Tests were made with both a.c. in phase and out of phase, and d.c. in the wire. The results are given in Tables XIII, XIV and XV. The temperature of the wire was measured by the resist- ance method. The values in the last column are all corrected from the wire temperature to 5 = 1. If the current has no appreciable effect, as appears to be the case, these should all be equal. The variation is probably due to difficulty in getting the

VISUAL CORONA

69

Table XIII. — Gobona Starting Point with Current Flowing through

Wire Concentric Cylinders

Radius of wire 0. 129 cm.

Radius of cylinder 6 . 46 cm.

Average

Kv. eff.

Amp. d.c.

temperature

Barom. cm.

i (uaing wire temp.)

0*

gv reduced

to 2-*l

Air

Wire

20.0

0.0

26

26

75.6

0.991

58.4

58.9

19.7

15.2

26

32

0.970

57.5

59.2

19.4

31.4

26

48

0.922

56.7

61.4

18.5

39.0

26

64

0.878

54.1

61.6

17.8

49.2

26

82

0.824

52.0

63.1

16.9

76.0

26

120

0.753

49.4

65.6

20.4

0.0

23

23

1.000

59.6

59.6

20.3

18.0

23

27

0.987

59.3

59.9

19.4

33.0

23

50

0.917

56.7

61.8

17.9

50.8

24

91

0.813

52.2

64.2

12.9

99.6

24

320

0.500

37.6

75.2

16.4

67.6

26

102

0.790

47.9

60.6

13.9

78.6

26

212

0.610

40.8

67.0

16.1

61.6

26

144

0.710

47.0

66.2

Table XIV. — Corona Starting Point with Current Flowing through

Wire Concentric Cylinders

Radius of wire 0.205 cm.

Radius of cylinder 5 . 46 cm.

Average

Kv. eff.

Amp.

temperature

Barom. cm.

i (using wire temp.)

9>

Qm reduced

a • 1

to 5 B 1

Air

Wire

25.3

14 (d.c.)

23

23

76.2

1.01

53.15

52.6

25.2

23

23

76.2

1.01

53.0

52.5

25.2

14 (a.c. in phase)

23

23

75.8

1.005

52.8

52.6

25.1

14 (a.c. out of phase)

23

23

75.8

1.006

52.6

52.3

25.1

23

23

75.8

1.006

52.6

52.3

25.2

24

24

75.25

0.994

52.8

53.2

25.2

14 (d.c.)

24

30

75.25

0.974

52.8

54.3

25.2

34 (d.c.)

25

60

76.25

0.886

52.4

59.1

23.8

56 (d.c.)

29

60

76.25

0.886

50.0

56.3

23.3

70 (d.c.)

30

73

75.25

0.853

48.8

57.3

21.8

114 (d.c.)

110

75.25

0.771

45.7

59.2

25.0

60 (d.c.)

31

31

75.25

0.971

52.4

53.9

25.0

31

31

76.26

0.971

52.4

53.9

24.8

23 (a.c.)

31

44

75.25

0.931

52.0

55.8

70

DIELECTRIC PHENOMENA

Table XV. — Corona Starting Point with Current Flowing through

Wire

Concentric Cylinders

Radius of wire 0.476 cm.

Radius of cylinder 5.465 cm.

Ky. eff.

Amp. d.c.

Average temperature

Barom. cm.

I (uaing wire temp.)

fh

0* reduced

tn 2 M 1

Air Wire

36.5 36.5

80

27 27

27 27

75.5 75.5

0.985 0.985

44.3 44.3

45 45

exact temperature. The air immediately surrounding the wire is assumed to be at the same temperature as the wire. Current Sowing in a wire thus does not appreciably effect the corona point unless the temperature of the wire is increased.

Stranded Conductors or Cables. — While the visual critical corona point is quite sharp and definite for wires, it is not so for

60

40

a

|80

e

iao

s

M

.2 .4 .6 .8 1.0 1.2 1.4 1.6

J>iameterln cmi.

FiQ. 64. — Apparent visual critical corona voltages for parallel cables. Numerals denote number of strands: I, polished copper wire; II, decided corona on cable, o; III, local corona all along cable, x.

-^

I

"^^

T^

II

tl

" 1

ft

^!"

m"

--

I:

T?

...»

"7?

"i?

cables or standard conductors. Corona, after it first appears, increases gradually for a considerable range of voltage until a certain definite voltage is reached where the increase is very rapid. The first point has been called the local corona point, and the second point the decided corona point. The curve, Fig. 54, for these corona points is compared with the curve for a smooth

VISUAL CORONA

71

conductor. The starting point for cables may be found by the use of an irregularity factor, m^.

Qv = gotnvl 1 H 7=- 1 kv. per cm.

where m« == .82 for decided corona lUp =^ .72 for local corona r = overall radius of cable.

This applies to cables of six strands or over.

It is interesting to note that for the decided corona point the visual critical voltage of a cable is about 3 per cent, lower than that of a wire with the same cross-section, or, more exactly "the diameter of a solid wire with the same critical voltage is about 97 per cent, that of the wire having the same cross-section as the cable."' This is shown m Table XVI.

Table XVI. — ^Effect op Stranding Whitehead, A.I.E.E, June, 1911, Table III

Cables, strands

Duunetsr

OYsr

all

Diameter solid

of equal

section

(B)

Diameter solid of equal crit- ical YOltS (C)

C/B

C/A

Pitch of spiral

outer layer

Cm.

Diameters

3

0.349

0.272

0.247

0.907

0.708

3.81

10.9

4

0.404

0.332

0.320

0.965

0.792

3.49

8.6

5

0.45

0.381

0.370

0.971

0.822

4.44

9.9

6

0.49

0.430

0.420

0.975

0.857

6.02

12.3

7

0.541

0.480

0.465

0.969

0.868

6.66

12.3

8

0.589

0.530

0.516

0.975

0.877

6.35

10.8

9

0.64

0.581

0.567

0.977

0.886

6.98

10.9

3

0.336

0.27

0.307

0.767

0.616

None

None

4

0.378

0.312

0.25

0.802

0.665

None

None

Conduetors of the Same Potential Close Together. — When conductors of the same potential are arranged close together the critical breakdown voltage is much greater than that of a single conductor or when they are far apart. The simplest case, that of two, is shown in Fig. 55. The two conductors for a given test were kept at a constant distance S/2 from the ground plate. Potential was applied between the conductors and plate. The separation m was then varied and critical voltages read at differ-

^ Whitehead, Dielectric Strength of Air, A.I.E.E., June, 1911.

72

DIELECTRIC PHENOMENA

ent spacings. Refer to Fig. 56 (0.163-cm. wire 30 cm. from neutral plane). When m = 0, 6, = 31.5 eflf. As the spacing m was in- creased, Cv increased to a maximum of 35.8 kv. With increasing m, Bv then gradually decreases to a constant value which is the same as that for a single wire. The maximum voltage is about 5

401

T^' ''^

(4

80

» «

20

<:.•>

Ground Plate

o

?:io

o

■2^

r- JCquivalcn; ^^ W r«

"^

-•-

Si J lie Wire

16 20268086 404660 Bepantion -m - cm.

FiQ. 55. — Arrangement for two FiQ. 56. — Critical voltage on two conductors at same potential, and conductors at the same potential and plate. various separations (see Fig. 55).

per cent, greater than the critical voltage of a single conductor of the same cross section.

With the same amount of conductor material, much higher voltages can be used without corona loss when the conductor is

k

mSismmmMmmsJ -.

pnnnnnnri

6 101&aOS8086l04&6056CO Spacing -•-cm.

Fig. 57. — Conductors of the Fia. 58. — Critical voltages for conductors same potential arranged in a arranged as in Fig. 57.

triangle.

split up into three or more small conductors, properly arranged, than with a single conductor. The results of tests made on a single-phase line with split conductors arranged in a triangle as in Fig. 57 are given in Fig. 58. Fig. 58 shows curves for a single split wire and also for a single wire of a cross section equal

VISUAL CORONA

73

to that of the three split conductors. Fig. 59 shows how the voltage varies with varying w.

With the split conductor arrangement, in the special case given, the critical voltage is from 20 to 30 per cent, greater than that of a single wire containing the same amount of material.

Whitehead has made similar tests on three wires in a triangle and also four wires placed on a square in the center of a cylinder.

uo

M

Ifl)

£ 80

o

TO

5 60 o

\

V

'v

XquI

ralcnl Ire

B

ugla

Vins

101ft»2&303ft404660 Bep«r»tiou 1R Cm

Fig. 59. — Critical voltage of conductors arranged as in Fig. 57. (S »

constant » 40 cm., m varying.)

He finds 16 per cent, increase for three wires and 20 per cent, for four over the voltage of a single conductor of the same cross section.

Stroboscopic and Photographic Study

Photographic Study. — A photographic study of corona on wires and cables was made as follows: Two parallel conductors were spaced 122 cm. between centers. The camera was focused on one conductor only. The distance to the lens was such as to show the conductors at approximately actual size. An exposure was made for a given time at a given voltage. The plate was then shifted slightly, the voltage increased and a second exposure was made for the same time. That is, a given series shows the same part of the same single wire at different voltages. This operation was repeated until the series for a given wire was complete. A glass lens was used unless otherwise stated. (See Fig. 60.) These photographs are shown in Figs. 61 to 68.

Photographs 67 and 68 were made to show the effects of mois- ture. In Fig. 67 the stranded cable was brought up to the critical point. Water was then thrown on the cable. The result is shown in Fig. 68. What was a glow at the surface of the dry

74

DIELECTRIC PHENOMENA

cable became at the wet spots, a discharge extending from 5 to 8 cm. from the conductor surface. The discharge has the appear- ance of an illuminated atomizer.

Diameter of Corona. — On a smooth wire the boundary line of corona appears to be fairly definite. The apparent visual diame- ter may be measured by viewing through a slit. The apparent diameter may also be found photographically. If the photo- graph is made through a quartz lens the ultraviolet rays will ^not be cut off from the plates as when a glass lens is used.

Whitehead has made some measurements on the apparent diame- ter, comparing the visual method and the photographic method with both quartz and glass lenses. He finds that the apparent diameters are respectively by the visual, glass lens, and quartz lens methods in the ratios of 1 : 1.6 : 1.9.^ It therefore appears that there is a considerable content of the corona at the ultra- violet which is not visible to the eye. As soon as corona appears it seems to have a definite finite thickness.

I I

I

Lens

/

Plate DlrectlOQ of Shift

Fig. 60. — Method of making corona photographs.

Table XVII.-

-Diameter op Corona on Wire in the Center op a

Cylinder

Diameter wire 0.233 cm., 18.6-cm. cylinder

Fig. 9 (Whitehead, A.I.E.E., June, 1912)

Kilovolta

Diameter corona, mm.

Time, min.

Lens

No.

Diameter corona,

visual method,

mm.

22.5

5.5

2

Glass

(a)

27.5

9.3

2

Glass

(b)

32.5

11.1

2

Glass

(c)

6.7

1 Whitehead, Electric Strength of Air, A.I.E.E., June, 1912.

Fia. 61.— Corona i

Fig. 62. — Corona on copper wire polished after each exposure. Diameler,

Fig. 64. — Corona on a weathered galvanized iron wire. Diameter, 168 ci

Fio, 67.— Corona on & No. 3/0 line cable. Dry.

Fio. 68.— Corona on a No. 3/0 line cable. Wet.

VISUAL CORONA

75

Table XVIII. — Diameter op Corona, With and Without Ultraviolet

Content

(On a Wire in the Center of a Cylinder)

Exposure 20 min., 32.5-kv. cylinder, diam. » 18.6 cm.

(Whitehead, A.I.E.E., June, 1912)

0.232-cin. wire

0.316-om. wire

0.399-cm. wire

Quarts

and glass

Quarts alone

Quarts and glass

Quarts alone

Quarts and glass

Quarts alone

12.0 11.5 11.5 11.4

12.4 12.6 12.6 13.0

12.5 13.0 13.0 12.8

13.3 14.0 14.0 14.0

11.4 11.6 12.0 12.0

13.0 13.0 12.8 12.8

11.6

12.6

12.8

13.8

11.7

12.9

Figs. 69, 70 and 71 and Tables XVII and XVIII taken from Whitehead are self explanatory. Fig. 72* shows the apparent diameter of corona on a given wire. At the start the corona

L4

o

31-0 s

S0.8 !0.6

a 0.4

i

1.4 L2

1 0.8

2 0.6

.•

gO.4 ^0.2

^

^^

^

/*

y

^

/

f

•

11

lami

ter c

\ W!

■e

.233

rm.

2022 24 262880828486 EilO'Volti BHectiTO

202224262880828436

Kllo-y«lti SSecftxs

Fig. 72. Fia. 73.

Figs. 72 and 73. — Diameter of corona (0.233 cm. wire in 18.6 cm. cylinder).

appears to take immediately a definite finite thickness; the rate of increase is then quite rapid, but gradually assumes a linear relation.

^ In Fig. 73 is a curve through the same points. Throughout this curve the correction of 1.18 has been used to include the ultraviolet*. How- ever, near the starting voltage the corona seems to be very largely ultraviolet. This explains the low point at 22.5 kv.

76 DIELECTRIC PHENOMENA

A study of the power loss equation leads one to suspect that the mechanism of corona loss is more complicated than might at first be supposed. This is also indicated by many peculiar phenomena of the spark discharge. For instance, while investigating a.c. spark-over and corona for parallel wires it was observed that when the end shields were not used, and the wires came directly in contact with the wooden wheel supports, corona often appeared to bridge completely between the conductors without a dynamic arc. In this case it seemed possible that the corona on the posi- tive wire extended out farther than the corona on the negative wire and that the positive dischai^es overlapped and combine in the eye, giving the effect of a single discharge completely across between the conductors.

In the hope of throwing further light on the discharge and loss mechanism, an investigation of corona and spark was made with the help of the stroboscope.

A needle gap was first arranged across the transformer with a high steadying resistance. The impressed voltage was adjusted until corona appeared all the way between the conductors as in Fig. 74.

Examination of this was then made through the stroboscope which was so set that the right needle, Fig. 74(2), was seen when positive, and the left when negative. To the eye, the discharge from the positive needle has a bluish- white color and extends out a considerable distance, the negative appears as a red and hot point. The photograph shows more of the negative than is seen by the eye. Fig. 74(1) is the discharge as it appears without strobo- scope, 74(2) with the right needle as positive, 74(3) with strobo- scope shifted 180 deg. to show left needle as positive. In 74(4) the stroboscope has the same position as 74(3), but the voltage is higher, and many fine ''static" sparks can be seen.

If voltage above the visual corona point is impressed on two parallel polished wires a more or less even glow appears around the wires. After a time the wires have a beaded appearance. On closer examination the beads appear as reddish tufts, while in between them appears a fine bluish-white needle-like fringe. On examination through the stroboscope it can be seen that the more or less evenly spaced beads are on the negative wire, while the positive wire has the appearance, if not roughened by points, of a smooth bluish-white glow. At "points" the positive discharge extends out at a great distance in the form of needles; it is possible that it always extends out but is not always visible except as sur-

Diameter of Corona. Fig. 69 (Upper).— Diameter of corona on 0,233 cm. wire in 18,6 cm. cylinder. <■. =21,5 kv. Glass lens kilovolts 22.5, 2.5, 27,5, 30, 32.5 respectively. (Whitehead.)

Fig. 70 (Middle). — Diameter of corona showing effect of ultra-violet. (a), 0.232 cm. (6). 0.316 cm. (c), 0.399 cm. Left side of (a)(&)(c), quartz lens. Right siiie of (a)(b)(c), kIiss lens. (Whitehead.)

Fio. 71 (Lower).— Corona on 233 cm. wire, at 22,5, 27,5, 32,5 kv. c, = 20.75 kv. Glass lens. (Whitehead.)

(1) Without atroboBcope, 72,000 volts.

(2) With atroboacope, 72,000 volts.

(3) Same as (2), stroboscope rotated 1

Lett {+) (4) Same as (3), voltage increased t^) 84,000. Right (-)

FiQ. 74. — Corona between copper needle points. 20.5 cm. gap-

1 5 ■I {

Si

I 3

"si

£1

II

||S

bS

(1) Without stroboscope.

■t(-) (3) With stroboscope Right ( + )

rotated 180°.

3. 77.— Corona on parallel wires. No. 13 B. and 8. copper wire. Spacina.

12,7 cm. Volts, 82,000.

Left(-) Right(+)

Fio. 79. — Polished brass rod. Diameter, 0.475

em. SpaciiiR, 120 cm., Volts, 150,000 Note that npftative "beads" are just starting to form.

Fio. 78.— SoPtion of wire (Fig. 77). "Dead." Bright spots position of negative

Left(-) Right{ + )

FiQ. 80.— Copper wire. Diameter . 2ti cm. Spac- ing, 120 em. Volts, 200.000. Polislied at start. Note negative corona apparently following spiral "grain" of wire.

II

[S

s

US s-3

its

If 111

VISUAL CORONA 77

face glow. Thus, the appearance of beads and fringe to the un- aided eye is really a combination of positive and negative corona. In Figs. 75 and 76 two wires are placed close together at the top. The bottom is bent out and needles are fastened on. Fig. 75 is without a stroboscope. Fig. 76 is taken with a stroboscope set to show positive right and negative left. Thus, positive and nega- tive coronas for points and wires are directly compared. Fig. 77(1) is taken without the stroboscope, (2) with right negative, (3) with stroboscope shifted 180 electrical degrees to show the right positive. These wires were, at the start, highly polished. At first corona appeared quite uniform, but, after a time, under voltage, the reddish negative tufts separated, more or less evenly spaced as shown. 24(2) is the same with stroboscope shifted 180 deg. Fig. 78 shows a section without voltage. The bright spots are still polished and correspond in position to the negative tufts. The space in between is oxidized. Thus, the negative discharge appears to throw metal or oxide from the surface at discharge points. This takes place with either copper or iron wire.

Fig. 79 shows positive and negative corona on wires widely spaced to get uniform field distribution. A close examination of the negative shows beads about to form. Fig. 80 shows a similar pair of conductors. The negative in this case has formed a spiral, apparently following the grain twist of the conductor.

A large fan-like bluish discharge is often observed extending several inches from the ends of transformer bushings, points on wires, etc. This discharge has the appearance of a bluish spray, reddish at the point. The stroboscope shows that the bluish spray is positive, while the red point at the base of the spray is negative. Fig. 81 shows one of two parallel polished rods (120 cm. spacing), supported at the top and brought to sharp points at the bottom; 81(1) shows how each wire appears without stroboscope; 81(2) is the wire when positive, 81(3) the wire when negative. Note the dark space on 81(3) between the point and negative corona spiral of tufts. 81(1) shows this space to have only the positive glow.

Water was placed on a pair of parallel conductors. At the wet places the positive corona extended out in long fine bluish-white streamers. (See Fig. 82 without stroboscope.) With certain forms of dirt on the wires the negative corona appears as red spots, the positive always as streamers. It is also interesting to note that if a uniformly rough wire is taken, as a galvanized wire or

78 DIELECTRIC PHENOMENA

''weathered" wire, the positive appears as bluish needles, while the reddish negative is more uniform than on the " corona-spotted " polished wire, in which case the negative corona appears as con- centrated at the non-oxidized spots. It is probable that the polished spots are kept so by metal and oxide being ''thrown out" at the negative, as suggested above.

Mechanical Vibration of Conductors and Other Phenomena. — Several years ago a pair of 20 mil steel conductors, 500 ft. long, were strung at about 10-ft. spacing, for power loss measurements. It was noticed at high voltage that the conductors vibrated, starting with a hardly perceptible movement, which in a few minutes had an amplitude of several feet at the center of the span. Generally one wire vibrated as fundamental, the other as third harmonic. The period of the fundamental in this case was about one per second.

Figs. 83 and 84 show this condition repeated in the laboratory on short lengths of conductor. In Fig. 83 one wire is vibrating as the fundamental, the other as the second harmonic. The motion is rotary. For the wire with a node in the center. Fig. 83, it is extremely interesting to note that for about one-half of the ro- tation the wire appears very bright, for the other half rota- tion the wire is much less bright. This seems to mean that each part of the wire is rotating at the power supply frequency — 60 cycles per second. Hence, it has the eflfect of the stroboscope, and for part of the rotation there is always negative corona and for the other part always positive corona.

Oscillograms of Corona Current. — Bennett has made some very interesting oscillograms of corona current.* Fig. 85(a), (5) and (c) shows the voltage wave applied between a cylinder and a concen- tric wire, and the resulting current. The part of the wave above the zero line occurs when the wire is — , and that below when the wire is -|- ; (a) is for a voltage very slightly above the critical voltage and shows a very sudden sharp hump in the current wave when the wire is -h, and a spread out hump when the wire is — . This gives the appearance of corona starting at a slightly lower voltage on the H- wire; (5) and (c) show the positive and nega- tive humps at higher voltage. The oscillation is caused by the sudden "corona spark" discharging through the reactance and capacity of the circuit.

Some tests made on the starting time appear to show that sev- eral cycles are necessary for stable conditions.

^ Bennett, An Oscillographic Study of Corona, A.I.E.E., June, 1913.

Flo. S3. — Mechanical vibration of parallel wires due to corona.

Fia. 85. — Oacilligrains of corona current. (Beimet, A. I. E. E., June, 1913.)

CHAPTER IV SPARK-OVER

By spark-over is generally meant a disruption of the dielectric from one conductor to another conductor. Corona is the same phenomena — spark from a conductor to space or local spark-over.

Parallel Wires. — If impressed voltage is gradually increased on two parallel wires placed a considerable distance apart in air, so that the ratio S/r is above a certain critical value, the first evidence of stress in the air is visual corona. If the voltage is still further increased the wires become brighter and the corona has the appearance of extending farther out from the surface. -'Finally, when the voltage has been sufficiently in- creased, at some chance place a spark will bridge between the conductors. When the spacing is small, so that S/r has a critical ratio, spark and corona may occur simultaneously, or the spark may bridge across before corona appears. If the spacing is still further reduced so that S/r is below the critical ratio the first evidence of stress is complete • spark-over and corona never appears. (See page 27.)

Extensive tests have been made. * The method of making tests was to start at the smaller spacings with a given value of r and measure the spark-over voltage. When the spacings were above the critical ratio of S/r, and corona formed before spark-over, the corona voltage was noted first. The voltage was then increased until spark-over occurred. The spark-over point is not as con- stant or consistent as the corona point and is susceptible to change with the slightest dirt spot on the conductor surface, and any unsteady condition in the circuit, humidity, etc. At the beginning of the tests it was found necessary, in order to get consistent results, to put water tube resistances in series with the conductors to eliminate resonance phenomena. These resistances were high, but not sufficiently so to cause an appreciable drop in voltage before arc-over.

Table XIX is a typical data table. Each point is the average of a number of readings.

See Law of Corona II, A.I.E.E., June, 1912.

79

I

80 DIELECTRIC PHENOMENA

Table XIX. — Corona and Spark-over for Parallel Wires Temperature 17 deg. C, bar. 75.3 cm. Wire No. 0, diameter 0.825 cm.

• Test No. 166 values read

No.

wire, corrected to 26*^ C,

76 bar.

Spacing

Effective k\

r. to neutral

Maximum values to neutral

Maximum

Cm. S

Corona e*

Spark e«

Corona «»

Spark e«

Corona o*

Spark 0*

2.54

None None None None None None 40.4

15.8

22.5

27.3

31.05

35.0

37.35

40.9

56.0

21.9 31.2 37.9 43.2 48.5 51.8 56.7

41.4

3.81

42.5

5.08

.

43.2

6.35

43.8

7.62

44.9

8.89

45.0

10.16

44.0

44.6

12.70

41.8

42.1

58.0

58.1

44.0

44.1

13.97

43.7

46.0

60.7

60.5

44.2 ^

46.7

15.24

45.9

48.1

63.6

67.0

45.1

48.9

15.78

46.6

54.1

64.8

75.0

43.8

50.8

20.32

48.9

59.6

67.7

82.8

44.0

53.7

22.86

50.1

66.2

69.7

91.7

43.7

56.8

25.40

51.1

71.5

70.7

99.2

43.1

60.4

27.94

52.1

79.0

72.4

109.7

42.9

65.1

30.48

53.1

84.5

74.0

117.0

42.9

67.9

33.02

54.1

89.6

74.8

124.0

42.4

70.2

35.56

55.1

95.5

76.5

132.5

42.6

73.9

38.10

56.1

102.3

77.8

141.9

42.7

77.8

40.64

57.1

106.5

79.4

149.0

42.9

80.5

60.96

63.3

87.0

42.9

In columns 4 and 5 are voltages reduced to the maximum value to neutral and corrected to standard b. Column 6 gives the surface gradient for corona. Column 7 gives the surface gradient for spark, up to the spacing where corona starts first; above this critical spacing it gives the apparent surface gradient as the conductor above this point must be larger on account of corona. As the field around the conductors at the small spacings is very much distorted it is necessary to use formula 12(a) or 12(&) to calculate the surface gradient.

Fig. 86 is a typical curve. Voltage is plotted with spacing for spark and corona. Up to spacing 12.4 cm. there is spark-over before corona. This curve seems to be continuous with the corona curve which starts at this point. The spark curve here

SPARK-OVER

81

branches and is very close to a straight line within the voltage range. In Fig. 87, the surface gradient curves are plotted. The

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10 208040600070 Spacing la cm. between Wire Oenteri

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Fig. 86. — Spark-over and visual Fig. 87. — Corona gradient and ap- corona voltages. parent spark gradient.

(Parallel polished copper wires, 0.825 cm. diameter. J » 1.)

corona gradient is a straight line parallel to the X axis with a slight hump at the critical ratio of S/r, The apparent spark

10 15 20

Spacing In em.

Fig. 88. — Apparent spark-over gradients for parallel wires. (Points meas- ured, curves calculated.)

gradient is also a straight line, within the test range. It inter- sects the corona line at the critical ratio point, or at what may be

82

DIELECTRIC PHENOMENA

termed the triangular point, and extended it cuts the g axis at g ^ 30. These are characteristic curves. (See also Figs. 50 and 51.) For a given spacing the spark-over voltage increases as the size of the conductor decreases.

It is important to note that for all sizes of wire the spark gradi- ent curve extehded as a straight line cuts the gradient axis at approximately g = 30. Spark curves extended as straight lines through the critical ratio point and intersecting the gradient axis at ^ =B 30 are shown in Fig. 88. The triangular point or critical ratio of S/r is tabulated in Table XX. Its average value is

Table XX. — Critical Ratios S/r — Experimental Values

InteiBection point of g^ and g.

Siie. B. AS.

Radius cood., cm.

Sf cm.

S/r

Site, B.AS.

Radius cond., cm.

o. cm.

s/r

0.461

13.5

29.3

6

0.205

6.2

30.2

0.412

11.7

28.4

8

0.162

4.8

29.6

2

0.327

10.2

31.2

10

0.129

4.0

31.0

4

0.260 0.230

7.9 7.3

30.4 31.7

12

0.103

3.0 Average

29.1

5

30.1

S/r = 30. If it is assumed that the spark-gradient curve is a straight line the conditions are, that it must cut the corona gradient line at S/r = 30 and extended must cut the g axis at go = 30.

The gradient for ^», or the gradient at the triangular point or below it, is

(18)

therefore, the approximate apparent gradient at or above the triangular point is

9*

/. , 0.301 S 1 \

• aofi +^-] lev.

Vr

r r

) kv. I

per cm. max.

This follows because of the assumption of a straight line through two fixed points.

SPARK-OVER

83

The approximate spark-over voltage above the triangular point is

e» = g9r log R/r kv. to neutral max.

Below the triangular point it may be found by substituting Qw for g».

In Fig. 88 each drawn curve is for g, values calculated for vary- ing spacing at constant radius. The points are measured values. The corona boundary line is the gv curve; it intersects the g, curves at S/r = 30. Corona does not form below this line, but spark jumps across immediately.

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Fig. 89. — Apparent spark-over gradients for parallel wires. (Points

measured, curves calculated.)

In Fig. 89 each curve is drawn for a constant spacing and varying radius. The broken line is the critical ratio line. It also corresponds to the g^ curve. For spacings below this line spark takes place immediately before corona forms, and the g« values fall pretty well on the g^ line as shown by triangles.

Fig. 90 is voltage plotted in the same way. Below the corona boundary, where spark occurs before corona, the e, curve does not hold. The broken lines are calculated from g^, and e,. The points are observed values. Thus corona gradient and spark-over gra- dient, and hence spark voltage and corona voltage below S/r = 30, are the same.

6

84 DIELECTRIC PHENOMENA

No great accuracy is claimed for this formula. It may, how- ever, be useful in approximately determining the arc-over between conductors in practice. Dirt or water, however, will greatly modify the results, as will appear below.

The reason that sparlc takes place before corona can form at small spacings or below S/r = <x is discussed on page 27 for con- centric cylinders, in which case g was taken as constant.

Fia. 90.— SpMk-over voltages between parallel wires. (Maiimum

values

We know, however, that fl, is a function of r,

and for air

g. = g.(l +

0.301 \ Vr)

e = ffo(l -t-

^Jrlog.BA

Differentiating for maximum

de /, ^ 0.301/ ,

. «/r - I -

0.301\ " Vr)

or, e is maximum when

(-^)('--

0.301

)=0

(31)

This gives a ratio of B/r greater than c. The experimental ratio in Fig. 91 is 3 and checks with the above.

If a very small value of r is taken corona forms and then after the voltage is sufficiently increased, spark-over occurs. It might

SPARK-OVER

85

be suppoeed that with increasing voltage the center wire would become larger and larger in effect due to conducting corona and

finally, when — = critical ratio, spark-over would

radius + corona

occur. This is not the case. It takes a much higher voltage for

the small wire corona than for metallic cylinders with R/r at

maximum ratio. Hence, corona seems to be either in effect a

01 -.«> 0,223332333 3333

BadlDf of InaeT Cylinder ( r )

Fia. 91. — Spark-over and corona voltages for concentric cylinders with vary- ing diameter of inner cylinder.

"series resistance/' or it grades or distributes the flux density. (See Fig. 91.) Taking the exact equation for parallel wires

Qv^

v

^-1

2r

yl2r + ^

/, , 0.301 \ 2r ~

cosh-^ 2^

(126)

Varying r for constant £» = 10 it is found that e^ is maximum when S/r = 6.67. Experiments show this ratio to be 30. This is probably because, at the small spacing, the corona acts as a flexible conductor which collapses and forms a point.

The visual corona voltages, or the spark-over voltages below the critical ratio of S/r or R/r, should be of practical value for

86

DIELECTRIC PHENOMENA

voltage measurement on account of the accuracy at which they may be determined or calculated for different temperatures, baro- metric pressures, etc.

Influence on Spark-over of Water and Oil on tiie Conductor Surface* — Tests with oil and water on the conductor surface were made in a manner exactly similar to the dry spark-K)ver and corona tests. 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, water was sprayed on the conductor surface before each reading by means of an atomizer. Figs. 50, 51 and 92 are dry, wet, and oil curves for three different sizes of wire.

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Fio . 92. — Spark-over and visual corona for parallel wires. ( Diameter, 0.825 cm. Polished copper. Surfaces dry, wet, and oiled. Maximum volts to neutral given.)

For spark-over both water and oil have approximately the same effect. This curve tends to approach the needle-gap curve.

For corona, water very greatly lowers ^,. Oil lowers g, but to a much less extent than water. Where the conductor is very small the per cent, increase in diameter due to oil more than com- pensates for the lowering effect.

The spark gaps which have been useful in measuring high vol- tages will now be considered.

SPARK-OVER

87

The Gap as a Means of Measuring High Voltages. — A gap method of measuring high voltages is often desirable in certain commercial and experimental tests. A gap measures the maxi- mum point of the voltage wave and is therefore used in many insulation tests where break- down also depends upon the maxunum voltage. In most commercial tests an accuracy of 2 or 3 per cent, is sufficient. A greater accuracy can be ob- tained with the sphere gap for special work where special pre- cautions are taken.

The Needle Gap.— The needle gap is unreliable at high vol- tages because, due to the brush and broken-down air that pre- cedes the spark-over, variations are caused by humidity, oscil- lations, and frequency.*

The needle gap is also incon- venient because needles must be replaced after each dis- cbarge; the spacing becomes very large at high voltages, and the calibration varies somewhat with the sharpness of the needle.

AvERAQB Needle Spark-over Voltaqes

No. 00 Needle, a = 1

A.I.E.E.

200

190

180

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140

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Approximate Mettlle Qap Carves

for Dlfforeat Relative Humidity ^^1

—

1

S 1

1

6 2

2 8pi

£8

icin

8

gin

5 4

cm

i

•

5 6

6

6 60

Fig. 93.

Kv. eff.

Spacing (cm.)

Kv. eff.

Spacing (cm.)

10

1.19

40

6.10

15

1.84

45

7.60

20

2.54

50

9.00

25

3.30

11.80

30

4.10

70

14.90

35

5.10

80

18.00

• F. W. Peek, Jr., Discussion, A.I.E.E., Feb., 1913. F. W. Peek, Jr., G. E. Review, May, 1913.

88 DIELECTRIC PHENOMENA

The effect of humidity is shown in Fig. 93, where it can be seen that a higher voltage is required to spark over a given needle gap when the humidity is high than when it ia low. (Curves, Fig. 93, are intended only to illustrate this effect.) It is probable that the corona streamers in humid air cause a "f<%," and then agglom- erate the water particles, which, in effect, increase the size of the eleotrodes.

All spark-gap curves of whatever form of gap must be cor- rected for air density — that is, altitude and temperature. For low voltages the spark-over of the needle gap decreases approxi- mately as the air density. At higher voltages the effect becomes more erratic, probably due to humidity.

The Sphere Gap.' — The voltt^e required to spark over a given gap between spheres increases with the diameter of the spheres. Corona cannot form on spheres, or rather, the spark-over point and corona point are coincident if the I spacing is not greater than the

I diameter of the spheres. In prac-

. tice a spacing as great as three

I times the radius may be used with-

g out appreciable corona. The vol-

t£^e limit of a given sphere in high- voltage measurements is thus reached when a gap setting greater than three times the radius is re- quired. For accurate work it is preferable to use spacings less than the diameter of the sphere. A larger sphere should then be used. With this space limit the first evidence of stress is complete spark- over; corona can never form, and all of the undesirable effects and variables due to brush discharge and broken-down lur are eliminated. Humidity has no measurable effect.

The space factor is relatively small. Several thousand measure- ments may be made without repolishing. The curve may be calculated. The only correction is the air-denMty correction. This has been investigated and the results are given below. The

'Chubb and Fortiacue, Al.E.E.. Feb., 1913. "The Calibration of the Sphere Gap Voltmeter."

F. W. Peek, Jr., A.I.E.E., Feb., 1913. "The Sphere Gap as a Meana of Measuring High Voltage."

F. W. Peek, Jr., G. E. Review, May, 1913.

SPARK-OVER

89

Table XXI. — Sphbbe Gap Spabk-oveb Voltages

6.25-cm. Spheres

Spaoinc

KilovoltB effective

Cm.

In.

Non-grounded

Grounded

0.5

0.197

12.0

12.0

1.0

0.394

22.5

22.5

1.5

0.591

31.5

31.5

2.0

0.787

41.0

41.0

3.0

1.181

57.5

56.0

4.0

1.575

70.5

66.0

5.0

1.969

81.0

73.0

6.0

2.362

89.0

79.0

7.0

2.756

96.0

83.0

8.0

3.150

102.0

88.0

Q.O

3.543

107.0

90.5

10.0

3.937

110.0

93.0

Each point is the average of five readings. The average variation between maximum and minimum for a given setting is less than 0.5 per cent.

Tablb XXII. — Spherb Gap Spark-over Voltages

12.5-cm. Spheres

Spacing

Kilovolta effective

Cm.

In.

Non-grounded

Grounded

0.25

0.098

6.5

6.5

0.50

0.197

12.0