Forwards addl info re Thermo-Lag related ampacity derating ...

RIGRITYCCELERATED RIDS PROCESSING)

REGULATORY INFORMATION DISTRIBUTION SYSTEM (RIDS)

ACCESSION NBR:9505190297 DOC.DATE: 95/05/12 NOTARIZED: NO DOCKET IFACIL:50-315 Donald C. Cook Nuclear Power Plant, Unit 1, Indiana M 05000315

50-316 Donald C. Cook Nuclear Power Plant, Unit 2, Indiana M 05000316AUTH.NAME AUTHOR AFFILIATION

FITZPATRICK,E. Indiana Michigan Power Co. (formerly Indiana & Michigan Ele PRECIP.NAME RECIPIENT AFFILIATION

Document Control Branch (Document Control Desk) ~)~SUBJECT: Forwards addi info'e Thermo-Lag related ampacity derating

calculations, as requested by NRC 950306 ltr.DISTRIBUTION CODE A029D COPIES RECEIVED:LTR ENCL SIZE:TITLE: Generic Letter 92-008 Thermal-Lag 330 Fare Barrier

0,'OTES:

R

RECIPIENTID CODE/NAME

PD3-1 LAHICKMAN,J

INTERNANRR/DRPW/PD3-1RGN3 ~ ...FILE

EXTERNAL: NOAC

COPIESLTTR ENCL

1 01 1

1 11 11 1

1 1

RECIPIENTID CODE/NAME

PD3-1 PD

NRR/DE/EELBNRR/DSSA/SPLB

NRC PDR

COPIESLTTR ENCL

1 1

1 12 2

1 1

D

N

i4OTE TO ALL"RIDS" RECIPIENT:TS:

PLEASE HELP VS TO REDUCE KV'iSTE! COYTACTTHE DOCL'ifEYTCONTROLDESk, ROOlif Pl-37 (EXT. 504-~OS3 ) TO f;LlliflbATE YOL'R iAXIL'ROilDISTR I BUTIOYLIS'I'S I'OR DOCL'5 IEi'I'S YOL'OY,"I'ffI'.D!

TOTAL NUMBER OF COPIES REQUIRED: LTTR 11 ENCL 10

Indiana MichiganPower CompanyP.O. Box 16631Columbus, OH 43216

FI

May 12, 1995 AEP:NRC:0692DF

Docket Nos.: 50-31550-316

U. S. Nuclear Regulatory CommissionATTN: Document Control DeskWashington, D. C. 20555

Gentlemen:

Donald C. Cook Nuclear Plant Units 1 and 2ADDITIONAL INFORMATION REGARDING THERMO-LAG

RELATED AMPACITY DERATING CALCULATIONSTAC NOS. M85538 AND M85539

By your letter dated March 6, 1995, we were requested to submitrepresentative ampacity derating calculations with respect tocables in raceways covered with Thermo-Lag used at Donald C. CookNuclear Plant. The calculations and methodologies, includingmathematical models, are addressed in the attachments to thisletter.

Attachment 1 provides an overall summary of our ampacity deratinganalyses. Attachment 2 contains the basis of our mathematicalmodel. Attachment 3 contains cable tray allowable fill designcriteria. Attachment 4 provides an in-depth discussion of thedevelopment of the mathematical model and analysis. Attachment 5contains representative calculation results. Attachment 6 providesresults from tests used to verify the accuracy of our computermodel.

Sincerely,

Vice President

cad

Attachments

ASQQ jg9505190297 95051'2PDR ADOi K 050003i5P PDR

U. S. Nuclear Regulatory CommissionPage 2

AEP:NRC:0692DF

CC; A. A. BlindG. CharnoffJ. B. MartinNFEM Section ChiefNRC Resident Inspector - BridgmanJ. R. Padgett

ATTACHMENT 1 TO AEP'NRC'0692DF

SUMMARY OF AMPACITY DERATXNG ANALYSES

. ~ -9505190297

Attachment 1 to AEP:NRC:0692DF Page 1

1.0 ~Back round

In 'the early 1980's, compliance with 10CPRSO Appendix "R" wasachieved for Cook Nuclear Plant (CNP) by enclosing certainraceways with Thermal Science Incorporated (TSI) Thermo-Lag330-1 fire barriers. Enclosing the power cable raceways withthe TSI material increases the thermal resistance to ambientthus restricting the quantity of heat released, resulting inreduced conductor» allowable ampacity.

Although TSI material specifications addressed specificpercent derating for the cables in tray and conduit wrappedwith Thermo-Lag barriers, AEPSC took an aggressive approachto independently determine the reduced allowable ampacitiesand documented that the full load currents for power cablesin the TSI wrapped raceways at CNP did not exceed allowablederated ampacities.

2,0 Theoret ca ana s s Mathematical mode

The process included the development of a mathematical modelbased on the theoretical analysis and work done by Neher,McGrath, and Buller in their AIEE transactions papers 57-660and 50-52 (attachment 2). This analysis is based on thephenomena of heat transfer with respect to energized cablesand the effect on the ampacity.

The temperature rating of a cable is the maximum conductortemperature that will not cause excessive deterioration ofthe cable insulation over the expected life of the cable.This maximum temperature limits the amount of heat which maybe generated by a conductor by resistive heating andtherefore limits the amount of current the cable can carry.

Enclosing, the conductor within layers of material(i.e.,insulation, raceway, or air space) increases thethermal resistance to the ambient heat sink and restricts thequantity of heat which may be transferred while stillmaintaining the maximum conductor temperature.

The objective then was to determine the allowable ampacity ofcables in various raceway and fire protected racewayconfigurations based on the heat transfer through a thermalresistance while not exceeding the temperature rating of thecables under steady state conditions.

The phenomena of heat transfer with respect to energizedcables and the effect on cable ampacity were examined. Thi.sincluded:


a) review of basic heat transfer mechanics,

b) evaluation of previous work done in the areas of cableampacity and heat transfer,,

c) analysis of the effects of conduction, convection andradiation with respect to CNP power cableinstallations, and

d) development of heat transfer theory for low fillcabletrays.

Per our design criteria (see attachment 3), the powercables installed in cable trays are positioned in asingle layer with a minimum space between cables of 1/3the diameter of the larger ad)acent cable.Furthermore, the sum of cable diameters can not exceed75% of the tray width. The above criteria limits thenumber of power cables installed in a cable tray, thuslimiting the total heat generated per foot and limitingthe conductor derating.

3.0 Calculations

A computer program was developed according to the criteriaoutlined in the mathematical model. The program calculatesthe allowable ampacities for the power cables in the TSIwrapped raceways. Assuming a maximum allowable cabletemperature of 90 C and an ambient temperature of 40'C, themaximum allowable heat generated(Q) was calculated for steadystate conditions. The allowable ampacity (I) was thencalculated using the known relationship between Q and I. Theanalysis and mathematical model are discussed in depth inattachment 4.

At CNP, the power cables in all TSI wrapped raceways wereanalyzed using this program and it was documented that thecable full load currents are within the calculated allowableampacities. Representative calculation results showing theallowable ampacities for the cable tray and conduit racewaydesign are included in attachment 5.


4.0 Tests

Finally, a series of tests was conducted in 1983 at ourCanton test lab to verify the accuracy of the computer model.These tests simulated exact raceway loading conditions at CNP

and demonstrated that the conductor temperatures for the TSIenclosed . cables are within the temperature rating of theconductors:. as. predicted by the computer model. Refer toattachment 6 for the test report ¹CL-542 datedDecember 16, 1983. The highest conductor temperature recordedfor the six tested configurations was 68.8'C. Cable trays andconduits were both included in this testing.

5.0 ~Conclusio

At CNP, the calculations for the cables enclosed with TSIThermo-Lag 330-1 fire barriers demonstrated that:

a) the connected full load currents are well withincalculated allowable ampacities,

b) the calculated heat generated per foot of raceway iswell under the calculated allowable heat generation perfoot of raceway, and

c) the raceway design criteria limits the total number ofcables in a raceway such that the cable temperatureratings are not exceeded.

ATTACHMENT 2 TO AEP'NRC'0692DF

AIEE TRANSACTIONS PAPERS 57-660 & 50-52

'iy, k l J. *4,

M. H. McGRATH

i'e

~e

,h

aN 1932 D. M. Simmons'ublished aseries of articles entitled, "Calculation

of the EIcctricaI Problems of UndergroundCables." Over the intervening 25 yearsthis work has achieved the status of ahandbook on the subject. During thisperiod, however, there have been numer-ous dcvdopmcnts in the cable art, andmuch theoretical and experimental workhas been done with a vievr to obtainingmore accurate methods of evaluating theparametas involved. The advent of thepipe-type cable system has emphasixedthe desirability of a more rational methodof calculating the performance of cablesin duct in order that a realistic comparisonmay be maCk betmeen the twa systans.

In this paper the authors have en-deavored ta extend the vrork of Simmonsby presenthig under one cover the basicprinciples involved, together vrith morerecently developed procedures for han-dling such problems as the effec of theloading cyde and the temperature riseof cables in various types of duct stxuc;turcs. Indudcd as wdl are expressionsrequired in the evaluation of the basicparaxneters for certain specialixed alliedprocedures. It is thought that, a mark ofthis type wiIIbe useful not only as a guideto engineers entering the Geld and as areference to the more experienced, butparticularly as a basis for setting up com-putation methods for the preparation ofindustry load capability and aw/d~ ratiocompilations.

The calculation of the temperature riseof cable systans under essentially steady-state conditions, which includes the effectof operation under a repetitive load cycle,as opposed to transient temperature risesdue to the sudden application of largeamounts of laad, is a relatively simpleprocedure and involves only thc applica-tian af the therxnal equivalents of Ohm'sand Kirchoff's Laws to a relatively simplethermal circuit. Because this circuitusually has a number of parallel pathswith heat Gams entering at several points,hovrcver, care must, be exercised in themethod used of expressing the heat fomsand thermal resistances involved, anddiffering methods are used by various en-gineers. The method employed in thispaper has been selected after careful con-

sideration as being the most cansistcntand most readily handled over the fullscope of the pxablan.

Alllosses willbe developed on the basis

QONrs and temperature rises due to dielec-tric loss and to current-produced lasses millbc treated separately, and, in the lattercase, all heat Horns"miII be expressed interms of thc current produced lossariginat-ing in one foot of conductor by means ofmultiplying factors which take into ac-count the added losses in the sheath andconduit.

In general, all thamal resistances miIIbe developed on the basis of the per con-ductor heat Qow through them. In thecase of underground cable systems, it is

'convenient to utilitc an effective thexxnal'esistance for the earth portion of thc

thcxxnaI circuit vrhich indudes the effectof the loading cyde and the mutual heat-ing cffcct af thc athcx'able of thc system,Allcables in the system wiIIbe consideredt~ocsrry e eeoie Ided eetieiite eed to be

operating under the same load cyde.The system'of nomendature employed

is in accordance with that adopted by theInsulated Conductor Committee as stand'-

ard, and diffas appreciablyfrom that usedin many of thc references. This systemrepresents an attempt to utilize in sa faras possible the various symbols appearingin the Amaican Standards AssociationStandards for Eectxicai Quintities, Me-chanics, Heat and Thaxna-Dynaxnics,

'and Hydraulics, when these symbols canbe used without ambiguity. Certainsymbols which have long been 'used bycable engineers have been retained, even

though they are in direct conQict miththe abaveementioned standards.

Nomenclature

(AF) attainment factor, per unit (pu)As«cross-sectioht area of a shieldiag tape

or skid rcire, square inchesdr«therznaI diffhhsivity. square inches pa

hourCI«conductor area, circular inchesd«distahhcc,

inches'th

etc. « from ceater of cable no. 1 to centerof cable no. 2 etc.

Cks'tc.«from center of cable no. 1 toimage of cable no. 2 etc.

As etc. from center of cable no. 1 to apoiat of icterfercace

$.'.',."''!7het Calculation of the Temperature Rise

''an'd Load Capability of'able Systems~

~ ~3. H. NEHERr . MEMSER dhtlEE

e

As'tc.«frohn iauge of cable no. 1 to apoint of intexfexeace

D«dhmcter, inches aq b.oDcdaiasidD, «Outxide Of Cahhduetar

~

Ds«outside of ixhsulatioaDs«outside of sheathD«,«incan diameter of sheathDf«outside of jacketDs'«effective (cixcuxnscribiag cirde) of

several cables in contactDp«inside of duct wal4 pipe or conduitDc«dlaxneter at start of the earth portion

of the thermal cixcchitDa«fictitious diameter at vrhich the effect

of loss hctor commencesE«line to neutral voltage, kilovolts (kv)~ «coefficient of surface emissivitycr «spccific inductive capacitance of insula-

tloa/«frequency, cycles per secoadF, Fs,h«pxxhducts of xatios of distancesF(x) «derived Bessei function'f x'Table

III and Fhg. 1)G«geometric factorGt «applying to insulatioa resistance (Fige 2

of referexhce 1)Gs«applying to dielectric loss (Fig. 2 of

reference 1)Ght«applying to a duct bank (Fig. 2)I conductor current. kiloampexeskd «skin effect co?rection factor for annuhr

and segxneatal conductorskp«relative txanshrexse coadclc&ity hctox

for caicuhting conductor pxoxihnityetfect

J«hy of a shielding tape or shd wire, inchesL«depth of reference cable below earth'

schxface, inches .

Lv«depth to center of a duct bank(ox'ackfill),inches

(lf)«load factor, per unit(LF) «loss hctor, per unitri number of conductors per cablexs'«nuxaber of coaductoxs within a stated

diaxneterN«number of cables or cable 'groups in a

systexnP«perihneter of a duct bank or backfiJI,

inchescos 4«povrer factor of the insuhtiontfc«ratio of the sum of the losses in the

conductors and sheaths to the lossesia thc coaductoxs 'I

tlc«ratio of the sum of the losses hx thecoadchctoxs, sheath and conduit tothe losses in the conductors

R «electrica resistance, ohmsRsc «dw resistance of conductorR„ total aw resistixhce per conductorRc«dw resistance of sheath or of the

parallel paths in a shield-skid vtrireassembly

8 « thexxnal resistance (per conductor losses)thexxnal ohm-feet

8s «of iaschlatioaAf«of jacketRhd «between cable surface aad schxxounding

endosure

Paper ST~, recomtaeadcd bT the hIBB InsulatedCoaductors Committee aod approrcd bT the hIEETcchaiccl Operations Pepartmcac for presentation~c the hlBB Summer Ccocrsl hfecttae. hfoocreal,Que.,'aosda, Juae 24-2S. 105T. hfaauscriptsubhoittcd starch "0, 10ST; made aransbte forpriociax hpril 18, 10$ T.

J. If. Nausa ls eectb the phiaadclphta Elec&aCompcor. Philadelphia. Pa.. and hf. H. hfcCaamIs reich the Ccocral Cable Cocporacloo, Pcrthhmbor, ¹ J.

c'Ceher, .VcGrctli—Terrlpercfnre crxd Load Ccpabilify oj Ccblc Systems QCTCnER lear

t ~

'

ajoOA9OA4OA7OA4005

Xo

2,5

IA0.9a40.70.4

g a5~ a4

~~ 0.25

a2

O.I5F(xv)

jIF(x9)

I I! I

I i lii

~ ~ I

; I I

@xi I l jrI I I! I'lji

i I

i ~ s

i. I I!

I I:(xj

0015 &

o Ipa009~ Iu

00040005

0~ hI

OA03

00025

0002

I.O

I.5

I.o

8

I

O.IO2 253 4 5 4 769IO l5 20 30 40 5060 4000

RucA

Fig. l (above). F(x) and F(xa') az functions of ~/k

Fig. q (right), GI for 4 duct bank

Wa~poztion developed in the conductorW,~portion developed in the sheath or

shieldW «portion developed in the pipe or con-

duitWc ~ portioa deveiopal m the dielectzicX~~ mutual reactance, conductor to sheath

or shield, microhms per footY~the incremen't of aw/dw ratio, puYa«due to losses originating in the con-

ductor, having components Yaa ducto shn efect and Y,jr due to prox-imity effect

Ya ~due to losses originating in the sheathor shield, having compobeats YIadue t'o cizcuhting cuzrent cffect andYi, due to eddy current effcct

YIr~due'to losses originating in the pipeor conduit

Ya ~ due to losses originating in the amor

General Considerations of theThermal Circuit

THs ~~TzoN op TsM2smTzzssRzss

The temperature rise of the conducmrof a cable above ambient temperature maybe considered as being composed of atemperature rise due to its own losses,

which may be divided into a rise due tocurrent produced (PR) losses (hereinafterreferred to merely as losses) in the, conduc-

tor, sheath and conduit b,Ta and the riscproduced by its dielectric loss hT4.

24~ of duct wall or asphalt mastic coveringR„~total between sheath aud diameter

Da Including Rt, Rrc and Rc~

~

~

R< ~between conduit and ambient. R,'~effective between diameter Da and

ambient earth including the cffects .of loss factor and mutual heating byother cables

Raa'~effective between conductor andambient for conductor loss

R4r' effcctive tzanslcnt thezznal resistanceof cable systan

Rca'~cffective between conductor aad am-bient for dielectric loss

Rr,I~of the interference efectRf4 ~ between a steam pipe and ambient

earthp~clectrical resistivity, circular mil ohms

per footit thermal resistivity, degrees centigrade

centimeters pcz'at'ts~distance in a 3mnductor cable between

the effective current center of theconductor and the axis of the cable,inches

S~axial spacing between adjacent cables,inches

t, T~thickncss (as indicated). inchesT~ tanperature. degrees centigradeTa~of ambient air or earthTa~ of conductorT~~mean temperature of mediumAT~tcmpaature rise, degrees centigradeATa~of conductor due to cturent produced

losseshT4~of conductor due to dielectri losstZTrxr~of a cable due to extraneous heat

sourcer infared tanpaature of zero resistance,

degrees centigrade (C) (used incorrecting R4, and R, to tempera-tures other than 20 C)

Vs~wind velocity, miles per hourW~lozses developed in a cable, watts per

conductor foot

RATIO Lb/P

Ta-Ta ~ hT,+4T4 degrees centigrade(1)

Each of them component temperaturerises may be considered as the result. of arate of heat flow expressed in wattsoot throu a ermal resistance

dinthermalohm eet degzcescenti-gra 0 eet per watt); in other words, the

Qow of one watt uniformly distributed.over a conductor length ofone foot.

Since the losses occur at. several posi-tions in the cable system, the heat Bow inthe thezznal circuit wB1 increase in steps.It is convenient to express all heat Qows interms of the loss per foot ofconductor, andthus,,

aT,- WgRr+q,R,.+qA)degrees centigrade (2)

in which W, represents the losses in one

conductor and RI is the thermal resistanceof the insulation, q> is the ratio of thesum of the losses in the conductors andsheath to the losses in the conductors,

R« is the total thamal resistance betweensheath and cocdmt, q, is the ratio of thesum of the losses in conductors, sheath and

conduit, to the conductor losses, and Ra

Oerosss 1957 Nchcr, McGrath—Tcrnpcratarc arrd Load Capability of Cable Systcrrrs

ls the thermal resistance between tt e<tr conduit and ambient." In practice, the load carried by a cableis rarely constant and varies according tost daily load cycle having a load factor(lj). Hence, the losses in the cable willvary according to the correspondingdaily loss cycle having a loss factor (LF).From an examination of a large number ofload cycles and their corresponding loadand loss factors, the follovringgeneral rda-tionship betvreen load factor and/ lossfactor has been found to

exist.'LF)

~ 0.3 (tf)+0.7 (tf)'er unit

In order to determine the maximumtemperature rise attained by a buriedcable system under a repeated daily loadcycle, the losses and resultant heat flowsare calculated on the basis of the maxi-mum load (usually taken as the averagecurrent for that hour of the daily loadcycle during which the average current isthe highest, i.e. the daily maximum one-hour average load) on vrhich the loss factoris based and the heat Qow in the last partof the earth portion of the thermal circuitis reduced by the "factor (LF). If thisreduction is considered to start at a pointin the earth corresponding to the diameterD„'quation 2 becomes

t2Tc Wc(lt+qc~tc+qc(~cs+(LF)@c)ldegrees centigrade (4)

In effect this means that the tempera-ture rise fitom conductor to'> is made todepend on the heat loss corresponding tothe maximum load vrhereas the tempera-ture rise from diameter Dc to ambient ismade to depend on the average loss over a24-hour period. Studies indicate that theprocedure of assuming a fictitious criticaldiameter D> at which an abrupt changeoccurs in loss factor from 100% to actualwill give results which very closelyapproximate those obtained by rigoroustransient analysis. For cables or ductin air where the thermal storage capacityof the system is relatively small, the maxi-mum temperature rise is based upon theheat Gow coizesponding to maximum loadvrithout reduction of any part of thetheimal circuit.

When a number of cables are installeddose together in the earth or in a ductbank, each cable wQI have a heating eEectupon all of the others. In calculatingthe temperature rise of any one cable, it isconvenient to handle the heating etfects ofthe other cables of the system by suitablyinodifying the last term of equatiot 4.This is permissible since it is assuinedthat all the cables are, carrying equal cur-rents and are operating on the same loadcycle. Thus for an P-cable system

aTc Wc(A+qc~cc+qcfffcc+(LF) X(Bcc)+(N-I)N¹I) (5)

Wc(lt+qcIcc+qcRc')degrees centigrade (Sh)

where the tenn in parentheses is indicatedby the etfective thamal resistance 8c'.

The temperature rise due to dielectricloss is a relatively small part of the totaltemperature rise of cable systems op-erating at the lower voltages, but athigher voltages it constitutes an appre-ciable part and must be consideretL Al-though the dielectric losses are dis-tributed throughout the insulation, itmaybe shown that for single conductor cableand multiconductor shielded cable withround conductors the correct temperaturerise ts obtained by considering for tran-sient and -steady. state that all of thedielectric loss Wtt occurs at the middleof the thermal resistince between conduc-tor and sheath or aitentateiy for steady-state conditions alone that 'the tempera-ture rise between conductor and sheath fora given loss in the dielectric is half as

much as if that loss were in the conductor.In the case of multiconductor beltedcables, however the conductors are takenas the source of the dielectric

loss.'he

resulting temperature rise due todielectric loss 42'tt may be expressed

dTtt~ Wit's'egrees centigrade (6)

in which the effective thermal resistanceib 'is based upon /It,8„,and)4'(at unityloss factor) according to .the particularcase. The temperature rise at points inthe cable system other than at. the con-ductor may be determined readily fromthe foregoing relationships.

THB ChiA'-UthTio)4 op Lohn ChPhnan)r

fn many cases the permissible maxi-mum temperature of the conductor isGxed and the magnitude of the conductorcurrent goad capaMity) required toproduce this temperature is desiretLEquation 5(A) may be written in the form

ATc~I'24c(I+yc)lcc'egrees

centigrade (7)

i which the qqaatity~lb, (1+ Y, qhiehill be ev uate re resents the

eE 've electn resistance of the con-ducto 'n hms and whichvrhen multiplied by P (I in kiloamperes)vrillequal the loss Wc in watts per conduc-tor foot actually generated in the conduc-tor; and 8ec's the e(fectlve thermalresistance of the thermal circuit

fIcc'IIt+qc8cc+qcffc'hermal ohm-feet(8)

From equation I it follows thatI

+lciloam eres

3 a,<I+ I;)~.

Ta6le I. Electrical Resbtlvity of VariousMateriab

btaterlcl

PCheater Mll

Ohms per Footat20C r, C

Copper (100% IhCS') ~ ~ ~ ~ ~ ~ ~ ~ 10.371..... 234. SAluminum (81% IhCS). e, ~ 17.002. ~ . ~ .228. 1Cotcmerelct Bronte (43.8% ~ ~ . 23.8 ~ ~ ~ ~ .584

IhCS)(90 Cu-10 Zo)

Bta$ 5 (2T.3% IhCS) ~ ~ ~ . ~ .. ~ ~ ~ 38.0 ~ ~ ~ ~ .912( 0 Cu-30 Zu)

Lead (7.84%c IhCS)... ~ . ~...132.3 . ~ . ~ .238

~ Isterssuoud hoaeale4 Copper StaodanL

Calculatioa of Losses andAssociated Parameters

37.9Rc ~—'or Iesd at 50 C

Dctttt(IIA)

4~—for 61% aluminum at 50,CDg 1

(IIB)

vrhere Dcttt is the mean diameter of thesheath and t ts its thickness, both ininches

Dccq ~Dc t laches (12)

The resistance of intercalated shieldsor skid wires may be determined from theexpfcsstOQ

rpc SDtetR, (pe: path) —) I+(

—)

microhms per foot at 20 C (13)

where A, is the cross section area of the

Gac~Tio)i CF DN RBsisThNcxs

The resistance of the conductor may bedetermined from the followingexpressionsvrhich include a lay factor of 2%; see

able L

1.02 pcmicrohms per foot at 20 C

CI(IO)

12.9for 100% IACS copper

CIconductor at 76 C (10A)

212~—for 61% IACSCI

alumlautn at 75 C (IOB)

vrhere CI represents the conductor size inCircular inCheS and Vrhere Pc rePreSentS

the electrical resistivity in circular milohms per foot. To determine the value ofresistance at temperature T multiply theresistance at 20 C by (r+T)/(r+20)where r is the inferred temperature ofZero resistance.

The resistance of the sheath is givenby the expressions

pcR, ~—mlcrohms per foot at 20 C (II~

4Dcctt

Kdhdr, hfcGra! h—Terripdratnrd and Load Capability of Ccbfe Sys.'crrts QcToBBR 19o<

s ~ ~ '

~

tape or sl.id wire and l is its lay. Theover-all ':esistancc, of the shield and skidrwire assembly, particularly for.noninter-calated shields, should be determined byJectrical measuremcnt when possible.

C~L.ctfuTioH oF Losslls

It is convenient to develop expressionsfor thc losses in the conductor, sheath andpipe or conduit in terms of the componentsof the aoc/doc ratio of the cable systemwhich may be expressed as followsl

r(wR CIRcc 1+Yc+Ys+Fp (14)

The aoc/doc ratio at conductor is 1+ Yc

and at sheath or shield is I+Y,+ Ys

and atpipeorconduit is I+Y,+Ys+YpThe corresponding losses physically gen-erated in the conductor, sheath, and pipeare

Ws I Rcs(l+ Yc) watts pcr conductor foot(IS)

Ws PRcc Ys watts Per conductor foot (16)

Wp ~I'24cYp watts per conductor foot (17)

'cisj»Il. Recommended Values of k,cndks

Conductor Construcuon Costing on Saends Treatment Lro

Concentric round,.............Hone..... ~ ~ . ~ ~ .~...".Noae..............l.o .....~.......1.0Concentric round..............Tlo or enoy........ ~ . ~ .None..........~...1.0 ........~....1.0Concentric round..............Hone.~............... Yes...............l.o .....~.......0.80Compact round o ~ Noae ~ ~ ~ Yes ~ ~ ~ I 0 ~ ~ ~ ~ ~ 0 0Compact segmental.......,....Hone..................Noae..............0.43$ .............0.0Compact segmental............Tin or aUoyoo „Hone ....O.S . ~.. 0.7Compact segmental............Hone..................Yes...............0.43$ .."...~.....0.37Compact sector................Hone............... ~ ..Ycs...............l.o.............(secnotc)Horns:1. The term "treated" denotes a completed conductor which has been subjected to a drylog and lmpregnatlng process simaer to that employed on paper power cahte.

2. Proximny edect on compact sector conductors may be tahen as ose half of that for compact roundhaving 'thc same cross scctloosl area asd Lnsutsuon thtchncss,

3. Proximity CUcct on annular eooductors may be approdmsted by using the value for a concentdcround conductor of the same cross-cctfsnnsL area and spadng, The locressed diameter ol the annulartype and the removal of metal from the center decreases the shin eifcct but, for a given adsl spsdng, tendsto. result tn an lnaease ln proximity. o

4. The values listed above for compact scgmentsl refer to four segment constructtooa The „uocoatcdtreated" values msy also be tahcn as apphcabi ~ to four segment compact segmental with hoaow core (approximately 0.7$ inch dear). For "uncoated treated" six segment houow core compact segmental limitedtest data lodicatcs ko and kp values of OA and OA respectively.

Tabl» III. Skin Effect fn % in Solid Round Conductor lnd in Conventionel Round ConcentricStr4nd Conductors

100 F(x), Skin Effect fo

3 4 5 d 7 d 9

his permits a ready determination of thelosses if the segregated a-c/doc ratios areknown, and conversely, the aoc/doc ratiois readily obtained after the values of Ycs

Ys and Y< have been calculated.It follows from the definitions of qs and

qc that

Wc+WC Ycqsw m]+

Wc 1+ Yc

Wc+WC+ Wp Yr+Ypqc i+-

We 1+ Yc

(18)

(ip)

The factor Y, is the sum of two compo-nents, Ymdue toskneffect and Y,p dueproximity effect.

Wc ~lsRefc(1+ Ycc+ Ycp)watts per conductor foot (20)

(21)

xs ~0.875 —~ —at 60 cycles$ Rcc QRcr/ks(22)

in which the factor hs depends upon theconductor construction. Forconventional conductors a

nctton F(x) may o tatne omTable'II

or from the curves of Fig. 1 in termsof the ratio Rs,/h at 60 cycles.

For annual conductors

solid or~Srrotnate

eIL The,

(2$ )

in vrhich D, and Ds represent the outer

The skin etfect may be determined fromthe skin effect function F(x)~ Ycc~F(xr)

0.00...0 Ol ~ ~ ~

0.04.. ~

0,13...

O.sd...0 $4o ~ ~

O.T9...1.11...I S2o ~ ~

2.02.. ~

2.as'�

.3.40oo ~

4.30...6.3$ ...d,syooT.Q0.. ~

11.3lo o ~

13.27...IS.43. ~ .IT.78...20.32...23.03...2$ . 02. ~

2$ .90...32.13...3$ .44oo ~

38.8$ ...42.3$ ...4$ .93...49.$ 7...S3.2$ ...Sd.90..00.09...

as.'la."..'1.89...

Ts. 00.70.30...82.98..r

90.2$ ...93.89...97.49...

IOL.OT...

0.01 ~ .. 0.01... O.OL.. 0.01...0.02. ~ . 0.02... 0.02... 0.02...0.04... 0.04... 0.0$ ... 0.0$ ...0.08... 0.08... 0.09... 0. 10...0.14... 0.1$ . ~ . 0.10.. ~ 0.17...0.24. ~ . 0.2$ ... 0.20. ~ ~ 0.2$ ...0.38.. ~ 0.39... 0.41. ~ . 0.43...0.60... 0.$8... 0.01... 0.03...0.81.. ~ O.dl... 0.87... 0.90...1.14 ~ . ~ 1.18. ~ ~ 1.22... '1.25.. ~

1.50... 1.01". L.dd... 1.71."2.08. ~ ~ 2. 14... 2.20... 2.20...2.72oo ~ 2.79.. ~ 2.6$ . ~ . 2.93...3.49... 3.6T." S.dd... 3.7$ ...4.40... 4oso... 4.50... 4.TO...$ 4To ~ ~ 6 6' ~ 6 TO ~ ~ 5 '2 ~ ~

0.70... 0.83... 0.97... 7.11...8.11... 8.25... $ .42... 8.$7...9,71... 9.88... 10.0$ .. 10.22..

11.50... Ll.d9... 11.88. ~ . 12.07. ~ .13.48. ~ . 13.08... 13.90... 14.11...1$ .00... LS.SO. ~ ~ lb.12... 10.3$ ...1$ .03... 18,27... 18.$ 2o.. LdoTS...20.$ 8o ~, 20.8$ .. ~ 21.12o,. 21.38...23.31... 23.50... 23.88... 24.17. ~ ~

25.21... 20.$ L... 25.8L... 2741...29.27, ~ 29,$ 8... 29.90. ~ 30.21.32.4$ .. ~ 32.78... 33.11... 33.44...3$ 78.. 30.11.„3d.4$ .. 35.TQ.39.20e. ~ 39.$ $ ... 39 89... 40.24...42.71... 43.05... 43.42... 43.78...40.29oo ~ 40,0d... 47.02... 47.38...49.94... 50.30... $0.07... $1.04...'k:::: ".:::::::::.02... 63.99... 64.35... Si.T3...d .33... ST.TL .. $8.08... 58.4$ ...01.00... 01.44... al.dl... a2.18...04.80... 0$ . 17... 0$ .$$ . ~ ~ 0$ .92...0$ .$3. . 08,91. ~ ~ 09.28... 09.0$ .. ~

72.20. ~ . 72.03... 73.00. „ 73.38.7$ .9T... 7d.34... 7d.TI... 77.0$ .o ~

79. 0T... 80. 04... 80. 41 .. ~ 80.7S. "83.3$ ... 83.01... 84.08. ~ . 84.4$ ..oST.OI.. 87.37.. ST.73... 8$ .10..90.04.. 91.00... 91.37,. 91.73.94.2$ ... Ol.dl... 94.97... 9$ .33...97.8$ ... 98.21... 98.$ 7... 98.92...

101.42...101.78".102.14...102.49."

0.3... 0.00...0.4... ~ 0,01...O.S... 0.03".0.0.. ~ 0.07...0.7... ~ 0.12...

0.01...0.02...0.0$ ...0.10.0.18...0.29...0.4$ „.0.0$ ...0.94...1.30..I.Td...2.32.. ~

3.01...3.$3.. ~4.81...$ .94...7,24..8.73.a.

10.40...12.27...14.33...1$ .$8..19.03o ~ .21.0$ ...24. 4$ . ~ .2T.42...30.$3...33.7T. o ~

ST.13...40.$ 9...4l.li...47.74...51.40...5$ .10...$8.82...d2.$ 0...00.29...

73.7$ ...T7.4$ ...SL.L4 ~ ..84.dl...88.40...92.09...9$ .09...99.2$ ...

102.$ $ ...

0.01... 0.01... 0.010.03... 0.03... 0.030.00... 0.05... 0.000.11... 0.11.;. 0.120.19... 0.19... 0.200.30oo ~ 0.3L... 0.330.4T... 0.4$ ... 0.$00.08... 0.70... 0.730 97 I 00' I 031.34. ~ . 1.3$ ... 1.421.81o ~ 1.8'. 1.922.39.. 2.4$ ... 2,$ 23.08... S.td... 3.243.92. ~ . 4.02oo ~ 4.114.91... 6.02... d.13d.od... 0.19.. ~ 0.317.38. ~ . 7.53.. 7.07$ .89. ~ ~ 9.0$ .. ~ 9.21

10.$8.„ 10.70.. 10,9412.4T. 12.0T. I'2.67I4.'$4.'.. ll.'70.'.. ll.'9$Ld.d2... 17.15.. 17.3019.28... I9.64... 19.8021.93.. ~ 22.20... 22.4824.T4 ~ ~2$ .03, 2$ .33

30.$ $ oo ~ 31.17... 31.4934.10... 34.43o.. 34.TT3T.4T. ~ . 3T.$2.. ~ 38.1040.94. 41.29 ~ . ~ 41.ds44.49... 44.8$ ... 4$ .2148.11... 48.4T... 48.84$ 1.77... 62.14... 62.$ 1

$$ .'4$ .".. ss.'Ss.".. Sa.'2$9.20.. ~ $9.$7.. ~ d9.94d'3.93. 03.30.. 03.dd00.07oo ~ 07.04... 07.4170.40... 70.7T... 71.14T4.12... 74.49... 74.80TT,82, ~ T8.19... 78.5061.$ 1.. ~ $ 1.8S... 82.2$8$ .18 .. ~ 8$ . 5$ . ~ ~ 8$ . 9188.82... 89.19... 89.$ S92.4$ ... 92.81... 93.1790.0$ ... 90.41... Od.TT99.d4...100.00...100.3$

103. 21... 103.$ 0... 103. 92

0.8... ~ 0.2L. ~ .0 9 0 34 ' ~

1.0' e Oo62.",I I~ ~ ~ 0 Tdo ~

1.2... I OT...1.3" ~, 1.47".1.4.. ~ I.OT. ~ ~

1.5... 2.$8...

1.7.. ~ 4.21...1.6... $ .24...

2.0... T.S2...2.1... 9.38" .2.2.. ~ 11.13" ~

2.3... 13.07. ~ .2.4.. ~ 15.21...2.$ ... LT.64...2.0... 20.00...2,7... 22.TS...2,$ .. ~ 2$ .62oo ~

2.9. 28. 0$ . ~

3.0... 31.$ 1...3.1... 3$ .10.„3.2... 3$ .$0...3.3... 42.00. ~ .3.4., ~ 4$ .$ 7oo8.5.. ~ 49.20...3.0... $2.8$ ...3.7... $0.59...3.8... 00.31 ..3.9... 04.OS...4,0... 07.79...4.1.. ~ TL.$2. "4,2... 7$ .23...4.3., ~ 78.93...4,4... 82.01...4.$ ... 80.28 ' ~

4,0. ~ ~ 89.91., ~

4.T... 93.$ 3..4.8. ~ . 97.13..4.9.. ~ L(tO.TL..

and inner diameters of the annular con-ductor. In comparison with the rigorousBcssel function solution for the skin effectin an isolated tubular conductor, it hasbeen found that the 60~cle skin effect of

annular conductor when computed byequation '23 will not be in error by morethan 0.01 in absolute magnitude forcopper or aluminum IPCEA (InsulatedPower Cable Engineers Association) Sled

OcTOUUR 1957 %cher, .lfcGrcfh—T~n(pcrc]nrc and Load Capability pf Cnbtc Sysfcfns 7M

6

as ~

I ~

Ta6I» IV. Mutual Reactance a160 Cyeiess Conyfudoe lo Sheath (or Shlelsf)

D~/28 --0 1 2 3 4 5 5 T 8 96

(2 S/D~) as in the case of lead sheaths.

«~—— 1+-—

't 'Ij 'I

~ tj

core conductors up through 5.0 CI and forhollow core concentrically stranded copperor aluminum oilrfiilled cable conductorsup through 4.0 CI.

For values of xp below 3.5, a rangevrhich appear to cover most cases of prac-tical Interest at povrer frequencies, theconductor proximity efect for cables inequilateral triangular, Eormation in thesame or in mpaiat'te ducts may be cal-culated from the followingequation basedon an approximate expression given byArnold'equation 7) for a system ofthree homogeneous, straight, parallel,solid conductors of circular cross sectionarranged in equilateral formation andcarrying balanced 3-phase current remotefrom all other conductors or conductingmaterial. The empirical transverse con-ductance factor kp is introduced to makethe expression applicable to strandedconductors. Experimental results sug-gest the values of kp shown in Table IL

Yep-F(xp)(-') Xis)+0.312 — (24)

6.60at 60 cyattt (25)

e p

When the second term in the bracketsis small vrith res pect to the Grst term as itusually is, equation 24 may be written

atI

I m)5(De/S)t 1Yep ~4F(xp)i

JF(x,)+om

~4(—') F(xp') (24h)()Ijt'"

r

6

~'li

'I

vrhere the function F(xp') is showa inFig. l.

The average proximity efect for con-ductors in cradle configuration in thesame duct or in separate ducts in a forma-tion approximating a regular polygon may

I~~ ~

Ta6l» V. Speci8» Intiuctiv» (:apadlance ofInsufations

also be estimated from equation 24 and24(A). In such cases, S should be takenas the axial spacing betvreen adjacentconductors.

The factor Ys is the sum of tvro factors,Y«due to circulating current efect andY«due to eddy current efects.

Ws I'Rd< Yes+Yes)watts p»r conductor foot (26)

Because of the large sheath losses vrhichresult from short~ited sheath opera-tion with appreciable separation betweenmetallic sheathed single conductor cables,this mode of operation is usually restrictedto triplex cable or three singie~nductorcables contained in the same duct. Thecirculating current dfect in three metallicsheathed singlemnductor cables arrangedin equilateral configuration is given by

Rs/Ree

1+(Rs/Xw)s(27)

. When (R,/X~)t is large vrith respect tounity as usually is the case of shielded non-leaded cables, equation 27 reduces to

X~Yse ~—approximately

RIRde

Xss ~0.882/ IOg 2S/Ds~microhms per foot (28)

~52.9 Iog 2S/Dsesmicrohms p»r foot at 60 cydes (28A)

where S is the axial spacing of adjacentcables. For a cradled configuration X~may be approximated f'rom

2.52S 0 / SX ~52,9 log '-(—)b,-S)

microhins per foot at 60 cydes (29)

~52.9 log 2.3 S/Dyes

approximately (29A)

Table IVprovides a convenient means foidetermining X for cables in equilateralconfiguration.

The eddy~eat efect for single-coaductor cables in equilateral configura-tion with open~cuited sheaths is

Materia)

Polyethyleae.................2. 3Paper lasuiatlou (solid type)...3. ~ (1PCEh ea)ue)Paper jose) atjoa (othee types) ..3, ~.2Rubber aod eubbee jjhe coos

pounds.... ~ ...............5 (lPCEh va)ue)Varnished eaesbrje.........,,.S (IPCEh value)

3RI/Rde

1+- — (30)

when (5.2 R,/J)'s large in respect to 1/5

0.4. ~ ."21 ~ 1. ~ ~ ~ 20.5,. ~ a19 9....r19 4.....18.9..".18.3.....1T.8... ~ .ly.i..."15.9..".15.40.3. ~ ~ ~ ~ 2T.T. ~ ~ ~ 25 ~ 9... ~ 25.2" ~ ..23 '.....24 as. ". ~ 24. l."..23.5.... ~ 22.9.....22.2.....21.50.2.....3T.0....33.9„,.34.8.....33.8. ~...32.8.....31.9.....31.0.....30.1.....29.3.....28.40. 1"".52.9. " 50.T....48.T... ~ .45.9. ~ . ~ .45.2.. ~ ~ .43.5.....42.1.....40.T*. ~ -.39.4 ~ ~ ~ ~ .3'

roximattly at 60 cycles (30A)

When the sheaths ale short~ted, thesheath eddy loss mal be reduced and maybe approximated by multiplyingequations30 or 30(A) by the ratio

R,'/(Res+Xmas)

In computing average eddy current forcradled configuration, S should be takenequal to the axial spacing and not to thegeometric-mean spacing. Equations 30and 30(A) may be ural to compute theeddyment-,ef »et for single-conductorcables installed in separate ducts.Strictl s ag, these uations a lyonl to three cables in equilateral con-

guration but can be used to estimateosses in e cable ou s when latter are

so oriented as to a roximate a re larpolygon.

TEe eddyment efect for a 3-conduc-tor cable is given by

ArnoId.'RI

(2s/D~)'2s/Dsw)'1

4 —+1

(2y/D~)s~ ~ ~

5.2R,16 —+1f

When (5.2R /f)i is hrge vrith respect tounity,

Y ~—approximately at 60 cyd»s (31A)

3~1.155T+0.60Xthe V gauge depth forcompact sectors

« 1.155T+0.58 D, foi round conductors

iuy)~ and T is the insulation thickness, indud-

ing thickness of shieldiag tapes, iE any.While equation 31(A) vrillsuKce for leadsheath cables, equation 31 should be used

for aluminum sheaths.

On 3~nductor shielded paper leadcable it is customary to employ a 3- or 5-mil copper tape or bronze tape inter-calated vrith a paper tape for shielding andbinder purposes. The lineal d-c resist-ance of a copper tape 5 mils by 0.75 inchis about 2,200 microhms per foot of tapeat 20 ('he drc resistance per footof cable will be equal to the lineal resist-ance of the tape multiplied by the laycorrection factor as given by the expres-

"

sion under the squ3:e.root sign in equation13. In practice the lay correction factormay vary froin 4 to 12 or more resultingIn shielding and binder asscinbly resist-

756 .i cher, McGrctl:—Tcn:pcrc! arc and Load CaPability oj Cable Systcn;s QCTOBER 195I

} s,'I

he .

ances of approximatdy 10,000 or moremicroi<ms per foot of cable. Even onthc assumption that the assembly resist-ance is halved because of contact with ad-jacent conductors and the lead sheathcomputations made using equations 2?

~ and 30 shocv that the resulting circulatingand eddy current losses are a fraction ot1% on sizes of practical Interest. For thisreason it is customary to assume that thelosses in the shielding and binder tapesof 3oconductor shielded paper lead cableare negligibleo In cases of nonleaded rub-ber power cables where lapped metallictapes are frequently employed, tubeeffects may be present and may materiaUylower the resistance of the shielding assem-bly and hence increase the losses to apoint where they are of practical signiG-CanCeo

An exact determination of the pipe losseffect Yp in the case of single~nductorcables instaHed in nonmagnetic conduitor pipe is a rather involved procedureas indicated in reference 7. Equation 31may be used to obtain a rough estimateof Yp for cables in cradled formation onthe bottom of a nonmagnetic pipe, how-ever by taking the average of the resultsobtained for wide triangular spacingwith saa(Dp'-Ds)/2 and for dose tri-angle spacing at the center of the pipewith 2~0.578'D„The mean diameter ofthe pipe and its resistance per foot shouldbe substituted forDr and R, respectively,

For magnetic pipes or conduit thefoUowing empirical reIationshipss may beemployed

1.54s-0.115D pYp ~ (3~nductor cable)Ac

(33)0.89$ -0.115D p

4

dose triangular) (34)

0.34$ +0. 175D pYp ~ (single-conductor,

244cradled) ( 5)

'These expressions apply to steel pipers

and should be multiplied by 0.8 for ironconduit.s

The expressions given for Y, and Ysabove should be multiplied by 1.7 to Gndthe corresponding in-pipe effects for mag-netic pipe or conduit for both triangularand cradled conGgurations.

CALCULATIONOF DIELECTRIC LOSS

The dielectric loss Ws for Saocdnetorshielded and a~in teaondnetor cable tsgiven by the expres'sion

0.00276Esrr cos c)

lo ( Lr :D )/DQ"--.-conductor foot at 60 cycles (36)

and for 3~nductor belted cableby'.019E'c,

cos c)Wg~ 'atts pers

coccdccctor foot at 60 cydes (37)

where Z is the phase to neutral voltagein kilovolts, er is the speciGc inductivecapacitance of the insulation (Table V) Tis its thickness and cos p is its power factor.The geemetric facter Gs may be foundfrom Fig. 2 of reference 1.

For compact sector conductors the di-electric loss may be taken equal to that fora concentric round conductor having thesame cross-sectional area and insulationthickness.

r'eo

Calculation of Thermal Resistance

THERMALRESISTANCE OF THB INSULATION

For a single conductor cable,rI Rf 0.012tif log Df/Dc thermal ohm-feet

(3S)

where sic is the thermal resistivity of theinsulation (Table VI) and Di is itsdiameter. In multicoaductor cablesthere is a multipath heat Gow between theconductor and sheath. The foUowing ex-pressionc represents an equivalent valuewhich, when multiplied by the heat Gowfrom one conductor, will produce theactual tern peraturre devation ef theconductor above the sheath.

Bf~0.00522ifcGc thermal ohm-feel (39)

Values of the geometric factor Gs for 3-conductor belted and shidded cables aregiven in Fig. 2 and Table VIIIrespec-tively of reference l. On large size sec-

tor conductors with rdatively thin in-sulation waUs (i.eo ratios of insulationthidmess to conductor diameter of theorder of 0.2 or less); values of Gl for 3-conductor shielded cable as de(erminedby back calculation, on the basis of anassumed insulation resistivity, from lab-oratory heat-run temperature-rise data,have not always confifmed theoreticalvalues, and, in some cases, have yieldedGi values which approach those for anonshielded, nonbelted construction.

T46fe Vl. Thermal Resistivity of VariousMa(erich

Material if, C Cm/W'acc

paper fosulacloo (solid Cype)...T00 GFCEA value)Varnished cambric.~.... ~ .. ~ ..000 (IPCEA value)Paper iosulacloa (ocher cy pes) ..500-MoRubbct aod rubbct.lihe.. ~ ~ ~...$00 (IPCEh value)JuCe aod Cessile prolectlve

COVeffaeo ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ $00Fiber duccoo ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 480Polycchyleae............... ~ .4$0Traaid'ce dticc ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 200Somasclcooooo ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 100

THBRNALRESISTANCE OF JACKETSr DUCTWALLs,ANUSo)MsTIc CohTINcs

The equivalent thermal resistance ofrelatively thin cylindrical sections such as

jackets and Gber duct waUs may'edetermined from the expression

,/t Ng ~0.0104)a'( —

)thermal ohcn-feet .(D-I)

(4O)

with appropriate subscripts applied to8, sI, and D in vrhich D represents theoutside diameter of the section and t itsthickness. rc'is the number ofconductorscontained with the section contributingto the heat Gow through it.

THERMAL REslsThNcE BETwEEN CABLE

SIFhcE ANU SIROUNnnfc PIPEs

CONUUTT,.OR DUcr WALL

Theoretical expressions for the thermalresistance between a cable surface and asurrounding endosure are given in refer-ence 10. ~ indicated in Appendix I,these have been simpliGed to the generalform

rcrdt

, thermal ohm-feet1+(B+C1'm)Ds'41)

in which dt, B, and C are constants,D,'epresentsthe equivalent diameter of the

cable or group of cables andrs'the numberof conductors contained within Ds'. T~is the mean temperature of the interven-ing medium. The constants d4, B, and C

Table Vil. (:onsfcnts for Use in Equc(fons dt and 4I(A)

Coadlcloa B cA''a

mecalliccondulC...................IT „~......3.0 .........0.0"0 .........3.2..... ~ ~ ~ oo 10In dbcr duet la air...................ly .........2.1 .........0.010 .........$ .0....." "0 ~ 33Io dbcf duet lo cooetece.. ~ ~ ~ ~...,,. IT,,,....,.2.8 ..., „..0.024 ......,..4.d.. ~ .0 2TIa Craaidce duec la afr................ly ~, ~......3.0 .........0.014 .........4.4...... ~ ~ .0 2dIa craosfce duec lo coucrecc... ~ ~ ~.....1T,.......2.0 .....,...0,020,........3.T....... ~ .0.2-Gas-&lied pipe cable ac 200 psl......... 3. 1 .........1.10.........0.00$ 3,......,.2. I....... ~ ~ 0. 0$Oil dlled pipe cable....~............. 0.$4...... ~ ..0 .........0.004$ .........2.1...... ~ "2 ~ 4$

fye'1.00 Xdlameser of «able for oae cableI.dsXdhmecer of eablc for cero cables2.1$ Xdlamccct of cable for Chree cables2.$0Xdlamcccr of cable for four cables

OcTQBER 1957 Kci:cr, If(GraK—Tern pcratffre arid Load Capcbili!y of Cable Systems foi

15.6n','Kaz'/D,')t«+I.Gal+0.OIGTT„)lthertnal ohm.feet (42)

log —+(LF) log —FIn this equation AT represents the. differ-

thcrtnal ohm.feet (44)ence between the cable surface tempera-ture T, and ambient air temperature T, indegrees centigrade, T~ the. average of in which D< is th 'ter at which the

portion oE the therm ctrcuit com-» 'hesetemperatures and c the coe6icient of

mene'.and tt Is the num of con uc-tors contained within D,. 'he Gctitiousdiameter D» at which the effect of loss

factor commences is a function of thediffusivityof themedium a and the lengthof the loss cyde.c

emissivity of the cable surface. Assum-ing representative. values of T,~60 andT»~30 C, and a range in D,'f from 2to 10 inches, equation 42 may be simpliGedto

9.5n', thermal obtn«feet

(42A)D, ~1.02> ct(length of cyde in hours)

inches (45)

The empirical development o! this equa-tion is discussed in Appendix IIL For adaily loss cyde and a representative valueof a~2.75 square inches per hour forearth, D» is equal to 8.3 inches. Itshouldbe noted that the value of D, obtainedErom equation 45 is applicable for pipediameters exceeding D„ in which case theGrst term of equatioa 44 is negative.

The factor F accounts for the mutualheating effect of the other cables of thecable system, and consists of the

product'f

the ratios of the distance from the,reference cable to the image of each

of the other cables to the distance to thatcable, Thus,

The value of c may be taken as ualto 0.95 or i c nduits or ucts, andpainted or braided surfaces, an 0.2to 0.5 for lead and aluminum sheaths,depending upon whether the, surface isbright or corroded. It is interesting tonote that equation 42(A) checks thcIPCEA method of determining R, verydosdy with c~0.41 for diameters up to3.5 inches. In the IPCEA method 8, ~0.00411 n'3/D~'here 9~050+314

D~'or

D,'-1.75 lacbes and B 1,200 for Imrgervalues of

Dt'I

FEOTrvE. TaEBMhL RESIsThNcEBETWEEN ChBLES, DUCTS, OR PII'ESyAD AhfBIENT EhRTH ( t ~ c tt.~t» )As previously indicated, an efFective

thermal resistance 8<'ay be employed torepresent the earth portion of the thermalci:cuit in the case of buried cable systems.This effective thermal resistattce includesthe effect oE loss factor ana, in the case ofa m 'lticable installation, also the mutual

F~ — —. ~ . —(N-I tertas)

(46)

It will be noted that the value of F willva~ depending upon which cable is

sdected as the reference, and the maxi-mum conductor temperature wi11 occurin the cable for which 4LF/D» is maxi-

given in Table VIIhave been determined. heating dfects of the other cables of thefrom the experimental data given in refer- system. In the case of cables in a con-cnces 10 anti Il. crete duct bank, it is desirable to further

If representative values of T~~60 C recognizcadifferencebetweenthe thermalare assumed, equation 41 reduces to resistivity oE the concrete rrc and thctt'ri'hermal resistivity of the surrounding

,thermal obm-feet (41A) earthA.The thermal resistance between any

It should be noted that in the case of point in the earth surrounding a buriedducts, A,e is calculated to the inside of the cable and ambient earth is given by theduct wall and the thermal resistance of expression'cthe duct wall should be added to obtain

EE»c ~0.012ts, Iog tt'/8 thermal obm-Feet(4>)

y, ERMhL RBsIsThNcE PRost ChBLEs> m which p~ th th al ti ty of the't 't Ta

is e tance from the imageCoNDUITs~ oR DUcTs SUsPENDBD IN earth rlr isof the cable to the point P, and d is the

The thermal resistance R, b tween„„distance Erom the cable center to 2'.cables,conduits,orductssuspendedinstill From this equation and the principlesair may be determined from the Following discussed in references 3, 12, and 13, theexpression which is developed in Ap- following expressions may be devdoped,pendix L a licable to directly buried cables .and

to~i;type'-cab es.cgC

8»'.~0.012Pgtt'X

mum. N refers to the number oE cables orpipes, and F is equal to unity when N~ l.

When the cable @stem is containedwithin a concrete enydope such as aduct bank, the effect of the differingthermal resistivity of the concrete en-velope is conveniently handled by Grst as-suming that the thermal resistivity of themedium i that of concrete rF, through-out and then correcting that. portion ly-ing beyond the concrete envelope to thethermal resistivity of the earth i4. Thus

1'g

~0.012tI,+'$( c(.3;[i. '-. (in')~]]'~

ohm-feet'44A)

The geometric factor Gc, as dcvdoped- in Appendix Ilis a function of the depth

to the center of the concrete cndosureQ and its perimeter P, and may be foundconveniently from Fig. 2 in terms of theratio 4/2'nd the ratio of the longest toshort dimension'of the endosure.

For buried cable systems T, shbuld betaken as the ambient temperature at thedepth of the hottest cable. As indicatedm reference 12, the expressions usedthroughout this paper for the thermalresistance and temperature rise of buriedcable systems are based on the hypothe-sis suggested by Keaaelly applied inaccordance with the principle. of super-position. According to this hypothesis,the isothermal-heat Qow Gdd and tem-perature rise at any point in the soil sur-rounding a buried cable can be represented

by the steady-state solution for the heatQow between two paraM cylinders(constituting a heat source and sink)located in a vertical plane in an inGnitemedium of uniform temperature andthermal resistivity with an axial separa-tion between cylinders of twice the actualdepth of burial and with source and sinkrespectively generating and absorbingheat at identical rates, thereby resultingin the temperature of thc horizontal mid-plane between cylinders (Le., correspond-

ing to the surface of the earth) remaining.

by symmetry, undisturbed.The principle of superposition, as

applied to the case at hand, can be statedin thmnal terms as follows: IE the ther-mal network has more than one source oftemperatu:e rise, the heat that Qows atany point, or the temperature drop be-

tween any two points, is the sum of theheat Qows and temperature drops at

. these points which would exist if each

source of temperature rise were conside:ed

separatdy. In the case at hand, thesources of beat Qow and temperature riseto be supcrimposed are, namdy, the heat

7OS rober, DfcGratls—Temperatttre and Loatf Capability of Cable Syste":s OcTooER 1957

from the cable, the outward Qovr of heatfrom thc core of. the earth, and thc in-ward h(at Qovr solar radiation, and, whenpresent, the heat Qow from interferingsources. By employing as the ambienttemperature in the calculations thc tem-perature at the depth of burial of thehottest cable, the combined heat Qowfrom earth core and solar radiation sourcesis superimposed upon that produced atthe surface of the hottest cable by theheat Qow from that cable and interferingsources vrhich are calculated separatelywith all other heat Qows absent. Thecombinedheat Qovr from earth core andsolar sources results in an earth tempera-ture which decreases withdepth insummer;increases.vrith depth in winter; remainsabout constant at any given depth on theaverage over a year; approximates con-stancy at all depths at midseason, andin turn results in Qovr of heat from cablesources to earth's surfac, directly to suz-face in midseason and winter and in-directly to surface in summer.

Factors vrhich tend to invalidate thecombined Kennelly-superposition princi-ple method are departure of the tempera-ture of the surface of earth from a trueisothermal (as evidenced by melting ofsnovr in vrinter directly over a buriedsteam main) and nonuniformity ofthermal resistivity (due to such phe-nognena as radial and vertical migrationof moisture). The extent to which theKennelly-superposition principle methodis invalidated, however, is not of practicalimportance provided that an over-all oreffective thermal resistivity is employedinthe Kennelly equation.

Special Conditions

Although the majority oE cable tem-perature calculations may be made bythe foregoing procedure, conditions fre-.quently arise vrhich require somewhatspecialized treatment. Some of theseare covered herein.

EMERCENCY RATINCS

Under emergency conditions it is fre-quently necessary to exceed the statednormal temperature limitof the conductorT, and to set an emergency tempegaturelimit T,'. If the duration of the emer-gency is Iong enough for steady-state con-ditions to obtain, ~then the emergencyrating I'ay be found by equation 9substituting T<'or T< and correcting ~,or the increased conductor temperature.

If the duration of thc emergency is lessthan that required for steady. state con-ditions to obtain, the emergency ratingof the line may be determined from

Tc'-I'~1+ YcXN~'-R«')-(2's+Z

(1+.Yg)8«'n

which 8«g's thc effectiv transientthermal resistance of the cable system forthe stated period of time. Proceduresfor calcuhting E,g'or times up to severalhours are given in reference 14, and forIpper times in references 15-17.

~ ~

C

THE EFIECT.op ExTIumoUs HEATSOUECEs .

In the case of multicable installationsthe assumption has been made that allcables are of the same size and are sim-ilarly loade«L When this is not,the casethe temperature risc or load capabilityofone particular equal cable group may bedetermined by treating the heating effectof other cable groups separately, intro-

. ducing an interference temperature risedTg„g in equations 1 and 9. Thus

T,-T~~dT<+dTc+dT«~gdegrees centigrade (1A)

T~-(T(«+dTa+ d Tg» g)I~gg(1+

Yc)~ca'iloamperes(9A)

in which dTg,g represents the sum of anumber of interference effects, for eachofvrhich .

d2 «»g (IVa/LF)+IVclksgdegrees centigrade (48)

Ag<«~0.012«r,»'Iog Fg,g thermal ohm-Eeet(49)

((Egg'X«E«g'X«E««')" (EN«'~)

(«Eg«X(E««X(E«g) "«EN«

(50)

where the parameters apply to each sys-tem vrhich may be considered as a unit.For cables in duct

A.g 0.012»'(r«log F«g+N(ggg-rr«%lthegnud ohm-Eeet (49A)

Because of the mutual heating betvreencable groups, the temperature rise of theinterferin groups should be recheci:ed.If all the cable groups arc to be givenmutually compatible ratings, it is neces-sary to evaluate IV< for each group bysuccessive approximations, or by settingup a system of simultaneous equations,substituting for W, its value by equation15 and solving for I.

In case dT«ng or a component of it isproduced by an adjacent steam main, thctemperature of the steam T„rather thanthe heat Qow from it is usually given.Thus

dT«»g

~gag

degrees centigrade (Sl )

I

kiloagnpeges (47)

vrhere 8« is the thermal resistance be-tween the steam pipe and ambient earth.

A RIAL CABLEs

In the case 'of aerial cables it may bedesirable to consider both the cffects ofsolar radiation which increases the tem-perature rise and the effect of thc vrindwhich decreases it.gg Under maximumsunlight conditions, a lead-sheathed cablevrill absorb about 4.3 watts per foot perinch of profiIe" which must be returnedto the atmosphere through thc thermalresistance 8,/»r. This effect is con-veniently treated as an interferencetemperature rise according to the rela-tionship

dT«((« ~4.3Dg'/I,/»rdegrees centigrade (47A)

For blacI: surfaces this value should bcincreased about, 75%.

As indicated in Appendix II, the follow-ing expression for l(I, may be used whereV» is the'velocity of thc vrind in miles perhour

3.5»'

'(~V/D,'+0.62 )thermal ohm-feet (42B)

UsE CF Low-R'EsrsTIvITY Bane.LIn cases where thc thermal resistivity

of the earth is excessively high, the valueof 8,r may be reduced by bacldiiling thetrench with soil or sand having a lowervalue of thermal resistivity. Equation44(A) may be used for this case if r r, thethermal resistivity of the bacldill is sub-stituted for grg, and Q applies to thezone having the bacldili in place of thc.zone occupied by the concrete.

SINOLE-CCNDUcroa C((1BLES IN DUcTwITH SCLIDLY BCNDED SHEhTHS

The relatively large and unequal sheathlosses in the three phases vrhich may resultfrom this type of operation may be deter-mined from Table VIoE reference 1. Itvrillbe noted that

Yrgg ~g

'gcg ~

~ IS

vrhere expressgons for I>gg/P etc., appearin the table. The resulting unequal valuesof Y, ia the three phases vrillyield unequalvalues of (E„and equation 5 becomes forphase no. 1, the instance given as equa-tion 5(A) on the following page.

OCTOBEE 1957 3 crgcr, rf&Gralig—Terr:pcrafggrc a»d Load Gxpabil«Iy of Cab!c Systcr»s 759

4Tci We[/fi+rfrsI/fre+/fe.+(LP)/f,pj+. 'fq«(fF)kpe] thermal ohm-feet (SA)

where qra Is the average of qrsI qrs> and qrs.

Table VIII. Coustanls for Use in Eque6on 53

AreraseAT

ARMORED CABl.EB

In multiconductor armored cables aloss occurs in the armor which may beconsidered as an alternate to the conduitor pipe loss. If the armor is nonmag-netic, the component of armor loss Yato be used instead of Yp in equations 14and 19 may be caIculated by the equa-tions for sheath loss substituting theresistance and mean diameter of thearmor for those of the sheath. In cal-culating the armor resistance, accountshould be taken of the spiralling"effect forwhich equation 13 suitably modifiedmay be used. If the armor Is mag-netic, one would expect an mcreasc inthe factors Y, and Y, in equation 14since this occurs in the case of magneticconduit. Unfortunately, no simple:

pro-'edure,

is available for calculating theseeffects. A rough estimate of the induc-tive effects may be made by using the pro-cedure given above for magnetic conduit.

A simple method of approximating thelosses in single conductor cables vrithsteel-wirc armor at spacings ordinarily,em-ployed in submarine installations is to as-sume that thc combined sheath and armorcurrent is equal to'the conductor current.sThe effective a.c resistance of the

armor'ay

be tdcen as 30 to 60% greater thanits d-c resistance corrected for lay as in-dicated above. Ifmore accurate calcula-tions are desired references 19 and 20willbe found usehl.

EPPEcT oP F0RcED CooUNG

The temperature risc of cables in pipesor tunnels may be reduced by forcing airaxially along the system. SimiIarly, inthe case of oil-Glied pipe cable, oil maybe circulated through the pipe. Underthese conditions, the temperature rise isnot uniform dong the cable and increasesin the dir'ection of EIow of the coolingmedium. The solution of this problem isdiscussed in reference 21.

based upon all of the data avaihbie andincluding the effect of the temperature ofthc intervening medium.

The theoretical expression for the casewhere the intervening medium h dr or gasas presented in reference 10 snay be genenI.Ised in thc following form:

and a range of 150-350 for De'T~ equation54 reduces to equation 41 «ith the valuesof A, B, and C given in Table VIZ .

In thc case of cables or yipes suspendedin still air, the heat loss by ndhtion maybe dctcrauncd by the Stchn-Bolznsannforsnuh

rs','

—, +b+cT~(53)

rs'W(radhtion)~0,139Ds eKTa+273)e (Ta+273)ej10»

watts ycr foot (55)

E,cathe effective thcrsnd reshtsuce be-tween cable and enclosure in thclnulobm-Eeet

D,'~ the uble diameter or equivaIcntdhsneter of three cables us Inches

4T~the tempcnture dIEfcrenthI in degreescentigrade

P~thc prcssure In atmospheresT~~mesn tesnperature of the medium in

degrees centigraders'~nusnber of conductors Involved

The constants a, b, and c in thh equationhave been established empiYicdly as follows:Conslderusg b+cTe as a constant for themoment, the analysis given in reference10 results in a value of a~0.07. With athus established, the data given ui reference10 for cable in pipe, 2nd in reference 11for cable in aber and txauslte ducts wereandyzcd in sinuhr nunner to give thevalues of b and c which are shown in TableVIIL

In order to avoid a reltentivc calcuhtloaprocedure, it is desirable to assume a valueEar 41 since its actual value will dependupon ffre and the heat flow. Fortunately,as 4T occurs to the 1/4 power in equation53, the use of an average value as Iadicatedin Table VIIIwill not introduce a seriouserror,

By further restrictissg the range ofD,'o I-I Inches Eor cable in duct orcoaduic and to 3"5 inches for pipe-typecables, equation 53 is reduced to equation41.

where e is the coeKcicnt of emisslvityof the cable or yipe surfaces Over thelimited temperature nssge in which wc areInterested, equation 55 snsy be shnplificdto"

rs'W (radiation) ~0.102Ds'4Te X(1+0.01671 ~) watts pcr foot (SSA)

Over the same tempenture nnge theheat loss by convection from horixoatalcables or pipes is given with sufficientacciuacy by the expression

rs'W(convection) ~0854 De'dT(dT/De') +e

watts yer foot (56)

m which the numcrica1 constant 0.064has been selected for the best Eit with thecarefully deternsined test results reportedby'cilaunss on 12, 3.5 aud IQB-Inchdhmctcr bhck pipes (e~0.95). Inci-dentally, this value also represents thebest Eit with the test data on 1~5 inchdiameter bhck pipes reported by Rosch."For vertical cables or pipes the value oEthis numeriesI constant may be hicrcasedby 22%"

Combiniag equations 55(A) 2nd 56 weobtain the relationship

4Trs'W(total)

15,8rs'r'K

AT/Dr') a+1.6e(I+0.0167') Ithen'hm.feet (42)

Cable lu suetatuc couduls,„...............0.07.. ~ .~.......0. 121...........0.0017..:. ~ .. ~ ....20Cable lu sber duce lu air..................0.07............0.03d...........0.0000............%Cable lu dberdu«t lu coucrete.. ~ ..~.......0.07...„,......0.043.... ~ ~.....0.0014..„... ~ ~ . ~ .20Cable la srauslse duct lu afr................0.07............0.08tl.. ~ ~......,0.0008......... ~ ..20Cable lu trauslie duct lu coucrete..~..... ~ ~ .0.07...., ~ ~.....0.079....~.....,0.0010..„,. ~ ~ ~...20Gas.elled pipe type cable at 200 pal.........0.07.„,....., ..0.121...........0.0017............10

Appendix I

Development of Equations 41, 42,and Table VIX

Theoretical 2nd semicmpiricd expressionsfor the thermal rcslstarice between cablessurd als eaclosirsg pipe or duct wail aregiven in refercricc 10. Further data on thethermal resistance between cables aridSber and tnrssitc ducts are given in ref-erericc 11. For purposes of cable cating,it is desirable to develop staudardhcdexpressions for these thermal resistances

rs'AAre~, thcrmd ohm-Eeet

(41)

in which the values of the constants A,B, arid C appear ln Table VII.

Ia the case of oil.6Iled pipe cable, theanalysis givers ia referesicc 10 gives thefollowing expression

rs'.60+0.025(Dr" T~'dT)~'hermalohm-Eeet (54)

Assumiug aa avenge value of 4T~7 C

If the cable h subjected to wind havinga velocity of V» miles pcr hour, the follow-ing cxprcssiors derived from the work ofSchurig and Prick" should be substitutedfor the convectiors comyoricnt.

rs'IV(coavectiors) ~0.286Dr'4TvVu/De'atts

per foot (56A)

Combining equations 55(A) arid 56(A)with T~~45 C

4T3.5rs's'IV(mlsl)

D;(QV„/D;+0.62e)thermal ehm-Eeet (42B)

760 iVeLer, yrlcGrc!r' Terrperafare and Load Capabilily o/ Cable Svs.'eras Ar-,nnm. 1057

g,g

Appendix'l Table IX. Compadsoa of Values of go (+F)for Sinusoidal Loss Cydes at 30$

Loss Factor

Da«8.3 Inches. As indicated in the Chirdpaper of reference 3. however, theorcQcallyD/c shouM vary as the square root of theproduct of the dilfusivity and thc thnelength of the loading cyde. Hence as thcdiifusivitywas taken as 2.?5 square inchespel hour ia the above,

Da « Ig02X

V acXlength of cyde in hours mches(45)

Table IX presents a comparison of thevalues of per cent attainmcnt factor forsinusoidal loss cydes at 30% loss factor ascalculated by equations 45, 66, 62(A), and 63and as they appear in Table IIof the Grstpaper of reference 3.

Appendix" IY.'Cafculaations forRepresentative Ca6le Systems

Determination of the GeometricFactor Gi for Duct Eanld

'

Considering the surface of the ductbank to act as an isothermal cirde ofradius ra, the thermal resistance betweenthe duct bank and the earth's surface wUIbe a logarithmh function of ri and Li thedistance of the center'f the bank bdowthe surface. Using the long form of theKennelly FonnuhLs we may deflne thegeometric factor Gi as

Li+O'Li'-ri'i«

log ri~og Igr/ro+O/(gr/ro)'-gl (gg>

In order to evaluate rb in"'terms of 'thedimensions of a rectangular duct bank, letthe snuiier dimension of the bank be xand the larger dimension bP'y. The radiusof a cizde inscribed within the duct banktouching the sides is

li fddIDesccfpdou,

Srst«u laches Ifehec ShsakllaV/lseugea

pipe.... 53/53... dl/d2...d3/ddpipe.....dd/dd... 50/57....53/50plpe..... 55/5... SO/58.. ~ .54/53plpe. o ~ ..58/58... 5 l/50...55/53cable. ~ e ~ \ ~ ~ ~ 80/80~le'....77j75. ~ '.77/75....77/77cableo ~ o oT1/71cableoooo ~ ~ ~ ~ ~ ~ ~ 53/52cablcoo ~ . ~ ~ ~ ~ ~ ~ ~ o75/74cable............77/Tdcable....83/80...83/81cable....Td/74...74/173cable....TO/55. ~ .To/5Tcable.. ~ . d0/54. ~ . 55/54 ..51/53

I ~ ~ ~ ~ ~ ~ 4 5Iloo ~ ee 5 dIIIoooooo 8 5Iveoooo ~ 10 dVo ~ ooo ~ ~ 0 dVIe ~ ~ ~ ~ 1 5VII~ eeo ~ I 0VIII.... 2.0IXooo oo 3 0Xo ~ ooo ~ 3 4Xa ~ roe 3 4XI ~ oooo 3 TXII eoo 4 2XIII 4.d

a Dhduglelcy«4.7 scuse» lucha pcr hour.

15-Kv 350-NCN—3«Conductor. Shielded Compact Sector Paper andLead Cable Suspended in Air

D, «0.618 (equivalent round); V«gaugedepth «0.539 inch

Dc «2.129; T«0.175 inch; l«0.120 inch

12.9 /234.5+SINcg ggcgg, —

('

0250(234.5+75)«37.6 microhms per foot (Eq. 10A)

Deca 2.129-0.120 2.009 inches (Eq. 12)

fs «x/2 (58)

and the radius of a hrger cirde embracingthe four corners is

/O/x'+g'r

rr2

Lct us assume thaC the cirde of radius rilies between these circles and the nugnitudeof ra Is such Chat it divides the thernulresistance between rl and rs in directrehtion to the portions of the heat Geldbetween rs and rs occupied and unoccupiedby'he duct bank. Thus

th~~1 cQcult co~I9SSSS3Equation 62 may be written in the form

8 '-8 +8 +(LFXd -8„)thernul ohmofeet (62A)

In terms of the attainment factor (cf F), onemay write

(AF)~ca (ci FXNcc+/t¹)thernul ohmofect (63)

Equating equations 62(A) and 63 obtainsChe rehtionship

Bcc«(1-x)8¹-x/t« thernul ohm.feet (64)

where

37.9C —'ggr roiororrroo

2.009(0.120)pcr foot at 50 C (Eq. 11A)

kg «1.0; kr«0.6 (equivalent round)(Table II)

lac/>c «37.6g Ycc O.OM

(Eq. 21 and Fig. 1)

$ «0.616+2(0.175+0.008) «0.982 inches

J4 Jkp «62.6; F(xp') «0.003 (Fig. 1)

Ycp«4 0 003 «0.002

(Eq. 24A, and aote to Table II)1+ Yc «1+0.008+0.002 «1.010

s «1.155(0. 175+0.OOS)+0.60(0.539)«0.534 inch (Eq. 32)

396 2(0.534)1 s

Yc«Y¹« —( «0.019

15?(3T.6) 2.009 J(Eq. 31A)

n xy-~ s f rsNlog- —r(log-) or~ ~**-.)( .)

~ ™xy/ rsNtog ——(log -)ri grss-r,s)( r<)

from 'which

log fi«( «) log (I+ +log-2A~ y) ( xs) 2(40)

It is desirable to derive ri hl terms of theperimeter P of the duct bank. Thus

P «2(x+y)«4- (1+y/x) .

2

I-(cfF)x«1-(LF) (45)

Since

8¹ «0.012/s'p log Dc/Dc ~

thermal ohm-feet (44)and therefore

83log Dc/Dc « —,KI-x)/tca-x/eccl»'/I (47)Plog- log—

2 4(1+y/x) (41)

Thc flrst paper of reference 3 presentsthe results of a study m which a numberof typical daily loss cydes and also sinu-soidal loss cydes of the same loss factorwere applied to a number of typical buriedcable systems. The results indicated thatin all cases the sinusoidal loss cycle of thesame loss factor adequately expressed themaximum temperature rise which wasobtained with any of the actual loss cyclesconsidered.

An analysis by equations 65 and 6T ofthe calcuhted values of attaiameot factorsfor sinusoidal loss cycles given in Table IIand tile corresPoading cable systcra Pscamoetcrs given in Table I of the Grst papa'freference 3 yields a most probable value of

The curves of Fig. 2 have been developedfrom equations 57, 60, and 81 for severalvalues of the ratio y/x. It should benoted in passing that thc value of ri«0.112P used in reference 13 applies to ay/x ratio of about 2/1 only.

R„/Rcc «1.010+0.019 «L029 (Eq. 14)

qg«qc«I+—'«1.019 (Eqs. 18-19)0.019

1.010

c,«3.7(Table V); E«15/Q«S.T;cos y «0.022

Appendix ill 0.00276 (8.7)'f3.7(0.022)i2(Q. 175)+O.BSC

0.681«0.094 watt per coaductor foot

(Eq. 36 and text)

(Vote: Ia computiag dielectric loss on

Empirical Evaluation of D,In order to evaluate the effect of a cyclic

load upon the maximum temperature riseof a cable system simply, it is customary toassume chat the heat Gow in the Goal

~ portion of the thermal circuit is reduced+by a factor equal to the loss factor of thecydic Ioado The point at which thisreduction commences may be convenientlyexpressed in terms of a Gctitious diameterDao Thus

Aca'«Dec+(LF)/tcs thcrnul ohm-feet (42)

For greater accuracy, it is desuable toestablish the value of Dc empiricaily ratherthan to assume that Ds is equal to the

hich the earth i~con o

hn~nggc ~ 10 Ar %I,M.o~/l. 7 ~/. g ~, o ~ 4 r 4 / -a g/g.'r. C / „:g.

*«agir'a" «t

Il'

sector conductors, the equivalent diameterof the conductor is tatcen equal to that of aconcentric round conductor, Le., 0.681inch for 350 MCM.)

700 (Table VI); Gr ~0.45(Table VIIIof reference 1)

~r 0.00522(700(0.45) } 1.64thermal ohm-feet (Eq. 39)

n'3; ~ ~0.41 (assumed)

9.5(3)1+1.7(2.129(0.41+0.41)]

~7.18 thermal ohm.feet (Eq. 42A)

Nca ~1 64;+1.019(?. 18) ~8.96thermal ohm-feet (Eq. 8)

dT<~0;094(0.82+7.18) ~0.75 C (Eq. 6)

T, ~40 C (assumed)

I 81-(40+0.8)37.6(1.010(8.96)1

~0.344 kiloampere (Eq. 9)

If the cable is outdoors in sunlight andsubjected to an 0.84 mile per hour wind

3.5(3)

2.129(V 0.84/2.129+0.62(0.41)i~5.59 thermal ohm-feet (Eq. 42B)

. Ace' 1.64+1.019(5.59) ~7.34thermal ohm-feet (Eq. 8)

ATrrrr (4.3)(2.129)(—) 17.1 C/5.59 i

(3)(Eq. 47A)

dg c96'e

cla"

L c4X5

/'r )images

~ sJ

dg ~ 96/"

dt ~ c 87.5"

cc. 78 5.3e.

I b~ 43.5

Te «30 C (assumed)

)81-(30+0.6+17.1)y (37.6)(1.010)(7.34)

~0.346 lriloampere (Eq. 9)

In this particuhr case the net effect ofsohr radiation and an 0.84 mile per hourwind is to effectively raise thc ambienttemperature by 10 degrees, which is arough estimating'alue commonly usecLIt should be noted,'owever, that thiswill not always be true, and the procedureoutlined above is preferable.'4

rcc ~

69-Kv Ir500-MEN—Single-"Conductor Oil-Filled Cable in DuctTwo identical cable circuits will be

considered in a 2 by 3 fiber and concreteduct structure having the dimensionsshown in Fig. 3.

De~0.600; De~ 1.543l Dr~2.113;T O.N; D, 2.373; r 0.130 inches

12.9Te~75 Cl Rec~ —~8.60

1.50 p,microhms per foot (Eq. 10A)

Dna ~2.373-0.)30~2.243 inches (Eq. 12)

37.9Rc

(2 243)(0 30)~ 130 microhms

per foot at 50 C (Eq. llA)1.543 -O.BOO(1.543+1.2003 c

1.543+0.600(1.543+0.600J0.72; k~ O.S (Eq. 23 and Table il)

5I.O

on 69-lcv $ ,500.MCM

ci: pre/kc ~ ll9r'cc ~0.075(Eq. 21 and Fig. 1)

$ ~9.0 (Fig. 3) i Rec/4~10.75'(x~')~0.075 (Fig. 1)

Ycrr 4( )0075 0007 (Eq 24A)(9.0) .

1+ Yc ~ 1+0.075+0.007 < li082

Assuming the. sheaths to be openwircuited,Yea ~0

1+- —'.006:"(Eq. 30A)

Rec/Rcr ~ ~ 1 082+0 006 1 088 (Eq 14)

0.006 ~

1.082qc aqc w1+.—'],006 (Eqs. 18-19)

I ~cr ~ (Table V); 8 ~69.'y 3 ~40;

cos 4 ~0.0050.00276(40) r(3.5.'(0.005)

2.113log—1.543

0.57 watt per cond ctor foot (Eq. 30)

Fig. 3. Assumed duct bonk conR9uratlon for typical calculations

tj 4. if oil@lied cable (Appendix lV)

7R'? rVchrr, N'd7rrrflr—Trrrr6crahurc and Load Caoabrvitv of Cable Svsfrrrrs QCTOBBR 1957

2

iv'h 2;(Pg «5.0 (Table VI) aTc 0.57(0.45+1.75+0.24+4.63) 4.0 C

2.113 ~ . (Eq. 6)88«0.012 550 log ~ ~

~

> 45r

Wcj (lr X8 BQX1.082) «9 31 Ir«0.90 thermal ohm-foot 6((Eq. 38) r watts per conductor foot (Eq. 1S)

4Trf6g «(9.31Irr KI.QOBX0.80)+0.5?l)3.812.37+087 «2>17'+28.5Irs degrees centigrade inthermal ohm-feet (Eq. 41A) circuit no. 2 (Eq. 48$

irc«480 (Table VI); 1«0.25; - Simihr calculations for the second circuitcp ., Dc«5.0+0.5«5.50 for aber duct yield the foUowing values.

0.0104(480X0.25) lgc'.18; 4T<«3.4; Wgg«17.44IEE',5.50-0M ~ 4T(,g «1.71+53.2IE'n circuit no. 1

120(asumed); jfc 85 (Table VI)'... ~ „:.(9.31)(6.$ 5)0.715-0.859I22 (Eq. 9A)

. -(-.)('-:)('=".)('-)("=) ';, ':-"'"..";".";;,",.„...«42,200 (Fig. 3 and Eq. 46)

Solving simultaneously Ir«0.714; Ir«1>(P 0.483; — hs: 0.487 kiloampere.

2(18+27)'

18

0> 0 87 (Ptg 2) 138-Kv 2000-2,102( 2(fgh-Pressure 5z~Oil-Filled Pipe-Type Cable 8.625-

'c'(at80% loss factor) (0.012)(85)(l)X Inch&utside-Diameter Pipe8.3

'I 4(43.5)

log —.+0.80log[~42~)J)+ The cable shielding will consist of anhrtercalated 7/8(0.003)-inch bronxe tape—

0.012(120-85X1)(6)(0.80)(0.87) l.inch lay and a single 0.1(02)-inch D-«6.79 thermal ohm-feet (Eq. 44A,) shaped brass skid «Ire—LS-inch ly. The

cables will lie in cradled conBguration.Ec'at unity loss factor) «8.44

~

~th hm.feet (Eq. 44A) Dc«1.632; Dr«2.642> T«0.505;16 Egg. l2 p

R'gtg'0.90+1.00$(1.7k+0.24+6.79)'

72 ther«) ehtu feet (Eu. 8) 7 70 <. 8 (189)(234 5+70 )4'.57(—+L?4+0.24+8.44 8M 625 microhms per foot (Eq. 10A)

«6.2 C (Eq. B) ForshfeIdfngtape448«7/8(0.003)«0.00263lf«I.Q; p«23.8; 2 «564 (Table 1)Tc 25 C assumed),

75-(25+62) 23.8 ( (2.68)',60(1.082)(9.72)4(0.00263)$ ( 1 j

«0.696 kiioampere (Eq. 9) 564+50)—) «62,900 mlcrohmsTo illustrate the case where the cable

564+20'ircuits

are not Identical, consider the'er foot at 50 C (Eq. 13)second circuit to have ?50-MC'hf con-ductors. For the erst circuit

. 'or skid wiregg r(Q 1)2 Q Q157'P «3; (IF) «0.80 (assumed);

(l«1.5; p«38; r«912 (Table I)

F« — —«92.4 (Eq. 46)9 9 38E. (2.6Br)2R, —1+ —X(8

tlog —+0.80 log (—92.4) J+

8.3 A(43.5) r I «11,100 microhmsS.S ( 8.3 . )J

0.012(120-8SX1X3)(0.80X0.87) per foot at 50 C (Eq. 13)

5

~

~

«3.74 thermal ohm-feet (Eq. 44A) l (62.9)(II.I)1R, (net) «L- JI>000

(L(62.9X11.1)J

«9,435 microhms per foot at 50 C

k8«0.435; kp «0.35 (Table II)0.012(1) X(85 log 456-;3(120-85)(0.87)) Rcg/kg «14.6l Ycg «0.052(L7) «0.088

«3.81 thermal ohrn feet. r (Eq, 49) (Eq. 21, Fig. I, and text)ls

l4'.90+1.006(1."4+0.24+3.74) S 2.66+0.10 2. 6; Rc /k 17.2;«6.65 therrrral ohm.feet (Eq. S) F(KP') «0.035 (Fig. 1)

/1.632% 8

Ycp «4( ) (0 035X1 7) 0 083( 2.76)(Eq. 24A and text)

1+ Yc «1+0 088+0.083 «1.1?1

' 52.9 leg—(2.3X2.76)2.66

«20.0 microhms per foot (Eq. 29A)

(20.0) 2(1.7)Yg«Ygc««0011(Eq. 2?A and text)

Y (0 34X2.76)+(0.1?SX8.13)6.35 ",* (Eq. 35)

Rcc/Rcc «1 171+0.011+0272 L554(Eq. 14)

0.011 . 0.011+0.372~ 1.171 '.171

I~ (Eqs. 18-19)

cr «3.5 (Table V); .E «138/Q3 «80;cos p «0.005

0.00276(80)2(3.5X0.005)

2.642log—1.632

«1.48 watts per conductor foot (Eq. 3B)

A«550 (Table VI); 8r 0.012X

(2.642(

550 log—') «128 thermal'.1.632)

ohm-feet (Eq. 38)

»2«3; Dc'.15(2.66) 5.72;

3(2.1)Ru —'

77 there.tet5.72+2.45

ohm-foot (Eq. 41A)

ptr«100 (Table VI); t«O.SO;D, «8.83+1.0 9.63 for 1/2-inch

wall of asphalt mastic

0.0104(100X3XQ.SO)

9.63-0.50«0.17 thermal ohm.foot (Eq. 40)

Assume pc«80, I «36 inches, (LF)«0.85;II«1, F 1

88'(at 85% loss factor) 0.012(80)(3) X

log—+0.85 log —(1)

«2.85 thermal ohm.feet (Eq. 44)

80'at unity loss factor) «3.38thermal obm.feet (Eq. 44)

Pgcg«1.38+1.M9(0.7?)+1.327(0.17+2.85)

«6.1? thermal ohrn-feet (Eq. 8)

4Tc «1.48(0.69+0.5 5 -,'0.17+3.3S) «7.4 C(Eq. B)

Tc «25 C (assumed);

70-(25'7.4)4 3 (6.35X1.171X6.17)

«0.905 ki!osmpere (Eq. 9)

References

1. Catcocattox or tna Euactstcu. Pooka,sxsar UNoskokoaNO Casass, D. )tL Shameae. TbcElectric Iosraol, Bast Pittsburgh. Pa MayNor. 1032.

Loca Pactoa axo EttotvaLsxt HoaasCoxraaso, P. H. Buiier, C. A. Woodrau; Ztec.tricot W'orld, Ncw York, ¹ Y., vai. 02, ao. 2, 1028pp. 50-60.

3. Stxroctatt ox Tsitrskatasa Rms or Casters,AIRE Caauaittee Report. AIEE Tre>aroctio>tl>vol. 72, yt. III, Juae 1053, pp. ~L4. h-C Rsarstaxcs or Ssoxaxraa Caucus ntSrsst. Prrs. L Meycrhotr, O. S. Eager, Jr. Ibid.,raL 68, pt. II, 1049, pp. 815-34.

d. Pkorttxttv Enact ix Souo axo HotaoerRomeo Coxooctoas, A, H. M. Araeid» Ieur>tot,Iaaututioa ol Eicctticai Eagiacecs, Laodoa,Eagiaad, vol. 88, pt. Il, Aug. 1941, pp. 340 59.

o,Eaov&aaksxv Loaass nc Mattress Parka.

INaotatso La*~russo Cast,aa, haxoasoar>o Uxakxokso, Cakavtxo Baaaxcsa 3-PrtaasCaaksxv, A. H. 5>L Arnot* Ibid., yt. I. Peb.1941, pp. 52-63.

T. Ptrs Loecss M Norocaoxsttc Ptrs,MeyerhotL AIEE Trouracliosr, vaL T2, yt. III,Dcc. 1053, yp. 1260-T$ ,

8. A»C Rsarstaxcs or Prrs-Casts Svatsxs

»mt Ssoxaxtaa Coxaactoks, AD1E CommiueeReyerL lbQ ~ roL Tl> pt. III,Ja>L 1952, pp. 30414.

'.

AN Rsstataxcs or Coxrsuttoxar. StaaxoPa»as Caucus nt Noxxstaaue Duct axo ueIaou Coxomt, R. W. Burteu> ItL Morda Ibid.,voL 74, pt. 111, Occ. 1055, yy. ION 23.

10. Tas Tasaxu. Rsetstaxcs Batvrssx Cosc,ssaxo a Saakoauonto Piro oa Duct Waar F> H»Boiler, J. H. Zcher. IbQ., vaL dy, yt. I. 1050,pp. 34~9.11. Haav Ta*xsrsa Stout ox Po»sa CasusDucts axo Deer heaaxsc,tss, Paul Cceebicr, OuyF. Baraett. Ibt>L, voL 69, pt. L 1050, pp. SST57.

12. Trts Tsxrseataas Rtss or Baatso CasuasaxttPtrss. J. K, Ireher, lbi>L, voL 68, pt. I. 1940,yp. 9-21.

13. Tas Taurus*toss Ries or Case,ss nt a, Doer Baxr, J. H. Neher» Ibid„pp. ~0.-.14. Ott Faow axo Pasaaaas Caacouattoxs roaS~Ntatxso Ott> Fttuso Casas Svstaxs»B. H. Bauer. J. H. Ifeher> P. O. Weutstoa» lb»d.>vaL 75, yt. III,hpr. 1055, pp. ISHl41$ . Tasaxax. Tkaxarsuts oN Boktso Castaa,F. P Bailer. IS@., vaL TO, yt. I, 10SI, pp. 4~.ld. Tas Dstsaxtxattox or TsxrsaatoksTaaxatsxts nt Cast,s Svatsxs sv Msaxs or axANaaooaa Coxrotak» J. H. )Ichor. Ibid., yt. II,1051, pp. 1361-T1.

17. h Stxrurtso M*tasxattcaL Paocsaakaroa Datsaxtxtxo tas Taaxatkxt TsxrskataasRtssor Casut Svstsxs.J.H, Irchcr IbQ, vol.72, pt. IILhug. 10$ 3, pp. 712-1S.

~ IiL Tss Hsattxo or C>tacks Exroaso to tasSax tx Raas, E» B. Wedmere. leuc>>oL Iaatituttoa at Electrical Eagloccra, vcL TS, 1034, pp.737&L10. Loaaas tx hat>ossa Stxaas~xaactok>La~russo h»C Cast.ss, O. R. Schurig> H P.KuehuL F. H. Buuer. AIEE Trc»roctk>ur> rai.48, hpr. 1020, yp 417~.2tL CostaisotroN to tas Svaov or Loaass axoor Ssar4>ooottox or StuoasCoxuoctoa Akxoaso Caaass, I Boaoae. Zt>ttrol>cairo, Miiaa,Italy, 1931, y, 2.

2L hattnctaa, Coouxo or Poxsa Cast.s, F. H.Bauer. ALEE Troarcctlear, vai. Tl, yt. 111, hug.19S2, pp. ~l.22 Soar acs Hs*TTaaNSxiaaIQK» R» K,HenaiaaTio>tt>xticer, htacricaa Society at hfcchaoicciBagiaecrv. Neer York, ¹ Y„roL 51, pt I, 1020.pp. 287~23. Tss Caakaxt-CakkvLvo Caracttv or Rosssa.INsuaatso Coxoacroaa. S. J. Roach. AIEETrout>xrioor, raL ST, hyr. 1038, pp. 15~7.24. Hsatnto *No Coaksut~kttxo Car*cttv0' Baa' Couattctoks rok Oataooa Sskvics>O. R. Schurig, O. W. Prick. Ce»>rot ZfcclricR>rserr, Scrtcaectady, ¹ Y„vaL 33, 1930, y. 141.

Discussion

C. C. Barnes (Central Electricity Authority,Londan, Enghnd): This paper is an excel-lent. and up-~te study of a most hnpar-tant subject. Par 25 yeirs D. M.

Simmons'rticled

have been used for fundamentalStudy on current rating problems, but thenumeraug cable deveiapmentg aud changesin indtaihtian techniques introduced inrecent years have made a modern assess-ment af this subject very neccsgary. Theessential duty af a power cable is that itshould transmit the maximum current (arpower) far Specified instaihtian canditiang.There are three main factarg which deter-mine the safe continuous current that acable willcarry.

1. The maximum yertnidgible temperatureat which itg campanentg may be aperatedwith a reaganable factor of safety.E. Thc heatMiggipathtg yrapertieg af thecable.

3. The instalhtian canditians and ambientcondithn5 obtaining.

In Great Britain the basic relerenccdocument is ERA (The British Electthaland AHied Industries Regeirch Asgachtha)reyatt F/TI31t published in 1939, and in1955 revised current tutiag tables forsolid-type cables up ta and including 33 kvwere pubHshed in ERA report F/TI83.A more detailed rcport sumtnarhing themethod of computing current ratings farSOHd-type, ail GHed, and gas.preggure cablesis naw being GnaHted and mn be publishedas ERA rcport F/TI87 satne time in 1958.

Until recent years currertt ratings ineat Britain have usually bten considered

an a continuous basis, but the ltnpartanceof taltittg into consideration cycHc ratingshag naw been eirefuny studied, since con-tinued high metal priced have forced cableusers to revietr carefully the effects ofcyclic laadings. A report has recently been

issued in which a simple methad h yre-gcnted for the rapid calcuhthn of cycHc

ratings.'ableV giveg Specific inductive capaci-

tance values far yaper ast paper htguhtion(SOHd type), 3.7 (IPCEA value); paperinguhtian (Other type), 33-4A Is it pad-sible ta Hdt the other types and theirapyrapriate Specific inductive capacitancevalues or alternatively gunply use anaverage Specific htductive capacitance valueaf 3.7, far etample> for aH types af paperinguhthn?

Reference 15 made ta the adaption of thehypothesis suggested by KenneHy as the

bash of the papu this ig'a logical approachbut it appears ta dEer fiant the basis ofcomputing ratings hitherto adopted in theUnited States. An ampHGcatian of theautharg'iewpoint aa this important issuewiH be »deemed.

With reference ta the use af low-resittivitybttchfiH, recent Studies in Great Britainhave Shown that the method of bachGHingcable trenches deserves careful cangidetathn as atteathn ta this point can resultin incretset up ta 20% iu had currents.

Equatha 43 gives the thettnal resistancebetween any point in the etrth Surroundinga buried cable and ambient earth. It is

Table X. Tempetblute Llmib for 8eHed; Screened- cnd HSL f'-Type Cebiet

LaM Direct or la A)r Ia Ducts

Syeteai Voltage aad Tyyeai Cable

Lead Sheathed

ArmoredUa-

armored

AiamiaumSheathed

Armeuredor Ua-

armored

Lead Sheathed

UaArmored armored

Atom)asmSheathed

Armoreder Ua

armored

1.1 krStogie>cate.. F 80 ~ ~ ~ ~ ~ ~ 80 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 60» ~ ~ ~ ~ ~ ~ ~

Ttria aad multicoce baited.» ~ ~ ~ 80 ~ ~ ~ ~ SO» ~ ~ ~ ~ ~ ~ ~ 80 ~ ~ ~ ~ ~ \ ~ 80 ~ \ »60 ~ ~ ~ 80

2.3 kr aad 5.5 krSiagtehae ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 80 ~ ~ ~ ~ ~ ~ ~ 80 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 50 ~ ~ » ~ ~ SO

Thf~rc baited type ~ ~ ~ ~ ~ ~ ~ 80 ~ » ~ ~ ~ ~ »80 ~ ~ ~ ~ ~ ~ ~ 80 ~ ~ ~ ~ ~ ~ SO ~ ~ ~ ~ ~ ~ »60 ~ ~ ~ ~ ~ ~ ~ 80

11 krSiagic~.. ~.......70.........70.....................50.........70Threncoee belted type....... ~ ..SS.....,...5$ ...,.....65...,......5$ .........50.........d5Three»care acrceacd type..~.....> 0..~......TO.........TO,........70.........50.....,...TO

22 kvStatic~re.. ..5$ .........6$ ............ ~ ........$ 0.... ~ . ~ ~ .5$Three-care betted type..........SS.........SS,...........,........$ 5.....,...50Threescore icrceocd type........6$ .........55.........5$ ..........5$ .........$ 0....... "5$Tht~c lSLI or Shl)........65................... A$..........65....................55

33 kr (ccrccacd)Static~re.. .55. 50 .

Three core HSL...............OS. .65

~ Mccauccd ia degrcca ccatigrade.t Hachttatcc separate lead.I Separate iced rheatbcd.1 Separate alumtouaa sheathed.

not clear, however, what value of soilthermal resistivity is used in this expressionand information on this important pointls desirable.

In Great Britain a value of soil thermalresistivity (g) of 120 C cm/watg is generaHyused but further test data are being slowlyacquired.'nd where tests have indicatedthat a lower value, e.g„90 C cm/watt,is justified. this value is used. Currentloading ~ tables in ERA report F/T183provide data for soil thermal resistivityvalues of 90 and 120 C an/watt, andcorrection factors for other values o! soilthermal resistivity are also provided.

In the United States buried cables areusually pulled into duct banks, but theremust be many cases where'irect burial,as aormaHy,.used in Great Britain, wiHresult in lower'instaHation coits. Formulasdealing with this instaHation techniqueare a desirable addition. Permissible tem-perature limits for the various types otcables and instalhtion conditions used inthe United States will be a helpful ap-pendix, and it is suggested that this informa-tion should be added to the paper. Forcomparison purposes, the limits recom-mended in Great Britain are summarigedin Table X and in the foHowingl

Phstic-insuhted power cables............70 C maximum conductor temperature

Gas-pressure and oH-HHed cable systems(« types).

85 C maxiniunl conductor temperature

Finally, it will be helpEul to know ifadoption of the formulas in the paper wiHnecessitate revision or ampliHcation ofexisting rating tables and, iE so, when therevised tables will be published.

REpERBBcas

1 ~ CQRRRNT RATcvo or CAsass roa TRANSsccsscoN *ND DcstacsonoN, S. Whitehead, E. E.Huichfngs. Rcporh Rcfcrcrccr P/PfJl, The BcfffshEfccccfcaf aad Allied fodusccfes Reseacch cfssocfacion. Lcaihechesd. Eogtaad, 1939; also Jo rsel,fastftutfoo of Elcetcfcal Baglaeecs, Loadon,Bagland, vol. 83, 1938, p. $ 1T.

2. Tss CAaeoaanoN or Ctcuc RAToco PActoasroa Case,ss LAco Dcaact oa sN Doers, E Goldenberg. Precccdfacc, foscffusfon of Electrical Eagfseers, Leaden, Eaglaod, TOL 104, pe. C, 195T, p.154.

H. Goldenberg (Electrical Research Asso-chtion, Leathcrhead, England): The cal-cuhtion of cable ratings ls a subject ofprime Importance to cable engineers.Nevertheless, it seems that until recentlythe American standard work on this subjecthas been that of Simmons,'hile thecorresponding British standard work hasbeen recorded by Whitehead and Hutch-lngs. These papers have been supple-mented by scattered pubHshed papers.including developments deaHng with cyclicloading.

The paper by 3fr. Neher and Mr. Mc-" Grath records up to date American cable-

rating practice in a manner that will proveinvaluable to engineers for many years tococne. It is a pleasing feature that theauthors are espcciaHy competent to dealwith this subject in view of their valuablecontributions to the cable-rating fieldover a number of years. Modern Britishcable rating prsctice has recently been

recorded in an ERA reports deaHng withcontinuous current ratings. and in twoIEE (Institution of Electrical Engineers)papersc> (based on ERA reports) deaHngwith cycHc hacHng, but the majority ofthis work ls in process of printing andpub Hcation.

An obvious dHEerence in British andAmerican technique is the method of cycHcrating factor calculation. Mr. Neher andMr. McGrath'5 method is based on anequivalence between typical daily losscycles and sinusoidal loss cydes of the sameloss factor, while a method recently hftro-duced in Britain'4 takes full accountof the form of a daily load cyde. Bothmethods are considerably shorter thanany that have been available'itherto.Nevertheless -,without further study Iwould not feel certain that for British.typecables, subject to their typical daily cycles,the Eorm of the cycHc load can be ade-quately taken into account by use of theloss factor independently of the cycHcload wave form giving rise to it. In hctthe conclusion reached in my second IEE

'paper,s is that a knowledge of the cyclicload wave form for thc 6 hours prior topeak conductoi temperature, together withthe loss factor, are adequate for cycHcrating hctor cdcuhtion. However, itwould be unhir to assess any of the rehtivemerits of the two methods prior to thepublication of one of them.

The difference between Britbh andAmerican cable rating technique is not somarked for continuous current rating cal-cuhtion as might appear to be the caseat Grst sight. In hct, such dilferences asexist are principally due to the dHIerenttypes of cables employed on each side ofthe Athntic, and to the diiferent standardaw frequencies in use. Nevertheless acomparison o! the present paper with theERA report dealing with continuous currentratingss gives rise to certain observations.

The present paper fs principaHy.directedto the calcuhtion OE a single current rating,but one use to which it might weH be putis the hrge-scale preparation of currentrating tables, with rating hctors for non-standard conditions. For such an applica-tion it Is often preferable to introduceexplicit formuhs for the rating factors, asthese formulas might be independent oEsome of the thermal resistances or lossfactors involved, with a consequent savingin calculation time.

The method employed for external ther-mal resistance calculation for groupedcables hid direct in the ground differssomewhat from that.recolnmended in arecent paper of mine.c For the preparationOE group rating factors for the more com-monly occurring groups of cables dealtwith in an ERA report,s the combinationof certain simpli6ed external thermal

'esistanceformuhs and my recommendedmethod has led to i substantial saving Incalculation time. I do not favor theintroduction cf a geometric mean distance,or its equivalent, as it is inconvenient forunequally loaded cables.

A brief rcsucn6 of other points is thatthe thermal resistivity values given inTable VI for thermal resistance calculationare generally somewhat lower than thecorresponding British values, that theproximity effect on cylindrical hoHoirconductors appears to mc to be best ob-

tained from Arnold'5 paper.s that wheresheath and nonferrous reinforcement lossesoccur a paraHel combination oE sheath andreinforcement resistance permits the cal-cuhtion of a single loss factor. that a simpleformula has been derived for the externalthermal resistance of one of three cablesin trefoil touching Eormation hid directin the ground,'nd that sector colrecriionfactors are often used ia British practicefor 3~re cable rating calcuhtions.

REFEaasfcss

1. See ccfeceaee 1 of the paper.

2. See cefeceaee 1 of bfc. Basses'fscossfoa.

Tss CAacoaano» or Cosnsccoos RAnsosAND RAnND FActoas roa TRANacccsscoN ANDDistacsictioN CAaass. K Galdeabefg RcpersRcfcnucr P/Tlry Elbl, Irsedea, Eoglaad, (ta bepublished).

4. Sce cefcccace 2 of Mr. Bacncs'fscossfoa.

5. Tss CAacoaanoN or Ctcccc RAnND PAccoasAND EicsRDSNCT LDADcso roa ONR oa MossCAscss LAiDDcRsct oa Dc Ducts, K, Gold enbecg.$feeorrepA cco. 3$l, fastftosfon ol Efcoscfcsf Engi-neers, July 1951.

8. Tss Esctsavao Tssauaa Rosie TANcs orBoacso CAai ss, E. Goldenbecg. Eceeccc Jeurccef,London, England, vof. $4, ao. 1, Fcb. 195T, p. 38.

T CQRRSNT RAIQcos roa ~ PArsa TNslKATRDC*sass To B.S.480, 1954; VARNcsssoCANsascINsccLATSD CAÃ.ss To B.S. $98, 1955. Rcport, Rcfcnacc P/I'lpp, The British Efccccfcal and AQfcdindustries Research hssocfasfeo, Leachcchcad, Eaglead.

8. See reference 5 of ihc papa.

Elwood A. Church (Boston Edison Com-pany, Bostoni Mass.): The authors presenta hrge amount of useful data and formulasfor the calcuhtion of cable thermal con-stants and suggest a new approach to theproblem of calcuhtion of temperature risefor various loss factofs including steady-load or 100% loss hctor. Cable engineersusually agree on the hctors to be takeninto account and the methods of calculationfor steady loads. However, there appearsstill to be disagreement on the problem o!cyclic loading.

At the AIEE General Meethig in January1953, a group of papers'as presentedsuggesting various approaches to theproblems of cycHc loading on buried cablesand on pipe-type cable. Of the methodssuggested in these papers, the one whichappealed to the author the most was Mr.Neher's methocl using sinusoidal loss cycles.In his paper it was shoitn that this methodyields reasonably accurate results for thehigher loss factors. For a low loss hctorsharply peaked cycle the results are nota5 accllrate

A modification of this method would beto represent the load cyde more accuratelyby splitting it into harmonics and com-puting the temperature rise Eor eachharmonic separately. This eatails morework. but with modern methods of machinecalcuhtion it is cconocnical to use themost accurate method available and letthe rnachine perforni the hborious cal-culations. In fact, it takes very littlemore time on the machine when the morerigorous methods are used instead of, anyof the approximate methods which havebeen suggested.

The author has invcsligslcd. the variousmethods of catculalioa of the cyclic com-ponecit of temperature rise of l,250-5ICM

P 'i>P Pa v e C4 ~ 1

4

Tab/c Xt. Thermal Impedance FuacQons

1,250.MCM 115-Kv Csb/c Enclosed /n 6s)to-Inchucx/dc-I}/eactcr P/pc

Tab/e XIII. Maximum Temyctature R/ce forCyclic Loading

'armonic

Ts/C}o To/f)o I s/(/o yo/C}o

oo............... 8.03/o'...........d.ss/o'...........s.pyio.„..........s.so/o't......,........lo.

sdlos ......,.....9. 08/Oo ....,...... ~ 8. $0/Oo ....,.......8.03/OoI............. 2.88/-30 ............1.57/ 43 ............1.24/-$ 4 ..~.........0.031-512 > ~......,...... 2.20/«38 ......„....1,19/ 54 .....~......O.S2/-58 .... ~ ~.... ~ .O.ST/-77

3 "~ ~ .. ~ .~...... 1.94/ 43o............0.94/ dto............o.dl/ 79o............0.39/ /-874 e ~ . ~ ~ .e" ~ ..... 1.58/ -50'............O.Td/ «dyo............0.48/ 87'............0.20/ 95

~ Steady.state componcaC for s/agic pipefSteady.state compoaenc for c«o pipes, 18 inches apart.Qo««acts copper ioss pct coaduccot pot footTs«'cctopctacute tise of conductor7's«tcmpotaiute t(sa of shiddiag tapeTs«cern pctacute tfse of oil ia pipe2'o«Cetapctatute tise of pipe

Coaductot P/peMethod Tempctacute, C Tetapetacute, Cof Ca)-

ca/ac/oa I Pfpe 2 Pipes .I P/pe 2 Pipes

For Loss Cyde I1.......39.1.....49.2......24.1 ....34.32.......30.8.....40.0......24.5 ....34.83.......30.0.....$ 0.1......23.2e.. ~ .33.4e

For Loss Cyde 2

I ~ ......30.0.....37.5...... 17. I .:..23.82.......32.d.....30.2......18.2 ....24.93.......32.8.....39.5......15.xe....22.8e

These dgutcs do aoc iaciude the Ccmpctacute cisedue co die)acetic ioss, «hfch would be added co the~ccady.state compoacaL~ These ste acetate ccmpctacutcs. It is aocpossible Co compute the maximum ccmpctaxute ofthe pipe by this method.

115-kv cables enclosed in 6s/s-inchwutslde-dianxeter pipe buried in the earth. Theresults of three such methods Eor tworepresentative load cycles are presentedin this discussion for comparison. Thethree methods compared are: (1) theHarmonic method using Bessel Eunctionsto compute the heat-Qow constants of thecable for each harmonic of the temperaturecycle, (2) the sinusoidal method suggestedby'r. Ncher in his 1953 paper, and (3)the latest method suggested by Mr. Neherand Mr. McOrath in their current paper.Space in this dhcussion does not permit acomplete derivation of the heat-Bow equa;tions for the hazznonic components of theheat-Bow cycle, but only the results, ascalculated by an IBM (IntenutloculBusiness Machines) 550, are tabuhtecl inTable XL It may be noted that theznachine tiznc to solve the eight simul-taneous equations necessary tor the solutionoE the tempecatures and heat Gows for eachhazmonlc was approximately 5 minutesper znatrix, with a separate solution neces-sary for each harmonic. The whole costof the job m rental tinxe on the machineand punching the data oa the cards formsertlon in the machine was $ 150 Eor three

Tab/c X/I. Hannon/c Componea/s of LossCycles

Loss Cyde I Loss Cyde 2

Hat Loss, Phase Loss, Phasemoa/c Watts hac(e, Waus Aag(~,

Desto so Decrees

0.......4.03...............2.54I~ ~ ~2500231 ~ ~2....... 1. 10..... +30......0.43...... +IS$3.......0.20..... 00......0.do......+ ds4.......0.$ 3..... +40......0.53...... 3$

Bxamp(e: The equation of loss cydc I using thefotegoiag data is as foiiooom (staximum Qo«d.d«acts ptt toot ptt coaduccot}Qo«4.03+2.$ 0 sin oot+I.IO sin (sot+30o)+

0."-0 sia (3ot-00o)+0.$ 3 sia (sc t+40o) «atesCottespoadiag ccmpttscute cycle fot cooduccottempstacutc is ss folio«s fot ~ siagie pipe: (I taxi.mum Ti «35.lo)7's«32.4+7.24 sia (ut-30')+2.$ 7 sin («ot 8 )+

0.30 sia (3«t 133') +0,80 sla (4a T')dcgttcs ccadgtsdc

Sere time«5,00 a,cs. ia the fotegoiog expressions.

ditferent sizes of cable (a total of 12 ma-trixes). The cost of pzogzanuning wassmall since the generai program for solutioaof complex simultaneous equations wasalready avaihble in the IBM library, andonly a small amount of work was necessaryto set up this particular problem.

The components ot the loss cycles withwhich the data in Table XI was multipliedto obtain thc tempezature cycles are givenin Table XII. These loss cycles are iHus-trated in Pigs. 4 and 5, with the cocre-syonding temperature cycles of the con-ductor and yiye,

In aH future calcuhtions of this soct,it is planned to cany the programmingstiH further and have the machine calculatethe temperature cycle for each size of cableand detecznine its maximum value. Thhhas been estimated to cost approxinutely$500 for programming and $15 extza persize of cable to compute,

Usually only the temperature of theconductor and the pipe are signiGcant incalculation ot the current.carrying capa-bility but the electronic calcuhtor auto-matlcaHy computes the other va/ucs'stedin Table XI. and they are recozded Eorwhatever use may be made of them.

A tabu/ation of maximum temperaturesfor the foregoing two load cycles and thethree dHfecent. methods of calculation Hscedpreviously are tabulated in Table XIIIin the same order. Examination of thistable wHI reveal that the sinusoidal methodyields results which are nearer to the znoreaccurate harmonic method tlun thc htestmethod proposed in thc paper. Theagreement between the various methods isseen to be better at the higher loss factors.

It may be argued that the agrcemcnt isclose enough between the three methodsfor aH practical purposes and that theaccuzacy of the original thermal constantsfrom which the computations were madedoes not warrant the extra work necessaryto use the harznonic method. However,the danger in using an approximate methodis that someone unEacniliar with its deriva-tion and its limitations wili use it where itdoes not apply. The author does not con-sider thc agrecznent close enough for 40 foloss factor.

The computation ot the pipe Ietnpctatureis just as important as the conductor tcm-

pezatures, especially in summer when highearth temperatures prevail and wherehigher daily loss hctozs arc more likelyto be encountered: If the earth next tothe pipe exceeds an avenge of 50 C, thereis danger of drying out the soH causingthezmal instability. Ca/culations ot cur-rent~ying capability should take thisliznit into account.

Rxcysaxcwcx

I. Sce tefcteacc 3 of the paper.

K J. Wiseman (The Okonite Company,Passaic, ¹ J.): The authors are to beconunended for thh very Gne technicalpaper. Thc nial for aa up-bxhtc com-.pihtioa ot engineering fonnuhs and con-stants for the calcuhtioa of current-cacrylng capacities of cables has been ofincreasing importance every year. WhenDr. Simmons wrote his series of yayccsabout 25 years ago we might say theelectrical cable industry was young inengineering knowledge, the types of cablefurnished were not too great in number,and the characteristics of the cables merenot too well known. Today our knowledgeof cable design, materials, ancl operatingconditions along with new types of cablesis hr ia advance ot 25 years ago. We havebeen using the tonnuhs as they becameknowa and it was desizable to bring thetatogether in one phce and, in addition, aH

of us who have occasion to make thesecalculations wiH be using the same fozznuhsand electrical and theznul constants.Also, this paper «iH be of great help toyounger men coming into the cable in-dustry. Although ic summarizes theformulas, anyone stishing to get a dearerappreciation of che text can refer to thebibliograyhy and study che original papers.

To cnake any tare of this kind gencraHyuseful, it is desirable that the procedurebe easy to follow sad the formulas readilyapplied. Theo recital fonnu/as involvinghigher mathematics can be used, but theytake time, and vcr) .olccn it is not possibleto take the tune to stock up a case. Aga/nconditions ot inscsi/scion ate varlab/edaily, so if we atcczapc io mal'e a Geld checkot ca/cuhcions wc can Gad dL~ctcrtccs;there/ore, cxaccnes) 'co 3 high degree is

l

l

5

~ ~ t' 4 I 4 "~ ~ ~ ~ '1J

~ r

l

II

3

100 100

X~ ao

O

~aoCD

O. 20

A

~doE ~

X>dO

O

l-aozuxrDco

O 20

AVE.I

Xc-..,r..",, a ~A.M. tiM

Flg. 4. Loss and temperature cycles for 75%%uo load factor> Qlllullcfload cycle

Ftg. 5. Loss and temperature cydes for 60%%uo load factor winterload cycle

Values same as in F>g. 4C4~coppcr toss cycleTx~tcmpcraturc ol conductorTc~tcmpcraturc of pipe

Tcmpcrdturcs are ln per cent of copper tcmpcraturc corrcspond-tng to steady load equal to the maximum.

not necessary. It has been suggested thaCit is now possible to use computers on theseproblems. This is true for those who havea computer, but here also time is taken forsetting up the probtan for the computer.Also we must show how to calcuhte thecurrents and in a Eorm thaC willbe used.

Vou willnote thaC many of Che focmuhsare new to mast ot you. These fonnuhswere developed to make the calculationseasily and quickly and yet do not cause alarge error in the ttnat answer from thehighly theoretical formula. It is naturalthat the formulas may bc a compromiseand some may feel that a particular formulaChat they use may bc superior to that recom-mended. Likewise the thermal constantsmay be a coxnpromisa This is true asfar as I am concerned, yet we are wittingto accept the recommendattons given in Che

paper. The calcuhtion of the variouslosses existing tn a cable systan and thclocation of these losses is well done andshould bc carefully studied by all newengineers.

The section dealing with the calculationof some of the thermal resistances needcareful study in order to appreciate thanas they depart from the usual manna'nwhich a thermal resistances are calculated.For example: the thermal resistancebetween a cable and a surrounding wall,such as a duct wall or a pipe; see equations41 and 41(A). Heretofore, we used 2>a~0.00411 B/D, and referred to as thc IPCEAmethod. This has been revised to takeinto consideration the condition existingand the materials. Equation 41(A) is ageneral one, and by inserting the correctvalues of >4'nd B's given in Table I,we can get R>. This is an example of howwe can accept a compromise in order toget agrecmcnc. We ac Okonite madetests years ago co determine the thermalconstants for the oil or gas medium sur-rounding cables in a pipe. Wc tried touse the cylindrical log fornxuta and found

the apparent thermal resistivity varieddue to the convection effects of the oil.IE we took the simple formula R>a~1.60/D where D is the diameter over cheshielding tape we found we goC goodagreement with test. We neglected tan- ~

perature effects as the actual value ofRra as coxnpaxed to thc thermal resistanceof the hsuhtion is very tow, many timesin the order of one. tenth; therefore,temperature effects are small. For a gasmedium using 200 pounds per square inchme use the equation 8>a 2.58/D. Howdo these focmuhe cocnpase with equation41(A) proposed by the authors)

Consider two cases, one having a diam-eter over the shieiding tape of 1 inch andanother having a diameter ot 2.5 inches.The Eollowing table compares the two typesof equations.

Dtameter ~ Diameter ~1 loch, XA laches,

Thermal ThermalOhmrPoot Ohm-Pool

on.....{

Ohoaite......t.do t.o.r....o.da t.o.f.Nehcr aad...1.3r ...0.80

Ohoaite......2.5d Co.t.... 1.03 C.o.f.Nehcr aad...2.22 ...1.04

htcCraxhCaa ~ ~ ~

Thc differences are not great and whenconsidered in relation to the total thecmalresistance, they are negligible. We canaccepC the authors'quations.

I am ghd to see the authors phce thcduct system in proper rehtionship to aburied cable system and that the samesoil thermal resistivity will be used whenmaking comparisons. This was the weak-ness in the cluct heating constants originallyset up by iVELA and hter known'sIPCEA constants. Also a better under-standing of the effect of multiple cab'tcs in aduct bank is obtainable, and th» decermina-

tion of the cable having th» highest thermalresistance is possible.

Appendix III discusses the'derivatton ofDr, a fictitious diameter in the soil up towhich it is assumed that a steady heatload exists and outside which the lossfactor of the load is taken into considera-tion. I have not been able to accepC thisassumption. It is an endeavor to obtaina thermal cesistance for the soil that willcheck with a study that Messcs. Neher,Butter, Shanklin and myselE made and isreferred to in reference 3 in the bibEographyof this paper. A study of the previouspapers will show thac the attahimentfactor is not exactly the same for att typesof cables studied and all shapes of loadcurves,

The authors tabulate in Table IX acomparison of the attainment tactor forthree methods of calcuhtion for a lossEactor of 30% Eor several cable designs.Rather than give results for one loss factoronly, it would have been betta'f they hadcovered the cange of loss factors which werestudied in 1953. It these attainment fac-tors were plotted against loss factor as Idid in my paper, it would have been notedthat a straight line could be drawn givinga good representation of how (>4F) varieswith loss factor, naxnely, (>4F)~0.43+0.57 (t/) for my method. This equationfollows the plot of (AF) and loss factorvay well down to about 35% loss factor,and in some cases, it gave a higher valueand other cases a lower value than actuallycalculatecL The (4F) values I reportedare based on careful calculations from thcexact load curve and no assumption thata single ine wave curve can be taken asrepresentuxg any load cucve. As it isararity that cables are designed for losshctors as low as 30% (50% toad factor).my formula gives results as accurate aswhen using D, and easier to use. However,for the sake of uaiforniity in methods ofcalculation, we wilt accept the

authors'ethod.

In thh connection, I ivould like to raisea question which I hope will be taken upby others interested in this subject. Theuse of the equxciou involving Da is an

Annn>r>oo 1OA ~ Arrhrr 1 fr/ rn>C —Trrrhr n> ~ >rr n»rf I'na:< I nnnVl~'t» ~

:,attesnpt to tn'crease the thernut resistance and have arrived at catatn condusions,for the soil for cables or small pipe sixes; some of mhich are discussed in the followinghi other words, the computed value oE paragraph.th emu! resistance is too Iow. Is it not The determination of thc losses m theIHldy that vre are leaving out of our equa- conductor, shield, sheath or pipe, and thetion a term involving a surface contact dielectric have been weH estabHshcd bybetween thc surface of the cable or pipe the authors and bear no furthand the saiL Thisis term would be of the Thc calculation of the thelmal resistances

no er comment.

cablessasne fostn as we now use for the case of of direct buried bl d 'l

es in air, namely, 8~0.00411 B/D. instalhtions appear to have'een well

soil thermal resIf we add this term to the log fortuna Eor founded; althou h the hod E

resistance, we willget a higher at the effect of cyclic loading scans to bctotal resistance and the Inliuence of the in question amottgst the various investiga-diameter of the cable or pipe willbe greater, toss (reference 3 of the paper). However,the tower the diameter. It vriH be neces- as Ear as duct bank Instathttons are con-sary to determine the value of B. Thc cerned, the difference between the NELAidea of such a tenn is showa in the paper'r IPCEA current rating method and that

Table I theby Mr. Matha and his coauthors. In proposed by the authors is so t th t

y give same thermal data one cannot help but «onder at the dearthgrea a

obtahtcd frotn tests made by them on a of practical data h the paper.pipe-type cable. They give a value of ln reading references 10, 12, 13. 16. andB for surface of Somastic to wata'f 218 17 of, the. paper,"there scans to be verythermal ohms pa cm'. I like this. Is it little data on cable 'temperature measurc-not likely that wc have a surface resisttvity ments takal in th 6dd ch

thecahleandthesoHmtmmedtate by the various utilities when the NELAc, sQ as mas doric

values mere established. The work re-

RBFEMtNCtsported in these reEerences ts almost atltheoretical, and laboratory measuranents

1. Bottrtava.aa powaa ttotttrrtssa*norr Hton. an,an~ogue mends u~ ~ ~ appr dVoc TAOC Ciaoa SjtrotÃsy R Js MathafJ Pe JsMaCattoa, E. Dautlrtlatt. AIEE Traarrurtoas, I am gi to u dets t there

a movement afoot to have this Neher-McGrath method accepted and to revisethe IPCEA current rating tables accord-

E. K Thomas (ConsoHdated Edison Com- htgty. I am not sure that this is the case-pany of New York, Inc., New York, N. Y.):The authors are tobe congratutated in settingup mathanatical equations to evaluate load

We have used the method given in thcgret that no mention was made of the pio paper to compute the current sathtg ofncerworkbyWathceE.~ketnthemtddte quite a number of high-voltage cable cir-1920's on the nthg of cables mstated m ~ts h a duct bank md 5 d complete dh-duct bank . Th work, I bdieve, f - agrcanent mith the NELA or IPCEAntshed thc b ~u of ~btc rating of thc nicthod. In every case the Neher.McGrathNELA and present IPCEA published rat- method results in a hrger conductor stxe

Ings of cable. The work of Zirke was pre- for a given current tathtg, m some cases

before thc AIEE anti pubHshcd in as much as 30% morc conductor metal is

Journal 1 required by the Neher-McGtath method.The work on ratings of cabte by Ktrke. Ha h mhere our di a ~ begins. One

5dd m~ of two things prevaHsl eitha Mr. ¹hermeats in the New Yorlc City area and tater and Mr. McGrath have cotstered the

nonfcrroQs lnctat maske't or they arcattanpting to make a pipe. type cable carry

which lead to the NELA„IPCEA satin the same load as a dua-bank tnstaHatton.Yet on the face of it, it is incomprehensible

Qse of pipe-type cable. Zt should be hom anyone can conceive o! a ~nductorobvious that the answer obtained by high-voltage cable (and a Pipe-type cable

mathenuttcai solution is never any betterassumptions ou which the equa colnpCtlng On a current sating basis with

gona are dcvdoped and the constants used single.conductor high-voltage cables sePa-

vrith the equations. ratdy spaced in a duct bank where awI bdtcve the actual heat ttow in under losses are a minimum and heat dissipation

g d cable sy t~ h constd~bly mo~ a ~m~ In either event we ~otcomplex than has been assumed in this undastand why so much thne should bc

paper and, therefore, actual ratings which ~ spent on devdoping a ncm method of cur-are obtained may be dHIcrcnt from those rent sating calculation for . duct-bankobtained by this calculation, systelns without Gsst having at least

obtained some actual In - service fieldRzt ttttstvcts measuranents to substantiate their

l. fosmtttas.~iuu Caactraanorl or Caaaa Tattraaazoaas On thc other hand, we must sincerely

commend the authors for attanpting toarrive at a realistic comparison betweenduct-bank and direct-buried systans. It

D. Shortts unfortunate, however, that in doing so

ort (Canada Wire and Cable they have not based their formttta dcvdop-ompany, Toronto, Ont., Canada): Sevant ment on extensive 5dd survey data as was

oE the engineer mho worL with me at Can- done at the time thc NELA duct constantsada Wire have been studying the Neher. were established.MCGrath a a over thP P e past few months, The only way in which we have as yet,

been able to make the Neher-McGrathmethod tsack with the old and well provedNELAmethod is to reduce the soil thermalresistivity to the order'of 40 C to 75 Ccm/lratt. The actual value which onemould use to ttsrive at the same conductolsixe as detamined by the NELA methodappears to depced upon the number ofcables in the duct bank and the value of thcdaHy load factor chosen. In contradis-tinction, Mr. Neher in reference 13 of thepapa'tates that his method agrees within10% of thc NELA method if a pa~75 Ccm matt is used.

We have nude some calcutattons of thethalnal resistance of cables in a duct bankfrom thc sheath to ground (or sink) usingthe ¹her-McGrath ~ method and theaverage conditions on «hich the NELAductconstants were obtained. Thc averageconditions were:

I. Most of the measurements were takentinder paved streets with the depth of pave-ment between 10 and 12 inches.

2. Majority of ducts wac made of fibre.

3. Avaage duct inner diasneter ~3.75inches.

* Concrete spacer between ducts 2inches, with duct..watt~1/4.tach, 3-inchouter concrete sheIL Spacing betweenduct centres ~6t/t inches.

5. Average depth of busial to top of ductbank ~30 inches.

6. Most measurements with ~nductorlead sheathed cables fran 2 inches to 3inches outside diameter. Avaage diameter2S inches.

7. AH Ioaded cables in outside ducts, allequaHy loaded.

8. Soil thatnat resistivity (i» situ) ~120 C cm/watt.

Two cases mere studied and the resultsare summasixed in the foHomingl

Care I—Thrcc cables in 2 by 2 duct bank(onc of lourcr ducts crnpty).

. NELA Valtte (Le. 4.93/D,'+LrNH3Loss factor........100%o..62.5%o..33%Rthc g thamal/

ohns-feet.......5.09 ..3.92 ..3.00Neher-McGtath Value

Loss Eactor, 100%o 62,5%,33%Upper cables

Rths s thalnal/ohms. feet... ~ ~ .6.68 ..5.02 ..3.71

Lower cableRths.s" """"6-63 -.4-99 ..3.70

Average values....6.66 ..6.01 ..3.71

In order for Nehcr-McGlath values oftherlnal resistances to be equal to NELAvalues, soil resistivity would have to be;

At 100% loss tactor p, 65 C an/wattAt 62.5% loss factor p< ~60 C cm/wattAt 33.0%o toss factor pa ~45 C an/watt

Case Il—Six cables in 2 uridc by 3 dccpduct bank.

NELA ValueLoss factor...... 100% ..62.5% ..33.0%Rths-z thermal

/ohms-feet....6.89 ..5.05%..3.60¹her-MCGrxth Value

Loss factor...... 100%..62.5%..33.0%

Jt/cher, rtfcGrath—Tcmpcratttrc and Load Capability rsf Cable Systcnls OCTOBER 1957

~ <

P

k Lt ~

I~

I'pper layer

Rths d ther-mal/ohms- "feet..........10.23..7.24 ..4.88

Middle layerRths-d ther-mal/ohms-feet..........10.95..7.69 ..5.12

Lower layerRthc d ther-mal/ohms-feet..........10.63,.7.49 ..5.02

Average values.. 10.60..7.47 ..5.01In order for Neher-McGrath values of

thermal resistances to be equal to NELAvalues, soil resistivity would have to be:

At 100% loss hctor p,~53 C cm/wattAt 62.5% loss factor pe~50 C cm/IrattAt 33% loss factor p, 43 C cm/watt

~<

Other calcuhtions on slngle~nductorhigh-voltage cables varying in conductorsize from 300 to 1,150 MCM instaHed inoutside ducts in a normal duct-bank systensIt was necessary to assutne a pe~75 Ccm/watt in order to make the Neher-McGrath fozmuhs agree with the currentratings calcuhted by the NELA method.

The NELA method is of course strictlyempirical and thc duct constants deter-mined from an average of a large numberof 6eld surveys. It has been in use forwell over 25 years; and there must of aconsequence be many thousands oE milesof cables operating at current ratings cal-culated by the use of these duct constants.So far as our experience in Canada is con-cerned we know of no hot-spot failures withhigh-voltage cables in duct-bank instalh-tions. On the contrary one is led to readwith great interest the recent paper byBrookes and Stazrs.t

Do the authors expect utility engineersoperating duct-bank instaHations to adoptthe method put forward in the paper andforthwith reduce their loads accordingly!This is a question of great importance,and we should have a categorical statementfrom the authors in this speci6c regard.

In Appendh IV the authors give a speci-men calcuhtion for a typical duct-bankhtstaHation and also a similar calcuhtionfor a pipe-type instaHation. In the onethey use a pe of 120 and in the other ape of 80. Would the authors enlightenme on the significance of these two differentvalues for p,. On this point Dr. Wisemanstated in his discussion of the paper thathe was glad to leam that. we can now basethe duct-bank calcuhtions on the same basisof pe as pipe-type cable, but the authorshave not done this in their Appendhc IV.

The use of the Kennelly fozmuh in thepractical case of cablet buried in the earthis at best an approximation. For'thetheoretical case of a heat source in a mediumthat is homogeneous, of uniform resistivityand temperature, the formula would apply.However, for the practinl case of cablesin the euth, there is considerable

deviation'rom

the ideal case such as honunifozznmedium, seasonal variation of temperaturegradient in the earth. nonuniform distribu-tion of. moisture in the earth, moisturemigration, and other factors, which renderthe Kennelly formula more or less inac-curate. Thus in its use one must bear inmind these limitations.

In Europe the Kennelly formula has

been'used extensively, but thc apparentthermal resistivity Inserte in the calcuh-tions are based on that value obtainedirt ziltr, as measure4 in accordance withreconunended methods. To get a veryaccurate value of the apparent thczznalresistivity, it seems that the method to beused should exactly duplicate the cable andits operating conditions; Le., thc samediameter as the cable, the same watts lossdissipated, the same depth oE burial. andat the titne when the thermal conditionsarc most onerous. Thus in the calcuhtionof thermal resistance Erom cable to ambient,it appears that the Kennelly fozmuh canbe used to a high degree of accuracy if anapparent thermal resistivity of the soil insitu is used. This measurement shouldautomatically take into account aH thefactors that otherwise limit thc KenneHyformula to a theoretical exercise.

There has been a great deal"o!.investiga-tion into the infiuence of moisture on soilresistivity. However, as yet there seemsto be no general agreement on anotherbasic problen, and that is the direction ofthe heat Qow. The authors and othersmaintain that the heat Qow is to the surfaceo! the euth whereas other investigatorsclaim sotne heat Qow is downwards to adeep isothermal, about 30 to 50 feet belowthe earth's surhce. In reference 12 Mr.Neher obtains the heat 6eld pattern bysuperimposing the Geld based on theKennelly fomtula on the temperaturegradient. It is obvious from the Geld ~

patterns that in the summer the heat Qowis predominantly down, whereas in the.winter the heat Qow is to the surface. Theauthors give no quantitative method ofevaluating the cffect of the temperaturegradient on the apparent soil resistivity.This could be one of the reasons foz'hedifference between the resistivity as meas-ured in the laboratory and h the field.An indication of the effect of change ofapparent thcrnul resistivity h shown ina paper by de Haas, SandiEord, andCamezon,t wherein the dfect oE introducinga deep isothcmzal (ground water) in combi-nation with the euth's surface as the sinkhas a theznul resistance oE approximately25% less than iE the earth's surface wasthe o=ly sink, This would indicate thatthe thermal resistivity of the medium ischanged whereas the change in tempera-ture cHstributlon due to the temperaturegradient should be investigated.

It should be enphasized that the Ken-nelly formula is applicable to steady-stateconditions only. The authors redize this,of course, and attempt to ccnnpcnsate forthis shortmming by applying a cydicalloading factor to the external thermal path.The factor they usc h based upon measuredvalues obtained on direct buried and/orpipe-type cables. Since thc thezznal cucuitof a duct bank is quite dHferent from thatof direct buried cables, we do not agreethat thh satne cyclical Ioadhg factor (asmeasured on direct buried cables) can beapplied to a duct. bank instalhtioa.

FinaHy it is pertinent to point out thatthc KenncHy formuh is premised upon aHthe heat energy Qowing to the earth'surface. One must thea ask the authorswhat they mean by ambient soil tempera-ture. Theoretiedly at least the tempera-

'ureof the earth at the cable depth ofburial is not thc ambient to be used in the

'enneHy

formuh if the sink is the earth'surface. Why is thc euth's surface tem-perature not the tzue ambient to use whenapplying the Kennelly fozmuh? Is theBritish usc of a 2/3 factor in reaHty acorrection for the virtual sink temperature.or sink tenperatures if the deep Isothcmultheory is valid.

L TssaxAL ANU MaatANTOAL PaoaLax oN128 Kr Ptas CASLS TN Nsw Jaaaar, h. S. BrooLee,T. B. Starre. A188 'Frearerrioar, roL TC, pt. 111,Oat. LOST, pp. TT2%4

2 AN ANotooos SoLUTIoN or CASLs HsarPLow Paoatsaa, B. de Eaaa. P. J. Saadtford,A, Vf. Vf. Caceeros ISfd., roL Td, pt. 111, JaaeIOSS, pp. 215-22.

F. O. WoHaston (British Columbia Engi-neering Company, Ltd., Vancouver, B. C.,Canada): This discussion is confined to theparts of the paper dealing with cables inducts. The paper is in many respectsmost adtnirable, notably the coverage ofsLin dfect in conductors. of special types,proximity and eddy current elfects, muttuIheating effect oE multicable instalhtions,and the diect of extraneous heat sources.For the 6rst time these are aH adequatelytreated in onc paper. The methods ofedculation must, however, be criticallyexamined before being acceptecL I amdisturbed to Gnd that the methods givenfor rating cables in ducts lead to sub-stantially hrger conductor sizes than doesthe IPCEA-NELA method. By thcIPCEA-MELAmethod I mean the methodgiven in an Anaconda publication.tbelieve this method is identical to thatused in preparing the existing IPCEA. cur-rent mtings for cables.

The Neher-McGzath method leads tomuch higher values for the duct heatingconstant (the thezznaI resistance fromduct. bank to eazth ambient) than does theIPCEA-NELA method, when the thezznalresistivity of the euth is taken as 120 Can/watt in the Neher-McGrath calcuh-tion. The value to bc used for earththeznul resistivity is of paramount izn-portance and wiH be discussed in moredetail later. A few Qlustrations of thedifferenc between the two methods wQIGzst be given.

The Gzst application of the Neher-McGrath method which we made was todetezznine the conductor size for a pro-posed 230-Lw cable instaHation. The cal-culated conductor size was 1,500 MCM,whereas by the IPCEA-NELA method thecalcuhted size was 1,150 MCM. Some42 mQes of cable were involved in theproposed project, so the Neher-McGrathresult would have meant substantial extracost for the cable compared to the IPCEA-NELA zcstdt.

In another tnztazcc, thc Ncbcr MCGzathmethod was used to determine the requiredsize of cable leads for a 75.mva trans-forzner. The calculated size was so largeas to be considered physicaffy Impractlad,whereas by the IPCEA.NELA method thecalcuhted size was pzactied. Rather thanrisL possible trouble H the IPCEA-NELAresult were adopted, it was decided touse aerial bus instead of cable for theseleuis.

In a third case, the cable leads of a 50-mva 13.S-L>'enerator were to be changed

OCTOBER 1967 %cher, iVcGraffs—'Tcrrtpcrafurc at:d Load Capabtl Ey of Cable Sys.'crtts 769

< l'~l- 1 $l Ch l

~ r'

Table XIV. It was necessary to measurethe air temperature in an occupied duct.since there werc no empty ducts. Theloading on the machine vras recorded andthe current division between the sixcables was detcsmhscd. The maximumdeparture from equal loading of the twocables on each phase was only 2%. After5 days the duct air temperature was 43 C.The ambient ground temperature was 19.5C at the same depth as the center of thcduct bank, Dividing thc temperature riseby 1/6 of the total losses, a thermal re-sistance of 4.6 ohms is obtained. Table

So s»

iIz ss ~l2us,g

cn rrs.'1 .'.Qi..'.QI~ ~

5 sr ZRsrrzrff, OVCZnr covcagrg. ZU shows the thermal resistances pertinent

to this case as dctesmincd by the Neher-McGrath method and the IPCEA-NELAznethod. The expcrisnental value (occuyiedduct air to earth ambient ot Table XV) isin good agrcemcnc with the IPCEA-NELA value given in "duct wall to earthambient" of Table XV, while the ¹her-

Fig. 6. Cross section of duct bank

because the associated ~o-Lw step-uptransfosmcr was being rephccd with a345.kv unit. The existing leads consistof two 2,500-MCM cables per phaseinstalled in a Mucc bank. hccording tothe Neher;McGrath method, these cablesshould be approximately 3,500 MCM eachif thc AEIC allowable temperature of 'F6 Cis not to be exceeded at full load in sununertiine. The unit has run at full load forlong periods on many occasions sincegoing into service in 1949. If our applica-tion of the Neher-McGrath method iscorrect, one'must conclude that the existingcables have been severely overloaded manytimes during their service period of 8years. No evidence o! such overloadinghas been seen; the cables have been entirelytrouble-Free. There are toro other unitsat this plant, identical in all respects tothe one described above except that one ofthan has been in service slightly longer,the other not quite as Iong. No troublehas occurred on the leads of these units.

It was decided to make a temperaturesurvey to establish the correct facts. Theunit was run at full load for 5 days. Testresults showed that the duct structureatcaisscd equilibrisun temperature in 24hours.. The bulb of a recording thcsxnom-cter was inserted 20 Eeet in the bottomxniddle duct. The details ot the ductbank and cable are, given in Pig. 6 and

value i! the two methods arc to give thesame results, as is obvious by inspection ofTable XV. The Neher-McGrath valueshould be lower than our experimentalvalue, since the fosmcr represents thethczmd resistance from the outside surfaceof the occupied duct wall to earth ambient,while the htter represents this same re-sistance plus the thcsmal resistance fromoccupied duct air to the outside surface otthe occupied duct wan.

One is not entitled,to say that the dis-crepancy between the Nchcr-McGsathvalue and the IPCEA-NELA value is realunless the value ot the specific thermalreshtivity of the earth ps is the same forboth. The ¹her-MCGsath value in thetabulation is obtained when a value otearth thermal resistivity ps m 120 C cm/wattand thcsmal resistivity of concrete ps~85are used m equation 44(A} ot the paper.There has ncvcr bccn asly general agrec-meat on what value of earth thcsmalresistivity is inherent in the IPCEA-NELAduct constants. Several years ago Mr.G. B. Shank!in and his coworkers in theGeneral Electric Company investigatedthis extensively and concluded that thevalue is about 180 C an/watt. If thisconclusion is correct the discrepancy be-twom thc Nchcr-MCGzath result and theIPCEA-NELA duct heating constant is

Table XIY. Cable and l.oss Data

2,500.MCM Scgiaentol Copper CondsrctorrPepcr inzuf4tcd.teed-Sheoshed Solid-Type,

13.8 Kv real and serious. Our test result citedabove does not give any information onthis point because the earth thczsnal re-sistivity was not measured, due to lack offacilities.

If the discrcyaucy is real, one h led toquestion the soundness of the Kennellyformula used by thc authors. It is basedon the premise that all heat generated inthe cable escapes to tbe surface of the earth.Some ccnnpetent engineers have argued chatpart of the heat escapes by another path,namely to a sink deep in the earth. Mathe-maticd development of this premise givesa result for the thermal resistance betweenduct bank and earth that is only abouttwo-thirds as large as the result by th

CurreasDaring Teat,

hmpercs

Wa Sic LossPer Bootof Cable

Cablezfo.

2.............. 0TS............... 5.13

5........... ~ ..1,020............... S.T3Total 30.50

Per cable average S. 1

Roses:hmbleat earsh tom peraiure durlag teat was 10.5 C.Cables are paired 2-3 for h-phase, CH for B-phase,5-5 for C-phase.

D(ameser over «oaductor, laches............2.000Cotton tape shicxaess. laches...............0.01Tzasulssloa thichaess, laches................0.210'lameser over insulation, laches............2.4S4sppcr tape shichaess, laches..............0.003

obeaib ihichaess, inches...................0.12$Over.all diaescser. laches..................2.T10h< resissanee at 5$ C~$ .41 (Xo») ohms.face

Kennelly formula. hccording to this, wemight expect the Nehcr.McGrath methodto agree with the NELA value iE the carchthcrznd resistivity is taken equal to 2/3X180~120 C crn/watt in equation 44(A}.It turns out thac agreement occurs when

.McGsath value is much higher. The='-:Neher-McGrath *value should be ap-

proximatciy equal to the IPCEA-NELA

Table XY. ThcrnNl Resistances Pertainingto Test

'hermalEeshsaaee, lfehet IPCEh Ezperi-C pcr Watsrryoos Mcarash Tfgch mensal

Znsuiasioa...~........0.73 ..".O.TSShesih so dues....'....1,52,....1.82Duct wall.............0.13Duce wall io carsh

~mblen!............8.7$ ».~...4.0Occupied duce air so

earth ambient........ ..4.51» Calculased from criuasfoa44(hj usiag p»~120 Ccmlwasz.

the earth resistbrity is taken as 55 C an/watt in equation 44(h). It does not seanlikely that the value of 55 is representativeof typical sail around duct banks. Manymeasurements in several laboratories have>-~-consistently shown that the specific thczma1 1

r'esistivityof earth varies frosn about100 C cm/watt Eor a moisture content. of15%, to about 300 or 400 C cm/watt forsero moisture content. A value of 180 Ccm/watt seems fairly representative ofaverage conditions. I conclude that thevalidity of the ¹her.McGrath method ofcdcuhting the thcrznd resistance from ductbank to earth. ambient should be desnon-strated by tests whczchs the «arth thermalresistivity is dcfinitcly known. Have theauthozs verified their findings by suchtests?

RETERENCE

t. Caaaaaz Raznros roa Baaczasoc CosanncroaL Anaconda Pssrrsstfen C4t, McCcaw-Hi0 BooL Com paar, Zoc Rew Yes ¹ Y., erstedlcfoa, Ocs. 1042.

J. K, Ifcher and M. IL MCGratht We areindebted to Mr. Baznes and Mr. Golden-berg for their dscuszions in which theysummarize the present cable rating prac-tkcs in Great Britain and point out somediifcrcnccs with hmczicxn practice. Promthis it would'ppeaz'hat in most respectsthe practices in the taro countries areshnihr. While the method ot handhnggroup cable ratings developed by'x;Goldenberg may appear to difFer hoax themethod ot the paper, actually both methodsarc derived from the same basic prhxciplcsand should give identical results for thesazne set of conditions.

To answer their questions with regardto tcsnpcrature lnnits and the relationshipof this paper to the published rating tables,we may say that IPCEA, in collaborationwith the AIEE, has under active con-sideration a xevision of the existing currentrating tables based on the methods of cal-cuhtion set !orth in this paper. The tem-yerature limits wfii be those

dready'dopted

by IPCEA, AEIC, ctc.. in industryspcclfications.

Mr. Church has outlined a procedure fordetermining the effect of the loading cymeon cable ratings which will be, we fear,an cnigsna to znost cable engineers despitethe fact that ic represents a chdlengeto those mathmssatically inc8ned. Mr.Goldcnbcrg also has referred to a differentbuc nevertheless machcsnatically involvedprocedure for doing this. For uorsnal cablecalcuhtions, the crcmmsdous asnount otcomputations required for each individual

7TO 1Vcher, McGrath —Terrs perature and broad Capabihty of Cable Systerrss OCTOBER 1951

a a ~ ~ ee0

1 '

casi,'is simply not warranted «ven iE adigital computer mere available to the cableengineer.

If the application of a particular loadcycle to a given cable system is to bestudied, we suggest that this may be donemore siniply, morc rapidly, and moreeconomically by using an analog computerdesigned for the purpose. We feel, how-ever, that the accuracy of thc method givenin the paper as compared to aB exact caI-culations which we have examined, includ-ing those of Mr. Church, is suificient, par-ticularly in view of the fact that any par-ticular load cycle may never repeat itself.

The method given in the paper is anapproximation, admittedly, but it has beenderived from the same fundamental prin-ciples which underlie Mr. Church's methodthrough a series of careMIy consideredsimplifications. It should be understoodthat there is nothing sacred about. the valueof 8.3 inches used for the fictitious diameterDc. This value happens to be the bestsingle value to use based on the studiesdescribed in reference 3. For Mr. Church'scase values of 7.1 for thc 75% load factorcycle, and of 5.1 for the 60% load factorcycle are indicated. The errors in using8.3, however, amount to only 2 and 5%high, respectively, m the conductor losscomponent of conductor temperature rise,which would be offset by a 10% error inthe value of earth thermal resistivity ein-ployed.

Dr. Wiseman's conunents in this con-nection are most interesting since he hasoften expressed the opinion that, prac-tically, it was sufiicient to consider Dc tobe equal to Ds, or in other words to applythe loss factor to aB of the earth portionoE the thezmal circuit. We can agreewith this in respect to pipe-type cables,but, as he has indicated, we do not considerthis further simplification desirable inthe case of small directly buried cables.Neither do we consider the forznuia whichhe gives for obtaining attainment factordirectly fram loss factor suitable in thiscase. This is readBy apparent fram Fig. 2af the Grst paper of reference 3 in ourpaper. Since the use of Dc has considerabletheoretical justification in our opinion, wefeel that it should be made a part of thegeneral procedure Eor calcuhting the effect.of the loading cycle.

The introduction of an additional thermalresistance to care for surface effects be-tween cable and earth is an entirely differ-ent nutter since this will increase thetemperature rise both for steady and forcyclic loads, whereas the use of D> isintended to give the correct result for cyclicloads on the assumption that the totalthermal resistance in the circuit which isunchanged by the value of Dc is correctfor steady loading. It is quite possiblethat such a surface effect term is presentand that it may attain an appreciablemagnitude in the case of small directlyburied cables. We concur in the hopethat this matter wBI be investigated further.

Ivfr. Thomas has noted the pioneer workof W. B. Kirke in connection with cablein duct and indicates that this worL: formedthc basis of the present NELA-IPCEAmethod. Employing a duct bank con-Gguration such as shown by Wollaston andutilizing equations 14 and 17 of the Kirkearticle, we Gnd that Kiri:e would use a

resultant thermal resistance from loadedduct mall to earth ambient of 9.0 for theworst soil in metropolitan New York and6.00 for the best soiL These values, whencompared with NELA constant of 4.9,scarcely confirm Mr. Thomas'tatement tothe effect that the present IPCEA-NELAmethod is based on or is even closelyrehted to Kirke's work, While Kirkemade some attempt to take into accountthe configuratioa o! the duct bank structure,he did not utilize resistivity as such,and as previously indicated we believe thata knowledge of this and other parametersignored by Kirke is essential to a realisticmethod o! handling this problem, par-tlcuhrly when one considers the problemof comparison between different types o!+steals.

hs Mr. Thomas has suggested, the heatQom in a duct structure is complex, but thiscomplexity results from the superpositionof a number of heat Bows any one of which,due to a particular cable, is readily deter-mined as indicated in reference 12. We arenot interested in these heat Qoms frcr zc,but only in the resulting temperaturedifference betNreen a reference cable andambient and the corresponding thermalresistance which is fully expressed by therelatively simple equation given. True,the situation is complicated by the concreteenvelope, but here extensive studies, bothmathematical and on a Geld plotter, in-dicate that the equation 44(A) is sufii~

ciently accurate in view of the inherenterrors in Gxing the earth resistivity andloss factor in a particular situation.

Mr. Short, at the start of his discussion,states in effect that he considers the methodfor determining the load capability .ofdirect earth-buried or pipe-type cable tobe "mell founded" for a 100% load factorbut, because of questions raised by variousinvestigators in reference 3 of our paper.does not seem to be too sure, that this isthe case for other load and loss factors.hll four investigators mho undertooL toitudy the problem for the Insuhted Con-ductor Comniittee, however, are on recordas recommending or agreeing to the methodgiven in the present paper. In acceptingthe given method for buried and pipe-typecable, Mr. Short does not seem to realizethat this method is based on the Kennellyfozmula because in the latter portion of hisdiscussion he questions thc applicabilityoE this premise to current rating determina-tions for any type of underground instalh-tion, and proceeds to attempt to resurrecta nuinber of the ghosts which plagued theInsuhted Conductor Committee some 10years ago when the latter started worL: ana critical review of the basic parametersinvolved iu load capability calculation.These ghosts were subsequently hid torest, at least to the satisfaction of the vastnujority of engineers in this country.Even at that time the Kennelly forznuhhad been in existence for over 50 years.Despite the fact that this fozmuia is basedon scientific principles found in most textbooks on physics and electrical engineering,some cable engineers had misgivings as toits applicability mainly because calculationsby it did not appear to checL with measure-znents in the Geld. This situation is dis.cussed in reference 12 of our paper whereinit is shown that the disagreement was notdue to the fozznula but to the fact that the

6eld meauraaents had not been carrieto a steady state, and that laboratorydeterminations of the earth resistivity werenot representative of thc soil in situ.Also, the appareqt discrepancy (whichappears because thc direction oE heat Qowimplied in the Eozmu!a Is toward the surfacewhereas in summer the total heat Qow inthe earth is obviausly in the reverse direc-tion) is explained by the application ofthe principle of superposition to the separateheat Gelds involved. As a result, cableengmeezs, with very fem exceptions, haveaccepted the formula for cakulations in-volving pipe-type and directly buriedcable systems. The method of handlingcables in duct, given ia the paper, is alogical extension of the priaciples under-lying the Kennelly fozmuIa in order toinclude in the calculations tmo very im-portant variables which are not a part ofthe NELA-IPCEA.method, namely theduct. configuration and the thermalsistivity of the surrounding soB. Thismethod is also not new. It mas Gzstdescribed by N. P. BaBey ia a paper in1929'nd subsequently ia reference 13 ofour paper.

Mr. Short also mentions the two-thirdsfactor, another resurrected ghost of thepast. Long'go the British establishedthat the two.thirds factor represents adiffezence between laboratory and in citsmeasurements of soil resistivity and that itdoes not stem from any lack of applicabilityof the Kennelly formula to the pzablezn.Numerous British publications point outthat the tmo-thirds factor is not to be usedwhere the resistivity is measured in sitsby buried sphere or by long or short cylinder.In addition, in recent years the Britishhave developed a new laboratory samplingprocedure'hich checks not only withthe buzied sphere, the buried cylhider, thetransient needle, but in addition alsochecks with results obtained on loadedcable installations.

Another ghost mentioned by Mr. Shortis the deep isothermal approach (a proposalwhich mas Grst suggested by Levy in

1930)'iting

the de Kus, Sandiford, and Camezanspaper to give new life to this old suggestion.However, in so doing Mr. Short faBs topoint out that the deep Isothermal in thiscase consists of a conducting paint electrodeof an analogue model connected electricaliyto another electrode representing theearth's surface and hence simulating alfrruiing (not stationary) ground watersink, a somewhat unusual condition thatis scaredy pertinent to the problem athand. Incidentally, Table I of this papergives results of an excellent analog checkof the given method as applied to a ductbank.

We wish to assure Mr. Short that wehave not cornered the nonferrous metalmarket, nor are we saymg that threesingle~nductor cables of a given sizeinsuBed in a buried pipe must have thesame rating as three conductors of the samesize Installed in separate ducts. Weshould point out, however, that this hasbeen a rule af thumb for the past 10 yearsor more and there are now many zniles afhigh.voltage pipe cable in successful servicewhich are rated and are being operated at aload capability level which Mr. Shortconsiders incomprehensible.

Mr. Short's dilemma results solely from

OCTOBER 1957 Nchcr, hfcGratli—T'crnpcraturc and Load Capabih.'.; of Cable Systcrnz 771

~ - eat 'd'i

lt

o

the Eact that he is attempting to comparethe r,cults of calcrdations made under a

~

~

~~

set of assumed conditions with the resultsof a procedure for which those same condi-tions are not stated and in fact are unknown.This Is a situation which existed imme-cHately EoHowing the waz and is one of theghosts previously nzentioned. Conductorsize determinations for cable in ductutHizfng the NELA constants require noknowledge nor consideration o! soil re-sistivity as such. On the other hand. suchdeterminations for pipe-type cable systemsby any practical method require a speciflcnumerica assumption to be made as tothe value oE soil resistivity in order to aniveat an answer. By taking the stand thatthe concealed resistivity in thc NELAconstants is 120 oz'ore, iC is thus possibleto obtain, an advantage in favor of duct-Iaycable.

Furthermore, because oE the use of cablespacing factors and earth and concretethermal resfstivltles in the proposed method,it mill be obvious that calcuhtions by thegiven method will check with those of theIPCEA method only for certain combina-tions oE the variable parameters in themethosL Since these parameters were notGxed and in Fact are now'nknown as re-gards the NELA duct heating constants,it is obviously hnpossible to make a factualcomparison o! the results obtained by thctwo methods. Here again, by assumingearth resistivities oE 120 or 180 as both Mr.Short and Mr. WoHaston have done, thcgiven method wHI result in hrger conductorsizes than the IPCEA method.

Despite the Fact that both Mr. Shortand Mr. Thomas refer to the presumablylarge amounC of Factual data which underliethe NELA duct constants, we have beenunable to ascertain the specfflc'conditionson which these constants were based noris there any indication Chat earth resistivitymcaswements were taken as a part of thedata. About aH that can be done, there-fore, Is to assume representative cable andduct conflguzations and then to caIcuhtethe earth resistiviCy required in the givenmethod to match thc value calculated bythe IPCEA method. We cannot agreeto the values given as "the average condi-tions on which the NELA duct constants

~vere obtained" as stated by Mr. Short.Rather, vre believe that the conditionsassumed in reference 18 are much morerepresentative, on'the basis of which anaverage earth resistivity of 75 was obtainedat 100% load Factor.

We take the position. therefore, thatthe validity of the proposed method is notto be judged by whether or not the calcuh-tions made by it using parameters arbi-trarily picked by Mr. Short (or by Mr.Wolhston) agree with calculations madeby the IPCEA method. Rather we feelthat the applicability of the IPCEAmethod to a particular case depends uponhow well it checks with the method whichwe have proposed, and which takes into

account more properly the essential param-eters which are pertineuC to the case aChand.

With respect to Mr. Short's speciflcquestion, we hope that utility engineersmill,adopt the proposed method but we donot think that they will Gnd it necessaryto reduce loads unless they have very highvalues o! earth resistivity. Regarding theneed for reduction in loads on existingdrcuits, iC should be kept in mind thatit is only rehtively recently that AEICspedflcatfons have made provision EorIncreased permissible temperature HmitsEor emergency periods, and for the greaterportion of the period that these emergencylimits have been in efect the nuznber ofcompanies who have utiHzed them isrelatively smaH. As a result, the greaterportion oE the cables now in service have"been sdected on the basis that normal

~permissible copper temperature would not,be exceeded under emergency conditions.Moreover, in recent years a number ofass zsfra measurements have been made withthe tzansient needle, the sphere, or theburie cylinder. Theoretical studies haveshown that measurement of ultimate soilresistivity can be obtained readily vrithsuch devices. WhHe in many cases thesehave been made in connection with pipe-type cable instalhtions, they apply equaHyweH to duct bank instalhtions in so faras the resistivity o! the soil itself is con-caned. The values in general range fronz50 to 100 with some higher values as theexception at certain times of the year.Moreover, over the past decade a numberoE pipe type InstaHatlons have been in-staHed in this country with design re-sistivities in the 70 to 90 range. Underthe circumstances, we do not believe thatit will be found necessary in most casesto reduce the loads on existing circuits.However. we do believe that engineersmill be well advised to take steps to ascer-tain the valuei o! thermal resistivity whichare applicable for their conditions becausewith the more liberal use of emergencytemperature limits and the tendency forshiEC in many areas in the load peaL fromwinter to summer, the existing margin maybe reduced to a lovr level hc the not toodistant Euture.

The values of soil resistivity of 80 and120 used in the examples of Appendix IVwere chosen merely Eor purposes of iHustra-tion and the value of 120 rather than 80was used in thc duct Iay case in order toemphasize the effect of a difference betweenthe resistivity o! earth at 120 and concreteat 85.

Unlike Mr. Short, Mr. Wolhston is verycareful in his discussion to make it quitedear that his comments relating to acomparison of the results obtained by thegiven method and the NELA-IPCEAmethod is preznised on his own arbitraryassumption of a concealed soil resistivityof 120 in the NELA constants and on bisimpression, presumably based hrgcly on

an unpublished 1947 memorandum byG. B. Shanklin, that a resistivity of 180 isrepresentative of average conditions; conse-quently, the value of 55 which was obtainedby back calcuhtion from the given methodutIHzing his test results indicates a dis-crepancy ia the method. We believe thatif Mr. Wolhston wiH consult somcrs ofthe many references which have appearedin the technical litemture over the pastfew years on determinations of soil re-sistivity h connection with experimentalduct bank, buried cable and pipe-type cableInstaHations, either alone or in conjunctionwith buried cylinders, spheres or transientneedles, that he will Gnd that there is nolonger any justiflcatfon for an Inferredresistivity oE the order of 120 in the NELAconstants or for his impression that a re-

o sistivity of 180 is representative of averageconditions.

In as much as no actual measurement wasmade of soil resistivity at the sIte at whichMr. WOHaston obtained an indicated valueof 55, there are, of course, several possibleexplanations that suggest themselves. As-suming the tern peratur'e measurementswerc made accurately. perhaps the soilactually had a resistivity of this order ofmagnitude. From recent studies on soilsand the effects o! such matters as composi-tion, density, compaction, particle size,etc., it Is evident that it is very difGcultto estimate the resistivity of a soil froncappearance alone. Alternatively, it couldbe that the measured value of resistivityis not the ultimate value as a constant loadapplied for 5 days would not suflice to bringthe duct structure to its ulthnate teznpera-ture rise over ambient, unless, o! course,it bad been canying substantially fuH loadfor some thne prior to the test in question.Mr. Wolhston mentions that the tempera-ture was measured 20 feet from the nzan-hole but does noC indicate the length of theduct zun orf which the test was conducted.This raises a question as to vrhether in hisparticular case, there could have been anyaHeviatioa of temperature rise by longi-tudinal heat flow or, alternatively. by longi-tudinal convection effects such as wereFound in the tests made with ducts openand

plugged.'s

psasscss

1. HsAT Paow roose UscosaoaoUND EtscralcPowso CAsass, Neil P Baser, AEEE Troarocrroer, voL 48. Jao. 1020. pp. 15&45.2. hN EvAAUAcrosc ov Two Rarro bfavsroos ovhsssssQco zsrs TosaMAl Rssrsrsvtvv or Soral

W. Marcosrsrd, E. blochrrar rcf. /o reer,lascrcncroa ol Elcccri«al Eazlacers. London.Eacland. vol. 103, pt. h, no. CZ, Ocz. 103d, p. 433.

3. CAsan Hoarrsco Uc Uscoeaoaoowo DUcrs.R. D. Levy. Ccacrer Erccrrlc Ecvrcsc, SchcncccadrrBL Y., hpr. 1030, p. 230.

4. See reference 2 ol Mr. Shocc's drscnsslon.

S ToktoaAcnao Rrso Aoo CUaaoscv Ravncoor CAsass LArn'sc DocTsz E Bo Wedrnote> E EoHorchlass, Rcporr, Rr/rrcrrcc P/T los, TheBclrlsh Electrical aod hrricd industries Researchhssoelacloa, Loadoa, Eazla'ad, 1035.

""2 Ndhdr, sVcGraffi—7drrrsrrr!Urn crt Ter> Crrsntrr:rsr nr / nln Vvrlrmr Ar vn rs o cr 1 rrX7

THXS PAGE XNTENTXONALLYLEFT BLANK

1

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ei I 0 ~

F. H. BULLER *-."=J-rH. NEHERMEM8Ert AlEE MEMEER AIEE

O NE step in the calculation of under-ground cable temperatures involves

the determination of the temperature riseof the.cable surface above the immediatelysurrounding inclosure such as a duct struc-ture or a gas- or oil-flied pipe. Since theintervening medimn is a Quid, the modeof heat transfer simultaneously involvesconvection, conduction, and radiation.

The semiempirical methods now in use

for this determination in the case of cablesin duct are not entirely satisfactory, andvrith the advent of gas- or oil-fliedpipe-type cables there has arisen a definiteneed for a method of evaluation for thesecable types as weU.

Because of the complex nature of theproblem and the number of independentvariables vrhich are present, it is imprac-tical to cover completely all possible

com-'inationswhich may be met within prac-tice solely by tests. By developing atheoretical relationship between the vari-ables, however, it is possible to developprocedures by which the test data avail-able may be analyzed in such a way thatrelatively simple working expressionsmay be derived which may be appliedwith suflicient accuracy over the entireworking range.

The theoretical relationship for thecase of cables in duct was recently pre-sented in a paper by one of the

authors.'n

the present paper this rehitionship hasbeen extended to cover oil and gas pipesystems as tvell, and from the test datapresented the requisite working expres-sions for thermal resistance or surface re-sistivity factors have been obtained.

Theoretical Considerations

The theoretical rckitionships given inAppendix II of reference 1 for the case of

cables in duct have been expressed morecompletely to account for the physicalcharacteristics of the media involved inAppendix I of this paper. The resultingequations for the the therinal conductiv-ity betvreen cable and duct or pipe vrithair or gas as the intervening medium are

Q 0.092 Ds "/'sT'/'P'/'sT

1,39+Dr /Dd

0.0213, +0.102Ds'c(1+0.0167Tm)

IogtsD4/Ds'atts

per degree centigrade foot (1)

and with oil as the medium

Q, 0.053D "/'nT'/ T '/s 0.116—(oII) ', +CsT 1.39+Dr'/D4

logisD4/Ds'atts


For a single cable D,'aa D„ the diameterof the cable. For three cables in the pipeor duct it is customary to base D,'n thecircumscribing circle of the cables in tri-angular configuration, D,'m .15 D,. Fortvro cables the relationshiP Dsraal.65 D,is satisfactory.

It will be noted that the primary vari-able in equation I is Dr As a result sllb-sequent analysis and development i»ill befacilitated if this equation is written inthe equivalent form

Q 0.092 CsT'/sP/'s'aT

Ds "/'(1.39+Dr'D4)

, +0.102c(1+0.0167Tm)0.0213

D,'ogD4/Ds'atts

per degree ccntigrad» foot inch (1A)

From the method of derivation whichassulnes a coaxial arrangement of thecable within the duct or pipe, the numeri-cal constants of the first two terms oiequations I, 1(A), and 2 must be con-sidered as being approximate only. Theywill serve, however, to evaluate the rela-

Btdlcr, iVchcr—Thcrnrcf Rcsislancc

The Thermal Resistance Between Cables«s '4 v ~

and a Surrounding Pipe or Duct Wall

tive magnitudes of the terms, and thecorresponding values finally employedwillbe based on test data

As a practical matter, a high degree ofaccuracy is not required since the thesmalresistivity betvreen cable and duct or pipe

represents a 'relatively small part of thetotal. thermal circuit and we are justifiedin materially simplifying these equations.From the standpoint of analysis of thetest data and the subsequent develop.ment of working expressions, it is desir-able to utilize the simple linear rehtion-ship

ymax+b

where y and x are variables and ti and b

are constants. Equations 1 and 2 are ofthis form provided that the second (con-duction) and third (radiation) terms inaybe considered as constants within the de-

sired accuracy of the Gnal result. Con-sidering equation 1A the conduction termconstitutes about 14 per cent of the totalin the case of a typical cable in duct in-stallation, and about 8 per cent for a

typical gas-flied pipe. type installation at200 pounds per square inch. The corre.

sponding values for the radiation term are

63 and 43 per cent.

Normal variations in D,'/Dd may pro-

duce considerable variation in the con.duction term, but the effect on the over-all picture is small, because conduction is

such a small part of the total heat Qotv.

Variations of T„can affect the radiationterm by as much as 20 per cent over a

sulliciently wide operating range; hot».

ever, when calcuhting a cable rating, witha fixed copper temperature of the order of70 degrees to SO degrees centigrade, th»

range of this variable is very small, and

an accuracy of the order of 3 per cent tn >

per cent may be expected.In the case of equation 2, the conduc.

Paper 50 Sz, reeommcoded by the AiEElated Cooductors Commsttce aad approvedthe Alas Tcchnical protram Committee ior

pres'otatioaat tbc hlEE Winter Qcacrat hfcctinc.He» YoA, H. Y.. January 30.February 3. I93".Sfaauscript subcaitted October sl. t949:available ior priories December y, 19t9.

F. H. Eot,tca is «ith tbe General ElectricCom'aay.

Scbcoeetady. H. Y„and J. H.«ith the philadelphia Elcetrie company.

Fhna'elphi

~, Pa.

AIEE TEAishcTtoHs

Table l. Test Data on Gas-Riled Pip» Type Cable Systems

TeatItumber Source

Q al'/ 7'/D'r p Q a7 i' a'7 D,"I

'able

1L Test Data on Cables ln Rber and Trantlte Ducts Encased ln Concrete

TestItomber Source

Q a7'I 7'ID l D,'Dr Q al','al'I

5........Bareoseher........Fiber.......o.d9....3.S .... 1.0.... d.4.....0.228........1.T41.7....11.8.....0.203........2.032.5.. ~ .IS.L.....0.235........2. LT4.4.. .24.8.....0.25T...... .2.44S.d....34.2.....0.281........2.SS8.1.. .39.T.....0.295........2.78

12.3.. ~ .Sd.1.....0.318........3.001. 13....3.5 .... 1.0.... 4.$ .. ~ ..0.20l ~ .......1.41

1.7.. ~ . 7.1...7.0.207..... ~ ..1.$ 94.S.. ~ .Id.3. ~ ...0.248........1.9S8.0....30.4.....0.233........2.28

11.0.. ~ .32.8.....0.300. ~ ~ .....2.3214.8....48.S.....0.288........2.8218.8....$ 2.4.....0.28$ ........2.dl18.4....S8.7.....0.278........2.89

3.13....3.5 .... 0.9.... I.d.....o. 194........0.S4I.T.... 3.2.....0.173........1.002.4.... 3.8.....0.203........1.0$4.5.... 7.7.....0. 188..... ~ ~ .1.758.1....12.1.....0.213..a.....1.40

)4.8....21.9.....0.217........1.53S........Jobos-Matteille....Piber.......s 38 ~ ~ 3 SS 12 5 ld 8 ~ 0 220 ~ ~ ~ ~ a I 50

14.9....19.2.....0.230.. ~ .. ~ a.l.sdLT.S....21.7.....0.238........1.$ 9

T........Johns-MaosiILe.... Traosite....3.38....3.88....1d.T....18.9.....0.292........1.5019.8, 19.4.....0,299.. .... 1.$ 523.3....22.0.....0.314........1.502d.4....24.$ .....0.318...... ~ . I.di

tion term constitutes about 24 per cent ofthe total for a typical oil pipe installation.Variation is more important than is thecase with the gas.pipe cable, but is stillwithin tolerable limits.

One peculiar phenomenon has been ob-served. The ratio of DJDQ', which ap-pears in the conduction term aIso, ap-pears in the first {convection) tenn ofequations 1 and 2 but in such a way thata change in this ratio produces an oppo-site, though lesser,'ffect on the totalvalue of these equations. A minimumerror should, therefore, prevail when theconduction term is treated as a constantif the denominator of the convectionterm also is treated as a constant. Thisprocedure will simplify the convectiontenn but it willhave the effect of approxi-mately halving its numerical constant ascompared with equations 1 and'2 since

the numerical value of the denominatoromitted is in the order of two. ActuaUythe test datC was analyzed both with andwithout this simplification, and no ap-parent change in consistency in the re-sults was observed.

Analysis of Test Data

It follows from the preceding discussionthat the test data for cables in duct andfor gas filled pipe. type installations maybe analyzed by plotting the observedvalues of

Q . CaT'I'pV'~—'gainst x~ (4)DD'II?" D ID/D

The data given in Table I were compiledfrom tests on gas.fille pipe. type cablesystems by The Detroit Edison Com-pany,'he General Electric Company,

I.....Detroit Bdlsota Compaay....3.42...8.07... I . ~ .23.4...20 ...$2....0.34......1.$ 87.8...27.3...15.8...$ 1....0.51......4.08

14.8...28.8...13.1...$ 1....0.84......5.3428.9... 17.1...50....0.49......5.7128.9... 14.4...$ L....0.59......$ .4827.5...14.0...51....0.$ 8......$ .43

2.. ~ ~ .Ceoerai BieetrieCompsoy...3.92...8.07... 1,7... 7 3... 8.2 .,39.. 0.30... I.d4Il.i". 9.T...4$ ....0.30......1.83IS.2... 12.4...50....0.31......1.73

7.8... 8.8... 4.7...39....0.37......2.9211.5... T.0...43....0.42......3.2214.9... 8.9. ~ .4S....0.43... ~ ..3.42

11.2... 5:8...40...;0.49..'.::;4;22 ""1$ .9. ~ 8.0...4$ . ~ ,0.$ 1 ~ ~ . ~ .4.$ S

3.....Ceoeral Cable Corporatioo...4.90...d.07...14.8...2$ .9... 9.2...$ d...'.0.'ST'.."..'.'.4'.47.4.....General Electric Compaay...4.90...8.07...14.8...23.1...11.8...44....0.40......4.77

and the General Cable Corporation. Thesedata are plotted in Figure 1 and the valuesof a and b in equation 3 are established asa~0.0?0; baeOM.

Table II presents similar data forcables in single dty fiber and Transiteducts in concrete taken from theBarcnschera and Johns Manville tests dis-cussed in reference 1. These data also areplotted in Figure 1 where it will be seen

that the Transite duct points fall on thegas in pipe calve, but the fiber ductpoints result in a different curve havingthe same value of a~0.07 but 5~0.10.This difference may be explained by thefact that the duct wall departs from anisothermal as a result of the relativelyhigh thermal resistance of the materialsused, that of the dly fiber being consider-ably higher than that of the

transite.'he

test data for oil-filled pipe-typecable systems from tests by The DetroitEdison Company,'he General ElectricCompany, and the Okonite Company arepresented in Table III and plotted inFigure 2. In this case, the analysis hasbeenmade by plotting the observed valuesof

y~—'itainst x~DQ"i'CaTi'Tea '5)CDT

and results in the values of am0.026b ~0.60 in equation 3.

It willbe seen from the analysis of thetest data that the agreement. betweentheoretical and observed numerical con-stants of the simplified convection term isextremely good in the case of oil as themedium, but in the case of gas, the ob-served value of 0.07 is somewhat higherthan the expected value of about 0.046.This is rather surprising since tests num-ber 2 (with gas) and number 9 (with oil)which are consistently dose to the es-

tablished curves in Figures 1 and 2 weremade with the same physical setup whichremained unchanged throughout thetests except for the change in the mediaemployed. Therefore, we should expectthe ratio of values obtained to be thesame as the ratio of the numerical con-stants of the convection terms in equa-tions 1 and 2.

This discrepancy seems to be due to thefact that in the case of several cableswithin the pipe, a condition of the major-ity of test data, there is an additional cir-culation of the gas between the cablesthemselves which is not properly ac-counted for by the use of an equivalentdiameter for thc three cables, but which is

apparently not effective when a moreviscous medium such as oil is employed.

As indicated before, however, a highdegree of accuracy is not required, and it is

1960, VoLUME 69 Brtllcr, Nchcr—Thcrrrral Rest'slancc 343

Table lll. Test Data on Oil Filled pipe Type Cabfc Sysleras

S.e" o ~ .rietraiae ~ . e ~........ ~ e ~....4.83...8.07"0.....o.Ceaerel Slleetrio CogaPsay...3.02...8.07

10.......0boaire Cogapeay... .....4.50...5.13

25.2.. o 8.0....40....2.04. ~ .~...e194S.S.. ~ 3.0....37....2.19..eo.... $5ll~ 4 ~ ~ e 4 ~ 5... ~ 44.. ~ .2.55. ~ e ~ 50lb.5... 6.8....48....2.88........ 704.1... 2.$ ....25.... 1.55...... 430.4 '. 4.4....31....2.14...,.. . 580.4 ~ .. 5.4....21....1.75... ..., 53.$l. l... 7.$ ....38....2.81..... ~ .. 70

21.6... 8.8....41....2.45... ~ .... 8$ .63$ .2... 11.4....50....3.00........10534.9...11.7....48....2.08. . .132

felt that a working expression based onthe foregoing analysis mill be sufficientlyaccurate.

Worhing Ezpressions = --'n

formulating the thermal resistancebetween cable and duct, itis customary toexpress this resistance in terms of anequivalent surface resistivity factor, as-suming that the entire resistance wasconcentrated at the cable surface, accord-ing to the expression

Hgc 0.00411 —,thermal ohm feet (6)p

Dg'n

which p is expressed in degrees centi-grade square centimeters per watt. SinceHgc~ chT//Q it follows from equation 6that

Dg'chTp 243 —degree centigrade centimeter

Q

per watt (7)

and

v ~ ~ L ~ a

Ka'(QDg"Tm')'+24feet (ll)

The value of p from equations 9 and 10 isplotted in Figure" 3 as a function of(Q'P/Dg')' and the, value of Z,c fromequation ll appears in Figure 4 as afunction on (QD,"T„')'. Also indi-cated on these figures are the values'fthese parameters for typical conditions.

In the case of cable in fiber duct, thethermal resistance of the duct wall isappreciable and should be accounted for.This is most readily accomplished bymodifying equation 6 to include this re-

.sistance. Thus

a7

Tost 0lratabor Source D 'a 0 4T T ol',/doT'/dT /i

Fpa'(Gber) 0.00411 —,+0.33thernial ohmp

D,'eet(12)

in which the second term represents thedifference in thesmal resistance between a4-inch fiber duct aad the correspondingsection of concrete which it replaces.

Discussion of Values for Cables inDuct

It wiH be seen that the method of de-termining the thermal resistance between

'able an'd duct presented herein differssomewhat from the method given inreference 1, although the results are sub-stantially the same for terra cotta andfibre ducts. For Transite ducts, the„values of thermal resistancI: derived in amore fundamental manner in the presentpaper, are slightly lower than thoseappearing in the reference, being equal tothose assumed for terra cotta.

it will be reoaUed that the reasoniagused in developing eigebraio eapressionsfor these, va ues assumes an isothermalduet wall. The test data presented in

Figurc 1 ~ Analysis of lest data for cables induct- and gas@lied pipes

0

pl/tQI/d4T '~0.253—„/, (degrees centigrade)'/'8)

It is thus possible to develop working ex-pressions in terms of p in the case ofcables in duct- or gas-filled pipe by sub-stituting equations 7 and 8 in equations 3and 4 with the appropriate values of o andb. In the case of oil-filled pipe a simplerexpression is obtained in terms of FI,a.

For cables in single dry fiber ducts

13,700p

Q /i /gd e gre e s c e n 1 i

p/e ~ +$ 7

D,'rade

square centimeters per walt (9)

For cables in other types of single dry

os

~ 4

Os oT

oR

13,700p .,/,,/, degrees ccuti-

p /'11.3D,'rade

square cciitimclers per walt (10)

For cables in oil.filled pipe

00 ev'r''"

p,v

Bullcr, Ãchcr—Thermal Rcsisksncc A,lEE TR~wsocTlo~s

~Q"aad plotted in Figure I, how-

> "dicate a.good correlation even

4~,there is substantial deviation from,@/assumed isothermal as indicated by

e hi'sic data on which the table is based.

ilia the range covered by the data, in-'ag the departure from the isother-

m changes the resulting constants some-ha't but does aot invalidate the method

lrf."analysis.'.;.It follows therefore that a considerable

tion in P for cables in single-fibre..may be expected depending upon

.Qative thermal resistivities of thewail and-theisurroundiag medium,'ther. data which has come to the

'. atteation confirms this. Thus~e'of Fi uct s~oul

asidered as an u limit.y, the application o the values

ca foi single ducts to the case of cables.;multiduct structure, depends uponQect which the total heat field has in

'er changing the temperature gradi-'tj'i'around the individual duct waHs.e.data given by Smith ia his discussion

7(ence 1 indicates a value of p for'riuitiple-fiberducts in concrete corre-

"adiag dosely to the curve for cable~mar: ~~pe

indicated in reference I, addi-aI:.test data taken on multiple-duct

blies are desirable to definitdylish the limitsunder these conditions.'reasons also indicated in reference Ivalues are not directly coinparable

'ithe values adopted by the Insulatedower'Cable Engineers Associations and

"aot directly adaptable to their calcula-oir'procedure,

X":nclusioas

t":.~The theoretical relationships between'various quaatities involved in the eQee-,:thermal resistance between cables and

;surrounding single duct or pipe have been'eveloped ia a manner which properly'ts for 'the simultaneous modes ol heat

cr by convection, conduction, andtlon.

I .'Ily means of these relationships certain

0: ~.

test data on cables in duct and in gas- andod.fiiled pipes have been analyted and work.

g,curves are'. presented for determining the'resistance lor any particular case ~

.. maY be encountered in practice..~j'-'Under typical conditions representative

. es of the equivalent surface resistivity4 for use in equation B are 800 degree

,.tlgrade square centimeters per watt lorfcs.'n pipe, single dry terra cotta or,„fslte ducts at atmospheric pressure, 450Scabies in gas-filled pipe. type installa-

at 200 pounds per square inch, and 350Ies in oil fillcd pipe type installation.

tative values of IS for cables indry fiber ducts will vary from 850 to

100.

~„..'Vot.vwit GO

Mf

J, ~,'\

p8

0Q.T

Appendix l. Theoretical'evelopmentof Thermal Con-

ductivity 6etween ConcentricIsothermal Cyclinders with Gasor Oil as the!ntervening Medium

The mechanism of heat transfer between acylindrical radiator and an enveloping iso-thernial enclosure through an interveningQuid medium is such that a portion of thetotal heat Qow Q is carried by convectionQ«, a portion by conduction Qrc, and thc re-mainder by radiarion Qi. ln fOrmuhtingthe components of thc thermal circuit.thcrcfore, it is morc convenient to «ork interms of thermal conductanccs rather thanthermal resistances since the foriner quanti-ties are directly ad<liiivc. Thus, if 3T is thetemperature drop in degrees centigradeacross the circuit

Q Qcr Qcc Qi—+—+ —watts perdegrcccenti-aT aT aT aT'grade foot (13)

Figuic 2. Anclysis of lest cfctc for cc6lcs inoil4lfccf pipe

The phenomenon of convection involvesthe conception of the temperature dropbeing conccntratcd in two films, one at thesurface of the cylindrical radiator of diame-ter substantially equal to the diameter of theradiator D, in inches, and one at the surfaceol the enclosing isothermal surface which willbe considered also being cylindrical ofdiameter Dc. The following formula basedon McAdams'equation 42, page 251, 1stedition only) is applicable to either film.

Q« ~ 12"DI 'GATI'I'Kwatts pcr foot (14)

in which DI ic in inches, and

/d'c gh i'~

(—-) watts pcr centimeter '~'c-

( ')grees centigrade '~'15)

Thc significancc ol the components olequation 15 and rcprcsentativc values lorgas (air or nitrogen) and Suniso number B oilare given in Table lv.

Bullcr, IVchcr—Thcnnal Rcsisfancc 340

0 lo '0 so 40 so Co 70 eo 90 00 no lao l30

0','T~ T

gooog

IaooTYPICAL,

a IOOF CAP«l

81 Eu IL

IN OUCT5

1100

BLE I

~ eeoON FIBRF OUC4 I Ised/Og+.33

doe 243 Nsd Os

~a

NOOUCT

CABLE IN PIPEsEAAA COTTA A

TAANSITE-1w2$

OFcy

oa.«4.$

FILLET v'S

O PIPE0

aoo

LE IN PIPE S FIL5.1,

TYPICAL Of CAPIPE AT 200 P.

2S Os 4.$

LE

20 40 40 oo goo uo lao goo goo goo rgo 240 Zoo

taiy,s T„s>'A

Figure 3 (left). Values ol p foc cables in dcy single dgccfs and gao-filled

pipe

Rgure 4(above). Yafueo of Hga for cables in oif-flllecfpipe

0 x,a,o,a la aa L4 aaLe 2 4 J.o xa 3.4 3.4 s ~ Ao 42

fo"P/0; l'*

In the case of air or inert gas, these physi-cal propesties are substantially independentof temperature over the working range butthe density is a direct function of thepressure. Thus, ifP represents the prcssurein acmospheres, from equation 15

Kcaa0.000755P'/'atts per centimeter'/'egreescentigrade '/'l6)

When oil Is employed as the medium thcphysical constants are substantially inde-pendent of prcssure and tempesatures withthe exception of the viscosity which for thetype of oil cornrnonly employed (Sunisonumber 6) may be taken as varying in-versely as th» cube of the temperature ac-cording to the rehtionship

94,000grams per ccncimetcr second (17)

The value of K for oil thus becomes

K~ 0.000434Teg'/'accs percentimeter'/'egrees

centigrade '/'18)

~ ~ ao *x 2 4 ao4.4 Aa 44 SO 4.2

The solution of equation 14 for the two6lms ia series and mith equation 16 or ISsubstituted therein is given with sufficientaccuracy by the expressions

Qcr Dc dT'/'P'—(gas) m0.092 watts pes de-d T 1.39+Dc/Dc

grec centigrade foot (19)

degree centigrade foot (20)

From a theoretical standpoint the ex.pression for the conduction componentshould take into account any eccentricitybetween the cyiindsical radiator and theenveloping isothermal enclosure. In thepractical case of cables in duce or pipe thecables willnot rest uniformly on the bottomof the duct, and also in the case of a non-metallic duct the duct Ieafi is not strictlymaintained as an Isothermal. Since theseeffects cannot be evaluated, the familiar

expressioa for the resistance between twoconcentric cylinders in terms of the dimen-sions of the cylinders and the thermal re-sistivity of che medium mill be used. Thus

Q 0 0213 ( 011CL4LC40gra—(gas) —'aas per degreedT loggo Dc/Dc

centigrade fooc (21)

Qcgr . 0.116—'goal) —walls par degreed T loggo Da/Dc

centigrade foot (22)

The radiation component with gas as themedium is given with sufficient accuracy bythe followingexpression based on McAdamssequation 5, page 61, Gsst editioI),

I 0 cNIAc~~—(gas) aa0.102Dgc(1+0.0167Teg) wattsd1


in which e is the emissivity coefficient of thesurface of the cable and T« is the averagetenlperature of the medium. The radiationterm is ineffective cohen oil is the medium.

The over.all thermal conductivity is ob-tained by substituting equations 19, 21, and23 or equations 20 and 22 in equation 13.

Table IV Appendix IL List of SymI3ots

Symbol Quaaiity Oaa al SO C OllalsOC

p........... Tbcrcasi resiscivicy...........,........C cm/«atc....... 3 900.......... ~ ~ .TISga.......e...Average absolute viscogicy.............grains/cm scc....., 0.000l95........0.75a ..~........ Deasicy.. .grams/cmg ......, .. 0.00l'lo P.......0.904Cr. ~ ~ ~ . ~ ~ ~ ~ ~ Specific bess ac coascaac pressure......,«acc see/C....... ~ . 0.99S ~ ~ .. ~ . ~....2.IO

gragaS........... Aeeeleratiaa due tO gravity.......... Cm/SCC1...........990. ~ ~ . ~ ~ ~ ~ ~ ~ .990r.s......, .. TIgcrgnal eocil'ieicnt oi ~ cpaasion........ I/C....... ~ ~, ~ ~ ~ ~ ~ 0 OOSIO. ~ ~ ~ ~ ~ ~ ~ .0.00008

Q~totaf heat floggr from equivalent sheathto duct wall or pipe in watts per foot

d7 aw temperature drop in degrees centigradeP aa prcssure in atmos pheresD, ~diameter of the sheath ininchesDc'«equivalent diacnetcr of a group of

cables in inchesDa ~inside diameter of chc duct wall or pipe

in inches

Buflcr, /I/cIIcr—Tr'crrnal Rcsisfancc 3, I EE TILAwsAcTIo85

T~'~averag» t»mperature of the medium indegrees centigradecoefficient of emissivity of the cable.sur-

facer and y~rectanguhr coordinatesa and b~»xperim»ntally determined con-

stantsH,a ~thermal resistance between equiva-

lent sheath and duct wall or pipe in ther-mal ohm fe»t

Hsa'~equivalent thermal resistance be-tween equivalent sheath and Gbrc ductwall including the increased tb»imal re.sistivity of the duct wall over that of thesurrounding mediuln in thermal ohm feet

J)~equivalent surface resistivity factor indegre»s centigrade square centimeters perwatt

sI ~ thermal resistivity in.degrc»s centigradecciltlnic'ters pcf wa'tt

'verageabsolute viscosity in grams percentimeters second

8~density in grams per cubic centisneterC„~speciffc heat at constant pressure in

watt seconds per degree centigrade gramg acceleration duc to gravity in centimeters

per second squaredc~ th»rmal coefficient of expansion in centi-

meters per centimeter degree centigrade .

E~a factor dependent upon the physicalconstants of the medium in watts perc»ntim»t»r'ia degrees centigrade'«.

a

References

1, TNR TaxtRRATVRR RIRR ot CARO'Rs IN A DvcrBANC, J H. Licker. AlEE Transassions, volume08, part 1, 1049, pages 840-40.

2. HRAT TRAicsaisstoN (book) W, H. Mchdams,htcCsaas.Hill Book Company, )re» York. Lc. Y.,dsst editloo, 1033.

3. TIIRRNAI CRARAcraatsTIcsoF A 120 VvHICII'aessvaaGas.PIu.ao CARI R lnsTAt tATICN,

W. D. Sandcsson, J. Sticker, M. H. Mcasath.AlEE 1 raasassiaas, volume dT, Psst 1, 1948, pages487-08.

4. A Srvor ot TKR TaiitaaATvae Dts'salsaTio'I IN EI Rcsasc CARtas IN UaocacRovaoDvcrs, P. J. Baseacches. T'assis, Depastmeot olElectsical Eagioecsing, Uaivessity ol Wisconsin(hfadlaon, Wis.), 192S.

S. CvaaRNT CARRTINo CAFAcITT oF LNtaao.NATRO PAFSR, RVS ~ RR ANO VARNISKRO CANRRIC1Nsw.ATRo CAaaas. Pablisasion lruaIb<r P 2P.Cgd, lasulatcd Pores Cable Eagineess Association(Nciv York, H. Y.), dsst cditioa, 1043.

DiscussionR. H. Norris and Mrs. B. O. Buckhtnd(Gen»ral Electric Company, Schenectady,N. Y.): Eiftci»nt work in the heat.transferfield on a variety of applications requiresawareness of the definitions and units, inorder Lo avoid confusion and misunder-standing. In this paper and other paperswritten by cable engineers, confusion arisesas to th»»acct meaning of th» expression"thermal resistivity." R»sistivity as nor-mally deffncd (by the American StandardsAssociation (ASA) for cxasnple) is a prop-erty of a substance and is not affected byits geometry; for example, the resistivity ofcopper has a constant value at any spcciffedtemperature, while its resistance dep«nds on

,its site and shape. Then the us» of thcword "resistivity" for surface phenomena isa misuse of thc terra.

To show ho» Lhc distinction betweenresistance and resistivity caters into lhc

picture. the thermal circuit for a single-conductor cable in air is given in Figure 1 ofthe discussion.

In this Ggure, iso, l,a, and ra are tempera-tures of copper, sheath, and ambient. re-spectively, 8 is insulation thickness, p isthermal resistivity of thc insuhting material,sf z, is the log mean area of the fnsuhtion forheat Gow, s(sa is sheath area, and fic andigs are the cabl» engineers'erms for "sur-face resistivity" for free convection andradiation. Each fraction in thc Figuri isthc th»rmal resistance; and when resist-ances and temperatures arc known, the heatdissipation of the cable is known. But inorder for the resistances to be dimensionallyconsistent, th» dimensions ofp must bediffer-ent from thc dimensions of l), and thereforep and ff should not be called by thc samenanlc

Since the d»Gnitlon of p as thermal resis-tivity conforms to ASA standards, it mightbc better to denote ll as th»rmal resistanceof a unit surface. Its reciprocal h, is de6ncdas surface heat transfer coclffcient, or alter-natively as surface Ghn conductance. Theconcept of ~ conductance is particuhrlyapplicable here, as the total Glm conduct-ance is the sum of hr and hc. and thereforenumerically easier to handle.

The units of length used in the paper seemto be a mixture of metric and engineeringunits. A combination of square centi-meters with feet has no logical basis. Ifanycable dimensions were expr»ss»d in centi-meters, the mixture lvould bc logical al-though not standard; but since dimensionsare not so expressed, it seems time to aban-don this practice and use the engineerinsystem of units throughout.

It is therefore proposed that the AIEECominittee on Insuiat»d Conductors takesteps to p»rsuade its adherents to becomefamiliar with ASA standards and to usethem «here they apply.

IL W. Burrell (Consolidated Edison Com-pany of Neir York, Inc., New YorL, N. Y.):The authors have presented a desirableelaboration of Appendix Il of a previouspaper by Mr. N»h»r.'lthough the ap-proach to the problem is uot changed, thelnaterial presented in the Appendix referredto is of sufficient importance to justify amore detailed presentation.

IL is apparent to those engaged in the 6eldof cable heating that the Insulated PoirerCable Engineers Association recommendedvalue of l), while perhaps sufficiently conser-vative for general design, lacks Lhc flexibilityneeded in comparing alternative construc-tions. Precise determinations of ig 'orvarious types of inslalhtions may noL bepossible because of inherent variations inthe physical constants involved; however,as additional test data are compiled. the

n,Aw

Flgvse l. 'hesincl circuit fos single conductorin ~ is

probable range of ig, for a particular case,will be better understood, Lh»reby makingpossible more realistic comparisons. Theauthors chrify our conception of the dfectof the various parameters involved in thetemperature drop between cable surface andduct or pipe walL For a given system ofcables in duct or pipe, the th»rmaf resistancewilldecrease sensibly with increasing wattsloss.

W. B. Kirk»iintroduced this modiffcationwhich is taken into account in determiningcable ratings for the Consolidat»d Edisonsystcfn

As one follows the assumptions made inthis paper, there appear various points towhich exception. might be taken .on theground that they are not substantiated,for exampl»l the assumption of the sameconstant in the expression for the convectionGhn at (he cable surface and at the innerduct wall, the treatment of conduction onthc basis of a concentric system, and thearbitrary assumption of an cmlssivity co-»fffcient of the cable surface of 1.0. Yet,the important point ls that putting all ofthese various assumptions together in theparticular form given in the paper, the over-all end result does produce expressions whichare reasonably satisfactory.

It is unfortunate that, while the basicequations and the selection of parametershard a reasonably sound theoretical basis,the Gnal working expressions given areessentially empirical and do not allow anaccurate determination of the separateeffect of the three modes of heat transfer.On the average, the calcuhted values ofQfcaT for the oil-6lled pipes, gas-611»d

pipes, and cable in duct are about 5 per cent15 per cent. and 55 per cent higher, respectively, than the measured vahtes given

'ablesI, II.and IIIof the paper. Special-ists in the 6eld of cable heating would beinterested in knowing which component orcomponents are responsible for these dis-crepancies so that »xtrapoLttion into newGelds could be Inade with conffdence.

It is stated in the paper that the agree-ment between theoretical and empiricalnumerical constants of the simplified con-vection term is dose for the case of an oilmedium, but is off appreciably for the caseof a gas medium. It also can bc said thatthe conduction.radLttion constant agreeslvith theory for the case of a gas medium;however, for the case of an oil medium. theconstant theoretically app»ars to rangefrom 0.60, as given in the paper, to n»arlytwice that value, depending upon the valuesof D,'and Da involved.

From the over-all standpoint, it neverthe-less appears chat the expressions for J) andH,a. as given in equations 9, 10, and 11 ofthe paper are quite workable and agree withtest data as well as could reasonably be ex-

pected. A high degree of accuracy in thecalculation of allowable current ratings ofcables is not yct to be expected but impor-tant worL has been done in the past fcwyears in chrifying our understanding of heatflow through duct stluctur»s and the earth,and this paper is an important contributionto such understanding.

RBFBRBNcas

1. See selcsence 1 ol the paper.

2. TK~ Caacvaastoa ot Caata Tallteaafva ~ sIN Svaw*r Ducts. W. B. Xlske. AlEE Joaraal.volume 40, 1030, pace SSS.

1950, VOLUME G9 Bisllcr, iYchcr—Ther»tnf Rcsisfasscc 347

f'a» lie

I~

R. J. Wlseman (The Okonite CompanycPassaic, N. J.): I like thc author's paper verymuch. It explains the three methods ofheat flow from a cable to a surroundingmediutn, nameiy, conduction, convection,and radlaticn. Also, they give the variousparameters which influenec each factornamely, cable diimeter, temperature, andtemperature difference, and viscosity of themedium. The various formulas look quite

"formidable when we note terms raised tofractional powers. It is not easy to obtainthc constants for each formuh as they aredependent on condicions not easily calcuhbleso it is necessary to gec test data and workback to nurnerics which will give the de-sired results. It so happens that as all threemodes of heat transfer are funccioning atche same time, a change in dimensioningtends to work in opposite directions, reduc-ing thereby.chc,effect of diame(er. AIso therange in temperature is not great and as wetake the one. fourth power ot temperaturedifference and three fourths power oftemperature, the variation with tempera.ture is not great.

About two years ago we decided to re-study the thermal constants tre obtainedwhen we originally set up thc Oilostaticcable system. At that time we used thecylindrical log forlnula of ra(io of internalpipe diatneter to circumscribed circle overthe assembled conductors, and also a con-stant which was a function of the tempera-ture.

Our more recent tests showed chat thethermal resistance was almost independent

~ of temperature (a variation of abo'ut 10 percent between 30 and 61 degrees centigrade)for an oil pressure zone and a very few percent for a gas pressure zone at 200 poundsper square inch. Wc also noted thatwithin the accuracy of testing we couldsafely assume the thermal resistance tovary as inversely as the diameter of theshielding tape over the insulation. As aresult, we have sec up two simple formulasfor the determination of the thermal resist-ance of che pressure zone for three cablesin a pipe, namely, for oil pressure systemH~1.60/D thermal ohms per foot per con-ductor where, D is thc diameter in inchesover the shielding tape; and H~2.58/Dthermal ohms per foot per conductor for agas pressure zone operating at 200 poundspcr square inch. You willflnd these valuesof thermal resistance for the pressure zonesamply accurate.

As the authors refer to the surface resis-tivity factor P, the values of 4 comparableto che above constants in H~0.00411 tt/Dare IS 390 tor an oil.pressure system as cora-pared to 350 given by the authors and P~827 for a gas pressure system at 200 poundsper square inch as compared to 450 given bythe authors. We are qutte confldent in ourvalues and have been'sin'g'theiii foi 'over ayear.

in the paper, since this analysis gives theorder of magnitude contributed by each ofthe three mechanisms of heat transfer.

The authors have assumed for cable induct that the component of the thermal con-ductivityduc to radiation can be treated as aconstant in the range of normal operatingtemperatures. Only the component duc toconvection was considered as variable withchanging cable diameter and heat flow.This assumption does not lead to a true pic.ture of the variation in thermal resis(ivitywith heat flow, or more fundamen(ally, withcable tetnperature. Mr. Darnctt and 1 havestated in our papert that the decrease inthertnal resistivity with increasing sheathtemperature is caused primarily by varia-tion in the radiation component of heattransfer, and that the effect of temperaturevariations on convection are negligible overthe normal operating range.. This state-menC is verified by calculations based uponequation 1A of the Huller-Ychcr paper,which is repeated here:

(q i 0.0920,T'/P'i

+ (Ih)Di'ciTg Da'(1 39+Dc /Dd)

(convection)0.0213

~t+0.102c(l +00 167T»t)Di'og Dd/Dc'"dt. )

(radiation)

in watts per degree centigrade toot inch.The emissivity factor, c, is assumed to beunity at attnospheric pressure.

Table I of the discussion lists two repre-sentative sheath temperatures from our testdata on flber duct in concrete, and thesetemperatures might very well be represent-ative of the operating range of a cable. Theterm (Q/D,'hT) evaluated in equation 1Ais inversely proportional to the surfaceresistivity factor, tt.

The three terms in the equation give thcthermal conductivity components due toconvection, conduction, and radiation respec-tively. As we increase the sheath tempera-ture over the range showa, the increase inthe radiation tenn produced by substitutingour experimental data in the Buller-ocherequation is five times grezCer than that ofthe convection term. This shows that theexperimentally obsetved decrease in tt overthis range is due ahnost entirely to the in-crease in the radiation tetm. These cal-culations are based, of course, on the ratherlarge cable size that we employed in ourtests. A smaller cable size will increase theeffect ot the convection term only slightly,however, and not nearly enough to make itsvariation with temperature equal to Chat ofthe radhtion term. Identical calculationswith our data on Transitc in concrete,Transite in air, and fiber in air, show simihr

relative variations in the radiation and coti-vection terms.

The authors have neglected thc variationin radiation component of conductivity withtempenture, pointing ouC thac these varia-tions are quite smalL This is justlfiablefrom a practical stand point. However, thevariations in the convection component withtemperature also should be neglected forpractical considerations, since, as is shownin Table 1 of thc discussion this factor iseven smaller thart thc change in the radia-tion tenn. This would considerably sirn-plify the Bailer-Heber equations for the sur-face resistivity factor. ln their equations9 and 10, (he surface resistivity factor. f4depends upon thc fourth root of the heacflow. This does noc have much significanccsmce it is based upon the variation in thcconvection tenn, a second order elfccc com-pared with the radiation term. Similarlythe dependence of ti upon the square root ofthe sheath diameter is doubtful, since chcchange from.a fourth root to a square roocdependence in the convection term also wasbased on the very small change in convectionconductivity with temperature.

The foregoing discussion tras confined tocable in duct with air as the interveningfluid. Its applicability to cable in gas-filled'pipe at high pressures, where convectionbecomes the principal mechanism of heattranster, requires further study.

The authors have done an excellent job inhelping co establish the theoretical ground-work necessary to both encourage and guideexperimental workers in the duct heatingproblem.

RBFERENCE

l. Hear TU*ttsrcx Srvov ott Powea Cast.aDvcts atto Dvcr Assctcstses. Pau( Gteeblcr,GU7 P. Batoctt. AlZZ 7 vaatoctioat, rolutoe 09,pan I, 1950, paces $$7-07.

I

i'

~I

ra

h

0

riL.

~ y

i

tc

Table l. Gtecblet-Becne(( Da( ~ ts

h. H. Kidder (Philadelphia Electric Com-pany, Phihdelphia. Pa.): This paper byBuller and Neher, together with two pre.vious papers by Mr. Neher,4t completespresentation of the steady-state considera-tions involved in a project which was startedabout four years ago when PhiladelphiaElectric Company interested Mr. archer inundertahng an investigation of funda-mental relationships.'s necessary to dc(er-mine approximately what pipe.cype cablecircuit load ratings would be accuratelycomparable with thc load ratings of con-ventional cable circuits in ducts.

The thermal resistance through the spacesbetween the cable sheaths and the pipe or

f'uct

wall inclosures is an important link inthe thermal circuit. Ithad beenhoped thata general rehtionship could be developed in i',such a form thac all of che differences bc-

' » ~ I

Pavl Greebler (Johns Manville Corpora-tion, Manville, N. J.): In this paper theauthors have contributed imrncnscly to-ward an understanding of the mechanistnsof heat transfer from (he cable to ics sur-rounding pipe or duct avail. The theoreti-cal analysis was necessarily based upon thcsimplifying assumption of a coaxial cable induce arrangetnent. This does not, however,detract from thc value of the analysis given

Lead SheathTemperature

Coclde Duct MesoV/all Sot(ace TemperatureTemperature''ullet

NehetTemperature Eeuatloo lA

Drop Cooccctlou Radlatlooar Tctm Term

GteebletBarnet tData

tt lo 'C(cm)'/»

dd.2...77.2...

...40.$ ...........50.$ ...

...5$ .0,....,.....0$ .4...~ ~ ~ ld. l. ~..., 0 0dx...o. Ipd.... ~ ~ .990~ ..22.0.....,.0 005...0.2ls ~ ...,..020

loctcaac 0 00$ ...0.0l5,..., .. 00~ decrease

Temperatures acc lo dcrtccc ceodetadc. Thc latldc duct »att cut(ace temperature lc au avctaee value.

,'34S Bttftcr, /V'cJtcr—Thcrnaf Rest'stattcc AIEE TRANSACTIONS

; ~ '~ ' ~( ~ q,

e

Si 6 1 ~

~ ~

s

tween cables in air in ducts and cables inhigh-pressure gas or oil-flied pipes could beexplained in terms of the physical constants

ich characterize the respective fiuids andoertinent geomctricat relationships.

: method presented by Buller andhas approximately achieval this re-

sult, at least to the extent of permitting thecorrelation of data obtained by various in-

„vestigators at various tiines in various con-'structions. It does not disturb ine par-

ticularly to find that there is some apparentdifference between the elects of Transiteand fiber duct walls, respectively, under theconditions which prevailed at the time thetests were made. I think we should hesitateto attach much significancc to these appar-ent differences because there was no attemptto control the moisture content in thc fiber orthe Transite, or even to make the testsunder conditions comparable to those to bcexpected in the usual exposures to naturalbut variable moisture conditions to bc en-countered in underground structures. Thesignificant point is that Buller and Neherhave obtained a correlation ivhich now per-mits estimating the thermal resistance froincable to pipe„or duct wall with sufficicutaccuracy, so that little, if any, practicaliinprovement in cable load ratings can begained by introducing furgher refinements intheir analysis of this part of the thermalcircuit.

RspsRBNcssI. Taa Tassraa*ruaa Rise or Bvaiao C*n,asAuo Piras, J. H Neher. AlEE Troasersioar,olume il8, pact 1, 1040, pages 0-1T.

Sce relcreace 1 ol the paper.

F. H. Buller and J. H. Neher: Mr. Norrisand Mrs. Bucldand have taken us somewhatto task for our apparent'inconsistency inexpressing our physical units in one systemand our geometric units in another. Forbetter or worse it has long been the customin cable rating procedure to express thephysical units involved in the watt-second-centimeter-gram system, and to ~ expresslength's in feet and diameters in inches. Indeveloping our equations itwould have beenmore consistent to have expressed the latterquantities also in centimeters, and thea tohave converted the final expressions to'hesystem of measurement used in practice.Wc chose to use the mixed system through-out, however, in order thag the reader mightbe able to use any equation in thc drvelop-ment, directly, without encountering theuncertainty which inevitably arises as towhether you multiplyor divide by the trans-formation constants.

The usc of the tarn "surface resistivityfactor" is a slightly different matter. and asour sncntors have yoin]ed.out, it has dimen-sions which are not those of true, or volu-metric, "resistivity." Here again, thisnomenclature has been hallowed by tiincand is thoroughly understood by cable engi ~

~ ~

neers, for whom this paper was written. Itshould be stressed, however, that this "sur-rvce resistivity" is not a fundamental

rsical quantity, in the sense that volu-..ctric resistivity is; but as pointed out, is

the resistance of a unit surface of a flinwhich, purely for purposes of convenience,is assumed arbitrarily to represent the entirethermal resistance of the composite heattransfer elects operating in the r'egion be-

tween cable sheath and duct wall. 'lt is un-fortunate that we do not have a more dis-tinctive name for it.

Mr. Burrell has presented a thoughtfuldis-cussion of the assumptions which we havemade in developing the theory used forcorrdating the test data. In this respect, abook by Prof. McAdamst gives a constantfor the convection film on thc outside of acylindrical surface in a free medium which isabout 20 pcr cent lower than that for the in-side of a pipe and which we have used forboth films. Wc have not distinguishal be-tween the Lwo constants because no informa-tion is given as to thc values of these can-stants when the cylinder is placed withinthe pipe. While a formula for the conduc.lion component in a nonwoncentric systemis given by Whitehead and Hutchings't isfar too complicated to use in this analysis,'and it reduces substantially to the concentricformula which we have employed except forextremely small separations between thecylinders at one point. Further there isconsiderable experimental evidence to sup-port the assumption that the emissivityconstant is substantially unity for the typesof cable surfaces employed.

Discrepancies were expectal, because ofthe assumptions which had to be made, a'ndbecause the physical location of the cableswithin the pipe cannot be controlled. Wehave used assumptions and theory only toobtain a sensible understanding of theproblem with which we have to deal and todetermine ivhat simplifications can justifi-ably be made in order to obtain practicalworhng expressions. These working ex-pressions were then developed directly fromactual tests rather than from theory. We donot share Mr. Burrell's desire for workingexpressions of sufficient complexity toidentify the separate elects of the threemodes of heat transfer.

Dr. Wiseman's simplified formulas forcalculating her (on a per cable basis) forthree 'cables in an oil-flied pipe or in a gas-filled pipe at 200 pounds per square inch arevery intaesting and similar formulas maybe derived from Figures 3 and 4 of the paperassuming that Q, P, and T~ have Gxedtypical values. Unfortunately Dr. Wise-man's derivation of the equivalent P in hisformulas gives values ivhich are not com-parable to P as defined in this paper. Thecorresponding rehtionship forP as defined inthe paper is

hgc 0.004110

3 2.15DN

and this yields P 290 for the oil.pressuresystem and P ~ 450 for the gas-pressure sys-tem

We cannot accept his formula for the oilsystem since its corresponding value on atotal heat'iow basis is" Hrc"

1.15/Dr'hich

is equivalent to Q/dT ~ 3.9 forDr' 4.5. Noae of the tests cited in Table~IIIof the paper give an('upport for so higha value.

Dr. Wiseman also assumes that the over-all thermal resistance varies inversely withthe diameter whereas we believe that a morerepresentative variation may be deducedfrom the slope of the curves of Figures 3 and4 in the vicinity of the typical operatirgpoints. Thus for Q 25 watts per foot andT~ 50 degrees centigrade, we derive thesimplified expressions

H,c (oil)~0.70/De"/s thermal ohm teeL (I)Hrc (gas at 200 psi) ~1.20/(Dr')'l thermal

ohin feet (2)

The conesponding equations on a percable basis and with three cables in thc pipeare

1.44 2.07hrc ~= and hrc m—respectively

Qp (D ) ~ s

Figures 3 and 4 are intended to give prac-tical working values ofhce or Hrd over a widerange of operating conditions. Mr. Grecb-ler is right in pointing out that the elect oftemperature variations upon the radiationcomponent is considerably greater than theeffect of variations in the convection tennwhich is the essential variant in Figure 3.The inclusion of the temperature of thcmedium in thc ivorking expressions wouldvastfy coinplicate them, however, and as apractical matter this is unnecessary.

In all of the Greebler.Barnett data't willbe observed that P varies inversely as Q'/<

within the accuracy of measurement. Thedependence of P upon Dr cannot be evalu-ated from this data since only a single valueof D, was employed, but since the convectionterm theoretically varies directly as Q'/</D'/swe believe that the temperatssre variation inthe radiation term which Greebler has mentioned will be accounted for with su%cientaccuracy by expressing the Greebler-Barnettdata for fiber and Transite ducts in the form

Ji(fiber) «1120Ds'/'/Q'/'egrees centi-grade square centimeters per watt (3)

lf(Transite) m 990Dr'/'/Q'/'egrees centi-grade square centimeters per ivatt (4)

This will have the elect of changing theslope of the curves «hen plotted in ac-cordance with Figure

3.'he

coiresponding values of Hrc assuming '

worhng value of Q m 10 watts per foot

Hrc (Gber) m(2.59/Dr'/ )+0.33 thermalohm feet (5)

Hrc (Transite) 2M/D, I'hermalohin feet (8)

While further theoretical and experimen-tal work may well be undertaken in order toclear up some of the apparent discrepanciesbetween theory and practice and to yiddmore factual data on thc pafonnancc ofcables in duct; we agree with Mr. Kidderthat little of any practical improvement incable load ratings will result. We do notwish to discourage further elorts in thisdirection, but we feel that it is sufficient tobase cable ratings on Figures 3 and 4 of thepaper or more simply on equations (1, 2, 5,and,8) just given.

Rspsasscss

1 See ccfcreace 2 ol the paper.

2, Cvaaairr Rarsuo or C*ai,as roa TaaNsaussiou auo Disraiavrsou, Se Whitehead, B. EHuichlags. sources lastliutioa ol ElectricalBaciaecrs (toodoa, Eagieod), volume 83, 1038.cqueiioa 10.3, page 531.

3. Hear Taausraa Srvov oN Porvaa Caai.aDoers auo Doer Assausaas, Paul Greebler, Gusp. Beraeu. AIEE Trcareaioas, volume 80. pert'1, 1030. paCes 337-5Z.

C. 'Dlscussioa br J. H. Lleher ol cclcreace 3~ bOve pegCs 385~

1950, VOL.URIB 69 Bsdlcr. >Vchcr—Thc.-nsal Ress'starve

ATTACHMENT 3 TO AEP:NRC:0692DF

CABLE TRAY ALLOWABLE FILL DESIGN STANDARD

e ~ l p ~ sir mao P

~ J

2.

In all tvpe trays, cables shall be placed in the travs ina neat workmanship like manner. Crossing of cables shallbe avoided, cable oile-uos shall be keot to a minimum andcables shall not extend above the top of the tray.(a) When installing cables in a power t ay place the oower

cables in a single layer soaced approximately 1/3 theO.D. (outside diameter of the cables) apart. SeeFigure l.

(b) The surmtation of the O.D. of the power cables ~ shall notexceed 75% of the tray width. See Table 1 for maximumallowable fill.

3. When installing cables in control and ~strILRoentation tr ytotal cross sectional area of installed cables shall notexceed 40% of the trav cross sectional area. See Table 2for maximum allowable fill.

4. When it is necessary to exceed the maximum allowable fillapproval from the responsible cable engineer is required.

0FOR SPACING OISTAHCE

KTWEEH CAMS 5EEHOTE5 I IZ.MLOW

FIGURE fPOWER CABLE SPACIAI6

NOTES:f. FOR CASLES OF EQIAL QL,SPACIH6 I& 0 EIL

Z. FOR CAELES OF UHEOUAL CLL SPAQH& IS I/AclL 0F LARGER )casLE. ~

TRAY WIDTH ALLOVYABLE FII.I.

9

TABLE I

POWER TRAY MA1IMUAI FILL

TRAY Vj IOTN ALLOWASLE FIU.HI<& TRAY

26.8

AI.I.OWAOLi FILI.Ii. HIGH TRAY

57.6 w<

TABLE Z~ CONTROL ( INSTRUMENTATION TRAY MAXIMllMPILL

HoTES:L AS TRAY FILL APPROACHES ITS ALLCWA8I ~ UAIIT THE FIELD SHALL'TAHE NOTE

It CAELES ARE REACHIH6 OVER THE'SIDES CF 'M TiIAY(Eli.OUE TI5 POOI4Y TTAIHEO

CASLES). IF HECESSARY, IM flED,AT ITS OWA OISCRETION SHALL INSTALL Coal. TRAY

SIOEMARO PER I-Z- EOS C 39(POS-.IIII).

Z. IN EATREAIE CASES oR VIHERE SIOEOOAROS c'AH HOT SG IIISTAuZO,&E, FIELO 5HAu.

INPORM THE 'ELECTRICAI PLANT ACTION Td CLONIC 'THC ThaY.

IND(ANAcl IVtCHlGAN ELECT. CO. D.C.COOK NUCLEAR PLANT Pos - I I9I.O

c.LECTRICAI PLANT OESIGN SECTION REVISION-CIPI ANT OESIGN STANOARO CABLE TRAY A«ONABL= =Al

APP O OR. i'. C ICH.LIST, I OATH'I-I'-54AM-RIC'N E' RIC PC'A'KR S=RVICK CORP. I 1 EOS g y.QISH I OI. I


ANALYSES AND MATHEMATICALMODELS

This attachment includes the pertinent sectionsof the report on ampacity program development.The original report and the computer programwere developed by the Electrical Section teammembers„ AEPSC, New York.

V y ~

APPENDIX A

THEORETICAL DEVELOPMENT OF HEAT TRANSFER PHENOMENA

WITH RESPECT TO CABLE AMPACITY IN LOW FILL CABLE TRAYS

A.l REVIEW OF BASIC HEAT TRANSFER MECHANISMS

Heat energy will flow through or from a body by meansof three different mechanisms:

Conduction is the flow of heat from a point of highertemperature to a point of lower temperature, through a bodyor from one body to another body in contact, without signizicantmolecular movement. The equation for one dimensional steadystate thermal conduction for a solid of constant cross sectionalarea is

q =kA—b,Tcd X

Where: qkAbT =X

Conductive heat transfer.Thermal conductivityArea normal to heat transfer flowTemperature difzerenceThickness of solid

Convection is the flow of heat away from the surfaceof a heated body by the motion of the surrounding fluid (gasor liquid). When the motion of the fluid is producedmechanically, the action is known as forced convection. Whenthe motion of the fluid is produced by differences in thefluid density resulting from temperature differences, theaction is known as natural convection. The equation for heattransfer by means of natural convection is:

(2)

Where:qhcvATs

sTa

Convective heat transferConvective heat transfer coefficientSurface area of the bodySurface temperature of the bodyAmbient temperature of the surround-ing fluid.

Any body at a temperature greater than absolute zerowill lose heat in the form of radian" energy. Likewise any bodywill absorb heat radiatec from any other heated body. The netexchange of heat is proportional to the difference of the forthpower of the'r absolute temperatures. The net transfer ofenergy by raciation from a body to ambient or from a body toa surrounding body separated by a nonabsorbing medium is givenby

(3)

Where: q = Radiant heat transferStefan — Boltzman constant

( = Surface emissivity (a factorbetween zero and unity, unitybeing a perfect emitter-or"black body")

A = Surface area of radiators

Absoluter temperature of surfaces of radiator.

Absolute temperature of ambienta or of surrounding body.

In actuality, the transfer of heat will be theresult of the summation of conductive, convective and radianttransmission mechanisms or:

@=a +q +q (4)

Where: Q= the total heat transfer

A.2 HEAT FLOW IN CABLE TRAYS

Presently, IPCEA Standard P-54-440 is the industrybenchmark for cable ampacities in open tgp tray. Much of thisstandard is based on work done by Stolpe . The ampacitiespresented in this standard depend heavily on the assumption thatthe cables are tightly packed and that there is no air flowthrough the cable bundle. The cable bundle is treated as ahomogeneous rectangular mass with uniform heat generation.Based on the above criteria, the allowable watts per linearfoot of cable tray is found to be constant for a given totalcross-sectional area of cables (at a given b,T). Referring tothe fundamental equations for heat transfer outlined in theprevious section, it is clear that conductive heat transfer isthe governing heat transfer mechanism. That is to say, allowableheat loss is inversely proportional to the thickness (i.e.,cross-sectional area) of the body through which the heat, flows,for a given b,T.

When a cable tray is filled with cables to a depthof one layer or less, the assumption can be made that eachcable wil'e exposed to a free flow of air. In this case theabove treatment of heat transfer does not apply. For low cabletray fills, convective and radiant heat transfer are thegoverninc mechanism. If this is true, the allowable heat lossper linea" foot of cable trav will .be constant for a giventotal surface area of cables as per equations (2) and (3) ~

Tne valica"ron of the above theory which is developed in thenext sect'on is the major emphasis of this discussion.

A.3 HEAT TRANSFER PHENOMENA FOR CABLE TRAYS WITH LOW FILL

Theory: When a cable tray is filled to a depth less than orequal to one layer of cables, the maximum allowableheat loss will be constant for a given total cablesurface area at constant aT.

An initial assumption will be made that the above theory istrue. Experimental data will be used to validate thisassumption. It will then be shown that the ampacity for anycable in the tray may be found based on the allowable heatloss.

The problem will be simplified by initially assumingthat the tray contains only one size cable and that each cableis carrying the same current. In this analysis, per unit arearefers to per unit area of cable tray.

The total cable surface area pei unit area is:

A = nTt'ds

Where: Asn

d

(4)

Total cable surface area P.U .Number of 3 P cables per unit areaDiameter of each cable P.U.

The percentage fillof the tray can be defined as thesummation of the per unit cable diameters or:

F = nd (5)

Note tha" this differs from the industry standard of definingpercentage fillbased on the summation of the cables cross-sectional areas.

From examination of equations (4) and (5) it is clearthat the surface area A will be constant for a given percentagefillF.

The total heat generated per unit area by resistiveheating of the cables is:

Q = 3n I R2 (6)

Where: Q

IRac

Total heat generated perunit area.Conductor currenta.c. resistance of conductorper unit length.

Rearranging equation (5)

n = F/d (7)

Substituting in equation (6)

Q = — I R3F 2d ac (8).

Solving for the current

(9)

or

(9a)

According to the initial assumption Q will be constant for agiven surface area that is to say, a certain oercentaae fill.Therefore a plot of l va ~dRac for a given percent fill ahoulcyield a straight line through the origin with slope equal toQ 3F.

Plots of I vs. Rac are shown in Figure A-1 forseveral raceway configurations at a constant tray fillof67%,. This data was determined experimentally at AEP's CantonTest Lab (see Appendix C). As predicted, the plots are linearand pass through the oiigin.

The maximum allowable heat for this tray fillmay bedetermined from the slope of the plots as shown below:

(10)

A.4 CALCULATION OF AMPACITY

In the previous section it was shown that the totalallowable heat, Q, was constant for a given percentage trayfill. In order to eliminate hot spots caused by locallv intenseheat sources, this allowable heat genera"ion should bedistributed uniformly across the occupied area of the tray-

This concept of uniform heat distribution isdiscussed in depth by Stolpe in Reference 2. However, whereasStolpe's analysis required a uniform heat distribution per unitvolume (for tightly packed cable trays), the calculation ofampacity for low fill trays is dependent upon a uniform heatdistribution per unit area of filled tray.

FIGURE A-I

700ventilated tray with ventilated co

600

500 solid tray with solid cover

I 400 ventilated tray with1 hour fire barriersystem

300

200

100

20 40I

100 120

A.4 CALCULATION OF AMPACITY (contd).,

Figure A-2 illustrates the differing requirementsof uniform heat distribution. As per Stolpe's analysisof tightly packed trays, seven Ol2 cables occupy the samevolume as one 4/0 cable and thus the heat generated by thetwo configurations should be equivalent under uniform heatdistribution conditions. For low filltrays, three il2cables occupy the same area of tray surface as one 4/0

- ..cable and therefore must generate the equivalent total heat.A discussion of this effect on the effective diameter of thecable group is given in Appendix B.

Keeping in mind the concept of uniform heatdistribution and rearranging equation,(8) it can be shownthat:

d3I R = F Q (ll)

or the heat produced by the resistive heatingphase cable is equal to the percentage of theheat, Q, as determined by the area that cablein the cable trays.

of one threetotal allo~ableoccupies, d/F,

The allowable ampacity of any cable in tray can becalculated if the allowable heat is known for a specified trayfill, from equation (9):

(9)

The determination of allowable heat for various trayfills and raceway configurations is discussed in Appendix B,Computer Model.

FlGURE A-2

effective

Equivalent heat sources for tightly packed trays as perStolpe in Reference 2.

Equivalent heat sources for lot. ill cable travs

~ ~~ .»a eke ~

B.2 Program Development

The heat transmission of cables contained in a rectangulartray enclosed with multiple layers of fire barrier material isquite complex and extremely difficult to model. Therefore, anassumption was made: treat the rectangular tray and fire barriersas cylindrical sections with the equivalent surface area.

Initially, the validity of this assumption was questionable.However, because of the excellent correlation between computer dataand test data,. it. is, felt that this approximation is sound.

.Utilizing the previous assumption, the program was developedbased on the excellent work done by Neher and McGrath in reference3 and Buller and Neher in reference 4.

Throughout this section, the concept of "thermal resistance"and "thermal resistivity" will be used, these terms being the inverseof thermal conductance and thermal conductivity respectively. It isoften easier to visualize thermal resistance analogous to resistancein an electrical circuit, with the thermal resistance of each mediumbe'ng in series, and with the conductive, convective anc radiantresistance acting in parallel through each medium. A typical thermalcircuit is shown in Fig. Bl.

The equation for load capability as developed in reference 3is given by the following equation:

in equation (12)

T — (T + ~Td)c aRd 1+7)dc c ca

(12)

Tc

D Td

dc

conductor current (kiloamps)

conductor temperature ( C)0

ambient temperature ( C)0

0dielectric losses in conductor ( C)

D.C. resistance (microhms/f t. )

increment of ac/dc ratio

Rca effective thermal resistance conductor toambient (thermal ohms-ft.)

1cd 2cd

Rlcv R 2cv Ta

R2

T T = Q(R + R )c .a 1 2

where: Tc ~ conductor temperature (typically 90 C)'a

= ambient temperature (typically 40 C)

Q = heat energy (watts p.u.)1 1 1 1+ — +Rl Rlcd R3 Rl1 1 1 1+ — +

2 2 cd 2cv R2r

(R in thermal ohm p. u, )

In the above thermalcircuit the conductive, convective and radiant thermal resistancecomponents through each medium are added in parallel. The equivalent thermalresistance of each mediumi Rl and R2 are added in series.

FIGURE 8-1

'B.2.1 Determination of Electrical Resistance

The D.C. resistance of a conductor may be found fromthe following expression:

Rg~ = —p< [(r+ r )i( c + 201]

where: p, = electrical resistivity of conductor(circular MZL OHMS/FT at 20 C)

CI = circular inch area

Y = inferred temaerature of zeroresistance ( C)

The factor 1 + Y may be determine if the ac/dc ratio is knownc

R /Rd= 1+I +Y+YP (14)

where: Y = increment of ac/dc ratio at shields

Y = increment of ac/dc ratio at pipeor conduit

Y will be zero provided shields are'pen-circuited andY will be negligable in light of the fact that most cables in atPay will be three phase twisted conductor. Therefore equation (14)reduces to

ac dc 1+ Yc

B.2.2 Determination of Thermal Resistance

(14a)

If shield and pipe losses are neglected as previouslydiscussed, the total thermal resistance conductor to ambient, Rcawill be the summation of the individual thermal resistances ofeach medium (i.e., insulation, jacket, air space, etc.).

The thermal resistance of the insulation may be calculatedby the following

0 ~ 012 ( j log (Dj/D )

where: R. = thermal resistance of insulation(thermal ohms- ft. )

p >= thermal resistivity ( C — CM/watt)

D. = diameter over insulation (IN. )3.

D = diameter of conductor (IN.)c

(16)

The thermal resistance through relatively thin cylinders(i.e, cable jacke), tray, fire barrier) may be calculated from thefollowing equation

R = 0.0104 n n'D-t,>

where: R = thermal resistance of the section(thermal ohms-ft. )

thermal resistivity of the section( C — CM/WATT).

n' number of conductors contained withinthe section.

thickness of the section (IN.)

D' .outside diameter of the section

The heat transfer between surfaces separated by a "dead-air"space involves the mechanisms of conduction convection and radiation.Each corres'ponding t'hermal resistance mast be added in parallel toobtain the effective thermal resistance. However, in this case itis simplier to take the inverse of the conductances added in series.Using the equations developed in reference 4:

C d= lcd = 0.0213

aT lo~go /D'),D 'ET''

DT

(17)

(18)

Cr = '2rAT

where: C

0.102 D' (1 + 0.016 Tm) (19)

thermal conductance due to conduction,convection and radiation respectively(watts/ C-ft)

respective heat loss (watts/ft)

~T = temperature drop through the air space (

D' outside diameter o inner surface (IN.)D" = inside diameter of outer surface (lb.)P = pressure of air (ATM.)

surface emissivity of inner surface

T = mean temperature of air space ( C)0

m

At this point, some clarification is necessary concerningthe equivalent diameter o the cable or cable group, the equivalentdiameter of a 3 twisted conductor cable is obtained by multiplvingthe individual cable diameters by 2.15. This factor will act toincrease the calculated thermal resistance which is what would beexpected due to the close spacing of a 3TC cable.

4NI

~ „~~

The e ffective diameter of the cable bundle should beobtained by multiplying the effective cable diameter (or jacketdiameter) by the number of three phase cables in the tray. Thiswill be D'hen calculating the thermal resistance of the air spaceinside the tray. The effect is to use the, cable surface area tocalculate the heat loss, which is in accordance with the theorydiscussed in Appendix A.

The thermal resistance per conductor will be the totalnumber of conductors divided by the total thermal conductance. If1 atmosphere pressure is assumed the thermal resistance of the airspace will be given by the expression.

n' - - '".log D" D')

'he thermal resistance from the last surface to ambient,in still air can be found from the following equation derived inreference 3.

1

[( ~ T/D"'" + 1.6 p (1 + 0.0167 Tm)]

IIIwhere: D = outside diameter of outer surface

(21)

As previously stated, the total thermal resistanceconductor to ambient, R'ill be the summation of the individualthermal resistances thrSugh each medium.

B.2.3 Determination of dielectric losses

From reference 3:

Td = Wd Rda (22)

where:

Wd

W. = dielectric lossdthermal resistivity based on

da individual thermal resistivitiesat unity power factor.

0.00276 E $ cos g2

log DEJ

(23)

where: E = phase to neutral voltage (KV)

( = specific inductive capacitance of insulatio.-.rcos P = power factor of insulation

D ~i = diameter of insulation (in. )

Rd , = R , — R./2 (24)

B. 3 Fire Barrier Ampacity Derating (FBAD2)

The program FBAD2 was developed according to the criteriaoutlined in section B.2. A program listing is included in section B.4.

When running the program for cables in ventilated traywith covers, enclosed in Fire Barrier Material it was determinedthat the thermal effects of the tray was insignificant and could beneglected. This agreed, with the results of tests at Canton (seeAppendix C).

When a ventilated tray without a cover is enclosed in aFire Barrier material, the thermal resistance introduced by the trayis negligable. Therefore the tray should not be input as a "layer"in the program.

The assumptions used to develop this program require thatthe tray be filled to less than or equal to one layer of cables.Therefore the number of circuits entered multiplied by the cablediameter should be less than or equal to the tray width.

'When entering "N" the number of layers, the cable insulationand jacket should not be entered as a layer. The program is designedto account for their effect.

B. 3.1

N

Data Input

The data required for running the program is as follows:

The number of layers of material enclosing the cable.See B.3

D (I) The equivalent diameter of layer I in inches.

T (I)S (I)

E (I)

P (I)

The thickness of layer I in inches.

The dead air space outside of layer I in inches.Enter ~ "1" if the air space is ambient air.Note: Enter '1" o~nl for ambient air.The emissivity of surface I. The emissivity is a number lessthan or equal to 1, used to determine the radiant losses, 1

being a perfect radiator (black body). See reference 1 foradditional information.

The thermal resistivity of layer I in C-cm/watt.0

Note: The variables D(I), T(I), S(I), E(I) and P(I) shall beentered for each layer input.

A~ i e

~ w '

J

Tl = Conductor temperature in oC.

T2 = Ambient Temperature in C.

P = Electrical resistivity of the conductor in circular mil ohmsper foot. See Reference 3.

TO = Inferred temperature of zero resistance for the conductormaterial. 'ee Referenec 3.

V = Line to line voltage in KV.

El = Specific.-inductive capacitance of the insulation. SeeReference 3.

Fl = Power factor of the insulation.

T5 = Thickness of the cable jacket in inches.

P5 = Thermal resistivity of the cable jacket in C-cm/watt.

Nl = The number of conductors per cable.

C = Area of the conductor in circular inches.

DO = The conductor diameter in inches.

DI = The insulation diameter in inches.

Pl = The thermal resistivity of the insulation in C-cm/watt.

A = The AC/DC ratioES = The emissivity of the cable surface.

D5 = The diameter of the cable in inches.

B.4 Computer printout: FBAD2

B.4. l The program FBAD2 is stored in the Warner Computer Systemunder the access code for Electrical Plant Design Section.

B.4.2 Program Listing:

* If 4

References

1. Heat Transmission, W.H. McAdams. McGraw-Hill Book Company,New York, N.Y., second edition, 1942.

3.

"Ampacities for Cables in Randomly Filled Trays," J. Stolpe.IEEE Transactions, Paper 70 TP 557 PWR.

"The Calculation of the Temperature Rise and Load Capabilityof Cable Systems," J.H. Neher and M.H. McGrath. AlEE Transactions,Paper 57-660.

4 "The Thermal Resistance Between Cables and a Surrounding Pipeor Duct Wall, " F.H. Buller and J.H. Neher. AZEE Transactions,Paper 50-52. Appendix l.

g 5.

6.

"Engineering Data for Copper and Aluminum Conductor ElectricalCables," The Okonite Company. Okonite Bulletin EHB-78. Pg. 5.

g cables in Trays Traversing Firestops or Wrapped inFireproofing," O.M. Esteves. ZEEE Transactions Paper 82JPGC 601-3.

7. "Ampacities Cables in Open-top Cable Trays," ZPCEA — NEMAStandards Publication. IPCEA Pub No..P-54-440~Second Edition);NEMA Pub. No. WC 5 - 975.

8.

9.

Industrial Heat Transfer, Alfred Schack, Dr. — Ing. John Wiley &

Sons, Inc. 1933. Pg. 18

TSZ response to AEP questionaire from Marilyn Grau to R.H. Bozgodated September 29, 1982.


REPRESENTATIVE AMPACITY DERATING CALCULATION RESULTS

Cable Tray: 1AZ-P8

Total Heat Generation Per Foot of Raceway:

Calculated Allowable: 36.98 Watts/Ft.

Actual: 9.70 Watts/Ft.

Connected Load Calculated

1470 R1469 R8067 R8024 R8187 R8026 R8027 R2349 R

*1476 R1488 R1991 R16666 R-2

3 TC 412 CU3 TC 412 CU3 TC 412 CU3 TC 412 CU3 TC 412 CU3 TC 412 CU3 TC 412 CU3 TC 412 CU3 TC 412 CU3 TC 412 CU3 TC 42 AL3 TC 412 CU

3.816.01.21.1

17.02.71.21.9

20.060.02.5

21.5821.5821.5821.5821.5821.5821.5821.58

21.58'0.67

21.58

*CABLE CUT IN TRAY AND TAPED

Dc —6 —F035. 92 — I. 5 Zev .5

CH&c'.a mC). Ch BLh rVPa BCpc//p. zp H.P,+W.KVA.

/'4.7'/r-gBobT ~

~Bo Zs8v'

goZ6 NgOZ 7 rZ234.5I 7@

/ /c// /Z./c<c< ~-z

C /29 ci/

<C /9rc9C /z3 c /2

c /z3 c /z9 c /S C /

C 2C /

cr cl

A/G uD4 G

6')b+acg u

0 9g0920 920 320 32O 3c

~$ 203z Cu0 2-

092 w''P2 DP

0 92

ER

srOT

0 1

/)N //

R CO

0- 0/E' //H 7 u

P s

Cy- R K

/7' HCOL,-2 /-2/

R/

PiP

ge7/7 //

. //P 2//H // //P /-

P goP C)

8P QI5

CABLE NCONDUIT CONNECTED LOAD CALCULATED ALLOWABLE

a2KCI5X ESRZBLet

+8003 R-1*8004 R-1*S004 G-1

8026 R-18505 R-l8506„R-,1

«8003 R-2~8004 R-2*8004 G-2

8154 G-28155 G-2

+8744 R-2

+5ZV CABLE

4% ~

4N4H0

4N4%4N1 s

1 II

4w

3 TC 42 SH-AL3 TC 42 SH-AL3 TC 42 SH-AL3 TC 412 CU3 TC 412 CU3 TC 412 CU

3 TC f2 SH-AL3 TC 42 SH-AL3 TC 42 SH-AL3 TC 412 CU3 TC 412 CU3 TC f2 SH-AT

57.5 3.3264.6 4.2064.6 4-202.7 .0452.6 .0422.6 042

57.5 3 3264.6 4.2059 3-502.6 0422.6 .04271.9 5.20

99.0499 0499 0425. 8525. S525.85

99 0499.0499 0425. S525.8599.04

9.S69.869.864.144.144.14

9.869.869.864.144.149.86

NOTES: 1. ALL CABLES ARE 600V EXCEPT AS NOTED.

2. CABLE FLA (FUEL LOAD AMP) AND MPACITY IS GlVZN.IN MPS.

3. AMBIENT TEMPERATURE WAS TAKEN TO BE 40 C

c888E'YPE OiD>~asH,

FL8FZP

KV8

Ml lM =L 2.

~u

gPHP~PaB.XP

P 22.d gP

9


RESULTS FROM TEST REPORT gCL-542

~, C

e

g Page I of ~TEST REPORT

American Electric Power Service Corp.Canton Laboratory

P.O. Box 487 Canton, Ohio 44701

ltle:AMPACITY TEST FOR POWER CABLES

es t o. CL-542December 16, 1983

Test By: L.J. Balanti; J. P. McCallinReport By: L. J. BalantiApproved By: - - A. P. Litsky

blade For: AEPS Corp.Sponsor: W. F. Wilson - New YorkTes t Comp le ted,: November 18, 1983

g

0

C)Cl

0CLECl

I ZNTRODVCTZON

For compliance with 10CFR50, Appendix R at the D. C.Cook Nuclear Plant, tests were conducted on power and controlcables enclosed in a TSZ, Znc. one-hour fire barrier system.The results of- the test will be compared to computer-generateddata to determine the validity of the computer model on heatrun flow and cable ampacity.

II. OBJECTIVE

g

o~~4J

E0g

The test objective was to simulate as closely as possiblethe actual conditions of tray and conduit runs proposed for CookPlant and determine the final conductor temperature for the specifiedamperage and tray fill.

ZII. TEST METEOD

The generalized test method consisted of:

l. Installing cables.2. Attaching thermocouples.3. Enclosing the TSZ fire barrier system.4. Applying the specified amperages.5. Maintaining a constant ambient temperature of

400C.6- Monitoring the temperature rise and final conductor

temperature.

Copies To: T. O. Argenta/B. R. Larson — CantonB. J. Ware - ColumbusC. B. Charlton - CantonT. E. King - ColumbusS. R. Kekane - Columbus

TEST METHOD (Cont 'd. )

The detailed test procedure was as follows:

Equipment

Cable Tray and Cover

1.1.1. Cable tray was galvanized steel, expanded metal bottom;size 12" x 6" x 8'-0" Long.

1.1.2. Cable tray cover was galvanized steel, ventilated12" wide.

1.1.3. 10'-0 Original tray length cut to 8'-0" to accommodateinstallation in environmental chamber.

1.1.4. Tray cover attached to tray by using 510 x 3/8" Parker-Kalon type B (Z) with "H" head.

1.2. Conduit

1.2.2.

4" I.D. Galvanized rigid steel.

1" I.D. Thinwall EMT

1.2.3. Conduits cut to 8'-0" to conform with cable traylength and installation in chamber.

1.3 fire Barrier Envelope

1.3.1. Thermo-Lag 330-1. subliming coating manufactured byTSI, Inc. for a one hour barrier. Thickness of barrierwas .500" (+.125", —.000").

1.3.2.

1.3.3.

1.3.4.

1.4.

Prefabricated panels 6'-0" x 4.6

Prefabricated conduit sections. ':

Steel banding.

Cables

The following cables were used for testing:

324339344348

31013102310331043120

3TC 012 Cu 600 V3TC N6 Al 600 V3TC N4 Al 600 V3TC 02 Al 600 V3TC 14 Al 5 kV shielded3TC N2 Al 5 kV shielded3TC '2/0 Al 5 kV shielded3TC N4/0 Al 5 kV shielded4/C 512 Cu 600 V.

~ ~" 1

Test Setup

2.1 Raceway

2.1.1. Cable tray and conduit were supoorted aoproximately2'-6" above floor to allow for natural ventilation.

2.1.2. Raceway ends were sealed durinc the test withthermal insulating material to orevent heatloss through these areas.

Note:

This procedure could cause excessive heatingof the cables passing through the thermal seal;therefore, all temperature readings were takena minimum of 1'-0" from the thermal seal.

2.2 TSl One Hour Fire Barrier System

2.2.1. The tray envelope was constructed of the pre-fabricated panels, cut so as to fit as shownin the Appendix (see Figure fl).

2.2.2.

2.3

The conduits were encased in the prefabricatedsections.Thermocouoles

2.3.1. T-Type thermocouples were used to measure tempera-tures of the following:

A. Ambient airB. Too and bottom of the fire barrier envelopeC. Air space in trayD. Conductors.

2.3.2. Thermocouples were installed on the inwardside of the conductor in a triplex arrangement(see Figure 2). A hole was bored in the insulationand the the mocouples were placed on the conductor.

2.3.3. Thermocouples were imbedded in Omegatherm 201high thermal conductivity paste.

2.3.4. Thermocouples were installed in a positionlocated on the cables in the cente. of thetray where:

A.B ~

Heat generation is greatest.:-: ar dissipation is the least (seeFigure 3).

~ ty, 1 'I ~ s ~ ~

2.3.5. The minimum number of thermocouples used tomeasure the conductor temperature was two (2)per cable circuit installed in the tray andfive (5) for single cables installed in theconduit.

2.4. Cables

2.4.1. Cables were positioned in the cable tray ina single layer in such a position that therewas a minimum spacing of 1/3 the diameter ofthe larger adjacent cable'.'Cables were thensecured with "Ty-Raps".

3. Test Procedure

3.1 Each test consisted of installing the cablesin the tray in one of six (6) configurationsas specified in the test request.

3.2 Once the proper setup was attained, cableswere subjected to a load of three phase,60 Hz sinusoidal current as specified in Section4 ~

3.3 Ambient temperature was set to 40oC.

3.4. Temperature rise of the cables was recordedon an Esterline Angus Hodel PD-2064 data acquisit-ion system at 4-hour intervals until the cabletemperatures stabilized.

3.5. The voltage and amperage of each circuit wasmonitored periodically throughout the test.

4 ~ Test Configurations

4.1 Test SI

Circuit No. Ztem No. Description Runs in Tray Ampacity

324 3TCr 12 Cu324 'TCr12 Cu348 3TC02 Al324 3TC512 Cu

3.820.060.0

0

f4

j pI H t

2.3.5. The minimum number of thermocouples used tomeasure the conductor temperature was two (2)per cable circuit installed in the tray andfive (5) for single cables installed in theconduit.

2.4. Cables

2.4.1. Cables were positioned in the cable'tray ina single layer in such a position that therewas a minimum spacing of 1/3 the diameter ofthe larger adjacent cable. Cables were thensecured with "Ty-Raps".

Test Procedure

3.1 Each test consisted of installing the cablesin the tray in one of six (6) configurationsas specified in the test request.

3.2 Once the proper setup was attained, cableswere subjected to a load of three phase,60 Hz sinusoidal current as specified in Section4.

3.3 Ambient temperature was set to 40oC.

3.4. Temperature rise of the cables was recordedon an Esterline Angus Model PD-2064 data acquisit-ion system at 4-hour intervals until the cabletemperatures stabilized.

3.5. The voltage and amperage of each circuit wasmonitored periodically throughout the test.

Test Configurations

4.1 Test fl

324 3TC 12 Cu 7324 3TC~412 Cu 3

348 3TC~2 Al 1

324 3TC e~ l2 Cu 1

3.820.060.0

0

4.2 Test 02

Circuit No. Item No. Description Runs in Tray Ampacity

324324324348

3120344

3TC512 Cu

3TCI12 Cu3TC012 Cu

3TC$ 12 Cu

4/C412 Cu3TC54 Al

.17

.712.86.86.8

53.0

4.3 Test 43

Circuit No. Item No. Description Runs in Tray Ampacity

324324

3120324

3120324339339344344348324

3TCf12 Cu

3TC$ 12 Cu

4/C012 CU

3TC012 CLI

4/C012 Cu3TC 12 Cu

3TC$ 6 Al3TC56 Al3TC54 Al3TC54 Al3TC02 Al3TC012 Cu

5

5

1222111121

.712.86.86.8

16.016.016.036.036.053.060.0

0

4.4 Test N4

4.5

Cable Size: 3TCN12 Cu 600 V.Conduit Size: 1" I.D. EMIAmpacity: 2 amps.

Test 05

4.6

Cable Size: 3TC52 Al 5 kV shielded withgrounded.

Conduit Size: 4" I.D. Galv. rigid.Ampacity: 72 amps.

Test 56

one end

Circuit No. Item No.

3101310231033104

3TCV4 Al Sh.3TCI2 Al Sh.3TC02/0 Al Sh.3TC54/0 Al Sh.

20254050

IV- TEST RESULTS

The complete temperature recordings are tabulated along with test commentson computer printouts and listed under data sheets in the Appendix.

The final conductor temperatures for each test are listed below:

Test No. CableAmpacity(ampm)

Runs inTray

Highest ConductorTemperature (o C)

3TCC12 Cum

3TCC2 Al3TC)12 Cu

m

4/C512 Cu3TCT'4

3TCN12 Cu

4/CR12 Cu~I

3TCe6 Al

3TCt4 Alm

3TC52 Al3TCC12 CU

3TC02 Al3TCS4 Al3TC52 Al3TCC2/0 Al3TCm4/0 Al

3.820.060.0

.17

.712.86.86.8

53.0.71

2.8'.8

16.06.8

16.016.036.036.053.060.02.0

72.020254050

45.659.755.742.642.745.144.443.958.354.657.960.467.355.2*62.7*57.665.9*57.9*68.863.742.965.045.645.445.544.5

* Thermocouple installed on insulation, not conductor

V. DISCUSSION

Due to a limited supply of variable power sources, several circuitswere consoLidated. In all cases, the loads were met or exceeded those thatwere originally requested.

As per the original request, conductors were placed in the cable trayin a single layer in such a position that there was a minimum spacing ofll3 the diameter of the larger adjacent cable.'lthough this probably isnot the best simulation of actual conditions, it was one criterion of thetest request. During Test f3, the amount of cables made it impossible tofollow this criterion. It was followed as closely as possible and the resultscan be viewed in the Appendix under "Photographs".

All results contained in this report were forwarded to W. F. Wilson,New York, immediately upon completion of the test. Any questions pertainingto the actual test results as compared to the computer-generated data shouldbe directed to him.

VI. APPENDIX

A. Data sheetsB. Test setuoC. Photographs.

' v f J

~ ~

l.)":. )v. )Lc. )5. )G. )7. )Q )9. )18. )11. 3

1:". )1 i,

~ )14. )15. )fE. )

COMMENTS - TEST No. l

TEST 1 CL 6 ~ 11/Sl/8~ IME IS 4:29 A.M.START A=. 785V B=. 798V C=. 81 BVi A' ~. 8 AMPSTART A=. 7~2V B=.G57V C=i.82Vv ALL GG AMPSTART A='. 17V B=i. i4V C='.19V~ ALL 28 AMPCHANNEL ~9= AMBIENTCHAN '=TRAY TOP~ "=TRAY BOTTQ,, 4=AIR N . RAYCHANNEL, E, 7 .ARE ON SG AMP CIRCUITCHANNEL 5~ 8 APE ON 28 AM. CIRCUITALL OTHER CHANNELS ON . 8 AMP CIRCUIT

CURR END A 3. 9 B 3. 9 C ~. 9'OLTEND A . 878 B . 805 C . 867

CURR END A 59. 2 B 59. 5 C 59. ~VOLT END A .818 B .7',' 1 ~ 8"CUP.R END A 28. 4 B 28.:" C 28. 2.VOLT END A 1 ~ "'8 B f. 418 C l. 259END TEST Nf CL-542 ff/f/8Z

CL-512

1

~ ~

TEST No.

ESTEr~: it1E Al'uGUS DATA

TINE CH..m CHc2 CHIC CH84 CHÃ5 CHNS CHN7 cH5aa CH".1=.

84:2884 4~85: 158 c' 4 cHF:1 ~

8S: 4587: 1587:458n ~ ac8n o4c89,158Q1 8 ~

ac'8:

4511 a~11-4512,15ls e ~ 45

14 4l~ic ~

1c

15: 45

17. "19. 4

o

n42S. 4

rsn so &a28. 7

"8~8. "i8.:"

8 5~8. SZ8. 9

va. 1v~a. 1

~a ~

<e

C'„;. 4

'948. 448. 541. r4 841. e41. 4

~ haA [

41a 1

41. 1

41. 441. S41. E

41 ~

4g c

41. S41. 541. "

r

«J ~ s s

="8. a

~S. 54148. 741. ""

48. 741. 441. 942. 1

41. 841. F42. 1

4r. 541. 941. 84 2 ~

4r. "41. 941. 9

Ja 7r84. 1

«an~aCI ~ I41. E4 or ~ M

44. 1

44. S44a 845. 445a 545. S45. 845. S4c'

45. 945. 945 ~

a

45. 945. 945. 94E

25. 54, .4.49. 5

cJar ~ J55a 957o57. 8

58. 959. 1

59. 1

595S.

='9.

759. u59. "59. i59. ~ca 759. 459. 5

"'5. S'E. 444a 1

951. 7

54. 454. 9

5555. "c'c''Jo J

55 a

cc'

55. Sc'5

c'J.

S55a 7

sr5o 74v. "4858. 4

4Jara

Jv. Sc'4

54. 1

54. 1

54a 4.

54a vc'4

54a E54a 5c'4

c'4.

S54a 554. S54. S54 ~ 5

«Jo M

495~. 95F. 1

57. S58. ~

59. 25959. 259. s59. J59. 259. 4

.59. 559. 559. 4

59. 4

59. S59. 4c'9 c'

c cJ ~

o So 85 40 c'os~ ~ J

41. 94v ~ ar

44. "44. 444. 444. 744. S44. 9li.4. 944. 9454c'4c

4J5a ~4c

45. ~4i

c'5.4

45. 4

25. S

ZS4.1. '.4r.5

4-V. J~

4:". S4" 84444. 1

44. 1

44. ~J

44. 244. '"

4444. "

44. v44.

"-'4.

2

erc'Ja h~ a

~~4. 5vS. 5

n42. a

8

4... r4~e ~ J4J. 74 ". 7

4~. 7

4"v. 9444.4. 1.

44. 144. 1

4". 944. 1

44. 1

T<s lr=~r7~ cia ~

~

C ".17 CH~18 CHUB CH .5 CH ' CH .7 CH.:" CH".6 CH~'7 CH/s33.

84: r884-458 c'

8 c' 4c'S:

1.5GS-4587- '587:45fpn ~

1 c'n

a4c'9:

158918o 15'8 ~ 4511: 1511ass ~ g

c'a ~ 4 c'o

lc

r4 4~~ C ~ 1 C~ C e

4C're'

«J ~ eJ

"4. SvS. F48. E4s s

4n4 .14v

4 ..44er o

4....

4 .,~

c'".

S4.. S

c':.

S4 . E,

rac c«Jo

~5. SMSa 541a 44"r. S

4«4v. S

c'".8

4". 74e ~ ~ 8

n4e s ~ Cl

444sso 8

n

44, 1

4 ..99

e ec'''Jo J

~4. 7~rSo 741. 1

42. 94 ~ .94v. ~

4i o,~ S

4~. 44'. 7

4:". 74,,7

~ 8

4„.. 7

4r. 74/s/ 7

4. ~ .::-:

~ 5. S~9 4o

C'z.

a

4 .1

4... 54v. 54~. S4 o

~c'

o~ 5

4... 7Q

4e. ~ . ~ 7l. -..34..94~. 94i

~ 8l 4. 1

<e C

.,8, 2v5. 9~9. 9

44444. 444...44. E,

4lr.. 744i44o 844. 944. 844. a44. E

44 nn

4 c'4.7

4i /.

38. 1

vS. 1

48. 1

4..,4.

44i

44. "44.lr.4. S44. 744. 744. 844. 744. 744. 544. 7

44. 7

44. 54 /s

Rc'

~8~S484n c

4". 9c'4.

844. 74

c'5.

1

45. 4

45. ~

45.

4Jo45. S4ic';

4c; c'

.9. av4. S-.n4842. 1

94". '"4'. 4

n

4s s ~ S4i, 74.. S

n44. 1

n4...94". 94v. 9444„. ~ .9le 4

nc n«iJo IJ:"8. Ssr 741. 1

4'". 444. 845. 54c''5.

S45. 9

4i8 ~

'S..~

4E. 44S

4S. —.

4F.'8o4

48s

r4.:"7. 948. 848. 4

848.

='8.

441. ~~

48. 848. S48. 748. 74148. 948. 748. 448. 448. 848. S48. 74a.1 4

CL-54".

1 ~ 3

a ~ ~

~. )4, )-. )C )7

~ )B. )9.?

)'1.)'.)1~,)1 4 )'5. )1B. )7. )

1B )Q )

2i7i ~ )~ ~

)

24, )

'.'7~ )

~+I )"9. )a8. 3

~1. )

COl'll«ENTS TEST No 2

THERM„1 AMB-. Ek'T t'CH„~9)THERMr".'OP TRAY' Rl lvr 'OT Of1 TRAYTHE -4 AIR S ACECURR STAR: A .2 8 ." C .2VOLT STAR.' ~ 815 8 ~ 81B C .82BCURR START A .9 B .9 C .9VO' STAPT A .84B 8 .848 C .8 5CURR START A G. B 8 S. B C E.B

VOLT START A . 471 8 . 478 C . 558CURR S ART A ".B B 2.B C ~ .BVOLT START A . ~89 B . '"7 C .>8ECUR% START A 5~.8 8 5 .8 C 5~.8VQ: START A 1. 587 8 '. ~7B C . B86CL-54" TEST Fr'2 1'/~/B~ START 8515VOLT END A .8189 8 .8147 C. 8.48CL'R END ALL . 28AMPVOLT END A . 84BS 8 . 8496 C . 8559 CURCUR END A .B8 B .88 C .B8VOLT END A .49S 8 .58 C .S8VOLT "END A .:2" 8 .~5 ~ C

VO' END A 1. 572 9 1. 4B2 C . B~BCUR EtlD ALL 5~. 8 AMPSEND TEST 2 CL 562 1688 TIMECH 9i 1B. 2E."'7t 2B '7 ON ='. B A... CIRCU TCH ~ B ON 5" A:"lP CIPCUITCH Bs 7 ON:-:' CABLE~ S. B AMP CIRCUITCH '8~ ' QN 4/C CABLE~ F. B AMP CIRCUITCH 17i ~E ON .17 AMP CIPCUCH 11~ 28~ 25 QN .71 AMP CIRCUIT

CL-542

rt ~s ~ a, ~ I t=* ~ . W

j

TEST No.

ESTERLINE ANGUS DATA

TT tlE CHUG CH CHir " CH 4 CH 5 CH"6 CH 7 CH - CH-9 CH" 18 CH «Gc ~ 4cGc-186:4 ~

87-}587- 4588-188-45GS 1

89-45}c

18 411:15ii:451. ~ ~ c

~ o J1 +ro4c

1":45'4:451c ~ ic

.9. 6VGvG. "

8 5v8. 8V}v1.

"='i

~

V'}o

~}. 5"}.5v}. 4o 1

1 ~

vi ~

re. 7

v76. 4

»,g

4848. 448. 548. 548. 748. 9414}. 1

48. 848. 94}. }41 ~

1

48. 841. 2

v .7»6 8'v. 4»9 P\

484}. "41. 74}. 441. ""

4}. 441. 7

41. 941. 54}o 64»+

41. 4

~ 7e»9

v4.='7

~6

':"9. 748. 941 ~ 84". 44 ~ c

4 ~ .94". 94r. 942. 94v. 1

4". 1

4V4v. "

V»J ~

4v. 649o 44~» ~

&So ~

'ho

'6.9&7»57. 657» 7

57o 7ce ee

C~J8SecwQGoSe. 1

se.'n

»J Vo

21. 4

o 4 5

48. 541. 9

84 ..44v 44v. 94'. 94 .94»4

4444. 1

444444» 444. 1

2}. 8r9, 1

"4. 6.e. 448. 741. 9

4<. 44v. 6

, ~ 94",8

44» 1

44. 1

44. 1

44. 1

44. 44444. ~

4~o 84n. 9C» eA~o54 ~ 1

cc cVSo Vc656. vc6 c

56. 956. 9

S6. 957o o

5757. 1

57. 1

S7, 1

err@

v8v4». 9» euo

4841 ~

41. 84r. 442. 6

4r. 94v. 1

42. 94V 1.

4u4>o .

er

p 'e~ ~ ~

8. 4iS. 6n»euo V

48. 541. 64J ~

~

4 ~ .7

4 ~ .44v. 4

4v. 64 ~ .44m» ~ 64v. 74v. 64v. 7

»rP ~

vGa4. 7v7. 9'z948. 941. 6

e

42. 442. 642. 542. 642. 54' 642. 442. 64r. 742. 7

T1i1E CHO} CHN}7 CH~18 CH-..28 CH-.. 25 CH026 Chill l7 C."t02nv CHOZ6 CHOi7 CHN'9

85: 45QC ~ o cu

'6:45

8787:4588: 1588:4589: 1589: 45}8-}5}8:4511: 'S':451 r-151.2: 45}v:}5O ~

1 4 4c15.15

o e ~ ~

vG. 7

v948 8

4 ...'='V.'"

4 ~ . 74v. 84 ~~

~c

4» e ~ Vn4» e ~ V

4 ..64u. 9

+ P'e

~ »9 c

v79. V

48. 941. "41. 54}. 741. 8

Cl

42. 1

4}o 942. 1

42. 1

"6. 1',

uo48. 641. 44(

f ~

42. 44r. 442. 742. 742 94r,74ro 8

4ro 94.4 '.

29. 4i4. 5V7» 5v9. 4484}o "41.. E41. 74» e

4'~ 1

42. 1

4 ~

4-'. 442

~1 '7~ ~

.4. 6'7. 6

48. 441. 1

4}. 5n

4~»~

1

4r. 44-'. 44r. 44r. 4

or o

"i. 56. 7

"9. 5

42. 14»~r 74v. 1

4". 54..44:.. 64...74l»7

n9

n

p~ V~

:}.4

41. 1,

4ro 1

42 ~ 7

4„..4". 4

4v 44i. 5

4..., 7

4u ~

4.'. 74 c

.0. 4

=-e.48o 54a. S

. ~ 1

4v. 1

4

4 er

4.~.4>e ~

.9. 6"4. 6

='7 7

48. 641 ~ 2

841. 9

4 ~

4»r

4r. 442. 442. 54r. 5

oo» 4~ ~>

a7. 448. F42. 54.". 444. 1

44. 4

44» 745. 1

n4544. 944. 9

n44. 845. 1.

45. 1

Vdo uv~9. 6

4848. 648. 748. 848. 548 ..i48. 748. 948. 748. 748. 548. 748. 548. 748. 748

CL-542

r ~~ '

4 ~ .:

5. )E.?

7 )

C )

9. )

18. )

i~. )

14. )15. )

16. )

'7. )

1 ~v'. )

19 )28. )'r 1

~ )

)5o )

2h )27. )

='9. )~3. )'1. )

~...?24 )u5. )

f.: .. ~ ..',; -' ',: . . ~ :

t' ~ sh, (LI i TP >. gt g ~ Q, P

HA 'MEL 4 Rc.Y P !ic.'A™E

Ofl THE INSU'TION NQT THL CONDUCTORCURP, START A 5~. 8 8 5~~. 8 C 5". 8

VOLT STAR: A . 64' . 744 C . 697CURR STAR: A >E. 8 8 ~6.8 C ~6.8

VO'. T START A 1.5 8 1.45 C '.6CURR START A 2.9 8 2. 9 C =.9

VOLT START A .~96 8 . ~99 C .426CJRR START A 16.. 8 16. ~ C16.

'OLTSTART A 1.9-7 8 2. 8. C i. 9m~

CUq~ cTART A78 86 9 C 78VQ'T STAPT A .Er 8 -61 C 6

CURR S ART A.9 8.8 C .8YO' 'START A .16 8 .16 C .16

CURR START A 56.8 8 57.=. eVOLT START A .64 8 . E4 C .67

. 7'MP CKT 512 CHAN'S iii17~252. 8 AMP CKT —..12 CH'S 9. 18'1 26 27 26

m91 &76. 8 AMP CKT 4/C CH' 18'2

6. 8 AMP CKT "-'= CH'S ~816 O'"IP CKT —..6 CH'S =' 24

' A~P CKT 4/C CH' "2 ZZ'6 Af"P CKT ~12 CH'S "E. -'6

:"6. 8 AiiP CKT N4 CH'S 28~ iB==. e f.~P CKT ."6 CH S -.4, ~5.:.. 8 ~MP CKT "4 CH' 5. 8

68. 8 AMP CKT 12 CH'S 6~ 7CURR END A 47.4 8 2.8 C 57.7VOL'. c.ND A . 643 8 . 692 C .712CUR% c.~D A ~E,.6 8 ~6.7 C 36.2VOLT END A i. 5 9 8 1 ~ 465 C 1- 687CURP. END A 2.9 8 ~ . "" C 2. 9VQL T END A .416 8 .414 C .441CUR.. END A 16. 2 8 '6. ~ C 16. 1

VOLT END A ~ . 48 8 2. 84 C 2.26CURR END A 6.7 8 6.8 C 7.8VOLT END A .594 8 .628 C .6 7CURR END A 8.9 8 8.9 C 8. SVOLT END A . 11,7 8 . 1.2 C . 1'5CURR ENID A 55. E 8 5'. 8 C 55.9VOLT END A . 6 "8 8 . 585 C .697END Q.= TEST R~ CL-542r '/1 'Sv 14 5

Y

W ~

'L s

TEST NO.

ESTER1 ENE ANGUS DATA

T 1'NE CHI8 CH-.. CH0 CH 4 CH CH-"..6 CH.7 CH-..B CH".9 CH"18 CH4} }QC ~ 4C86 ~

1C

86:4587:1587-458S:158n ~ () c89: 1589 45}8-151,8- 45}1-1511-45ier ~

ic'':r-45

~ 1 c

1=-.: 45

C'

~ ~ «J

rB. 929. 1

29. 9

u8. 4"8. 7V8. 7>8. 8u 8 ~ 'v«8«8>8. 6

.:"8. 4

«ree I Q~ u

'1. 5VE. 6

9. "41. 1

4r. 66

4...744.

-'4...

44« 444. 644, 644« 5

44. ~

44. 6

u4. 1

v9. 7

4r. 74« e ~ ld44, 744. 5

844. 945. u

4c45. 644. 845. 1

»7o 5C

~J 1J ~ IJ4r. 447. 7

~r

C'e~J '54o 2C'C«J IJ

C'''C''J ~ IJ55. 855. 6sJsJ ~ 75»' 755o 755. 8

24. v48. 458. 9c,'7

61. 4

65. 566. 767. 667. 9GB. 467. 967. 667 c67. F67. 1

F7

r4. 45. 4

5n56. 659. 468. 9Gr. 1

6"Ev. 4Gu. 7Gv. 4Ei. 1

Gc6 sr ~ «J

62. 9Gn

n4e«5a 7

5. ~ 1

56. 759. 468. 9Er. 1

6". 4Gv. 6E".4Gv. 1

F .„16u ~

Gu. 1

2r448. 65}. 5CQI

62. ~

F4EG. v67. 6

68. 869GB. 768. u68. 468. 468. =68. 1

~8,nu'U ~ u

44. 849 'r51. 8

54 ~ 5J

CC'5.4

55. 555. 7

55. 655. 655. 655. 6

29. 7%7o 74448. 558. 9c'IJ« ~ ~

5v ~ 55 aJ ~ 7c'4

S4 v54o 454 ~ 554o 554. 554. 554o 5

r9«7o

47. 558. 25}. S5ra 6

5«re 70

~J' ~ u

5~. 95Z ~ '9c'«

5u. 7

T I tlE CHN}'Hn'15 CH=: 7 CHN}8 Cl-'-'28 CH-.. ri CIJI'P'e CH-.. 4 CHvr25 CHr. 25 CHc'

85-'4586:1586-4587e}587-4588:158ne4589:158a:45'8 1

18- 4511: 1,511-45'-1512-45}u:}51 4c

24. 429. 8VB

48 951. uC'JI '

W'4.

4

C'/DC'C«J sJ ~

sJ «JC''5

a 1

5«J ~ a

55e 1.

C'C ~e«J «J ~ »r

VG. 745. 451. 8c658. 468FG. 8FJ8a a

68. 5eu 'i.

1

6'8.9

61. 268 uo

68. 8

lC'}.

445 u47. 649. ",

49. 7c8

C1

C'1 «e

}.2C'

~ «J

51. ""C1c 1

24c''So

74c49. 7C'e e

~J ~ «J

5»I ~ 754. 6

C'O';«J «J ~ »'

655o 5CC

55. 6«J 5/ ~ 455« 4

c'1

AG. 9c'«J ~ eC''J«

e ~

5555. 656. 957o»57 a

c7 457e 5c'7

c'7.

557o«e57. 4

r4. 41 ~

1

48. 546. 8c1

~Il'«

~

CC'«J «J ~ «J

56. u

57. 657. 757. 4c7 J/

57. 4~J7« ee

r4

41. 4485254

5. 9

56. i56e 556. 755. 9c5 Q

5756. 95F. 755. 7

~ 4. 4

47. 751. 8

55occ 6r~J«Jo uCC'«J «J ~ uC'C«Jm o

cC

5F. 1

uh5c

24 ~ u

«rue u44. 44IB. 4515='. 75u ~ N

a54C'/e

C'J»

~

54. 654. 554. 654. 554o 554. 5

24. 4r9. 4

e'.IB« 745. 5

52a 5c455. 1

5p. 5SDo 8

C''6«

1cC

5 9C Q«J» ~ V

'r4. urt

45. 549. 7c'n

~ «J

54o 154o 7C'J sJ ~ «J

5s/e 5cEC'/5

»«J ~ ucc n«J «J ~

5«Je 9C'JQ s PS

7

CL-542

~ ~ ~ ~ ~

1

I ~ ~ 7

Csgr ~ - C PL/!~, 1 s i <os Qglll» CHN S

PC' 4C'

(

8S:4587:1587:4c~8' 1

c'S-

4589- 1589-4518:'518-411 ei5'1-451": 1.5

'-151:": 45

'r4. 4='9. 7

4cc'8C'!»» ~ 7O''a

5S. 75S. 9

7 rsJ s ~

57.'J

~ ~

57. '::

57c'7c 7

r»4 c

=:9. S.n 1

4S58a 5e! ae» ~ »r

54 S7

5Se 1

cS c5S. 75S. 7C'I<Ge s

Cl

5B, 75Sa E56e 5

4

4':.'. 549. "

5S. 459. 're5» ~ 7S8. 1

S8, 4S8SQ..:.SQ. ~S+S8.

='8.

'„.:4.

4.r'. 1

41. 447. 751.

i-'~.

9O''sJe

855. S55 a FrO'

5Ee 1cS55a 95F. 1

56. 1rr

~ ~ Iir sl

45 85'. 9C'C''a!

~ <c'7 4

595SCCs&4l

rer

58. u~

L Q

5 »L

QSa 4

~~7 1

47. "54e 1

sJ A a

S8 4i

S'. S7

Ei. 9

g r' 1

Sr. 1

E".

='t

oC

4»gl c

C'C rsada»»»

DMeSs ~

1

F -'. 4,S:-'. 9S4. rS4. 5S4. 8E4. 9E4.. 8S4. 7,64. 9S4i ~ 7S4. S

»rg,~ I a

QPJe S4S. 9C'C

C'Je

c9 cSi. SSv. '"S~. SS5S5. ~Sc'

E5. 9S5. 6S5. 7E5. 7S5. SS5. 7

4i 1~

»

51. Se! S e

E='. 4E4. 9BS. 567. 5SE. 7S7S7V7

~ ~

F7. 1

P7S7. 1

Su. 9tS 7

» ~

41.47.51.54.5S.5S.57e57.C'Pl4GaC'QWva57a57.57.57.57 a

9

Ql

C

b

Pl

9

7

% ~ ~

47.51Qi 'C''4e

55 a

57 a

57.57 a

57.57.CiP

57o57.57 a

99

Ql

CHI:98C'

4C'S:'585: 4587: 1587:458G: '58g e

4c'9et

589: 45'8-1518-45':15'1-451 r ~ 451 e ~ 1 C

» '

~S. S4» Ql

48o 448. 548. 748. 748. 748. 748. 748. S4848. 94,1. 1

48. 941

'

0

C'542

~ ~

~ ~

o ~

TEST NO. 4

E'ST=. LLNK ANGUS DATP

T:: I"iE CHNS CH-:. 'H-.: " CH-.. ~ CHI4 CHN5 CH-..S CHS7 CHNS CHI9

QW ~ Pg

Se'9:88

89 'p18:8818:>811-8811:. 8

~ 88~ 8

1 i:88'i:~814:88'::"8

«'4 o Sl

26. 627, 6

Clo 6

r9. E:

38Z8. ~~8. 4'v,8

>8. 7>8. 7

"6. 6

~6. ~

~9. 1

~9. 5o,9 0v9. 9~9. 6484848, 1

48. 1

48. 2~9. 8

c'oraJ ~

7~

gw<Mo

o 'Bo 4C

mq~ ~

v9. 9v9. 948.

"-'8.

548. 7484848 Ql

48 ~

..9. 4"B. 4

~o7—.9

48. 1

48. 548. 6

41 ~ 541. 948. 54141. 741. 7

2Qu5 4\ ~7o

.7 ~ 9:"9. 448. ~

48. 448. 64848. 848. S4148. 848. 5

7o M

N7

«>9o 548.;48. 848. 741

4141. 1

48. 94f. 1

"S. 1

i7. 17 9

"9. 748o 448. 548. 548. 741. 242. 948. 941 ~ 1

48. 9

-6. 8~5'VM o

o,T 4"9. 1

48 1

48. 248. 1

48. 5484841. 748. ~

48. 6

7034. 7i6. 9~7. uv9. 1

48o 248. 548. 648. 648. 848. 948. 941 ~ 1

48o 8

2".4~~So ~>

i5. 6~6. 4m5o 7

~~7. u~

48. 5~S. 4v9. 1

"5. 7

COt"i."fENTS

i. )='. )s. )4. )C'

TES!VOLTQl [RACHANCURR

4START A f'9.5 B 119.4 C i21. SSTART A 2.8 B '.8 C ~ .89 NYALID CL 54'r TEST 4,

FINISH A =.8 B 2. 8 C 2.8

TEST NO. 5

ESTERLINE ANGUS DATA

TIME CH08 CHQi CH "" CH03 CHSA CH~S CHC7 CHC9 CHc18 CHn 1 1 CH51 ~

8 e ~ cgr

8G8G:489 ic8aeAc18:1518 451> ~ 1

1 1 ~ 4512 ~

1 ~:451 ~:151':4514: 1514: 4515: 15

19

21. 9'r3e 4

.6. ep

.e. F

=9. 6

38,38. 4'8 738. 9

5-.45Ic if3 I I

~6. 71

39. 7ie. 6

39. 748, 1

48AQ~9 948v9. un

939. 739. 9~9. 939. 648

o'r o

34. 7'73e. 439. 348, 2

Ai

4'. 541. e41. 741. 441. 7

41 ~ 6

35. 637, 1

e"v ~ 7"9. 748. 4.

48. e41. 5

4r. 442. 541. 9'i. 7

4:Are cArr 7Ai. 9

.7. 7C

3-. 54r. 946. ~

Ae. A.

58. 451. e52e 7C iD~ ~

53o 753. 953. 9

54 454. 354. 5

"8. 1

47. 458.

7'3.

5CCopere oi56e 657. e58. 6

CaU» ~ o

59. 559. 759. 96868. 3

'4 ~

.e 645. 951. 1c5r rr

59. 961. 9

63. 363. e64. 564. 364. 464. S64. e65

29e e. c41. e46e 758. 6

C5~. ~55e 356. 457. 4cnerGe u58. 6

erGe 959. 1

59. 359. 5

38. 2"5 7

4 ~ .64e. 1cr,Vo'

44o 057cnDGo ~59. =68,68. 568. 968. 968. 961. 261. ~

61. 5

31. 737. 444. 5585456. 958. 768. 468. 96'62

n62. 46 ~o

6='. 76=. 86 I ~

9o34. 64'. 546. e58e e

5ere 4cS n57. e5n c5ee 959. 459o 5

9. 659. 659. 759'. 9

1~ )

". )... )Ao )5. )6. )7. )n9. )

COMMENTS

TEST 5 CL-54 '8/28/e3 8738VOLT START A . 5S9 B . 844 C . 611CURR START A 72. 8 B 72. 8 C 7 .. 8CHN 1 " ON OUTSI DE h!SULATION'-A.lBIENT 2-TOP CONDUIT

BOTTO!" CONDUIT 4-AIR SPACEYOLT FINISH A . 631 B -997 C -S57CURR FIN1SH A 7 .8 B 7.. 1 C 71.9END TEST 5 CL 54= 18/ r8/83 1545

C -542

1. ))

v. )4. )

)E. )7. )8. )9. )i8. )11. )2 ~

1". )14. )15. )lbI )17. )18. )19. )

28, )

CQ+gENTS - TEST NO. 6

CL- 4':: TEST 8 .ND RU" ll/18 8CHANNEL m9 AHBl+NTCHANNEL " iRAY TOPCHANN"L ~ TRAY BQ.TQl'iCHANNEL 4 AIR SPAC-28 A."lP C!(7 CHANNELS 925 AMP CKT CHANiNELS 8 1848 Ai~iP CKT CHANNELS 5~ 758 AilP CKT CHANNELS 18~ 28~ ~S

CURR START A 28. ~ B 28. 4 C .8. ~VOLT START A . 748 B . 769 C ..'SSCURR START A .5. 4 B 25. 8 C "5. iVQl T S ART g j 88' 1 058 C 1, 59(CURR START A 48. ~ 8 48. 8 C 48. ZVOL. S ART A . 22K 8 . 214 C . 245CUR% SiAR: A 53.8 8 58.8 C 58.8VOLT START A . "84 B . "89 C .287END TEST S biD '' /18/8 Tl!CE 1545CURR c'!>D A ""8. 5 B 21. 5 C ~i. 1

VOLT END A . 78c B. 8~8 C .8~7CURR END A 25. 4 B 25. Z C .5. =

VQl T END A i. 31S ei l. 797 C 1.285CURR END A 41. 1 8 08. 4 C 4F. 9

VOLT END A . 48 8 . "25 C. 25KCURR END A 58. 8 B 49. 8 C58.4

VOLT END A ..'"7 B. 211, C.278

CL-S42

TEST Ho. 6

ESTERL:NE ANGUS DATA

CHC2 CHr-.'' CHc4 CHN5 CHi"-.7 CHCS CH=::9 CH018 CH: 1 CH 16 CH5'"8

8'c85-4586-1 ~

86:4u87:1587:4588-158S:4589:189:4518:1518:45'1:1512o 15iso 4c

15'-4514:45f.5- 151c ~ 4c

21. 5i7. 7o9. 7'49o u48 Jg

48. 648. 7"9. 4

uSo48. 1

48. 948, 2u9. 248, 1

48. 948. 7>9. 44.8a9. 1

«8. 1

v9. 7

.9c

ZSYQ

>9. 648. 1

48. 448, 'r48. 741. u41. 541. "41. 1

41. 841. 641 ~ 241. 541. u41 ~ 641. 5

ore«4

~ So 8u « ~,.u

5o6 5u8. 1

u9. 448 or

41. 1

41. 84 Pg

4r. 7, ~

1

..4v. r44...44u. 6

4v. 5

5o«6o 8

, 29.Sgo'«o J

C'b/ ~ 4 ~

u7. 4

48. 641. 94r. 84 or ~

4 .644. 1

44. 644. 84c44. 945. u45. 445. 44c c

o JoeO7o ~ ~

=-.8. 1,.:":". 9

C''sJ ~ uu7. 8u9. 741

4Z. 1

4",44v. 844. 1

44o 644. 845. 1

44o 945. 1

45. 2

45. u

24. 9

"r9. S

C>o IIJo

:"7. 94

41. 1

41. 84",44u.

='u

4

4u. 844. 1

44. 244. 444o 544. 644. 644. 6

ore«do ~

~~a

"7. Su9 648. 94 +r

4u. 4.

4444. 444 Qi

45 ~1

l c

45o 545. 445.

E'5.

6

25. 6

~r9~ 7

2.'.,7,v5. 1

37. 4v9. 1

48. 741. 64r.4

4". 743. 944. u~

44. 6

454c45o Z45. 445. 2

+c cuo 47

-vvo uMMo 7>7,9

4141. 84r. 54u. 4

744. "44o 544. 844. 945. 1

45. ~

4c4c c4c c

wz c«do V26. 729. 6

n~ u

5 7u7 ~ 759. 248. 441. 542 ~

4 ~ .54r.9l-.. 14". 5

4",94". 84~. 944. 1

44. "

'5. 626. 729o 6

T5c

37. a~'3, 448. 541. 5

4r. 7

4v. 54u 84444. ~

44. ~

44. u44. 444. 444. 5

TE IE CHOu6 CHOZS

85 '5Qc ~ 4c86: 1586:4587: 1587: 458So 15BS: 4589: '589:4518o18 '511 -1511 -4512: 15ior 4c1 1

1 lL:45ico icI co45

ac«uo 56. 7

Q9 Ql

u5. 4"7. iZ9. u48. 5

42. 1

74u. 2

7p

44

44...44. 444. 444. "

"6. 7'S. 5v9. 948. ~

4848, 248. ~

48. 548. 648. 748o 1

4848. 54$ o 548. 549. 048. 540. 448. 748. 5

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