ML17334B543

Forwards Addl Info Re Thermo-Lag Related Ampacity Derating Calculations,As Requested by NRC 950306 Ltr

ML17334B543
Person / Time
Site:	Cook
Issue date:	05/12/1995
From:	FITZPATRICK E INDIANA MICHIGAN POWER CO. (FORMERLY INDIANA & MICHIG
To:	NRC OFFICE OF INFORMATION RESOURCES MANAGEMENT (IRM)
References
AEP:NRC:0692DF, AEP:NRC:692DF, TAC-M85538, TAC-M85539, NUDOCS 9505190297
Download: ML17334B543 (136)

Text

RIGRITYCCELERATED RIDSPROCESSING)

REGULATORY INFORMATION DISTRIBUTION SYSTEM(RIDS)ACCESSION NBR:9505190297 DOC.DATE:

95/05/12NOTARIZED:

NODOCKETIFACIL:50-315 DonaldC.CookNuclearPowerPlant,Unit1,IndianaM0500031550-316DonaldC.CookNuclearPowerPlant,Unit2,IndianaM05000316AUTH.NAMEAUTHORAFFILIATION FITZPATRICK,E.

IndianaMichiganPowerCo.(formerly Indiana&MichiganElePRECIP.NAME RECIPIENT AFFILIATION DocumentControlBranch(Document ControlDesk)~)~

SUBJECT:

Forwardsaddiinfo'eThermo-Lag relatedampacityderatingcalculations, asrequested byNRC950306ltr.DISTRIBUTION CODEA029DCOPIESRECEIVED:LTR ENCLSIZE:TITLE:GenericLetter92-008Thermal-Lag 330FareBarrier0,'OTES:RRECIPIENT IDCODE/NAME PD3-1LAHICKMAN,J INTERNANRR/DRPW/PD3-1 RGN3~...FILEEXTERNAL:

NOACCOPIESLTTRENCL101111111111RECIPIENT IDCODE/NAME PD3-1PDNRR/DE/EELB NRR/DSSA/SPLB NRCPDRCOPIESLTTRENCL11112211DNi4OTETOALL"RIDS"RECIPIENT:TS:

PLEASEHELPVSTOREDUCEKV'iSTE!COYTACTTHEDOCL'ifEYT CONTROLDESk,ROOlifPl-37(EXT.504-~OS3)TOf;Llliflb ATEYOL'RiAXIL'ROil DISTRIBUTIOYLIS'I'SI'ORDOCL'5IEi'I'SYOL'OY,"I'ff I'.D!TOTALNUMBEROFCOPIESREQUIRED:

LTTR11ENCL10 IndianaMichiganPowerCompanyP.O.Box16631Columbus, OH43216FIMay12,1995AEP:NRC:0692DF DocketNos.:50-31550-316U.S.NuclearRegulatory Commission ATTN:DocumentControlDeskWashington, D.C.20555Gentlemen:

DonaldC.CookNuclearPlantUnits1and2ADDITIONAL INFORMATION REGARDING THERMO-LAG RELATEDAMPACITYDERATINGCALCULATIONS TACNOS.M85538ANDM85539ByyourletterdatedMarch6,1995,wewererequested tosubmitrepresentative ampacityderatingcalculations withrespecttocablesinracewayscoveredwithThermo-Lag usedatDonaldC.CookNuclearPlant.Thecalculations andmethodologies, including mathematical models,areaddressed intheattachments tothisletter.Attachment 1providesanoverallsummaryofourampacityderatinganalyses.

Attachment 2containsthebasisofourmathematical model.Attachment 3containscabletrayallowable filldesigncriteria.

Attachment 4providesanin-depthdiscussion ofthedevelopment ofthemathematical modelandanalysis.

Attachment 5containsrepresentative calculation results.Attachment 6providesresultsfromtestsusedtoverifytheaccuracyofourcomputermodel.Sincerely, VicePresident cadAttachments ASQQjg9505190297 95051'2PDRADOiK050003i5PPDR jI U.S.NuclearRegulatory Commission Page2AEP:NRC:0692DF CC;A.A.BlindG.CharnoffJ.B.MartinNFEMSectionChiefNRCResidentInspector

-BridgmanJ.R.Padgett ATTACHMENT 1TOAEP'NRC'0692DF SUMMARYOFAMPACITYDERATXNGANALYSES.~-9505190297 Attachment 1toAEP:NRC:0692DF Page11.0~BackroundIn'theearly1980's,compliance with10CPRSOAppendix"R"wasachievedforCookNuclearPlant(CNP)byenclosing certainracewayswithThermalScienceIncorporated (TSI)Thermo-Lag 330-1firebarriers.

Enclosing thepowercableracewayswiththeTSImaterialincreases thethermalresistance toambientthusrestricting thequantityofheatreleased, resulting inreducedconductor>>

allowable ampacity.

AlthoughTSImaterialspecifications addressed specificpercentderatingforthecablesintrayandconduitwrappedwithThermo-Lag

barriers, AEPSCtookanaggressive approachtoindependently determine thereducedallowable ampacities anddocumented thatthefullloadcurrentsforpowercablesintheTSIwrappedracewaysatCNPdidnotexceedallowable deratedampacities.

2,0TheoretcaanassMathematical modeTheprocessincludedthedevelopment ofamathematical modelbasedonthetheoretical analysisandworkdonebyNeher,McGrath,andBullerintheirAIEEtransactions papers57-660and50-52(attachment 2).Thisanalysisisbasedonthephenomena ofheattransferwithrespecttoenergized cablesandtheeffectontheampacity.

Thetemperature ratingofacableisthemaximumconductor temperature thatwillnotcauseexcessive deterioration ofthecableinsulation overtheexpectedlifeofthecable.Thismaximumtemperature limitstheamountofheatwhichmaybegenerated byaconductor byresistive heatingandtherefore limitstheamountofcurrentthecablecancarry.Enclosing, theconductor withinlayersofmaterial(i.e.,insulation, raceway,orairspace)increases thethermalresistance totheambientheatsinkandrestricts thequantityofheatwhichmaybetransferred whilestillmaintaining themaximumconductor temperature.

Theobjective thenwastodetermine theallowable ampacityofcablesinvariousracewayandfireprotected racewayconfigurations basedontheheattransferthroughathermalresistance whilenotexceeding thetemperature ratingofthecablesundersteadystateconditions.

Thephenomena ofheattransferwithrespecttoenergized cablesandtheeffectoncableampacitywereexamined.

Thi.sincluded:

Attachment 1toAEP:NRC:0692DF Page2a)reviewofbasicheattransfermechanics, b)evaluation ofpreviousworkdoneintheareasofcableampacityandheattransfer,,

c)analysisoftheeffectsofconduction, convection andradiation withrespecttoCNPpowercableinstallations, andd)development ofheattransfertheoryforlowfillcabletrays.Perourdesigncriteria(seeattachment 3),thepowercablesinstalled incabletraysarepositioned inasinglelayerwithaminimumspacebetweencablesof1/3thediameterofthelargerad)acentcable.Furthermore, thesumofcablediameters cannotexceed75%ofthetraywidth.Theabovecriterialimitsthenumberofpowercablesinstalled inacabletray,thuslimitingthetotalheatgenerated perfootandlimitingtheconductor derating.

3.0 Calculations

Acomputerprogramwasdeveloped according tothecriteriaoutlinedinthemathematical model.Theprogramcalculates theallowable ampacities forthepowercablesintheTSIwrappedraceways.

Assumingamaximumallowable cabletemperature of90Candanambienttemperature of40'C,themaximumallowable heatgenerated(Q) wascalculated forsteadystateconditions.

Theallowable ampacity(I)wasthencalculated usingtheknownrelationship betweenQandI.Theanalysisandmathematical modelarediscussed indepthinattachment 4.AtCNP,thepowercablesinallTSIwrappedracewayswereanalyzedusingthisprogramanditwasdocumented thatthecablefullloadcurrentsarewithinthecalculated allowable ampacities.

Representative calculation resultsshowingtheallowable ampacities forthecabletrayandconduitracewaydesignareincludedinattachment

5.

Attachment 1toAEP:NRC:0692DF Page34.0TestsFinally,aseriesoftestswasconducted in1983atourCantontestlabtoverifytheaccuracyofthecomputermodel.Thesetestssimulated exactracewayloadingconditions atCNPanddemonstrated thattheconductor temperatures fortheTSIenclosed.cablesarewithinthetemperature ratingoftheconductors:.

as.predicted bythecomputermodel.Refertoattachment 6forthetestreport¹CL-542datedDecember16,1983.Thehighestconductor temperature recordedforthesixtestedconfigurations was68.8'C.Cabletraysandconduitswerebothincludedinthistesting.5.0~Conclusio AtCNP,thecalculations forthecablesenclosedwithTSIThermo-Lag 330-1firebarriersdemonstrated that:a)theconnected fullloadcurrentsarewellwithincalculated allowable ampacities, b)thecalculated heatgenerated perfootofracewayiswellunderthecalculated allowable heatgeneration perfootofraceway,andc)theracewaydesigncriterialimitsthetotalnumberofcablesinaracewaysuchthatthecabletemperature ratingsarenotexceeded.

ATTACHMENT 2TOAEP'NRC'0692DF AIEETRANSACTIONS PAPERS57-660&50-52

'iy,klJ.*4, M.H.McGRATHi'e~e,haN1932D.M.Simmons'ublished aseriesofarticlesentitled, "Calculation oftheEIcctricaI ProblemsofUnderground Cables."Overtheintervening 25yearsthisworkhasachievedthestatusofahandbookonthesubject.Duringthisperiod,however,therehavebeennumer-ousdcvdopmcnts inthecableart,andmuchtheoretical andexperimental workhasbeendonewithavievrtoobtaining moreaccuratemethodsofevaluating theparametas involved.

Theadventofthepipe-type cablesystemhasemphasixed thedesirability ofamorerationalmethodofcalculating theperformance ofcablesinductinorderthatarealistic comparison maybemaCkbetmeenthetwasystans.Inthispapertheauthorshaveen-deavoredtaextendthevrorkofSimmonsbypresenthig underonecoverthebasicprinciples

involved, togethervrithmorerecentlydeveloped procedures forhan-dlingsuchproblemsastheeffecoftheloadingcydeandthetemperature riseofcablesinvarioustypesofductstxuc;turcs.Indudcdaswdlareexpressions requiredintheevaluation ofthebasicparaxneters forcertainspecialixed alliedprocedures.

Itisthoughtthat,amarkofthistypewiIIbeusefulnotonlyasaguidetoengineers enteringtheGeldandasareference tothemoreexperienced, butparticularly asabasisforsettingupcom-putationmethodsforthepreparation ofindustryloadcapability andaw/d~ratiocompilations.

Thecalculation ofthetemperature riseofcablesystansunderessentially steady-stateconditions, whichincludestheeffectofoperation underarepetitive loadcycle,asopposedtotransient temperature risesduetothesuddenapplication oflargeamountsoflaad,isarelatively simpleprocedure andinvolvesonlythcapplica-tianafthetherxnalequivalents ofOhm'sandKirchoff's Lawstoarelatively simplethermalcircuit.BecausethiscircuitusuallyhasanumberofparallelpathswithheatGamsenteringatseveralpoints,hovrcver, caremust,beexercised inthemethodusedofexpressing theheatfomsandthermalresistances

involved, anddiffering methodsareusedbyvariousen-gineers.Themethodemployedinthispaperhasbeenselectedaftercarefulcon-sideration asbeingthemostcansistcnt andmostreadilyhandledoverthefullscopeofthepxablan.Alllosseswillbedeveloped onthebasisQONrsandtemperature risesduetodielec-triclossandtocurrent-produced lassesmillbctreatedseparately, and,inthelattercase,allheatHorns"miII beexpressed intermsofthccurrentproducedlossariginat-inginonefootofconductor bymeansofmultiplying factorswhichtakeintoac-counttheaddedlossesinthesheathandconduit.Ingeneral,allthamalresistances miIIbedeveloped onthebasisofthepercon-ductorheatQowthroughthem.Inthecaseofunderground cablesystems,itis'convenient toutilitcaneffective thexxnal'esistance fortheearthportionofthcthcxxnaIcircuitvrhichindudestheeffectoftheloadingcydeandthemutualheat-ingcffcctafthcathcx'able ofthcsystem,AllcablesinthesystemwiIIbeconsidered t~ocsrryeeeoieIdedeetieiite eedtobeoperating underthesameloadcyde.Thesystem'of nomendature employedisinaccordance withthatadoptedbytheInsulated Conductor Committee asstand'-ard,anddiffasappreciablyfrom thatusedinmanyofthcreferences.

Thissystemrepresents anattempttoutilizeinsafaraspossiblethevarioussymbolsappearing intheAmaicanStandards Association Standards forEectxicai Quintities, Me-chanics,HeatandThaxna-Dynaxnics,

'andHydraulics, whenthesesymbolscanbeusedwithoutambiguity.

Certainsymbolswhichhavelongbeen'usedbycableengineers havebeenretained, eventhoughtheyareindirectconQictmiththeabaveementioned standards.

Nomenclature (AF)attainment factor,perunit(pu)As<<cross-sectioht areaofashieldiag tapeorskidrcire,squareinchesdr<<therznaI diffhhsivity.

squareinchespahourCI<<conductor area,circularinchesd<<distahhcc, inches'th etc.<<fromceaterofcableno.1tocenterofcableno.2etc.Cks'tc.<<from centerofcableno.1toimageofcableno.2etc.Asetc.fromcenterofcableno.1toapoiatoficterfercace

$.'.',."!7het Calculation oftheTemperature Risean'dLoadCapability of'ableSystems~~~3.H.NEHERr.MEMSERdhtlEEeAs'tc.<<frohn iaugeofcableno.1toapointofintexfexeace D<<dhmcter, inchesaqb.oDcdaiasid D,<<OutxideOfCahhduetar

~Ds<<outside ofixhsulatioa Ds<<outside ofsheathD<<,<<incan diameterofsheathDf<<outsideofjacketDs'<<effective (cixcuxnscribiag cirde)ofseveralcablesincontactDp<<inside ofductwal4pipeorconduitDc<<dlaxneter atstartoftheearthportionofthethermalcixcchitDa<<fictitious diameteratvrhichtheeffectoflosshctorcommences E<<linetoneutralvoltage,kilovolts (kv)~<<coefficient ofsurfaceemissivity cr<<spccific inductive capacitance ofinsula-tloa/<<frequency, cyclespersecoadF,Fs,h<<pxxhducts ofxatiosofdistances F(x)<<derivedBesseifunction'f x'TableIIIandFhg.1)G<<geometric factorGt<<applying toinsulatioa resistance (Fige2ofreferexhce 1)Gs<<applying todielectric loss(Fig.2ofreference 1)Ght<<applying toaductbank(Fig.2)Iconductor current.kiloampexes kd<<skineffectco?rection factorforannuhrandsegxneatal conductors kp<<relative txanshrexse coadclc&ity hctoxforcaicuhting conductor pxoxihnity etfectJ<<hyofashielding tapeorshdwire,inchesL<<depthofreference cablebelowearth'schxface, inches.Lv<<depthtocenterofaductbank(ox'ackfill),

inches(lf)<<loadfactor,perunit(LF)<<losshctor,perunitrinumberofconductors percablexs'<<nuxaber ofcoaductoxs withinastateddiaxneter N<<numberofcablesorcable'groupsinasystexnP<<perihneter ofaductbankorbackfiJI, inchescos4<<povrerfactoroftheinsuhtion tfc<<ratio ofthesumofthelossesintheconductors andsheathstothelossesiathccoaductoxs

'Itlc<<ratio ofthesumofthelosseshxthecoadchctoxs, sheathandconduittothelossesintheconductors R<<electrica resistance, ohmsRsc<<dwresistance ofconductor Rtotalawresistixhce perconductor Rc<<dwresistance ofsheathoroftheparallelpathsinashield-skid vtrireassembly8<<thexxnalresistance (perconductor losses)thexxnalohm-feet8s<<ofiaschlatioa Af<<ofjacketRhd<<betweencablesurfaceaadschxxounding endosurePaperST~,recomtaeadcd bTthehIBBInsulated Coaductors Committee aodapprorcdbTthehIEETcchaiccl Operations Pepartmcac forpresentation

~cthehlBBSummerCcocrslhfecttae.

hfoocreal, Que.,'aosda, Juae24-2S.105T.hfaauscript subhoittcd starch"0,10ST;madearansbteforpriociaxhpril18,10$T.J.If.Nausalseectbthephiaadclphta Elec&aCompcor.Philadelphia.

Pa..andhf.H.hfcCaamIsreichtheCcocralCableCocporacloo, Pcrthhmbor,¹J.c'Ceher,.VcGrctli

-Terrlpercfnre crxdLoadCcpabilify ojCcblcSystemsQCTCnERlear t~'ajoOA9OA4OA7OA4005Xo2,5IA0.9a40.70.4ga5~a4~~0.25a2O.I5F(xv)jIF(x9)II!IIilii~~I;II@xiIljrIII!I'ljiiIi~si.II!II:(xj0015&oIpa009~Iu000400050~hIOA03000250002I.OI.5I.o8IO.IO2253454769IOl520304050604000RucAFig.l(above).F(x)andF(xa')azfunctions of~/kFig.q(right),GIfor4ductbankWa~poztion developed intheconductor W,~portion developed inthesheathorshieldW<<portiondeveloped inthepipeorcon-duitWc~portioadeveiopal mthedielectzic X~~mutualreactance, conductor tosheathorshield,microhmsperfootY~theincremen't ofaw/dwratio,puYa<<duetolossesoriginating inthecon-ductor,havingcomponents YaaductoshnefectandY,jrduetoprox-imityeffectYa~duetolossesoriginating inthesheathorshield,havingcompobeats YIaduet'ocizcuhting cuzrentcffectandYi,duetoeddycurrenteffcctYIr~due'to lossesoriginating inthepipeorconduitYa~duetolossesoriginating intheamorGeneralConsiderations oftheThermalCircuitTHs~~TzoNopTsM2smTzzss RzssThetemperature riseoftheconducmrofacableaboveambienttemperature maybeconsidered asbeingcomposedofatemperature riseduetoitsownlosses,whichmaybedividedintoariseduetocurrentproduced(PR)losses(hereinafter referredtomerelyaslosses)inthe,conduc-tor,sheathandconduitb,Taandtheriscproducedbyitsdielectric losshT4.24~ofductwallorasphaltmasticcoveringR~totalbetweensheathauddiameterDaIncluding Rt,RrcandRc~~~R<~betweenconduitandambient.R,'~effective betweendiameterDaandambientearthincluding thecffects.oflossfactorandmutualheatingbyothercablesRaa'~effective betweenconductor andambientforconductor lossR4r'effcctive tzanslcnt thezznalresistance ofcablesystanRca'~cffective betweenconductor aadam-bientfordielectric lossRr,I~oftheinterference efectRf4~betweenasteampipeandambientearthp~clectrical resistivity, circularmilohmsperfootitthermalresistivity, degreescentigrade centimeters pcz'at'ts~distance ina3mnductor cablebetweentheeffective currentcenteroftheconductor andtheaxisofthecable,inchesS~axialspacingbetweenadjacentcables,inchest,T~thickncss (asindicated).

inchesT~tanperature.

degreescentigrade Ta~ofambientairorearthTa~ofconductor T~~meantemperature ofmediumAT~tcmpaature rise,degreescentigrade ATa~ofconductor duetocturentproducedlosseshT4~ofconductor duetodielectri losstZTrxr~of acableduetoextraneous heatsourcerinfaredtanpaature ofzeroresistance, degreescentigrade (C)(usedincorrecting R4,andR,totempera-turesotherthan20C)Vs~windvelocity, milesperhourW~lozsesdeveloped inacable,wattsperconductor footRATIOLb/PTa-Ta~hT,+4T4degreescentigrade (1)Eachofthemcomponent temperature risesmaybeconsidered astheresult.ofarateofheatflowexpressed inwattsootthrouaermalresistance dinthermalohm eetdegzcescenti-gra0eetperwatt);inotherwords,theQowofonewattuniformly distributed.

overaconductor lengthofonefoot.Sincethelossesoccurat.severalposi-tionsinthecablesystem,theheatBowinthethezznalcircuitwB1increaseinsteps.Itisconvenient toexpressallheatQowsintermsofthelossperfootofconductor, andthus,,aT,-WgRr+q,R,.+qA) degreescentigrade (2)inwhichW,represents thelossesinoneconductor andRIisthethermalresistance oftheinsulation, q>istheratioofthesumofthelossesintheconductors andsheathtothelossesintheconductors, R<<isthetotalthamalresistance betweensheathandcocdmt,q,istheratioofthesumofthelossesinconductors, sheathandconduit,totheconductor losses,andRaOerosss1957Nchcr,McGrath-Tcrnpcratarc arrdLoadCapability ofCableSystcrrrs lsthethermalresistance betweentte<trconduitandambient."Inpractice, theloadcarriedbyacableisrarelyconstantandvariesaccording tostdailyloadcyclehavingaloadfactor(lj).Hence,thelossesinthecablewillvaryaccording tothecorresponding dailylosscyclehavingalossfactor(LF).Fromanexamination ofalargenumberofloadcyclesandtheircorresponding loadandlossfactors,thefollovring generalrda-tionshipbetvreenloadfactorand/lossfactorhasbeenfoundtoexist.'LF)

~0.3(tf)+0.7(tf)'erunitInordertodetermine themaximumtemperature riseattainedbyaburiedcablesystemunderarepeateddailyloadcycle,thelossesandresultant heatflowsarecalculated onthebasisofthemaxi-mumload(usuallytakenastheaveragecurrentforthathourofthedailyloadcycleduringwhichtheaveragecurrentisthehighest,i.e.thedailymaximumone-houraverageload)onvrhichthelossfactorisbasedandtheheatQowinthelastpartoftheearthportionofthethermalcircuitisreducedbythe"factor(LF).Ifthisreduction isconsidered tostartatapointintheearthcorresponding tothediameterD'quation 2becomest2TcWc(lt+qc~tc+qc(~cs+(LF)@c)l degreescentigrade (4)Ineffectthismeansthatthetempera-turerisefitomconductor to'>ismadetodependontheheatlosscorresponding tothemaximumloadvrhereasthetempera-turerisefromdiameterDctoambientismadetodependontheaveragelossovera24-hourperiod.Studiesindicatethattheprocedure ofassumingafictitious criticaldiameterD>atwhichanabruptchangeoccursinlossfactorfrom100%toactualwillgiveresultswhichverycloselyapproximate thoseobtainedbyrigoroustransient analysis.

Forcablesorductinairwherethethermalstoragecapacityofthesystemisrelatively small,themaxi-mumtemperature riseisbasedupontheheatGowcoizesponding tomaximumloadvrithoutreduction ofanypartofthetheimalcircuit.Whenanumberofcablesareinstalled dosetogetherintheearthorinaductbank,eachcablewQIhaveaheatingeEectuponalloftheothers.Incalculating thetemperature riseofanyonecable,itisconvenient tohandletheheatingetfectsoftheothercablesofthesystembysuitablyinodifying thelasttermofequatiot4.Thisispermissible sinceitisassuinedthatallthecablesare,carryingequalcur-rentsandareoperating onthesameloadcycle.ThusforanP-cablesystemaTcWc(A+qc~cc+qcfffcc+(LF)

X(Bcc)+(N-I)N¹ I)(5)Wc(lt+qcIcc+qcRc')

degreescentigrade (Sh)wherethetenninparentheses isindicated bytheetfective thamalresistance 8c'.Thetemperature riseduetodielectric lossisarelatively smallpartofthetotaltemperature riseofcablesystemsop-eratingatthelowervoltages, butathighervoltagesitconstitutes anappre-ciablepartandmustbeconsideretL Al-thoughthedielectric lossesaredis-tributedthroughout theinsulation, itmaybeshownthatforsingleconductor cableandmulticonductor shieldedcablewithroundconductors thecorrecttemperature risetsobtainedbyconsidering fortran-sientand-steady.statethatallofthedielectric lossWttoccursatthemiddleofthethermalresistince betweenconduc-torandsheathoraitentateiy forsteady-stateconditions alonethat'thetempera-turerisebetweenconductor andsheathforagivenlossinthedielectric ishalfasmuchasifthatlosswereintheconductor.

Inthecaseofmulticonductor beltedcables,howevertheconductors aretakenasthesourceofthedielectric loss.'heresulting temperature riseduetodielectric loss42'ttmaybeexpressed dTtt~Wit's'egrees centigrade (6)inwhichtheeffective thermalresistance ib'isbasedupon/It,8,and)4'(at unitylossfactor)according to.theparticular case.Thetemperature riseatpointsinthecablesystemotherthanat.thecon-ductormaybedetermined readilyfromtheforegoing relationships.

THBChiA'-UthTio)4 opLohnChPhnan)r fnmanycasesthepermissible maxi-mumtemperature oftheconductor isGxedandthemagnitude oftheconductor currentgoadcapaMity) requiredtoproducethistemperature isdesiretLEquation5(A)maybewrittenintheformATc~I'24c(I+

yc)lcc'egrees centigrade (7)iwhichtheqqaatity~lb, (1+Y,qhiehillbeevuatereresentstheeE'veelectnresistance ofthecon-ducto'nhmsandwhichvrhenmultiplied byP(Iinkiloamperes) vrillequalthelossWcinwattsperconduc-torfootactuallygenerated intheconduc-tor;and8ec'sthee(fectlve thermalresistance ofthethermalcircuitfIcc'IIt+qc8cc+qcffc'hermal ohm-feet(8)FromequationIitfollowsthatI+lciloameres3a,<I+I;)~.Ta6leI.Electrical Resbtlvity ofVariousMateriabbtaterlcl PCheaterMllOhmsperFootat20Cr,CCopper(100%IhCS')~~~~~~~~10.371.....

234.SAluminum(81%IhCS).e,~17.002.~.~.228.1Cotcmerelct Bronte(43.8%~~.23.8~~~~.584IhCS)(90Cu-10Zo)Bta$5(2T.3%IhCS)~~~.~..~~~38.0~~~~.912(0Cu-30Zu)Lead(7.84%cIhCS)...~.~...132.3

.~.~.238~Isterssuoud hoaeale4CopperStaodanLCalculatioa ofLossesandAssociated Parameters 37.9Rc~-'orIesdat50CDctttt(IIA)4~-for61%aluminumat50,CDg1(IIB)vrhereDctttisthemeandiameterofthesheathandttsitsthickness, bothininchesDccq~Dctlaches(12)Theresistance ofintercalated shieldsorskidwiresmaybedetermined fromtheexpfcsstOQ rpcSDtetR,(pe:path)-)I+(-)microhmsperfootat20C(13)whereA,isthecrosssectionareaoftheGac~Tio)i CFDNRBsisThNcxs Theresistance oftheconductor maybedetermined fromthefollowing expressions vrhichincludealayfactorof2%;seeableL1.02pcmicrohmsperfootat20CCI(IO)12.9for100%IACScopperCIconductor at76C(10A)212~-for61%IACSCIalumlautn at75C(IOB)vrhereCIrepresents theconductor sizeinCircularinCheSandVrherePcrePreSentS theelectrical resistivity incircularmilohmsperfoot.Todetermine thevalueofresistance attemperature Tmultiplytheresistance at20Cby(r+T)/(r+20) whereristheinferredtemperature ofZeroresistance.

Theresistance ofthesheathisgivenbytheexpressions pcR,~-mlcrohmsperfootat20C(II~4DccttKdhdr,hfcGra!h-TerripdratnrdandLoadCapability ofCcbfeSys.'crrts QcToBBR19o<

s~~'~tapeorsl.idwireandlisitslay.Theover-all':esistancc, oftheshieldandskidrwireassembly, particularly for.noninter-calatedshields,shouldbedetermined byJectrical measuremcnt whenpossible.

C~L.ctfuTioH oFLossllsItisconvenient todevelopexpressions forthclossesintheconductor, sheathandpipeorconduitintermsofthecomponents oftheaoc/docratioofthecablesystemwhichmaybeexpressed asfollowslr(wRCIRcc1+Yc+Ys+Fp (14)Theaoc/docratioatconductor is1+YcandatsheathorshieldisI+Y,+Ysandatpipeorconduit isI+Y,+Ys+Yp Thecorresponding lossesphysically gen-eratedintheconductor, sheath,andpipeareWsIRcs(l+Yc)wattspcrconductor foot(IS)WsPRccYswattsPerconductor foot(16)Wp~I'24cYpwattsperconductor foot(17)'cisj>>Il.Recommended Valuesofk,cndksConductor Construcuon CostingonSaendsTreatment LroConcentric round,.............Hone.....

~~.~~.~...".Noae..............l.o

.....~.......1.0 Concentric round..............Tlo orenoy........

~.~.None..........~...1.0

........~....1.0 Concentric round..............Hone.~...............

Yes...............l.o

.....~.......0.80 Compactroundo~Noae~~~Yes~~~I0~~~~~00Compactsegmental.......,....Hone..................Noae..............0.43$

.............0.0 Compactsegmental............Tin oraUoyooHone....O.S.~..0.7Compactsegmental............Hone..................Yes...............0.43$

.."...~.....0.37 Compactsector................Hone...............

~..Ycs...............l.o.............(secnotc)

Horns:1.Theterm"treated" denotesacompleted conductor whichhasbeensubjected toadrylogandlmpregnat lngprocesssimaertothatemployedonpaperpowercahte.2.Proximnyedectoncompactsectorconductors maybetahenasosehalfofthatforcompactroundhaving'thcsamecrossscctloosl areaasdLnsutsuon thtchncss, 3.Proximity CUcctonannulareooductors maybeapprodmsted byusingthevalueforaconcentdc roundconductor ofthesamecross-cctfsnnsL areaandspadng,Thelocressed diameteroltheannulartypeandtheremovalofmetalfromthecenterdecreases theshineifcctbut,foragivenadslspsdng,tendsto.resulttnanlnaeaselnproximity.

o4.Thevalueslistedaboveforcompactscgmentsl refertofoursegmentconstructtooa Theuocoatcd treated"valuesmsyalsobetahcnasapphcabi~tofoursegmentcompactsegmental withhoaowcore(approximately 0.7$inchdear).For"uncoated treated"sixsegmenthouowcorecompactsegmental limitedtestdatalodicatcs koandkpvaluesofOAandOArespectively.

Tabl>>III.SkinEffectfn%inSolidRoundConductor lndinConventionel RoundConcentric Str4ndConductors 100F(x),SkinEffectfo345d7d9hispermitsareadydetermination ofthelossesifthesegregated a-c/docratiosareknown,andconversely, theaoc/docratioisreadilyobtainedafterthevaluesofYcsYsandY<havebeencalculated.

Itfollowsfromthedefinitions ofqsandqcthatWc+WCYcqswm]+Wc1+YcWc+WC+WpYr+Ypqci+-We1+Yc(18)(ip)ThefactorY,isthesumoftwocompo-nents,Ymduetoskneffect andY,pdueproximity effect.Wc~lsRefc(1+

Ycc+Ycp)wattsperconductor foot(20)(21)xs~0.875-~-at60cycles$RccQRcr/ks(22)inwhichthefactorhsdependsupontheconductor construction.

Forconventional conductors ancttonF(x)mayotatneomTable'IIorfromthecurvesofFig.1intermsoftheratioRs,/hat60cycles.Forannualconductors solidor~Srrotnate eILThe,(2$)invrhichD,andDsrepresent theouterTheskinetfectmaybedetermined fromtheskineffectfunctionF(x)~Ycc~F(xr) 0.00...0Ol~~~0.04..~0,13...O.sd...0$4o~~O.T9...1.11...IS2o~~2.02..~2.as'~.3.40oo~4.30...6.3$...d,syooT.Q0..~11.3loo~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..r90.2$...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...$4To~~66'~6TO~~5'2~~0.70...0.83...0.97...7.11...8.11...8.25...$.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.$$...3989...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.$00.08...0.70...0.73097I00'I031.34.~.1.3$...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$..~9.2110.$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$.3330.$$oo~31.17...31.4934.10...34.43o..34.TT3T.4T.~.3T.$2..~38.1040.94.41.29~.~41.ds44.49...44.8$...4$.2148.11...48.4T...48.84$1.77...62.14...62.$1$$.'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...103.920.8...~0.2L.~.09034'~1.0'eOo62.",II~~~0Tdo~1.2...IOT...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..

andinnerdiameters oftheannularcon-ductor.Incomparison withtherigorousBcsselfunctionsolutionfortheskineffectinanisolatedtubularconductor, ithasbeenfoundthatthe60~cleskineffectofannularconductor whencomputedbyequation'23willnotbeinerrorbymorethan0.01inabsolutemagnitude forcopperoraluminumIPCEA(Insulated PowerCableEngineers Association)

SledOcTOUUR1957%cher,.lfcGrcfh

-T~n(pcrc]nrc andLoadCapability pfCnbtcSysfcfns7M

6as~I~Ta6I>>IV.MutualReactance a160CyeiessConyfudoe loSheath(orShlelsf)D~/28--0123455T896(2S/D~)asinthecaseofleadsheaths.<<~--1+--'t'Ij'I~tjcoreconductors upthrough5.0CIandforhollowcoreconcentrically strandedcopperoraluminumoilrfiilled cableconductors upthrough4.0CI.Forvaluesofxpbelow3.5,arangevrhichappeartocovermostcasesofprac-ticalInterestatpovrerfrequencies, theconductor proximity efectforcablesinequilateral triangular, Eormation inthesameorinmpaiat'te ductsmaybecal-culatedfromthefollowing equationbasedonanapproximate expression givenbyArnold'equation 7)forasystemofthreehomogeneous,

straight, parallel, solidconductors ofcircularcrosssectionarrangedinequilateral formation andcarryingbalanced3-phasecurrentremotefromallotherconductors orconducting material.

Theempirical transverse con-ductancefactorkpisintroduced tomaketheexpression applicable tostrandedconductors.

Experimental resultssug-gestthevaluesofkpshowninTableILYep-F(xp)(-')

Xis)+0.312-(24)6.60at60cyattt(25)epWhenthesecondterminthebracketsissmallvrithrespecttotheGrsttermasitusuallyis,equation24maybewrittenatIIm)5(De/S)t 1Yep~4F(xp)iJF(x,)+om~4(-')F(xp')(24h)()Ijt'"r6~'li'IvrherethefunctionF(xp')isshowainFig.l.Theaverageproximity efectforcon-ductorsincradleconfiguration inthesameductorinseparateductsinaforma-tionapproximating aregularpolygonmayI~~~Ta6l>>V.Speci8>>Intiuctiv>>

(:apadlance ofInsufations alsobeestimated fromequation24and24(A).Insuchcases,Sshouldbetakenastheaxialspacingbetvreenadjacentconductors.

ThefactorYsisthesumoftvrofactors,Y<<duetocirculating currentefectandY<<duetoeddycurrentefects.WsI'Rd<Yes+Yes)wattsp>>rconductor foot(26)Becauseofthelargesheathlossesvrhichresultfromshort~ited sheathopera-tionwithappreciable separation betweenmetallicsheathedsingleconductor cables,thismodeofoperation isusuallyrestricted totriplexcableorthreesingie~nductor cablescontained inthesameduct.Thecirculating currentdfectinthreemetallicsheathedsinglemnductor cablesarrangedinequilateral configuration isgivenbyRs/Ree1+(Rs/Xw)s (27).When(R,/X~)tislargevrithrespecttounityasusuallyisthecaseofshieldednon-leadedcables,equation27reducestoX~Yse~-approximately RIRdeXss~0.882/IOg2S/Ds~microhmsperfoot(28)~52.9Iog2S/Dsesmicrohmsp>>rfootat60cydes(28A)whereSistheaxialspacingofadjacentcables.Foracradledconfiguration X~maybeapproximated f'rom2.52S0/SX~52,9log'-(-)b,-S)microhins perfootat60cydes(29)~52.9log2.3S/Dyesapproximately (29A)TableIVprovidesaconvenient meansfoidetermining Xforcablesinequilateral configuration.

Theeddy~eatefectforsingle-coaductor cablesinequilateral configura-tionwithopen~cuited sheathsisMateria)Polyethyleae.................2.

3Paperlasuiatlou (solidtype)...3.

~(1PCEhea)ue)Paperjose)atjoa(otheetypes)..3,~.2Rubberaodeubbeejjhecoospounds....

~...............5 (lPCEhva)ue)Varnished eaesbrje.........,,.S (IPCEhvalue)3RI/Rde1+--(30)when(5.2R,/J)'slargeinrespectto1/50.4.~."21~1.~~~20.5,.~a199....r194.....18.9..".18.3.....1T.8...

~.ly.i..."15.9..".15.4 0.3.~~~~2T.T.~~~25~9...~25.2"~..23'.....24as.".~24.l."..23.5....

~22.9.....22.2.....21.5 0.2.....3T.0....33.9,.34.8.....33.8.

~...32.8.....31.9.....31.0.....30.1.....29.3.....28.4 0.1"".52.9."50.T....48.T...

~.45.9.~.~.45.2..~~.43.5.....42.1.....40.T*.

~-.39.4~~~~.3'roximattly at60cycles(30A)Whenthesheathsaleshort~ted, thesheatheddylossmalbereducedandmaybeapproximated bymultiplying equations 30or30(A)bytheratioR,'/(Res+Xmas)

Incomputing averageeddycurrentforcradledconfiguration, Sshouldbetakenequaltotheaxialspacingandnottothegeometric-mean spacing.Equations 30and30(A)maybeuraltocomputetheeddyment-,ef

>>etforsingle-conductor cablesinstalled inseparateducts.Strictlsag,theseuationsalyonltothreecablesinequilateral con-gurationbutcanbeusedtoestimateossesinecableouswhenlatteraresoorientedastoaroximatearelarpolygon.TEeeddymentefectfora3-conduc-torcableisgivenbyArnoId.'RI (2s/D~)'2s/Dsw)'1 4-+1(2y/D~)s~~~5.2R,16-+1fWhen(5.2R/f)iishrgevrithrespecttounity,Y~-approximately at60cyd>>s(31A)3~1.155T+0.60Xthe Vgaugedepthforcompactsectors<<1.155T+0.58 D,foiroundconductors iuy)~andTistheinsulation thickness, indud-ingthickness ofshieldiag tapes,iEany.Whileequation31(A)vrillsuKceforleadsheathcables,equation31shouldbeusedforaluminumsheaths.On3~nductor shieldedpaperleadcableitiscustomary toemploya3-or5-milcoppertapeorbronzetapeinter-calatedvrithapapertapeforshielding andbinderpurposes.

Thelineald-cresist-anceofacoppertape5milsby0.75inchisabout2,200microhmsperfootoftapeat20('hedrcresistance perfootofcablewillbeequaltothelinealresist-anceofthetapemultiplied bythelaycorrection factorasgivenbytheexpres-"sionunderthesqu3:e.root signinequation13.Inpracticethelaycorrection factormayvaryfroin4to12ormoreresulting Inshielding andbinderasscinbly resist-756.icher,McGrctl:-Tcn:pcrc!

arcandLoadCaPability ojCableSystcn;sQCTOBER195I

}s,'Ihe.ancesofapproximatdy 10,000ormoremicroi<ms perfootofcable.Evenonthcassumption thattheassemblyresist-anceishalvedbecauseofcontactwithad-jacentconductors andtheleadsheathcomputations madeusingequations 2?~and30shocvthattheresulting circulating andeddycurrentlossesareafractionot1%onsizesofpractical Interest.

Forthisreasonitiscustomary toassumethatthelossesintheshielding andbindertapesof3oconductor shieldedpaperleadcablearenegligibleo Incasesofnonleaded rub-berpowercableswherelappedmetallictapesarefrequently

employed, tubeeffectsmaybepresentandmaymateriaUy lowertheresistance oftheshielding assem-blyandhenceincreasethelossestoapointwheretheyareofpractical signiG-CanCeoAnexactdetermination ofthepipelosseffectYpinthecaseofsingle~nductor cablesinstaHedinnonmagnetic conduitorpipeisaratherinvolvedprocedure asindicated inreference 7.Equation31maybeusedtoobtainaroughestimateofYpforcablesincradledformation onthebottomofanonmagnetic pipe,how-everbytakingtheaverageoftheresultsobtainedforwidetriangular spacingwithsaa(Dp'-Ds)/2 andfordosetri-anglespacingatthecenterofthepipewith2~0.578'DThe meandiameterofthepipeanditsresistance perfootshouldbesubstituted forDrandR,respectively, FormagneticpipesorconduitthefoUowingempirical reIationshipss maybeemployed1.54s-0.115D pYp~(3~nductor cable)Ac(33)0.89$-0.115Dp4dosetriangular)

(34)0.34$+0.175DpYp~(single-conductor, 244cradled)(5)'Theseexpressions applytosteelpipersandshouldbemultiplied by0.8forironconduit.s Theexpressions givenforY,andYsaboveshouldbemultiplied by1.7toGndthecorresponding in-pipeeffectsformag-neticpipeorconduitforbothtriangular andcradledconGgurations.

CALCULATION OFDIELECTRIC LOSSThedielectric lossWsforSaocdnetor shieldedanda~inteaondnetor cabletsgivenbytheexpres'sion

0.0 0276Esrr

cosc)lo(Lr:D)/DQ"--.-conductor footat60cycles(36)andfor3~nductor beltedcableby'.019E'c, cosc)Wg~'attsperscoccdccctor footat60cydes(37)whereZisthephasetoneutralvoltageinkilovolts, eristhespeciGcinductive capacitance oftheinsulation (TableV)Tisitsthickness andcospisitspowerfactor.Thegeemetric facterGsmaybefoundfromFig.2ofreference 1.Forcompactsectorconductors thedi-electriclossmaybetakenequaltothatforaconcentric roundconductor havingthesamecross-sectional areaandinsulation thickness.

r'eoCalculation ofThermalResistance THERMALRESISTANCE OFTHBINSULATION Forasingleconductor cable,rIRf0.012tiflogDf/Dcthermalohm-feet(3S)wheresicisthethermalresistivity oftheinsulation (TableVI)andDiisitsdiameter.

Inmulticoaductor cablesthereisamultipath heatGowbetweentheconductor andsheath.ThefoUowingex-pressionc represents anequivalent valuewhich,whenmultiplied bytheheatGowfromoneconductor, willproducetheactualternperaturre devationeftheconductor abovethesheath.Bf~0.00522ifcGc thermalohm-feel(39)Valuesofthegeometric factorGsfor3-conductor beltedandshiddedcablesaregiveninFig.2andTableVIIIrespec-tivelyofreference l.Onlargesizesec-torconductors withrdatively thinin-sulationwaUs(i.eoratiosofinsulation thidmesstoconductor diameteroftheorderof0.2orless);valuesofGlfor3-conductor shieldedcableasde(ermined bybackcalculation, onthebasisofanassumedinsulation resistivity, fromlab-oratoryheat-runtemperature-rise data,havenotalwaysconfifmed theoretical values,and,insomecases,haveyieldedGivalueswhichapproachthoseforanonshielded, nonbelted construction.

T46feVl.ThermalResistivity ofVariousMa(erichMaterialif,CCm/W'accpaperfosulacloo (solidCype)...T00 GFCEAvalue)Varnished cambric.~....

~..~..000(IPCEAvalue)Paperiosulacloa (ochercypes)..500-MoRubbctaodrubbct.lihe..

~~~...$00(IPCEhvalue)JuCeaodCessileprolectlve COVeffaeo

~~~~~~~~~~$00Fiberduccoo~~~~~~~~~~~~~~~~480Polycchyleae...............

~.4$0Traaid'ce dticc~~~~~~~~~~200Somasclcooooo

~~~~~~~~~~~~100THBRNALRESISTANCE OFJACKETSrDUCTWALLs,ANUSo)MsTIcCohTINcsTheequivalent thermalresistance ofrelatively thincylindrical sectionssuchasjacketsandGberductwaUsmay'edetermined fromtheexpression

,/tNg~0.0104)a'(

-)thermalohcn-feet

.(D-I)(4O)withappropriate subscripts appliedto8,sI,andDinvrhichDrepresents theoutsidediameterofthesectionandtitsthickness.

rc'isthenumberofconductors contained withthesectioncontributing totheheatGowthroughit.THERMALREslsThNcE BETwEENCABLESIFhcEANUSIROUNnnfc PIPEsCONUUTT,.OR DUcrWALLTheoretical expressions forthethermalresistance betweenacablesurfaceandasurrounding endosurearegiveninrefer-ence10.~indicated inAppendixI,thesehavebeensimpliGed tothegeneralformrcrdt,thermalohm-feet1+(B+C1'm)Ds'41) inwhichdt,B,andCareconstants, D,'epresents theequivalent diameterofthecableorgroupofcablesandrs'the numberofconductors contained withinDs'.T~isthemeantemperature oftheinterven-ingmedium.Theconstants d4,B,andCTableVil.(:onsfcnts forUseinEquc(fons dtand4I(A)Coadlcloa BcAamecalliccondulC...................IT

~......3.0

.........0.0"0

.........3.2.....

~~~oo10Indbcrduetlaair...................ly

.........2.1

.........0.010

.........$

.0.....""0~33Iodbcfduetlocooetece..

~~~~...,,.IT,,,....,.2.8

...,..0.024......,..4.d..

~.02TIaCraaidcedueclaafr................ly

~,~......3.0

.........0.014

.........4.4......

~~.02dIacraosfcedueclocoucrecc...

~~~.....1T,.......2.0

.....,...0,020,........3.T.......

~.0.2-Gas-&lied pipecableac200psl.........

3.1.........1.10.........0.00$

3,......,.2.

I.......~~0.0$Oildlledpipecable....~.............

0.$4......~..0.........0.004$

.........2.1......

~"2~4$fye'1.00Xdlameser of<<ableforoaecableI.dsXdhmecer ofeablcforcerocables2.1$Xdlamccct ofcableforChreecables2.$0Xdlamcccr ofcableforfourcablesOcTQBER1957Kci:cr,If(GraK-Ternpcratffre aridLoadCapcbili!

yofCableSystemsfoi 15.6n','Kaz'/D,')

t<<+I.Gal+0.OIGTT)l thertnalohm.feet(42)log-+(LF)log-FInthisequationATrepresents the.differ-thcrtnalohm.feet(44)encebetweenthecablesurfacetempera-tureT,andambientairtemperature T,indegreescentigrade, T~the.averageofinwhichD<isth'teratwhichtheportionoEthethermctrcuitcom->>'hesetemperatures andcthecoe6icient ofmene'.and ttIsthenumofconuc-torscontained withinD,.'heGctitious diameterD>>atwhichtheeffectoflossfactorcommences isafunctionofthediffusivity ofthemedium aandthelengthofthelosscyde.cemissivity ofthecablesurface.Assum-ingrepresentative.

valuesofT,~60andT>>~30C,andarangeinD,'ffrom2to10inches,equation42maybesimpliGed to9.5n',thermalobtn<<feet (42A)D,~1.02>ct(length ofcydeinhours)inches(45)Theempirical development o!thisequa-tionisdiscussed inAppendixIILForadailylosscydeandarepresentative valueofa~2.75squareinchesperhourforearth,D>>isequalto8.3inches.ItshouldbenotedthatthevalueofD,obtainedEromequation45isapplicable forpipediameters exceeding DinwhichcasetheGrsttermofequatioa44isnegative.

ThefactorFaccountsforthemutualheatingeffectoftheothercablesofthecablesystem,andconsistsoftheproduct'f theratiosofthedistancefromthe,reference cabletotheimageofeachoftheothercablestothedistancetothatcable,Thus,Thevalueofcmaybetakenasualto0.95oricnduitsoructs,andpaintedorbraidedsurfaces, an0.2to0.5forleadandaluminumsheaths,depending uponwhetherthe,surfaceisbrightorcorroded.

Itisinteresting tonotethatequation42(A)checksthcIPCEAmethodofdetermining R,verydosdywithc~0.41fordiameters upto3.5inches.IntheIPCEAmethod8,~0.00411n'3/D~'here 9~050+314 D~'orD,'-1.75lacbesandB1,200forImrgervaluesofDt'IFEOTrvE.TaEBMhLRESIsThNcE BETWEENChBLES,DUCTS,ORPII'ESyADAhfBIENTEhRTH(t~ctt.~t>>)Aspreviously indicated, anefFective thermalresistance 8<'aybeemployedtorepresent theearthportionofthethermalci:cuitinthecaseofburiedcablesystems.Thiseffective thermalresistattce includestheeffectoElossfactorana,inthecaseofam'lticable installation, alsothemutualF~--.~.-(N-Itertas)(46)ItwillbenotedthatthevalueofFwillva~depending uponwhichcableissdectedasthereference, andthemaxi-mumconductor temperature wi11occurinthecableforwhich4LF/D>>ismaxi-giveninTableVIIhavebeendetermined.

heatingdfectsoftheothercablesofthefromtheexperimental datagiveninrefer-system.Inthecaseofcablesinacon-cnces10antiIl.creteductbank,itisdesirable tofurtherIfrepresentative valuesofT~~60Crecognizcadifferencebetweenthe thermalareassumed,equation41reducestoresistivity oEtheconcreterrcandthctt'ri'hermal resistivity ofthesurrounding

,thermalobm-feet(41A)earthA.Thethermalresistance betweenanyItshouldbenotedthatinthecaseofpointintheearthsurrounding aburiedducts,A,eiscalculated totheinsideofthecableandambientearthisgivenbytheductwallandthethermalresistance ofexpression'c theductwallshouldbeaddedtoobtainEE>>c~0.012ts, Iogtt'/8thermalobm-Feet(4>)y,ERMhLRBsIsThNcE PRostChBLEs>mwhichp~ththaltityofthe't'tTaisetancefromtheimageCoNDUITs~

oRDUcTsSUsPENDBD INearthrlrisofthecabletothepointP,anddistheThethermalresistance R,btweendistance Eromthecablecenterto2'.cables,conduits,orductssuspendedinstill Fromthisequationandtheprinciples airmaybedetermined fromtheFollowing discussed inreferences 3,12,and13,theexpression whichisdeveloped inAp-following expressions maybedevdoped, pendixLalicabletodirectlyburiedcables.andto~i;type'-cab es.cgC8>>'.~0.012Pgtt'X mum.NreferstothenumberoEcablesorpipes,andFisequaltounitywhenN~l.Whenthecable@stemiscontained withinaconcreteenydopesuchasaductbank,theeffectofthediffering thermalresistivity oftheconcreteen-velopeisconveniently handledbyGrstas-sumingthatthethermalresistivity ofthemediumithatofconcreterF,through-outandthencorrecting that.portionly-ingbeyondtheconcreteenvelopetothethermalresistivity oftheearthi4.Thus1'g~0.012tI,+'$(

c(.3;[i.'-.(in')~]]'~

ohm-feet'44A)

Thegeometric factorGc,asdcvdoped-inAppendixIlisafunctionofthedepthtothecenteroftheconcretecndosureQanditsperimeter P,andmaybefoundconveniently fromFig.2intermsoftheratio4/2'ndtheratioofthelongesttoshortdimension'of theendosure.

ForburiedcablesystemsT,shbuldbetakenastheambienttemperature atthedepthofthehottestcable.Asindicated mreference 12,theexpressions usedthroughout thispaperforthethermalresistance andtemperature riseofburiedcablesystemsarebasedonthehypothe-sissuggested byKeaaellyappliedinaccordance withtheprinciple.

ofsuper-position.

According tothishypothesis, theisothermal-heat QowGddandtem-peratureriseatanypointinthesoilsur-roundingaburiedcablecanberepresented bythesteady-state solutionfortheheatQowbetweentwoparaMcylinders (constituting aheatsourceandsink)locatedinaverticalplaneinaninGnitemediumofuniformtemperature andthermalresistivity withanaxialsepara-tionbetweencylinders oftwicetheactualdepthofburialandwithsourceandsinkrespectively generating andabsorbing heatatidentical rates,therebyresulting inthetemperature ofthchorizontal mid-planebetweencylinders (Le.,correspond-ingtothesurfaceoftheearth)remaining.

bysymmetry, undisturbed.

Theprinciple ofsuperposition, asappliedtothecaseathand,canbestatedinthmnaltermsasfollows:IEthether-malnetworkhasmorethanonesourceoftemperatu:e rise,theheatthatQowsatanypoint,orthetemperature dropbe-tweenanytwopoints,isthesumoftheheatQowsandtemperature dropsat.thesepointswhichwouldexistifeachsourceoftemperature risewereconside:ed separatdy.

Inthecaseathand,thesourcesofbeatQowandtemperature risetobesupcrimposed are,namdy,theheat7OSrober,DfcGratls

-Temperatttre andLoatfCapability ofCableSyste":sOcTooER1957 fromthecable,theoutwardQovrofheatfromthccoreof.theearth,andthcin-wardh(atQovrsolarradiation, and,whenpresent,theheatQowfrominterfering sources.Byemploying astheambienttemperature inthecalculations thctem-peratureatthedepthofburialofthehottestcable,thecombinedheatQowfromearthcoreandsolarradiation sourcesissuperimposed uponthatproducedatthesurfaceofthehottestcablebytheheatQowfromthatcableandinterfering sourcesvrhicharecalculated separately withallotherheatQowsabsent.Thecombinedheat Qovrfromearthcoreandsolarsourcesresultsinanearthtempera-turewhichdecreases withdepthinsummer;increases.vrith depthinwinter;remainsaboutconstantatanygivendepthontheaverageoverayear;approximates con-stancyatalldepthsatmidseason, andinturnresultsinQovrofheatfromcablesourcestoearth'ssurfac,directlytosuz-faceinmidseason andwinterandin-directlytosurfaceinsummer.Factorsvrhichtendtoinvalidate thecombinedKennelly-superposition princi-plemethodaredeparture ofthetempera-tureofthesurfaceofearthfromatrueisothermal (asevidenced bymeltingofsnovrinvrinterdirectlyoveraburiedsteammain)andnonuniformity ofthermalresistivity (duetosuchphe-nognenaasradialandverticalmigration ofmoisture).

TheextenttowhichtheKennelly-superposition principle methodisinvalidated, however,isnotofpractical importance providedthatanover-alloreffective thermalresistivity isemployedin theKennellyequation.

SpecialConditions AlthoughthemajorityoEcabletem-peraturecalculations maybemadebytheforegoing procedure, conditions fre-.quentlyarisevrhichrequiresomewhatspecialized treatment.

Someofthesearecoveredherein.EMERCENCY RATINCSUnderemergency conditions itisfre-quentlynecessary toexceedthestatednormaltemperature limitoftheconductor T,andtosetanemergency tempegature limitT,'.Ifthedurationoftheemer-gencyisIongenoughforsteady-state con-ditionstoobtain,~thentheemergency ratingI'aybefoundbyequation9substituting T<'orT<andcorrecting

~,ortheincreased conductor temperature.

Ifthedurationofthcemergency islessthanthatrequiredforsteady.statecon-ditionstoobtain,theemergency ratingofthelinemaybedetermined fromTc'-I'~1+YcXN~'-R<<')

-(2's+Z(1+.Yg)8<<'n which8<<g'sthceffectivtransient thermalresistance ofthecablesystemforthestatedperiodoftime.Procedures forcalcuhting E,g'ortimesuptoseveralhoursaregiveninreference 14,andforIppertimesinreferences 15-17.~~CTHEEFIECT.op ExTIumoUs HEATSOUECEs.Inthecaseofmulticable installations theassumption hasbeenmadethatallcablesareofthesamesizeandaresim-ilarlyloade<<LWhenthisisnot,thecasethetemperature riscorloadcapability ofoneparticular equalcablegroupmaybedetermined bytreatingtheheatingeffectofothercablegroupsseparately, intro-.ducinganinterference temperature risedTgginequations 1and9.ThusT,-T~~dT<+dTc+dT<<~g degreescentigrade (1A)T~-(T(<<+d Ta+dTg>>g)I~gg(1+Yc)~ca'iloamperes (9A)inwhichdTg,grepresents thesumofanumberofinterference effects,foreachofvrhich.d2<<>>g(IVa/LF)+IVclksg degreescentigrade (48)Ag<<<~0.012<<r,>>'Iog Fg,gthermalohm-Eeet(49)((Egg'X<<E<<g'X<<E<<<<')"

(EN<<'~)(<<Eg<<X(E<<<<X(E<<g)

"<<EN<<(50)wheretheparameters applytoeachsys-temvrhichmaybeconsidered asaunit.ForcablesinductA.g0.012>>'(r<<log F<<g+N(ggg-rr<<%l thegnudohm-Eeet(49A)Becauseofthemutualheatingbetvreencablegroups,thetemperature riseoftheinterferin groupsshouldberecheci:ed.

Ifallthecablegroupsarctobegivenmutuallycompatible ratings,itisneces-sarytoevaluateIV<foreachgroupbysuccessive approximations, orbysettingupasystemofsimultaneous equations, substituting forW,itsvaluebyequation15andsolvingforI.IncasedT<<ngoracomponent ofitisproducedbyanadjacentsteammain,thctemperature ofthesteamTratherthantheheatQowfromitisusuallygiven.ThusdT<<>>g~gagdegreescentigrade (Sl)Ikiloagnpeges (47)vrhere8<<isthethermalresistance be-tweenthesteampipeandambientearth.ARIALCABLEsInthecase'ofaerialcablesitmaybedesirable toconsiderboththecffectsofsolarradiation whichincreases thetem-peratureriseandtheeffectofthcvrindwhichdecreases it.ggUndermaximumsunlightconditions, alead-sheathed cablevrillabsorbabout4.3wattsperfootperinchofprofiIe"whichmustbereturnedtotheatmosphere throughthcthermalresistance 8,/>>r.Thiseffectiscon-veniently treatedasaninterference temperature riseaccording totherela-tionshipdT<<((<<~4.3Dg'/I,/>>r degreescentigrade (47A)ForblacI:surfacesthisvalueshouldbcincreased about,75%.Asindicated inAppendixII,thefollow-ingexpression forl(I,maybeusedwhereV>>isthe'velocity ofthcvrindinmilesperhour3.5>>(~V/D,'+0.62

)thermalohm-feet(42B)UsECFLow-R'EsrsTIvITY Bane.LIncaseswherethcthermalresistivity oftheearthisexcessively high,thevalueof8,rmaybereducedbybacldiiling thetrenchwithsoilorsandhavingalowervalueofthermalresistivity.

Equation44(A)maybeusedforthiscaseifrr,thethermalresistivity ofthebacldillissub-stitutedforgrg,andQappliestothezonehavingthebacldiliinplaceofthc.zoneoccupiedbytheconcrete.

SINOLE-CCNDUcroa C((1BLESINDUcTwITHSCLIDLYBCNDEDSHEhTHSTherelatively largeandunequalsheathlossesinthethreephasesvrhichmayresultfromthistypeofoperation maybedeter-minedfromTableVIoEreference 1.ItvrillbenotedthatYrgg~g'gcg~~ISvrhereexpressgons forI>gg/Petc.,appearinthetable.Theresulting unequalvaluesofY,iathethreephasesvrillyieldunequalvaluesof(Eandequation5becomesforphaseno.1,theinstancegivenasequa-tion5(A)onthefollowing page.OCTOBEE19573crgcr,rf&Gralig

-Terr:pcrafggrc a>>dLoadGxpabil<<Iy ofCab!cSystcr>>s759

4TciWe[/fi+rfrsI/fre+/fe.+(LP)/f,p j+.'fq<<(fF)kpe]thermalohm-feet(SA)whereqraIstheaverageofqrsIqrs>andqrs.TableVIII.Coustanls forUseinEque6on53AreraseATARMOREDCABl.EBInmulticonductor armoredcablesalossoccursinthearmorwhichmaybeconsidered asanalternate totheconduitorpipeloss.Ifthearmorisnonmag-netic,thecomponent ofarmorlossYatobeusedinsteadofYpinequations 14and19maybecaIculated bytheequa-tionsforsheathlosssubstituting theresistance andmeandiameterofthearmorforthoseofthesheath.Incal-culatingthearmorresistance, accountshouldbetakenofthespiralling"effect forwhichequation13suitablymodifiedmaybeused.IfthearmorIsmag-netic,onewouldexpectanmcreascinthefactorsY,andY,inequation14sincethisoccursinthecaseofmagneticconduit.Unfortunately, nosimple:pro-'edure, isavailable forcalculating theseeffects.Aroughestimateoftheinduc-tiveeffectsmaybemadebyusingthepro-ceduregivenaboveformagneticconduit.Asimplemethodofapproximating thelossesinsingleconductor cablesvrithsteel-wircarmoratspacingsordinarily,em-ployedinsubmarine installations istoas-sumethatthccombinedsheathandarmorcurrentisequalto'theconductor current.s Theeffective a.cresistance ofthearmor'aybetdcenas30to60%greaterthanitsd-cresistance corrected forlayasin-dicatedabove.Ifmoreaccuratecalcula-tionsaredesiredreferences 19and20willbefoundusehl.EPPEcToPF0RcEDCooUNGThetemperature riscofcablesinpipesortunnelsmaybereducedbyforcingairaxiallyalongthesystem.SimiIarly, inthecaseofoil-Glied pipecable,oilmaybecirculated throughthepipe.Undertheseconditions, thetemperature riseisnotuniformdongthecableandincreases inthedir'ection ofEIowofthecoolingmedium.Thesolutionofthisproblemisdiscussed inreference 21.baseduponallofthedataavaihbieandincluding theeffectofthetemperature ofthcintervening medium.Thetheoretical expression forthecasewheretheintervening mediumhdrorgasaspresented inreference 10snaybegenenI.Isedinthcfollowing form:andarangeof150-350forDe'T~equation54reducestoequation41<<iththevaluesofA,B,andCgiveninTableVIZ.Inthccaseofcablesoryipessuspended instillair,theheatlossbyndhtionmaybedctcrauncd bytheStchn-Bolznsann forsnuhrs','-,+b+cT~(53)rs'W(radhtion)

~0,139DseKTa+273)e (Ta+273)ej10>>

wattsycrfoot(55)E,catheeffective thcrsndreshtsuce be-tweencableandenclosure inthclnulobm-EeetD,'~theublediameterorequivaIcnt dhsneterofthreecablesusInches4T~thetempcnture dIEfcrenthI indegreescentigrade P~thcprcssureInatmospheres T~~mesntesnperature ofthemediumindegreescentigrade rs'~nusnber ofconductors InvolvedTheconstants a,b,andcinthhequationhavebeenestablished empiYicdly asfollows:Conslderusg b+cTeasaconstantforthemoment,theanalysisgiveninreference 10resultsinavalueofa~0.07.Withathusestablished, thedatagivenuireference 10forcableinpipe,2ndinreference 11forcableinaberandtxauslteductswereandyzcdinsinuhrnunnertogivethevaluesofbandcwhichareshowninTableVIILInordertoavoidareltentivc calcuhtloa procedure, itisdesirable toassumeavalueEar41sinceitsactualvaluewilldependuponffreandtheheatflow.Fortunately, as4Toccurstothe1/4powerinequation53,theuseofanaveragevalueasIadicated inTableVIIIwillnotintroduce aseriouserror,Byfurtherrestrictissg therangeofD,'oI-IInchesEorcableinductorcoaduicandto3"5inchesforpipe-type cables,equation53isreducedtoequation41.whereeisthecoeKcicnt ofemisslvity ofthecableoryipesurfacesOverthelimitedtemperature nssgeinwhichwcareInterested, equation55snsybeshnplificd to"rs'W(radiation)

~0.102Ds'4Te X(1+0.01671

~)wattspcrfoot(SSA)Overthesametempenture nngetheheatlossbyconvection fromhorixoatal cablesorpipesisgivenwithsufficient acciuacybytheexpression rs'W(convection)

~0854De'dT(dT/De')

+ewattsyerfoot(56)mwhichthenumcrica1 constant0.064hasbeenselectedforthebestEitwiththecarefully deternsined testresultsreportedby'cilaunss on12,3.5audIQB-Inchdhmctcrbhckpipes(e~0.95).

Inci-dentally, thisvaluealsorepresents thebestEitwiththetestdataon1~5inchdiameterbhckpipesreportedbyRosch."ForverticalcablesorpipesthevalueoEthisnumeriesI constantmaybehicrcased by22%"Combiniag equations 55(A)2nd56weobtaintherelationship 4Trs'W(total) 15,8rs'r'K AT/Dr')a+1.6e(I+0.0167')

Ithen'hm.feet (42)Cablelusuetatuccouduls,...............0.07..

~.~.......0.

121...........0.0017..:.

~..~....20Cablelusberduceluair..................0.07............0.03d...........0.0000............%

Cableludberdu<<tlucoucrete..

~..~.......0.07...,......0.043....

~~.....0.0014.....

~~.~.20Cablelasrauslseductluafr................0.07............0.08tl..

~~......,0.0008.........

~..20Cablelutrauslieductlucoucrete..~.....

~~.0.07....,

~~.....0.079....~.....,0.0010..,.

~~~...20Gas.elled pipetypecableat200pal.........0.07.,.....,

..0.121...........0.0017............10 AppendixIDevelopment ofEquations 41,42,andTableVIXTheoretical 2ndsemicmpiricd expressions forthethermalrcslstarice betweencablessurdalseaclosirsg pipeorductwailaregiveninrefercricc 10.Furtherdataonthethermalresistance betweencablesaridSberandtnrssitcductsaregiveninref-erericc11.Forpurposesofcablecating,itisdesirable todevelopstaudardhcd expressions forthesethermalresistances rs'AAre~,thcrmdohm-Eeet(41)inwhichthevaluesoftheconstants A,B,aridCappearlnTableVII.Iathecaseofoil.6Iled pipecable,theanalysisgiversiareferesicc 10givesthefollowing expression rs'.60+0.025(Dr" T~'dT)~'hermalohm-Eeet(54)Assumiugaaavengevalueof4T~7CIfthecablehsubjected towindhavingavelocityofV>>milespcrhour,thefollow-ingcxprcssiors derivedfromtheworkofSchurigandPrick"shouldbesubstituted fortheconvectiors comyoricnt.

rs'IV(coavectiors)

~0.286Dr'4Tv Vu/De'atts perfoot(56A)Combining equations 55(A)arid56(A)withT~~45C4T3.5rs's'IV(mlsl)

D;(QV/D;+0.62e) thermalehm-Eeet(42B)760iVeLer,yrlcGrc!r' TerrperafareandLoadCapabilily o/CableSvs.'eras Ar-,nnm.1057 g,gAppendix'l TableIX.Compadsoa ofValuesofgo(+F)forSinusoidal LossCydesat30$LossFactorDa<<8.3Inches.Asindicated intheChirdpaperofreference 3.however,theorcQcally D/cshouMvaryasthesquarerootoftheproductofthedilfusivity andthcthnelengthoftheloadingcyde.Henceasthcdiifusivity wastakenas2.?5squareinchespelhouriatheabove,Da<<Ig02XVacXlength ofcydeinhoursmches(45)TableIXpresentsacomparison ofthevaluesofpercentattainmcnt factorforsinusoidal losscydesat30%lossfactorascalculated byequations 45,66,62(A),and63andastheyappearinTableIIoftheGrstpaperofreference 3.Appendix" IY.'Cafculaations forRepresentative Ca6leSystemsDetermination oftheGeometric FactorGiforDuctEanld'Considering thesurfaceoftheductbanktoactasanisothermal cirdeofradiusra,thethermalresistance betweentheductbankandtheearth'ssurfacewUIbealogarithmh functionofriandLithedistanceofthecenter'fthebankbdowthesurface.UsingthelongformoftheKennellyFonnuhLswemaydeflnethegeometric factorGiasLi+O'Li'-ri'i<<

logri~ogIgr/ro+O/(gr/ro)'-gl (gg>Inordertoevaluaterbin"'terms of'thedimensions ofarectangular ductbank,letthesnuiierdimension ofthebankbexandthelargerdimension bP'y.Theradiusofacizdeinscribed withintheductbanktouchingthesidesislifddIDesccfpdou, Srst<<ulachesIfehecShsakllaV/lseugea pipe....53/53...dl/d2...d3/dd pipe.....dd/dd...

50/57....53/50 plpe.....55/5...SO/58..~.54/53plpe.o~..58/58...

5l/50...55/53 cable.~e~\~~~80/80~le'....77j75.

~'.77/75....77/77 cableo~ooT1/71cableoooo

~~~~~~~53/52cablcoo~.~~~~~~~o75/74cable............77/Td cable....83/80...83/81 cable....Td/74...74/173 cable....TO/55.

~.To/5Tcable..~.d0/54.~.55/54..51/53I~~~~~~45Iloo~ee5dIIIoooooo 85Iveoooo~10dVo~ooo~~0dVIe~~~~15VII~eeo~I0VIII....2.0IXooooo30Xo~ooo~34Xa~roe34XI~oooo3TXIIeoo42XIII4.daDhduglelcy<<4.7 scuse>>luchapcrhour.15-Kv350-NCN-3<<Conductor

.ShieldedCompactSectorPaperandLeadCableSuspended inAirD,<<0.618(equivalent round);V<<gaugedepth<<0.539inchDc<<2.129;T<<0.175inch;l<<0.120inch12.9/234.5+SIN cgggcgg,-('0250(234.5+75)

<<37.6microhmsperfoot(Eq.10A)Deca2.129-0.120 2.009inches(Eq.12)fs<<x/2(58)andtheradiusofahrgercirdeembracing thefourcornersis/O/x'+g'rrr2LctusassumethaCthecirdeofradiusriliesbetweenthesecirclesandthenugnitude ofraIssuchChatitdividesthethernulresistance betweenrlandrsindirectrehtiontotheportionsoftheheatGeldbetweenrsandrsoccupiedandunoccupied by'heductbank.Thusth~~1cQcultco~I9SSSS3 Equation62maybewrittenintheform8'-8+8+(LFXd-8)thernulohmofeet(62A)Intermsoftheattainment factor(cfF),onemaywrite(AF)~ca(ciFXNcc+/t¹)

thernulohmofect(63)Equatingequations 62(A)and63obtainsCherehtionship Bcc<<(1-x)8¹-x/t<<

thernulohm.feet(64)where37.9C-'ggrroiororrroo 2.009(0.120) pcrfootat50C(Eq.11A)kg<<1.0;kr<<0.6(equivalent round)(TableII)lac/>c<<37.6gYccO.OM(Eq.21andFig.1)$<<0.616+2(0.175+0.008)

<<0.982inchesJ4Jkp<<62.6;F(xp')<<0.003(Fig.1)Ycp<<40003<<0.002(Eq.24A,andaotetoTableII)1+Yc<<1+0.008+0.002

<<1.010s<<1.155(0.

175+0.OOS)+0.60(0.539)

<<0.534inch(Eq.32)3962(0.534)1 sYc<<Y¹<<-(<<0.01915?(3T.6) 2.009J(Eq.31A)nxy-~sfrsNlog--r(log-)or~~**-.)(.)~Žxy/rsNtog--(log-)rigrss-r,s)(

r<)from'whichlogfi<<(<<)log(I++log-2A~y)(xs)2(40)Itisdesirable toderiverihltermsoftheperimeter Poftheductbank.ThusP<<2(x+y)<<4-(1+y/x).2I-(cfF)x<<1-(LF)(45)Since8¹<<0.012/s'p logDc/Dc~thermalohm-feet(44)andtherefore 83logDc/Dc<<-,KI-x)/tca-x/eccl

>>'/I(47)Plog-log-24(1+y/x)(41)Thcflrstpaperofreference 3presentstheresultsofastudymwhichanumberoftypicaldailylosscydesandalsosinu-soidallosscydesofthesamelossfactorwereappliedtoanumberoftypicalburiedcablesystems.Theresultsindicated thatinallcasesthesinusoidal losscycleofthesamelossfactoradequately expressed themaximumtemperature risewhichwasobtainedwithanyoftheactuallosscyclesconsidered.

Ananalysisbyequations 65and6Tofthecalcuhted valuesofattaiameot factorsforsinusoidal losscyclesgiveninTableIIandtilecorresPoading cablesystcraPscamoetcrsgiveninTableIoftheGrstpapa'freference 3yieldsamostprobablevalueofThecurvesofFig.2havebeendeveloped fromequations 57,60,and81forseveralvaluesoftheratioy/x.Itshouldbenotedinpassingthatthcvalueofri<<0.112Pusedinreference 13appliestoay/xratioofabout2/1only.R/Rcc<<1.010+0.019

<<L029(Eq.14)qg<<qc<<I+-'<<1.019(Eqs.18-19)0.0191.010c,<<3.7(Table V);E<<15/Q<<S.T; cosy<<0.022Appendixill0.00276(8.7)'f3.7(0.022)i 2(Q.175)+O.BSC 0.681<<0.094wattpercoaductor foot(Eq.36andtext)(Vote:Iacomputiag dielectric lossonEmpirical Evaluation ofD,Inordertoevaluatetheeffectofacyclicloaduponthemaximumtemperature riseofacablesystemsimply,itiscustomary toassumechattheheatGowintheGoal~portionofthethermalcircuitisreduced+byafactorequaltothelossfactorofthecydicIoadoThepointatwhichthisreduction commences maybeconveniently expressed intermsofaGctitious diameterDaoThusAca'<<Dec+(LF)/tcs thcrnulohm-feet(42)Forgreateraccuracy, itisdesuabletoestablish thevalueofDcempiricaily ratherthantoassumethatDsisequaltothehichtheearthi~conohn~nggc~10Ar%I,M.o~/l.

7~/.g~,o~4r4/-ag/g.'r.C/:g.

• <<agir'a"<<tIl' sectorconductors, theequivalent diameteroftheconductor istatcenequaltothatofaconcentric roundconductor, Le.,0.681inchfor350MCM.)700(TableVI);Gr~0.45(TableVIIIofreference 1)~r0.00522(700(0.45)

}1.64thermalohm-feet(Eq.39)n'3;~~0.41(assumed) 9.5(3)1+1.7(2.129(0.41+0.41)]

~7.18thermalohm.feet(Eq.42A)Nca~164;+1.019(?.

18)~8.96thermalohm-feet(Eq.8)dT<~0;094(0.82+7.18)

~0.75C(Eq.6)T,~40C(assumed)

I81-(40+0.8) 37.6(1.010(8.96)1

~0.344kiloampere (Eq.9)Ifthecableisoutdoorsinsunlightandsubjected toan0.84mileperhourwind3.5(3)2.129(V0.84/2.129+0.62(0.41)i

~5.59thermalohm-feet(Eq.42B).Ace'1.64+1.019(5.59)

~7.34thermalohm-feet(Eq.8)ATrrrr(4.3)(2.129)(

-)17.1C/5.59i(3)(Eq.47A)dgc96'ecla"Lc4X5/'r)images~sJdg~96/"dt~c87.5"cc.785.3e.Ib~43.5Te<<30C(assumed)

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

~0.346lriloampere (Eq.9)Inthisparticuhr casetheneteffectofsohrradiation andan0.84mileperhourwindistoeffectively raisethcambienttemperature by10degrees,whichisaroughestimating'alue commonlyusecLItshouldbenoted,'owever, thatthiswillnotalwaysbetrue,andtheprocedure outlinedaboveispreferable.'4 rcc~69-KvIr500-MEN

-Single-"Conductor Oil-Filled CableinDuctTwoidentical cablecircuitswillbeconsidered ina2by3fiberandconcreteductstructure havingthedimensions showninFig.3.De~0.600; De~1.543lDr~2.113; TO.N;D,2.373;r0.130inches12.9Te~75ClRec~-~8.601.50p,microhmsperfoot(Eq.10A)Dna~2.373-0.)30~2.243 inches(Eq.12)37.9Rc(2243)(030)~130microhmsperfootat50C(Eq.llA)1.543-O.BOO(1.543+1.2003 c1.543+0.600(1.543+0.600J 0.72;k~O.S(Eq.23andTableil)5I.Oon69-lcv$,500.MCMci:pre/kc~ll9r'cc~0.075(Eq.21andFig.1)$~9.0(Fig.3)iRec/4~10.75'(x~')

~0.075(Fig.1)Ycrr4()00750007(Eq24A)(9.0).1+Yc~1+0.075+0.007

<li082Assumingthe.sheathstobeopenwircuited, Yea~01+--'.006:"(Eq.

30A)Rec/Rcr~~1082+00061088(Eq14)0.006~1.082qcaqcw1+.-'],006(Eqs.18-19)I~cr~(TableV);8~69.'y3~40;cos4~0.0050.00276(40) r(3.5.'(0.005) 2.113log-1.5430.57wattpercondctorfoot(Eq.30)Fig.3.AssumedductbonkconR9uratlon fortypicalcalculations tj4.ifoil@liedcable(Appendix lV)7R'?rVchrr,N'd7rrrflr

-Trrrr6crahurcandLoadCaoabrvitv ofCableSvsfrrrrs QCTOBBR1957 I

2iv'h2;(Pg<<5.0(TableVI)aTc0.57(0.45+1.75+0.24+4.63) 4.0C2.113~.(Eq.6)88<<0.012550log~~~>45rWcj(lrX8BQX1.082)

<<931Ir<<0.90thermalohm-foot6((Eq.38)rwattsperconductor foot(Eq.1S)4Trf6g<<(9.31Irr KI.QOBX0.80)+0.5?l)3.81 2.37+087<<2>17'+28.5Irs degreescentigrade inthermalohm-feet(Eq.41A)circuitno.2(Eq.48$irc<<480(TableVI);1<<0.25;-Simihrcalculations forthesecondcircuitcp.,Dc<<5.0+0.5<<5.50 foraberductyieldthefoUowingvalues.0.0104(480X0.25) lgc'.18;4T<<<3.4;Wgg<<17.44IEE',

5.50-0M~4T(,g<<1.71+53.2IE'n circuitno.1120(asumed);

jfc85(TableVI)'...~:.(9.31)(6.$

5)0.715-0.859I22 (Eq.9A).-(-.)('-:)('=".)('-)("=)

';,':-"'"..";".";;,",....

<<42,200(Fig.3andEq.46)Solvingsimultaneously Ir<<0.714;Ir<<1>(P0.483;-hs:0.487kiloampere.

2(18+27)'180>087(Ptg2)138-Kv2000-2,102(

2(fgh-Pressure 5z~Oil-Filled Pipe-Type Cable8.625-'c'(at80%lossfactor)(0.012)(85)(l)X Inch&utside-Diameter Pipe8.3'I4(43.5)log-.+0.80log[~42~)J)+

Thecableshielding willconsistofanhrtercalated 7/8(0.003)-inch bronxetape-0.012(120-85X1)(6)(0.80)(0.87) l.inchlayandasingle0.1(02)-inch D-<<6.79thermalohm-feet(Eq.44A,)shapedbrassskid<<Ire-LS-inchly.ThecableswilllieincradledconBguration.

Ec'atunitylossfactor)<<8.44~~thhm.feet(Eq.44A)Dc<<1.632; Dr<<2.642>

T<<0.505;16Egg.l2pR'gtg'0.90+1.00$

(1.7k+0.24+6.79)

'72ther<<)ehtufeet(Eu.8)770<.8(189)(234 5+70)4'.57(-+L?4+0.24+8.44 8M625microhmsperfoot(Eq.10A)<<6.2C(Eq.B)ForshfeIdfngtape448<<7/8(0.003)<<0.00263l f<<I.Q;p<<23.8;2<<564(Table1)Tc25Cassumed),

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

(1j<<0.696kiioampere (Eq.9)564+50)-)<<62,900mlcrohmsToillustrate thecasewherethecable564+20'ircuits arenotIdentical, considerthe'erfootat50C(Eq.13)secondcircuittohave?50-MC'hf con-ductors.Fortheerstcircuit.'orskidwireggr(Q1)2QQ157'P<<3;(IF)<<0.80(assumed);

(l<<1.5;p<<38;r<<912(TableI)F<<--<<92.4(Eq.46)9938E.(2.6Br)2R,-1+-X(8tlog-+0.80log(-92.4)J+8.3A(43.5)rI<<11,100microhmsS.S(8.3.)J0.012(120-8SX1X3)(0.80X0.87) perfootat50C(Eq.13)5~~<<3.74thermalohm-feet(Eq.44A)l(62.9)(II.I)1 R,(net)<<L-JI>000(L(62.9X11.1)

J<<9,435microhmsperfootat50Ck8<<0.435; kp<<0.35(TableII)0.012(1)X(85log456-;3(120-85)(0.87))

Rcg/kg<<14.6lYcg<<0.052(L7)

<<0.088<<3.81thermalohrnfeet.r(Eq,49)(Eq.21,Fig.I,andtext)lsl4'.90+1.006(1."4+0.24+3.74)

S2.66+0.10 2.6;Rc/k17.2;<<6.65therrrral ohm.feet(Eq.S)F(KP')<<0.035(Fig.1)/1.632%8Ycp<<4()(0035X17)0083(2.76)(Eq.24Aandtext)1+Yc<<1+0088+0.083

<<1.1?1'52.9leg-(2.3X2.76) 2.66<<20.0microhmsperfoot(Eq.29A)(20.0)2(1.7)Yg<<Ygc<<<<0011 (Eq.2?Aandtext)Y(034X2.76)+(0.1?SX8.13) 6.35",*(Eq.35)Rcc/Rcc<<1171+0.011+0272 L554(Eq.14)0.011.0.011+0.372

~1.171'.171I~(Eqs.18-19)cr<<3.5(TableV);.E<<138/Q3<<80;cosp<<0.0050.00276(80)2(3.5X0.005) 2.642log-1.632<<1.48wattsperconductor foot(Eq.3B)A<<550(TableVI);8r0.012X(2.642(550log-')<<128thermal'.1.632)ohm-feet(Eq.38)>>2<<3;Dc'.15(2.66) 5.72;3(2.1)Ru-'77there.tet 5.72+2.45 ohm-foot(Eq.41A)ptr<<100(TableVI);t<<O.SO;D,<<8.83+1.0 9.63for1/2-inchwallofasphaltmastic0.0104(100X3XQ.SO) 9.63-0.50

<<0.17thermalohm.foot(Eq.40)Assumepc<<80,I<<36inches,(LF)<<0.85;II<<1,F188'(at85%lossfactor)0.012(80)(3)

Xlog-+0.85log-(1)<<2.85thermalohm.feet(Eq.44)80'atunitylossfactor)<<3.38thermalobm.feet(Eq.44)Pgcg<<1.38+1.M9(0.7?)+

1.327(0.17+2.85)

<<6.1?thermalohrn-feet (Eq.8)4Tc<<1.48(0.69+0.5 5-,'0.17+3.3S)

<<7.4C(Eq.B)Tc<<25C(assumed);

70-(25'7.4) 43(6.35X1.171X6.17)

<<0.905ki!osmpere (Eq.9)

References 1.Catcocattox ortnaEuactstcu.

Pooka,sxs arUNoskokoaNO Casass,D.)tLShameae.TbcElectricIosraol,BastPittsburgh.

PaMayNor.1032.LocaPactoaaxoEttotvaLsxt HoaasCoxraaso, P.H.Buiier,C.A.Woodrau;Ztec.tricotW'orld,NcwYork,¹Y.,vai.02,ao.2,1028pp.50-60.3.Stxroctatt oxTsitrskatasa RmsorCasters,AIRECaauaittee Report.AIEETre>aroctio>tl>

vol.72,yt.III,Juae1053,pp.~L4.h-CRsarstaxcs orSsoxaxraa CaucusntSrsst.Prrs.LMeycrhotr, O.S.Eager,Jr.Ibid.,raL68,pt.II,1049,pp.815-34.d.Pkorttxttv EnactixSouoaxoHotaoerRomeoCoxooctoas, A,H.M.Araeid>>Ieur>tot, Iaaututioa olEicctticai Eagiacecs, Laodoa,Eagiaad,vol.88,pt.Il,Aug.1941,pp.34059.o,Eaov&aaksxv LoaassncMattressParka.INaotatso La*~russo Cast,aa,haxoasoar>oUxakxokso, CakavtxoBaaaxcsa3-PrtaasCaaksxv,A.H.5>LArnot*Ibid.,yt.I.Peb.1941,pp.52-63.T.PtrsLoecssMNorocaoxsttc Ptrs,MeyerhotL AIEETrouracliosr, vaLT2,yt.III,Dcc.1053,yp.1260-T$,8.A>>CRsarstaxcs orPrrs-Casts Svatsxs>>mtSsoxaxtaa Coxaactoks, AD1ECommiueeReyerLlbQ~roLTl>pt.III,Ja>L1952,pp.30414.'.ANRsstataxcs orCoxrsuttoxar.

StaaxoPa>>asCaucusntNoxxstaaue DuctaxoueIaouCoxomt,R.W.Burteu>ItLMordaIbid.,voL74,pt.111,Occ.1055,yy.ION23.10.TasTasaxu.Rsetstaxcs BatvrssxCosc,ssaxoaSaakoauonto PirooaDuctWaarF>H>>Boiler,J.H.Zcher.IbQ.,vaLdy,yt.I.1050,pp.34~9.11.HaavTa*xsrsaStoutoxPo>>saCasusDuctsaxoDeerheaaxsc,tss, PaulCceebicr, OuyF.Baraett.Ibt>L,voL69,pt.L1050,pp.SST57.12.TrtsTsxrseataas RtssorBaatsoCasuasaxttPtrss.

J.K,Ireher,lbi>L,voL68,pt.I.1940,yp.9-21.13.TasTaurus*toss RiesorCase,ssnta,DoerBaxr,J.H.Neher>>Ibidpp.~0.-.14.OttFaowaxoPasaaaasCaacouattoxs roaS~Ntatxso Ott>FttusoCasasSvstaxs>>B.H.Bauer.J.H.Ifeher>P.O.Weutstoa>>

lb>>d.>vaL75,yt.III,hpr.1055,pp.ISHl41$.Tasaxax.Tkaxarsuts oNBoktsoCastaa,F.PBailer.IS@.,vaLTO,yt.I,10SI,pp.4~.ld.TasDstsaxtxattox orTsxrsaatoks Taaxatsxts ntCast,sSvatsxssvMsaxsoraxANaaooaaCoxrotak>>

J.H.)Ichor.Ibid.,yt.II,1051,pp.1361-T1.17.hStxrurtso M*tasxattcaL Paocsaaka roaDatsaxtxtxo tasTaaxatkxt Tsxrskataas RtssorCasutSvstsxs.J.H, IrchcrIbQ,vol.72,pt.IILhug.10$3,pp.712-1S.~IiLTssHsattxoorC>tacksExroasototasSaxtxRaas,E>>B.Wedmere.leuc>>oLIaatituttoaatElectrical Eagloccra, vcLTS,1034,pp.737&L10.Loaaastxhat>ossaStxaas~xaactok>

La~russoh>>CCast.ss,O.R.Schurig>HP.KuehuLF.H.Buuer.AIEETrc>>roctk>ur>

rai.48,hpr.1020,yp417~.2tLCostaisotroN totasSvaovorLoaassaxoorSsar4>ooottox orStuoasCoxuoctoa AkxoasoCaaass,IBoaoae.Zt>ttrol>cairo, Miiaa,Italy,1931,y,2.2Lhattnctaa, CoouxoorPoxsaCast.s,F.H.Bauer.ALEETroarcctlear, vai.Tl,yt.111,hug.19S2,pp.~l.22SoaracsHs*TTaaNSxiaaIQK>>

R>>K,HenaiaaTio>tt>xticer, htacricaa Societyathfcchaoicci Bagiaecrv.

NeerYork,¹YroL51,ptI,1020.pp.287~23.TssCaakaxt-CakkvLvo CaracttvorRosssa.INsuaatso Coxoacroaa.

S.J.Roach.AIEETrout>xrioor, raLST,hyr.1038,pp.15~7.24.Hsatnto*NoCoaksut~kttxo Car*cttv0'Baa'Couattctoks rokOataooaSskvics>O.R.Schurig,O.W.Prick.Ce>>>rotZfcclricR>rserr,Scrtcaectady,

¹YvaL33,1930,y.141.Discussion C.C.Barnes(CentralElectricity Authority, Londan,Enghnd):Thispaperisanexcel-lent.andup-~testudyofamosthnpar-tantsubject.Par25yeirsD.M.Simmons'rticled havebeenusedforfundamental Studyoncurrentratingproblems, butthenumeraugcabledeveiapmentg audchangesinindtaihtian techniques introduced inrecentyearshavemadeamodernassess-mentafthissubjectveryneccsgary.

Theessential dutyafapowercableisthatitshouldtransmitthemaximumcurrent(arpower)farSpecified instaihtian canditiang.

Therearethreemainfactargwhichdeter-minethesafecontinuous currentthatacablewillcarry.1.Themaximumyertnidgible temperature atwhichitgcampanentg maybeaperatedwithareaganable factorofsafety.E.ThcheatMiggipathtg yrapertieg afthecable.3.Theinstalhtian canditians andambientcondithn5 obtaining.

InGreatBritainthebasicrelerencc documentisERA(TheBritishElectthal andAHiedIndustries RegeirchAsgachtha) reyattF/TI31tpublished in1939,andin1955revisedcurrenttutiagtablesforsolid-type cablesuptaandincluding 33kvwerepubHshedinERAreportF/TI83.Amoredetailedrcportsumtnarhing themethodofcomputing currentratingsfarSOHd-type, ailGHed,andgas.preggure cablesisnawbeingGnaHtedandmnbepublished asERArcportF/TI87satnetimein1958.UntilrecentyearscurrerttratingsineatBritainhaveusuallybtenconsidered anacontinuous basis,buttheltnpartance oftaltittgintoconsideration cycHcratingshagnawbeeneirefunystudied,sincecon-tinuedhighmetalpricedhaveforcedcableuserstorevietrcarefully theeffectsofcycliclaadings.

Areporthasrecentlybeenissuedinwhichasimplemethadhyre-gcntedfortherapidcalcuhthn ofcycHcratings.'able VgivegSpecificinductive capaci-tancevaluesfaryaperastpaperhtguhtion (SOHdtype),3.7(IPCEAvalue);paperinguhtian (Othertype),33-4AIsitpad-sibletaHdttheothertypesandtheirapyrapriate Specificinductive capacitance valuesoralternatively gunplyuseanaverageSpecifichtductive capacitance valueaf3.7,faretample>foraHtypesafpaperinguhthn?

Reference 15madetatheadaptionofthehypothesis suggested byKenneHyasthebashofthepaputhisig'alogicalapproachbutitappearstadEerfiantthebasisofcomputing ratingshithertoadoptedintheUnitedStates.AnampHGcatian oftheautharg'iewpoint aathisimportant issuewiHbe>>deemed.Withreference tatheuseaflow-resittivity

bttchfiH, recentStudiesinGreatBritainhaveShownthatthemethodofbachGHing cabletrenchesdeservescarefulcangideta thnasatteathntathispointcanresultinincretset upta20%iuhadcurrents.

Equatha43givesthethettnalresistance betweenanypointintheetrthSurrounding aburiedcableandambientearth.ItisTableX.Tempetblute Llmibfor8eHed;Screened-cndHSLf'-TypeCebietLaMDirectorlaA)rIaDuctsSyeteaiVoltageaadTyyeaiCableLeadSheathedArmoredUa-armoredAiamiaumSheathedArmeuredorUa-armoredLeadSheathedUaArmoredarmoredAtom)asmSheathedArmorederUaarmored1.1krStogie>cate..

F80~~~~~~80~~~~~~~~~~~~~~~~60>>~~~~~~~Ttriaaadmulticoce baited.>>~~~80~~~~SO>>~~~~~~~80~~~~~\~80~\>>60~~~802.3kraad5.5krSiagtehae

~~~~~~~~~~~~~~~~~~~~~~~~~~~~80~~~~~~~80~~~~~~~~~~~~~~~~~~50~~>>~~SOThf~rcbaitedtype~~~~~~~80~>>~~~~>>80~~~~~~~80~~~~~~SO~~~~~~>>60~~~~~~~8011krSiagic~..

~.......70.........70.....................50.........70 Threncoee beltedtype.......

~..SS.....,...5$

...,.....65...,......5$

.........50.........d5 Three>>care acrceacdtype..~.....>

0..~......TO.........TO,........70.........50.....,...TO 22kvStatic~re..

..5$.........6$

............

~........$

0....~.~~.5$Three-care bettedtype..........SS.........SS,...........,........$

5.....,...50 Threescore icrceocdtype........6$

.........55.........5$

..........5$

.........$

0......."5$Tht~clSLIorShl)........65...................

A$..........65....................55 33kr(ccrccacd)

Static~re..

.55.50.ThreecoreHSL...............OS.

.65~Mccauccdiadegrccaccatigrade.

tHachttatcc separatelead.ISeparateicedrheatbcd.

1Separatealumtouaa sheathed.

notclear,however,whatvalueofsoilthermalresistivity isusedinthisexpression andinformation onthisimportant pointlsdesirable.

InGreatBritainavalueofsoilthermalresistivity (g)of120Ccm/watgisgeneraHyusedbutfurthertestdataarebeingslowlyacquired.'nd wheretestshaveindicated thatalowervalue,e.g90Ccm/watt,isjustified.

thisvalueisused.Currentloading~tablesinERAreportF/T183providedataforsoilthermalresistivity valuesof90and120Can/watt,andcorrection factorsforothervalueso!soilthermalresistivity arealsoprovided.

IntheUnitedStatesburiedcablesareusuallypulledintoductbanks,buttheremustbemanycaseswhere'irect burial,asaormaHy,.used inGreatBritain,wiHresultinlower'instaHation coits.FormulasdealingwiththisinstaHation technique areadesirable addition.

Permissible tem-peraturelimitsforthevarioustypesotcablesandinstalhtion conditions usedintheUnitedStateswillbeahelpfulap-pendix,anditissuggested thatthisinforma-tionshouldbeaddedtothepaper.Forcomparison

purposes, thelimitsrecom-mendedinGreatBritainaresummariged inTableXandinthefoHowingl Phstic-insuhted powercables............

70Cmaximumconductor temperature Gas-pressure andoH-HHedcablesystems(<<types).85Cmaxiniunl conductor temperature Finally,itwillbehelpEultoknowifadoptionoftheformulasinthepaperwiHnecessitate revisionorampliHcation ofexistingratingtablesand,iEso,whentherevisedtableswillbepublished.

REpERBBcas 1~CQRRRNTRATcvoorCAsassroaTRANSsccsscoN*NDDcstacsonoN, S.Whitehead, E.E.Huichfngs.

RcporhRcfcrcrccr P/PfJl,TheBcfffshEfccccfcaf aadAlliedfodusccfes Reseacchcfssocfacion.Lcaihechesd.

Eogtaad,1939;alsoJorsel,fastftutfoo ofElcetcfcal Baglaeecs, Loadon,Bagland,vol.83,1938,p.$1T.2.TssCAaeoaanoN orCtcucRATocoPActoasroaCase,ssLAcoDcaactoasNDoers,EGoldenberg.Precccdfacc, foscffusfon ofElectrical Eagfseers,Leaden,Eaglaod,TOL104,pe.C,195T,p.154.H.Goldenberg (Electrical ResearchAsso-chtion,Leathcrhead, England):

Thecal-cuhtionofcableratingslsasubjectofprimeImportance tocableengineers.

Nevertheless, itseemsthatuntilrecentlytheAmericanstandardworkonthissubjecthasbeenthatofSimmons,'hile thecorresponding BritishstandardworkhasbeenrecordedbyWhitehead andHutch-lngs.Thesepapershavebeensupple-mentedbyscattered pubHshedpapers.including developments deaHngwithcyclicloading.Thepaperby3fr.NeherandMr.Mc-"GrathrecordsuptodateAmericancable-ratingpracticeinamannerthatwillproveinvaluable toengineers formanyyearstococne.ItisapleasingfeaturethattheauthorsareespcciaHy competent todealwiththissubjectinviewoftheirvaluablecontributions tothecable-rating fieldoveranumberofyears.ModernBritishcableratingprscticehasrecentlybeenrecordedinanERAreportsdeaHngwithcontinuous currentratings.andintwoIEE(Institution ofElectrical Engineers) papersc>(basedonERAreports)deaHngwithcycHchacHng,butthemajorityofthisworklsinprocessofprintingandpubHcation.AnobviousdHEerence inBritishandAmericantechnique isthemethodofcycHcratingfactorcalculation.

Mr.NeherandMr.McGrath'5 methodisbasedonanequivalence betweentypicaldailylosscyclesandsinusoidal losscydesofthesamelossfactor,whileamethodrecentlyhftro-ducedinBritain'4 takesfullaccountoftheformofadailyloadcyde.Bothmethodsareconsiderably shorterthananythathavebeenavailable'itherto.

Nevertheless

-,without furtherstudyIwouldnotfeelcertainthatforBritish.typecables,subjecttotheirtypicaldailycycles,theEormofthecycHcloadcanbeade-quatelytakenintoaccountbyuseofthelossfactorindependently ofthecycHcloadwaveformgivingrisetoit.Inhcttheconclusion reachedinmysecondIEE'paper,sisthataknowledge ofthecyclicloadwaveformforthc6hourspriortopeakconductoi temperature, togetherwiththelossfactor,areadequateforcycHcratinghctorcdcuhtion.

However,itwouldbeunhirtoassessanyoftherehtivemeritsofthetwomethodspriortothepublication ofoneofthem.Thedifference betweenBritbhandAmericancableratingtechnique isnotsomarkedforcontinuous currentratingcal-cuhtionasmightappeartobethecaseatGrstsight.Inhct,suchdilferences asexistareprincipally duetothedHIerenttypesofcablesemployedoneachsideoftheAthntic,andtothediiferent standardawfrequencies inuse.Nevertheless acomparison o!thepresentpaperwiththeERAreportdealingwithcontinuous currentratingssgivesrisetocertainobservations.

ThepresentpaperfsprincipaHy.directed tothecalcuhtion OEasinglecurrentrating,butoneusetowhichitmightweHbeputisthehrge-scale preparation ofcurrentratingtables,withratinghctorsfornon-standardconditions.

Forsuchanapplica-tionitIsoftenpreferable tointroduce explicitformuhsfortheratingfactors,astheseformulasmightbeindependent oEsomeofthethermalresistances orlossfactorsinvolved, withaconsequent savingincalculation time.Themethodemployedforexternalther-malresistance calculation forgroupedcableshiddirectinthegrounddifferssomewhatfromthat.recolnmended inarecentpaperofmine.cForthepreparation OEgroupratingfactorsforthemorecom-monlyoccurring groupsofcablesdealtwithinanERAreport,sthecombination ofcertainsimpli6ed externalthermal'esistance formuhsandmyrecommended methodhasledtoisubstantial savingIncalculation time.Idonotfavortheintroduction cfageometric meandistance, oritsequivalent, asitisinconvenient forunequally loadedcables.Abriefrcsucn6ofotherpointsisthatthethermalresistivity valuesgiveninTableVIforthermalresistance calculation aregenerally somewhatlowerthanthecorresponding Britishvalues,thattheproximity effectoncylindrical hoHoirconductors appearstomctobebestob-tainedfromArnold'5paper.sthatwheresheathandnonferrous reinforcement lossesoccuraparaHelcombination oEsheathandreinforcement resistance permitsthecal-cuhtionofasinglelossfactor.thatasimpleformulahasbeenderivedfortheexternalthermalresistance ofoneofthreecablesintrefoiltouchingEormation hiddirectintheground,'nd thatsectorcolrecriion factorsareoftenusediaBritishpracticefor3~recableratingcalcuhtions.

REFEaasfcss 1.Seeccfeceaee 1ofthepaper.2.Seecefeceaee 1ofbfc.Basses'fscossfoa.

TssCAacoaano>>

orCosnsccoos RAnsosANDRAnNDFActoasroaTRANacccsscoN ANDDistacsictioN CAaass.KGaldeabefg RcpersRcfcnucrP/TlryElbl,Irsedea,Eoglaad,(tabepublished).

4.Scecefcccace 2ofMr.Bacncs'fscossfoa.

5.TssCAacoaanoN orCtccccRAnNDPAccoasANDEicsRDSNCT LDADcsoroaONRoaMossCAscssLAiDDcRsctoaDcDucts,K,Goldenbecg.$feeorrepA cco.3$l,fastftosfon olEfcoscfcsf Engi-neers,July1951.8.TssEsctsavao TssauaaRosieTANcsorBoacsoCAaiss,E.Goldenbecg.

EceecccJeurccef, London,England,vof.$4,ao.1,Fcb.195T,p.38.TCQRRSNTRAIQcosroa~PArsaTNslKATRD C*sassToB.S.480,1954;VARNcsssoCANsasc INsccLATSD CAÃ.ssToB.S.$98,1955.Rcport,RcfcnaccP/I'lpp,TheBritishEfccccfcal andAQfcdindustries Researchhssocfasfeo, Leachcchcad, Eaglead.8.Seereference 5ofihcpapa.ElwoodA.Church(BostonEdisonCom-pany,BostoniMass.):Theauthorspresentahrgeamountofusefuldataandformulasforthecalcuhtion ofcablethermalcon-stantsandsuggestanewapproachtotheproblemofcalcuhtion oftemperature riseforvariouslossfactofsincluding steady-loador100%losshctor.Cableengineers usuallyagreeonthehctorstobetakenintoaccountandthemethodsofcalculation forsteadyloads.However,thereappearsstilltobedisagreement ontheproblemo!cyclicloading.AttheAIEEGeneralMeethiginJanuary1953,agroupofpapers'as presented suggesting variousapproaches totheproblemsofcycHcloadingonburiedcablesandonpipe-type cable.Ofthemethodssuggested inthesepapers,theonewhichappealedtotheauthorthemostwasMr.Neher'smethoclusingsinusoidal losscycles.Inhispaperitwasshoitnthatthismethodyieldsreasonably accurateresultsforthehigherlossfactors.Foralowlosshctorsharplypeakedcycletheresultsarenota5accllrate Amodification ofthismethodwouldbetorepresent theloadcydemoreaccurately bysplitting itintoharmonics andcom-putingthetemperature riseEoreachharmonicseparately.

Thiseatailsmorework.butwithmodernmethodsofmachinecalcuhtion itiscconocnical tousethemostaccuratemethodavailable andletthernachineperfornithehboriouscal-culations.

Infact,ittakesverylittlemoretimeonthemachinewhenthemorerigorousmethodsareusedinsteadof,anyoftheapproximate methodswhichhavebeensuggested.

Theauthorhasinvcsligslcd.

thevariousmethodsofcatculalioa ofthecycliccom-ponecitoftemperature riseofl,250-5ICM P'i>PPaveC4~14 Tab/cXt.ThermalImpedance FuacQons1,250.MCM 115-KvCsb/cEnclosed/n6s)to-Inchucx/dc-I}/eactcr P/pcTab/eXIII.MaximumTemyctature R/ceforCyclicLoading'armonicTs/C}oTo/f)oIs/(/oyo/C}ooo...............

8.03/o'...........d.ss/o'...........s.pyio

...........s.so/o't......,........lo.

sdlos......,.....9.

08/Oo....,......

~8.$0/Oo....,.......8.03/Oo I.............

2.88/-30............1.57/

43............1.24/-$

4..~.........0.031-51 2>~......,......

2.20/<<38..........1,19/

54.....~......O.S2/-58

....~~....~.O.ST/-77 3"~~..~.~......1.94/43o............0.94/

dto............o.dl/

79o............0.39/

/-874e~.~~.e"~.....1.58/-50'............O.Td/

<<dyo............0.48/

87'............0.20/

95~Steady.state componcaC fors/agicpipefSteady.state compoaenc forc<<opipes,18inchesapart.Qo<<<<actscopperiosspctcoaduccot potfootTs<<'cctopctacute tiseofconductor 7's<<tcmpotaiute t(saofshiddiagtapeTs<<cernpctacutetfseofoiliapipe2'o<<Cetapctatute tiseofpipeCoaductot P/peMethodTempctacute, CTetapetacute, CofCa)-ca/ac/oaIPfpe2Pipes.IP/pe2PipesForLossCydeI1.......39.1.....49.2......24.1

....34.32.......30.8.....40.0......24.5

....34.83.......30.0.....$

0.1......23.2e..

~.33.4eForLossCyde2I~......30.0.....37.5......

17.I.:..23.82.......32.d.....30.2......18.2

....24.93.......32.8.....39.5......15.xe....22.8e ThesedgutcsdoaociaciudetheCcmpctacute ciseduecodie)acetic ioss,<<hfchwouldbeaddedcothe~ccady.state compoacaL

~Thesesteacetateccmpctacutcs.

ItisaocpossibleCocomputethemaximumccmpctaxute ofthepipebythismethod.115-kvcablesenclosedin6s/s-inchwutslde-dianxeter pipeburiedintheearth.TheresultsofthreesuchmethodsEortworepresentative loadcyclesarepresented inthisdiscussion forcomparison.

Thethreemethodscomparedare:(1)theHarmonicmethodusingBesselEunctions tocomputetheheat-Qowconstants ofthecableforeachharmonicofthetemperature cycle,(2)thesinusoidal methodsuggested by'r.Ncherinhis1953paper,and(3)thelatestmethodsuggested byMr.NeherandMr.McOrathintheircurrentpaper.Spaceinthisdhcussion doesnotpermitacompletederivation oftheheat-Bowequa;tionsforthehazznonic components oftheheat-Bowcycle,butonlytheresults,ascalculated byanIBM(Intenutlocul BusinessMachines) 550,aretabuhtecl inTableXLItmaybenotedthattheznachinetiznctosolvetheeightsimul-taneousequations necessary torthesolutionoEthetempecatures andheatGowsforeachhazmonlcwasapproximately 5minutesperznatrix,withaseparatesolutionneces-saryforeachharmonic.

Thewholecostofthejobmrentaltinxeonthemachineandpunchingthedataoathecardsformsertloninthemachinewas$150EorthreeTab/cX/I.Hannon/cComponea/s ofLossCyclesLossCydeILossCyde2HatLoss,PhaseLoss,Phasemoa/cWattshac(e,WausAag(~,DestosoDecrees0.......4.03...............2.54 I~~~2500231~~2.......1.10.....+30......0.43......

+IS$3.......0.20.....

00......0.do......+

ds4.......0.$

3.....+40......0.53......

3$Bxamp(e:TheequationoflosscydcIusingthefotegoiag dataisasfoiiooom(staximum Qo<<d.d<<actsptttootpttcoaduccot}

Qo<<4.03+2.$

0sinoot+I.IOsin(sot+30o)+

0."-0sia(3ot-00o)+0.$

3sia(sct+40o)<<atesCottespoadiag ccmpttscute cyclefotcooduccot tempstacutc isssfolio<<sfot~siagiepipe:(Itaxi.mumTi<<35.lo)7's<<32.4+7.24 sia(ut-30')+2.$

7sin(<<ot8)+0.30sia(3<<t133')+0,80sla(4aT')dcgttcsccadgtsdc Seretime<<5,00 a,cs.iathefotegoiog expressions.

ditferent sizesofcable(atotalof12ma-trixes).Thecostofpzogzanuning wassmallsincethegeneraiprogramforsolutioaofcomplexsimultaneous equations wasalreadyavaihbleintheIBMlibrary,andonlyasmallamountofworkwasnecessary tosetupthisparticular problem.Thecomponents otthelosscycleswithwhichthedatainTableXIwasmultiplied toobtainthctempezature cyclesaregiveninTableXII.TheselosscyclesareiHus-tratedinPigs.4and5,withthecocre-syondingtemperature cyclesofthecon-ductorandyiye,InaHfuturecalcuhtions ofthissoct,itisplannedtocanytheprogramming stiHfurtherandhavethemachinecalculate thetemperature cycleforeachsizeofcableanddetecznine itsmaximumvalue.Thhhasbeenestimated tocostapproxinutely

$500forprogramming and$15extzapersizeofcabletocompute,Usuallyonlythetemperature oftheconductor andthepipearesigniGcant incalculation otthecurrent.carrying capa-bilitybuttheelectronic calcuhtor auto-matlcaHycomputestheotherva/ucs'sted inTableXI.andtheyarerecozdedEorwhateverusemaybemadeofthem.Atabu/ation ofmaximumtemperatures fortheforegoing twoloadcyclesandthethreedHfecent.

methodsofcalculation Hscedpreviously aretabulated inTableXIIIinthesameorder.Examination ofthistablewHIrevealthatthesinusoidal methodyieldsresultswhicharenearertotheznoreaccurateharmonicmethodtlunthchtestmethodproposedinthcpaper.Theagreement betweenthevariousmethodsisseentobebetteratthehigherlossfactors.Itmaybearguedthattheagrcemcnt iscloseenoughbetweenthethreemethodsforaHpractical purposesandthattheaccuzacyoftheoriginalthermalconstants fromwhichthecomputations weremadedoesnotwarranttheextraworknecessary tousetheharznonic method.However,thedangerinusinganapproximate methodisthatsomeoneunEacniliar withitsderiva-tionanditslimitations wiliuseitwhereitdoesnotapply.Theauthordoesnotcon-siderthcagrecznent closeenoughfor40folossfactor.Thecomputation otthepipeIetnpctature isjustasimportant astheconductor tcm-pezatures, especially insummerwhenhighearthtemperatures prevailandwherehigherdailylosshctozsarcmorelikelytobeencountered:

Iftheearthnexttothepipeexceedsanavengeof50C,thereisdangerofdryingoutthesoHcausingthezmalinstability.

Ca/culations otcur-rent~ying capability shouldtakethisliznitintoaccount.Rxcysaxcwcx I.Scetefcteacc 3ofthepaper.KJ.Wiseman(TheOkoniteCompany,Passaic,¹J.):Theauthorsaretobeconunended forthhveryGnetechnical paper.Thcnialforaaup-bxhtccom-.pihtioaotengineering fonnuhsandcon-stantsforthecalcuhtioa ofcurrent-cacrylngcapacities ofcableshasbeenofincreasing importance everyyear.WhenDr.Simmonswrotehisseriesofyayccsabout25yearsagowemightsaytheelectrical cableindustrywasyounginengineering knowledge, thetypesofcablefurnished werenottoogreatinnumber,andthecharacteristics ofthecablesmerenottoowellknown.Todayourknowledge ofcabledesign,materials, ancloperating conditions alongwithnewtypesofcablesishriaadvanceot25yearsago.Wehavebeenusingthetonnuhsastheybecameknowaanditwasdesizable tobringthetatogetherinonephceand,inaddition, aHofuswhohaveoccasiontomakethesecalculations wiHbeusingthesamefozznuhsandelectrical andtheznulconstants.

Also,thispaper<<iHbeofgreathelptoyoungermencomingintothecablein-dustry.Althoughicsummarizes theformulas, anyonestishingtogetadearerappreciation ofchetextcanrefertothebibliograyhy andstudycheoriginalpapers.TocnakeanytareofthiskindgencraHyuseful,itisdesirable thattheprocedure beeasytofollowsadtheformulasreadilyapplied.Theorecitalfonnu/asinvolving highermathematics canbeused,buttheytaketime,andvcr).olccnitisnotpossibletotakethetunetostockupacase.Aga/nconditions otinscsi/scion atevarlab/edaily,soifweatcczapciomal'eaGeldcheckotca/cuhcions wccanGaddL~ctcrtccs; there/ore, cxaccnes)

'co3highdegreeis ll5~~t'4I4"~~~~'1J~rlII 3100100X~aoO~aoCDO.20A~doE~X>dOOl-aozuxrDcoO20AVE.IXc-..,r..",,

a~A.M.tiMFlg.4.Lossandtemperature cyclesfor75%%uoloadfactor>Qlllullcf loadcycleFtg.5.Lossandtemperature cydesfor60%%uoloadfactorwinterloadcycleValuessameasinF>g.4C4~coppcr tosscycleTx~tcmpcraturc olconductor Tc~tcmpcraturc ofpipeTcmpcrdturcs arelnpercentofcoppertcmpcraturc corrcspond-tngtosteadyloadequaltothemaximum.notnecessary.

Ithasbeensuggested thaCitisnowpossibletousecomputers ontheseproblems.

Thisistrueforthosewhohaveacomputer, butherealsotimeistakenforsettinguptheprobtanforthecomputer.

AlsowemustshowhowtocalcuhtethecurrentsandinaEormthaCwillbeused.VouwillnotethaCmanyofChefocmuhsarenewtomastotyou.Thesefonnuhsweredeveloped tomakethecalculations easilyandquicklyandyetdonotcausealargeerrorinthettnatanswerfromthehighlytheoretical formula.Itisnaturalthattheformulasmaybcacompromise andsomemayfeelthataparticular formulaChattheyusemaybcsuperiortothatrecom-mended.Likewisethethermalconstants maybeacoxnpromisa ThisistrueasfarasIamconcerned, yetwearewittingtoaccepttherecommendattons giveninChepaper.Thecalcuhtion ofthevariouslossesexistingtnacablesystanandthclocationoftheselossesiswelldoneandshouldbccarefully studiedbyallnewengineers.

Thesectiondealingwiththecalculation ofsomeofthethermalresistances needcarefulstudyinordertoappreciate thanastheydepartfromtheusualmanna'nwhichathermalresistances arecalculated.

Forexample:thethermalresistance betweenacableandasurrounding wall,suchasaductwallorapipe;seeequations 41and41(A).Heretofore, weused2>a~0.00411B/D,andreferredtoasthcIPCEAmethod.Thishasbeenrevisedtotakeintoconsideration thecondition existingandthematerials.

Equation41(A)isageneralone,andbyinserting thecorrectvaluesof>4'ndB'sgiveninTableI,wecangetR>.Thisisanexampleofhowwecanacceptacompromise inordertogetagrecmcnc.

WeacOkonitemadetestsyearsagocodetermine thethermalconstants fortheoilorgasmediumsur-roundingcablesinapipe.Wctriedtousethecylindrical logfornxutaandfoundtheapparentthermalresistivity variedduetotheconvection effectsoftheoil.IEwetookthesimpleformulaR>a~1.60/DwhereDisthediameterovercheshielding tapewefoundwegoCgoodagreement withtest.Weneglected tan-~peratureeffectsastheactualvalueofRraascoxnpaxed tothcthermalresistance ofthehsuhtionisverytow,manytimesintheorderofone.tenth;therefore, temperature effectsaresmall.Foragasmediumusing200poundspersquareinchmeusetheequation8>a2.58/D.Howdothesefocmuhecocnpasewithequation41(A)proposedbytheauthors)Considertwocases,onehavingadiam-eterovertheshieiding tapeof1inchandanotherhavingadiameterot2.5inches.TheEollowing tablecomparesthetwotypesofequations.

Dtameter~Diameter~1loch,XAlaches,ThermalThermalOhmrPootOhm-Poolon.....{Ohoaite......t.do t.o.r....o.da t.o.f.Nehcraad...1.3r

...0.80Ohoaite......2.5d Co.t....1.03C.o.f.Nehcraad...2.22

...1.04htcCraxhCaa~~~Thcdifferences arenotgreatandwhenconsidered inrelationtothetotalthecmalresistance, theyarenegligible.

WecanaccepCtheauthors'quations.

Iamghdtoseetheauthorsphcethcductsysteminproperrehtionship toaburiedcablesystemandthatthesamesoilthermalresistivity willbeusedwhenmakingcomparisons.

Thiswastheweak-nessinthecluctheatingconstants originally setupbyiVELAandhterknown'sIPCEAconstants.

Alsoabetterunder-standingoftheeffectofmultiplecab'tcsinaductbankisobtainable, andth>>decermina-tionofthecablehavingth>>highestthermalresistance ispossible.

AppendixIIIdiscusses the'derivatton ofDr,afictitious diameterinthesoiluptowhichitisassumedthatasteadyheatloadexistsandoutsidewhichthelossfactoroftheloadistakenintoconsidera-tion.IhavenotbeenabletoaccepCthisassumption.

Itisanendeavortoobtainathermalcesistance forthesoilthatwillcheckwithastudythatMesscs.Neher,Butter,ShanklinandmyselEmadeandisreferredtoinreference 3inthebibEography ofthispaper.Astudyofthepreviouspaperswillshowthactheattahiment factorisnotexactlythesameforatttypesofcablesstudiedandallshapesofloadcurves,TheauthorstabulateinTableIXacomparison oftheattainment tactorforthreemethodsofcalcuhtion foralossEactorof30%Eorseveralcabledesigns.Ratherthangiveresultsforonelossfactoronly,itwouldhavebeenbetta'ftheyhadcoveredthecangeoflossfactorswhichwerestudiedin1953.Ittheseattainment fac-torswereplottedagainstlossfactorasIdidinmypaper,itwouldhavebeennotedthatastraightlinecouldbedrawngivingagoodrepresentation ofhow(>4F)varieswithlossfactor,naxnely,(>4F)~0.43+

0.57(t/)formymethod.Thisequationfollowstheplotof(AF)andlossfactorvaywelldowntoabout35%lossfactor,andinsomecases,itgaveahighervalueandothercasesalowervaluethanactuallycalculatecL The(4F)valuesIreportedarebasedoncarefulcalculations fromthcexactloadcurveandnoassumption thatasingleinewavecurvecanbetakenasrepresentuxg anyloadcucve.Asitisararitythatcablesaredesignedforlosshctorsaslowas30%(50%toadfactor).myformulagivesresultsasaccurateaswhenusingD,andeasiertouse.However,forthesakeofuaiforniity inmethodsofcalculation, wewiltaccepttheauthors'ethod.

Inthhconnection, IivouldliketoraiseaquestionwhichIhopewillbetakenupbyothersinterested inthissubject.Theuseoftheequxciouinvolving DaisanAnnn>r>oo 1OA~Arrhrr1fr/rn>C-Trrrhrn>~>rrn>>rfI'na:<InnnVl~'t>>

~

,attesnpt totn'crease thethernutresistance andhavearrivedatcatatncondusions, forthesoilforcablesorsmallpipesixes;someofmhicharediscussed inthefollowing hiotherwords,thecomputedvalueoEparagraph.

themu!resistance istooIow.IsitnotThedetermination ofthclossesmtheIHldythatvreareleavingoutofourequa-conductor, shield,sheathorpipe,andthetionaterminvolving asurfacecontactdielectric havebeenweHestabHshcd bybetweenthcsurfaceofthecableorpipetheauthorsandbearnofurthandthesaiLThisistermwouldbeoftheThccalculation ofthethelmalresistances noercomment.cablessasnefostnaswenowuseforthecaseofofdirectburiedbld'lesinair,namely,8~0.00411 B/D.instalhtions appeartohave'eenwellsoilthermalresIfweaddthistermtothelogfortunaEorfounded;althouhthehodEresistance, wewillgetahigherattheeffectofcyclicloadingscanstobctotalresistance andtheInliuence oftheinquestionamottgstthevariousinvestiga-diameterofthecableorpipewillbegreater,toss(reference 3ofthepaper).However,thetowerthediameter.

ItvriHbeneces-asEarasductbankInstathttons arecon-sarytodetermine thevalueofB.Thccerned,thedifference betweentheNELAideaofsuchatennisshowainthepaper'rIPCEAcurrentratingmethodandthatTableIthebyMr.Mathaandhiscoauthors.

Inproposedbytheauthorsissotthtygivesamethermaldataonecannothelpbut<<onderatthedearthgreaaobtahtcdfrotntestsmadebythemonaofpractical datahthepaper.pipe-type cable.Theygiveavalueoflnreadingreferences 10,12,13.16.andBforsurfaceofSomastictowata'f21817of,the.paper,"there scanstobeverythermalohmspacm'.Ilikethis.Isitlittledataoncable'temperature measurc-notlikelythatwchaveasurfaceresisttvity mentstakalinth6ddchthecahleandthesoHmtmmedtate bythevariousutilities whentheNELAc,sQasmasdoricvaluesmereestablished.

Theworkre-RBFEMtNCts portedinthesereEerences tsalmostatltheoretical, andlaboratory measuranents 1.Bottrtava.aa powaattotttrrtssa*norr Hton.an,an~ogue mendsu~~~apprdVocTAOCCiaoaSjtrotÃsy RJsMathafJPeJsMaCattoa, E.Dautlrtlatt.

AIEETraarrurtoas, IamgitoudetstthereamovementafoottohavethisNeher-McGrathmethodacceptedandtorevisetheIPCEAcurrentratingtablesaccord-E.KThomas(ConsoHdated EdisonCom-htgty.Iamnotsurethatthisisthecase-panyofNewYork,Inc.,NewYork,N.Y.):Theauthorsaretobecongratutated insettingupmathanatical equations toevaluateloadWehaveusedthemethodgiveninthcgretthatnomentionwasmadeofthepiopapertocomputethecurrentsathtgofncerworkbyWathceE.~ketnthemtddte quiteanumberofhigh-voltage cablecir-1920'sonthenthgofcablesmstatedm~tshaductbankmd5dcompletedh-ductbank.Thwork,Ibdieve,f-agrcanent miththeNELAorIPCEAntshedthcb~uof~btcratingofthcnicthod.IneverycasetheNeher.McGrath NELAandpresentIPCEApublished rat-methodresultsinahrgerconductor stxeIngsofcable.TheworkofZirkewaspre-foragivencurrenttathtg,msomecasesbeforethcAIEEantipubHshcdinasmuchas30%morcconductor metalisJournal1requiredbytheNeher-McGtath method.TheworkonratingsofcabtebyKtrke.Hahmhereourdia~begins.One5ddm~oftwothingsprevaHsleithaMr.¹hermeatsintheNewYorlcCityareaandtaterandMr.McGrathhavecotstered thenonfcrroQs lnctatmaske'tortheyarcattanpting tomakeapipe.typecablecarrywhichleadtotheNELAIPCEA satinthesameloadasadua-banktnstaHatton.

Yetonthefaceofit,itisincomprehensible Qseofpipe-type cable.Ztshouldbehomanyonecanconceiveo!a~nductorobviousthattheanswerobtainedbyhigh-voltage cable(andaPipe-type cablemathenuttcai solutionisneveranybetterassumptions ouwhichtheequacolnpCtlng Onacurrentsatingbasiswithgonaaredcvdopedandtheconstants usedsingle.conductor high-voltage cablessePa-vriththeequations.

ratdyspacedinaductbankwhereawIbdtcvetheactualheatttowinunderlossesareaminimumandheatdissipation gdcablesyt~hconstd~bly mo~a~m~Ineithereventwe~otcomplexthanhasbeenassumedinthisundastand whysomuchthneshouldbcpaperand,therefore, actualratingswhich~spentondevdoping ancmmethodofcur-areobtainedmaybedHIcrcntfromthoserentsatingcalculation for.duct-bank obtainedbythiscalculation, systelnswithoutGssthavingatleastobtainedsomeactualIn-servicefieldRztttttstvcts measuranents tosubstantiate theirl.fosmtttas.

~iuuCaactraanorl orCaaaaTattraaazoaas Onthcotherhand,wemustsincerely commendtheauthorsforattanpting toarriveatarealistic comparison betweenduct-bank anddirect-buried systans.ItD.Shorttsunfortunate, however,thatindoingsoort(CanadaWireandCabletheyhavenotbasedtheirformtttadcvdop-ompany,Toronto,Ont.,Canada):Sevantmentonextensive 5ddsurveydataaswasoEtheengineermhoworLwithmeatCan-doneatthetimethcNELAductconstants adaWirehavebeenstudyingtheNeher.wereestablished.

MCGrathaaoverthPPepastfewmonths,Theonlywayinwhichwehaveasyet,beenabletomaketheNeher-McGrath methodtsackwiththeoldandwellprovedNELAmethodistoreducethesoilthermalresistivity totheorder'of40Cto75Ccm/lratt.

Theactualvaluewhichonemouldusetottsriveatthesameconductol sixeasdetamined bytheNELAmethodappearstodepceduponthenumberofcablesintheductbankandthevalueofthcdaHyloadfactorchosen.Incontradis-

tinction, Mr.Neherinreference 13ofthepapa'tates thathismethodagreeswithin10%ofthcNELAmethodifapa~75Ccmmattisused.Wehavenudesomecalcutattons ofthethalnalresistance ofcablesinaductbankfromthcsheathtoground(orsink)usingthe¹her-McGrath

~methodandtheaverageconditions on<<hichtheNELAductconstants wereobtained.

Thcaverageconditions were:I.Mostofthemeasurements weretakentinderpavedstreetswiththedepthofpave-mentbetween10and12inches.2.Majorityofductswacmadeoffibre.3.Avaageductinnerdiasneter

~3.75inches.*Concretespacerbetweenducts2inches,withduct..watt~1/4.tach, 3-inchouterconcretesheILSpacingbetweenductcentres~6t/tinches.5.Averagedepthofbusialtotopofductbank~30inches.6.Mostmeasurements with~nductorleadsheathedcablesfran2inchesto3inchesoutsidediameter.

Avaagediameter2Sinches.7.AHIoadedcablesinoutsideducts,allequaHyloaded.8.Soilthatnatresistivity (i>>situ)~120Ccm/watt.Twocasesmerestudiedandtheresultsaresummasixed inthefoHomingl CareI-Thrcccablesin2by2ductbank(oncoflourcrductscrnpty)..NELAValtte(Le.4.93/D,'+LrNH3 Lossfactor........100%o..62.5%o..33%

Rthcgthamal/ohns-feet.......5.09

..3.92..3.00Neher-McGtath ValueLossEactor,100%o62,5%,33%

UppercablesRthssthalnal/ohms.feet...~~.6.68..5.02..3.71LowercableRths.s"""""6-63-.4-99..3.70Averagevalues....6.66

..6.01..3.71InorderforNehcr-McGlath valuesoftherlnalresistances tobeequaltoNELAvalues,soilresistivity wouldhavetobe;At100%losstactorp,65Can/wattAt62.5%lossfactorp<~60Ccm/wattAt33.0%otossfactorpa~45Can/wattCaseIl-Sixcablesin2uridcby3dccpductbank.NELAValueLossfactor......

100%..62.5%..33.0%Rths-zthermal/ohms-feet....6.89

..5.05%..3.60

¹her-MCGrxth ValueLossfactor......

100%..62.5%..33.0%

Jt/cher,rtfcGrath

-Tcmpcratttrc andLoadCapability rsfCableSystcnlsOCTOBER1957

~<PkLt~

I~I'pperlayerRthsdther-mal/ohms-

"feet..........10.23..7.24

..4.88MiddlelayerRths-dther-mal/ohms-feet..........10.95..7.69

..5.12LowerlayerRthcdther-mal/ohms-feet..........10.63,.7.49

..5.02Averagevalues..10.60..7.47

..5.01InorderforNeher-McGrath valuesofthermalresistances tobeequaltoNELAvalues,soilresistivity wouldhavetobe:At100%losshctorp,~53Ccm/wattAt62.5%lossfactorpe~50Ccm/IrattAt33%lossfactorp,43Ccm/watt~<Othercalcuhtions onslngle~nductor high-voltage cablesvaryinginconductor sizefrom300to1,150MCMinstaHedinoutsideductsinanormalduct-bank systensItwasnecessary toassutneape~75Ccm/wattinordertomaketheNeher-McGrathfozmuhsagreewiththecurrentratingscalcuhted bytheNELAmethod.TheNELAmethodisofcoursestrictlyempirical andthcductconstants deter-minedfromanaverageofalargenumberof6eldsurveys.Ithasbeeninuseforwellover25years;andtheremustofaconsequence bemanythousands oEmilesofcablesoperating atcurrentratingscal-culatedbytheuseoftheseductconstants.

Sofarasourexperience inCanadaiscon-cernedweknowofnohot-spotfailureswithhigh-voltage cablesinduct-bank instalh-tions.OnthecontraryoneisledtoreadwithgreatinteresttherecentpaperbyBrookesandStazrs.tDotheauthorsexpectutilityengineers operating duct-bank instaHations toadoptthemethodputforwardinthepaperandforthwith reducetheirloadsaccordingly!

Thisisaquestionofgreatimportance, andweshouldhaveacategorical statement fromtheauthorsinthisspeci6cregard.InAppendhIVtheauthorsgiveaspeci-mencalcuhtion foratypicalduct-bank htstaHation andalsoasimilarcalcuhtion forapipe-type instaHation.

Intheonetheyuseapeof120andintheotherapeof80.Wouldtheauthorsenlighten meonthesignificance ofthesetwodifferent valuesforp,.OnthispointDr.Wisemanstatedinhisdiscussion ofthepaperthathewasgladtoleamthat.wecannowbasetheduct-bank calcuhtions onthesamebasisofpeaspipe-type cable,buttheauthorshavenotdonethisintheirAppendhcIV.TheuseoftheKennellyfozmuhinthepractical caseofcabletburiedintheearthisatbestanapproximation.

For'thetheoretical caseofaheatsourceinamediumthatishomogeneous, ofuniformresistivity andtemperature, theformulawouldapply.However,forthepractinlcaseofcablesintheeuth,thereisconsiderable deviation'rom theidealcasesuchashonunifozzn medium,seasonalvariation oftemperature gradientintheearth.nonuniform distribu-tionof.moistureintheearth,moisturemigration, andotherfactors,whichrendertheKennellyformulamoreorlessinac-curate.Thusinitsuseonemustbearinmindtheselimitations.

InEuropetheKennellyformulahasbeen'used extensively, butthcapparentthermalresistivity Inserteinthecalcuh-tionsarebasedonthatvalueobtainedirtziltr,asmeasure4inaccordance withreconunended methods.Togetaveryaccuratevalueoftheapparentthczznalresistivity, itseemsthatthemethodtobeusedshouldexactlyduplicate thecableanditsoperating conditions; Le.,thcsamediameterasthecable,thesamewattslossdissipated, thesamedepthoEburial.andatthetitnewhenthethermalconditions arcmostonerous.Thusinthecalcuhtion ofthermalresistance Eromcabletoambient,itappearsthattheKennellyfozmuhcanbeusedtoahighdegreeofaccuracyifanapparentthermalresistivity ofthesoilinsituisused.Thismeasurement shouldautomatically takeintoaccountaHthefactorsthatotherwise limitthcKenneHyformulatoatheoretical exercise.

Therehasbeenagreatdeal"o!.investiga-tionintotheinfiuence ofmoistureonsoilresistivity.

However,asyetthereseemstobenogeneralagreement onanotherbasicproblen,andthatisthedirection oftheheatQow.TheauthorsandothersmaintainthattheheatQowistothesurfaceo!theeuthwhereasotherinvestigators claimsotneheatQowisdownwards toadeepisothermal, about30to50feetbelowtheearth'ssurhce.Inreference 12Mr.Neherobtainstheheat6eldpatternbysuperimposing theGeldbasedontheKennellyfomtulaonthetemperature gradient.

ItisobviousfromtheGeld~patternsthatinthesummertheheatQowispredominantly down,whereasinthe.wintertheheatQowistothesurface.Theauthorsgivenoquantitative methodofevaluating thecffectofthetemperature gradientontheapparentsoilresistivity.

Thiscouldbeoneofthereasonsfoz'hedifference betweentheresistivity asmeas-uredinthelaboratory andhthefield.Anindication oftheeffectofchangeofapparentthcrnulresistivity hshowninapaperbydeHaas,SandiEord, andCamezon,t whereinthedfectoEintroducing adeepisothcmzal (groundwater)incombi-nationwiththeeuth'ssurfaceasthesinkhasatheznulresistance oEapproximately 25%lessthaniEtheearth'ssurfacewastheo=lysink,Thiswouldindicatethatthethermalresistivity ofthemediumischangedwhereasthechangeintempera-turecHstributlon duetothetemperature gradientshouldbeinvestigated.

Itshouldbeenphasized thattheKen-nellyformulaisapplicable tosteady-state conditions only.Theauthorsredizethis,ofcourse,andattempttoccnnpcnsate forthisshortmming byapplyingacydicalloadingfactortotheexternalthermalpath.Thefactortheyuschbaseduponmeasuredvaluesobtainedondirectburiedand/orpipe-type cables.SincethcthezznalcucuitofaductbankisquitedHferentfromthatofdirectburiedcables,wedonotagreethatthhsatnecyclicalIoadhgfactor(asmeasuredondirectburiedcables)canbeappliedtoaduct.bankinstalhtioa.

FinaHyitispertinent topointoutthatthcKenncHyformuhispremiseduponaHtheheatenergyQowingtotheearth'surface.Onemusttheaasktheauthorswhattheymeanbyambientsoiltempera-ture.Theoretiedly atleastthetempera-'ureoftheearthatthecabledepthofburialisnotthcambienttobeusedinthe'enneHyformuhifthesinkistheearth'surface.Whyisthceuth'ssurfacetem-peraturenotthetzueambienttousewhenapplyingtheKennellyfozmuh?IstheBritishuscofa2/3factorinreaHtyacorrection forthevirtualsinktemperature.

orsinktenperatures ifthedeepIsothcmul theoryisvalid.LTssaxALANUMaatANTOAL PaoaLaxoN128KrPtasCASLSTNNswJaaaar,h.S.BrooLee,T.B.Starre.A188'Frearerrioar, roLTC,pt.111,Oat.LOST,pp.TT2%42ANANotooosSoLUTIoNorCASLsHsarPLowPaoatsaa, B.deEaaa.P.J.Saadtford, A,Vf.Vf.CaceerosISfd.,roLTd,pt.111,JaaeIOSS,pp.215-22.F.O.WoHaston(BritishColumbiaEngi-neeringCompany,Ltd.,Vancouver, B.C.,Canada):Thisdiscussion isconfinedtothepartsofthepaperdealingwithcablesinducts.Thepaperisinmanyrespectsmostadtnirable, notablythecoverageofsLindfectinconductors.

ofspecialtypes,proximity andeddycurrentelfects,muttuIheatingeffectoEmulticable instalhtions, andthediectofextraneous heatsources.Forthe6rsttimetheseareaHadequately treatedinoncpaper.Themethodsofedculation must,however,becritically examinedbeforebeingacceptecL Iamdisturbed toGndthatthemethodsgivenforratingcablesinductsleadtosub-stantially hrgerconductor sizesthandoestheIPCEA-NELA method.BythcIPCEA-MELA methodImeanthemethodgiveninanAnacondapublication.t believethismethodisidentical tothatusedinpreparing theexistingIPCEA.cur-rentmtingsforcables.TheNeher-McGzath methodleadstomuchhighervaluesfortheductheatingconstant(thethezznaIresistance fromduct.banktoeazthambient)thandoestheIPCEA-NELA method,whenthethezznalresistivity oftheeuthistakenas120Can/wattintheNeher-McGrath calcuh-tion.Thevaluetobcusedforearththeznulresistivity isofparamount izn-portanceandwiHbediscussed inmoredetaillater.AfewQlustrations ofthedifferenc betweenthetwomethodswQIGzstbegiven.TheGzstapplication oftheNeher-McGrathmethodwhichwemadewastodetezznine theconductor sizeforapro-posed230-LwcableinstaHation.

Thecal-culatedconductor sizewas1,500MCM,whereasbytheIPCEA-NELA methodthecalcuhted sizewas1,150MCM.Some42mQesofcablewereinvolvedintheproposedproject,sotheNeher-McGrath resultwouldhavemeantsubstantial extracostforthecablecomparedtotheIPCEA-NELAzcstdt.Inanothertnztazcc, thcNcbcrMCGzathmethodwasusedtodetermine therequiredsizeofcableleadsfora75.mvatrans-forzner.Thecalculated sizewassolargeastobeconsidered physicaffy Impractlad, whereasbytheIPCEA.NELA methodthecalcuhted sizewaspzactied.

RatherthanrisLpossibletroubleHtheIPCEA-NELA resultwereadopted,itwasdecidedtouseaerialbusinsteadofcablefortheseleuis.Inathirdcase,thecableleadsofa50-mva13.S-L>'enerator weretobechangedOCTOBER1967%cher,iVcGraffs

-'Tcrrtpcrafurcat:dLoadCapabtlEyofCableSys.'crtts 769

<l'~l-1$lChl~r' TableXIV.Itwasnecessary tomeasuretheairtemperature inanoccupiedduct.sincetherewercnoemptyducts.Theloadingonthemachinevrasrecordedandthecurrentdivisionbetweenthesixcableswasdetcsmhscd.

Themaximumdeparture fromequalloadingofthetwocablesoneachphasewasonly2%.After5daystheductairtemperature was43C.Theambientgroundtemperature was19.5Catthesamedepthasthecenterofthcductbank,Dividingthctemperature riseby1/6ofthetotallosses,athermalre-sistanceof4.6ohmsisobtained.

TableSos>>iIzss~l2us,gcnrrs.'1.'.Qi..'.QI

~~5srZRsrrzrff, OVCZnrcovcagrg.

ZUshowsthethermalresistances pertinent tothiscaseasdctesmincd bytheNeher-McGrathmethodandtheIPCEA-NELA znethod.Theexpcrisnental value(occuyied ductairtoearthambientotTableXV)isingoodagrcemcnc withtheIPCEA-NELAvaluegivenin"ductwalltoearthambient"ofTableXV,whilethe¹her-Fig.6.Crosssectionofductbankbecausetheassociated

~o-Lwstep-uptransfosmcr wasbeingrephccdwitha345.kvunit.Theexistingleadsconsistoftwo2,500-MCM cablesperphaseinstalled inaMuccbank.hccording totheNeher;McGrath method,thesecablesshouldbeapproximately 3,500MCMeachifthcAEICallowable temperature of'F6Cisnottobeexceededatfullloadinsununertiine.Theunithasrunatfullloadforlongperiodsonmanyoccasions sincegoingintoservicein1949.Ifourapplica-tionoftheNeher-McGrath methodiscorrect,one'mustconcludethattheexistingcableshavebeenseverelyoverloaded manytimesduringtheirserviceperiodof8years.Noevidenceo!suchoverloading hasbeenseen;thecableshavebeenentirelytrouble-Free.

Therearetorootherunitsatthisplant,identical inallrespectstotheonedescribed aboveexceptthatoneofthanhasbeeninserviceslightlylonger,theothernotquiteasIong.Notroublehasoccurredontheleadsoftheseunits.Itwasdecidedtomakeatemperature surveytoestablish thecorrectfacts.Theunitwasrunatfullloadfor5days.Testresultsshowedthattheductstructure atcaisscd equilibrisun temperature in24hours..Thebulbofarecording thcsxnom-cterwasinserted20Eeetinthebottomxniddleduct.Thedetailsottheductbankandcableare,giveninPig.6andvaluei!thetwomethodsarctogivethesameresults,asisobviousbyinspection ofTableXV.TheNeher-McGrath valueshouldbelowerthanourexperimental value,sincethefosmcrrepresents thethczmdresistance fromtheoutsidesurfaceoftheoccupiedductwalltoearthambient,whilethehtterrepresents thissamere-sistanceplusthethcsmalresistance fromoccupiedductairtotheoutsidesurfaceottheoccupiedductwan.Oneisnotentitled,to saythatthedis-crepancybetweentheNchcr-McGsath valueandtheIPCEA-NELA valueisrealunlessthevalueotthespecificthermalreshtivity oftheearthpsisthesameforboth.The¹her-MCGsath valueinthetabulation isobtainedwhenavalueotearththermalresistivity psm120Ccm/wattandthcsmalresistivity ofconcreteps~85areusedmequation44(A}otthepaper.Therehasncvcrbccnaslygeneralagrec-meatonwhatvalueofearththcsmalresistivity isinherentintheIPCEA-NELA ductconstants.

SeveralyearsagoMr.G.B.Shank!inandhiscoworkers intheGeneralElectricCompanyinvestigated thisextensively andconcluded thatthevalueisabout180Can/watt.Ifthisconclusion iscorrectthediscrepancy be-twomthcNchcr-MCGzath resultandtheIPCEA-NELA ductheatingconstantisTableXIY.Cableandl.ossData2,500.MCM Scgiaentol CopperCondsrctorr Pepcrinzuf4tcd.teed-Sheoshed Solid-Type, 13.8Kvrealandserious.Ourtestresultcitedabovedoesnotgiveanyinformation onthispointbecausetheearththczsnalre-sistivity wasnotmeasured, duetolackoffacilities.

Ifthediscrcyaucy isreal,onehledtoquestionthesoundness oftheKennellyformulausedbythcauthors.Itisbasedonthepremisethatallheatgenerated inthecableescapestotbesurfaceoftheearth.Someccnnpetent engineers havearguedchatpartoftheheatescapesbyanotherpath,namelytoasinkdeepintheearth.Mathe-maticddevelopment ofthispremisegivesaresultforthethermalresistance betweenductbankandearththatisonlyabouttwo-thirds aslargeastheresultbythCurreasDaringTeat,hmpercsWaSicLossPerBootofCableCablezfo.2..............

0TS...............

5.135...........

~..1,020...............

S.T3Total30.50PercableaverageS.1Roses:hmbleatearshtomperaiuredurlagteatwas10.5C.Cablesarepaired2-3forh-phase,CHforB-phase,5-5forC-phase.D(ameserover<<oaductor, laches............2.000 Cottontapeshicxaess.

laches...............0.01T zasulssloa thichaess, laches................0.210

'lameseroverinsulation, laches............2.4S4 sppcrtapeshichaess, laches..............0.003 obeaibihichaess, inches...................0.12$

Over.alldiaescser.

laches..................2.T10 h<resissanee at5$C~$.41(Xo>>)ohms.face Kennellyformula.hccording tothis,wemightexpecttheNehcr.McGrath methodtoagreewiththeNELAvalueiEthecarchthcrzndresistivity istakenequalto2/3X180~120Ccrn/wattinequation44(A}.Itturnsoutthacagreement occurswhen.McGsathvalueismuchhigher.The='-:Neher-McGrath

• valueshouldbeap-proximatciy equaltotheIPCEA-NELA TableXY.ThcrnNlResistances Pertaining toTest'hermalEeshsaaee, lfehetIPCEhEzperi-CpcrWatsrryoos McarashTfgchmensalZnsuiasioa...~........0.73

..".O.TSShesihsodues....'....1,52,....1.82 Ductwall.............0.13 Ducewalliocarsh~mblen!............8.7$

>>.~...4.0 Occupiedduceairsoearthambient........

..4.51>>Calculased fromcriuasfoa44(hj usiagp>>~120Ccmlwasz.theearthresistbrity istakenas55Can/wattinequation44(h).Itdoesnotseanlikelythatthevalueof55isrepresentative oftypicalsailaroundductbanks.Manymeasurements inseverallaboratories have>-~-consistently shownthatthespecificthczma11r'esistivity ofearthvariesfrosnabout100Ccm/wattEoramoisturecontent.of15%,toabout300or400Ccm/wattforseromoisturecontent.Avalueof180Ccm/wattseemsfairlyrepresentative ofaverageconditions.

Iconcludethatthevalidityofthe¹her.McGrath methodofcdcuhting thethcrzndresistance fromductbanktoearth.ambientshouldbedesnon-stratedbytestswhczchsthe<<arththermalresistivity isdcfinitcly known.Havetheauthozsverifiedtheirfindingsbysuchtests?RETERENCE t.CaaaaazRaznrosroaBaaczasoc CosanncroaLAnacondaPssrrsstfen C4t,McCcaw-Hi0BooLCompaar,ZocRewYes¹Y.,erstedlcfoa,Ocs.1042.J.K,IfcherandM.ILMCGrathtWeareindebtedtoMr.BaznesandMr.Golden-bergfortheirdscuszions inwhichtheysummarize thepresentcableratingprac-tkcsinGreatBritainandpointoutsomediifcrcnccs withhmczicxnpractice.

Promthisitwould'ppeaz'hat inmostrespectsthepractices inthetarocountries areshnihr.Whilethemethodothandhnggroupcableratingsdeveloped by'x;GoldenbergmayappeartodifFerhoaxthemethodotthepaper,actuallybothmethodsarcderivedfromthesamebasicprhxciplcs andshouldgiveidentical resultsforthesaznesetofconditions.

Toanswertheirquestions withregardtotcsnpcrature lnnitsandtherelationship ofthispapertothepublished ratingtables,wemaysaythatIPCEA,incollaboration withtheAIEE,hasunderactivecon-sideration axevisionoftheexistingcurrentratingtablesbasedonthemethodsofcal-cuhtionset!orthinthispaper.Thetem-yeraturelimitswfiibethosedready'dopted byIPCEA,AEIC,ctc..inindustryspcclfications.

Mr.Churchhasoutlinedaprocedure fordetermining theeffectoftheloadingcymeoncableratingswhichwillbe,wefear,ancnigsnatoznostcableengineers despitethefactthaticrepresents achdlengetothosemathmssatically inc8ned.Mr.Goldcnbcrg alsohasreferredtoadifferent bucnevertheless machcsnatically involvedprocedure fordoingthis.Foruorsnalcablecalcuhtions, thecrcmmsdous asnountotcomputations requiredforeachindividual 7TO1Vcher,McGrath-TerrsperatureandbroadCapabihty ofCableSysterrss OCTOBER1951 aa~~ee01' casi,'issimplynotwarranted

<<veniEadigitalcomputermereavailable tothecableengineer.

Iftheapplication ofaparticular loadcycletoagivencablesystemistobestudied,wesuggestthatthismaybedonemoresiniply,morcrapidly,andmoreeconomically byusingananalogcomputerdesignedforthepurpose.Wefeel,how-ever,thattheaccuracyofthcmethodgiveninthepaperascomparedtoaBexactcaI-culations whichwehaveexamined, includ-ingthoseofMr.Church,issuificient, par-ticularly inviewofthefactthatanypar-ticularloadcyclemayneverrepeatitself.Themethodgiveninthepaperisanapproximation, admittedly, butithasbeenderivedfromthesamefundamental prin-cipleswhichunderlieMr.Church'smethodthroughaseriesofcareMIyconsidered simplifications.

Itshouldbeunderstood thatthereisnothingsacredabout.thevalueof8.3inchesusedforthefictitious diameterDc.Thisvaluehappenstobethebestsinglevaluetousebasedonthestudiesdescribed inreference 3.ForMr.Church'scasevaluesof7.1forthc75%loadfactorcycle,andof5.1forthe60%loadfactorcycleareindicated.

Theerrorsinusing8.3,however,amounttoonly2and5%high,respectively, mtheconductor losscomponent ofconductor temperature rise,whichwouldbeoffsetbya10%errorinthevalueofearththermalresistivity ein-ployed.Dr.Wiseman's conunents inthiscon-nectionaremostinteresting sincehehasoftenexpressed theopinionthat,prac-tically,itwassufiicient toconsiderDctobeequaltoDs,orinotherwordstoapplythelossfactortoaBoftheearthportionoEthethezmalcircuit.Wecanagreewiththisinrespecttopipe-type cables,but,ashehasindicated, wedonotconsiderthisfurthersimplification desirable inthecaseofsmalldirectlyburiedcables.Neitherdoweconsidertheforznuiawhichhegivesforobtaining attainment factordirectlyframlossfactorsuitableinthiscase.ThisisreadByapparentframFig.2aftheGrstpaperofreference 3inourpaper.SincetheuseofDchasconsiderable theoretical justification inouropinion,wefeelthatitshouldbemadeapartofthegeneralprocedure Eorcalcuhting theeffect.oftheloadingcycle.Theintroduction ofanadditional thermalresistance tocareforsurfaceeffectsbe-tweencableandearthisanentirelydiffer-entnuttersincethiswillincreasethetemperature risebothforsteadyandforcyclicloads,whereastheuseofD>isintendedtogivethecorrectresultforcyclicloadsontheassumption thatthetotalthermalresistance inthecircuitwhichisunchanged bythevalueofDciscorrectforsteadyloading.Itisquitepossiblethatsuchasurfaceeffecttermispresentandthatitmayattainanappreciable magnitude inthecaseofsmalldirectlyburiedcables.WeconcurinthehopethatthismatterwBIbeinvestigated further.Ivfr.ThomashasnotedthepioneerworkofW.B.Kirkeinconnection withcableinductandindicates thatthisworL:formedthcbasisofthepresentNELA-IPCEA method.Employing aductbankcon-Gguration suchasshownbyWollaston andutilizing equations 14and17oftheKirkearticle,weGndthatKiri:ewouldusearesultant thermalresistance fromloadedductmalltoearthambientof9.0fortheworstsoilinmetropolitan NewYorkand6.00forthebestsoiLThesevalues,whencomparedwithNELAconstantof4.9,scarcelyconfirmMr.Thomas'tatement totheeffectthatthepresentIPCEA-NELA methodisbasedonorisevencloselyrehtedtoKirke'swork,WhileKirkemadesomeattempttotakeintoaccounttheconfiguratioa o!theductbankstructure, hedidnotutilizeresistivity assuch,andaspreviously indicated webelievethataknowledge ofthisandotherparameters ignoredbyKirkeisessential toarealistic methodo!handlingthisproblem,par-tlcuhrlywhenoneconsiders theproblemofcomparison betweendifferent typeso!+steals.hsMr.Thomashassuggested, theheatQominaductstructure iscomplex,butthiscomplexity resultsfromthesuperposition ofanumberofheatBowsanyoneofwhich,duetoaparticular cable,isreadilydeter-minedasindicated inreference 12.Wearenotinterested intheseheatQomsfrcrzc,butonlyintheresulting temperature difference betNreenareference cableandambientandthecorresponding thermalresistance whichisfullyexpressed bytherelatively simpleequationgiven.True,thesituation iscomplicated bytheconcreteenvelope, buthereextensive studies,bothmathematical andonaGeldplotter,in-dicatethattheequation44(A)issufii~cientlyaccurateinviewoftheinherenterrorsinGxingtheearthresistivity andlossfactorinaparticular situation.

Mr.Short,atthestartofhisdiscussion, statesineffectthatheconsiders themethodfordetermining theloadcapability

.ofdirectearth-buried orpipe-type cabletobe"mellfounded"fora100%loadfactorbut,becauseofquestions raisedbyvariousinvestigators inreference 3ofourpaper.doesnotseemtobetoosure,thatthisisthecaseforotherloadandlossfactors.hllfourinvestigators mhoundertooL toitudytheproblemfortheInsuhtedCon-ductorComniittee, however,areonrecordasrecommending oragreeingtothemethodgiveninthepresentpaper.Inaccepting thegivenmethodforburiedandpipe-type cable,Mr.ShortdoesnotseemtorealizethatthismethodisbasedontheKennellyfozmulabecauseinthelatterportionofhisdiscussion hequestions thcapplicability oEthispremisetocurrentratingdetermina-tionsforanytypeofunderground instalh-tion,andproceedstoattempttoresurrect anuinberoftheghostswhichplaguedtheInsuhtedConductor Committee some10yearsagowhenthelatterstartedworL:anacriticalreviewofthebasicparameters involvediuloadcapability calculation.

Theseghostsweresubsequently hidtorest,atleasttothesatisfaction ofthevastnujorityofengineers inthiscountry.EvenatthattimetheKennellyforznuhhadbeeninexistence forover50years.Despitethefactthatthisfozmuiaisbasedonscientific principles foundinmosttextbooksonphysicsandelectrical engineering, somecableengineers hadmisgivings astoitsapplicability mainlybecausecalculations byitdidnotappeartochecLwithmeasure-znentsintheGeld.Thissituation isdis.cussedinreference 12ofourpaperwhereinitisshownthatthedisagreement wasnotduetothefozznulabuttothefactthatthe6eldmeauraaents hadnotbeencarrietoasteadystate,andthatlaboratory determinations oftheearthresistivity werenotrepresentative ofthcsoilinsitu.Also,theappareqtdiscrepancy (whichappearsbecausethcdirection oEheatQowimpliedintheEozmu!aIstowardthesurfacewhereasinsummerthetotalheatQowintheearthisobviausly inthereversedirec-tion)isexplained bytheapplication oftheprinciple ofsuperposition totheseparateheatGeldsinvolved.

Asaresult,cableengmeezs, withveryfemexceptions, haveacceptedtheformulaforcakulations in-volvingpipe-type anddirectlyburiedcablesystems.Themethodofhandlingcablesinduct,giveniathepaper,isalogicalextension ofthepriaciples under-lyingtheKennellyfozmuIainordertoincludeinthecalculations tmoveryim-portantvariables whicharenotapartoftheNELA-IPCEA.method, namelytheduct.configuration andthethermalsistivity ofthesurrounding soB.Thismethodisalsonotnew.ItmasGzstdescribed byN.P.BaBeyiaapaperin1929'ndsubsequently iareference 13ofourpaper.Mr.Shortalsomentionsthetwo-thirds factor,anotherresurrected ghostofthepast.Long'gotheBritishestablished thatthetwo.thirds factorrepresents adiffezence betweenlaboratory andincitsmeasurements ofsoilresistivity andthatitdoesnotstemfromanylackofapplicability oftheKennellyformulatothepzablezn.

NumerousBritishpublications pointoutthatthetmo-thirds factorisnottobeusedwheretheresistivity ismeasuredinsitsbyburiedsphereorbylongorshortcylinder.

Inaddition, inrecentyearstheBritishhavedeveloped anewlaboratory samplingprocedure'hich checksnotonlywiththebuziedsphere,theburiedcylhider, thetransient needle,butinadditionalsocheckswithresultsobtainedonloadedcableinstallations.

Anotherghostmentioned byMr.Shortisthedeepisothermal approach(aproposalwhichmasGrstsuggested byLevyin1930)'iting thedeKus,Sandiford, andCamezanspapertogivenewlifetothisoldsuggestion.

However,insodoingMr.ShortfaBstopointoutthatthedeepIsothermal inthiscaseconsistsofaconducting paintelectrode ofananaloguemodelconnected electricaliy toanotherelectrode representing theearth'ssurfaceandhencesimulating alfrruiing (notstationary) groundwatersink,asomewhatunusualcondition thatisscaredypertinent totheproblemathand.Incidentally, TableIofthispapergivesresultsofanexcellent analogcheckofthegivenmethodasappliedtoaductbank.WewishtoassureMr.Shortthatwehavenotcorneredthenonferrous metalmarket,norarewesaymgthatthreesingle~nductor cablesofagivensizeinsuBedinaburiedpipemusthavethesameratingasthreeconductors ofthesamesizeInstalled inseparateducts.Weshouldpointout,however,thatthishasbeenaruleafthumbforthepast10yearsormoreandtherearenowmanyznilesafhigh.voltagepipecableinsuccessful servicewhichareratedandarebeingoperatedataloadcapability levelwhichMr.Shortconsiders incomprehensible.

Mr.Short'sdilemmaresultssolelyfromOCTOBER1957Nchcr,hfcGratli

-T'crnpcraturc andLoadCapabih.'.;

ofCableSystcrnz771

~-eat'd'ilt otheEactthatheisattempting tocomparether,cultsofcalcrdations madeundera~~~~setofassumedconditions withtheresultsofaprocedure forwhichthosesamecondi-tionsarenotstatedandinfactareunknown.ThisIsasituation whichexistedimme-cHatelyEoHowingthewazandisoneoftheghostspreviously nzentioned.

Conductor sizedeterminations forcableinductutHizfngtheNELAconstants requirenoknowledge norconsideration o!soilre-sistivity assuch.Ontheotherhand.suchdeterminations forpipe-type cablesystemsbyanypractical methodrequireaspeciflcnumericaassumption tobemadeastothevalueoEsoilresistivity inordertoaniveatananswer.Bytakingthestandthattheconcealed resistivity inthcNELAconstants is120oz'ore,iCisthuspossibletoobtain,anadvantage infavorofduct-Iaycable.Furthermore, becauseoEtheuseofcablespacingfactorsandearthandconcretethermalresfstivltles intheproposedmethod,itmillbeobviousthatcalcuhtions bythegivenmethodwillcheckwiththoseoftheIPCEAmethodonlyforcertaincombina-tionsoEthevariableparameters inthemethosLSincetheseparameters werenotGxedandinFactarenow'nknown asre-gardstheNELAductheatingconstants, itisobviously hnpossible tomakeafactualcomparison o!theresultsobtainedbythctwomethods.Hereagain,byassumingearthresistivities oE120or180asbothMr.ShortandMr.WoHastonhavedone,thcgivenmethodwHIresultinhrgerconductor sizesthantheIPCEAmethod.DespitetheFactthatbothMr.ShortandMr.Thomasrefertothepresumably largeamounCofFactualdatawhichunderlietheNELAductconstants, wehavebeenunabletoascertain thespecfflc'conditions onwhichtheseconstants werebasednoristhereanyindication Chatearthresistivity mcaswements weretakenasapartofthedata.AboutaHthatcanbedone,there-fore,Istoassumerepresentative cableandductconflguzations andthentocaIcuhtetheearthresistiviCy requiredinthegivenmethodtomatchthcvaluecalculated bytheIPCEAmethod.Wecannotagreetothevaluesgivenas"theaveragecondi-tionsonwhichtheNELAductconstants

~vereobtained" asstatedbyMr.Short.Rather,vrebelievethattheconditions assumedinreference 18aremuchmorerepresentative, on'thebasisofwhichanaverageearthresistivity of75wasobtainedat100%loadFactor.Wetaketheposition.

therefore, thatthevalidityoftheproposedmethodisnottobejudgedbywhetherornotthecalcuh-tionsmadebyitusingparameters arbi-trarilypickedbyMr.Short(orbyMr.Wolhston) agreewithcalculations madebytheIPCEAmethod.Ratherwefeelthattheapplicability oftheIPCEAmethodtoaparticular casedependsuponhowwellitcheckswiththemethodwhichwehaveproposed, andwhichtakesintoaccountmoreproperlytheessential param-eterswhicharepertineuC tothecaseaChand.WithrespecttoMr.Short'sspeciflcquestion, wehopethatutilityengineers mill,adopttheproposedmethodbutwedonotthinkthattheywillGnditnecessary toreduceloadsunlesstheyhaveveryhighvalueso!earthresistivity.

Regarding theneedforreduction inloadsonexistingdrcuits,iCshouldbekeptinmindthatitisonlyrehtively recentlythatAEICspedflcatfons havemadeprovision EorIncreased permissible temperature HmitsEoremergency periods,andforthegreaterportionoftheperiodthattheseemergency limitshavebeeninefectthenuznberofcompanies whohaveutiHzedthemisrelatively smaH.Asaresult,thegreaterportionoEthecablesnowinservicehave"beensdectedonthebasisthatnormal~permissible coppertemperature wouldnot,beexceededunderemergency conditions.

Moreover, inrecentyearsanumberofasszsframeasurements havebeenmadewiththetzansient needle,thesphere,ortheburiecylinder.

Theoretical studieshaveshownthatmeasurement ofultimatesoilresistivity canbeobtainedreadilyvrithsuchdevices.WhHeinmanycasesthesehavebeenmadeinconnection withpipe-typecableinstalhtions, theyapplyequaHyweHtoductbankinstalhtions insofarastheresistivity o!thesoilitselfiscon-caned.Thevaluesingeneralrangefronz50to100withsomehighervaluesastheexception atcertaintimesoftheyear.Moreover, overthepastdecadeanumberoEpipetypeInstaHatlons havebeenin-staHedinthiscountrywithdesignre-sistivities inthe70to90range.Underthecircumstances, wedonotbelievethatitwillbefoundnecessary inmostcasestoreducetheloadsonexistingcircuits.

However.wedobelievethatengineers millbewelladvisedtotakestepstoascer-tainthevalueio!thermalresistivity whichareapplicable fortheirconditions becausewiththemoreliberaluseofemergency temperature limitsandthetendencyforshiECinmanyareasintheloadpeaLfromwintertosummer,theexistingmarginmaybereducedtoalovrlevelhcthenottoodistantEuture.Thevaluesofsoilresistivity of80and120usedintheexamplesofAppendixIVwerechosenmerelyEorpurposesofiHustra-tionandthevalueof120ratherthan80wasusedinthcductIaycaseinordertoemphasize theeffectofadifference betweentheresistivity o!earthat120andconcreteat85.UnlikeMr.Short,Mr.Wolhstonisverycarefulinhisdiscussion tomakeitquitedearthathiscommentsrelatingtoacomparison oftheresultsobtainedbythegivenmethodandtheNELA-IPCEA methodispreznised onhisownarbitrary assumption ofaconcealed soilresistivity of120intheNELAconstants andonbisimpression, presumably basedhrgclyonanunpublished 1947memorandum byG.B.Shanklin, thataresistivity of180isrepresentative ofaverageconditions; conse-quently,thevalueof55whichwasobtainedbybackcalcuhtion fromthegivenmethodutIHzinghistestresultsindicates adis-crepancyiathemethod.WebelievethatifMr.WolhstonwiHconsultsomcrsofthemanyreferences whichhaveappearedinthetechnical litemture overthepastfewyearsondeterminations ofsoilre-sistivity hconnection withexperimental ductbank,buriedcableandpipe-type cableInstaHations, eitheraloneorinconjunction withburiedcylinders, spheresortransient needles,thathewillGndthatthereisnolongeranyjustiflcatfon foranInferredresistivity oEtheorderof120intheNELAconstants orforhisimpression thatare-osistivity of180isrepresentative ofaverageconditions.

Inasmuchasnoactualmeasurement wasmadeofsoilresistivity atthesIteatwhichMr.WOHastonobtainedanindicated valueof55,thereare,ofcourse,severalpossibleexplanations thatsuggestthemselves.

As-sumingtheternperatur'e measurements wercmadeaccurately.

perhapsthesoilactuallyhadaresistivity ofthisorderofmagnitude.

Fromrecentstudiesonsoilsandtheeffectso!suchmattersascomposi-tion,density,compaction, particlesize,etc.,itIsevidentthatitisverydifGculttoestimatetheresistivity ofasoilfroncappearance alone.Alternatively, itcouldbethatthemeasuredvalueofresistivity isnottheultimatevalueasaconstantloadappliedfor5dayswouldnotsuflicetobringtheductstructure toitsulthnateteznpera-tureriseoverambient,unless,o!course,itbadbeencanyingsubstantially fuHloadforsomethnepriortothetestinquestion.

Mr.Wolhstonmentionsthatthetempera-turewasmeasured20feetfromthenzan-holebutdoesnoCindicatethelengthoftheductzunorfwhichthetestwasconducted.

Thisraisesaquestionastovrhetherinhisparticular case,therecouldhavebeenanyaHeviatioa oftemperature risebylongi-tudinalheatflowor,alternatively.

bylongi-tudinalconvection effectssuchaswereFoundinthetestsmadewithductsopenandplugged.'s psasscss1.HsATPaowrooseUscosaoaoUND EtscralcPowsoCAsass,NeilPBaser,AEEETroarocrroer,voL48.Jao.1020.pp.15&45.2.hNEvAAUAcrosc ovTwoRarrobfavsroos ovhsssssQco zsrsTosaMAlRssrsrsvtvv orSoralW.Marcosrsrd, E.blochrrar rcf./oreer,lascrcncroa olElcccri<<al Eazlacers.

London.Eacland.vol.103,pt.h,no.CZ,Ocz.103d,p.433.3.CAsanHoarrscoUcUscoeaoaoowo DUcrs.R.D.Levy.CcacrerErccrrlcEcvrcsc,Schcncccadrr BLY.,hpr.1030,p.230.4.Seereference 2olMr.Shocc'sdrscnsslon.

SToktoaAcnao RrsoAooCUaaoscvRavncoorCAsassLArn'scDocTszEBoWedrnote>

EEoHorchlass, Rcporr,Rr/rrcrrcc P/Tlos,TheBclrlshElectrical aodhrricdindustries Researchhssoelacloa, Loadoa,Eazla'ad, 1035.""2Ndhdr,sVcGraffi

-7drrrsrrr!Urn crtTer>Crrsntrr:rsr nr/nlnVvrlrmrArvnrsocr1rrX7 THXSPAGEXNTENTXONALLY LEFTBLANK 1~*CeiI0~

F.H.BULLER*-."=J-rH.

NEHERMEM8ErtAlEEMEMEERAIEEONEstepinthecalculation ofunder-groundcabletemperatures involvesthedetermination ofthetemperature riseofthe.cablesurfaceabovetheimmediately surrounding inclosure suchasaductstruc-tureoragas-oroil-flied pipe.Sincetheintervening medimnisaQuid,themodeofheattransfersimultaneously involvesconvection, conduction, andradiation.

Thesemiempirical methodsnowinuseforthisdetermination inthecaseofcablesinductarenotentirelysatisfactory, andvriththeadventofgas-oroil-flied pipe-typecablestherehasarisenadefiniteneedforamethodofevaluation forthesecabletypesasweU.Becauseofthecomplexnatureoftheproblemandthenumberofindependent variables vrhicharepresent,itisimprac-ticaltocovercompletely allpossiblecom-'inations whichmaybemetwithinprac-ticesolelybytests.Bydeveloping atheoretical relationship betweenthevari-ables,however,itispossibletodevelopprocedures bywhichthetestdataavail-ablemaybeanalyzedinsuchawaythatrelatively simpleworkingexpressions maybederivedwhichmaybeappliedwithsuflicient accuracyovertheentireworkingrange.Thetheoretical relationship forthecaseofcablesinductwasrecentlypre-sentedinapaperbyoneoftheauthors.'n thepresentpaperthisrehitionship hasbeenextendedtocoveroilandgaspipesystemsastvell,andfromthetestdatapresented therequisite workingexpres-sionsforthermalresistance orsurfacere-sistivity factorshavebeenobtained.

Theoretical Considerations Thetheoretical rckitionships giveninAppendixIIofreference 1forthecaseofcablesinducthavebeenexpressed morecompletely toaccountforthephysicalcharacteristics ofthemediainvolvedinAppendixIofthispaper.Theresulting equations forthethetherinalconductiv-itybetvreencableandductorpipevrithairorgasastheintervening mediumareQ0.092Ds"/'sT'/'P'/'sT 1,39+Dr/Dd0.0213,+0.102Ds'c(1+0.0167Tm)

IogtsD4/Ds'atts perdegreecentigrade foot(1)andwithoilasthemediumQ,0.053D"/'nT'/T'/s0.116-(oII)',+CsT1.39+Dr'/D4 logisD4/Ds'atts perdegreecentigrade foot(2)ForasinglecableD,'aaDthediameterofthecable.Forthreecablesinthepipeorductitiscustomary tobaseD,'nthecircumscribing circleofthecablesintri-angularconfiguration, D,'m.15D,.FortvrocablestherelationshiP Dsraal.65 D,issatisfactory.

Itwillbenotedthattheprimaryvari-ableinequationIisDrAsaresultsllb-sequentanalysisanddevelopment i>>illbefacilitated ifthisequationiswrittenintheequivalent formQ0.092CsT'/sP/'s'aTDs"/'(1.39+Dr'D4)

,+0.102c(1+0.0167Tm) 0.0213D,'ogD4/Ds'atts perdegreeccntigrad>>

footinch(1A)Fromthemethodofderivation whichassulnesacoaxialarrangement ofthecablewithintheductorpipe,thenumeri-calconstants ofthefirsttwotermsoiequations I,1(A),and2mustbecon-sideredasbeingapproximate only.Theywillserve,however,toevaluatetherela-Btdlcr,iVchcr-ThcrnrcfRcsislancc TheThermalResistance BetweenCables<<s'4v~andaSurrounding PipeorDuctWalltivemagnitudes oftheterms,andthecorresponding valuesfinallyemployedwillbebasedontestdataAsapractical matter,ahighdegreeofaccuracyisnotrequiredsincethethesmalresistivity betvreencableandductorpiperepresents a'relatively smallpartofthetotal.thermalcircuitandwearejustified inmaterially simplifying theseequations.

Fromthestandpoint ofanalysisofthetestdataandthesubsequent develop.mentofworkingexpressions, itisdesir-abletoutilizethesimplelinearrehtion-shipymax+bwhereyandxarevariables andtiandbareconstants.

Equations 1and2areofthisformprovidedthatthesecond(con-duction)andthird(radiation) termsinaybeconsidered asconstants withinthede-siredaccuracyoftheGnalresult.Con-sideringequation1Atheconduction termconstitutes about14percentofthetotalinthecaseofatypicalcableinductin-stallation, andabout8percentforatypicalgas-flied pipe.typeinstallation at200poundspersquareinch.Thecorre.spondingvaluesfortheradiation termare63and43percent.Normalvariations inD,'/Ddmaypro-duceconsiderable variation inthecon.ductionterm,buttheeffectontheover-allpictureissmall,becauseconduction issuchasmallpartofthetotalheatQotv.Variations ofTcanaffecttheradiation termbyasmuchas20percentoverasulliciently wideoperating range;hot>>.ever,whencalcuhting acablerating,withafixedcoppertemperature oftheorderof70degreestoSOdegreescentigrade, th>>rangeofthisvariableisverysmall,andanaccuracyoftheorderof3percenttn>percentmaybeexpected.

Inthecaseofequation2,theconduc.Paper50Sz,reeommcoded bytheAiEElatedCooductors Commsttce aadapprovedtheAlasTcchnical protramCommittee iorpres'otatioa attbchlEEWinterQcacrathfcctinc.

He>>YoA,H.Y..January30.February 3.I93".Sfaauscript subcaitted Octobersl.t949:available iorprioriesDecembery,19t9.F.H.Eot,tcais<<ithtbeGeneralElectricCom'aay.Scbcoeetady.

H.YandJ.H.<<iththephiladelphia Elcetriecompany.Fhna'elphi

~,Pa.AIEETEAishcTtoHs r

Tablel.TestDataonGas-Riled Pip>>TypeCableSystemsTeatItumberSourceQal'/7'/D'rpQa7i'a'7D,"I'able1LTestDataonCableslnRberandTrantlteDuctsEncasedlnConcreteTestItomberSourceQa7'I7'IDlD,'DrQal','al'I 5........Bareoseher........Fiber.......o.d9....3.S

....1.0....d.4.....0.228........1.T4 1.7....11.8.....0.203........2.03 2.5..~.IS.L.....0.235........2.

LT4.4...24.8.....0.25T......

.2.44S.d....34.2.....0.281........2.SS 8.1...39.T.....0.295........2.78 12.3..~.Sd.1.....0.318........3.00 1.13....3.5

....1.0....4.$..~..0.20l~.......1.41 1.7..~.7.1...7.0.207.....

~..1.$94.S..~.Id.3.~...0.248........1.9S 8.0....30.4.....0.233........2.28 11.0..~.32.8.....0.300.

~~.....2.32 14.8....48.S.....0.288........2.82 18.8....$

2.4.....0.28$

........2.dl 18.4....S8.7.....0.278........2.89 3.13....3.5

....0.9....I.d.....o.

194........0.S4 I.T....3.2.....0.173........1.00 2.4....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........1.53 S........Jobos-Matteille....Piber.......s 38~~3SS125ld8~0220~~~~aI5014.9....19.2.....0.230..

~..~a.l.sdLT.S....21.7.....0.238........1.$

9T........Johns-MaosiILe....

Traosite....3.38....3.88....1d.T....18.9.....0.292........1.50 19.8,19.4.....0,299..

....1.$523.3....22.0.....0.314........1.50 2d.4....24.$

.....0.318......

~.I.ditiontermconstitutes about24percentofthetotalforatypicaloilpipeinstallation.

Variation ismoreimportant thanisthecasewiththegas.pipecable,butisstillwithintolerable limits.Onepeculiarphenomenon hasbeenob-served.TheratioofDJDQ',whichap-pearsintheconduction termaIso,ap-pearsinthefirst{convection) tennofequations 1and2butinsuchawaythatachangeinthisratioproducesanoppo-site,thoughlesser,'ffect onthetotalvalueoftheseequations.

Aminimumerrorshould,therefore, prevailwhentheconduction termistreatedasaconstantifthedenominator oftheconvection termalsoistreatedasaconstant.

Thisprocedure willsimplifytheconvection tennbutitwillhavetheeffectofapproxi-matelyhalvingitsnumerical constantascomparedwithequations 1and'2sincethenumerical valueofthedenominator omittedisintheorderoftwo.ActuaUythetestdatCwasanalyzedbothwithandwithoutthissimplification, andnoap-parentchangeinconsistency inthere-sultswasobserved.

AnalysisofTestDataItfollowsfromthepreceding discussion thatthetestdataforcablesinductandforgasfilledpipe.typeinstallations maybeanalyzedbyplottingtheobservedvaluesofQ.CaT'I'pV'~

-'gainstx~(4)DD'II?"DID/DThedatagiveninTableIwerecompiledfromtestsongas.fille pipe.typecablesystemsbyTheDetroitEdisonCom-pany,'heGeneralElectricCompany,I.....Detroit BdlsotaCompaay....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......5.34 28.9...17.1...50....0.49......5.71 28.9...14.4...$L....0.59......$

.4827.5...14.0...51....0.$

8......$.432..~~.CeoeraiBieetrieCompsoy...3.92...8.07...

1,7...73...8.2.,39..0.30...I.d4Il.i".9.T...4$....0.30......1.83 IS.2...12.4...50....0.31......1.73 7.8...8.8...4.7...39....0.37......2.92 11.5...T.0...43....0.42......3.22 14.9...8.9.~.4S....0.43...

~..3.4211.2...5:8...40...;0.49..'.::;4;22

""1$.9.~8.0...4$.~,0.$1~~.~.4.$S3.....Ceoeral CableCorporatioo...4.90...d.07...14.8...2$

.9...9.2...$d...'.0.'ST'.."..'.'.4'.47.

4.....General ElectricCompaay...4.90...8.07...14.8...23.1...11.8...44....0.40......4.77 andtheGeneralCableCorporation.

ThesedataareplottedinFigure1andthevaluesofaandbinequation3areestablished asa~0.0?0;baeOM.TableIIpresentssimilardataforcablesinsingledtyfiberandTransiteductsinconcretetakenfromtheBarcnschera andJohnsManvilletestsdis-cussedinreference 1.ThesedataalsoareplottedinFigure1whereitwillbeseenthattheTransiteductpointsfallonthegasinpipecalve,butthefiberductpointsresultinadifferent curvehavingthesamevalueofa~0.07but5~0.10.Thisdifference maybeexplained bythefactthattheductwalldepartsfromanisothermal asaresultoftherelatively highthermalresistance ofthematerials used,thatofthedlyfiberbeingconsider-ablyhigherthanthatofthetransite.'he testdataforoil-filled pipe-type cablesystemsfromtestsbyTheDetroitEdisonCompany,'he GeneralElectricCompany,andtheOkoniteCompanyarepresented inTableIIIandplottedinFigure2.Inthiscase,theanalysishasbeenmadebyplottingtheobservedvaluesofy~-'itainstx~DQ"i'CaTi'Tea

'5)CDTandresultsinthevaluesofam0.026b~0.60inequation3.Itwillbeseenfromtheanalysisofthetestdatathattheagreement.

betweentheoretical andobservednumerical con-stantsofthesimplified convection termisextremely goodinthecaseofoilasthemedium,butinthecaseofgas,theob-servedvalueof0.07issomewhathigherthantheexpectedvalueofabout0.046.Thisisrathersurprising sincetestsnum-ber2(withgas)andnumber9(withoil)whichareconsistently dosetothees-tablished curvesinFigures1and2weremadewiththesamephysicalsetupwhichremainedunchanged throughout thetestsexceptforthechangeinthemediaemployed.

Therefore, weshouldexpecttheratioofvaluesobtainedtobethesameastheratioofthenumerical con-stantsoftheconvection termsinequa-tions1and2.Thisdiscrepancy seemstobeduetothefactthatinthecaseofseveralcableswithinthepipe,acondition ofthemajor-ityoftestdata,thereisanadditional cir-culationofthegasbetweenthecablesthemselves whichisnotproperlyac-countedforbytheuseofanequivalent diameterforthcthreecables,butwhichisapparently noteffective whenamoreviscousmediumsuchasoilisemployed.

Asindicated before,however,ahighdegreeofaccuracyisnotrequired, anditis1960,VoLUME69Brtllcr,Nchcr-Thcrrrral Rest'slancc 343 R,~4 Tablelll.TestDataonOilFilledpipeTypeCabfcSyslerasS.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..o8.0....40....2.04.

~.~...e194 S.S..~3.0....37....2.19..eo....

$5ll~4~~e4~5...~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.....

~..7021.6...8.8....41....2.45...

~....8$.63$.2...11.4....50....3.00........105 34.9...11.7....48....2.08.

..132feltthataworkingexpression basedontheforegoing analysismillbesufficiently accurate.

WorhingEzpressions

=--'nformulating thethermalresistance betweencableandduct,itiscustomary toexpressthisresistance intermsofanequivalent surfaceresistivity factor,as-sumingthattheentireresistance wasconcentrated atthecablesurface,accord-ingtotheexpression Hgc0.00411-,thermalohmfeet(6)pDg'nwhichpisexpressed indegreescenti-gradesquarecentimeters perwatt.SinceHgc~chT//Qitfollowsfromequation6thatDg'chTp243-degreecentigrade centimeter Qperwatt(7)andv~~L~aKa'(QDg"Tm')'+24feet(ll)Thevalueofpfromequations 9and10isplottedinFigure"3asafunctionof(Q'P/Dg')'

andthe,valueofZ,cfromequationllappearsinFigure4asafunctionon(QD,"T')'.

Alsoindi-catedonthesefiguresarethevalues'ftheseparameters fortypicalconditions.

Inthecaseofcableinfiberduct,thethermalresistance oftheductwallisappreciable andshouldbeaccounted for.Thisismostreadilyaccomplished bymodifying equation6toincludethisre-.sistance.

Thusa7Tost0lrataborSourceD'a04TTol',/doT'/dT

/iFpa'(Gber) 0.00411-,+0.33thernialohmpD,'eet(12)inwhichthesecondtermrepresents thedifference inthesmalresistance betweena4-inchfiberductaadthecorresponding sectionofconcretewhichitreplaces.

Discussion ofValuesforCablesinDuctItwiHbeseenthatthemethodofde-termining thethermalresistance between'ablean'dductpresented hereindifferssomewhatfromthemethodgiveninreference 1,althoughtheresultsaresub-stantially thesameforterracottaandfibreducts.ForTransiteducts,thevaluesofthermalresistancI:

derivedinamorefundamental mannerinthepresentpaper,areslightlylowerthanthoseappearing inthereference, beingequaltothoseassumedforterracotta.itwillbereoaUedthatthereasoniag usedindeveloping eigebraio eapressions forthese,vauesassumesanisothermal duetwall.Thetestdatapresented inFigurc1~Analysisoflestdataforcablesinduct-andgas@liedpipes0pl/tQI/d4T'~0.253-/,(degreescentigrade)'/'8)

Itisthuspossibletodevelopworkingex-pressions intermsofpinthecaseofcablesinduct-orgas-filled pipebysub-stituting equations 7and8inequations 3and4withtheappropriate valuesofoandb.Inthecaseofoil-filled pipeasimplerexpression isobtainedintermsofFI,a.Forcablesinsingledryfiberducts13,700pQ/i/gdegreescen1ip/e~+$7D,'radesquarecentimeters perwalt(9)Forcablesinothertypesofsingledryos~4OsoToR13,700p.,/,,/,degreesccuti-p/'11.3D,'radesquarecciitimclers perwalt(10)Forcablesinoil.filled pipe00ev'r"p,vBullcr,Ãchcr-ThermalRcsisksncc A,lEETR~wsocTlo~s

~Q"aadplottedinFigureI,how->"dicatea.goodcorrelation even4~,thereissubstantial deviation from,@/assumed isothermal asindicated byehi'sicdataonwhichthetableisbased.iliatherangecoveredbythedata,in-'agthedeparture fromtheisother-mchangestheresulting constants some-ha'tbutdoesaotinvalidate themethodlrf."analysis.

'.;.Itfollowstherefore thataconsiderable tioninPforcablesinsingle-fibre

..maybeexpecteddepending upon.Qativethermalresistivities ofthewailand-theisurroundiag medium,'ther.datawhichhascometothe'.atteation confirmsthis.Thus~e'ofFiucts~oulasideredasanulimit.y,theapplication othevaluescafoisingleductstothecaseofcables.;multiduct structure, dependsuponQectwhichthetotalheatfieldhasin'erchangingthetemperature gradi-'tj'i'around theindividual ductwaHs.e.datagivenbySmithiahisdiscussion 7(ence1indicates avalueofpfor'riuitiple-fiber ductsinconcretecorre-"adiagdoselytothecurveforcable~mar:~~peindicated inreference I,addi-aI:.testdatatakenonmultiple-duct bliesaredesirable todefinitdy lishthelimitsundertheseconditions.

'reasonsalsoindicated inreference Ivaluesarenotdirectlycoinparable

'ithevaluesadoptedbytheInsulated ower'Cable Engineers Associations and"aotdirectlyadaptable totheircalcula-oir'procedure, X":nclusioas t":.~Thetheoretical relationships between'variousquaatities involvedintheeQee-,:thermal resistance betweencablesand;surrounding singleductorpipehavebeen'eveloped iaamannerwhichproperly'tsfor'thesimultaneous modesolheatcrbyconvection, conduction, andtlon.I.'Ilymeansoftheserelationships certain0:~.testdataoncablesinductandingas-andod.fiiled pipeshavebeenanalytedandwork.g,curvesare'.presented fordetermining the'resistance loranyparticular case~..maYbeencountered inpractice.

.~j'-'Under typicalconditions representative

.esoftheequivalent surfaceresistivity 4foruseinequationBare800degree,.tlgrade squarecentimeters perwattlorfcs.'npipe,singledryterracottaor,fslteductsatatmospheric

pressure, 450Scabiesingas-filled pipe.typeinstalla-at200poundspersquareinch,and350Iesinoilfillcdpipetypeinstallation.

tativevaluesofISforcablesindryfiberductswillvaryfrom850to100.~..'Vot.vwit GOMfJ,~,'\p80Q.TAppendixl.Theoretical

'evelopment ofThermalCon-ductivity 6etweenConcentric Isothermal Cyclinders withGasorOilasthe!ntervening MediumThemechanism ofheattransferbetweenacylindrical radiatorandanenveloping iso-thernialenclosure throughanintervening QuidmediumissuchthataportionofthetotalheatQowQiscarriedbyconvection Q<<,aportionbyconduction Qrc,andthcre-mainderbyradiarion Qi.lnfOrmuhting thecomponents ofthcthermalcircuit.thcrcfore, itismorcconvenient to<<orkintermsofthermalconductanccs ratherthanthermalresistances sincetheforinerquanti-tiesaredirectlyad<liiivc.

Thus,if3Tisthetemperature dropindegreescentigrade acrossthecircuitQQcrQccQi-+-+-wattsperdegrcccenti-aTaTaTaT'gradefoot(13)Figuic2.Anclysisoflestcfctcforcc6lcsinoil4lfccf pipeThephenomenon ofconvection involvestheconception ofthetemperature dropbeingconccntratcd intwofilms,oneatthesurfaceofthecylindrical radiatorofdiame-tersubstantially equaltothediameteroftheradiatorD,ininches,andoneatthesurfaceoltheenclosing isothermal surfacewhichwillbeconsidered alsobeingcylindrical ofdiameterDc.Thefollowing formulabasedonMcAdams'equation 42,page251,1steditiononly)isapplicable toeitherfilm.Q<<~12"DI'GATI'I'K wattspcrfoot(14)inwhichDIicininches,and/d'cghi'~(--)wattspcrcentimeter

'~'c-(')greescentigrade

'~'15)Thcsignificancc olthecomponents olequation15andrcprcsentativc valueslorgas(airornitrogen) andSunisonumberBoilaregiveninTablelv.Bullcr,IVchcr-ThcnnalRcsisfancc 3400lo'0so40soCo70eo9000nolaol300','T~T gooogIaooTYPICAL,aIOOFCAP<<l81EuILINOUCT51100BLEI~eeoONFIBRFOUC4IIsed/Og+.33 doe243NsdOs~aNOOUCTCABLEINPIPEsEAAACOTTAATAANSITE-1w2$OFcyoa.<<4.$FILLETv'SOPIPE0aooLEINPIPESFIL5.1,TYPICALOfCAPIPEAT200P.2SOs4.$LE204040oogoouolaogoogoogoorgo240Zootaiy,sTs>'AFigure3(left).Valuesolpfoccablesindcysingledgccfsandgao-filled pipeRgure4(above).

YafueoofHgaforcablesinoif-flllecf pipe0x,a,o,alaaaL4aaLe24J.oxa3.43.4s~Ao42fo"P/0;l'*Inthecaseofairorinertgas,thesephysi-calpropesties aresubstantially independent oftemperature overtheworkingrangebutthedensityisadirectfunctionofthepressure.

Thus,ifPrepresents theprcssureinacmospheres, fromequation15Kcaa0.000755P'/'atts percentimeter

'/'egrees centigrade

'/'l6)WhenoilIsemployedasthemediumthcphysicalconstants aresubstantially inde-pendentofprcssureandtempesatures withtheexception oftheviscosity whichforthetypeofoilcornrnonly employed(Sunisonumber6)maybetakenasvaryingin-verselyasth>>cubeofthetemperature ac-cordingtotherehtionship 94,000gramsperccncimetcr second(17)ThevalueofKforoilthusbecomesK~0.000434Teg'/'accs percentimeter'/'egrees centigrade

'/'18)~~ao*x24ao4.4Aa44SO4.2Thesolutionofequation14forthetwo6lmsiaseriesandmithequation16orISsubstituted thereinisgivenwithsufficient accuracybytheexpressions QcrDcdT'/'P'-(gas)m0.092wattspesde-dT1.39+Dc/Dc greccentigrade foot(19)degreecentigrade foot(20)Fromatheoretical standpoint theex.pressionfortheconduction component shouldtakeintoaccountanyeccentricity betweenthecyiindsical radiatorandtheenveloping isothermal enclosure.

Inthepractical caseofcablesinduceorpipethecableswillnotrestuniformly onthebottomoftheduct,andalsointhecaseofanon-metallicducttheductIeafiisnotstrictlymaintained asanIsothermal.

Sincetheseeffectscannotbeevaluated, thefamiliarexpressioa fortheresistance betweentwoconcentric cylinders intermsofthedimen-sionsofthecylinders andthethermalre-sistivity ofchemediummillbeused.ThusQ00213(011CL4LC40gra

-(gas)-'aasperdegreedTloggoDc/Dccentigrade fooc(21)Qcgr.0.116-'goal)-wallspardegreedTloggoDa/Dccentigrade foot(22)Theradiation component withgasasthemediumisgivenwithsufficient accuracybythefollowing expression basedonMcAdamssequation5,page61,GssteditioI),

I0cNIAc~~-(gas)aa0.102Dgc(1+0.0167Teg) wattsd1perdegreecentigrade foot(23)inwhicheistheemissivity coefficient ofthesurfaceofthecableandT<<istheaveragetenlperature ofthemedium.Theradiation termisineffective cohenoilisthemedium.Theover.allthermalconductivity isob-tainedbysubstituting equations 19,21,and23orequations 20and22inequation13.TableIVAppendixILListofSymI3otsSymbolQuaaiityOaaalSOCOllalsOCp...........

Tbcrcasiresiscivicy...........,........C cm/<<atc.......

3900..........

~~.TISga.......e...Average absoluteviscogicy.............grains/cm scc.....,

0.000l95........0.75 a..~........

Deasicy..

.grams/cmg

......,..0.00l'loP.......0.904 Cr.~~~.~~~~~Specificbessaccoascaacpressure......,<<acc see/C.......

~.0.99S~~..~.~....2.IO gragaS...........

Aeeeleratiaa duetOgravity..........

Cm/SCC1...........990.

~~.~~~~~~.990r.s......,

..TIgcrgnal eocil'ieicnt oi~cpaasion........

I/C.......

~~,~~~~~0OOSIO.~~~~~~~.0.00008Q~totafheatfloggrfromequivalent sheathtoductwallorpipeinwattsperfootd7awtemperature dropindegreescentigrade PaaprcssureinatmospheresD,~diameter ofthesheathininchesDc'<<equivalent diacnetcr ofagroupofcablesininchesDa~insidediameterofchcductwallorpipeininchesBuflcr,/I/cIIcr-Tr'crrnal Rcsisfancc 3,IEETILAwsAcTIo85 T~'~averag>>

t>>mperature ofthemediumindegreescentigrade coefficient ofemissivity ofthecable.sur-facerandy~rectanguhr coordinates aandb~>>xperim>>ntally determined con-stantsH,a~thermalresistance betweenequiva-lentsheathandductwallorpipeinther-malohmfe>>tHsa'~equivalent thermalresistance be-tweenequivalent sheathandGbrcductwallincluding theincreased tb>>imalre.sistivity oftheductwalloverthatofthesurrounding mediulninthermalohmfeetJ)~equivalent surfaceresistivity factorindegre>>scentigrade squarecentimeters perwattsI~thermalresistivity in.degrc>>s centigrade cciltlnic'ters pcfwa'tt'verageabsoluteviscosity ingramspercentimeters second8~density ingramspercubiccentisneter C~speciffc heatatconstantpressureinwattsecondsperdegreecentigrade gramgacceleration ductogravityincentimeters persecondsquaredc~th>>rmalcoefficient ofexpansion incenti-meterspercentimeter degreecentigrade

.E~afactordependent uponthephysicalconstants ofthemediuminwattsperc>>ntim>>t>>r'ia degreescentigrade'<<.

aReferences 1,TNRTaxtRRATVRR RIRRotCARO'RsINADvcrBANC,JH.Licker.AlEETransassions, volume08,part1,1049,pages840-40.2.HRATTRAicsaisstoN (book)W,H.Mchdams,htcCsaas.Hill BookCompany,)re>>York.Lc.Y.,dssteditloo,1033.3.TIIRRNAICRARAcraatsTIcsoF A120VvHICII'aessvaa Gas.PIu.ao CARIRlnsTAttATICN,W.D.Sandcsson, J.Sticker,M.H.Mcasath.AlEE1raasassiaas, volumedT,Psst1,1948,pages487-08.4.ASrvorotTKRTaiitaaATvae Dts'salsa Tio'IINEIRcsascCARtasINUaocacRovao Dvcrs,P.J.Baseacches.

T'assis,Depastmeot olElectsical Eagioecsing, Uaivessity olWisconsin (hfadlaon, Wis.),192S.S.CvaaRNTCARRTINoCAFAcITToFLNtaao.NATROPAFSR,RVS~RRANOVARNISKRO CANRRIC1Nsw.ATRo CAaaas.Pablisasion lruaIb<rP2P.Cgd,lasulatcd PoresCableEagineess Association (NcivYork,H.Y.),dsstcditioa,1043.Discussion R.H.NorrisandMrs.B.O.Buckhtnd(Gen>>ralElectricCompany,Schenectady, N.Y.):Eiftci>>nt workintheheat.transfer fieldonavarietyofapplications requiresawareness ofthedefinitions andunits,inorderLoavoidconfusion andmisunder-standing.

Inthispaperandotherpaperswrittenbycableengineers, confusion arisesastoth>>>>acctmeaningofth>>expression "thermalresistivity."

R>>sistivity asnor-mallydeffncd(bytheAmericanStandards Association (ASA)forcxasnple) isaprop-ertyofasubstance andisnotaffectedbyitsgeometry; forexample,theresistivity ofcopperhasaconstantvalueatanyspcciffed temperature, whileitsresistance dep<<ndson,itssiteandshape.Thentheus>>ofthcword"resistivity" forsurfacephenomena isamisuseofthcterra.Toshowho>>Lhcdistinction betweenresistance andresistivity catersintolhcpicture.thethermalcircuitforasingle-conductor cableinairisgiveninFigure1ofthediscussion.

InthisGgure,iso,l,a,andraaretempera-turesofcopper,sheath,andambient.re-spectively, 8isinsulation thickness, pisthermalresistivity ofthcinsuhting

material, sfz,isthelogmeanareaofthefnsuhtion forheatGow,s(saissheatharea,andficandigsarethecabl>>engineers'erms for"sur-faceresistivity" forfreeconvection andradiation.

EachfractioninthcFiguriisthcth>>rmalresistance; andwhenresist-ancesandtemperatures arcknown,theheatdissipation ofthecableisknown.Butinorderfortheresistances tobedimensionally consistent, th>>dimensions ofpmustbediffer-entfromthcdimensions ofl),andtherefore pandffshouldnotbecalledbythcsamenanlcSincethed>>Gnitlon ofpasthermalresis-tivityconformstoASAstandards, itmightbcbettertodenotellasth>>rmalresistance ofaunitsurface.Itsreciprocal h,isde6ncdassurfaceheattransfercoclffcient, oralter-nativelyassurfaceGhnconductance.

Theconceptof~conductance isparticuhrly applicable here,asthetotalGlmconduct-anceisthesumofhrandhc.andtherefore numerically easiertohandle.Theunitsoflengthusedinthepaperseemtobeamixtureofmetricandengineering units.Acombination ofsquarecenti-meterswithfeethasnologicalbasis.Ifanycabledimensions wereexpr>>ss>>d incenti-meters,themixturelvouldbclogicalal-thoughnotstandard; butsincedimensions arenotsoexpressed, itseemstimetoaban-donthispracticeandusetheengineerin systemofunitsthroughout.

Itistherefore proposedthattheAIEECominittee onInsuiat>>d Conductors takestepstop>>rsuadeitsadherents tobecomefamiliarwithASAstandards andtousethem<<heretheyapply.ILW.Burrell(Consolidated EdisonCom-panyofNeirYork,Inc.,NewYorL,N.Y.):Theauthorshavepresented adesirable elaboration ofAppendixIlofapreviouspaperbyMr.N>>h>>r.'lthough theap-proachtotheproblemisuotchanged,thelnaterial presented intheAppendixreferredtoisofsufficient importance tojustifyamoredetailedpresentation.

ILisapparenttothoseengagedinthe6eldofcableheatingthattheInsulated PoirerCableEngineers Association recommended valueofl),whileperhapssufficiently conser-vativeforgeneraldesign,lacksLhcflexibility neededincomparing alternative construc-tions.Precisedeterminations ofig'orvarioustypesofinslalhtions maynoLbepossiblebecauseofinherentvariations inthephysicalconstants involved; however,asadditional testdataarecompiled.

then,AwFlgvsel.'hesinclcircuitfossingleconductor in~isprobablerangeofig,foraparticular case,willbebetterunderstood, Lh>>rebymakingpossiblemorerealistic comparisons.

Theauthorschrifyourconception ofthedfectofthevariousparameters involvedinthetemperature dropbetweencablesurfaceandductorpipewalLForagivensystemofcablesinductorpipe,theth>>rmafresistance willdecreasesensiblywithincreasing wattsloss.W.B.Kirk>>iintroduced thismodiffcation whichistakenintoaccountindetermining cableratingsfortheConsolidat>>d EdisonsystcfnAsonefollowstheassumptions madeinthispaper,thereappearvariouspointstowhichexception.

mightbetaken.onthegroundthattheyarenotsubstantiated, forexampl>>ltheassumption ofthesameconstantintheexpression fortheconvection Ghnat(hecablesurfaceandattheinnerductwall,thetreatment ofconduction onthcbasisofaconcentric system,andthearbitrary assumption ofancmlssivity co->>fffcient ofthecablesurfaceof1.0.Yet,theimportant pointlsthatputtingallofthesevariousassumptions togetherintheparticular formgiveninthepaper,theover-allendresultdoesproduceexpressions whicharereasonably satisfactory.

Itisunfortunate that,whilethebasicequations andtheselection ofparameters hardareasonably soundtheoretical basis,theGnalworkingexpressions givenareessentially empirical anddonotallowanaccuratedetermination oftheseparateeffectofthethreemodesofheattransfer.

Ontheaverage,thecalcuhted valuesofQfcaTfortheoil-6lled pipes,gas-611>>d pipes,andcableinductareabout5percent15percent.and55percenthigher,respectively,thanthemeasuredvahtesgiven'ablesI,II.andIIIofthepaper.Special-istsinthe6eldofcableheatingwouldbeinterested inknowingwhichcomponent orcomponents areresponsible forthesedis-crepancies sothat>>xtrapoLttion intonewGeldscouldbeInadewithconffdence.

Itisstatedinthepaperthattheagree-mentbetweentheoretical andempirical numerical constants ofthesimplified con-vectiontermisdoseforthecaseofanoilmedium,butisoffappreciably forthecaseofagasmedium.Italsocanbcsaidthattheconduction.radLttion constantagreeslviththeoryforthecaseofagasmedium;however,forthecaseofanoilmedium.theconstanttheoretically app>>arstorangefrom0.60,asgiveninthepaper,ton>>arlytwicethatvalue,depending uponthevaluesofD,'andDainvolved.

Fromtheover-allstandpoint, itneverthe-lessappearschattheexpressions forJ)andH,a.asgiveninequations 9,10,and11ofthepaperarequiteworkableandagreewithtestdataaswellascouldreasonably beex-pected.Ahighdegreeofaccuracyinthecalculation ofallowable currentratingsofcablesisnotycttobeexpectedbutimpor-tantworLhasbeendoneinthepastfcwyearsinchrifying ourunderstanding ofheatflowthroughductstluctur>>s andtheearth,andthispaperisanimportant contribution tosuchunderstanding.

RBFBRBNcas 1.Seeselcsence 1olthepaper.2.TK~Caacvaastoa otCaataTallteaafva

~sINSvaw*rDucts.W.B.Xlske.AlEEJoaraal.volume40,1030,paceSSS.1950,VOLUMEG9Bisllcr,iYchcr-Ther>>tnfRcsisfasscc 347 f'a>>lieI~

R.J.Wlseman(TheOkoniteCompanycPassaic,N.J.):Ilikethcauthor'spaperverymuch.Itexplainsthethreemethodsofheatflowfromacabletoasurrounding mediutn,nameiy,conduction, convection, andradlaticn.

Also,theygivethevariousparameters whichinfluenec eachfactornamely,cablediimeter, temperature, andtemperature difference, andviscosity ofthemedium.Thevariousformulaslookquite"formidable whenwenotetermsraisedtofractional powers.Itisnoteasytoobtainthcconstants foreachformuhastheyaredependent oncondicions noteasilycalcuhble soitisnecessary togectestdataandworkbacktonurnerics whichwillgivethede-siredresults.Itsohappensthatasallthreemodesofheattransferarefunccioning atchesametime,achangeindimensioning tendstoworkinoppositedirections, reduc-ingthereby.chc,effect ofdiame(er.

AIsotherangeintemperature isnotgreatandaswetaketheone.fourthpowerottemperature difference andthreefourthspoweroftemperature, thevariation withtempera.tureisnotgreat.Abouttwoyearsagowedecidedtore-studythethermalconstants treobtainedwhenweoriginally setupthcOilostatic cablesystem.Atthattimeweusedthecylindrical logforlnulaofra(ioofinternalpipediatneter tocircumscribed circleovertheassembled conductors, andalsoacon-stantwhichwasafunctionofthetempera-ture.Ourmorerecenttestsshowedchatthethermalresistance wasalmostindependent

~oftemperature (avariation ofabo'ut10percentbetween30and61degreescentigrade) foranoilpressurezoneandaveryfewpercentforagaspressurezoneat200poundspersquareinch.Wcalsonotedthatwithintheaccuracyoftestingwecouldsafelyassumethethermalresistance tovaryasinversely asthediameteroftheshielding tapeovertheinsulation.

Asaresult,wehavesecuptwosimpleformulasforthedetermination ofthethermalresist-anceofchepressurezoneforthreecablesinapipe,namely,foroilpressuresystemH~1.60/Dthermalohmsperfootpercon-ductorwhere,Disthcdiameterininchesovertheshielding tape;andH~2.58/Dthermalohmsperfootperconductor foragaspressurezoneoperating at200poundspcrsquareinch.Youwillflndthesevaluesofthermalresistance forthepressurezonesamplyaccurate.

Astheauthorsrefertothesurfaceresis-tivityfactorP,thevaluesof4comparable tocheaboveconstants inH~0.00411 tt/DareIS390toranoil.pressure systemascora-paredto350givenbytheauthorsandP~827foragaspressuresystemat200poundspersquareinchascomparedto450givenbytheauthors.Wearequtteconfldent inourvaluesandhavebeen'sin'g'theiii foi'overayear.inthepaper,sincethisanalysisgivestheorderofmagnitude contributed byeachofthethreemechanisms ofheattransfer.

Theauthorshaveassumedforcableinductthatthecomponent ofthethermalcon-ductivity ductoradiation canbetreatedasaconstantintherangeofnormaloperating temperatures.

Onlythecomponent ductoconvection wasconsidered asvariablewithchangingcablediameterandheatflow.Thisassumption doesnotleadtoatruepic.tureofthevariation inthermalresis(ivity withheatflow,ormorefundamen(ally, withcabletetnperature.

Mr.Darncttand1havestatedinourpapertthatthedecreaseinthertnalresistivity withincreasing sheathtemperature iscausedprimarily byvaria-tionintheradiation component ofheattransfer, andthattheeffectoftemperature variations onconvection arenegligible overthenormaloperating range..Thisstate-menCisverifiedbycalculations baseduponequation1AoftheHuller-Ychcr paper,whichisrepeatedhere:(qi0.0920,T'/P'i

+(Ih)Di'ciTgDa'(139+Dc/Dd)(convection) 0.0213~t+0.102c(l

+00167T>>t)Di'ogDd/Dc'"dt.)(radiation) inwattsperdegreecentigrade tootinch.Theemissivity factor,c,isassumedtobeunityatattnospheric pressure.

TableIofthediscussion liststworepre-sentative sheathtemperatures fromourtestdataonflberductinconcrete, andthesetemperatures mightverywellberepresent-ativeoftheoperating rangeofacable.Theterm(Q/D,'hT) evaluated inequation1Aisinversely proportional tothesurfaceresistivity factor,tt.Thethreetermsintheequationgivethcthermalconductivity components duetoconvection, conduction, andradiation respec-tively.Asweincreasethesheathtempera-tureovertherangeshowa,theincreaseintheradiation tennproducedbysubstituting ourexperimental dataintheBuller-ocher equationisfivetimesgrezCerthanthatoftheconvection term.Thisshowsthattheexperimentally obsetveddecreaseinttoverthisrangeisdueahnostentirelytothein-creaseintheradiation tetm.Thesecal-culations arebased,ofcourse,ontheratherlargecablesizethatweemployedinourtests.Asmallercablesizewillincreasetheeffectottheconvection termonlyslightly, however,andnotnearlyenoughtomakeitsvariation withtemperature equaltoChatoftheradhtionterm.Identical calculations withourdataonTransitcinconcrete, Transiteinair,andfiberinair,showsimihrrelativevariations intheradiation andcoti-vectionterms.Theauthorshaveneglected thcvariation inradiation component ofconductivity withtempenture, pointingouCthacthesevaria-tionsarequitesmalLThisisjustlfiable fromapractical standpoint.However,thevariations intheconvection component withtemperature alsoshouldbeneglected forpractical considerations, since,asisshowninTable1ofthcdiscussion thisfactorisevensmallerthartthcchangeintheradia-tiontenn.Thiswouldconsiderably sirn-plifytheBailer-Heber equations forthesur-faceresistivity factor.lntheirequations 9and10,(hesurfaceresistivity factor.f4dependsuponthcfourthrootoftheheacflow.Thisdoesnochavemuchsignificancc smceitisbaseduponthevariation inthcconvection tenn,asecondorderelfccccom-paredwiththeradiation term.Similarly thedependence oftiuponthesquarerootofthesheathdiameterisdoubtful, sincechcchangefrom.afourthroottoasquareroocdependence intheconvection termalsowasbasedontheverysmallchangeinconvection conductivity withtemperature.

Theforegoing discussion trasconfinedtocableinductwithairastheintervening fluid.Itsapplicability tocableingas-filled

'pipeathighpressures, whereconvection becomestheprincipal mechanism ofheattranster, requiresfurtherstudy.Theauthorshavedoneanexcellent jobinhelpingcoestablish thetheoretical ground-worknecessary tobothencourage andguideexperimental workersintheductheatingproblem.RBFERENCE l.HearTU*ttsrcx SrvovottPoweaCast.aDvctsattoDvcrAssctcstses.

Pau(Gteeblcr, GU7P.Batoctt.AlZZ7vaatoctioat, rolutoe09,panI,1950,paces$$7-07.Ii'~Irah0riL.~yitcTablel.Gtecblet-Becne((

Da(~tsh.H.Kidder(Philadelphia ElectricCom-pany,Phihdelphia.

Pa.):ThispaperbyBullerandNeher,togetherwithtwopre.viouspapersbyMr.Neher,4tcompletes presentation ofthesteady-state considera-tionsinvolvedinaprojectwhichwasstartedaboutfouryearsagowhenPhiladelphia ElectricCompanyinterested Mr.archerinundertahng aninvestigation offunda-mentalrelationships.'s necessary todc(er-mineapproximately whatpipe.cype cablecircuitloadratingswouldbeaccurately comparable withthcloadratingsofcon-ventional cablecircuitsinducts.Thethermalresistance throughthespacesbetweenthecablesheathsandthepipeorf'uctwallinclosures isanimportant linkinthethermalcircuit.Ithadbeenhoped thatageneralrehtionship couldbedeveloped ini',suchaformthacallofchedifferences bc-'>>~IPavlGreebler(JohnsManvilleCorpora-tion,Manville, N.J.):Inthispapertheauthorshavecontributed imrncnscly to-wardanunderstanding ofthemechanistns ofheattransferfrom(hecabletoicssur-roundingpipeorductavail.Thetheoreti-calanalysiswasnecessarily baseduponthcsimplifying assumption ofacoaxialcableinducearrangetnent.

Thisdoesnot,however,detractfromthcvalueoftheanalysisgivenLeadSheathTemperature CocldeDuctMesoV/allSot(aceTemperature Temperatureullet NehetTemperature EeuatloolADropCooccctlou Radlatloo arTctmTermGteebletBarnettDatattlo'C(cm)'/>>

dd.2...77.2......40.$...........50.$

......5$.0,....,.....0$

.4...~~~ld.l.~...,00dx...o.Ipd....~~.990~..22.0.....,.0 005...0.2ls

~...,..020 loctcaac000$...0.0l5,...,

..00~decreaseTemperatures acclodcrtcccceodetadc.

Thclatldcduct>>attcut(acetemperature lcauavctaeevalue.,'34SBttftcr,/V'cJtcr-ThcrnafRest'stattcc AIEETRANSACTIONS

~'~'~(~q,eSi61~~~

stweencablesinairinductsandcablesinhigh-pressure gasoroil-flied pipescouldbeexplained intermsofthephysicalconstants ichcharacterize therespective fiuidsandoertinent geomctricat relationships.

methodpresented byBullerandhasapproximately achievalthisre-sult,atleasttotheextentofpermitting thecorrelation ofdataobtainedbyvariousin-vestigators atvarioustiinesinvariouscon-'structions.

Itdoesnotdisturbinepar-ticularly tofindthatthereissomeapparentdifference betweentheelectsofTransiteandfiberductwalls,respectively, undertheconditions whichprevailed atthetimethetestsweremade.Ithinkweshouldhesitatetoattachmuchsignificancc totheseappar-entdifferences becausetherewasnoattempttocontrolthemoisturecontentinthcfiberortheTransite, oreventomakethetestsunderconditions comparable tothosetobcexpectedintheusualexposures tonaturalbutvariablemoistureconditions tobcen-countered inunderground structures.

Thesignificant pointisthatBullerandNeherhaveobtainedacorrelation ivhichnowper-mitsestimating thethermalresistance froincabletopipeorductwallwithsufficicut

accuracy, sothatlittle,ifany,practical iinprovement incableloadratingscanbegainedbyintroducing furgherrefinements intheiranalysisofthispartofthethermalcircuit.RspsRBNcss I.TaaTassraa*ruaa RiseorBvaiaoC*n,asAuoPiras,J.HNeher.AlEETroasersioar, olumeil8,pact1,1040,pages0-1T.Scerelcreace 1olthepaper.F.H.BullerandJ.H.Neher:Mr.NorrisandMrs.Bucldandhavetakenussomewhattotaskforourapparent'inconsistency inexpressing ourphysicalunitsinonesystemandourgeometric unitsinanother.Forbetterorworseithaslongbeenthecustomincableratingprocedure toexpressthephysicalunitsinvolvedinthewatt-second-centimeter-gram system,andto~expresslength'sinfeetanddiameters ininches.Indeveloping ourequations itwouldhavebeenmoreconsistent tohaveexpressed thelatterquantities alsoincentimeters, andtheatohaveconverted thefinalexpressions to'hesystemofmeasurement usedinpractice.

Wcchosetousethemixedsystemthrough-out,however,inorderthagthereadermightbeabletouseanyequationinthcdrvelop-ment,directly, withoutencountering theuncertainty whichinevitably arisesastowhetheryoumultiplyordividebythetrans-formation constants.

Theuscofthetarn"surfaceresistivity factor"isaslightlydifferent matter.andasoursncntorshaveyoin]ed.out, ithasdimen-sionswhicharenotthoseoftrue,orvolu-metric,"resistivity."

Hereagain,thisnomenclature hasbeenhallowedbytiincandisthoroughly understood bycableengi~~~neers,forwhomthispaperwaswritten.Itshouldbestressed, however,thatthis"sur-rvceresistivity" isnotafundamental rsicalquantity, inthesensethatvolu-..ctricresistivity is;butaspointedout,istheresistance ofaunitsurfaceofaflinwhich,purelyforpurposesofconvenience, isassumedarbitrarily torepresent theentirethermalresistance ofthecomposite heattransferelectsoperating inther'egionbe-tweencablesheathandductwall.'ltisun-fortunate thatwedonothaveamoredis-tinctivenameforit.Mr.Burrellhaspresented athoughtfuldis-cussionoftheassumptions whichwehavemadeindeveloping thetheoryusedforcorrdating thetestdata.Inthisrespect,abookbyProf.McAdamstgivesaconstantfortheconvection filmonthcoutsideofacylindrical surfaceinafreemediumwhichisabout20pcrcentlowerthanthatforthein-sideofapipeandwhichwehaveusedforbothfilms.Wchavenotdistinguishal be-tweentheLwoconstants becausenoinforma-tionisgivenastothcvaluesofthesecan-stantswhenthecylinderisplacedwithinthepipe.Whileaformulafortheconduc.lioncomponent inanonwoncentric systemisgivenbyWhitehead andHutchings't isfartoocomplicated touseinthisanalysis,

'anditreducessubstantially totheconcentric formulawhichwehaveemployedexceptforextremely smallseparations betweenthecylinders atonepoint.Furtherthereisconsiderable experimental evidencetosup-porttheassumption thattheemissivity constantissubstantially unityforthetypesofcablesurfacesemployed.

Discrepancies wereexpectal, becauseoftheassumptions whichhadtobemade,a'ndbecausethephysicallocationofthecableswithinthepipecannotbecontrolled.

Wehaveusedassumptions andtheoryonlytoobtainasensibleunderstanding oftheproblemwithwhichwehavetodealandtodetermine ivhatsimplifications canjustifi-ablybemadeinordertoobtainpractical worhngexpressions.

Theseworkingex-pressions werethendeveloped directlyfromactualtestsratherthanfromtheory.WedonotshareMr.Burrell's desireforworkingexpressions ofsufficient complexity toidentifytheseparateelectsofthethreemodesofheattransfer.

Dr.Wiseman's simplified formulasforcalculating her(onapercablebasis)forthree'cablesinanoil-flied pipeorinagas-filledpipeat200poundspersquareinchareveryintaesting andsimilarformulasmaybederivedfromFigures3and4ofthepaperassumingthatQ,P,andT~haveGxedtypicalvalues.Unfortunately Dr.Wise-man'sderivation oftheequivalent Pinhisformulasgivesvaluesivhicharenotcom-parabletoPasdefinedinthispaper.Thecorresponding rehtionship forPasdefinedinthepaperishgc0.00411032.15DNandthisyieldsP290fortheoil.pressure systemandP~450forthegas-pressure sys-temWecannotaccepthisformulafortheoilsystemsinceitscorresponding valueonatotalheat'iowbasisis"Hrc"1.15/Dr'hich isequivalent toQ/dT~3.9forDr'4.5.NoaeofthetestscitedinTable~IIIofthepapergivean('upport forsohighavalue.Dr.Wisemanalsoassumesthattheover-allthermalresistance variesinversely withthediameterwhereaswebelievethatamorerepresentative variation maybededucedfromtheslopeofthecurvesofFigures3and4inthevicinityofthetypicaloperatirg points.ThusforQ25wattsperfootandT~50degreescentigrade, wederivethesimplified expressions H,c(oil)~0.70/De"/s thermalohmteeL(I)Hrc(gasat200psi)~1.20/(Dr')'l thermalohinfeet(2)Theconesponding equations onapercablebasisandwiththreecablesinthcpipeare1.442.07hrc~=andhrcm-respectively Qp(D)~sFigures3and4areintendedtogiveprac-ticalworkingvaluesofhceorHrdoverawiderangeofoperating conditions.

Mr.Grecb-lerisrightinpointingoutthattheelectoftemperature variations upontheradiation component isconsiderably greaterthantheeffectofvariations intheconvection tennwhichistheessential variantinFigure3.Theinclusion ofthetemperature ofthcmediuminthcivorkingexpressions wouldvastfycoinplicate them,however,andasapractical matterthisisunnecessary.

InalloftheGreebler.Barnett data'twillbeobservedthatPvariesinversely asQ'/<withintheaccuracyofmeasurement.

Thedependence ofPuponDrcannotbeevalu-atedfromthisdatasinceonlyasinglevalueofD,wasemployed, butsincetheconvection termtheoretically variesdirectlyasQ'/</D'/s webelievethatthetemperatssre variation intheradiation termwhichGreeblerhasmentionedwillbeaccounted forwithsu%cientaccuracybyexpressing theGreebler-Barnett dataforfiberandTransiteductsintheformJi(fiber)

<<1120Ds'/'/Q'/'egrees centi-gradesquarecentimeters perwatt(3)lf(Transite) m990Dr'/'/Q'/'egrees centi-gradesquarecentimeters perivatt(4)Thiswillhavetheelectofchangingtheslopeofthecurves<<henplottedinac-cordancewithFigure3.'hecoiresponding valuesofHrcassuming'worhngvalueofQm10wattsperfootHrc(Gber)m(2.59/Dr'/

)+0.33thermalohmfeet(5)Hrc(Transite) 2M/D,I'hermalohinfeet(8)Whilefurthertheoretical andexperimen-talworkmaywellbeundertaken inordertoclearupsomeoftheapparentdiscrepancies betweentheoryandpracticeandtoyiddmorefactualdataonthcpafonnancc ofcablesinduct;weagreewithMr.Kidderthatlittleofanypractical improvement incableloadratingswillresult.Wedonotwishtodiscourage furtherelortsinthisdirection, butwefeelthatitissufficient tobasecableratingsonFigures3and4ofthepaperormoresimplyonequations (1,2,5,and,8)justgiven.Rspsasscss 1Seeccfcreace 2olthepaper.2,CvaaairrRarsuoorC*ai,asroaTaaNsaussiouauoDisraiavrsou, SeWhitehead, B.EHuichlags.

sourceslastliutioa olElectrical Baciaecrs (toodoa,Eagieod),

volume83,1038.cqueiioa10.3,page531.3.HearTaausraaSrvovoNPorvaaCaai.aDoersauoDoerAssausaas, PaulGreebler, Gusp.Beraeu.AIEETrcareaioas, volume80.pert'1,1030.paCes337-5Z.C.'Dlscussioa brJ.H.Lleherolcclcreace 3~bOvepegCs385~1950,VOL.URIB69Bsdlcr.>Vchcr-Thc.-nsal Ress'starve ATTACHMENT 3TOAEP:NRC:0692DF CABLETRAYALLOWABLE FILLDESIGNSTANDARD e~lp~sirmaoP

~J2.Inalltvpetrays,cablesshallbeplacedinthetravsinaneatworkmanship likemanner.Crossingofcablesshallbeavoided,cableoile-uosshallbekeottoaminimumandcablesshallnotextendabovethetopofthetray.(a)Wheninstalling cablesinapowertayplacetheoowercablesinasinglelayersoacedapproximately 1/3theO.D.(outsidediameterofthecables)apart.SeeFigurel.(b)Thesurmtation oftheO.D.ofthepowercables~shallnotexceed75%ofthetraywidth.SeeTable1formaximumallowable fill.3.Wheninstalling cablesincontroland~strILRoentation trytotalcrosssectional areaofinstalled cablesshallnotexceed40%ofthetravcrosssectional area.SeeTable2formaximumallowable fill.4.Whenitisnecessary toexceedthemaximumallowable fillapprovalfromtheresponsible cableengineerisrequired.

0FORSPACINGOISTAHCEKTWEEHCAMS5EEHOTE5IIZ.MLOWFIGUREfPOWERCABLESPACIAI6NOTES:f.FORCASLESOFEQIALQL,SPACIH6 I&0EILZ.FORCAELESOFUHEOUALCLLSPAQH&ISI/AclL0FLARGER)casLE.~TRAYWIDTHALLOVYABLE FII.I.9TABLEIPOWERTRAYMA1IMUAIFILLTRAYVjIOTNALLOWASLE FIU.HI<&TRAY26.8AI.I.OWAOLi FILI.Ii.HIGHTRAY57.6w<TABLEZ~CONTROL(INSTRUMENTATION TRAYMAXIMllMPILLHoTES:LASTRAYFILLAPPROACHES ITSALLCWA8I~UAIITTHEFIELDSHALL'TAHE NOTEItCAELESAREREACHIH6OVERTHE'SIDES CF'MTiIAY(Eli.OUE TI5POOI4YTTAIHEOCASLES).IFHECESSARY, IMflED,ATITSOWAOISCRETION SHALLINSTALLCoal.TRAYSIOEMAROPERI-Z-EOSC39(POS-.IIII).

Z.INEATREAIECASESoRVIHERESIOEOOAROS c'AHHOTSGIIISTAuZO,&E, FIELO5HAu.INPORMTHE'ELECTRICAI PLANTACTIONTdCLONIC'THCThaY.IND(ANAclIVtCHlGAN ELECT.CO.D.C.COOKNUCLEARPLANTPos-II9I.Oc.LECTRICAI PLANTOESIGNSECTIONREVISION-CI PIANTOESIGNSTANOAROCABLETRAYA<<ONABL==AlAPPOOR.i'.CICH.LIST, IOATH'I-I'-54AM-RIC'NE'RICPC'A'KRS=RVICKCORP.I1EOSgy.QISHIOI.I ATTACHMENT 4TOAEP:NRC:0692DF ANALYSESANDMATHEMATICAL MODELSThisattachment includesthepertinent sectionsofthereportonampacityprogramdevelopment.

Theoriginalreportandthecomputerprogramweredeveloped bytheElectrical SectionteammembersAEPSC,NewYork.

l Vy~APPENDIXATHEORETICAL DEVELOPMENT OFHEATTRANSFERPHENOMENA WITHRESPECTTOCABLEAMPACITYINLOWFILLCABLETRAYSA.lREVIEWOFBASICHEATTRANSFERMECHANISMS Heatenergywillflowthroughorfromabodybymeansofthreedifferent mechanisms:

Conduction istheflowofheatfromapointofhighertemperature toapointoflowertemperature, throughabodyorfromonebodytoanotherbodyincontact,withoutsignizicant molecular movement.

Theequationforonedimensional steadystatethermalconduction forasolidofconstantcrosssectional areaisq=kA-b,TcdXWhere:qkAbT=XConductive heattransfer.

Thermalconductivity AreanormaltoheattransferflowTemperature difzerence Thickness ofsolidConvection istheflowofheatawayfromthesurfaceofaheatedbodybythemotionofthesurrounding fluid(gasorliquid).Whenthemotionofthefluidisproducedmechanically, theactionisknownasforcedconvection.

Whenthemotionofthefluidisproducedbydifferences inthefluiddensityresulting fromtemperature differences, theactionisknownasnaturalconvection.

Theequationforheattransferbymeansofnaturalconvection is:(2)Where:qhcvATssTaConvective heattransferConvective heattransfercoefficient SurfaceareaofthebodySurfacetemperature ofthebodyAmbienttemperature ofthesurround-ingfluid.Anybodyatatemperature greaterthanabsolutezerowillloseheatintheformofradian"energy.Likewiseanybodywillabsorbheatradiatecfromanyotherheatedbody.Thenetexchangeofheatisproportional tothedifference oftheforthpowerofthe'rabsolutetemperatures.

Thenettransferofenergybyraciation fromabodytoambientorfromabodytoasurrounding bodyseparated byanonabsorbing mediumisgivenby (3)Where:q=RadiantheattransferStefan-Boltzmanconstant(=Surfaceemissivity (afactorbetweenzeroandunity,unitybeingaperfectemitter-or "blackbody")A=SurfaceareaofradiatorsAbsoluter temperature ofsurfacesofradiator.

Absolutetemperature ofambientaorofsurrounding body.Inactuality, thetransferofheatwillbetheresultofthesummation ofconductive, convective andradianttransmission mechanisms or:@=a+q+q(4)Where:Q=thetotalheattransferA.2HEATFLOWINCABLETRAYSPresently, IPCEAStandardP-54-440istheindustrybenchmark forcableampacities inopentgptray.MuchofthisstandardisbasedonworkdonebyStolpe.Theampacities presented inthisstandarddependheavilyontheassumption thatthecablesaretightlypackedandthatthereisnoairflowthroughthecablebundle.Thecablebundleistreatedasahomogeneous rectangular masswithuniformheatgeneration.

Basedontheabovecriteria, theallowable wattsperlinearfootofcabletrayisfoundtobeconstantforagiventotalcross-sectional areaofcables(atagivenb,T).Referring tothefundamental equations forheattransferoutlinedintheprevioussection,itisclearthatconductive heattransferisthegoverning heattransfermechanism.

Thatistosay,allowable heatlossisinversely proportional tothethickness (i.e.,cross-sectional area)ofthebodythroughwhichtheheat,flows,foragivenb,T.Whenacabletrayisfilledwithcablestoadepthofonelayerorless,theassumption canbemadethateachcablewil'eexposedtoafreeflowofair.Inthiscasetheabovetreatment ofheattransferdoesnotapply.Forlowcabletrayfills,convective andradiantheattransferarethegoverninc mechanism.

Ifthisistrue,theallowable heatlossperlinea"footofcabletravwill.beconstantforagiventotalsurfaceareaofcablesasperequations (2)and(3)~Tnevalica"ron oftheabovetheorywhichisdeveloped inthenextsect'onisthemajoremphasisofthisdiscussion.

A.3HEATTRANSFERPHENOMENA FORCABLETRAYSWITHLOWFILLTheory:Whenacabletrayisfilledtoadepthlessthanorequaltoonelayerofcables,themaximumallowable heatlosswillbeconstantforagiventotalcablesurfaceareaatconstantaT.Aninitialassumption willbemadethattheabovetheoryistrue.Experimental datawillbeusedtovalidatethisassumption.

Itwillthenbeshownthattheampacityforanycableinthetraymaybefoundbasedontheallowable heatloss.Theproblemwillbesimplified byinitially assumingthatthetraycontainsonlyonesizecableandthateachcableiscarryingthesamecurrent.Inthisanalysis, perunitareareferstoperunitareaofcabletray.Thetotalcablesurfaceareapeiunitareais:A=nTt'dsWhere:Asnd(4)TotalcablesurfaceareaP.U.Numberof3PcablesperunitareaDiameterofeachcableP.U.Thepercentage fillofthetraycanbedefinedasthesummation oftheperunitcablediameters or:F=nd(5)Notetha"thisdiffersfromtheindustrystandardofdefiningpercentage fillbasedonthesummation ofthecablescross-sectional areas.Fromexamination ofequations (4)and(5)itisclearthatthesurfaceareaAwillbeconstantforagivenpercentage fillF.Thetotalheatgenerated perunitareabyresistive heatingofthecablesis:Q=3nIR2(6)Where:QIRacTotalheatgenerated perunitarea.Conductor currenta.c.resistance ofconductor perunitlength.

Rearranging equation(5)n=F/d(7)Substituting inequation(6)Q=-IR3F2dac(8).Solvingforthecurrent(9)or(9a)According totheinitialassumption Qwillbeconstantforagivensurfaceareathatistosay,acertainoercentaae fill.Therefore aplotoflva~dRacforagivenpercentfillahoulcyieldastraightlinethroughtheoriginwithslopeequaltoQ3F.PlotsofIvs.RacareshowninFigureA-1forseveralracewayconfigurations ataconstanttrayfillof67%,.Thisdatawasdetermined experimentally atAEP'sCantonTestLab(seeAppendixC).Aspredicted, theplotsarelinearandpassthroughtheoiigin.Themaximumallowable heatforthistrayfillmaybedetermined fromtheslopeoftheplotsasshownbelow:(10)A.4CALCULATION OFAMPACITYIntheprevioussectionitwasshownthatthetotalallowable heat,Q,wasconstantforagivenpercentage trayfill.Inordertoeliminate hotspotscausedbylocallvintenseheatsources,thisallowable heatgenera"ion shouldbedistributed uniformly acrosstheoccupiedareaofthetray-Thisconceptofuniformheatdistribution isdiscussed indepthbyStolpeinReference 2.However,whereasStolpe'sanalysisrequiredauniformheatdistribution perunitvolume(fortightlypackedcabletrays),thecalculation ofampacityforlowfilltraysisdependent uponauniformheatdistribution perunitareaoffilledtray.

FIGUREA-I700ventilated traywithventilated co600500solidtraywithsolidcoverI400ventilated traywith1hourfirebarriersystem3002001002040I100120 A.4CALCULATION OFAMPACITY(contd).,

FigureA-2illustrates thediffering requirements ofuniformheatdistribution.

AsperStolpe'sanalysisoftightlypackedtrays,sevenOl2cablesoccupythesamevolumeasone4/0cableandthustheheatgenerated bythetwoconfigurations shouldbeequivalent underuniformheatdistribution conditions.

Forlowfilltrays,threeil2cablesoccupythesameareaoftraysurfaceasone4/0-..cableandtherefore mustgeneratetheequivalent totalheat.Adiscussion ofthiseffectontheeffective diameterofthecablegroupisgiveninAppendixB.Keepinginmindtheconceptofuniformheatdistribution andrearranging equation,(8) itcanbeshownthat:d3IR=FQ(ll)ortheheatproducedbytheresistive heatingphasecableisequaltothepercentage oftheheat,Q,asdetermined bytheareathatcableinthecabletrays.ofonethreetotalallo~able

occupies, d/F,Theallowable ampacityofanycableintraycanbecalculated iftheallowable heatisknownforaspecified trayfill,fromequation(9):(9)Thedetermination ofallowable heatforvarioustrayfillsandracewayconfigurations isdiscussed inAppendixB,ComputerModel.

FlGUREA-2effective Equivalent heatsourcesfortightlypackedtraysasperStolpeinReference 2.Equivalent heatsourcesforlot.illcabletravs

~~~.>>aeke~

B.2ProgramDevelopment Theheattransmission ofcablescontained inarectangular trayenclosedwithmultiplelayersoffirebarriermaterialisquitecomplexandextremely difficult tomodel.Therefore, anassumption wasmade:treattherectangular trayandfirebarriersascylindrical sectionswiththeequivalent surfacearea.Initially, thevalidityofthisassumption wasquestionable.

However,becauseoftheexcellent correlation betweencomputerdataandtestdata,.it.is,feltthatthisapproximation issound..Utilizing thepreviousassumption, theprogramwasdeveloped basedontheexcellent workdonebyNeherandMcGrathinreference 3andBullerandNeherinreference 4.Throughout thissection,theconceptof"thermalresistance" and"thermalresistivity" willbeused,thesetermsbeingtheinverseofthermalconductance andthermalconductivity respectively.

Itisofteneasiertovisualize thermalresistance analogous toresistance inanelectrical circuit,withthethermalresistance ofeachmediumbe'nginseries,andwiththeconductive, convective ancradiantresistance actinginparallelthrougheachmedium.AtypicalthermalcircuitisshowninFig.Bl.Theequationforloadcapability asdeveloped inreference 3isgivenbythefollowing equation:

inequation(12)T-(T+~Td)caRd1+7)dccca(12)TcDTddcconductor current(kiloamps) conductor temperature (C)0ambienttemperature (C)00dielectric lossesinconductor (C)D.C.resistance (microhms/f t.)increment ofac/dcratioRcaeffective thermalresistance conductor toambient(thermalohms-ft.)

1cd2cdRlcvR2cvTaR2TT=Q(R+R)c.a12where:Tc~conductor temperature (typically 90C)'a=ambienttemperature (typically 40C)Q=heatenergy(wattsp.u.)1111+-+RlRlcdR3Rl1111+-+22cd2cvR2r(Rinthermalohmp.u,)Intheabovethermalcircuit theconductive, convective andradiantthermalresistance components througheachmediumareaddedinparallel.

Theequivalent thermalresistance ofeachmediumiRlandR2areaddedinseries.FIGURE8-1

'B.2.1Determination ofElectrical Resistance TheD.C.resistance ofaconductor maybefoundfromthefollowing expression:

Rg~=-p<[(r+r)i(c+201]where:p,=electrical resistivity ofconductor (circular MZLOHMS/FTat20C)CI=circularinchareaY=inferredtemaerature ofzeroresistance (C)Thefactor1+Ymaybedetermine iftheac/dcratioisknowncR/Rd=1+I+Y+YP(14)where:Y=increment ofac/dcratioatshieldsY=increment ofac/dcratioatpipeorconduitYwillbezeroprovidedshieldsare'pen-circuited andYwillbenegligable inlightofthefactthatmostcablesinatPaywillbethreephasetwistedconductor.

Therefore equation(14)reducestoacdc1+YcB.2.2Determination ofThermalResistance (14a)Ifshieldandpipelossesareneglected aspreviously discussed, thetotalthermalresistance conductor toambient,Rcawillbethesummation oftheindividual thermalresistances ofeachmedium(i.e.,insulation, jacket,airspace,etc.).Thethermalresistance oftheinsulation maybecalculated bythefollowing 0~012(jlog(Dj/D)where:R.=thermalresistance ofinsulation (thermalohms-ft.)p>=thermalresistivity (C-CM/watt)D.=diameteroverinsulation (IN.)3.D=diameterofconductor (IN.)c(16)Thethermalresistance throughrelatively thincylinders (i.e,cablejacke),tray,firebarrier)maybecalculated fromthefollowing equationR=0.0104nn'D-t,>

3 where:R=thermalresistance ofthesection(thermalohms-ft.)thermalresistivity ofthesection(C-CM/WATT).

n'numberofconductors contained withinthesection.thickness ofthesection(IN.)D'.outsidediameterofthesectionTheheattransferbetweensurfacesseparated bya"dead-air" spaceinvolvesthemechanisms ofconduction convection andradiation.

Eachcorres'ponding t'hermalresistance mastbeaddedinparalleltoobtaintheeffective thermalresistance.

However,inthiscaseitissimpliertotaketheinverseoftheconductances addedinseries.Usingtheequations developed inreference 4:Cd=lcd=0.0213aTlo~go/D'),D'ETDT(17)(18)Cr='2rATwhere:C0.102D'(1+0.016Tm)(19)thermalconductance duetoconduction, convection andradiation respectively (watts/C-ft)respective heatloss(watts/ft)

~T=temperature dropthroughtheairspace(D'outsidediameteroinnersurface(IN.)D"=insidediameterofoutersurface(lb.)P=pressureofair(ATM.)surfaceemissivity ofinnersurfaceT=meantemperature ofairspace(C)0mAtthispoint,someclarification isnecessary concerning theequivalent diameterothecableorcablegroup,theequivalent diameterofa3twistedconductor cableisobtainedbymultiplving theindividual cablediameters by2.15.Thisfactorwillacttoincreasethecalculated thermalresistance whichiswhatwouldbeexpectedduetotheclosespacingofa3TCcable.

4NI~~~

Theeffectivediameterofthecablebundleshouldbeobtainedbymultiplying theeffective cablediameter(orjacketdiameter) bythenumberofthreephasecablesinthetray.ThiswillbeD'hencalculating thethermalresistance oftheairspaceinsidethetray.Theeffectistousethe,cablesurfaceareatocalculate theheatloss,whichisinaccordance withthetheorydiscussed inAppendixA.Thethermalresistance perconductor willbethetotalnumberofconductors dividedbythetotalthermalconductance.

If1atmosphere pressureisassumedthethermalresistance oftheairspacewillbegivenbytheexpression.

n'--'".logD"D')'hethermalresistance fromthelastsurfacetoambient,instillaircanbefoundfromthefollowing equationderivedinreference 3.1[(~T/D"'"+1.6p(1+0.0167Tm)]IIIwhere:D=outsidediameterofoutersurface(21)Aspreviously stated,thetotalthermalresistance conductor toambient,R'illbethesummation oftheindividual thermalresistances thrSugheachmedium.B.2.3Determination ofdielectric lossesFromreference 3:Td=WdRda(22)where:WdW.=dielectric lossdthermalresistivity basedondaindividual thermalresistivities atunitypowerfactor.0.00276E$cosg2logDEJ(23)where:E=phasetoneutralvoltage(KV)(=specificinductive capacitance ofinsulatio.-.

rcosP=powerfactorofinsulation D~i=diameterofinsulation (in.)

I~

Rd,=R,-R./2(24)B.3FireBarrierAmpacityDerating(FBAD2)TheprogramFBAD2wasdeveloped according tothecriteriaoutlinedinsectionB.2.AprogramlistingisincludedinsectionB.4.Whenrunningtheprogramforcablesinventilated traywithcovers,enclosedinFireBarrierMaterialitwasdetermined thatthethermaleffectsofthetraywasinsignificant andcouldbeneglected.

Thisagreed,withtheresultsoftestsatCanton(seeAppendixC).Whenaventilated traywithoutacoverisenclosedinaFireBarriermaterial, thethermalresistance introduced bythetrayisnegligable.

Therefore thetrayshouldnotbeinputasa"layer"intheprogram.Theassumptions usedtodevelopthisprogramrequirethatthetraybefilledtolessthanorequaltoonelayerofcables.Therefore thenumberofcircuitsenteredmultiplied bythecablediametershouldbelessthanorequaltothetraywidth.'Whenentering"N"thenumberoflayers,thecableinsulation andjacketshouldnotbeenteredasalayer.Theprogramisdesignedtoaccountfortheireffect.B.3.1NDataInputThedatarequiredforrunningtheprogramisasfollows:Thenumberoflayersofmaterialenclosing thecable.SeeB.3D(I)Theequivalent diameteroflayerIininches.T(I)S(I)E(I)P(I)Thethickness oflayerIininches.ThedeadairspaceoutsideoflayerIininches.Enter~"1"iftheairspaceisambientair.Note:Enter'1"o~nlforambientair.Theemissivity ofsurfaceI.Theemissivity isanumberlessthanorequalto1,usedtodetermine theradiantlosses,1beingaperfectradiator(blackbody).Seereference 1foradditional information.

Thethermalresistivity oflayerIinC-cm/watt.

0Note:Thevariables D(I),T(I),S(I),E(I)andP(I)shallbeenteredforeachlayerinput.

A~ie~w'J Tl=Conductor temperature inoC.T2=AmbientTemperature inC.P=Electrical resistivity oftheconductor incircularmilohmsperfoot.SeeReference 3.TO=Inferredtemperature ofzeroresistance fortheconductor material.

'eeReferenec 3.V=LinetolinevoltageinKV.El=Specific.-inductive capacitance oftheinsulation.

SeeReference 3.Fl=Powerfactoroftheinsulation.

T5=Thickness ofthecablejacketininches.P5=Thermalresistivity ofthecablejacketinC-cm/watt.

Nl=Thenumberofconductors percable.C=Areaoftheconductor incircularinches.DO=Theconductor diameterininches.DI=Theinsulation diameterininches.Pl=Thethermalresistivity oftheinsulation inC-cm/watt.

A=TheAC/DCratioES=Theemissivity ofthecablesurface.D5=Thediameterofthecableininches.B.4Computerprintout:

FBAD2B.4.lTheprogramFBAD2isstoredintheWarnerComputerSystemundertheaccesscodeforElectrical PlantDesignSection.B.4.2ProgramListing:

• If4 References 1.HeatTransmission, W.H.McAdams.McGraw-Hill BookCompany,NewYork,N.Y.,secondedition,1942.3."Ampacities forCablesinRandomlyFilledTrays,"J.Stolpe.IEEETransactions, Paper70TP557PWR."TheCalculation oftheTemperature RiseandLoadCapability ofCableSystems,"

J.H.NeherandM.H.McGrath.AlEETransactions, Paper57-660.4"TheThermalResistance BetweenCablesandaSurrounding PipeorDuctWall,"F.H.BullerandJ.H.Neher.AZEETransactions, Paper50-52.Appendixl.g5.6."Engineering DataforCopperandAluminumConductor Electrical Cables,"TheOkoniteCompany.OkoniteBulletinEHB-78.Pg.5.gcablesinTraysTraversing Firestops orWrappedinFireproofing,"

O.M.Esteves.ZEEETransactions Paper82JPGC601-3.7."Ampacities CablesinOpen-topCableTrays,"ZPCEA-NEMAStandards Publication.

IPCEAPubNo..P-54-440~Second Edition);

NEMAPub.No.WC5-975.8.9.Industrial HeatTransfer, AlfredSchack,Dr.-Ing.JohnWiley&Sons,Inc.1933.Pg.18TSZresponsetoAEPquestionaire fromMarilynGrautoR.H.BozgodatedSeptember 29,1982.

ATTACHMENT 5TOAEP:NRC:0692DF REPRESENTATIVE AMPACITYDERATINGCALCULATION RESULTS CableTray:1AZ-P8TotalHeatGeneration PerFootofRaceway:Calculated Allowable:

36.98Watts/Ft.

Actual:9.70Watts/Ft.

Connected LoadCalculated 1470R1469R8067R8024R8187R8026R8027R2349R*1476R1488R1991R16666R-23TC412CU3TC412CU3TC412CU3TC412CU3TC412CU3TC412CU3TC412CU3TC412CU3TC412CU3TC412CU3TC42AL3TC412CU3.816.01.21.117.02.71.21.920.060.02.521.5821.5821.5821.5821.5821.5821.5821.5821.58'0.67 21.58*CABLECUTINTRAYANDTAPED Dc-6-F035.92-I.5Zev.5CH&c'.amC).ChBLhrVPaBCpc//p.zpH.P,+W.KVA./'4.7'/r-gBobT~~BoZs8v'goZ6NgOZ7rZ234.5I7@//c///Z./c<c<~-zC/29ci/<C/9rc9C/z3c/2c/z3c/z9c/SC/C2C/crclA/GuD4G6')b+acgu09g092092032032O3c~$203zCu02-092wP2DP092ERsrOT01/)N//RCO0-0/E'//H7uPsCy-RK/7'HCOL,-2/-2/R/PiPge7/7//.//P2//H////P/-PgoPC)8PQI5 CABLENCONDUITCONNECTED LOADCALCULATED ALLOWABLE a2KCI5XESRZBLet+8003R-1*8004R-1*S004G-18026R-18505R-l8506R-,1

<<8003R-2~8004R-2*8004G-28154G-28155G-2+8744R-2+5ZVCABLE4%~4N4H04N4%4N1s1II4w3TC42SH-AL3TC42SH-AL3TC42SH-AL3TC412CU3TC412CU3TC412CU3TCf2SH-AL3TC42SH-AL3TC42SH-AL3TC412CU3TC412CU3TCf2SH-AT57.53.3264.64.2064.64-202.7.0452.6.0422.604257.533264.64.20593-502.60422.6.04271.95.2099.049904990425.8525.S525.85990499.04990425.S525.8599.049.S69.869.864.144.144.149.869.869.864.144.149.86NOTES:1.ALLCABLESARE600VEXCEPTASNOTED.2.CABLEFLA(FUELLOADAMP)ANDMPACITYISGlVZN.INMPS.3.AMBIENTTEMPERATURE WASTAKENTOBE40C

~~

c888E'YPE OiD>~asH,FL8FZPKV8MllM=L2.~ugPHP~PaB.XPP22.dgP9

ATTACHMENT 6TOAEP:NRC:0692DF RESULTSFROMTESTREPORTgCL-542 4

~,CegPageIof~TESTREPORTAmericanElectricPowerServiceCorp.CantonLaboratory P.O.Box487Canton,Ohio44701ltle:AMPACITYTESTFORPOWERCABLESesto.CL-542December16,1983TestBy:L.J.Balanti;J.P.McCallinReportBy:L.J.BalantiApprovedBy:--A.P.LitskybladeFor:AEPSCorp.Sponsor:W.F.Wilson-NewYorkTestCompleted,:November18,1983g0C)Cl0CLEClIZNTRODVCTZON Forcompliance with10CFR50,AppendixRattheD.C.CookNuclearPlant,testswereconducted onpowerandcontrolcablesenclosedinaTSZ,Znc.one-hourfirebarriersystem.Theresultsof-thetestwillbecomparedtocomputer-generated datatodetermine thevalidityofthecomputermodelonheatrunflowandcableampacity.

II.OBJECTIVE go~~4JE0gThetestobjective wastosimulateascloselyaspossibletheactualconditions oftrayandconduitrunsproposedforCookPlantanddetermine thefinalconductor temperature forthespecified amperageandtrayfill.ZII.TESTMETEODThegeneralized testmethodconsisted of:l.Installing cables.2.Attaching thermocouples.

3.Enclosing theTSZfirebarriersystem.4.Applyingthespecified amperages.

5.Maintaining aconstantambienttemperature of400C.6-Monitoring thetemperature riseandfinalconductor temperature.

CopiesTo:T.O.Argenta/B.

R.Larson-CantonB.J.Ware-ColumbusC.B.Charlton-CantonT.E.King-ColumbusS.R.Kekane-Columbus TESTMETHOD(Cont'd.)Thedetailedtestprocedure wasasfollows:Equipment CableTrayandCover1.1.1.Cabletraywasgalvanized steel,expandedmetalbottom;size12"x6"x8'-0"Long.1.1.2.Cabletraycoverwasgalvanized steel,ventilated 12"wide.1.1.3.10'-0Originaltraylengthcutto8'-0"toaccommodate installation inenvironmental chamber.1.1.4.Traycoverattachedtotraybyusing510x3/8"Parker-KalontypeB(Z)with"H"head.1.2.Conduit1.2.2.4"I.D.Galvanized rigidsteel.1"I.D.ThinwallEMT1.2.3.Conduitscutto8'-0"toconformwithcabletraylengthandinstallation inchamber.1.3fireBarrierEnvelope1.3.1.Thermo-Lag 330-1.subliming coatingmanufactured byTSI,Inc.foraonehourbarrier.Thickness ofbarrierwas.500"(+.125",-.000").1.3.2.1.3.3.1.3.4.1.4.Prefabricated panels6'-0"x4.6Prefabricated conduitsections.

':Steelbanding.CablesThefollowing cableswereusedfortesting:324339344348310131023103310431203TC012Cu600V3TCN6Al600V3TCN4Al600V3TC02Al600V3TC14Al5kVshielded3TCN2Al5kVshielded3TC'2/0Al5kVshielded3TCN4/0Al5kVshielded4/C512Cu600V.

~~"1 TestSetup2.1Raceway2.1.1.Cabletrayandconduitweresupoorted aoproximately 2'-6"abovefloortoallowfornaturalventilation.

2.1.2.Racewayendsweresealeddurincthetestwiththermalinsulating materialtooreventheatlossthroughtheseareas.Note:Thisprocedure couldcauseexcessive heatingofthecablespassingthroughthethermalseal;therefore, alltemperature readingsweretakenaminimumof1'-0"fromthethermalseal.2.2TSlOneHourFireBarrierSystem2.2.1.Thetrayenvelopewasconstructed ofthepre-fabricated panels,cutsoastofitasshownintheAppendix(seeFigurefl).2.2.2.2.3Theconduitswereencasedintheprefabricated sections.

Thermocouoles 2.3.1.T-Typethermocouples wereusedtomeasuretempera-turesofthefollowing:

A.AmbientairB.TooandbottomofthefirebarrierenvelopeC.AirspaceintrayD.Conductors.

2.3.2.Thermocouples wereinstalled ontheinwardsideoftheconductor inatriplexarrangement (seeFigure2).Aholewasboredintheinsulation andthethemocouples wereplacedontheconductor.

2.3.3.Thermocouples wereimbeddedinOmegatherm 201highthermalconductivity paste.2.3.4.Thermocouples wereinstalled inapositionlocatedonthecablesinthecente.ofthetraywhere:A.B~Heatgeneration isgreatest.

-:ardissipation istheleast(seeFigure3).

~ty,1'I~s~~

2.3.5.Theminimumnumberofthermocouples usedtomeasuretheconductor temperature wastwo(2)percablecircuitinstalled inthetrayandfive(5)forsinglecablesinstalled intheconduit.2.4.Cables2.4.1.Cableswerepositioned inthecabletrayinasinglelayerinsuchapositionthattherewasaminimumspacingof1/3thediameterofthelargeradjacentcable'.'Cables werethensecuredwith"Ty-Raps".

3.TestProcedure 3.1Eachtestconsisted ofinstalling thecablesinthetrayinoneofsix(6)configurations asspecified inthetestrequest.3.2Oncethepropersetupwasattained, cablesweresubjected toaloadofthreephase,60Hzsinusoidal currentasspecified inSection4~3.3Ambienttemperature wassetto40oC.3.4.Temperature riseofthecableswasrecordedonanEsterline AngusHodelPD-2064dataacquisit-ionsystemat4-hourintervals untilthecabletemperatures stabilized.

3.5.Thevoltageandamperageofeachcircuitwasmonitored periodically throughout thetest.4~TestConfigurations 4.1TestSICircuitNo.ZtemNo.Description RunsinTrayAmpacity3243TCr12Cu324'TCr12Cu3483TC02Al3243TC512Cu3.820.060.00 f4jpIHt 2.3.5.Theminimumnumberofthermocouples usedtomeasuretheconductor temperature wastwo(2)percablecircuitinstalled inthetrayandfive(5)forsinglecablesinstalled intheconduit.2.4.Cables2.4.1.Cableswerepositioned inthecable'tray inasinglelayerinsuchapositionthattherewasaminimumspacingof1/3thediameterofthelargeradjacentcable.Cableswerethensecuredwith"Ty-Raps".

TestProcedure 3.1Eachtestconsisted ofinstalling thecablesinthetrayinoneofsix(6)configurations asspecified inthetestrequest.3.2Oncethepropersetupwasattained, cablesweresubjected toaloadofthreephase,60Hzsinusoidal currentasspecified inSection4.3.3Ambienttemperature wassetto40oC.3.4.Temperature riseofthecableswasrecordedonanEsterline AngusModelPD-2064dataacquisit-ionsystemat4-hourintervals untilthecabletemperatures stabilized.

3.5.Thevoltageandamperageofeachcircuitwasmonitored periodically throughout thetest.TestConfigurations 4.1Testfl3243TC12Cu73243TC~412Cu33483TC~2Al13243TCe~l2Cu13.820.060.00 P

4.2Test02CircuitNo.ItemNo.Description RunsinTrayAmpacity32432432434831203443TC512Cu3TCI12Cu3TC012Cu3TC$12Cu4/C412Cu3TC54Al.17.712.86.86.853.04.3Test43CircuitNo.ItemNo.Description RunsinTrayAmpacity324324312032431203243393393443443483243TCf12Cu3TC$12Cu4/C012CU3TC012CLI4/C012Cu3TC12Cu3TC$6Al3TC56Al3TC54Al3TC54Al3TC02Al3TC012Cu551222111121.712.86.86.816.016.016.036.036.053.060.004.4TestN44.5CableSize:3TCN12Cu600V.ConduitSize:1"I.D.EMIAmpacity:

2amps.Test054.6CableSize:3TC52Al5kVshieldedwithgrounded.

ConduitSize:4"I.D.Galv.rigid.Ampacity:

72amps.Test56oneendCircuitNo.ItemNo.31013102310331043TCV4AlSh.3TCI2AlSh.3TC02/0AlSh.3TC54/0AlSh.20254050

IV-TESTRESULTSThecompletetemperature recordings aretabulated alongwithtestcommentsoncomputerprintouts andlistedunderdatasheetsintheAppendix.

Thefinalconductor temperatures foreachtestarelistedbelow:TestNo.CableAmpacity(ampm)RunsinTrayHighestConductor Temperature (oC)3TCC12Cum3TCC2Al3TC)12Cum4/C512Cu3TCT'43TCN12Cu4/CR12Cu~I3TCe6Al3TCt4Alm3TC52Al3TCC12CU3TC02Al3TCS4Al3TC52Al3TCC2/0Al3TCm4/0Al3.820.060.0.17.712.86.86.853.0.712.8'.816.06.816.016.036.036.053.060.02.072.02025405045.659.755.742.642.745.144.443.958.354.657.960.467.355.2*62.7*57.665.9*57.9*68.863.742.965.045.645.445.544.5*Thermocouple installed oninsulation, notconductor 0

V.DISCUSSION Duetoalimitedsupplyofvariablepowersources,severalcircuitswereconsoLidated.

Inallcases,theloadsweremetorexceededthosethatwereoriginally requested.

Aspertheoriginalrequest,conductors wereplacedinthecabletrayinasinglelayerinsuchapositionthattherewasaminimumspacingofll3thediameterofthelargeradjacentcable.'lthough thisprobablyisnotthebestsimulation ofactualconditions, itwasonecriterion ofthetestrequest.DuringTestf3,theamountofcablesmadeitimpossible tofollowthiscriterion.

ItwasfollowedascloselyaspossibleandtheresultscanbeviewedintheAppendixunder"Photographs".

Allresultscontained inthisreportwereforwarded toW.F.Wilson,NewYork,immediately uponcompletion ofthetest.Anyquestions pertaining totheactualtestresultsascomparedtothecomputer-generated datashouldbedirectedtohim.VI.APPENDIXA.DatasheetsB.TestsetuoC.Photographs.

'vfJ

~~l.)":.)v.)Lc.)5.)G.)7.)Q)9.)18.)11.31:".)1i,~)14.)15.)fE.)COMMENTS-TESTNo.lTEST1CL6~11/Sl/8~IMEIS4:29A.M.STARTA=.785VB=.798VC=.81BViA'~.8AMPSTARTA=.7~2VB=.G57VC=i.82VvALLGGAMPSTARTA='.17VB=i.i4VC='.19V~ALL28AMPCHANNEL~9=AMBIENTCHAN'=TRAYTOP~"=TRAYBOTTQ,,4=AIRN.RAYCHANNEL,E,7.AREONSGAMPCIRCUITCHANNEL5~8APEON28AM.CIRCUITALLOTHERCHANNELSON.8AMPCIRCUITCURRENDA3.9B3.9C~.9'OLTENDA.878B.805C.867CURRENDA59.2B59.5C59.~VOLTENDA.818B.7','1~8"CUP.RENDA28.4B28.:"C28.2.VOLTENDA1~"'8Bf.418Cl.259ENDTESTNfCL-542ff/f/8ZCL-512 1~~

TESTNo.ESTEr~:it1EAl'uGUSDATATINECH..mCHc2CHICCH84CHÃ5CHNSCHN7cH5aaCH".1=.84:28844~85:158c'4cHF:1~8S:4587:1587:458n~ac8no4c89,158Q18~ac'8:4511a~11-4512,15lse~45144l~ic~1c15:4517."19.4on42S.4rsnso&a28.7"8~8."i8.:"85~8.SZ8.9va.1v~a.1~a~<eC';.4'948.448.541.r4841.e41.4~haA[41a141.141.441.S41.E41~4gc41.S41.541."r<<J~ss="8.a~S.54148.741.""48.741.441.942.141.841.F42.14r.541.941.842~4r."41.941.9Ja7r84.1<<an~aCI~I41.E4or~M44.144.S44a845.445a545.S45.845.S4c'45.945.945~a45.945.945.94E25.54,.4.49.5cJar~J55a957o57.858.959.159.1595S.='9.759.u59."59.i59.~ca759.459.5"'5.S'E.444a1951.754.454.95555."c'cJoJ55acc'55.Sc'5c'J.S55a7sr5o74v."4858.44JaraJv.Sc'454.154.154a4.54avc'454aE54a5c'4c'4.S54a554.S54.S54~5<<JoM495~.95F.157.S58.~59.25959.259.s59.J59.259.4.59.559.559.459.459.S59.4c'9c'ccJ~oSo8540c'os~~J41.94v~ar44."44.444.444.744.S44.9li.4.944.9454c'4c4J5a~4c45.~4ic'5.445.425.SZS4.1.'.4r.54-V.J~4:".S4"84444.144.144.~J44.244.'"4444."44.v44."-'4.2erc'Jah~a~~4.5vS.5n42.a84...r4~e~J4J.74".74~.74"v.9444.4.1.44.144.14".944.144.1T<slr=~r7~cia~~C".17CH~18CHUBCH.5CH'CH.7CH.:"CH".6CH~'7CH/s33.84:r884-458c'8c'4c'S:1.5GS-4587-'587:45fpn~1c'na4c'9:158918o15'8~4511:1511ass~gc'a~4c'olcr44~~C~1C~Ce4C're'<<J~eJ"4.SvS.F48.E4ss4n4.14v4..44ero4....4.,~c'".S4..Sc':.S4.E,racc<<Jo~5.SMSa541a44"r.S4<<4v.Sc'".84".74e~~8n4es~Cl444sso8n44,14..99eecJoJ~4.7~rSo741.142.94~.94v.~4io,~S4~.44'.74:".74,,7~84..74r.74/s/74.~.::-:~5.S~94oC'z.a4.14...54v.54~.S4o~c'o~54...7Q4e.~.~7l.-..34..94~.94i~8l4.1<eC.,8,2v5.9~9.944444.444...44.E,4lr..744i44o844.944.844.a44.E44nn4c'4.74i/.38.1vS.148.14..,4.44i44."44.lr.4.S44.744.744.844.744.744.544.744.744.54/sRc'~8~S484nc4".9c'4.844.74c'5.145.445.~45.4Jo45.S4ic';4c;c'.9.av4.S-.n4842.194".'"4'.4n4ss~S4i,74..Sn44.1n4...94".94v.9444.~.9le4ncn<<iJoIJ:"8.Ssr741.14'".444.845.54c5.S45.94i8~'S..~4E.44S4S.-.4F.'8o448sr4.:"7.948.848.4848.='8.441.~~48.848.S48.748.74148.948.748.448.448.848.S48.74a.14CL-54".

1~3a~~~.)4,)-.)C)7~)B.)9.?)'1.)'.)1~,)14)'5.)1B.)7.)1B)Q)2i7i~)~~)24,)'.'7~)~+I)"9.)a8.3~1.)COl'll<<ENTS TESTNo2THERM1AMB-.Ek'Tt'CH~9)THERMr".'OP TRAY'Rllvr'OTOf1TRAYTHE-4AIRSACECURRSTAR:A.28."C.2VOLTSTAR.'~8158~81BC.82BCURRSTARTA.9B.9C.9VO'STAPTA.84B8.848C.85CURRSTARTAG.B8S.BCE.BVOLTSTARTA.4718.478C.558CURRSARTA".BB2.BC~.BVOLTSTARTA.~89B.'"7C.>8ECUR%STARTA5~.885.8C5~.8VQ:STARTA1.5878'.~7BC.B86CL-54"TESTFr'21'/~/B~START8515VOLTENDA.81898.8147C.8.48CL'RENDALL.28AMPVOLTENDA.84BS8.8496C.8559CURCURENDA.B8B.88C.B8VOLTENDA.49S8.58C.S8VOLT"ENDA.:2"8.~5~CVO'ENDA1.57291.4B2C.B~BCUREtlDALL5~.8AMPSENDTEST2CL5621688TIMECH9i1B.2E."'7t2B'7ON='.BA...CIRCUTCH~BON5"A:"lPCIPCUITCHBs7ON:-:'CABLE~S.BAMPCIRCUITCH'8~'QN4/CCABLE~F.BAMPCIRCUITCH17i~EON.17AMPCIPCUCH11~28~25QN.71AMPCIRCUITCL-542 rt~s~a,~It=*~.Wj TESTNo.ESTERLINE ANGUSDATATTtlECHUGCHCHir"CH4CH5CH"6CH7CH-CH-9CH"18CH<<Gc~4cGc-186:4~87-}587-4588-188-45GS189-45}c18411:15ii:451.~~c~oJ1+ro4c1":45'4:451c~ic.9.6VGvG."85v8.8V}v1."='i~V'}o~}.5"}.5v}.4o11~vi~re.7v76.4>>,g4848.448.548.548.748.9414}.148.848.94}.}41~148.841.2v.7>>68'v.4>>9P\484}."41.74}.441.""4}.441.741.941.54}o64>>+41.4~7e>>9v4.='7~6':"9.748.941~84".44~c4~.94".94r.942.94v.14".14V4v."V>>J~4v.649o44~>>~&So~'ho'6.9&7>>57.657>>757o7ceeeC~J8SecwQGoSe.1se.'n>>JVo21.4o4548.541.984..44v44v.94'.94.94>>44444.1444444>>444.12}.8r9,1"4.6.e.448.741.94<.44v.6,~94",844>>144.144.144.144.44444.~4~o84n.9C>>eA~o54~1cccVSoVc656.vc6c56.956.9S6.957oo5757.157.1S7,1err@v8v4>>.9>>euo4841~41.84r.442.64r.94v.142.94V1.4u4>o.erp'e~~~8.4iS.6n>>euoV48.541.64J~~4~.74~.44v.44v.64~.44m>>~64v.74v.64v.7>>rP~vGa4.7v7.9'z948.941.6e42.442.642.542.642.54'642.442.64r.742.7T1i1ECHO}CHN}7CH~18CH-..28CH-..25CH026Chilll7C."t02nvCHOZ6CHOi7CHN'985:45QC~ocu'6:458787:4588:1588:4589:1589:45}8-}5}8:4511:'S':451r-151.2:45}v:}5O~144c15.15oe~~vG.7v94884...'='V.'"4~.74v.84~~~c4>>e~Vn4>>e~V4..64u.9+P'e~>>9cv79.V48.941."41.54}.741.8Cl42.14}o942.142.1"6.1',uo48.641.44(f~42.44r.442.742.74294r,74ro84ro94.4'.29.4i4.5V7>>5v9.4484}o"41..E41.74>>e4'~142.14~4-'.442~1'7~~.4.6'7.648.441.14}.5n4~>>~14r.44-'.44r.44r.4oro"i.56.7"9.542.14>>~r74v.14".54..44:..64...74l>>7n9np~V~:}.441.1,4ro142~74..4".44v44i.54...,74u~4.'.74c.0.4=-e.48o54a.S.~14v.144er4.~.4>e~.9.6"4.6='7748.641~2841.94~4>>r4r.442.442.54r.5oo>>4~~>a7.448.F42.54.".444.144.444>>745.1n4544.944.9n44.845.1.45.1Vdouv~9.64848.648.748.848.548..i48.748.948.748.748.548.748.548.748.748CL-542 r~~'

4~.:5.)E.?7)C)9.)18.)i~.)14.)15.)16.)'7.)1~v'.)19)28.)'r1~))5o)2h)27.)='9.)~3.)'1.)~...?24)u5.)f.:..~..',;-,:..~:t'~sh,(LIiTP>.gtg~Q,PHA'MEL4Rc.YP!ic.'AŽEOflTHEINSU'TION NQTTHLCONDUCTOR CURP,STARTA5~.885~~.8C5".8VOLTSTAR:A.64'.744C.697CURRSTAR:A>E.88~6.8C~6.8VO'.TSTARTA1.581.45C'.6CURRSTARTA2.982.9C=.9VOLTSTARTA.~968.~99C.426CJRRSTARTA16..816.~C16.'OLTSTARTA1.9-782.8.Ci.9m~CUq~cTARTA78869C78VQ'TSTAPTA.Er8-61C6CURRSARTA.98.8C.8YOSTARTA.168.16C.16CURRSTARTA56.8857.=.eVOLTSTARTA.648.E4C.67.7'MPCKT512CHAN'Siii17~252.8AMPCKT-..12CH'S9.18'1262726m91&76.8AMPCKT4/CCH'18'26.8AMPCKT"-'=CH'S~816O'"IPCKT-..6CH'S='24'A~PCKT4/CCH'"2ZZ'6Af"PCKT~12CH'S"E.-'6:"6.8AiiPCKTN4CH'S28~iB==.ef.~PCKT."6CHS-.4,~5.:..8~MPCKT"4CH'5.868.8AMPCKT12CH'S6~7CURRENDA47.482.8C57.7VOL'.c.NDA.6438.692C.712CUR%c.~DA~E,.68~6.7C36.2VOLTENDAi.5981~465C1-687CURP.ENDA2.98~.""C2.9VQLTENDA.4168.414C.441CUR..ENDA16.28'6.~C16.1VOLTENDA~.4882.84C2.26CURRENDA6.786.8C7.8VOLTENDA.5948.628C.67CURRENDA8.988.9C8.SVOLTENDA.11,78.1.2C.1'5CURRENIDA55.E85'.8C55.9VOLTENDA.6"88.585C.697ENDQ.=TESTR~CL-542r'/1'Sv145 YW~'Ls TESTNO.ESTER1ENEANGUSDATAT1'NECHI8CH-..CH0CH4CHCH-"..6CH.7CH-..BCH".9CH"18CH4QC~4C86~1C86:4587:1587-458S:158n~()c89:158945}8-151,8-45}1-1511-45ier~ic:r-45 ~1c1=-.:45C'~~<<JrB.929.129.9u8.4"8.7V8.7>8.8u8~'v<<8<<8>8.6.:"8.4<<reeIQ~u'1.5VE.69."41.14r.664...744.-'4...44<<444.644,644<<544.~44.6u4.1v9.74r.74<<e~ld44,744.5844.945.u4c45.644.845.1>>7o5C~J1J~IJ4r.447.7~rC'e~J'54o2C'C<<JIJC'CJ~IJ55.855.6sJsJ~75>>'755o755.824.v48.458.9c,'761.465.566.767.667.9GB.467.967.667c67.F67.1F7r4.45.45n56.659.468.9Gr.16"Ev.4Gu.7Gv.4Ei.1Gc6sr~<<J62.9Gnn4e<<5a75.~156.759.468.9Er.16".4Gv.6E".4Gv.1F.16u~Gu.12r448.65}.5CQI62.~F4EG.v67.668.869GB.768.u68.468.468.=68.1~8,nu'U~u44.849'r51.854~5JCC'5.455.555.755.655.655.655.629.7%7o74448.558.9c'IJ<<~~5v~55aJ~7c'4S4v54o454~554o554.554.554o5r9<<7o47.558.25}.S5ra65<<re70~J'~u5~.95Z~'9c'<<5u.7TItlECHN}'Hn'15 CH=:7CHN}8Cl-'-'28CH-..riCIJI'P'eCH-..4CHvr25CHr.25CHc'85-'4586:1586-4587e}587-4588:158ne4589:158a:45'8118-4511:1,511-45'-1512-45}u:}514c24.429.8VB48951.uC'JI'W'4.4C'/DC'C<<JsJ~sJ<<JC5a15<<J~a55e1.C'C~e<<J<<J~>>rVG.745.451.8c658.468FG.8FJ8aa68.5eu'i.16'8.961.268uo68.8lC'}.445u47.649.",49.7c8C1C'1<<e}.2C'~<<J51.""C1c124cSo74c49.7C'ee~J~<<J5>>I~754.6C'O';<<J<<J~>>'655o5CC55.6<<J5/~455<<4c'1AG.9c'<<J~eCJ<<e~5555.656.957o>>57ac7457e5c'7c'7.557o<<e57.4r4.41~148.546.8c1~Il'<<~CC'<<J<<J~<<J56.u57.657.757.4c7J/57.4~J7<<eer441.44852545.956.i56e556.755.9c5Q5756.95F.755.7~4.447.751.855occ6r~J<<JouCC'<<J<<J~uC'C<<JmocC5F.1uh5c24~u<<rueu44.44IB.4515='.75u~Na54C'/eC'J>>~54.654.554.654.554o554.524.4r9.4e'.IB<<745.552a5c455.15p.5SDo8C6<<1cC59CQ<<J>>~V'r4.urt45.549.7c'n~<<J54o154o7C'JsJ~<<J5s/e5cEC'/5>><<J~uccn<<J<<J~5<<Je9C'JQsPS7CL-542 ~~~~~1I~~7 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