... jate ,.. .~

..... ~~ a:;rne.ak,: At:~t

tt!.: toient

..:..::~

,

1

..~) ,:1'j

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'1 -

GE Review Marc.~ \llUshilleand of special factors such as small en-closures, warmer or cooler connections, etc., thataliect conductor heating indoors or outdoors.Data on and analYsis of the. prevailing wind

velocities and ~e sheltering effect of buildings,\

;Ij

f

I

142 11arch, 1930 GENERAL ELECTRIC REVIEW {Vo!.33. ~o.'3The following symbols are Used:

A (sq. in.) Area of surface of conductor.4,41 (cir. mils) Area of cross-section of conductor.C Factor in formulas for current-carrying

capacity, defined by Equation (11).Outside diameter of conductor.Inside diameter of tubular conductor.Relative emissivity of conductor sur-face (E -1.0 for a "black body").

I (amp.) Current in conductor.It, Itl Skin effect ratio.p (atmospheres) Absolute pressure of air (I' -1.0 for

atmospheric pressure).. r.r;;; Ratio used for the calculation of current-

,q - '\J-k;G capacity.R (ohms) Resistance of conductor.RI (microhms) D-c. resistance per ft. of conducter., (ohms per mil-foot) Specific resistance of conductor

, material.T, (deg. K.) Absolute temperature of conductor.T.(deg. K.) Average of absolute temperatures of

conductor and air. a ~ h;er:.!T. (deg, K.) Absolute temperature of ~Q'1I11' SS.at (deg. C.) Temperature rise.17 (ft. per sec.) ,velocity of ~.cro~wise to conductor.!II (watts per sq, in.) . Heat dissipation factor... .1'< (watts per sq. in.) Component of. heat dissipation

factor due to convection.!II~(watts per sq. in.) Component of heat dissipation

factor due to radiation.

tl (in.)41 (in.)E.

, -

).

,.,.'

Conducton In Still Air (F~ Convection)

The h~at which comes from the electrical losses inthe conductor is dissipated in two ways: by convectionand by radiation. Convection takes place because theair adjacent to the conductor becomes heated andtends to rise, When the surrounding air is still, as in a, large closed room, all of the heat dissipated by con-'vection is carried away by the natural air currents.It is estimated that when the temperature rise is about

, 30 deg. C. the velocity of the convection currents is'~oi-der of 0.2 ft. per sec. for the smaller conduc-tors (0.5 in. diameter) and 0.5 ft. per sec. for thelarger conductors considered in this article.

The heat dissipated by convection per square inchof conductor surface for a given temperature risedepends upon the size and shape of the conductor;.the smaller conductors dissipating heat more readily.The heat dissipated by radiation per square inch ofconductor surface depends upon the' absolute tem-peratures of the conductor and of the surroundingsand upon the emissivity of the surface. In the case of aone-inch diameter copper conductor at 30 deg. C.rise, about two-thirds of the heat is dissipated byconvection and one-third by radiation. For smallerconductors, the convection component is more thantwo-thirds: for larger conductors it is less than two-thirds of the total.

For"the steady-state conditions, (2) the rate of h~dissipation is equal to the rate of heat supply which is 'the ]2R loss in the conductor. Thus

; :

.'J. ';~ .

PR-wA wattswhere

W-We+W, watts per sq. in.('lIt is sometimes necessary to conaider the beatie, d!,e to CWT~nts

applied for a ahort time only. for innanee durinlf short-orcu!tL The,.~b)eCtis covered in an article entitled "Short-time Current Carryinlf Capactty of ,Copper Wire." by E. R. Stauffacher. GaN&RAL EUCTklC RBvl&W, June.1!12l!. p. 326.

For the particular case of cylindrical conductors inair-at atmospheric pressure-and at 40 deg. C. when~c..temperature rise is 30 deg. C.

0.01805 We - watts per ~' ,~

d loglor-J.;~+1]or when d is more than three inches

0.14 . ( )We= cf.19 watts per sq. In. approx.

Also(5)

Formulas (3), (4). and (5) were used to calculate t~watts dissipated from the conductors for 30-deg,t:.i,rise in a 40-deg. C. room temperature for the ind~J-condition (free convection). iFor the calculation of the watts dissipated froth

indoor conductors (free convection), for any temt-perature rise, at any air temperature, the genen~formulas for long horizontal cylinders at pressure!~(atmospheres) an: as follows: !

Ii.5 X 10-8 T.O.7M At Vp . - G~tw(:z 094- watts per sq. m. ,r-.0031 T.,' ] ed log. JJ'sl 27 +1 iAt . i

'w,=36.8E [(T /1000)4- (To/lOOO)4] wattspersq. in.a} - 't':.

w,==0.154 E watts per sq. in.

In either case the convection and radiation~m~:-nents are calculated separately and added to givethetotal watts w. according to Equation (2). The curre.-1.tis then calculated from Equation (1). A numerie

"'-'---,.-.~- ...--..---.-----------...-:-.,'- ...;::;::*'-_ ....-.--_ ... -_ ...__..._----"~... !

~.3 -,,e i

f

: .... 3j I~ f

..>.':- "1 tI I

.

Iifor forced convection. The wind velocity at anyparticular location depends upon the general windconditions and the sheltering effect of surroundingssuch as buildings, trees, and hills.

In this investigation a study was made of windconditions at Schenectady, which is believed to befairly typfcal of New York State locetions, with viewtoward obtaining a representative minimum airvelocity that can be used as a basis of currentratings for outdoor service, This study includedconsideration of wind conditions shown by a record-ing anemometer about 150 ft .. above the groundand measurements made with a vane-type anemom-eter at several points on the ground and on the roofof a fiat-top building.' .

4;","

To avoid this condition, the anemometer was turned ..!.around when the vane started to turn backWard so I,that the average velocity in .the north 'and .sou~ ~direction, for example, was measured. A small amountof lost motion was of course unavoidable when makingthese reversals:

Effect of Locauo em Wind V,locity and Sheitmn~Effect of Buildings. Measurements of wind velocitywere made between 1:45 and 2 :45 p.m. on September6, 1929 at the following locations: No. I, the location' :.used for heating tests shown in Fig. 1 on the roof ofabuilding; No.2, another point on the roof of the same :building; Nos. 3 to 7, points on the ground as indio .cated in Figs. 2 to 4. At locations 2 to i the anemom- ~eter was held in the general direction of ~he air cur- :.

~..,.--..- .\

~)!~

Fie. 1. View of Part17 SbcItcred Locatkm No. 1 Ueed lor Outdoor HeatiAlT_ OIl Bare Copper Coaducton

A~s Used. The recording anemometermentioned js permanently located on a.. seven-storybuilding which is higher than the surrounding build-ings. The revolving cups are abo1,1t30 ft .. above theroof and about 150 ft. above the ground. This instru-ment measures wind velocities irrespective of direc-tion; and the records correspond to those. kept atstations of the Weather Bureau. The records consistof ink marks on a moving strip of paper, each markrepresentating one mile of wind travel so that 'thenumber of marks in a one-hour period is. the averagevelocity in miles per hour for. that particular one-hourperiod. ..

The vane-type anemometers used in these investiga-tions registered the air travel in feet, the averagevelocity being the number of feet divided by .thecorresponding time measured with a stop watch. It.was found by trial that the minimum period overwhich a satisfactory average velocity can be obtainedwas about three minutes on account of gusts, eddies,and other variable conditions .. These anemometersmeasured the. air velocity in the direction of the axisof the vane. If the wind changed from north to south,for instance, the instrument would read backward.

.. " . ..7.;

I

rents as indicated on the sketches. The velocitiesobserved were as follows:Averare wind velocity by recor~ anemome-

ter 1150 ft. above ground..... . . . . . . . . 15.4 ft./see.Wind velocities at Location No. 1 (Fig. 2)

1:45 p.m., crosswise to conductors .... 3.3 It./s.lengthwise 1.7

2:15 p.m., crosswise . 3.0lencthwise 1.0

2:45 p.m., crosswise 2.1 . lencthwise 0.8

Wmd velocity at Location No.2 (Fie.2). . . . . . . 3.9 - . No.3" 2 .. . . . . . 2.3 No.4 2 i.O No.5" 2 ..... 3.0 _.. No.6 3 ...... 1.9 - .- No.7" 4 . . . . . 4.5

These locations. represent various degrees of Shelter-ing. N~. I, 2, 3 and 5 represent partly shelteredlocations. No. 6 shows somewhat more sheltering.. No.4 was in a passage of 25-ft. width between build-ings where there is generally a strong air current.No.7 was in a fairly large open space .. It is seen thatthe average of the wind velocities at locations 1.2.3, and 5 is about one-fifth of the wind velocity athigher elevation.

In Figs. 5 and 6 wind velocity readings at locatiOSl. No.1 are plotted covering a period Qf two or three

uth

~'-~::f:;~-~.'_:'J~~~:

.. :'ihber.1

.. ; c.. }tion,.''\0 a

4~:. ;.:~l1cur-

, "

... >

..1

':''OJ.; J

.;.1.~

~

1 ..'.,::'::.~cities

:'01

::It./see.. ':. /,1'':

...., ..:.'fltered

.' 0:":: terlng.... build-=,::,

--""'

146 March, 1930 VV!. oo , au..:>

TABLIlIWIND VELOCITY MEASUREMENTS AT SCHENECTADY. N. Y. '~

. MIDIIIlDIIlVeloddea for Period froID June 1 to October 1928. Meaeureaaau. b? Rec:ordin,AIleaaometer 150 It. AbcweGrouad

' .....).~..(

No. of 20M. Pwftet.Dace 1 I 3 f 5 1 10 11 11 .1 Wh_ V.loritrWuX-n.a.5miles/hooorc

June 1-2 (Ave. 9 miles per hour) 3 3' 14 ' 14 - 15-6 5 3 " 2 3 3 3 2 4 - "7-8 4 7 ,5 5 io 4 2 2 3 - 312-13 3 3 5 6 1 1 2 2 6 2 - 3

July 6-7 .. .. 1 2 2 t 117-18 .. 6 - 0' ,20-21 2 2 - 123-24 2 3 3 3 2 3 2 2 3 5 8 ' . - 425-26 3 2 4 4 3 3 - 326-27 2 5 5 3 5 4 2 2 2 3 2. 2 3 330-31 ' 1 0 3 5 .5' 5 8 1

Aug. 3-4 ., 3 3 '. - ,. 19-10 2 1 1 1 1 2 - 313-14 ' . .. 3 2 3 2 2 2 2 314-15 - 3 3 3 3 1 2 1 2 2 2 2 2 525-26 1 1 2 3 3 3 3 3 2 2 2 1 6

Sept. 6-7 3 2 2 3 3 3 2 1 3 3 3 3 3 67-8 - 3 3 3 3 2 2 2 2 2 - "12-13 " 5 3 1 0 7 115-16 4 4 3 " 3 2 " 13 - 317-18 - a 1 2 4 3 " 3 3 3Oct. 3-4 3 3 3 6 6 1 1 2 2 2 4 2 5

Total No. of 2-br. periods ......................... : ......... 64Total No. of hours for entire period ............ : .............. 3000.

WiDd Yelocity _ tbaa 5 milee per hoar. ,tRecord ;'u:omplete.NOTE: The figures in the table rive the average wind velocity ill miles per hour for the on~bour period endiug at the ti:-

indicated. The corresponding velocities in ft. per see. are as follows:1 mile per hr. -1.465 ft. per sec. " miles per hr. -5.87 ft. per see, .2 miles per hr. -2.93 ft. per sec. 5 mues per hr. -7.33 ft. per see,3 miles per hr. -4.40 ft. per sec. ,6 miles per hr, -8.80 ft. per see.

TABU nWIND VELOCITY MEASUREMENTS AT SCHENECTADY. N. Y.

SEP'I'BWBER J TO %1. 1929Meuuremenn by Recordlns AIlemometer as b, Table I ~

No. of :'hr. Periot'

10 Jl 12 1 p ' J 3 .5 II WheD VelocityWas Lea'l'bu" miles/hOOlt -

Sept. 3 t 3.5 9.5 IS 17 19. 13 19 17 16 0" 3 3 4 '4 5 6 6 6 8 4 25 5 ,4 6.5 < 3 3.5 6 5.5 14 13 26 8.5. 9 8.6 8.5 8 10 10.5 10 7.5 7.5 07 5.5 3.5 . 2.5 2 1.5 2 4 4 10 4 38. 3 3.5 5 4 6 '4 3.5 3 2.5 2 39- t 0 1 1 1 1 " 4 4.5 3.5 410 11 14 14 14 16.5 17 16 15 17 13 011 ".26.5 23.5 14.5 10 10.5 10 10 9.5 . 7.5 6.5 012 1.5 1.5 1.5 4 4.5 6.5 11.5 13 14 14 2.. ]3 S- 8.5 9 14 15 -t t 23 17 14 015 19 25 21 18 13.5 15 12 12 8 4 016 2 f> 8.5 14 16 17 18 18 19 16 017 17 19 15 10 11 14 '17 6.5 9 12 018 9 13 18 18 20 ]9 18 23 25 16 019 4 5' 7 5 7 t t 6 5 5 020 3 6 6 ,7 6 5 6 6 4 5 021 3 7 '7 6 5 5 5 4.5 4 " 1 ;-

Total No. of 2-hr. periodS .................. ',' ................ IiTotal No. of hours for entire period .............................. : 456 --

\. ,

-------- ------- ._--_._,-- --...... -----------

I~~~;.;.:;:::.-i:::- ~~-::i-:....~-.~'z:=< ....-==_rt __ ..::4._ !- '--.------::..0;.-__- .=................""--...;;.o.- ;.;.o..;.====-~___..;~;.;;;..:.___. .,- 'G::O:: _ :::::;;:=:: - - --. ~ . ~-- ---I ' ..I!. No. a

-~i

-'. :J.' - .,~

:-~;:(.'.i

'}=:: ==}. Periodo1eloeity

:.... ~. Th&o-_{hour

'~>1-' --: ;1

..~......~.jl

-,

:-~. " -:1/~1 -.;'~'~ii~.1---

:lit at. the

CURRENT-CARRYING CAPACITY OF CONDUCTORS FOR OUTDOOR SERVICE 147

eliminated, Those showing lower velocities wereanalyzed. ~_JaQle _I each line represents entriescovering an afternoon and the following morning, -:H~c Abtorbed by Radiation !rom th~ Sun _. becauseeach chart covered a 24-hr. period generally . Conductors exposed to the rays of the sun 'absorbcommencing at noon. In connection with conductor heat by radiation. Th~_t_emperature rise above .the airheating, only the periods of low velccity which occur temperature (4) is the~fore higherthan ,it would beduring the daylight hours and which last, -say, two ifthe sun were obscured, .other ~onditions remaininghoursor more are of particular interest. Referring to the same. In the outdoor tests presently 'to be de-Table I it is seen that there were 64 two-hour periods scribed, _the additional temperature rise due to theduring which !he wind velocity was less than five sun was 'two to' three deg. C. for conductors at aboutmi1~_p~~hour(7.3 ft. per sec.). The time represented 30 deg. C. above the air tempe1"!.~~. At the sameby these periods of low wind velocity is 128 hr., or tinl~,_the temperature of an_i~e con4~c_tOrexpo~d toapproximately five per cent of the total time, which the sun was eight _de~,- !l!b9veJQ~_air. temperatyre.was about 3000 hr. The test data relating to the effect of sun are~ble II is similar to Table ! and shows wind .summarized in the section on Discussion of Results of

velocities taken with the same anemometer 150 ft. Heating Tests. .abovethe ground from day to day for the period dur-in~ which outdoor tests were made. During thisperiodthere were 14 two-hour periods when the wind~i.tx was less than five miles per hour. These~!~s-repreSent about six per cent of the total time~is about the same percentage as in Table I.._~._thenthe wind velocity at partly sheltered loca-1I~ is Ween as one-fourth of the values in Tables I4'd 11, the velocity' at such locatiOns- is ~o;e t~~t~ ieetper second for about' 95 per' c~n~of the.time.

::f)Urs,measurements being made at intervals of 15 orJo min. Th~ average velocity .crosswise to the con-6:ctorswas from one-third to one-fourth of the windl'docitr recorded by the anemometer at higher eleva-tf)n. (Further data of a similar character are given inTableV.) .It appears from these data that the wind velocity

aL partly sheltered outdoor locations is from one-third to one-fifth of the wind velocity prevailing at anunshclteredlocation 150 ft. above the ground.:ilzaiysis 0/ Wind Velocity Variations throughout

Slimmer Season. In order to examine wind-velocity

.----.- --.-+---.--.~-- ..'---~ -- _------. .-.-148 March, 1930 . . . GENERAL ELECTRIC REVIEW __ Vel. 33, No. ~ .

.'

No. I, is shown in Figs. 1 and 2. The conductors testedwere suspended from the wooden frame as shown inFig. 7. The location is fairly representative of a partlysheltered location, the sheltering being due to theparapet and the elevator shaft.The teJt samples included solid and tubular copper Raultl ofHeado. Tem

conductors in lengths of about ten feet. These con- The values of temperature rise obtained outdOlmductors are listed in Table III. The conductors were and indoors were plotted against the current valueSa;-placed in a horizontal position and heated with 60- _shown in Figs. S to 12, inclusive. Curves for indO

:~O.3I

;ts per:. ~st the".~ (still.!; the;tlated; using

--'--..:.::5 also.re' of\ ';d'"'-,.,:.;.,a 15.. ,

h nse

t dis-J rise).t

'-~ . ~. !.

CURRENT-CARRYING CAPACITY OF CONDUCTORS FOR OUTDOOR SERVICE 149

the effect of the sun upon conductors with and with-out electrical heating,

The temperature readings given were selected fortwo occasions, the weather being cloudy on oneoccasion (see reference Nos. 5 to 11 In Table V)

1rf

II1fI

If

tI

is not the same for all conductor sizes but decreases asthe diameter increases. This is in accordance with thetheoretical formulas given. .Effect 0/ Sun. The data given in Table IV have been

summarized from Table V for the purpose of showing

OutdOOrs.(I~r outdoo . ,.,-tl., cloudy OutdoO. cloudy.tndOO"'.r"t f;9u,..a .,.. "'fct"VtCC MI;~ iq_._ .~Iuc~ of "6 .cIO'it~ (ros~to M ,t f1. r

50

"r

-s...i10

110.-;0 0o

I 4

4'lO-LOi-1.62n.

.00 iOO _ lOOO IZIIO 1400 MOO _ 1_4'"p .

Currmt N. Tcm~tuN RI8e Outdoon a.ad lA.s-..Cccductcw A. 2.'7 iD. ouWde diameter

Temperature rise indoo . by ~Temperature rise outdoors. c:&leulated for wind 'relocity oftwo feet per second cro wiae to conducto .

\ ~ ~ * ~ ~ ~ ~ ~AmPClr9S

1"\&. 11. Cunalt Temperature RI8e OutcSoon aDd lAdoon.Ccoducton D md T, No. 0000 A.W.Q., 0.46 iD..

outaIcle cna-C",., A: Temperature rise indoors. by test. ' .C",., B: Temperature riM outdoo .cia1cu1atedfor wind Ye10city

of two feet per HCODdCtOIIwiM to conduc:to .~~~[[~~~~~~:::::::l~~~~~~~I- Outdoo cl Outdoors. pa tly cloudy90 + OutdoOl"S, cloudy- Indoo r..t fiQu~. a~ r&fu-.nc:&nu",'be ; Sec:ond fi9urn . value..; aoll~o~f~w~ln~dlv~&IIO~c~iftl'JI~C;I'OI~...lisi&ttio~1111IiIcj. CO"ductor'S i" ft. 'per sac:-

i70.600.8" 30.~III

'" .,

1" 4

C_A:C_B:

." ., Mr- owtoo,.. r1..y ~" Ow.do C,lowOy lr\C.oo~.

!::~~"~icJ':::~04 wfoot4 Ioc.~t... . i.&

20

It

o u _ _ _ _ ~ ~ _ ~ _ ._ _,,~.

r.t, Currat P. Temper.ture RiM'Outdoon ad.lD.s-..Coa4uc:tw 8, 1.St iD. outa1de dIa..ur

C_ A: Temperature rise indoora. by test.C_ B: Temperature rise outdoors. c:aIc:ulated lor willd 'relocity

of two feet per aec:ond c:ronwiae to conductora.

10

00 100 ZOO ~ 400 500 600 700 aoo. Amp

Flit 12. .CuneDt PI. Temperature RiM OutcSoon aDd Iadoon.c-cbac:tar Z, 01a. ~ ~

C_.A: TemperetUJ"e riM indoors. by test.C . IS: TemperaWro riM OtItdoors. c:aIc:ulat4ldfoe wind. ..tocity

. of two feet per d. crouwiae to CODducto

Outdoo..,., cl ,. -I-- Outdoo ~Iy cloudy -i-+Outdoora, cloudy i-I-- I"doo,..ri,..t fiqur-c. r9fUllnet. num-b4ra; S.cond f!~u e 1'. ~Iu

-- of wi"d ve.loc:jti t CI'OMwi to" ,.." .'m In

C I -a: ., ~ 0< -. ~~b.o

'1: o~....... .,'. < .I!.1..ti4-~V,>-....,500200 ~OO 400

Ampcan&.po 10. Cunalt Tcmperatve Riae OutcSoon m.t lDdoon.

c-d_ C. 0.75 iD. -aide diameter .C_ A~ Temperature rise indoo .. by ~C_ B: Temperatur. riM outdoora, c:&leulat4ldfor wind ..-elocity

of two feet per _d c:roaawiM to conductora.

100

......\: .. ~.i ..~,..., c :' ',"'; fe'" _ ..L~.~.L:.::..ij;\:;-.:..,

-~.'

~-- ~~-===.~__M~ '~ _

;>; .c,",

CURRENT-CARRYING CAPACITY OF CONDUCTORS. FOR OUTDOOR SERVICE 1.;1

andclear on the other occasion (see reference Nos.. 1 .to5). In Table IV.the conductors have been listed inorder of terflperature rise without the sun (cloudyweather):It will be seea that there is a consistentdecreaseof heating due to the sun as the temperatureriseabove the air becomes higher. Thus the tempera-lure of conductor D, which was 28 deg. C: abovethe air temperature in the absence of sunshine, wasincreasedonly two degrees C. by the sun, while the

u

Si~ce.the. temperature increase due to the sunwhen the temperature rise was of the order of :~odeg.C. was two to. three deg. C. ~ the .idle conductor.showed a rise of 8 deg. C., and since the temperaturerise of the conductors in the sun was generally lessthan the temperature rise.calculated for an air velocitytwo feet per second, it is concluded that currentratings for 3O-deg.Cirise in locations partly shelteredfrom the wind can be determined as a .first approx-

"url'.. Outdoo~;

The curves agree very we4 _or the smaller Isizes ofconductors. but not. quite so well for the larger sizes,the maximum difference being about 10 per' cent.The difference may,' at least partly, be accountedfor by l1evalue of emissivity used in the calculations.which value was 0.5. Since the emissivity of theconductors used in the heating tests was not measured,and since they were not exposed outdoors for a verylong time it may be expected that their emissivitywas somewhatlower than O..j. Values given (3) rangefrom 0.15 for bright copper to 0.60 for oxidized copper.The value of 0.;) was 'used in establishing outdoorratings because of the relatively rapid oxidation ofoutdoor copper conductors. In determining indoorratings, however, the test data (Curve A, Fig. 14)rather than calculated data were used.

~0.4rT~~~-r~~~~rT~~~rT~rT~~~~

I :. aTe~t ,,~Iue~

..;&. I"~ 0.3 I r. ~ 'I ,:: i~ I I I I Ie i! .....~.IIIU,. I I i I_~- , I I , I , I ..,.:::.e..,.e..:.~lculetedlj'""l.S ~.2i ! I I i I If' .~+!-i-~~+-+';""';";""':' "~.Jr"11 A - by te ~t..:~ 1: $ I I

I '

! I , I

;~l~~~~:~'~~~~-'~I~rr~'rr+4+~'~' ~-+;:l. I I I,;; ; , I , , I

; 0~~~~~~~~~~~~'~1~~~~~~~~6~. ~. 0.8 1.2. 1.6 2.0 2..4 ",v

Q.!sidv e iamccl" ar conductor 'In inCl'lUl":z. 14. Watt. Per Square Inch for 30-del. C. Tempe:ra~

. Rise liS. Conductor Diameter, IndoonC..,~.10, By teS!: conduetors A !o F.Cur~.. COieuiated by formulas ~or still air.

..

In Fig. 16 the results of the indoor tests made .during this investigation are compared with similartest data from a number of different sources. Thedotted curve was published by G. E. Luke. (~) Itagrees very well with the test curve obtained here forconductor diameters between 0.7 in. and 1.3. in.but less close1v for smaller diameters, the differencebeing about 20 per cent for the diameter, correspond-ing to No. 0 A.'\V.G.wire (O.325iJl. diameter). Accord-ingly, in tables of current values based upon Luke'scurve the current value given for No. 0 wire for30-deg. C. rise is about 10 per cent higher than thecorresponding value given here.Test values obtained by Melsom and Booth (S)

for a O. i,5 in. diameter bright copper rod and for thesame rod painted black are also shown in Fig: 14.T.'1e point for the bright conductor falls below thet~st curve and the point for the black conductor fallsabove t:ne curve, as would be expected.T~~ "duel; obtained by R. J C. Wood (7) for three

siz~ Df alumi. .urn cable have been plotted. Two ofthe cablK ""ere. :'1(;'\',' and the third was taken fromsetvtc. The sl.lr(o,ct. of : r..; used. cond uctor was cov eredff) 'C'-""-i of :.: .. ' ,c_O"," !:>;' t~.E. L,:':e. A.r.E..E.. Trens .. Vol. !!:.1923,#:. C,),.: :,:~ea:":=: ":,,")~,.;':..,, ,.:- S,.::~ !3::Lr~CCp~:)t"~ant! ':\~.:::::".Jm(J~~rh1;~;tI~~iJ.~T;;'i:~:J~~:~;'~

with a hard. smooth, black deoosit. The point for theblack conductor is above the test curve and. the.othersare below the curve. as would be e!!tpected:', :. ,;;: ". Test ..alues br -:~ree sizes' of bare copper cablesobtained by Wo!! and Gable ('I) at the MassachusettsInstitute of Technology are also plotted. Two of thepoints' agree very well with the cun:e; but the otherpoint; which represents a 500,000-circular mil cable,falls considerably below the curve. The condition ofthe cables was not stated and it is .possible that thisparticular cable may have been new.Other points include No.4 /0 trolley wire and two

sizes of aluminum cable from tests made at Sche-

H-+l-++-I-+-HHaCOOpel" condueto~ Ato F''0/ 0.5 o No.0000 tl"'OlIey wir-e-C. ElAluminum cable~.; , ; I '>Alumi"um tables (!tJ.C.Wood) .S'0.4 r~ ur ve BI 'xlin.cooper- I"'od(Mel~o,..,e.-deoo~:').~ !\ +CO'p041'" cable:! (Woll and Ga::.:e),., \1

C\..0.3 1-+1 +"'~'ik-i'H!!" +.' ~r...;.+"-+-;-!--+-' -':!-+-f-io+';"'; .:..! -' '","",,"~H-1 ~: !;)16C1c I, .."f !a I"ck' I.E I ~":'t. ilI-+-+-+-!++-+~~';';=-H-""'-f--;:~"""~:-'.'-:to:'2 ;. '.i.~' ; Curv{.i. --.~r'Q~~"~~."T~:~~,~~~~~~~;::::t~

L. I.! ~ ~A!~,., i1~:1 0.1~t~:~t::~I~jtt;3:,~t::::~~J::t::r_-_;,-._--_-+H~

0, 0.4 Ml,2, I. 2.0 1..4 2.6. Out~jde diamctc:r 0' eo~ductc!" In inc:-:~s

Fie. IS. Valu~ orWatts Per S(l':~~ I::.~'\!e'4~~~G. '.M.UUt,.

nectady several years ago, ~. hoi:ey ~.~-tioned was also "ested D'u.t-of-d~\rs,N. tk Q...... -perature rise was 100 deg. C. at 800~ ~ "tic.wind velocity was ~~ee :eet p?r second W(h s..."as obscured. This point IS indicated 0:1 F'6 13 ~the dissipation in ,,:~,~~~r Scl. in. for 3O.d.ij. C ~: in~i~~tedhin F!~;.1.3.~~~::~g:~e~~~n~p'Y~_~~....en." ith tne res _.s oc vc . I.~C. .-us ~

It is well known t~a": the method of ~temoeratures makes a considerable &i'::eTettce. IN.~results. It was found. for example, h 'tia: ~tests that the temperatures by thermocouple ~two or three degrees ~ghe!" than the'~by therm?~eter,- ~ te~pem:~:-es ~Y ~were usea In obtaining tne ~su;~.: sine. ~ ~pond most near:)" to the actual ~ ~ ..uc..conductors. Under Outdoor conditions, )!owevtr .cIrLdifference between the the:m0cct!ple reac:lit\~ ~ tie.thermometer readings "as not so emiste,,~ ~na~-fore averages of the rea6nr b~bo~h ",e~hoclt -Wttttaken.It ~ "f interest to CC:11::'",re.:~. ~~'sulti0( ~ ~ ~

room w~~h~r~jts ~rodt!c{'.d~Yf~e~~:':c~or:, .: l>~,tj..c .WDt>4,, Wl~:1 va.ucs ca.cuta: .".:...:,. the' ~ C4C"')~('e" convection T1,,, res .. ~ " .... '.:ve:, ~ ~_ftL -YVIJ.. \.- \- .' ~;... ~ 1.'''' . - ".- ~ . ~ .!L

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eVRRE~T-CARRYIXG CAPACITY OF CONDUCTORS FOR OUTDOOR ~ER~rCE

It.~tl.e calculations the emissi vity was taken' Current ratings lower than thcise~!~cn in 'Tub!e~.t'~~black ~o::Juctor and 0.;) for .the new, VII for outdoor service are to be used for locations. T~..: ~ak\4;:..~."d rcsults show satisfactory with more than usual sheltering or when the normal

:~lIIIfIat\\'id:the test \';-Ju~:s.. . air currents are lengthwise rather than crosswise: to~~~" the conductors.

.;l:RRENT.C ...RRYING C...PACITYI~~ Currcnt-carryin:;: Capacity for 30-deg. C. Rise, \IcaJ.uU of current-carrying capacity for 30-deg. C.~W been determined from the heating data~ !:

'. 154 ~larch. 1930----~------..------ ..---.--~---------.--"--_._ .._--

----- .--- .. ~.. (-";.Vol. 33, No.~ !

.-,-----GENERAL ELECTRIC REVIEW

l'\c. II. ValU" 01Factor C iIa 1'_uJu (10) _d (1"2)'or CurreatC8n)'iA& Capaeit)' ofR-.s c-.sucton LImited to 3O-4q;. C. Rloe

C"". A: Indocn. larae enc10sureawithout drafts.C ..,. IJ: Outdoon. partly sheltered locations. 2+' .

I I 1!::.r.~") fcurrent values based on 100 per cent conductivity!copper. as from Table VII. by the relative current-!

For solid rods or wires d1-O. carrying capacity gives the corresponding current!values for conductors of the conductivity specified, I

Values of the factor C for 3O-deg. C. rise outdoorS In calculating the data for Table VIII the conductor;and indoors are given in.Fig. 16 for conductor.diam- temperature was considered as 70 deg. C. and the !eters ranging from 0.3 in. to 4.5 in. Similar curves temperature coefficient of resistance was consideredas ~can be plotted for other values of temperature rise. . proportional to the conductivity. (10) t." iGo~eoml~ 'HIe ._~ uliillMiii\~ fFor conductors of high-conductivity copper (97 to Tests have shown that aluminum conductors dissij

100 per cent) values of current for 3O-deg:C. rise can pate heat at Abou~the~if'&te;as~~'(fflaut-ttr! ; "be taken directly from Table VII. For sizes of con- of the same outside diameter when the temperaturt i "ductors not included in the table. Formula (10). rise is the same. Therefore. the current value for 30- ~.or Fonnula (12) may be used with the proper value deg. C. rise for an aluminum conductor of the saI\lt i~of resistance at the operating temperature, considered actual size as. a copper conductor in Table VII may :~~as 70 deg. C. in computing the current values for be obtained by multiplying the current value for the rii.Table VII. The temperature coefficient of resistance copper condu.ctor by the relative current-carryint Vfor 100 per cent conductivity copper is 0.00393 capacity for aluminum of the proper conducti\';ty;referred to. 20 deg. C" The value of the specific from Table VIII.resistance (1') is 12.59 ohms per mil-foot at 70 deg. C.

..I

Formulas for Curreac

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(13)

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.rE~plP#~' To find the current carrying capacityof a 1.500,000 cir.smil , 98 per cent con-ductivity copper, for 3O-deg. y. rise outdoors at 60

~A~Z OF THE CALCULATION OF CURRENT. cycles. Cct=f.4\t). ~ ~ ~.;-.CARRTING CAPACITY AND TEMl'ERATURE RISE The outside diameter of the cable is L412 in. and the!Nl- "folloWing.ex-amples~,musttate the'b''Pr8cticM' resistance r" is 0.00719 obmper 1000 ft. at 25-deg. C.

Substitute the following nwnerical values in.applieati6l1 of9;he:idata~ven~hiS~t:1e':~:- - 1 T find h .. Formula (10):QMlmp . : 0 t e current-carrymg capacity

of a . 1.315 in. outside diameter and 1.022 in.--...... R1-.0.OO719XI0* [1+0.00385 (70-25)1insidediameter of 85 per cent conductivity ~ I'~ - 8-,ii3 microhms per ft; (at 7O-deg.C.)for' 3O-deg.C. rise outdoors at 60 cycles. g-.J I.'ai' ! k -ffi (see references (t) )The. outside diameter is exactly equal to thatC~' C -4030 (from Fig. 16, for outdoor service)

oi the one-inch extra heavy pipe size given in Table Thus .VII, Item 4, which is rated at 1010 amp. for outdoor I _ 4030 _ 1300amp .service.Allowance fort~e difference of copper cross. v'1.14X8.43section is made as follows: .The cross-section of the one-inch tube specified in

TableVII is

i:l\cstigation.Theoretical formulas for the heating of~tangu1ar con.ductors have been worked out but the.:lpplication. .' Un 1 '. . . .'eo~tl:JrS, especially in the case of laminated bars.~~",probable~~n"OreaseS 0 curren th' reeP'0- en .over.the {)J"resp0nding...lm'en~~tiltwai~e-..possibJ .

TABLE vmRELATIn CURRENT -CARRYING CAP ACmES

for Conductor. ofrhe Same Diameter and Cro~cion ofMetal Having Dift'erent Value. of Conductivity

CONDUCfOR TEMPERATURE. 71)DBO. c.

Matmal Pet Cent Relative CUrTellt-Conductivity carry;nl( Capacity

Copper 100 1.00and 95 0.98

Corcper 90 0.96Aloys

85 .0.9480 0.9175 0.88

70 0.8665 0.8360 0.8055 0.7750 0.74

,Aluminum 61 0.78

55 0.7450 0.71

0-13152-9512-1,730,000-905,000-825,000cir, mils

The cross-section of the tube in this example is ..

(11-13152-10222= 1,730.000-1,045,OOQ-6~,OOOcir. mils .

- The sJ...in effeet ratio is practically 1.0 at 60 cycles for .both tubes. Thus, according to Equation (13)

~kal . ~685.000 0 91q- -- - ..k1a 825,Q(M) '.

The outdoor current rating for the tube of crosssectional for 100 per cent conductivity copper is.

0.91 X 1010-920 amp. ~.

, ~- .-The relative current-carrying capacity for 85 per centconductivity copper from Table VIII is 0.94.

Thus the current-carrying capacity of the tube.specified is

0.94 X 920-865 amp.

~~~;~:To find the current-carrying capacityof a in. outside diameter and 3-i in. insidediameter of }.OO per cent conductivity copper 'for p~eg. C. rise outdoors at 60 cycles. . ~ a! .Substitute the following numerical values in C Y .

Formula (l2):

C-3350 from Fig. 16, for outdoor service. d "-0.75 in.d1-0.50 in; .r -12.59 ohms per mil-foot at 7O-deg.C.k -"1.0.

Thus

I -3350 I 0.751-0.501 -528 am .'\j. 1X 12.59 . P

where I is the current-carrying capacity of the tubespecified. .

The relative current-carrying capacity for 98 per centconductivity copper is 0.99, from Table VIII.Thus the 'current-carrying capacity of the cable

specified is .0.99X 1300-1290 amp.

. 'EiiifillU * To find the current-carrying capacityat 60 cycles of the 1,500,000 cir.smil ponents of the heat dissipated due to convection andradiation and add them to get the total heat dis-sipated. Then substitute in Equation (1) .and solvefor the current.

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'CONCLUSIONS lOCi fa o' aJ!tly'(1). This article gives current ratings for .' al:1eitefeoeatiens-ma. ~~_GU

conductorsin ~'!mta a sunder specified ~oci~~cindconditions, and .~ installations, for _~d't~towance-fl :he30-