric strength appears to be capable of
explanation by means of the principles of the motion of ions
and ionization by impact.
VI. SUGGESTIONS FOR FUTURE WORK.
Although there is still considerable work to be done in the
study of sample cables, the problem resolves itself rather into
a study of the dielectric strength of slabs than of cable samples.
25
It will be well to give the ionization theory a thorough study
and test. The possibility of making tests proving this theory
seems slight. The idea of supplying the dielectric with more
ions before making a test lacks strength in that the number
supplied is probably many times smaller than the actual
number present when conduction occurs. The change in
breakdown voltage due to the presence of the extra ions may
be too small to detect with accuracy. A study of the change
in the capacity due to ionization, by comparison with what
occurs under similar conditions in air, promises a good basis
for the testing of this theory. It will be necessary to design
special apparatus capable of detecting very slight and sudden
changes in the capacity.
The question of the affect of impurity is not fully settled.
If an absolutely pure material can be obtained, it would be
valuable to test it with different amounts of impurities added,
attempting to form a law of variation of dielectric strength
with purity. Oils offer a good field for this investigation.
VII. RELATION TO PREVIOUS WORK.
Other investigators have used for purposes of testing, short
lengths of commercial rubber-covered cable. These samples
are of practical value in so far as they represent practical con-
ditions. But there is so much difference between the results
of theory and practice that very little benefit can be gained
by taking the results of experiment on commercial cable as
illustrating theory. By taking cable samples with wax as
the dielectric, wax being more nearly homogeneous than
rubber, we eliminate thereby one complicating factor, and
more satisfactory results are thus obtainable.
As the sizes of wax cable samples correspond closely to
commercial sizes, the applications of the results to cables
under actual conditions of operation have not been lost.
The problem has been investigated in several directions in
order to ascertain the effects of particular influences.
VIII. ENGINEERING VALUE OF INVESTIGATION.
Cable manufacturers should not permit themselves to be
disquieted by departures of the breakdown voltage from com-
26
puted values. The results here reported have shown that no
material has a constant dielectric strength and, consequently,
discrepancies between theory and practice must for the present
be expected. w
From the tests with sample cable having the diameter of
wire variable, it is shown that it is useless to make the ratio
of diameter of sheath to diameter of wire greater than 2.72
as the breakdown voltage decreases with further increase of
this ratio. Also, for the cable samples having the diameter
of sheath variable, the limiting ratio of diameters should
likewise be 2.72, since the dielectric strength decreases so
much for greater ratios, the insulating material not being
used to best advantage.
A means of overcoming these difficulties may be obtained
by grading the cable as suggested by O'Gorman" and Osborne.”
Great care should be exercised by manufacturers of elec-
trical equipment in obtaining and keeping the insulation free
from foreign material. Again, it should be remembered that
the insulating power of any insulation material is not pro-
portional to thickness, but decreases with increase in thickness.
The conditions of testing insulation, such as the method
of applying voltage and the shape of electrodes, should be
standardized, in order to compare properly different kinds of
insulation.
* O'Gorman, Journal of Inst. Elec. Eng., Vol. 30, p. 608; 190I.
* Osborne, Trans. A.I.E.E., Vol. 29, Part II, p. 1553; 1910.
G-5-1915-325.
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