Dielectric Phenomena in High Voltage Engineering (1915) — part 3 of 12

We have found experimentally that the energy storage distance*

-v/r / Wl \

o = 0.301 ^ cm.; that is, g, = 305(1 +^^ j

The electron theory may also be applied here:

• This formula may be used to determine the strength of compressed air.

VISUAL CORONA 43

go, the strength of air, varies directly with 8, g», however, cannot vary directly with 5 because with the greater molecular spacing or mean free path of the ions at lower air densities, a greater "accelerating" distance is necessary in the equation a = 0.301 y/r/S that is, "a" increases with decreasing 5. This is shown experimentally by sphere gap tests.

For parallel planes r = » -' • Ov = Qo^, as expected. The equation for the visual critical corona voltage may now be written:

ev - gvdr log, S/r = goSn + ^ jr log. S/r kv. (20)

where e^ is Kv to neutral, go = 30 for max., go = 21.1 for effective sine wave.

It may be of interest to note that with a pair of smooth wires, of a known diameter, high voltages may be accurately measured anywhere by noting the spacing at which corona starts, the tem- perature and barometric pressure, and substituting in the above formula.

The various other factors affecting visual corona will be mentioned.

Cosductor Surface — Cables — Material. — For rough or weath- ered conductors corona starts at lower voltages. This is taken care of by the irregularity factor, m„. For cables and weathered wires the complete formula becomes

Cv = m^Sgr, r log. S/r For the same surface condition the starting point is independent of the conductor material.

Oil and Water, Ctirrent in the Conductor, Wave Shape, Etc. — Water, sleet and snow lower the visual corona voltage.

Oil on the conductor surface has very little effect.

Humidity has no effect upon the starting point of visual corona.

Initial ionization over a considerable range has no appreciable effect at commercial frequencies.

Current in the wire has no effect except that due to heating of the conductor and surrounding air.

Wave Shape. — The corona point at commercial frequencies depends upon the maximum value of the wave. When results are given in effective volts a sine wave is assumed. With peaked wave, corona starts at a lower effective voltage than with a

44

DIELECTRIC PHENOMENA

Shield tor Bmall Wire

m

Shield for Large Wire

flat-top wave. D.c. corona starts at a value corresponding to the maximum of the a.e. wave or 41 per cent, higher than the effective a.c. critical voltage.

The above summary will now be taken up more in detail and experimental proof given.

Experimental Study op Visual Corona

Effect of Spacing and Size of Conductor. — The visual critical voltage, or voltage at which visual corona starts on

polished conductors of a given diameter and spacing, at con- stant air density, can be repeat- edly checked within a small per cent. Visual tests were made on two parallel polished con- ductors supported indoors on wooden wheels in a wooden framework. The wires were not allowed to come directly in contact with the wood but rested on aluminum shields. (See Fig. 26.) The object of the shields was to prevent the glow at low voltages which would take place if the wires came in contact with the wood. The tests were made in a dark room, and method of procedure was as follows: Conductors of a given size were placed upon a framework; voltage was applied and gradually increased until

O

O

o

Fig. 26. — Wire support for visual corona tests.

the visual critical corona point was reached. Critical points were taken at various spacings and recorded as in Table I.

As the visual critical voltage, €», is the voltage at breakdown of the air, the surface gradient corresponding to this voltage must be the stress at which air ruptures. This is called the visual critical gradient Qv. Where the wires are far apart or S/r is large

de dr

= ^r =

r log, S/r

VISUAL CORONA

45

where

e« s the (maximum) voltage to neutral.

r s radius of the conductor in cm.

8 s distance between centers of conductors in cm. Values of gradient calculated for a given conductor at various spacings are given in Table I. (See Fig. 27.) It is seen that the breakdown gradient is constant, or independent of the spacing. This test was repeated for various diameters. The values of the gradients are tabulated in Table II and plotted in Fig. 28.

Juo

•0

8

o

u

^, ^ It- -.

•41.1 ~~^

•

^80

cfteo

I 1

ft MM ■«■ HMi a^ ■««

l^^^i^ ^IH^HI M^BV^ m^f^^m IMMMMM P^B^BM Mi^^^ ^BMimi

60 Spacing. 5-0111

too

o

5 Badlttt of Ovtw OyliadM - R

(a)

(6)

10

Fig. 27(a). — Variation of visual Fio. 27(b). — ^Variation of visual crit-

critical gradient with spacing, ical gradient with radius of outer cyl-

(Parallel wires. Diameter constant inder. (Concentric cylinders. Diam-

s . 034 cm. ) eter of inner wire constant » . 118 cm. )

Table I. — Visual Critical Voltages and g^ with Varying Spacing and

Constant Diameter

(Polished Parallel Copper Conductors — Diameter 0.0343 cm.)

e«^ kilovolia between oon-

•^ kilovolts between con-

fh kv./om.

9 om.

ducton (effective)

duotora (maximum)

(maximum)

2.54

12.1

17.0

99.5

2.93

12.4

17.4

99.0

3.18

12.5

17.7

98.5

3.81

13.0

18.4

99.0

4.45

13.5

19.0

99.5

5.08

13.8

19.4

100.0

5.73

14.0

19.8

99.0

7.62

14.5

20.5

99.0

15. 2

16.0

22.6

97.2

30. 5

17.7

25.0

97.2

45. 6

18.7

26.3

96.1

19.4

27.4

98.0

106. 8

20.6

29.0 Average,

97.2

99.0

46

DIELECTRIC PHENOMENA

Table II. — Variation of g^ with Diameter op Conductors

(Average Values for Polished Parallel Wire. Corrected to 25 deg. C. 76 cm.

Barometric Pressure) ^

<u

dt

Diameter,

dr-f'

Material

Diameter,

— « ^,

dr

Material

cm.

kv./cm. (maximum)

cm.

kv./cm. (maximum)

0.0196

116

Tungsten

0.2043

59.0

Copper

0.0343

99

Copper

0.2560

57.0

Aluminum

0.0351

94

Copper

0.3200

54.0

Copper

0.0508

84

Aluminum

0.3230

50.5

Copper

0.0677

82

Aluminum

0.5130

49.0

Copper

0.0635

81

Tungsten

0.5180

46.0

Copper

0.0780

76

Copper

0.6550

44.0

Copper

, 0.0813

74

Copper

0.8260

42.5

Copper

0.1637

64

Copper

0.9280

41.0

Copper

0.1660

64

Iron

lao

110 100

I

Visual Critical Gndlent

Two Parallel Wires OymtX 70 0*1 and 7X!*0 • 29.8 (l 4-.a01 'S g^ m Yoliage Gradient Ajw/cm -yp ^

g 90

.is.

|70 |80 ^60 ;3 40 rSW

V

\

y

^

o

"^

—u

„_

»20

10

(

•

L A

t .1

,{

I .

.f

\ .1

f ,i

1

vauBt

.0 1 etln

1 L ctn

2 1

8 L

4 1.

6 1

6 1

.7 1

8 1

.9 2i)

Fig. 28. — Variation of visual critical gradient with size of wire.

The gradient at breakdown at the conductor surface is not constant with varying diameters, but increases with decreasing diameters of conductors — in other words, air is apparently stronger at the surface of small wires than large ones.

The apparent increase in the dielectric strength of air surround- ing small conductors was explained some years ago as due to a condensed air film at the surface of the conductor. If this were so, a higher critical gradient would be expected for tungsten than for aluminum. That is, the air film should be denser aroimd the

VISUAL CORONA 47

denser metals. These experiments show that the gradient is not affected by the material or density of the conductor. Ryan* has also explained the apparent increase by the electron theory. The explanation first offered in Law of Corona I, ^ and already outlined in this chapter, will now be given more in detail: Assume that air at a given density has a constant strength Qo, but that a

finite amount of energy, be this energy the 2 -^ of the moving

ions or whatever form it may, is necessary to cause rupture or start corona. Then the stress at the conductor surface must exceed the elastic limit gfo, or be increased to Qv in order to supply the rupturing energy between the conductor surface and a finite radial distance in space where the stress is go and breakdown occurs, or, in other words, a finite thickness of insulation must be under a stress equal to, or more than go.

Just before rupture occurs the gradient at the conductor sur- face is

^" = r log!' STr ^^^^

the gradient a cm. away from the surface is

^^ = (r +a) log, S/r ^^^^

Theoretically, one is also led to believe

a = 0(r)

or go = y-i—TTWl ly r (23)

It now remains to test this out experimentally and find </)(r). The equation of the experimental curve is found to be:

^ / 0.301 \

g. =go{l + a/Vr) = 29.8(1 + -^H (24)

Substituting (24) in (21)

/ 0.301 \ e.

^\ ^ Vr ) " T log. .S/r

^' (r + 0.301 V7) log. *SVr Thus the experimental values bear out the above theory

a = 0(r) = O.SOlVr g = 29.8 = constant

• A.I.E.E., Januao", 1911. See also papers by Whitehead, A.I.E.E., June, 1910, 1911, etc. 'A.I.E.E., June, 1911.

48

DIELECTRIC PHENOMENA

That is, at rupture the gradient a finite distance away from the conductor surface, which is a definite function of r, is always constant. (See Fig. 29.)

Qv = 29.8( 1 H /-- I kv. per cm.

A similar investigation made on wires in the centers of metal cylinders (see Figs. 27 and 30) shows as above that the visual

Fig. 29. — gv and go for small and large wires.

critical gradient, Qv, increases with decreasing radius r, of the wire, but is independent of the radius R, of the outer cylinder. The relation between r and Qv is given in Table V. For a wire in the center of a cylinder the gradient Qo is slightly higher than for similar parallel wires, apparently due to the fact that the field is everywhere balanced for a wire in the center of a

Fig. 30. — Apparatus for determining the visual corona voltage in con- centric cylinders.

cylinder, which is not the case for parallel wires. The expression for the apparent strength of air for a wire in the center of a cylin- der is

^J. , 0.308 \ , gv = 31( 1 H -r^l kv. per cm.

It thus seems that gc = 31 is the true dielectric strength of air.

VISUAL CORONA

49

The method of reducing the results to equations was as follows: Various functions of r and Qv were plotted for parallel wires from Table 11, until it was found that a straight-line law obtained between Qv and l/y/F. All values of gv and l/-/r were then tabu- lated as in Table III and plotted as in curve (Fig. 31). Points

120

r— ■

_•

^

■

KWk

^

^

r

• lOv

a

r^

r

u

^

^

"^

1 60

1

^^

i~

^

!>•

Yisaal Critical Gradient

Mathod of BedDClng Relatlo

between Om and r

i<

"

^

^

tl

ao

D

L

1

1

B

i

{

1

^1

i

»

'

»

10

in cms.

-^

FiQ. 31. — Relation between g, and

V:

Table III. — Relation of Visual Critical Voltage Gradient

TO Radius

(Experimental Values Corrected to 76 cm. Barometer and 25 deg. C. Parallel

Wires)

DiAmeter, cm.

0*

kv./cm. (max.)

Radius, r — cm.

1

cm.

Diameter, cm.

0*

kv./cm. (max.)

Radius,

r " cm.

1 cm.

0.0196

116.0

0.0098

10.10

0.202

59.1

0.101

3.13

0.0343

99.0

0.0172

7.65

0.257

56.7

0.128

2.76

0.0350

94.0

0.0175

7.58

0.320

54.3

0.160

2.51

0.050S

84.0

0.0254

6.27

0.322

49.6

0.161

2.51

0.0577

81.5

0.0288

5.90

0.513

48.8

0.256

2.01

0.0635

81.0

0.0317

5.64

0.518

44.5

0.259

1.94

0.078

76.0

0.0390

5.08

0.655

43.7

0.327

1.82

0.0813

73.5

0.0406

4.96

0.826

42.2

0.413

1.57

0.1635

63.8

0.0818

3.51

0.928

40.6

0.464

1.44

0.1660

63.4

0.0830

3.45

1 I

varying widely from the average straight line were then discarded as probably in experimental error. The remaining points were then divided into two equal groups and tabulated as in Table IV.

50

DIELECTRIC PHENOMENA

Table IV. — Relation op Qv and (Showing 2A Reduction)

Vr

1

1

a.

y/7

09

Vr

99

7.65

59.0

3.13

82

5.90

54.0

2.51

81

5.64

50.5

2.51

76

5.08

49.0

2.01

74

4.96

41.0

1.44

Z412

Z29.23

S253.6

S11.60

AZgv = 158.5

AS — /- = 17.63 Vr

ZZgv = 666.5

Cl

ZZ

158.5 17.63

9.00

V^

« 40.83

665.5 - (9 X 40.8)

Therefore:

9 =

Qv = 29.8 +

10 9

= 29.8

— ('%)

In order to give proper weight to the points the 2A method was used in the evaluations of the constants for the equation above. This method of reduction, which is self explanatory, is very convenient and especially suitable where a large number of experimental points have been obtained, in which case the results are as reliable as, or more so, than when few points are taken and the unwieldy method of least squares used.

Temperature and Barometric Pressure. — The density of the air varies directly with the pressure, and inversely as the absolute temperature. In these investigations the air density at a tem- perature of 25 deg. C. and a barometric pressure of 76 cm. has been taken as standard. If the air density at this temperature

VISUAL CORONA 61

and pressure is taken as unity, the relative density at other tem- peratures and pressures may be expressed in terms of it, thus:

0.004656

w =

273 + t

where w = the weight of air in grams per cubic centimeter

b = barometric pressure in centimeters t = temperature in degrees centigrade.

At 25 deg. C. and 76 cm. pressure

0.00465 X 76 nmiift«; ^ot«o tOss" - 76cm. = — 27Q J- 25 — " 0.001185 grams

w at any other temperature and pressure is

0.004656

""'' "^ 273+1 wtb 0.004656 3.926

u^6» 7ecm. (273 + 00.001185 273 + t 5 = ^^^

= 6

(273 +

On the theory that definite energy is necessary to start dis- ruption or glow, Qo should vary directly with the air density factor d; gv, however, should not vary directly with 5, as the thickness of the energy or ionizing film should also be a function of 5. The equation for g, should take the form

Whether 5 is varied by change of temperature or air pressure the effect should be the same as long as the temperature is not so high that the air is changed or affected by the heat, as ioniza- tion, etc.

Temperattire.— A series of experiments on visual corona was carried on over a temperature range of —20 deg. C. to 140 deg. C. The apparatus is shown in Fig. 30. It consists of a polished wire in the center of a brass cylinder. The cylinder was placed hori- zontally in a large asbestos lined '^ hot box," heated by grids at the bottom. In order to get uniform temperature the cylinder was shielded, and time was allowed to elapse after each reading. Temperature was observed by a number of thermometers dis- tributed in the hot box.

52

DIELECTRIC PHENOMENA

Table V. — Relation of Visual Critical Voltage Gradient to Radius (76 cm. Barometer — 25 deg. C. — Concentric Cylinders)

Radius r cm.

a.c. a*

kv./cm. (max.)

R

cm.

d.c.i kv./cm.

r cm.

a.c.

0*

kv./cm.

(max.)

R

cm.

d.c.

0.059 0.103 0.127

70.4 60.7 58.4 56.6 52.7 52.7 51.6 49.9 47.1

3

CO

k

00

69.0 59.5 55.5 54.5 49.5 48.5 47.5 44.5 43.0

0.327 0.476 0.794 0.953 1.113 1.270 1.588 1.905 2.540

48.1 44.9 41.9 41.2 39.7 39.2 38.4 37.8 35.0

•

1

o6 3.81

3.81

3.81

3.81

42.0 39.0

0.129

0.190

0.199

0.206

0.254

0.318

After the heating became uniform, voltage was applied and gradually increased until the glow appeared. The central con- ductor was observed through a window placed in the front part of the box so that the whole length of the conductor could be seen. It was found that it made no appreciable difference in the starting voltage whether or not the box and tube were "aired out" after each test.

Three sizes of brass cylinders were used having inside radii of 8.89, 5.65, and 3.66 cm. respectively. The central conductors ranged in size from 0.059 to 0.953 cm. radii. Tables VI and VII are typical data tables.

Table VI. — Variation of Strength op Air with Temperature

For Polished Copper Tube Inside of Brass Cylinder

r = 0.963 R = 5.55 cm.

Observed values

Calculated from equation

Kv. effective

Temp.

h em.

a

0»(maz.)

^v(maz.)

48.5

18

75.4

1.016

40.7

41.4

46.5

37

75.4

0.954

39.1

39.1

45.2

50

75.4

0.915

38.0

37.7

43.4

66

75.4

0.873

36.5

36.2

41.0

85

75.4

0.826

34.5

34.5

39.6

100

75.4

0.793

33.3

33.3

37.6

119

75.4

0.754

31.6

31.9

^ D.c. values from Watson, Jour. I. £. £., June, 1910, Fig. 21.

VISUAL CORONA

53

Table VII. — Variation op Stbenqth of Air with Temperature

For Polished Copper Tube Inside of Brass Cylinder

r = 0.476 cm. R ^ 5.55 cm.

Observed values

Calculated from equation

Kv. effective

t

b

a

(7*(inaz.)

(/'•(max.)

41.0

-13

75.5

1.139

49.6

50.0

40.0

75.5

1.084

48.3

48.0

37.0

20

74.9

1.001

44.8

44.9

35.7

41

75.5

0.942

43.2

42.7

33.2

70

75.5

0.863

40.1

39.7

31.5

87

75.5

0.823

38.1

38.1

29.5

121

75.5

0.753

35.7

35.4

28.7

130

75.5 '

0.734

34.7

34.7

Columns 1, 2 and 3 give observed values, surface of the inner cylinder is

e

The gradient at the

9 =

r log, R/r

Column 5 gives the surface gradient for the voltage, Cv, calculated directly from observed values. It can be seen from the data, that Qv for a given r, varies with 6, but is independent of R or S. By Z A reduction of all of the data the following equations connecting Qv with r and 5 were obtained:

90 80

'J70

»60

240

?30

M-20

10

Jj

.1

1

^

^

.0

.^

!■•-

^

■ ,^

--*

■^

'^

^

K

8-

^

^

-^

'^

«^

J^

^

^

— '

*^

'^

^

TbQM Garvei show Straight Line Belation between av rad ^ iof Ooastant 5

_

Th

erel

[ore

LJ

■tf

Lu

(ive

D 0'

,'Q

.H

Y 9

7;)

.6 1.0 1.6

2.0 2.5

8.0 8.6 4.0

Fia. 32. — Effect of temperature on the strength of air. X measured values.

For Concentric Cylinders,

0.308\

,. = 315(1 +-^)kv. per cm. max

(26a)

54

DIELECTRIC PHENOMENA

For ParaUel Wires.

0.301\

g, = 29.85 (1 H — ~j=^) ^^' ^' '™' ™*

(266)

90

80

r^^"'

■

1

C^

g70

1 ^

^

t

^

y

^

r:|^

• B

y^

^

^

^

e

^

v^

^

^

^

^

9 EA

^

^

r

If

^

^

i^

^

^

^^K^ <^^

mCO

^

-^

r^

^

^

^

\

'S*

;:;

-^

^

"^

<

^

■^

^

^

^

80

Jl

^

'^

r-^

&

a

1

J

3

A

' I

1

.0

1.1

\A

L8

Fia. 33. — Effect of temperature on the strength of air. (r = radius of wire in cm. X measured values. Drawn curves calculated.)

Referring to the tables, column 6 gives values of gv calculated from equation (25a). By comparing with the experimental values in column 5 it is seen that the difference is generally less than 1 per cent.

90 80

B 70

u GO

«

Ck

^•60 ii 40 •^ 80

ao

10

I

s

P

f

^

^

9^

^

M

»

^

f:

L>^ ^

^'

0'

^

y

r^

^

*^

y

^

f^

^

^

'^

V

y

/

^

'<i

^

.1 .2 .8 .4 .5 .6 .7^.8 .9 1.0 \X 1.2 1.3 1.4

FiQ. 34. — Effect of temperature on the strength of air. ( X measured values.

Drawn curves calculated.)

Qo has a slightly higher value for wires in a concentric cylinder than for parallel wires. This does not mean that the strength of air differs in the two cases. For a wire in a cylinder the field is balanced all around and should give more nearly the true value.

VISUAL CORONA

65

In Figs. 32| 33 and 34 the drawn lines are the calculated values, while the crosses are the observed values.

Barometric Pressure. — It will be noted in Fig. 34 that while the calculated curve is almost a straight line down to 5 = 0.5, below this point there is a decided bend to zero. The lower part of this curve was drawn from calculations. In order to check experimen- tally the above law over a wide range of 5, and also to show that the effect was the same whether the change was made by varying tem- perature or pressure, tests were made over a large pressure range.

Terminal

Fig. 35. — Apparatus for determining the effect of pressure on strength of air.

A glass cylinder lined with tin foil 7.36 cm. in diameter with a small slit window in the center was used for this purpose. (See Fig. 35.) Tests were made on wires 0.508 cm. to 0.157 cm. in diameter, and

Table VIII. — Variation of Strenqth op Air with Pressure Diameter of Brass Rod » 0.381 cm. in 7.36-cm. Diameter Glass

Tube Covered with Tin Foil

Prea. aba

Volte read

(eff.)

Temp, deg. C.

3.02b 273 + t

0w -

09 max.,

measured

kv./cm.

0w max., calculated

/ 0.301 V

31«(l + - )

^ V6r /

kv./cm.

cm. Hg

T(loo.R/r) kv./cm. (eff.)

5.3

2,880

27.0

0.069

6.08

7.19

7.80

10.7

4,680

24.0

0.141

8.09

11.46

12.40

11.2

4,920

27.0

0.146

8.68

12.28

12.15

19.3

7,400

27.0

0.262

13.06

18.47

18.58

27.7

9,560

27.0

0.362

16.87

23.86

24.06

36.6

12,000

27.0

0.478

21.20

30.00

29.60

46.4

14,460

26.0

0.612

26.60

36.07

36.70

47.0

14,600

27.0

0.614

26.80

36.60

36.80

65.7

16,300

27.0

0.728

28.80

40.76

40.76

60.0

17,760

26.6

0.792

31.36

44.30

43.60

66.0

18,400

27.0

0.867

32.60

46.00

46.76

76.0

21,100

26.0

0.997

37.26

62.70

52.25

56

DIELECTRIC PHENOMENA

66

60 B46 |40

|86

126

« M

10 6

.

Wire Radiae«.254cni.

^

o ■ Kxperimenial Yaloea ' ' Drawn Canre -Calculated Yaluei

^

^

-^

^

■^

^

^

^

^

^

^

_^

^

^^

^

if-

^

•

l

.\

I

A

\

•^

(

.1

S,o

» A«S

.7

.1

»

.9

LO

60 66

.60

S

«46

d

■ |86

iso

^26 10

a-

3734 £

FiQ. 36. — ^Effect of pressure on the strength of air.

Wire Kadlua-.lMScni. o ■ KxperimaQtal Values Drawn Cunre -Oalculated

^

«»

1^

''

^

^

^

^

^

^

^

^

y^

"^

■

^

r

/^

X'

^

/

.1 .2 .8 .4 -B 3.92 6'® '"^ *^ *^ ^^

^" S73+f

FiQ. 37. — Effect of pressure on the strength of air.

60

66

. 60

l»

M g26

10 6

-^

Wire Radius -.IS? cm.

o ■ Sxpedmaiital Values Drawn. Curre - Calculated

e

^

^

^

^'

^

^

x^

^

y'

y

A

y-

/

it^

C

(

• '

■

.!

\

a a

s

.^

I

.1

»3.»

ih'^

J

r •

.8

;

.1

»

1

.0

973-1- 1

FiQ. 38. — Effect of pressure on the strength of air.

VISUAL CORONA

57

a pressure range of 1.7 om. to 76 cm. Table VIII is typical

of observed and calculated values. Figs. 36, 37 and 38 show

how these follow the previously predicted curve. A SA reduction

of the values also confirms the above formulse. For concentric

cylinders

oit/i ^ 0.308\ ,

gv = 315(1 H -7=-\ max. kv. per cm.

For parallel wires

0.301\

Qv = 306 [1 H — ~7==n T^^T^' kv. per cm.

The change in g« with the density is apparently due to change in the molecular spacing, and thus depends only upon the relative density and not the absolute density. Heavy COs at the same pressure and temperature has the same strength as air. This was not checked on hydrogen.

Electric Strength of Air Films. — If a definite amount of energy is necessary to start rupture at a finite distance a from the con-

:o:)

v.—-'

^

a

CQ) @(P)(c

Sa

rc:r\

rfini

^LwM than •J 2a

FiQ. 39.

ductor, with a surface gradient g„, it is interesting to speculate what will happen at very small spacings or when the distance between conductor surfaces is in the order of o. (See Fig. 39.)^

As the free "energy storage," "accelerating" or "ionizing" distance is then limited, a greater force or gradient should be required when the distance between the conductors approaches a. Experiments were made to determine this, using spheres as elec- trodes. The ideal electrodes for this purpose would be concentric cylinders, but the use of these as well as parallel wires at small spacing seemed impracticable. Spark-over and corona curves were made on spheres ranging in diameter from 0.3 cm. to 50 cm. and spacings from 0.0025 cm. to 50 cm. This discussion applies only to spacings up to 2/2 where corona cannot form.

' Actually, the '*energy-zone" is not as shown, as the field is distorted at these small spacings.

58

DIELECTRIC PHENOMENA

In these tests a 60-cycle sine wave voltage was used. For the small spacing the spheres were placed in a very rigid stand. One shank was threaded with a fine thread, the other was non-adjust- able (Fig. 40). In making a setting the adjustable shank was screwed in until the sphere surfaces just touched, as indicated by completing the circuit of an electric bell and single cell of a dry battery. A pointer at the end of the shank was then locked in place, after which the shank was screwed out any given number of turns or fraction of turns as indicated on the stationary dial. For larger spacings other stands were used.

A typical spark-over spacing curve and corona spacing curve is shown in Fig. 41. Theoretically, up to a spacing of 2R corona cannot form but spark-over must be the first evidence of stress.

Practically, corona cannot be detected at 60— until a spacing of 8ft is reached. This is because up to this point the difference

'Pointer

Dial Stationary

Wood

Fig. 40.

between the corona starting points and the spark point is very small. Above 8B the spark-over curve approaches a straight line as in the case of the needle gap curve. The corona curve above 2/2 and the spark curve below 2R are apparently continuous. The gradient curve. Fig. 42, is calculated from the voltage curve, Fig. 41. Where the spacing is less than 0.54/i? the gradient increases first slowly and then very rapidly with decreasing spacing. Between X = 0.54/B and 2R the gradient is very nearly con- stant. Above about SR spacing the gradient apparently increases. This apparent increase is probably due to the effect of the shanks, etc., which become greater as X is increased. The effect of the shanks is to better distribute the flux on the sphere surface, and cannot be taken account of in the equation for gradient. This was shown experimentally by using different sizes of shanks at

VISUAL CORONA

the larger spacing. Thus, when the spacing is greater than 35 the sphere is not suitable for studying the strength of air, as the gradient cannot be conveniently calculated. It is hence not a suitable electrode for studying corona, as corona does not form until the spacing is greater than 2R. The maximum gradient at the surface of a sphere (non-grounded) may be calculated from the equation.

,

SM

n

A

h-

1

d

^

k

In

•^

(13o)

where X is the spacing E the voltage

-/<f+'+>/(F7^)'

The gradient for the non-grounded case may be conveniently calculated by use of the table on page 27. The gradient on the line connecting the sphere centers at any distance a from the sphere surface may be calculated ttom the complicated equation*

1^

«--7

|2X>[X'(/-|-1)+4(|

I (/-I)

[X'(/H

-4(1-

a) Cf-

(26)

Some of the experimental values are given in Tables IX and X. Typical voltage gradient curves are shown in Figs. 43, 44 and 45.

■ G. R. Dean, G. £. Review, March, 1913.

• G. R. Dean, also Physical Review, Dec., 1912, April, 1913.

60

DIELECTRIC PHENOMENA

8S a88a«aa83a3gsoo*>-*^<=>'

QB

U3

5

40AO-ijad8 moA-otTS 'WK

3

M * ft"

"ft;

•4J

aaisis§s§i§ai8«^8S58

9a»ipu{) '010 9d moA'Oll'H '"W iBAo-i|Md9 •)(OAoiTS 'nn

'3

OpE(

I"! "Pi

8S§§SS§§§3§§§§83?8S9

9V9IPVJO 'IU3 i»d i^IoA-oiia 'X'K

00

o

VISUAL CORONA

61

Table IX. — Spark-over of Spheres at Small Spactngs Brass Spheres R ^ 3.33 cm.» Diameter = 2-5/8 in.

Spacing

In.

Cm.

Kv.

3.92b

273 +<

€masm

(corrected)

" X ' kv./cm.

Jf/ft

0.001 0.002 0.003 0.004 0.005 0.010 0.020 0.040 0.076 0.100 0.200 0.300 0.400 0.500

0.00254

0.363

0.00508

0.531

0.00762

0.654

0.01016

0.775

0.0127

0.845

0.0254

1.07

0.0508

1.86

0.1016

3.27

0.1905

5.43

0.254

6.92

0.508

12.40

0.762

17.70

1.016

22.70

1.270

27.75

1.028 1.030 1.027 1.026 1.016 1.000 1.002 1.002 1.002 1.002 1.002 1.002 1.002 1.002

0.497 0.729 0.899 1.07 1.17 1.52 2.62 4.62 7.66 9.77 17.50 25.00 32.00 39.20

196.0

143.6

118.1

105.2

92.3

60.0

51.8

45.9

41.0

39.5

36.3

35.4

34.8

34.9

0.00076

0.00152

0.00228

0.00305

0.00382

0.00764

0.01528

0.03056

0.05730

0.0764

0.1528

0.2292

0.3056

0.382

Table X. — Spark-over of Spheres at Small Spaci ngs Brass Spheres R » 12.5 cm., Diameter. » g.g4 in.

X

Spaeinc

Kv. (read)

6 3.92b

273+1

tmaxm _/2(e.//.)

i (corrected)

Qma*'

kv./cm.

In.

Cm.

X/R

0.005

0.0127

0.807

1.023

1.116

87.9

0.00101

0.010

0.0254

1.220

1.021

1.689

66.5

0.00203

0.020

0.0508

2.050

1.031

2.849

55.9

0.00406

0.040

0.1016

3.38

1.022

4.68

46.2

0.00813

0.100

0.254

7.03

1.020

' 9.75

38.6

0.0203

0.200

0.508

12.54

1.012

17.44

34.8

0.0406

0.300

0.762

17.91

1.016

24.92

33.5

0.0609

0.400

1.016

22.82

1.010

31.76

32.0

0.0812

0.500

1.27

27.63

1.010

38.67

31.5

0.1016

1.000

2.54

53.0

1.000

74.90

31.6

0.2032

1.500

3.81

75.3

1.000

106.30

30.9

0.3048

2.000

5.08

96.4

1.000

136.20

30.5

0.4064

2.500

6.35

117.4

1.000

166.00

30.7

0.5080

3.000

7.62

139.2

1.000

196.90

31.2

0.6096

3.500

8.89

158.0

1.000

223.40

31.3

0.7112

4.000

10.16

174.9

1.000

247 . 10

31.0

0.8128

4.500

11.43

190.8

1.000

269.50

31.0

0.9144

5.000

12.70

203.6

1.000

287.20

30.8

1.0160

62

DIELECTRIC PHENOMENA

In Table XI are tabulated, for different sizes of spheres, the spark-over gradient at the constant part of the curve, the aver- age gradient between X = 0.54/fi and X = 3/J, and the approxi- mate minimum spacing at which the gradient begins to increase

Table XI. — Maximum Rupturing Gradients for Spheres (Average for Constant Part of the Curve)

R

Spacing Z, where g^ begins

Oa max. kv./cm. for constant

Raditia ib cm.

to increase (cm.)

part of curve

0.159

0.18

63.8

0.238

0.25

55.6

0.356

0.26

51.4

0.555

0.40

46.9

1.270

0.51

40.0

2.540

0.85

36.8

3.120

35.8

3.330

0.95

34.8

6.25

1.30

32.5

12.60

2.0

31.3

25.00

30.0

65

jm

\

\

^

V

a

a"

—

•^

..

HT

^» 820

lis

%

6

•

1

I •

I

B ^

I

atii

acq

B as.

]

10 ]

LI 1

2 IS

Fig. 46. — Variation of the apparent strength of air with sphere radius. Points measured gradient from constant part of curve. Drawn curve, calculated from equation (27).

in value. The gradient-radius curve is plotted in Fig. 46. This curve is very closely given by the equation

g* = Qoy

1 +

oc

Vr

)

(27)

VISUAL CORONA

63

For a wire in a cylinder go = 31 g«

For parallel wires

For spheres

go = 30 gr,

= 3or

(25a)

(256)

(28)'

which has exactly the same form as the similar curve for cylinders. The value of go is, however, lower than for the balanced field of a wire in a cylinder.

0.308 \

/ 0.54 \ go = 27.2 fir. = 27.2(^1 + ^)

It is probable that the true strength of air is 31 kv. per centimeter as represented by the balanced field, it is apparently less for parallel wires due to the unbalanced field, and still less for spheres where the field is unbalanced to a greater extent.

The curve between the sphere radius and the ap- proximate minimum spacing below which the gradient be- gins to increase appreciably is plotted in Fig. 47 from Table XI. The curve is rep- resented by the equation

X = OMy/R (29)

which means that when the

spacing is less than 0.54/J2 the gradient increases in value, at

first slowly, then very rapidly.

It is now interesting to investigate the meaning of equation (27). In Fig. 48 the exact gradient is plotted from equation (26) for different distances from the sphere surface on the line con- necting the centers and at given spacings as indicated by the small diagram in the upper corner of the figure. It is seen that for small distances from the sphere surface the curves for the differ- ent spacings fall together. Over the small range the gradient ga at any point a centimeters from the sphere surface on the center line may be found approximately from

The only reason for giving this approximation, which holds only for very small values of a and is only true when a = 0, is

S2.0

^ * A

^J

^

^

^

^

^

-^

y^

^

11.2

4 A

y

8 1*0

o

X

^

y^

i «

/

t .4

y

r—

t

~^

r

J 1

:

I 1

1 1

1 4

L 1

5 <

B '

7 J

B 1

» 1

01

1]

Z]

181

4

Radius in Oentimeters

FiQ. 47. — Sphere spacing below which apparent strength oegins to increase.

64

DIELECTRIC PHENOMENA

that (26) is too complicated to handle. The error due to this approximation is shown in Table XII.

Table XII

R -

1.27 cm.

A a 12.5 cm.

Energy distance, a

= 0.27 VR

= 0.3 cm.

Energy distance

s, o = 0.95 \

sm.

a

Exact

Approx.

X

a

Exact

Approx.

X

0.0

39.9

39.9

0.76

0.0

31.3

31.3

4

0.1

34.6

34.0

0.76

0.2

30.3

30.3

4

0.2

31.9

30.0

0.76

0.4

29.5

29.4

4

0.4

29.7

24.1

0.76

0.6

28.6

28.5

4

0.8

28.3

27.7

4

0.0

39.9

39.9

1.21

1.0

27.5

26.9

4

0.1

34.2

33.4

1.21

0.2

30.5

29.5

1.21

0.0

31.3

31.3

10

0.4

26.5

23.7

1.21

0.2

30.3

30.3

10

0.4

29.5

29.4

10

0.6

28.6

28.7

10

0.8

28.0

27.7

10

1.0

27.5

26.9

10

Then

(E.)

= tyt/ = p^(y/) ®x^c* mathematical.

9oll +

Vr)

experimental for approximately

= go(

^* ^ /p I 9 \ ( y/) approximate mathematical.

y/RJ constant part of curve. E /R

Equating (13a) and (27)

f(i/)-'-('+^)

E. (R^

go =

(ft + « Vft)

{§)'

(13a) (27)

(30)

which is the same form as (30) and means that at a distance

«V^ ^ O^VS = 0.27VR cm.

from the sphere surface the gradient at rupture is always approxi- mately constant and is go. As breakdown must take place at approximately a = 0.2^^/R cm. from the sphere surface, the

VISUAL CORONA

65

gradient should begin to increase at the spacing 2a = CMVA. This is approximately so as shown in Fig. 47 and equation (30). The increase is at first slow at X = 2a, and very rapid &t X = a. Fig. 48 shows that at a = 0.27/A the gradient is not exactly constant for different spacings, or the curves do not fall together.

Jculati

Calculated from {'

This means that g, and « in equation (27) cannot be exactly constant for a given radius, but must also be a function of X. This is experimentally shown to be the case, as there is a slight variation over the range X =■ O.Hv'B and X = 2R. Influence of Frequency on the Visual Gradient. — The effect

■J'" 1

Li-^zi^

r "

^

ti

5

TOO 800 MO 1000

Flo. 49. — Variation of the apparent strength of air with frequency.

of frequency on g, for the practical range of 25 to 60 cycles, if any, is very small and can be delected. A few measurements are shown in Fig. 49. For the test range it is difficult to tell whether the slight variations are due to changes in wave shape or to fre-

66 DIELECTRIC PHENOMENA

quency. There is a possibtlity of frequency entering this as a function :

'"'-(^^rnvt)

Inveetigations up to 1000 cycles show very little if any change. In this investigation the sine wave voltage was measured with a static voltmeter calibrated at 60 cycles. Measurement at 30,000 cycles (sine wave from a generator) made by the static volt- meter showed a slightly lower voltage than at 60 cycles.^ Direct current points by Watson are given in Fig. 49. Over the com- mereial range of frequency, however, there is no appreciable effect of frequency.

Effect of Oil, Water or Dirt on the Visual Corona Point.— These tests were made in a manner exactly similar to the dry testa.

OIOZOIOMGOCOIO 10 2<1I0 4I)WMTD

Figs. 60 and 61. — Spark-over and corona voltages tor parallel wires. (Wire surfaces dry, wet, and oiled. Max. kv to neutral, 8 = 1, Fig. SO. — Wire radius 0.205 cm. Fig. 51.— Wire radius 0. 129 cm.)

In the oil tests, the surface of the wire was coated with a thin, even film by means of an oiled cloth. For the wet tests wat«r was sprayed on the conductor surface before each reading by means of an atomizer. Figs. 50 and 51 are dry, wet and oil curves for two different sizes of wire.

For spark-over, both water and oil have approximately the same effect, that is, give very nearly the same spark-over voltage for all sizes of conductor. The curves very closely follow the needle gap curve.

For corona, water very greatly lowers g,. Oil lowers gt but to a

■ See pages 106, 107.

VISUAL CORONA

67

much less extent than water. When the conductor is very small the per cent, mcrease in diameter due to oil more than com- pensates for the lowering effect. The approximate apparent visual corona gradient for oil and water coated conductors may be found Water surfaces by fine spray or fog

• n/i . 0.815\ ,

g, = 9[ 1 H y-^ 1 max. kv. per cm.

Oil film surfaces

Qv = 19/ 1 H j=- 1 max. kv. per cm.

See Fig. 52.

If a water coated wire above the visual corona point is exam- ined in the dark, it has the appearance of an illuminated atomizer. The surface quickly becomes dry.

eo

60 40

P80

M20

10

^

^

S*

^

^

x*^

<]

€

^

y

^

^

^

-^

^

^

"*

^

cv

^

•^

Fig. 52. — Apparent strength of air around wires with wet and oiled surfaces.

Dirt on the surface of the conductor, by increasing the gradient,

causes local brush discharges, and if the surface is rough, corona

starts at a lower voltage. This is taken care of in the formulse

by an irregularity factor m». Thus for a weathered or oxidized

wire

J^ , 0.301 \ Qv = QortivoX 1 H j=^ \

The corona starting voltage for wet or oiled wires may be found by calculating Qj, in above equations and substituting in equation (20).

5

68

DIELECTRIC PHENOMENA

Conductor Material. — With the same surface condition the visual corona point is independent of the material. This is shown in Table II.

Humidity. — Tests made over a very wide humidity range show that humidity has no appreciable affect upon the starting point of visual corona. After corona is present humidity has an effect on the spark-over voltage. This is discussed in Chapter IV.

Ionization. — Change of initial ionization of the air even to a considerable extent has no appreciable effect on the starting point of corona. This was found by test by increasing the voltage on the wire in the cylinder until considerably above the corona voltage, and then, while the cylinder was full of ionized air, lower- ing the voltage below the corona point and again raising it until glow appeared. The starting point was not appreciably changed. Initial ionization should, however, effect the time in which the discharge takes place. This will be discussed later.

Current in Wire. — A test was made to see if heavy currents flowing in the wire would change the starting point of visual corona. The test arrangement was as shown in the Fig. 53.

^

MaybeOoi ne< ted in Either Or< er

ZZhr

Fig. 63. — Apparatus for measuring corona starting point with current in

the wires.