ML17334B543

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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
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RIGRITYCCELERATEDRIDSPROCESSING)REGULATORYINFORMATIONDISTRIBUTIONSYSTEM(RIDS)ACCESSIONNBR:9505190297DOC.DATE:95/05/12NOTARIZED:NODOCKETIFACIL:50-315DonaldC.CookNuclearPowerPlant,Unit1,IndianaM0500031550-316DonaldC.CookNuclearPowerPlant,Unit2,IndianaM05000316AUTH.NAMEAUTHORAFFILIATIONFITZPATRICK,E.IndianaMichiganPowerCo.(formerlyIndiana&MichiganElePRECIP.NAMERECIPIENTAFFILIATIONDocumentControlBranch(DocumentControlDesk)~)~

SUBJECT:

Forwardsaddiinfo'eThermo-Lagrelatedampacityderatingcalculations,asrequestedbyNRC950306ltr.DISTRIBUTIONCODEA029DCOPIESRECEIVED:LTRENCLSIZE:TITLE:GenericLetter92-008Thermal-Lag330FareBarrier0,'OTES:RRECIPIENTIDCODE/NAMEPD3-1LAHICKMAN,JINTERNANRR/DRPW/PD3-1RGN3~...FILEEXTERNAL:NOACCOPIESLTTRENCL101111111111RECIPIENTIDCODE/NAMEPD3-1PDNRR/DE/EELBNRR/DSSA/SPLBNRCPDRCOPIESLTTRENCL11112211DNi4OTETOALL"RIDS"RECIPIENT:TS:PLEASEHELPVSTOREDUCEKV'iSTE!COYTACTTHEDOCL'ifEYTCONTROLDESk,ROOlifPl-37(EXT.504-~OS3)TOf;LlliflbATEYOL'RiAXIL'ROilDISTRIBUTIOYLIS'I'SI'ORDOCL'5IEi'I'SYOL'OY,"I'ffI'.D!TOTALNUMBEROFCOPIESREQUIRED:LTTR11ENCL10 IndianaMichiganPowerCompanyP.O.Box16631Columbus,OH43216FIMay12,1995AEP:NRC:0692DFDocketNos.:50-31550-316U.S.NuclearRegulatoryCommissionATTN:DocumentControlDeskWashington,D.C.20555Gentlemen:DonaldC.CookNuclearPlantUnits1and2ADDITIONALINFORMATIONREGARDINGTHERMO-LAGRELATEDAMPACITYDERATINGCALCULATIONSTACNOS.M85538ANDM85539ByyourletterdatedMarch6,1995,wewererequestedtosubmitrepresentativeampacityderatingcalculationswithrespecttocablesinracewayscoveredwithThermo-LagusedatDonaldC.CookNuclearPlant.Thecalculationsandmethodologies,includingmathematicalmodels,areaddressedintheattachmentstothisletter.Attachment1providesanoverallsummaryofourampacityderatinganalyses.Attachment2containsthebasisofourmathematicalmodel.Attachment3containscabletrayallowablefilldesigncriteria.Attachment4providesanin-depthdiscussionofthedevelopmentofthemathematicalmodelandanalysis.Attachment5containsrepresentativecalculationresults.Attachment6providesresultsfromtestsusedtoverifytheaccuracyofourcomputermodel.Sincerely,VicePresidentcadAttachmentsASQQjg950519029795051'2PDRADOiK050003i5PPDR jI U.S.NuclearRegulatoryCommissionPage2AEP:NRC:0692DFCC;A.A.BlindG.CharnoffJ.B.MartinNFEMSectionChiefNRCResidentInspector-BridgmanJ.R.Padgett ATTACHMENT1TOAEP'NRC'0692DFSUMMARYOFAMPACITYDERATXNGANALYSES.~-9505190297 Attachment1toAEP:NRC:0692DFPage11.0~BackroundIn'theearly1980's,compliancewith10CPRSOAppendix"R"wasachievedforCookNuclearPlant(CNP)byenclosingcertainracewayswithThermalScienceIncorporated(TSI)Thermo-Lag330-1firebarriers.EnclosingthepowercableracewayswiththeTSImaterialincreasesthethermalresistancetoambientthusrestrictingthequantityofheatreleased,resultinginreducedconductor>>allowableampacity.AlthoughTSImaterialspecificationsaddressedspecificpercentderatingforthecablesintrayandconduitwrappedwithThermo-Lagbarriers,AEPSCtookanaggressiveapproachtoindependentlydeterminethereducedallowableampacitiesanddocumentedthatthefullloadcurrentsforpowercablesintheTSIwrappedracewaysatCNPdidnotexceedallowablederatedampacities.2,0TheoretcaanassMathematicalmodeTheprocessincludedthedevelopmentofamathematicalmodelbasedonthetheoreticalanalysisandworkdonebyNeher,McGrath,andBullerintheirAIEEtransactionspapers57-660and50-52(attachment2).Thisanalysisisbasedonthephenomenaofheattransferwithrespecttoenergizedcablesandtheeffectontheampacity.Thetemperatureratingofacableisthemaximumconductortemperaturethatwillnotcauseexcessivedeteriorationofthecableinsulationovertheexpectedlifeofthecable.Thismaximumtemperaturelimitstheamountofheatwhichmaybegeneratedbyaconductorbyresistiveheatingandthereforelimitstheamountofcurrentthecablecancarry.Enclosing,theconductorwithinlayersofmaterial(i.e.,insulation,raceway,orairspace)increasesthethermalresistancetotheambientheatsinkandrestrictsthequantityofheatwhichmaybetransferredwhilestillmaintainingthemaximumconductortemperature.Theobjectivethenwastodeterminetheallowableampacityofcablesinvariousracewayandfireprotectedracewayconfigurationsbasedontheheattransferthroughathermalresistancewhilenotexceedingthetemperatureratingofthecablesundersteadystateconditions.Thephenomenaofheattransferwithrespecttoenergizedcablesandtheeffectoncableampacitywereexamined.Thi.sincluded:

Attachment1toAEP:NRC:0692DFPage2a)reviewofbasicheattransfermechanics,b)evaluationofpreviousworkdoneintheareasofcableampacityandheattransfer,,c)analysisoftheeffectsofconduction,convectionandradiationwithrespecttoCNPpowercableinstallations,andd)developmentofheattransfertheoryforlowfillcabletrays.Perourdesigncriteria(seeattachment3),thepowercablesinstalledincabletraysarepositionedinasinglelayerwithaminimumspacebetweencablesof1/3thediameterofthelargerad)acentcable.Furthermore,thesumofcablediameterscannotexceed75%ofthetraywidth.Theabovecriterialimitsthenumberofpowercablesinstalledinacabletray,thuslimitingthetotalheatgeneratedperfootandlimitingtheconductorderating.3.0CalculationsAcomputerprogramwasdevelopedaccordingtothecriteriaoutlinedinthemathematicalmodel.TheprogramcalculatestheallowableampacitiesforthepowercablesintheTSIwrappedraceways.Assumingamaximumallowablecabletemperatureof90Candanambienttemperatureof40'C,themaximumallowableheatgenerated(Q)wascalculatedforsteadystateconditions.Theallowableampacity(I)wasthencalculatedusingtheknownrelationshipbetweenQandI.Theanalysisandmathematicalmodelarediscussedindepthinattachment4.AtCNP,thepowercablesinallTSIwrappedracewayswereanalyzedusingthisprogramanditwasdocumentedthatthecablefullloadcurrentsarewithinthecalculatedallowableampacities.Representativecalculationresultsshowingtheallowableampacitiesforthecabletrayandconduitracewaydesignareincludedinattachment5.

Attachment1toAEP:NRC:0692DFPage34.0TestsFinally,aseriesoftestswasconductedin1983atourCantontestlabtoverifytheaccuracyofthecomputermodel.ThesetestssimulatedexactracewayloadingconditionsatCNPanddemonstratedthattheconductortemperaturesfortheTSIenclosed.cablesarewithinthetemperatureratingoftheconductors:.as.predictedbythecomputermodel.Refertoattachment6forthetestreport¹CL-542datedDecember16,1983.Thehighestconductortemperaturerecordedforthesixtestedconfigurationswas68.8'C.Cabletraysandconduitswerebothincludedinthistesting.5.0~ConclusioAtCNP,thecalculationsforthecablesenclosedwithTSIThermo-Lag330-1firebarriersdemonstratedthat:a)theconnectedfullloadcurrentsarewellwithincalculatedallowableampacities,b)thecalculatedheatgeneratedperfootofracewayiswellunderthecalculatedallowableheatgenerationperfootofraceway,andc)theracewaydesigncriterialimitsthetotalnumberofcablesinaracewaysuchthatthecabletemperatureratingsarenotexceeded.

ATTACHMENT2TOAEP'NRC'0692DFAIEETRANSACTIONSPAPERS57-660&50-52

'iy,klJ.*4, M.H.McGRATHi'e~e,haN1932D.M.Simmons'ublishedaseriesofarticlesentitled,"CalculationoftheEIcctricaIProblemsofUndergroundCables."Overtheintervening25yearsthisworkhasachievedthestatusofahandbookonthesubject.Duringthisperiod,however,therehavebeennumer-ousdcvdopmcntsinthecableart,andmuchtheoreticalandexperimentalworkhasbeendonewithavievrtoobtainingmoreaccuratemethodsofevaluatingtheparametasinvolved.Theadventofthepipe-typecablesystemhasemphasixedthedesirabilityofamorerationalmethodofcalculatingtheperformanceofcablesinductinorderthatarealisticcomparisonmaybemaCkbetmeenthetwasystans.Inthispapertheauthorshaveen-deavoredtaextendthevrorkofSimmonsbypresenthigunderonecoverthebasicprinciplesinvolved,togethervrithmorerecentlydevelopedproceduresforhan-dlingsuchproblemsastheeffecoftheloadingcydeandthetemperatureriseofcablesinvarioustypesofductstxuc;turcs.Indudcdaswdlareexpressionsrequiredintheevaluationofthebasicparaxnetersforcertainspecialixedalliedprocedures.Itisthoughtthat,amarkofthistypewiIIbeusefulnotonlyasaguidetoengineersenteringtheGeldandasareferencetothemoreexperienced,butparticularlyasabasisforsettingupcom-putationmethodsforthepreparationofindustryloadcapabilityandaw/d~ratiocompilations.Thecalculationofthetemperatureriseofcablesystansunderessentiallysteady-stateconditions,whichincludestheeffectofoperationunderarepetitiveloadcycle,asopposedtotransienttemperaturerisesduetothesuddenapplicationoflargeamountsoflaad,isarelativelysimpleprocedureandinvolvesonlythcapplica-tianafthetherxnalequivalentsofOhm'sandKirchoff'sLawstoarelativelysimplethermalcircuit.BecausethiscircuitusuallyhasanumberofparallelpathswithheatGamsenteringatseveralpoints,hovrcver,caremust,beexercisedinthemethodusedofexpressingtheheatfomsandthermalresistancesinvolved,anddifferingmethodsareusedbyvariousen-gineers.Themethodemployedinthispaperhasbeenselectedaftercarefulcon-siderationasbeingthemostcansistcntandmostreadilyhandledoverthefullscopeofthepxablan.AlllosseswillbedevelopedonthebasisQONrsandtemperaturerisesduetodielec-triclossandtocurrent-producedlassesmillbctreatedseparately,and,inthelattercase,allheatHorns"miIIbeexpressedintermsofthccurrentproducedlossariginat-inginonefootofconductorbymeansofmultiplyingfactorswhichtakeintoac-counttheaddedlossesinthesheathandconduit.Ingeneral,allthamalresistancesmiIIbedevelopedonthebasisofthepercon-ductorheatQowthroughthem.Inthecaseofundergroundcablesystems,itis'convenienttoutilitcaneffectivethexxnal'esistancefortheearthportionofthcthcxxnaIcircuitvrhichindudestheeffectoftheloadingcydeandthemutualheat-ingcffcctafthcathcx'ableofthcsystem,AllcablesinthesystemwiIIbeconsideredt~ocsrryeeeoieIdedeetieiiteeedtobeoperatingunderthesameloadcyde.Thesystem'ofnomendatureemployedisinaccordancewiththatadoptedbytheInsulatedConductorCommitteeasstand'-ard,anddiffasappreciablyfromthatusedinmanyofthcreferences.ThissystemrepresentsanattempttoutilizeinsafaraspossiblethevarioussymbolsappearingintheAmaicanStandardsAssociationStandardsforEectxicaiQuintities,Me-chanics,HeatandThaxna-Dynaxnics,'andHydraulics,whenthesesymbolscanbeusedwithoutambiguity.Certainsymbolswhichhavelongbeen'usedbycableengineershavebeenretained,eventhoughtheyareindirectconQictmiththeabaveementionedstandards.Nomenclature(AF)attainmentfactor,perunit(pu)As<<cross-sectiohtareaofashieldiagtapeorskidrcire,squareinchesdr<<therznaIdiffhhsivity.squareinchespahourCI<<conductorarea,circularinchesd<<distahhcc,inches'thetc.<<fromceaterofcableno.1tocenterofcableno.2etc.Cks'tc.<<fromcenterofcableno.1toimageofcableno.2etc.Asetc.fromcenterofcableno.1toapoiatoficterfercace$.'.',."!7hetCalculationoftheTemperatureRisean'dLoadCapabilityof'ableSystems~~~3.H.NEHERr.MEMSERdhtlEEeAs'tc.<<frohniaugeofcableno.1toapointofintexfexeaceD<<dhmcter,inchesaqb.oDcdaiasidD,<<OutxideOfCahhduetar~Ds<<outsideofixhsulatioaDs<<outsideofsheathD<<,<<incandiameterofsheathDf<<outsideofjacketDs'<<effective(cixcuxnscribiagcirde)ofseveralcablesincontactDp<<insideofductwal4pipeorconduitDc<<dlaxneteratstartoftheearthportionofthethermalcixcchitDa<<fictitiousdiameteratvrhichtheeffectoflosshctorcommencesE<<linetoneutralvoltage,kilovolts(kv)~<<coefficientofsurfaceemissivitycr<<spccificinductivecapacitanceofinsula-tloa/<<frequency,cyclespersecoadF,Fs,h<<pxxhductsofxatiosofdistancesF(x)<<derivedBesseifunction'fx'TableIIIandFhg.1)G<<geometricfactorGt<<applyingtoinsulatioaresistance(Fige2ofreferexhce1)Gs<<applyingtodielectricloss(Fig.2ofreference1)Ght<<applyingtoaductbank(Fig.2)Iconductorcurrent.kiloampexeskd<<skineffectco?rectionfactorforannuhrandsegxneatalconductorskp<<relativetxanshrexsecoadclc&ityhctoxforcaicuhtingconductorpxoxihnityetfectJ<<hyofashieldingtapeorshdwire,inchesL<<depthofreferencecablebelowearth'schxface,inches.Lv<<depthtocenterofaductbank(ox'ackfill),inches(lf)<<loadfactor,perunit(LF)<<losshctor,perunitrinumberofconductorspercablexs'<<nuxaberofcoaductoxswithinastateddiaxneterN<<numberofcablesorcable'groupsinasystexnP<<perihneterofaductbankorbackfiJI,inchescos4<<povrerfactoroftheinsuhtiontfc<<ratioofthesumofthelossesintheconductorsandsheathstothelossesiathccoaductoxs'Itlc<<ratioofthesumofthelosseshxthecoadchctoxs,sheathandconduittothelossesintheconductorsR<<electricaresistance,ohmsRsc<<dwresistanceofconductorRtotalawresistixhceperconductorRc<<dwresistanceofsheathoroftheparallelpathsinashield-skidvtrireassembly8<<thexxnalresistance(perconductorlosses)thexxnalohm-feet8s<<ofiaschlatioaAf<<ofjacketRhd<<betweencablesurfaceaadschxxoundingendosurePaperST~,recomtaeadcdbTthehIBBInsulatedCoaductorsCommitteeaodapprorcdbTthehIEETcchaicclOperationsPepartmcacforpresentation~cthehlBBSummerCcocrslhfecttae.hfoocreal,Que.,'aosda,Juae24-2S.105T.hfaauscriptsubhoittcdstarch"0,10ST;madearansbteforpriociaxhpril18,10$T.J.If.NausalseectbthephiaadclphtaElec&aCompcor.Philadelphia.Pa..andhf.H.hfcCaamIsreichtheCcocralCableCocporacloo,Pcrthhmbor,¹J.c'Ceher,.VcGrctli-TerrlpercfnrecrxdLoadCcpabilifyojCcblcSystemsQCTCnERlear 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')azfunctionsof~/kFig.q(right),GIfor4ductbankWa~poztiondevelopedintheconductorW,~portiondevelopedinthesheathorshieldW<<portiondevelopedinthepipeorcon-duitWc~portioadeveiopalmthedielectzicX~~mutualreactance,conductortosheathorshield,microhmsperfootY~theincremen'tofaw/dwratio,puYa<<duetolossesoriginatinginthecon-ductor,havingcomponentsYaaductoshnefectandY,jrduetoprox-imityeffectYa~duetolossesoriginatinginthesheathorshield,havingcompobeatsYIaduet'ocizcuhtingcuzrentcffectandYi,duetoeddycurrenteffcctYIr~due'tolossesoriginatinginthepipeorconduitYa~duetolossesoriginatingintheamorGeneralConsiderationsoftheThermalCircuitTHs~~TzoNopTsM2smTzzssRzssThetemperatureriseoftheconducmrofacableaboveambienttemperaturemaybeconsideredasbeingcomposedofatemperatureriseduetoitsownlosses,whichmaybedividedintoariseduetocurrentproduced(PR)losses(hereinafterreferredtomerelyaslosses)inthe,conduc-tor,sheathandconduitb,TaandtheriscproducedbyitsdielectriclosshT4.24~ofductwallorasphaltmasticcoveringR~totalbetweensheathauddiameterDaIncludingRt,RrcandRc~~~R<~betweenconduitandambient.R,'~effectivebetweendiameterDaandambientearthincludingthecffects.oflossfactorandmutualheatingbyothercablesRaa'~effectivebetweenconductorandambientforconductorlossR4r'effcctivetzanslcntthezznalresistanceofcablesystanRca'~cffectivebetweenconductoraadam-bientfordielectriclossRr,I~oftheinterferenceefectRf4~betweenasteampipeandambientearthp~clectricalresistivity,circularmilohmsperfootitthermalresistivity,degreescentigradecentimeterspcz'at'ts~distanceina3mnductorcablebetweentheeffectivecurrentcenteroftheconductorandtheaxisofthecable,inchesS~axialspacingbetweenadjacentcables,inchest,T~thickncss(asindicated).inchesT~tanperature.degreescentigradeTa~ofambientairorearthTa~ofconductorT~~meantemperatureofmediumAT~tcmpaaturerise,degreescentigradeATa~ofconductorduetocturentproducedlosseshT4~ofconductorduetodielectrilosstZTrxr~ofacableduetoextraneousheatsourcerinfaredtanpaatureofzeroresistance,degreescentigrade(C)(usedincorrectingR4,andR,totempera-turesotherthan20C)Vs~windvelocity,milesperhourW~lozsesdevelopedinacable,wattsperconductorfootRATIOLb/PTa-Ta~hT,+4T4degreescentigrade(1)Eachofthemcomponenttemperaturerisesmaybeconsideredastheresult.ofarateofheatflowexpressedinwattsootthrouaermalresistancedinthermalohmeetdegzcescenti-gra0eetperwatt);inotherwords,theQowofonewattuniformlydistributed.overaconductorlengthofonefoot.Sincethelossesoccurat.severalposi-tionsinthecablesystem,theheatBowinthethezznalcircuitwB1increaseinsteps.ItisconvenienttoexpressallheatQowsintermsofthelossperfootofconductor,andthus,,aT,-WgRr+q,R,.+qA)degreescentigrade(2)inwhichW,representsthelossesinoneconductorandRIisthethermalresistanceoftheinsulation,q>istheratioofthesumofthelossesintheconductorsandsheathtothelossesintheconductors,R<<isthetotalthamalresistancebetweensheathandcocdmt,q,istheratioofthesumofthelossesinconductors,sheathandconduit,totheconductorlosses,andRaOerosss1957Nchcr,McGrath-TcrnpcratarcarrdLoadCapabilityofCableSystcrrrs lsthethermalresistancebetweentte<trconduitandambient."Inpractice,theloadcarriedbyacableisrarelyconstantandvariesaccordingtostdailyloadcyclehavingaloadfactor(lj).Hence,thelossesinthecablewillvaryaccordingtothecorrespondingdailylosscyclehavingalossfactor(LF).Fromanexaminationofalargenumberofloadcyclesandtheircorrespondingloadandlossfactors,thefollovringgeneralrda-tionshipbetvreenloadfactorand/lossfactorhasbeenfoundtoexist.'LF)~0.3(tf)+0.7(tf)'erunitInordertodeterminethemaximumtemperatureriseattainedbyaburiedcablesystemunderarepeateddailyloadcycle,thelossesandresultantheatflowsarecalculatedonthebasisofthemaxi-mumload(usuallytakenastheaveragecurrentforthathourofthedailyloadcycleduringwhichtheaveragecurrentisthehighest,i.e.thedailymaximumone-houraverageload)onvrhichthelossfactorisbasedandtheheatQowinthelastpartoftheearthportionofthethermalcircuitisreducedbythe"factor(LF).IfthisreductionisconsideredtostartatapointintheearthcorrespondingtothediameterD'quation2becomest2TcWc(lt+qc~tc+qc(~cs+(LF)@c)ldegreescentigrade(4)Ineffectthismeansthatthetempera-turerisefitomconductorto'>ismadetodependontheheatlosscorrespondingtothemaximumloadvrhereasthetempera-turerisefromdiameterDctoambientismadetodependontheaveragelossovera24-hourperiod.StudiesindicatethattheprocedureofassumingafictitiouscriticaldiameterD>atwhichanabruptchangeoccursinlossfactorfrom100%toactualwillgiveresultswhichverycloselyapproximatethoseobtainedbyrigoroustransientanalysis.Forcablesorductinairwherethethermalstoragecapacityofthesystemisrelativelysmall,themaxi-mumtemperatureriseisbasedupontheheatGowcoizespondingtomaximumloadvrithoutreductionofanypartofthetheimalcircuit.Whenanumberofcablesareinstalleddosetogetherintheearthorinaductbank,eachcablewQIhaveaheatingeEectuponalloftheothers.Incalculatingthetemperatureriseofanyonecable,itisconvenienttohandletheheatingetfectsoftheothercablesofthesystembysuitablyinodifyingthelasttermofequatiot4.Thisispermissiblesinceitisassuinedthatallthecablesare,carryingequalcur-rentsandareoperatingonthesameloadcycle.ThusforanP-cablesystemaTcWc(A+qc~cc+qcfffcc+(LF)X(Bcc)+(N-I)N¹I)(5)Wc(lt+qcIcc+qcRc')degreescentigrade(Sh)wherethetenninparenthesesisindicatedbytheetfectivethamalresistance8c'.Thetemperatureriseduetodielectriclossisarelativelysmallpartofthetotaltemperatureriseofcablesystemsop-eratingatthelowervoltages,butathighervoltagesitconstitutesanappre-ciablepartandmustbeconsideretLAl-thoughthedielectriclossesaredis-tributedthroughouttheinsulation,itmaybeshownthatforsingleconductorcableandmulticonductorshieldedcablewithroundconductorsthecorrecttemperaturerisetsobtainedbyconsideringfortran-sientand-steady.statethatallofthedielectriclossWttoccursatthemiddleofthethermalresistincebetweenconduc-torandsheathoraitentateiyforsteady-stateconditionsalonethat'thetempera-turerisebetweenconductorandsheathforagivenlossinthedielectricishalfasmuchasifthatlosswereintheconductor.Inthecaseofmulticonductorbeltedcables,howevertheconductorsaretakenasthesourceofthedielectricloss.'heresultingtemperatureriseduetodielectricloss42'ttmaybeexpresseddTtt~Wit's'egreescentigrade(6)inwhichtheeffectivethermalresistanceib'isbasedupon/It,8,and)4'(atunitylossfactor)accordingto.theparticularcase.Thetemperatureriseatpointsinthecablesystemotherthanat.thecon-ductormaybedeterminedreadilyfromtheforegoingrelationships.THBChiA'-UthTio)4opLohnChPhnan)rfnmanycasesthepermissiblemaxi-mumtemperatureoftheconductorisGxedandthemagnitudeoftheconductorcurrentgoadcapaMity)requiredtoproducethistemperatureisdesiretLEquation5(A)maybewrittenintheformATc~I'24c(I+yc)lcc'egreescentigrade(7)iwhichtheqqaatity~lb,(1+Y,qhiehillbeevuatereresentstheeE'veelectnresistanceofthecon-ducto'nhmsandwhichvrhenmultipliedbyP(Iinkiloamperes)vrillequalthelossWcinwattsperconduc-torfootactuallygeneratedintheconduc-tor;and8ec'sthee(fectlvethermalresistanceofthethermalcircuitfIcc'IIt+qc8cc+qcffc'hermalohm-feet(8)FromequationIitfollowsthatI+lciloameres3a,<I+I;)~.Ta6leI.ElectricalResbtlvityofVariousMateriabbtaterlclPCheaterMllOhmsperFootat20Cr,CCopper(100%IhCS')~~~~~~~~10.371.....234.SAluminum(81%IhCS).e,~17.002.~.~.228.1CotcmerelctBronte(43.8%~~.23.8~~~~.584IhCS)(90Cu-10Zo)Bta$5(2T.3%IhCS)~~~.~..~~~38.0~~~~.912(0Cu-30Zu)Lead(7.84%cIhCS)...~.~...132.3.~.~.238~Isterssuoudhoaeale4CopperStaodanLCalculatioaofLossesandAssociatedParameters37.9Rc~-'orIesdat50CDctttt(IIA)4~-for61%aluminumat50,CDg1(IIB)vrhereDctttisthemeandiameterofthesheathandttsitsthickness,bothininchesDccq~Dctlaches(12)TheresistanceofintercalatedshieldsorskidwiresmaybedeterminedfromtheexpfcsstOQrpcSDtetR,(pe:path)-)I+(-)microhmsperfootat20C(13)whereA,isthecrosssectionareaoftheGac~Tio)iCFDNRBsisThNcxsTheresistanceoftheconductormaybedeterminedfromthefollowingexpressionsvrhichincludealayfactorof2%;seeableL1.02pcmicrohmsperfootat20CCI(IO)12.9for100%IACScopperCIconductorat76C(10A)212~-for61%IACSCIalumlautnat75C(IOB)vrhereCIrepresentstheconductorsizeinCircularinCheSandVrherePcrePreSentStheelectricalresistivityincircularmilohmsperfoot.TodeterminethevalueofresistanceattemperatureTmultiplytheresistanceat20Cby(r+T)/(r+20)whereristheinferredtemperatureofZeroresistance.TheresistanceofthesheathisgivenbytheexpressionspcR,~-mlcrohmsperfootat20C(II~4DccttKdhdr,hfcGra!h-TerripdratnrdandLoadCapabilityofCcbfeSys.'crrtsQcToBBR19o<

s~~'~tapeorsl.idwireandlisitslay.Theover-all':esistancc,oftheshieldandskidrwireassembly,particularlyfor.noninter-calatedshields,shouldbedeterminedbyJectricalmeasuremcntwhenpossible.C~L.ctfuTioHoFLossllsItisconvenienttodevelopexpressionsforthclossesintheconductor,sheathandpipeorconduitintermsofthecomponentsoftheaoc/docratioofthecablesystemwhichmaybeexpressedasfollowslr(wRCIRcc1+Yc+Ys+Fp(14)Theaoc/docratioatconductoris1+YcandatsheathorshieldisI+Y,+YsandatpipeorconduitisI+Y,+Ys+YpThecorrespondinglossesphysicallygen-eratedintheconductor,sheath,andpipeareWsIRcs(l+Yc)wattspcrconductorfoot(IS)WsPRccYswattsPerconductorfoot(16)Wp~I'24cYpwattsperconductorfoot(17)'cisj>>Il.RecommendedValuesofk,cndksConductorConstrucuonCostingonSaendsTreatmentLroConcentricround,.............Hone.....~~.~~.~...".Noae..............l.o.....~.......1.0Concentricround..............Tloorenoy........~.~.None..........~...1.0........~....1.0Concentricround..............Hone.~...............Yes...............l.o.....~.......0.80Compactroundo~Noae~~~Yes~~~I0~~~~~00Compactsegmental.......,....Hone..................Noae..............0.43$.............0.0Compactsegmental............TinoraUoyooHone....O.S.~..0.7Compactsegmental............Hone..................Yes...............0.43$.."...~.....0.37Compactsector................Hone...............~..Ycs...............l.o.............(secnotc)Horns:1.Theterm"treated"denotesacompletedconductorwhichhasbeensubjectedtoadrylogandlmpregnatlngprocesssimaertothatemployedonpaperpowercahte.2.Proximnyedectoncompactsectorconductorsmaybetahenasosehalfofthatforcompactroundhaving'thcsamecrossscctlooslareaasdLnsutsuonthtchncss,3.ProximityCUcctonannulareooductorsmaybeapprodmstedbyusingthevalueforaconcentdcroundconductorofthesamecross-cctfsnnsLareaandspadng,Thelocresseddiameteroltheannulartypeandtheremovalofmetalfromthecenterdecreasestheshineifcctbut,foragivenadslspsdng,tendsto.resulttnanlnaeaselnproximity.o4.ThevalueslistedaboveforcompactscgmentslrefertofoursegmentconstructtooaTheuocoatcdtreated"valuesmsyalsobetahcnasapphcabi~tofoursegmentcompactsegmentalwithhoaowcore(approximately0.7$inchdear).For"uncoatedtreated"sixsegmenthouowcorecompactsegmentallimitedtestdatalodicatcskoandkpvaluesofOAandOArespectively.Tabl>>III.SkinEffectfn%inSolidRoundConductorlndinConventionelRoundConcentricStr4ndConductors100F(x),SkinEffectfo345d7d9hispermitsareadydeterminationofthelossesifthesegregateda-c/docratiosareknown,andconversely,theaoc/docratioisreadilyobtainedafterthevaluesofYcsYsandY<havebeencalculated.ItfollowsfromthedefinitionsofqsandqcthatWc+WCYcqswm]+Wc1+YcWc+WC+WpYr+Ypqci+-We1+Yc(18)(ip)ThefactorY,isthesumoftwocompo-nents,YmduetoskneffectandY,pdueproximityeffect.Wc~lsRefc(1+Ycc+Ycp)wattsperconductorfoot(20)(21)xs~0.875-~-at60cycles$RccQRcr/ks(22)inwhichthefactorhsdependsupontheconductorconstruction.ForconventionalconductorsancttonF(x)mayotatneomTable'IIorfromthecurvesofFig.1intermsoftheratioRs,/hat60cycles.Forannualconductorssolidor~SrrotnateeILThe,(2$)invrhichD,andDsrepresenttheouterTheskinetfectmaybedeterminedfromtheskineffectfunctionF(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..andinnerdiametersoftheannularcon-ductor.IncomparisonwiththerigorousBcsselfunctionsolutionfortheskineffectinanisolatedtubularconductor,ithasbeenfoundthatthe60~cleskineffectofannularconductorwhencomputedbyequation'23willnotbeinerrorbymorethan0.01inabsolutemagnitudeforcopperoraluminumIPCEA(InsulatedPowerCableEngineersAssociation)SledOcTOUUR1957%cher,.lfcGrcfh-T~n(pcrc]nrcandLoadCapabilitypfCnbtcSysfcfns7M

6as~I~Ta6I>>IV.MutualReactancea160CyeiessConyfudoeloSheath(orShlelsf)D~/28--0123455T896(2S/D~)asinthecaseofleadsheaths.<<~--1+--'t'Ij'I~tjcoreconductorsupthrough5.0CIandforhollowcoreconcentricallystrandedcopperoraluminumoilrfiilledcableconductorsupthrough4.0CI.Forvaluesofxpbelow3.5,arangevrhichappeartocovermostcasesofprac-ticalInterestatpovrerfrequencies,theconductorproximityefectforcablesinequilateraltriangular,Eormationinthesameorinmpaiat'teductsmaybecal-culatedfromthefollowingequationbasedonanapproximateexpressiongivenbyArnold'equation7)forasystemofthreehomogeneous,straight,parallel,solidconductorsofcircularcrosssectionarrangedinequilateralformationandcarryingbalanced3-phasecurrentremotefromallotherconductorsorconductingmaterial.Theempiricaltransversecon-ductancefactorkpisintroducedtomaketheexpressionapplicabletostrandedconductors.Experimentalresultssug-gestthevaluesofkpshowninTableILYep-F(xp)(-')Xis)+0.312-(24)6.60at60cyattt(25)epWhenthesecondterminthebracketsissmallvrithrespecttotheGrsttermasitusuallyis,equation24maybewrittenatIIm)5(De/S)t1Yep~4F(xp)iJF(x,)+om~4(-')F(xp')(24h)()Ijt'"r6~'li'IvrherethefunctionF(xp')isshowainFig.l.Theaverageproximityefectforcon-ductorsincradleconfigurationinthesameductorinseparateductsinaforma-tionapproximatingaregularpolygonmayI~~~Ta6l>>V.Speci8>>Intiuctiv>>(:apadlanceofInsufationsalsobeestimatedfromequation24and24(A).Insuchcases,Sshouldbetakenastheaxialspacingbetvreenadjacentconductors.ThefactorYsisthesumoftvrofactors,Y<<duetocirculatingcurrentefectandY<<duetoeddycurrentefects.WsI'Rd<Yes+Yes)wattsp>>rconductorfoot(26)Becauseofthelargesheathlossesvrhichresultfromshort~itedsheathopera-tionwithappreciableseparationbetweenmetallicsheathedsingleconductorcables,thismodeofoperationisusuallyrestrictedtotriplexcableorthreesingie~nductorcablescontainedinthesameduct.ThecirculatingcurrentdfectinthreemetallicsheathedsinglemnductorcablesarrangedinequilateralconfigurationisgivenbyRs/Ree1+(Rs/Xw)s(27).When(R,/X~)tislargevrithrespecttounityasusuallyisthecaseofshieldednon-leadedcables,equation27reducestoX~Yse~-approximatelyRIRdeXss~0.882/IOg2S/Ds~microhmsperfoot(28)~52.9Iog2S/Dsesmicrohmsp>>rfootat60cydes(28A)whereSistheaxialspacingofadjacentcables.ForacradledconfigurationX~maybeapproximatedf'rom2.52S0/SX~52,9log'-(-)b,-S)microhinsperfootat60cydes(29)~52.9log2.3S/Dyesapproximately(29A)TableIVprovidesaconvenientmeansfoideterminingXforcablesinequilateralconfiguration.Theeddy~eatefectforsingle-coaductorcablesinequilateralconfigura-tionwithopen~cuitedsheathsisMateria)Polyethyleae.................2.3Paperlasuiatlou(solidtype)...3.~(1PCEhea)ue)Paperjose)atjoa(otheetypes)..3,~.2Rubberaodeubbeejjhecoospounds....~...............5(lPCEhva)ue)Varnishedeaesbrje.........,,.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..".15.40.3.~~~~2T.T.~~~25~9...~25.2"~..23'.....24as.".~24.l."..23.5....~22.9.....22.2.....21.50.2.....3T.0....33.9,.34.8.....33.8.~...32.8.....31.9.....31.0.....30.1.....29.3.....28.40.1"".52.9."50.T....48.T...~.45.9.~.~.45.2..~~.43.5.....42.1.....40.T*.~-.39.4~~~~.3'roximattlyat60cycles(30A)Whenthesheathsaleshort~ted,thesheatheddylossmalbereducedandmaybeapproximatedbymultiplyingequations30or30(A)bytheratioR,'/(Res+Xmas)Incomputingaverageeddycurrentforcradledconfiguration,Sshouldbetakenequaltotheaxialspacingandnottothegeometric-meanspacing.Equations30and30(A)maybeuraltocomputetheeddyment-,ef>>etforsingle-conductorcablesinstalledinseparateducts.Strictlsag,theseuationsalyonltothreecablesinequilateralcon-gurationbutcanbeusedtoestimateossesinecableouswhenlatteraresoorientedastoaroximatearelarpolygon.TEeeddymentefectfora3-conduc-torcableisgivenbyArnoId.'RI(2s/D~)'2s/Dsw)'14-+1(2y/D~)s~~~5.2R,16-+1fWhen(5.2R/f)iishrgevrithrespecttounity,Y~-approximatelyat60cyd>>s(31A)3~1.155T+0.60XtheVgaugedepthforcompactsectors<<1.155T+0.58D,foiroundconductorsiuy)~andTistheinsulationthickness,indud-ingthicknessofshieldiagtapes,iEany.Whileequation31(A)vrillsuKceforleadsheathcables,equation31shouldbeusedforaluminumsheaths.On3~nductorshieldedpaperleadcableitiscustomarytoemploya3-or5-milcoppertapeorbronzetapeinter-calatedvrithapapertapeforshieldingandbinderpurposes.Thelineald-cresist-anceofacoppertape5milsby0.75inchisabout2,200microhmsperfootoftapeat20('hedrcresistanceperfootofcablewillbeequaltothelinealresist-anceofthetapemultipliedbythelaycorrectionfactorasgivenbytheexpres-"sionunderthesqu3:e.rootsigninequation13.Inpracticethelaycorrectionfactormayvaryfroin4to12ormoreresultingInshieldingandbinderasscinblyresist-756.icher,McGrctl:-Tcn:pcrc!arcandLoadCaPabilityojCableSystcn;sQCTOBER195I

}s,'Ihe.ancesofapproximatdy10,000ormoremicroi<msperfootofcable.Evenonthcassumptionthattheassemblyresist-anceishalvedbecauseofcontactwithad-jacentconductorsandtheleadsheathcomputationsmadeusingequations2?~and30shocvthattheresultingcirculatingandeddycurrentlossesareafractionot1%onsizesofpracticalInterest.Forthisreasonitiscustomarytoassumethatthelossesintheshieldingandbindertapesof3oconductorshieldedpaperleadcablearenegligibleoIncasesofnonleadedrub-berpowercableswherelappedmetallictapesarefrequentlyemployed,tubeeffectsmaybepresentandmaymateriaUylowertheresistanceoftheshieldingassem-blyandhenceincreasethelossestoapointwheretheyareofpracticalsigniG-CanCeoAnexactdeterminationofthepipelosseffectYpinthecaseofsingle~nductorcablesinstaHedinnonmagneticconduitorpipeisaratherinvolvedprocedureasindicatedinreference7.Equation31maybeusedtoobtainaroughestimateofYpforcablesincradledformationonthebottomofanonmagneticpipe,how-everbytakingtheaverageoftheresultsobtainedforwidetriangularspacingwithsaa(Dp'-Ds)/2andfordosetri-anglespacingatthecenterofthepipewith2~0.578'DThemeandiameterofthepipeanditsresistanceperfootshouldbesubstitutedforDrandR,respectively,FormagneticpipesorconduitthefoUowingempiricalreIationshipssmaybeemployed1.54s-0.115DpYp~(3~nductorcable)Ac(33)0.89$-0.115Dp4dosetriangular)(34)0.34$+0.175DpYp~(single-conductor,244cradled)(5)'Theseexpressionsapplytosteelpipersandshouldbemultipliedby0.8forironconduit.sTheexpressionsgivenforY,andYsaboveshouldbemultipliedby1.7toGndthecorrespondingin-pipeeffectsformag-neticpipeorconduitforbothtriangularandcradledconGgurations.CALCULATIONOFDIELECTRICLOSSThedielectriclossWsforSaocdnetorshieldedanda~inteaondnetorcabletsgivenbytheexpres'sion0.00276Esrrcosc)lo(Lr:D)/DQ"--.-conductorfootat60cycles(36)andfor3~nductorbeltedcableby'.019E'c,cosc)Wg~'attsperscoccdccctorfootat60cydes(37)whereZisthephasetoneutralvoltageinkilovolts,eristhespeciGcinductivecapacitanceoftheinsulation(TableV)Tisitsthicknessandcospisitspowerfactor.ThegeemetricfacterGsmaybefoundfromFig.2ofreference1.Forcompactsectorconductorsthedi-electriclossmaybetakenequaltothatforaconcentricroundconductorhavingthesamecross-sectionalareaandinsulationthickness.r'eoCalculationofThermalResistanceTHERMALRESISTANCEOFTHBINSULATIONForasingleconductorcable,rIRf0.012tiflogDf/Dcthermalohm-feet(3S)wheresicisthethermalresistivityoftheinsulation(TableVI)andDiisitsdiameter.InmulticoaductorcablesthereisamultipathheatGowbetweentheconductorandsheath.ThefoUowingex-pressioncrepresentsanequivalentvaluewhich,whenmultipliedbytheheatGowfromoneconductor,willproducetheactualternperaturredevationeftheconductorabovethesheath.Bf~0.00522ifcGcthermalohm-feel(39)ValuesofthegeometricfactorGsfor3-conductorbeltedandshiddedcablesaregiveninFig.2andTableVIIIrespec-tivelyofreferencel.Onlargesizesec-torconductorswithrdativelythinin-sulationwaUs(i.eoratiosofinsulationthidmesstoconductordiameteroftheorderof0.2orless);valuesofGlfor3-conductorshieldedcableasde(erminedbybackcalculation,onthebasisofanassumedinsulationresistivity,fromlab-oratoryheat-runtemperature-risedata,havenotalwaysconfifmedtheoreticalvalues,and,insomecases,haveyieldedGivalueswhichapproachthoseforanonshielded,nonbeltedconstruction.T46feVl.ThermalResistivityofVariousMa(erichMaterialif,CCm/W'accpaperfosulacloo(solidCype)...T00GFCEAvalue)Varnishedcambric.~....~..~..000(IPCEAvalue)Paperiosulacloa(ochercypes)..500-MoRubbctaodrubbct.lihe..~~~...$00(IPCEhvalue)JuCeaodCessileprolectlveCOVeffaeo~~~~~~~~~~$00Fiberduccoo~~~~~~~~~~~~~~~~480Polycchyleae...............~.4$0Traaid'cedticc~~~~~~~~~~200Somasclcooooo~~~~~~~~~~~~100THBRNALRESISTANCEOFJACKETSrDUCTWALLs,ANUSo)MsTIcCohTINcsTheequivalentthermalresistanceofrelativelythincylindricalsectionssuchasjacketsandGberductwaUsmay'edeterminedfromtheexpression,/tNg~0.0104)a'(-)thermalohcn-feet.(D-I)(4O)withappropriatesubscriptsappliedto8,sI,andDinvrhichDrepresentstheoutsidediameterofthesectionandtitsthickness.rc'isthenumberofconductorscontainedwiththesectioncontributingtotheheatGowthroughit.THERMALREslsThNcEBETwEENCABLESIFhcEANUSIROUNnnfcPIPEsCONUUTT,.ORDUcrWALLTheoreticalexpressionsforthethermalresistancebetweenacablesurfaceandasurroundingendosurearegiveninrefer-ence10.~indicatedinAppendixI,thesehavebeensimpliGedtothegeneralformrcrdt,thermalohm-feet1+(B+C1'm)Ds'41)inwhichdt,B,andCareconstants,D,'epresentstheequivalentdiameterofthecableorgroupofcablesandrs'thenumberofconductorscontainedwithinDs'.T~isthemeantemperatureoftheinterven-ingmedium.Theconstantsd4,B,andCTableVil.(:onsfcntsforUseinEquc(fonsdtand4I(A)CoadlcloaBcAamecalliccondulC...................IT~......3.0.........0.0"0.........3.2.....~~~oo10Indbcrduetlaair...................ly.........2.1.........0.010.........$.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-&liedpipecableac200psl.........3.1.........1.10.........0.00$3,......,.2.I.......~~0.0$Oildlledpipecable....~.............0.$4......~..0.........0.004$.........2.1......~"2~4$fye'1.00Xdlameserof<<ableforoaecableI.dsXdhmecerofeablcforcerocables2.1$XdlamccctofcableforChreecables2.$0XdlamcccrofcableforfourcablesOcTQBER1957Kci:cr,If(GraK-TernpcratffrearidLoadCapcbili!yofCableSystemsfoi 15.6n','Kaz'/D,')t<<+I.Gal+0.OIGTT)lthertnalohm.feet(42)log-+(LF)log-FInthisequationATrepresentsthe.differ-thcrtnalohm.feet(44)encebetweenthecablesurfacetempera-tureT,andambientairtemperatureT,indegreescentigrade,T~the.averageofinwhichD<isth'teratwhichtheportionoEthethermctrcuitcom->>'hesetemperaturesandcthecoe6icientofmene'.andttIsthenumofconuc-torscontainedwithinD,.'heGctitiousdiameterD>>atwhichtheeffectoflossfactorcommencesisafunctionofthediffusivityofthemediumaandthelengthofthelosscyde.cemissivityofthecablesurface.Assum-ingrepresentative.valuesofT,~60andT>>~30C,andarangeinD,'ffrom2to10inches,equation42maybesimpliGedto9.5n',thermalobtn<<feet(42A)D,~1.02>ct(lengthofcydeinhours)inches(45)Theempiricaldevelopmento!thisequa-tionisdiscussedinAppendixIILForadailylosscydeandarepresentativevalueofa~2.75squareinchesperhourforearth,D>>isequalto8.3inches.ItshouldbenotedthatthevalueofD,obtainedEromequation45isapplicableforpipediametersexceedingDinwhichcasetheGrsttermofequatioa44isnegative.ThefactorFaccountsforthemutualheatingeffectoftheothercablesofthecablesystem,andconsistsoftheproduct'ftheratiosofthedistancefromthe,referencecabletotheimageofeachoftheothercablestothedistancetothatcable,Thus,Thevalueofcmaybetakenasualto0.95oricnduitsoructs,andpaintedorbraidedsurfaces,an0.2to0.5forleadandaluminumsheaths,dependinguponwhetherthe,surfaceisbrightorcorroded.Itisinterestingtonotethatequation42(A)checksthcIPCEAmethodofdeterminingR,verydosdywithc~0.41fordiametersupto3.5inches.IntheIPCEAmethod8,~0.00411n'3/D~'here9~050+314D~'orD,'-1.75lacbesandB1,200forImrgervaluesofDt'IFEOTrvE.TaEBMhLRESIsThNcEBETWEENChBLES,DUCTS,ORPII'ESyADAhfBIENTEhRTH(t~ctt.~t>>)Aspreviouslyindicated,anefFectivethermalresistance8<'aybeemployedtorepresenttheearthportionofthethermalci:cuitinthecaseofburiedcablesystems.ThiseffectivethermalresistattceincludestheeffectoElossfactorana,inthecaseofam'lticableinstallation,alsothemutualF~--.~.-(N-Itertas)(46)ItwillbenotedthatthevalueofFwillva~dependinguponwhichcableissdectedasthereference,andthemaxi-mumconductortemperaturewi11occurinthecableforwhich4LF/D>>ismaxi-giveninTableVIIhavebeendetermined.heatingdfectsoftheothercablesofthefromtheexperimentaldatagiveninrefer-system.Inthecaseofcablesinacon-cnces10antiIl.creteductbank,itisdesirabletofurtherIfrepresentativevaluesofT~~60Crecognizcadifferencebetweenthethermalareassumed,equation41reducestoresistivityoEtheconcreterrcandthctt'ri'hermalresistivityofthesurrounding,thermalobm-feet(41A)earthA.ThethermalresistancebetweenanyItshouldbenotedthatinthecaseofpointintheearthsurroundingaburiedducts,A,eiscalculatedtotheinsideofthecableandambientearthisgivenbytheductwallandthethermalresistanceofexpression'ctheductwallshouldbeaddedtoobtainEE>>c~0.012ts,Iogtt'/8thermalobm-Feet(4>)y,ERMhLRBsIsThNcEPRostChBLEs>mwhichp~ththaltityofthe't'tTaisetancefromtheimageCoNDUITs~oRDUcTsSUsPENDBDINearthrlrisofthecabletothepointP,anddistheThethermalresistanceR,btweendistanceEromthecablecenterto2'.cables,conduits,orductssuspendedinstillFromthisequationandtheprinciplesairmaybedeterminedfromtheFollowingdiscussedinreferences3,12,and13,theexpressionwhichisdevelopedinAp-followingexpressionsmaybedevdoped,pendixLalicabletodirectlyburiedcables.andto~i;type'-cabes.cgC8>>'.~0.012Pgtt'Xmum.NreferstothenumberoEcablesorpipes,andFisequaltounitywhenN~l.Whenthecable@stemiscontainedwithinaconcreteenydopesuchasaductbank,theeffectofthedifferingthermalresistivityoftheconcreteen-velopeisconvenientlyhandledbyGrstas-sumingthatthethermalresistivityofthemediumithatofconcreterF,through-outandthencorrectingthat.portionly-ingbeyondtheconcreteenvelopetothethermalresistivityoftheearthi4.Thus1'g~0.012tI,+'$(c(.3;[i.'-.(in')~]]'~ohm-feet'44A)ThegeometricfactorGc,asdcvdoped-inAppendixIlisafunctionofthedepthtothecenteroftheconcretecndosureQanditsperimeterP,andmaybefoundconvenientlyfromFig.2intermsoftheratio4/2'ndtheratioofthelongesttoshortdimension'oftheendosure.ForburiedcablesystemsT,shbuldbetakenastheambienttemperatureatthedepthofthehottestcable.Asindicatedmreference12,theexpressionsusedthroughoutthispaperforthethermalresistanceandtemperatureriseofburiedcablesystemsarebasedonthehypothe-sissuggestedbyKeaaellyappliedinaccordancewiththeprinciple.ofsuper-position.Accordingtothishypothesis,theisothermal-heatQowGddandtem-peratureriseatanypointinthesoilsur-roundingaburiedcablecanberepresentedbythesteady-statesolutionfortheheatQowbetweentwoparaMcylinders(constitutingaheatsourceandsink)locatedinaverticalplaneinaninGnitemediumofuniformtemperatureandthermalresistivitywithanaxialsepara-tionbetweencylindersoftwicetheactualdepthofburialandwithsourceandsinkrespectivelygeneratingandabsorbingheatatidenticalrates,therebyresultinginthetemperatureofthchorizontalmid-planebetweencylinders(Le.,correspond-ingtothesurfaceoftheearth)remaining.bysymmetry,undisturbed.Theprincipleofsuperposition,asappliedtothecaseathand,canbestatedinthmnaltermsasfollows:IEthether-malnetworkhasmorethanonesourceoftemperatu:erise,theheatthatQowsatanypoint,orthetemperaturedropbe-tweenanytwopoints,isthesumoftheheatQowsandtemperaturedropsat.thesepointswhichwouldexistifeachsourceoftemperaturerisewereconside:edseparatdy.Inthecaseathand,thesourcesofbeatQowandtemperaturerisetobesupcrimposedare,namdy,theheat7OSrober,DfcGratls-TemperatttreandLoatfCapabilityofCableSyste":sOcTooER1957 fromthecable,theoutwardQovrofheatfromthccoreof.theearth,andthcin-wardh(atQovrsolarradiation,and,whenpresent,theheatQowfrominterferingsources.Byemployingastheambienttemperatureinthecalculationsthctem-peratureatthedepthofburialofthehottestcable,thecombinedheatQowfromearthcoreandsolarradiationsourcesissuperimposeduponthatproducedatthesurfaceofthehottestcablebytheheatQowfromthatcableandinterferingsourcesvrhicharecalculatedseparatelywithallotherheatQowsabsent.ThecombinedheatQovrfromearthcoreandsolarsourcesresultsinanearthtempera-turewhichdecreaseswithdepthinsummer;increases.vrithdepthinwinter;remainsaboutconstantatanygivendepthontheaverageoverayear;approximatescon-stancyatalldepthsatmidseason,andinturnresultsinQovrofheatfromcablesourcestoearth'ssurfac,directlytosuz-faceinmidseasonandwinterandin-directlytosurfaceinsummer.FactorsvrhichtendtoinvalidatethecombinedKennelly-superpositionprinci-plemethodaredepartureofthetempera-tureofthesurfaceofearthfromatrueisothermal(asevidencedbymeltingofsnovrinvrinterdirectlyoveraburiedsteammain)andnonuniformityofthermalresistivity(duetosuchphe-nognenaasradialandverticalmigrationofmoisture).TheextenttowhichtheKennelly-superpositionprinciplemethodisinvalidated,however,isnotofpracticalimportanceprovidedthatanover-alloreffectivethermalresistivityisemployedintheKennellyequation.SpecialConditionsAlthoughthemajorityoEcabletem-peraturecalculationsmaybemadebytheforegoingprocedure,conditionsfre-.quentlyarisevrhichrequiresomewhatspecializedtreatment.Someofthesearecoveredherein.EMERCENCYRATINCSUnderemergencyconditionsitisfre-quentlynecessarytoexceedthestatednormaltemperaturelimitoftheconductorT,andtosetanemergencytempegaturelimitT,'.Ifthedurationoftheemer-gencyisIongenoughforsteady-statecon-ditionstoobtain,~thentheemergencyratingI'aybefoundbyequation9substitutingT<'orT<andcorrecting~,ortheincreasedconductortemperature.Ifthedurationofthcemergencyislessthanthatrequiredforsteady.statecon-ditionstoobtain,theemergencyratingofthelinemaybedeterminedfromTc'-I'~1+YcXN~'-R<<')-(2's+Z(1+.Yg)8<<'nwhich8<<g'sthceffectivtransientthermalresistanceofthecablesystemforthestatedperiodoftime.ProceduresforcalcuhtingE,g'ortimesuptoseveralhoursaregiveninreference14,andforIppertimesinreferences15-17.~~CTHEEFIECT.opExTIumoUsHEATSOUECEs.Inthecaseofmulticableinstallationstheassumptionhasbeenmadethatallcablesareofthesamesizeandaresim-ilarlyloade<<LWhenthisisnot,thecasethetemperatureriscorloadcapabilityofoneparticularequalcablegroupmaybedeterminedbytreatingtheheatingeffectofothercablegroupsseparately,intro-.ducinganinterferencetemperaturerisedTgginequations1and9.ThusT,-T~~dT<+dTc+dT<<~gdegreescentigrade(1A)T~-(T(<<+dTa+dTg>>g)I~gg(1+Yc)~ca'iloamperes(9A)inwhichdTg,grepresentsthesumofanumberofinterferenceeffects,foreachofvrhich.d2<<>>g(IVa/LF)+IVclksgdegreescentigrade(48)Ag<<<~0.012<<r,>>'IogFg,gthermalohm-Eeet(49)((Egg'X<<E<<g'X<<E<<<<')"(EN<<'~)(<<Eg<<X(E<<<<X(E<<g)"<<EN<<(50)wheretheparametersapplytoeachsys-temvrhichmaybeconsideredasaunit.ForcablesinductA.g0.012>>'(r<<logF<<g+N(ggg-rr<<%lthegnudohm-Eeet(49A)Becauseofthemutualheatingbetvreencablegroups,thetemperatureriseoftheinterferingroupsshouldberecheci:ed.Ifallthecablegroupsarctobegivenmutuallycompatibleratings,itisneces-sarytoevaluateIV<foreachgroupbysuccessiveapproximations,orbysettingupasystemofsimultaneousequations,substitutingforW,itsvaluebyequation15andsolvingforI.IncasedT<<ngoracomponentofitisproducedbyanadjacentsteammain,thctemperatureofthesteamTratherthantheheatQowfromitisusuallygiven.ThusdT<<>>g~gagdegreescentigrade(Sl)Ikiloagnpeges(47)vrhere8<<isthethermalresistancebe-tweenthesteampipeandambientearth.ARIALCABLEsInthecase'ofaerialcablesitmaybedesirabletoconsiderboththecffectsofsolarradiationwhichincreasesthetem-peratureriseandtheeffectofthcvrindwhichdecreasesit.ggUndermaximumsunlightconditions,alead-sheathedcablevrillabsorbabout4.3wattsperfootperinchofprofiIe"whichmustbereturnedtotheatmospherethroughthcthermalresistance8,/>>r.Thiseffectiscon-venientlytreatedasaninterferencetemperatureriseaccordingtotherela-tionshipdT<<((<<~4.3Dg'/I,/>>rdegreescentigrade(47A)ForblacI:surfacesthisvalueshouldbcincreasedabout,75%.AsindicatedinAppendixII,thefollow-ingexpressionforl(I,maybeusedwhereV>>isthe'velocityofthcvrindinmilesperhour3.5>>(~V/D,'+0.62)thermalohm-feet(42B)UsECFLow-R'EsrsTIvITYBane.LIncaseswherethcthermalresistivityoftheearthisexcessivelyhigh,thevalueof8,rmaybereducedbybacldiilingthetrenchwithsoilorsandhavingalowervalueofthermalresistivity.Equation44(A)maybeusedforthiscaseifrr,thethermalresistivityofthebacldillissub-stitutedforgrg,andQappliestothezonehavingthebacldiliinplaceofthc.zoneoccupiedbytheconcrete.SINOLE-CCNDUcroaC((1BLESINDUcTwITHSCLIDLYBCNDEDSHEhTHSTherelativelylargeandunequalsheathlossesinthethreephasesvrhichmayresultfromthistypeofoperationmaybedeter-minedfromTableVIoEreference1.ItvrillbenotedthatYrgg~g'gcg~~ISvrhereexpressgonsforI>gg/Petc.,appearinthetable.TheresultingunequalvaluesofY,iathethreephasesvrillyieldunequalvaluesof(Eandequation5becomesforphaseno.1,theinstancegivenasequa-tion5(A)onthefollowingpage.OCTOBEE19573crgcr,rf&Gralig-Terr:pcrafggrca>>dLoadGxpabil<<IyofCab!cSystcr>>s759

4TciWe[/fi+rfrsI/fre+/fe.+(LP)/f,pj+.'fq<<(fF)kpe]thermalohm-feet(SA)whereqraIstheaverageofqrsIqrs>andqrs.TableVIII.CoustanlsforUseinEque6on53AreraseATARMOREDCABl.EBInmulticonductorarmoredcablesalossoccursinthearmorwhichmaybeconsideredasanalternatetotheconduitorpipeloss.Ifthearmorisnonmag-netic,thecomponentofarmorlossYatobeusedinsteadofYpinequations14and19maybecaIculatedbytheequa-tionsforsheathlosssubstitutingtheresistanceandmeandiameterofthearmorforthoseofthesheath.Incal-culatingthearmorresistance,accountshouldbetakenofthespiralling"effectforwhichequation13suitablymodifiedmaybeused.IfthearmorIsmag-netic,onewouldexpectanmcreascinthefactorsY,andY,inequation14sincethisoccursinthecaseofmagneticconduit.Unfortunately,nosimple:pro-'edure,isavailableforcalculatingtheseeffects.Aroughestimateoftheinduc-tiveeffectsmaybemadebyusingthepro-ceduregivenaboveformagneticconduit.Asimplemethodofapproximatingthelossesinsingleconductorcablesvrithsteel-wircarmoratspacingsordinarily,em-ployedinsubmarineinstallationsistoas-sumethatthccombinedsheathandarmorcurrentisequalto'theconductorcurrent.sTheeffectivea.cresistanceofthearmor'aybetdcenas30to60%greaterthanitsd-cresistancecorrectedforlayasin-dicatedabove.Ifmoreaccuratecalcula-tionsaredesiredreferences19and20willbefoundusehl.EPPEcToPF0RcEDCooUNGThetemperatureriscofcablesinpipesortunnelsmaybereducedbyforcingairaxiallyalongthesystem.SimiIarly,inthecaseofoil-Gliedpipecable,oilmaybecirculatedthroughthepipe.Undertheseconditions,thetemperatureriseisnotuniformdongthecableandincreasesinthedir'ectionofEIowofthecoolingmedium.Thesolutionofthisproblemisdiscussedinreference21.baseduponallofthedataavaihbieandincludingtheeffectofthetemperatureofthcinterveningmedium.Thetheoreticalexpressionforthecasewheretheinterveningmediumhdrorgasaspresentedinreference10snaybegenenI.Isedinthcfollowingform:andarangeof150-350forDe'T~equation54reducestoequation41<<iththevaluesofA,B,andCgiveninTableVIZ.Inthccaseofcablesoryipessuspendedinstillair,theheatlossbyndhtionmaybedctcrauncdbytheStchn-Bolznsannforsnuhrs','-,+b+cT~(53)rs'W(radhtion)~0,139DseKTa+273)e(Ta+273)ej10>>wattsycrfoot(55)E,catheeffectivethcrsndreshtsucebe-tweencableandenclosureinthclnulobm-EeetD,'~theublediameterorequivaIcntdhsneterofthreecablesusInches4T~thetempcnturedIEfcrenthIindegreescentigradeP~thcprcssureInatmospheresT~~mesntesnperatureofthemediumindegreescentigraders'~nusnberofconductorsInvolvedTheconstantsa,b,andcinthhequationhavebeenestablishedempiYicdlyasfollows:Conslderusgb+cTeasaconstantforthemoment,theanalysisgiveninreference10resultsinavalueofa~0.07.Withathusestablished,thedatagivenuireference10forcableinpipe,2ndinreference11forcableinaberandtxauslteductswereandyzcdinsinuhrnunnertogivethevaluesofbandcwhichareshowninTableVIILInordertoavoidareltentivccalcuhtloaprocedure,itisdesirabletoassumeavalueEar41sinceitsactualvaluewilldependuponffreandtheheatflow.Fortunately,as4Toccurstothe1/4powerinequation53,theuseofanaveragevalueasIadicatedinTableVIIIwillnotintroduceaseriouserror,ByfurtherrestrictissgtherangeofD,'oI-IInchesEorcableinductorcoaduicandto3"5inchesforpipe-typecables,equation53isreducedtoequation41.whereeisthecoeKcicntofemisslvityofthecableoryipesurfacesOverthelimitedtemperaturenssgeinwhichwcareInterested,equation55snsybeshnplificdto"rs'W(radiation)~0.102Ds'4TeX(1+0.01671~)wattspcrfoot(SSA)Overthesametempenturenngetheheatlossbyconvectionfromhorixoatalcablesorpipesisgivenwithsufficientacciuacybytheexpressionrs'W(convection)~0854De'dT(dT/De')+ewattsyerfoot(56)mwhichthenumcrica1constant0.064hasbeenselectedforthebestEitwiththecarefullydeternsinedtestresultsreportedby'cilaunsson12,3.5audIQB-Inchdhmctcrbhckpipes(e~0.95).Inci-dentally,thisvaluealsorepresentsthebestEitwiththetestdataon1~5inchdiameterbhckpipesreportedbyRosch."ForverticalcablesorpipesthevalueoEthisnumeriesIconstantmaybehicrcasedby22%"Combiniagequations55(A)2nd56weobtaintherelationship4Trs'W(total)15,8rs'r'KAT/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.elledpipetypecableat200pal.........0.07.,.....,..0.121...........0.0017............10AppendixIDevelopmentofEquations41,42,andTableVIXTheoretical2ndsemicmpiricdexpressionsforthethermalrcslstaricebetweencablessurdalseaclosirsgpipeorductwailaregiveninrefercricc10.FurtherdataonthethermalresistancebetweencablesaridSberandtnrssitcductsaregiveninref-erericc11.Forpurposesofcablecating,itisdesirabletodevelopstaudardhcdexpressionsforthesethermalresistancesrs'AAre~,thcrmdohm-Eeet(41)inwhichthevaluesoftheconstantsA,B,aridCappearlnTableVII.Iathecaseofoil.6Iledpipecable,theanalysisgiversiareferesicc10givesthefollowingexpressionrs'.60+0.025(Dr"T~'dT)~'hermalohm-Eeet(54)Assumiugaaavengevalueof4T~7CIfthecablehsubjectedtowindhavingavelocityofV>>milespcrhour,thefollow-ingcxprcssiorsderivedfromtheworkofSchurigandPrick"shouldbesubstitutedfortheconvectiorscomyoricnt.rs'IV(coavectiors)~0.286Dr'4TvVu/De'attsperfoot(56A)Combiningequations55(A)arid56(A)withT~~45C4T3.5rs's'IV(mlsl)D;(QV/D;+0.62e)thermalehm-Eeet(42B)760iVeLer,yrlcGrc!r'TerrperafareandLoadCapabililyo/CableSvs.'erasAr-,nnm.1057 g,gAppendix'lTableIX.CompadsoaofValuesofgo(+F)forSinusoidalLossCydesat30$LossFactorDa<<8.3Inches.AsindicatedintheChirdpaperofreference3.however,theorcQcallyD/cshouMvaryasthesquarerootoftheproductofthedilfusivityandthcthnelengthoftheloadingcyde.Henceasthcdiifusivitywastakenas2.?5squareinchespelhouriatheabove,Da<<Ig02XVacXlengthofcydeinhoursmches(45)TableIXpresentsacomparisonofthevaluesofpercentattainmcntfactorforsinusoidallosscydesat30%lossfactorascalculatedbyequations45,66,62(A),and63andastheyappearinTableIIoftheGrstpaperofreference3.Appendix"IY.'CafculaationsforRepresentativeCa6leSystemsDeterminationoftheGeometricFactorGiforDuctEanld'Consideringthesurfaceoftheductbanktoactasanisothermalcirdeofradiusra,thethermalresistancebetweentheductbankandtheearth'ssurfacewUIbealogarithmhfunctionofriandLithedistanceofthecenter'fthebankbdowthesurface.UsingthelongformoftheKennellyFonnuhLswemaydeflnethegeometricfactorGiasLi+O'Li'-ri'i<<logri~ogIgr/ro+O/(gr/ro)'-gl(gg>Inordertoevaluaterbin"'termsof'thedimensionsofarectangularductbank,letthesnuiierdimensionofthebankbexandthelargerdimensionbP'y.TheradiusofacizdeinscribedwithintheductbanktouchingthesidesislifddIDesccfpdou,Srst<<ulachesIfehecShsakllaV/lseugeapipe....53/53...dl/d2...d3/ddpipe.....dd/dd...50/57....53/50plpe.....55/5...SO/58..~.54/53plpe.o~..58/58...5l/50...55/53cable.~e~\~~~80/80~le'....77j75.~'.77/75....77/77cableo~ooT1/71cableoooo~~~~~~~53/52cablcoo~.~~~~~~~o75/74cable............77/Tdcable....83/80...83/81cable....Td/74...74/173cable....TO/55.~.To/5Tcable..~.d0/54.~.55/54..51/53I~~~~~~45Iloo~ee5dIIIoooooo85Iveoooo~10dVo~ooo~~0dVIe~~~~15VII~eeo~I0VIII....2.0IXooooo30Xo~ooo~34Xa~roe34XI~oooo3TXIIeoo42XIII4.daDhduglelcy<<4.7scuse>>luchapcrhour.15-Kv350-NCN-3<<Conductor.ShieldedCompactSectorPaperandLeadCableSuspendedinAirD,<<0.618(equivalentround);V<<gaugedepth<<0.539inchDc<<2.129;T<<0.175inch;l<<0.120inch12.9/234.5+SINcgggcgg,-('0250(234.5+75)<<37.6microhmsperfoot(Eq.10A)Deca2.129-0.1202.009inches(Eq.12)fs<<x/2(58)andtheradiusofahrgercirdeembracingthefourcornersis/O/x'+g'rrr2LctusassumethaCthecirdeofradiusriliesbetweenthesecirclesandthenugnitudeofraIssuchChatitdividesthethernulresistancebetweenrlandrsindirectrehtiontotheportionsoftheheatGeldbetweenrsandrsoccupiedandunoccupiedby'heductbank.Thusth~~1cQcultco~I9SSSS3Equation62maybewrittenintheform8'-8+8+(LFXd-8)thernulohmofeet(62A)Intermsoftheattainmentfactor(cfF),onemaywrite(AF)~ca(ciFXNcc+/t¹)thernulohmofect(63)Equatingequations62(A)and63obtainsCherehtionshipBcc<<(1-x)8¹-x/t<<thernulohm.feet(64)where37.9C-'ggrroiororrroo2.009(0.120)pcrfootat50C(Eq.11A)kg<<1.0;kr<<0.6(equivalentround)(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)1sYc<<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)ItisdesirabletoderiverihltermsoftheperimeterPoftheductbank.ThusP<<2(x+y)<<4-(1+y/x).2I-(cfF)x<<1-(LF)(45)Since8¹<<0.012/s'plogDc/Dc~thermalohm-feet(44)andtherefore83logDc/Dc<<-,KI-x)/tca-x/eccl>>'/I(47)Plog-log-24(1+y/x)(41)Thcflrstpaperofreference3presentstheresultsofastudymwhichanumberoftypicaldailylosscydesandalsosinu-soidallosscydesofthesamelossfactorwereappliedtoanumberoftypicalburiedcablesystems.Theresultsindicatedthatinallcasesthesinusoidallosscycleofthesamelossfactoradequatelyexpressedthemaximumtemperaturerisewhichwasobtainedwithanyoftheactuallosscyclesconsidered.Ananalysisbyequations65and6TofthecalcuhtedvaluesofattaiameotfactorsforsinusoidallosscyclesgiveninTableIIandtilecorresPoadingcablesystcraPscamoetcrsgiveninTableIoftheGrstpapa'freference3yieldsamostprobablevalueofThecurvesofFig.2havebeendevelopedfromequations57,60,and81forseveralvaluesoftheratioy/x.Itshouldbenotedinpassingthatthcvalueofri<<0.112Pusedinreference13appliestoay/xratioofabout2/1only.R/Rcc<<1.010+0.019<<L029(Eq.14)qg<<qc<<I+-'<<1.019(Eqs.18-19)0.0191.010c,<<3.7(TableV);E<<15/Q<<S.T;cosy<<0.022Appendixill0.00276(8.7)'f3.7(0.022)i2(Q.175)+O.BSC0.681<<0.094wattpercoaductorfoot(Eq.36andtext)(Vote:IacomputiagdielectriclossonEmpiricalEvaluationofD,Inordertoevaluatetheeffectofacyclicloaduponthemaximumtemperatureriseofacablesystemsimply,itiscustomarytoassumechattheheatGowintheGoal~portionofthethermalcircuitisreduced+byafactorequaltothelossfactorofthecydicIoadoThepointatwhichthisreductioncommencesmaybeconvenientlyexpressedintermsofaGctitiousdiameterDaoThusAca'<<Dec+(LF)/tcsthcrnulohm-feet(42)Forgreateraccuracy,itisdesuabletoestablishthevalueofDcempiricailyratherthantoassumethatDsisequaltothehichtheearthi~conohn~nggc~10Ar%I,M.o~/l.7~/.g~,o~4r4/-ag/g.'r.C/:g.

  • <<agir'a"<<tIl' sectorconductors,theequivalentdiameteroftheconductoristatcenequaltothatofaconcentricroundconductor,Le.,0.681inchfor350MCM.)700(TableVI);Gr~0.45(TableVIIIofreference1)~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)Ifthecableisoutdoorsinsunlightandsubjectedtoan0.84mileperhourwind3.5(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)Inthisparticuhrcasetheneteffectofsohrradiationandan0.84mileperhourwindistoeffectivelyraisethcambienttemperatureby10degrees,whichisaroughestimating'aluecommonlyusecLItshouldbenoted,'owever,thatthiswillnotalwaysbetrue,andtheprocedureoutlinedaboveispreferable.'4rcc~69-KvIr500-MEN-Single-"ConductorOil-FilledCableinDuctTwoidenticalcablecircuitswillbeconsideredina2by3fiberandconcreteductstructurehavingthedimensionsshowninFig.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.)30~2.243inches(Eq.12)37.9Rc(2243)(030)~130microhmsperfootat50C(Eq.llA)1.543-O.BOO(1.543+1.2003c1.543+0.600(1.543+0.600J0.72;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.AssumedductbonkconR9uratlonfortypicalcalculationstj4.ifoil@liedcable(AppendixlV)7R'?rVchrr,N'd7rrrflr-Trrrr6crahurcandLoadCaoabrvitvofCableSvsfrrrrsQCTOBBR1957 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)rwattsperconductorfoot(Eq.1S)4Trf6g<<(9.31IrrKI.QOBX0.80)+0.5?l)3.812.37+087<<2>17'+28.5Irsdegreescentigradeinthermalohm-feet(Eq.41A)circuitno.2(Eq.48$irc<<480(TableVI);1<<0.25;-Simihrcalculationsforthesecondcircuitcp.,Dc<<5.0+0.5<<5.50foraberductyieldthefoUowingvalues.0.0104(480X0.25)lgc'.18;4T<<<3.4;Wgg<<17.44IEE',5.50-0M~4T(,g<<1.71+53.2IE'ncircuitno.1120(asumed);jfc85(TableVI)'...~:.(9.31)(6.$5)0.715-0.859I22(Eq.9A).-(-.)('-:)('=".)('-)("=)';,':-"'"..";".";;,",....<<42,200(Fig.3andEq.46)SolvingsimultaneouslyIr<<0.714;Ir<<1>(P0.483;-hs:0.487kiloampere.2(18+27)'180>087(Ptg2)138-Kv2000-2,102(2(fgh-Pressure5z~Oil-FilledPipe-TypeCable8.625-'c'(at80%lossfactor)(0.012)(85)(l)XInch&utside-DiameterPipe8.3'I4(43.5)log-.+0.80log[~42~)J)+Thecableshieldingwillconsistofanhrtercalated7/8(0.003)-inchbronxetape-0.012(120-85X1)(6)(0.80)(0.87)l.inchlayandasingle0.1(02)-inchD-<<6.79thermalohm-feet(Eq.44A,)shapedbrassskid<<Ire-LS-inchly.ThecableswilllieincradledconBguration.Ec'atunitylossfactor)<<8.44~~thhm.feet(Eq.44A)Dc<<1.632;Dr<<2.642>T<<0.505;16Egg.l2pR'gtg'0.90+1.00$(1.7k+0.24+6.79)'72ther<<)ehtufeet(Eu.8)770<.8(189)(2345+70)4'.57(-+L?4+0.24+8.448M625microhmsperfoot(Eq.10A)<<6.2C(Eq.B)ForshfeIdfngtape448<<7/8(0.003)<<0.00263lf<<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)-)<<62,900mlcrohmsToillustratethecasewherethecable564+20'ircuitsarenotIdentical,considerthe'erfootat50C(Eq.13)secondcircuittohave?50-MC'hfcon-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)1R,(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+0.102.6;Rc/k17.2;<<6.65therrrralohm.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+0272L554(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<<1.48wattsperconductorfoot(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.tet5.72+2.45ohm-foot(Eq.41A)ptr<<100(TableVI);t<<O.SO;D,<<8.83+1.09.63for1/2-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+0.55-,'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)

References1.CatcocattoxortnaEuactstcu.Pooka,sxsarUNoskokoaNOCasass,D.)tLShameae.TbcElectricIosraol,BastPittsburgh.PaMayNor.1032.LocaPactoaaxoEttotvaLsxtHoaasCoxraaso,P.H.Buiier,C.A.Woodrau;Ztec.tricotW'orld,NcwYork,¹Y.,vai.02,ao.2,1028pp.50-60.3.StxroctattoxTsitrskatasaRmsorCasters,AIRECaauaitteeReport.AIEETre>aroctio>tl>vol.72,yt.III,Juae1053,pp.~L4.h-CRsarstaxcsorSsoxaxraaCaucusntSrsst.Prrs.LMeycrhotr,O.S.Eager,Jr.Ibid.,raL68,pt.II,1049,pp.815-34.d.PkorttxttvEnactixSouoaxoHotaoerRomeoCoxooctoas,A,H.M.Araeid>>Ieur>tot,IaaututioaolEicctticaiEagiacecs,Laodoa,Eagiaad,vol.88,pt.Il,Aug.1941,pp.34059.o,Eaov&aaksxvLoaassncMattressParka.INaotatsoLa*~russoCast,aa,haxoasoar>oUxakxokso,CakavtxoBaaaxcsa3-PrtaasCaaksxv,A.H.5>LArnot*Ibid.,yt.I.Peb.1941,pp.52-63.T.PtrsLoecssMNorocaoxsttcPtrs,MeyerhotLAIEETrouracliosr,vaLT2,yt.III,Dcc.1053,yp.1260-T$,8.A>>CRsarstaxcsorPrrs-CastsSvatsxs>>mtSsoxaxtaaCoxaactoks,AD1ECommiueeReyerLlbQ~roLTl>pt.III,Ja>L1952,pp.30414.'.ANRsstataxcsorCoxrsuttoxar.StaaxoPa>>asCaucusntNoxxstaaueDuctaxoueIaouCoxomt,R.W.Burteu>ItLMordaIbid.,voL74,pt.111,Occ.1055,yy.ION23.10.TasTasaxu.RsetstaxcsBatvrssxCosc,ssaxoaSaakoauontoPirooaDuctWaarF>H>>Boiler,J.H.Zcher.IbQ.,vaLdy,yt.I.1050,pp.34~9.11.HaavTa*xsrsaStoutoxPo>>saCasusDuctsaxoDeerheaaxsc,tss,PaulCceebicr,OuyF.Baraett.Ibt>L,voL69,pt.L1050,pp.SST57.12.TrtsTsxrseataasRtssorBaatsoCasuasaxttPtrss.J.K,Ireher,lbi>L,voL68,pt.I.1940,yp.9-21.13.TasTaurus*tossRiesorCase,ssnta,DoerBaxr,J.H.Neher>>Ibidpp.~0.-.14.OttFaowaxoPasaaaasCaacouattoxsroaS~NtatxsoOtt>FttusoCasasSvstaxs>>B.H.Bauer.J.H.Ifeher>P.O.Weutstoa>>lb>>d.>vaL75,yt.III,hpr.1055,pp.ISHl41$.Tasaxax.TkaxarsutsoNBoktsoCastaa,F.PBailer.IS@.,vaLTO,yt.I,10SI,pp.4~.ld.TasDstsaxtxattoxorTsxrsaatoksTaaxatsxtsntCast,sSvatsxssvMsaxsoraxANaaooaaCoxrotak>>J.H.)Ichor.Ibid.,yt.II,1051,pp.1361-T1.17.hStxrurtsoM*tasxattcaLPaocsaakaroaDatsaxtxtxotasTaaxatkxtTsxrskataasRtssorCasutSvstsxs.J.H,IrchcrIbQ,vol.72,pt.IILhug.10$3,pp.712-1S.~IiLTssHsattxoorC>tacksExroasototasSaxtxRaas,E>>B.Wedmere.leuc>>oLIaatituttoaatElectricalEagloccra,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~.2tLCostaisotroNtotasSvaovorLoaassaxoorSsar4>ooottoxorStuoasCoxuoctoaAkxoasoCaaass,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,htacricaaSocietyathfcchaoicciBagiaecrv.NeerYork,¹YroL51,ptI,1020.pp.287~23.TssCaakaxt-CakkvLvoCaracttvorRosssa.INsuaatsoCoxoacroaa.S.J.Roach.AIEETrout>xrioor,raLST,hyr.1038,pp.15~7.24.Hsatnto*NoCoaksut~kttxoCar*cttv0'Baa'CouattctoksrokOataooaSskvics>O.R.Schurig,O.W.Prick.Ce>>>rotZfcclricR>rserr,Scrtcaectady,¹YvaL33,1930,y.141.DiscussionC.C.Barnes(CentralElectricityAuthority,Londan,Enghnd):Thispaperisanexcel-lent.andup-~testudyofamosthnpar-tantsubject.Par25yeirsD.M.Simmons'rticledhavebeenusedforfundamentalStudyoncurrentratingproblems,butthenumeraugcabledeveiapmentgaudchangesinindtaihtiantechniquesintroducedinrecentyearshavemadeamodernassess-mentafthissubjectveryneccsgary.Theessentialdutyafapowercableisthatitshouldtransmitthemaximumcurrent(arpower)farSpecifiedinstaihtiancanditiang.Therearethreemainfactargwhichdeter-minethesafecontinuouscurrentthatacablewillcarry.1.Themaximumyertnidgibletemperatureatwhichitgcampanentgmaybeaperatedwithareaganablefactorofsafety.E.ThcheatMiggipathtgyrapertiegafthecable.3.Theinstalhtiancanditiansandambientcondithn5obtaining.InGreatBritainthebasicrelerenccdocumentisERA(TheBritishElectthalandAHiedIndustriesRegeirchAsgachtha)reyattF/TI31tpublishedin1939,andin1955revisedcurrenttutiagtablesforsolid-typecablesuptaandincluding33kvwerepubHshedinERAreportF/TI83.AmoredetailedrcportsumtnarhingthemethodofcomputingcurrentratingsfarSOHd-type,ailGHed,andgas.preggurecablesisnawbeingGnaHtedandmnbepublishedasERArcportF/TI87satnetimein1958.UntilrecentyearscurrerttratingsineatBritainhaveusuallybtenconsideredanacontinuousbasis,buttheltnpartanceoftaltittgintoconsiderationcycHcratingshagnawbeeneirefunystudied,sincecon-tinuedhighmetalpricedhaveforcedcableuserstorevietrcarefullytheeffectsofcycliclaadings.Areporthasrecentlybeenissuedinwhichasimplemethadhyre-gcntedfortherapidcalcuhthnofcycHcratings.'ableVgivegSpecificinductivecapaci-tancevaluesfaryaperastpaperhtguhtion(SOHdtype),3.7(IPCEAvalue);paperinguhtian(Othertype),33-4AIsitpad-sibletaHdttheothertypesandtheirapyrapriateSpecificinductivecapacitancevaluesoralternativelygunplyuseanaverageSpecifichtductivecapacitancevalueaf3.7,faretample>foraHtypesafpaperinguhthn?Reference15madetatheadaptionofthehypothesissuggestedbyKenneHyasthebashofthepaputhisig'alogicalapproachbutitappearstadEerfiantthebasisofcomputingratingshithertoadoptedintheUnitedStates.AnampHGcatianoftheautharg'iewpointaathisimportantissuewiHbe>>deemed.Withreferencetatheuseaflow-resittivitybttchfiH,recentStudiesinGreatBritainhaveShownthatthemethodofbachGHingcabletrenchesdeservescarefulcangidetathnasatteathntathispointcanresultinincretsetupta20%iuhadcurrents.Equatha43givesthethettnalresistancebetweenanypointintheetrthSurroundingaburiedcableandambientearth.ItisTableX.TempetbluteLlmibfor8eHed;Screened-cndHSLf'-TypeCebietLaMDirectorlaA)rIaDuctsSyeteaiVoltageaadTyyeaiCableLeadSheathedArmoredUa-armoredAiamiaumSheathedArmeuredorUa-armoredLeadSheathedUaArmoredarmoredAtom)asmSheathedArmorederUaarmored1.1krStogie>cate..F80~~~~~~80~~~~~~~~~~~~~~~~60>>~~~~~~~Ttriaaadmulticocebaited.>>~~~80~~~~SO>>~~~~~~~80~~~~~\~80~\>>60~~~802.3kraad5.5krSiagtehae~~~~~~~~~~~~~~~~~~~~~~~~~~~~80~~~~~~~80~~~~~~~~~~~~~~~~~~50~~>>~~SOThf~rcbaitedtype~~~~~~~80~>>~~~~>>80~~~~~~~80~~~~~~SO~~~~~~>>60~~~~~~~8011krSiagic~..~.......70.........70.....................50.........70Threncoeebeltedtype.......~..SS.....,...5$...,.....65...,......5$.........50.........d5Three>>careacrceacdtype..~.....>0..~......TO.........TO,........70.........50.....,...TO22kvStatic~re....5$.........6$............~........$0....~.~~.5$Three-carebettedtype..........SS.........SS,...........,........$5.....,...50Threescoreicrceocdtype........6$.........55.........5$..........5$.........$0......."5$Tht~clSLIorShl)........65...................A$..........65....................5533kr(ccrccacd)Static~re...55.50.ThreecoreHSL...............OS..65~Mccauccdiadegrccaccatigrade.tHachttatccseparatelead.ISeparateicedrheatbcd.1Separatealumtouaasheathed.

notclear,however,whatvalueofsoilthermalresistivityisusedinthisexpressionandinformationonthisimportantpointlsdesirable.InGreatBritainavalueofsoilthermalresistivity(g)of120Ccm/watgisgeneraHyusedbutfurthertestdataarebeingslowlyacquired.'ndwheretestshaveindicatedthatalowervalue,e.g90Ccm/watt,isjustified.thisvalueisused.Currentloading~tablesinERAreportF/T183providedataforsoilthermalresistivityvaluesof90and120Can/watt,andcorrectionfactorsforothervalueso!soilthermalresistivityarealsoprovided.IntheUnitedStatesburiedcablesareusuallypulledintoductbanks,buttheremustbemanycaseswhere'irectburial,asaormaHy,.usedinGreatBritain,wiHresultinlower'instaHationcoits.FormulasdealingwiththisinstaHationtechniqueareadesirableaddition.Permissibletem-peraturelimitsforthevarioustypesotcablesandinstalhtionconditionsusedintheUnitedStateswillbeahelpfulap-pendix,anditissuggestedthatthisinforma-tionshouldbeaddedtothepaper.Forcomparisonpurposes,thelimitsrecom-mendedinGreatBritainaresummarigedinTableXandinthefoHowinglPhstic-insuhtedpowercables............70CmaximumconductortemperatureGas-pressureandoH-HHedcablesystems(<<types).85CmaxiniunlconductortemperatureFinally,itwillbehelpEultoknowifadoptionoftheformulasinthepaperwiHnecessitaterevisionorampliHcationofexistingratingtablesand,iEso,whentherevisedtableswillbepublished.REpERBBcas1~CQRRRNTRATcvoorCAsassroaTRANSsccsscoN*NDDcstacsonoN,S.Whitehead,E.E.Huichfngs.RcporhRcfcrcrccrP/PfJl,TheBcfffshEfccccfcafaadAlliedfodusccfesReseacchcfssocfacion.Lcaihechesd.Eogtaad,1939;alsoJorsel,fastftutfooofElcetcfcalBaglaeecs,Loadon,Bagland,vol.83,1938,p.$1T.2.TssCAaeoaanoNorCtcucRATocoPActoasroaCase,ssLAcoDcaactoasNDoers,EGoldenberg.Precccdfacc,foscffusfonofElectricalEagfseers,Leaden,Eaglaod,TOL104,pe.C,195T,p.154.H.Goldenberg(ElectricalResearchAsso-chtion,Leathcrhead,England):Thecal-cuhtionofcableratingslsasubjectofprimeImportancetocableengineers.Nevertheless,itseemsthatuntilrecentlytheAmericanstandardworkonthissubjecthasbeenthatofSimmons,'hilethecorrespondingBritishstandardworkhasbeenrecordedbyWhiteheadandHutch-lngs.Thesepapershavebeensupple-mentedbyscatteredpubHshedpapers.includingdevelopmentsdeaHngwithcyclicloading.Thepaperby3fr.NeherandMr.Mc-"GrathrecordsuptodateAmericancable-ratingpracticeinamannerthatwillproveinvaluabletoengineersformanyyearstococne.ItisapleasingfeaturethattheauthorsareespcciaHycompetenttodealwiththissubjectinviewoftheirvaluablecontributionstothecable-ratingfieldoveranumberofyears.ModernBritishcableratingprscticehasrecentlybeenrecordedinanERAreportsdeaHngwithcontinuouscurrentratings.andintwoIEE(InstitutionofElectricalEngineers)papersc>(basedonERAreports)deaHngwithcycHchacHng,butthemajorityofthisworklsinprocessofprintingandpubHcation.AnobviousdHEerenceinBritishandAmericantechniqueisthemethodofcycHcratingfactorcalculation.Mr.NeherandMr.McGrath'5methodisbasedonanequivalencebetweentypicaldailylosscyclesandsinusoidallosscydesofthesamelossfactor,whileamethodrecentlyhftro-ducedinBritain'4takesfullaccountoftheformofadailyloadcyde.Bothmethodsareconsiderablyshorterthananythathavebeenavailable'itherto.Nevertheless-,withoutfurtherstudyIwouldnotfeelcertainthatforBritish.typecables,subjecttotheirtypicaldailycycles,theEormofthecycHcloadcanbeade-quatelytakenintoaccountbyuseofthelossfactorindependentlyofthecycHcloadwaveformgivingrisetoit.InhcttheconclusionreachedinmysecondIEE'paper,sisthataknowledgeofthecyclicloadwaveformforthc6hourspriortopeakconductoitemperature,togetherwiththelossfactor,areadequateforcycHcratinghctorcdcuhtion.However,itwouldbeunhirtoassessanyoftherehtivemeritsofthetwomethodspriortothepublicationofoneofthem.ThedifferencebetweenBritbhandAmericancableratingtechniqueisnotsomarkedforcontinuouscurrentratingcal-cuhtionasmightappeartobethecaseatGrstsight.Inhct,suchdilferencesasexistareprincipallyduetothedHIerenttypesofcablesemployedoneachsideoftheAthntic,andtothediiferentstandardawfrequenciesinuse.Neverthelessacomparisono!thepresentpaperwiththeERAreportdealingwithcontinuouscurrentratingssgivesrisetocertainobservations.ThepresentpaperfsprincipaHy.directedtothecalcuhtionOEasinglecurrentrating,butoneusetowhichitmightweHbeputisthehrge-scalepreparationofcurrentratingtables,withratinghctorsfornon-standardconditions.Forsuchanapplica-tionitIsoftenpreferabletointroduceexplicitformuhsfortheratingfactors,astheseformulasmightbeindependentoEsomeofthethermalresistancesorlossfactorsinvolved,withaconsequentsavingincalculationtime.Themethodemployedforexternalther-malresistancecalculationforgroupedcableshiddirectinthegrounddifferssomewhatfromthat.recolnmendedinarecentpaperofmine.cForthepreparationOEgroupratingfactorsforthemorecom-monlyoccurringgroupsofcablesdealtwithinanERAreport,sthecombinationofcertainsimpli6edexternalthermal'esistanceformuhsandmyrecommendedmethodhasledtoisubstantialsavingIncalculationtime.Idonotfavortheintroductioncfageometricmeandistance,oritsequivalent,asitisinconvenientforunequallyloadedcables.Abriefrcsucn6ofotherpointsisthatthethermalresistivityvaluesgiveninTableVIforthermalresistancecalculationaregenerallysomewhatlowerthanthecorrespondingBritishvalues,thattheproximityeffectoncylindricalhoHoirconductorsappearstomctobebestob-tainedfromArnold'5paper.sthatwheresheathandnonferrousreinforcementlossesoccuraparaHelcombinationoEsheathandreinforcementresistancepermitsthecal-cuhtionofasinglelossfactor.thatasimpleformulahasbeenderivedfortheexternalthermalresistanceofoneofthreecablesintrefoiltouchingEormationhiddirectintheground,'ndthatsectorcolrecriionfactorsareoftenusediaBritishpracticefor3~recableratingcalcuhtions.REFEaasfcss1.Seeccfeceaee1ofthepaper.2.Seecefeceaee1ofbfc.Basses'fscossfoa.TssCAacoaano>>orCosnsccoosRAnsosANDRAnNDFActoasroaTRANacccsscoNANDDistacsictioNCAaass.KGaldeabefgRcpersRcfcnucrP/TlryElbl,Irsedea,Eoglaad,(tabepublished).4.Scecefcccace2ofMr.Bacncs'fscossfoa.5.TssCAacoaanoNorCtccccRAnNDPAccoasANDEicsRDSNCTLDADcsoroaONRoaMossCAscssLAiDDcRsctoaDcDucts,K,Goldenbecg.$feeorrepAcco.3$l,fastftosfonolEfcoscfcsfEngi-neers,July1951.8.TssEsctsavaoTssauaaRosieTANcsorBoacsoCAaiss,E.Goldenbecg.EceecccJeurccef,London,England,vof.$4,ao.1,Fcb.195T,p.38.TCQRRSNTRAIQcosroa~PArsaTNslKATRDC*sassToB.S.480,1954;VARNcsssoCANsascINsccLATSDCAÃ.ssToB.S.$98,1955.Rcport,RcfcnaccP/I'lpp,TheBritishEfccccfcalandAQfcdindustriesResearchhssocfasfeo,Leachcchcad,Eaglead.8.Seereference5ofihcpapa.ElwoodA.Church(BostonEdisonCom-pany,BostoniMass.):Theauthorspresentahrgeamountofusefuldataandformulasforthecalcuhtionofcablethermalcon-stantsandsuggestanewapproachtotheproblemofcalcuhtionoftemperatureriseforvariouslossfactofsincludingsteady-loador100%losshctor.Cableengineersusuallyagreeonthehctorstobetakenintoaccountandthemethodsofcalculationforsteadyloads.However,thereappearsstilltobedisagreementontheproblemo!cyclicloading.AttheAIEEGeneralMeethiginJanuary1953,agroupofpapers'aspresentedsuggestingvariousapproachestotheproblemsofcycHcloadingonburiedcablesandonpipe-typecable.Ofthemethodssuggestedinthesepapers,theonewhichappealedtotheauthorthemostwasMr.Neher'smethoclusingsinusoidallosscycles.Inhispaperitwasshoitnthatthismethodyieldsreasonablyaccurateresultsforthehigherlossfactors.Foralowlosshctorsharplypeakedcycletheresultsarenota5accllrateAmodificationofthismethodwouldbetorepresenttheloadcydemoreaccuratelybysplittingitintoharmonicsandcom-putingthetemperatureriseEoreachharmonicseparately.Thiseatailsmorework.butwithmodernmethodsofmachinecalcuhtionitiscconocnicaltousethemostaccuratemethodavailableandletthernachineperfornithehboriouscal-culations.Infact,ittakesverylittlemoretimeonthemachinewhenthemorerigorousmethodsareusedinsteadof,anyoftheapproximatemethodswhichhavebeensuggested.Theauthorhasinvcsligslcd.thevariousmethodsofcatculalioaofthecycliccom-ponecitoftemperatureriseofl,250-5ICM P'i>PPaveC4~14 Tab/cXt.ThermalImpedanceFuacQons1,250.MCM115-KvCsb/cEnclosed/n6s)to-Inchucx/dc-I}/eactcrP/pcTab/eXIII.MaximumTemyctatureR/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/OoI.............2.88/-30............1.57/43............1.24/-$4..~.........0.031-512>~......,......2.20/<<38..........1,19/54.....~......O.S2/-58....~~....~.O.ST/-773"~~..~.~......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.statecomponcaCfors/agicpipefSteady.statecompoaencforc<<opipes,18inchesapart.Qo<<<<actscopperiosspctcoaduccotpotfootTs<<'cctopctacutetiseofconductor7's<<tcmpotaiutet(saofshiddiagtapeTs<<cernpctacutetfseofoiliapipe2'o<<CetapctatutetiseofpipeCoaductotP/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....22.8eThesedgutcsdoaociaciudetheCcmpctacuteciseduecodie)aceticioss,<<hfchwouldbeaddedcothe~ccady.statecompoacaL~Thesesteacetateccmpctacutcs.ItisaocpossibleCocomputethemaximumccmpctaxuteofthepipebythismethod.115-kvcablesenclosedin6s/s-inchwutslde-dianxeterpipeburiedintheearth.TheresultsofthreesuchmethodsEortworepresentativeloadcyclesarepresentedinthisdiscussionforcomparison.Thethreemethodscomparedare:(1)theHarmonicmethodusingBesselEunctionstocomputetheheat-Qowconstantsofthecableforeachharmonicofthetemperaturecycle,(2)thesinusoidalmethodsuggestedby'r.Ncherinhis1953paper,and(3)thelatestmethodsuggestedbyMr.NeherandMr.McOrathintheircurrentpaper.Spaceinthisdhcussiondoesnotpermitacompletederivationoftheheat-Bowequa;tionsforthehazznoniccomponentsoftheheat-Bowcycle,butonlytheresults,ascalculatedbyanIBM(IntenutloculBusinessMachines)550,aretabuhteclinTableXLItmaybenotedthattheznachinetiznctosolvetheeightsimul-taneousequationsnecessarytorthesolutionoEthetempecaturesandheatGowsforeachhazmonlcwasapproximately5minutesperznatrix,withaseparatesolutionneces-saryforeachharmonic.Thewholecostofthejobmrentaltinxeonthemachineandpunchingthedataoathecardsformsertloninthemachinewas$150EorthreeTab/cX/I.Hannon/cComponea/sofLossCyclesLossCydeILossCyde2HatLoss,PhaseLoss,Phasemoa/cWattshac(e,WausAag(~,DestosoDecrees0.......4.03...............2.54I~~~2500231~~2.......1.10.....+30......0.43......+IS$3.......0.20.....00......0.do......+ds4.......0.$3.....+40......0.53......3$Bxamp(e:TheequationoflosscydcIusingthefotegoiagdataisasfoiiooom(staximumQo<<d.d<<actsptttootpttcoaduccot}Qo<<4.03+2.$0sinoot+I.IOsin(sot+30o)+0."-0sia(3ot-00o)+0.$3sia(sct+40o)<<atesCottespoadiagccmpttscutecyclefotcooduccottempstacutcisssfolio<<sfot~siagiepipe:(Itaxi.mumTi<<35.lo)7's<<32.4+7.24sia(ut-30')+2.$7sin(<<ot8)+0.30sia(3<<t133')+0,80sla(4aT')dcgttcsccadgtsdcSeretime<<5,00a,cs.iathefotegoiogexpressions.ditferentsizesofcable(atotalof12ma-trixes).ThecostofpzogzanuningwassmallsincethegeneraiprogramforsolutioaofcomplexsimultaneousequationswasalreadyavaihbleintheIBMlibrary,andonlyasmallamountofworkwasnecessarytosetupthisparticularproblem.ThecomponentsotthelosscycleswithwhichthedatainTableXIwasmultipliedtoobtainthctempezaturecyclesaregiveninTableXII.TheselosscyclesareiHus-tratedinPigs.4and5,withthecocre-syondingtemperaturecyclesofthecon-ductorandyiye,InaHfuturecalcuhtionsofthissoct,itisplannedtocanytheprogrammingstiHfurtherandhavethemachinecalculatethetemperaturecycleforeachsizeofcableanddetecznineitsmaximumvalue.Thhhasbeenestimatedtocostapproxinutely$500forprogrammingand$15extzapersizeofcabletocompute,UsuallyonlythetemperatureoftheconductorandthepipearesigniGcantincalculationotthecurrent.carryingcapa-bilitybuttheelectroniccalcuhtorauto-matlcaHycomputestheotherva/ucs'stedinTableXI.andtheyarerecozdedEorwhateverusemaybemadeofthem.Atabu/ationofmaximumtemperaturesfortheforegoingtwoloadcyclesandthethreedHfecent.methodsofcalculationHscedpreviouslyaretabulatedinTableXIIIinthesameorder.ExaminationofthistablewHIrevealthatthesinusoidalmethodyieldsresultswhicharenearertotheznoreaccurateharmonicmethodtlunthchtestmethodproposedinthcpaper.Theagreementbetweenthevariousmethodsisseentobebetteratthehigherlossfactors.ItmaybearguedthattheagrcemcntiscloseenoughbetweenthethreemethodsforaHpracticalpurposesandthattheaccuzacyoftheoriginalthermalconstantsfromwhichthecomputationsweremadedoesnotwarranttheextraworknecessarytousetheharznonicmethod.However,thedangerinusinganapproximatemethodisthatsomeoneunEacniliarwithitsderiva-tionanditslimitationswiliuseitwhereitdoesnotapply.Theauthordoesnotcon-siderthcagrecznentcloseenoughfor40folossfactor.ThecomputationotthepipeIetnpctatureisjustasimportantastheconductortcm-pezatures,especiallyinsummerwhenhighearthtemperaturesprevailandwherehigherdailylosshctozsarcmorelikelytobeencountered:Iftheearthnexttothepipeexceedsanavengeof50C,thereisdangerofdryingoutthesoHcausingthezmalinstability.Ca/culationsotcur-rent~yingcapabilityshouldtakethisliznitintoaccount.RxcysaxcwcxI.Scetefcteacc3ofthepaper.KJ.Wiseman(TheOkoniteCompany,Passaic,¹J.):TheauthorsaretobeconunendedforthhveryGnetechnicalpaper.Thcnialforaaup-bxhtccom-.pihtioaotengineeringfonnuhsandcon-stantsforthecalcuhtioaofcurrent-cacrylngcapacitiesofcableshasbeenofincreasingimportanceeveryyear.WhenDr.Simmonswrotehisseriesofyayccsabout25yearsagowemightsaytheelectricalcableindustrywasyounginengineeringknowledge,thetypesofcablefurnishedwerenottoogreatinnumber,andthecharacteristicsofthecablesmerenottoowellknown.Todayourknowledgeofcabledesign,materials,ancloperatingconditionsalongwithnewtypesofcablesishriaadvanceot25yearsago.Wehavebeenusingthetonnuhsastheybecameknowaanditwasdesizabletobringthetatogetherinonephceand,inaddition,aHofuswhohaveoccasiontomakethesecalculationswiHbeusingthesamefozznuhsandelectricalandtheznulconstants.Also,thispaper<<iHbeofgreathelptoyoungermencomingintothecablein-dustry.Althoughicsummarizestheformulas,anyonestishingtogetadearerappreciationofchetextcanrefertothebibliograyhyandstudycheoriginalpapers.TocnakeanytareofthiskindgencraHyuseful,itisdesirablethattheprocedurebeeasytofollowsadtheformulasreadilyapplied.Theorecitalfonnu/asinvolvinghighermathematicscanbeused,buttheytaketime,andvcr).olccnitisnotpossibletotakethetunetostockupacase.Aga/nconditionsotinscsi/scionatevarlab/edaily,soifweatcczapciomal'eaGeldcheckotca/cuhcionswccanGaddL~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.Lossandtemperaturecyclesfor75%%uoloadfactor>QlllullcfloadcycleFtg.5.Lossandtemperaturecydesfor60%%uoloadfactorwinterloadcycleValuessameasinF>g.4C4~coppcrtosscycleTx~tcmpcraturcolconductorTc~tcmpcraturcofpipeTcmpcrdturcsarelnpercentofcoppertcmpcraturccorrcspond-tngtosteadyloadequaltothemaximum.notnecessary.IthasbeensuggestedthaCitisnowpossibletousecomputersontheseproblems.Thisistrueforthosewhohaveacomputer,butherealsotimeistakenforsettinguptheprobtanforthecomputer.AlsowemustshowhowtocalcuhtethecurrentsandinaEormthaCwillbeused.VouwillnotethaCmanyofChefocmuhsarenewtomastotyou.Thesefonnuhsweredevelopedtomakethecalculationseasilyandquicklyandyetdonotcausealargeerrorinthettnatanswerfromthehighlytheoreticalformula.ItisnaturalthattheformulasmaybcacompromiseandsomemayfeelthataparticularformulaChattheyusemaybcsuperiortothatrecom-mended.LikewisethethermalconstantsmaybeacoxnpromisaThisistrueasfarasIamconcerned,yetwearewittingtoaccepttherecommendattonsgiveninChepaper.Thecalcuhtionofthevariouslossesexistingtnacablesystanandthclocationoftheselossesiswelldoneandshouldbccarefullystudiedbyallnewengineers.Thesectiondealingwiththecalculationofsomeofthethermalresistancesneedcarefulstudyinordertoappreciatethanastheydepartfromtheusualmanna'nwhichathermalresistancesarecalculated.Forexample:thethermalresistancebetweenacableandasurroundingwall,suchasaductwallorapipe;seeequations41and41(A).Heretofore,weused2>a~0.00411B/D,andreferredtoasthcIPCEAmethod.Thishasbeenrevisedtotakeintoconsiderationtheconditionexistingandthematerials.Equation41(A)isageneralone,andbyinsertingthecorrectvaluesof>4'ndB'sgiveninTableI,wecangetR>.Thisisanexampleofhowwecanacceptacompromiseinordertogetagrecmcnc.WeacOkonitemadetestsyearsagocodeterminethethermalconstantsfortheoilorgasmediumsur-roundingcablesinapipe.Wctriedtousethecylindricallogfornxutaandfoundtheapparentthermalresistivityvariedduetotheconvectioneffectsoftheoil.IEwetookthesimpleformulaR>a~1.60/DwhereDisthediameterovercheshieldingtapewefoundwegoCgoodagreementwithtest.Weneglectedtan-~peratureeffectsastheactualvalueofRraascoxnpaxedtothcthermalresistanceofthehsuhtionisverytow,manytimesintheorderofone.tenth;therefore,temperatureeffectsaresmall.Foragasmediumusing200poundspersquareinchmeusetheequation8>a2.58/D.Howdothesefocmuhecocnpasewithequation41(A)proposedbytheauthors)Considertwocases,onehavingadiam-eterovertheshieidingtapeof1inchandanotherhavingadiameterot2.5inches.TheEollowingtablecomparesthetwotypesofequations.Dtameter~Diameter~1loch,XAlaches,ThermalThermalOhmrPootOhm-Poolon.....{Ohoaite......t.dot.o.r....o.dat.o.f.Nehcraad...1.3r...0.80Ohoaite......2.5dCo.t....1.03C.o.f.Nehcraad...2.22...1.04htcCraxhCaa~~~Thcdifferencesarenotgreatandwhenconsideredinrelationtothetotalthecmalresistance,theyarenegligible.WecanaccepCtheauthors'quations.Iamghdtoseetheauthorsphcethcductsysteminproperrehtionshiptoaburiedcablesystemandthatthesamesoilthermalresistivitywillbeusedwhenmakingcomparisons.Thiswastheweak-nessinthecluctheatingconstantsoriginallysetupbyiVELAandhterknown'sIPCEAconstants.Alsoabetterunder-standingoftheeffectofmultiplecab'tcsinaductbankisobtainable,andth>>decermina-tionofthecablehavingth>>highestthermalresistanceispossible.AppendixIIIdiscussesthe'derivattonofDr,afictitiousdiameterinthesoiluptowhichitisassumedthatasteadyheatloadexistsandoutsidewhichthelossfactoroftheloadistakenintoconsidera-tion.IhavenotbeenabletoaccepCthisassumption.ItisanendeavortoobtainathermalcesistanceforthesoilthatwillcheckwithastudythatMesscs.Neher,Butter,ShanklinandmyselEmadeandisreferredtoinreference3inthebibEographyofthispaper.Astudyofthepreviouspaperswillshowthactheattahimentfactorisnotexactlythesameforatttypesofcablesstudiedandallshapesofloadcurves,TheauthorstabulateinTableIXacomparisonoftheattainmenttactorforthreemethodsofcalcuhtionforalossEactorof30%Eorseveralcabledesigns.Ratherthangiveresultsforonelossfactoronly,itwouldhavebeenbetta'ftheyhadcoveredthecangeoflossfactorswhichwerestudiedin1953.Ittheseattainmentfac-torswereplottedagainstlossfactorasIdidinmypaper,itwouldhavebeennotedthatastraightlinecouldbedrawngivingagoodrepresentationofhow(>4F)varieswithlossfactor,naxnely,(>4F)~0.43+0.57(t/)formymethod.Thisequationfollowstheplotof(AF)andlossfactorvaywelldowntoabout35%lossfactor,andinsomecases,itgaveahighervalueandothercasesalowervaluethanactuallycalculatecLThe(4F)valuesIreportedarebasedoncarefulcalculationsfromthcexactloadcurveandnoassumptionthatasingleinewavecurvecanbetakenasrepresentuxganyloadcucve.Asitisararitythatcablesaredesignedforlosshctorsaslowas30%(50%toadfactor).myformulagivesresultsasaccurateaswhenusingD,andeasiertouse.However,forthesakeofuaiforniityinmethodsofcalculation,wewiltaccepttheauthors'ethod.Inthhconnection,IivouldliketoraiseaquestionwhichIhopewillbetakenupbyothersinterestedinthissubject.TheuseoftheequxciouinvolvingDaisanAnnn>r>oo1OA~Arrhrr1fr/rn>C-Trrrhrn>~>rrn>>rfI'na:<InnnVl~'t>>~

,attesnpttotn'creasethethernutresistanceandhavearrivedatcatatncondusions,forthesoilforcablesorsmallpipesixes;someofmhicharediscussedinthefollowinghiotherwords,thecomputedvalueoEparagraph.themu!resistanceistooIow.IsitnotThedeterminationofthclossesmtheIHldythatvreareleavingoutofourequa-conductor,shield,sheathorpipe,andthetionaterminvolvingasurfacecontactdielectrichavebeenweHestabHshcdbybetweenthcsurfaceofthecableorpipetheauthorsandbearnofurthandthesaiLThisistermwouldbeoftheThccalculationofthethelmalresistancesnoercomment.cablessasnefostnaswenowuseforthecaseofofdirectburiedbld'lesinair,namely,8~0.00411B/D.instalhtionsappeartohave'eenwellsoilthermalresIfweaddthistermtothelogfortunaEorfounded;althouhthehodEresistance,wewillgetahigherattheeffectofcyclicloadingscanstobctotalresistanceandtheInliuenceoftheinquestionamottgstthevariousinvestiga-diameterofthecableorpipewillbegreater,toss(reference3ofthepaper).However,thetowerthediameter.ItvriHbeneces-asEarasductbankInstathttonsarecon-sarytodeterminethevalueofB.Thccerned,thedifferencebetweentheNELAideaofsuchatennisshowainthepaper'rIPCEAcurrentratingmethodandthatTableIthebyMr.Mathaandhiscoauthors.Inproposedbytheauthorsissotthtygivesamethermaldataonecannothelpbut<<onderatthedearthgreaaobtahtcdfrotntestsmadebythemonaofpracticaldatahthepaper.pipe-typecable.Theygiveavalueoflnreadingreferences10,12,13.16.andBforsurfaceofSomastictowata'f21817of,the.paper,"therescanstobeverythermalohmspacm'.Ilikethis.Isitlittledataoncable'temperaturemeasurc-notlikelythatwchaveasurfaceresisttvitymentstakalinth6ddchthecahleandthesoHmtmmedtatebythevariousutilitieswhentheNELAc,sQasmasdoricvaluesmereestablished.Theworkre-RBFEMtNCtsportedinthesereEerencestsalmostatltheoretical,andlaboratorymeasuranents1.Bottrtava.aapowaattotttrrtssa*norrHton.an,an~oguemendsu~~~apprdVocTAOCCiaoaSjtrotÃsyRJsMathafJPeJsMaCattoa,E.Dautlrtlatt.AIEETraarrurtoas,IamgitoudetstthereamovementafoottohavethisNeher-McGrathmethodacceptedandtorevisetheIPCEAcurrentratingtablesaccord-E.KThomas(ConsoHdatedEdisonCom-htgty.Iamnotsurethatthisisthecase-panyofNewYork,Inc.,NewYork,N.Y.):TheauthorsaretobecongratutatedinsettingupmathanaticalequationstoevaluateloadWehaveusedthemethodgiveninthcgretthatnomentionwasmadeofthepiopapertocomputethecurrentsathtgofncerworkbyWathceE.~ketnthemtddtequiteanumberofhigh-voltagecablecir-1920'sonthenthgofcablesmstatedm~tshaductbankmd5dcompletedh-ductbank.Thwork,Ibdieve,f-agrcanentmiththeNELAorIPCEAntshedthcb~uof~btcratingofthcnicthod.IneverycasetheNeher.McGrathNELAandpresentIPCEApublishedrat-methodresultsinahrgerconductorstxeIngsofcable.TheworkofZirkewaspre-foragivencurrenttathtg,msomecasesbeforethcAIEEantipubHshcdinasmuchas30%morcconductormetalisJournal1requiredbytheNeher-McGtathmethod.TheworkonratingsofcabtebyKtrke.Hahmhereourdia~begins.One5ddm~oftwothingsprevaHsleithaMr.¹hermeatsintheNewYorlcCityareaandtaterandMr.McGrathhavecotsteredthenonfcrroQslnctatmaske'tortheyarcattanptingtomakeapipe.typecablecarrywhichleadtotheNELAIPCEAsatinthesameloadasadua-banktnstaHatton.Yetonthefaceofit,itisincomprehensibleQseofpipe-typecable.Ztshouldbehomanyonecanconceiveo!a~nductorobviousthattheanswerobtainedbyhigh-voltagecable(andaPipe-typecablemathenuttcaisolutionisneveranybetterassumptionsouwhichtheequacolnpCtlngOnacurrentsatingbasiswithgonaaredcvdopedandtheconstantsusedsingle.conductorhigh-voltagecablessePa-vriththeequations.ratdyspacedinaductbankwhereawIbdtcvetheactualheatttowinunderlossesareaminimumandheatdissipationgdcablesyt~hconstd~blymo~a~m~Ineithereventwe~otcomplexthanhasbeenassumedinthisundastandwhysomuchthneshouldbcpaperand,therefore,actualratingswhich~spentondevdopingancmmethodofcur-areobtainedmaybedHIcrcntfromthoserentsatingcalculationfor.duct-bankobtainedbythiscalculation,systelnswithoutGssthavingatleastobtainedsomeactualIn-servicefieldRztttttstvctsmeasuranentstosubstantiatetheirl.fosmtttas.~iuuCaactraanorlorCaaaaTattraaazoaasOnthcotherhand,wemustsincerelycommendtheauthorsforattanptingtoarriveatarealisticcomparisonbetweenduct-bankanddirect-buriedsystans.ItD.Shorttsunfortunate,however,thatindoingsoort(CanadaWireandCabletheyhavenotbasedtheirformtttadcvdop-ompany,Toronto,Ont.,Canada):Sevantmentonextensive5ddsurveydataaswasoEtheengineermhoworLwithmeatCan-doneatthetimethcNELAductconstantsadaWirehavebeenstudyingtheNeher.wereestablished.MCGrathaaoverthPPepastfewmonths,Theonlywayinwhichwehaveasyet,beenabletomaketheNeher-McGrathmethodtsackwiththeoldandwellprovedNELAmethodistoreducethesoilthermalresistivitytotheorder'of40Cto75Ccm/lratt.TheactualvaluewhichonemouldusetottsriveatthesameconductolsixeasdetaminedbytheNELAmethodappearstodepceduponthenumberofcablesintheductbankandthevalueofthcdaHyloadfactorchosen.Incontradis-tinction,Mr.Neherinreference13ofthepapa'tatesthathismethodagreeswithin10%ofthcNELAmethodifapa~75Ccmmattisused.Wehavenudesomecalcutattonsofthethalnalresistanceofcablesinaductbankfromthcsheathtoground(orsink)usingthe¹her-McGrath~methodandtheaverageconditionson<<hichtheNELAductconstantswereobtained.Thcaverageconditionswere:I.Mostofthemeasurementsweretakentinderpavedstreetswiththedepthofpave-mentbetween10and12inches.2.Majorityofductswacmadeoffibre.3.Avaageductinnerdiasneter~3.75inches.*Concretespacerbetweenducts2inches,withduct..watt~1/4.tach,3-inchouterconcretesheILSpacingbetweenductcentres~6t/tinches.5.Averagedepthofbusialtotopofductbank~30inches.6.Mostmeasurementswith~nductorleadsheathedcablesfran2inchesto3inchesoutsidediameter.Avaagediameter2Sinches.7.AHIoadedcablesinoutsideducts,allequaHyloaded.8.Soilthatnatresistivity(i>>situ)~120Ccm/watt.TwocasesmerestudiedandtheresultsaresummasixedinthefoHominglCareI-Thrcccablesin2by2ductbank(oncoflourcrductscrnpty)..NELAValtte(Le.4.93/D,'+LrNH3Lossfactor........100%o..62.5%o..33%Rthcgthamal/ohns-feet.......5.09..3.92..3.00Neher-McGtathValueLossEactor,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-McGlathvaluesoftherlnalresistancestobeequaltoNELAvalues,soilresistivitywouldhavetobe;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%..3.60¹her-MCGrxthValueLossfactor......100%..62.5%..33.0%Jt/cher,rtfcGrath-TcmpcratttrcandLoadCapabilityrsfCableSystcnlsOCTOBER1957

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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-McGrathvaluesofthermalresistancestobeequaltoNELAvalues,soilresistivitywouldhavetobe:At100%losshctorp,~53Ccm/wattAt62.5%lossfactorpe~50Ccm/IrattAt33%lossfactorp,43Ccm/watt~<Othercalcuhtionsonslngle~nductorhigh-voltagecablesvaryinginconductorsizefrom300to1,150MCMinstaHedinoutsideductsinanormalduct-banksystensItwasnecessarytoassutneape~75Ccm/wattinordertomaketheNeher-McGrathfozmuhsagreewiththecurrentratingscalcuhtedbytheNELAmethod.TheNELAmethodisofcoursestrictlyempiricalandthcductconstantsdeter-minedfromanaverageofalargenumberof6eldsurveys.Ithasbeeninuseforwellover25years;andtheremustofaconsequencebemanythousandsoEmilesofcablesoperatingatcurrentratingscal-culatedbytheuseoftheseductconstants.SofarasourexperienceinCanadaiscon-cernedweknowofnohot-spotfailureswithhigh-voltagecablesinduct-bankinstalh-tions.OnthecontraryoneisledtoreadwithgreatinteresttherecentpaperbyBrookesandStazrs.tDotheauthorsexpectutilityengineersoperatingduct-bankinstaHationstoadoptthemethodputforwardinthepaperandforthwithreducetheirloadsaccordingly!Thisisaquestionofgreatimportance,andweshouldhaveacategoricalstatementfromtheauthorsinthisspeci6cregard.InAppendhIVtheauthorsgiveaspeci-mencalcuhtionforatypicalduct-bankhtstaHationandalsoasimilarcalcuhtionforapipe-typeinstaHation.Intheonetheyuseapeof120andintheotherapeof80.Wouldtheauthorsenlightenmeonthesignificanceofthesetwodifferentvaluesforp,.OnthispointDr.Wisemanstatedinhisdiscussionofthepaperthathewasgladtoleamthat.wecannowbasetheduct-bankcalcuhtionsonthesamebasisofpeaspipe-typecable,buttheauthorshavenotdonethisintheirAppendhcIV.TheuseoftheKennellyfozmuhinthepracticalcaseofcabletburiedintheearthisatbestanapproximation.For'thetheoreticalcaseofaheatsourceinamediumthatishomogeneous,ofuniformresistivityandtemperature,theformulawouldapply.However,forthepractinlcaseofcablesintheeuth,thereisconsiderabledeviation'romtheidealcasesuchashonunifozznmedium,seasonalvariationoftemperaturegradientintheearth.nonuniformdistribu-tionof.moistureintheearth,moisturemigration,andotherfactors,whichrendertheKennellyformulamoreorlessinac-curate.Thusinitsuseonemustbearinmindtheselimitations.InEuropetheKennellyformulahasbeen'usedextensively,butthcapparentthermalresistivityInserteinthecalcuh-tionsarebasedonthatvalueobtainedirtziltr,asmeasure4inaccordancewithreconunendedmethods.Togetaveryaccuratevalueoftheapparentthczznalresistivity,itseemsthatthemethodtobeusedshouldexactlyduplicatethecableanditsoperatingconditions;Le.,thcsamediameterasthecable,thesamewattslossdissipated,thesamedepthoEburial.andatthetitnewhenthethermalconditionsarcmostonerous.ThusinthecalcuhtionofthermalresistanceEromcabletoambient,itappearsthattheKennellyfozmuhcanbeusedtoahighdegreeofaccuracyifanapparentthermalresistivityofthesoilinsituisused.ThismeasurementshouldautomaticallytakeintoaccountaHthefactorsthatotherwiselimitthcKenneHyformulatoatheoreticalexercise.Therehasbeenagreatdeal"o!.investiga-tionintotheinfiuenceofmoistureonsoilresistivity.However,asyetthereseemstobenogeneralagreementonanotherbasicproblen,andthatisthedirectionoftheheatQow.TheauthorsandothersmaintainthattheheatQowistothesurfaceo!theeuthwhereasotherinvestigatorsclaimsotneheatQowisdownwardstoadeepisothermal,about30to50feetbelowtheearth'ssurhce.Inreference12Mr.Neherobtainstheheat6eldpatternbysuperimposingtheGeldbasedontheKennellyfomtulaonthetemperaturegradient.ItisobviousfromtheGeld~patternsthatinthesummertheheatQowispredominantlydown,whereasinthe.wintertheheatQowistothesurface.Theauthorsgivenoquantitativemethodofevaluatingthecffectofthetemperaturegradientontheapparentsoilresistivity.Thiscouldbeoneofthereasonsfoz'hedifferencebetweentheresistivityasmeas-uredinthelaboratoryandhthefield.AnindicationoftheeffectofchangeofapparentthcrnulresistivityhshowninapaperbydeHaas,SandiEord,andCamezon,twhereinthedfectoEintroducingadeepisothcmzal(groundwater)incombi-nationwiththeeuth'ssurfaceasthesinkhasatheznulresistanceoEapproximately25%lessthaniEtheearth'ssurfacewastheo=lysink,Thiswouldindicatethatthethermalresistivityofthemediumischangedwhereasthechangeintempera-turecHstributlonduetothetemperaturegradientshouldbeinvestigated.ItshouldbeenphasizedthattheKen-nellyformulaisapplicabletosteady-stateconditionsonly.Theauthorsredizethis,ofcourse,andattempttoccnnpcnsateforthisshortmmingbyapplyingacydicalloadingfactortotheexternalthermalpath.Thefactortheyuschbaseduponmeasuredvaluesobtainedondirectburiedand/orpipe-typecables.SincethcthezznalcucuitofaductbankisquitedHferentfromthatofdirectburiedcables,wedonotagreethatthhsatnecyclicalIoadhgfactor(asmeasuredondirectburiedcables)canbeappliedtoaduct.bankinstalhtioa.FinaHyitispertinenttopointoutthatthcKenncHyformuhispremiseduponaHtheheatenergyQowingtotheearth'surface.Onemusttheaasktheauthorswhattheymeanbyambientsoiltempera-ture.Theoretiedlyatleastthetempera-'ureoftheearthatthecabledepthofburialisnotthcambienttobeusedinthe'enneHyformuhifthesinkistheearth'surface.Whyisthceuth'ssurfacetem-peraturenotthetzueambienttousewhenapplyingtheKennellyfozmuh?IstheBritishuscofa2/3factorinreaHtyacorrectionforthevirtualsinktemperature.orsinktenperaturesifthedeepIsothcmultheoryisvalid.LTssaxALANUMaatANTOALPaoaLaxoN128KrPtasCASLSTNNswJaaaar,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):Thisdiscussionisconfinedtothepartsofthepaperdealingwithcablesinducts.Thepaperisinmanyrespectsmostadtnirable,notablythecoverageofsLindfectinconductors.ofspecialtypes,proximityandeddycurrentelfects,muttuIheatingeffectoEmulticableinstalhtions,andthediectofextraneousheatsources.Forthe6rsttimetheseareaHadequatelytreatedinoncpaper.Themethodsofedculationmust,however,becriticallyexaminedbeforebeingacceptecLIamdisturbedtoGndthatthemethodsgivenforratingcablesinductsleadtosub-stantiallyhrgerconductorsizesthandoestheIPCEA-NELAmethod.BythcIPCEA-MELAmethodImeanthemethodgiveninanAnacondapublication.tbelievethismethodisidenticaltothatusedinpreparingtheexistingIPCEA.cur-rentmtingsforcables.TheNeher-McGzathmethodleadstomuchhighervaluesfortheductheatingconstant(thethezznaIresistancefromduct.banktoeazthambient)thandoestheIPCEA-NELAmethod,whenthethezznalresistivityoftheeuthistakenas120Can/wattintheNeher-McGrathcalcuh-tion.Thevaluetobcusedforearththeznulresistivityisofparamountizn-portanceandwiHbediscussedinmoredetaillater.AfewQlustrationsofthedifferencbetweenthetwomethodswQIGzstbegiven.TheGzstapplicationoftheNeher-McGrathmethodwhichwemadewastodetezzninetheconductorsizeforapro-posed230-LwcableinstaHation.Thecal-culatedconductorsizewas1,500MCM,whereasbytheIPCEA-NELAmethodthecalcuhtedsizewas1,150MCM.Some42mQesofcablewereinvolvedintheproposedproject,sotheNeher-McGrathresultwouldhavemeantsubstantialextracostforthecablecomparedtotheIPCEA-NELAzcstdt.Inanothertnztazcc,thcNcbcrMCGzathmethodwasusedtodeterminetherequiredsizeofcableleadsfora75.mvatrans-forzner.ThecalculatedsizewassolargeastobeconsideredphysicaffyImpractlad,whereasbytheIPCEA.NELAmethodthecalcuhtedsizewaspzactied.RatherthanrisLpossibletroubleHtheIPCEA-NELAresultwereadopted,itwasdecidedtouseaerialbusinsteadofcablefortheseleuis.Inathirdcase,thecableleadsofa50-mva13.S-L>'eneratorweretobechangedOCTOBER1967%cher,iVcGraffs-'Tcrrtpcrafurcat:dLoadCapabtlEyofCableSys.'crtts769

<l'~l-1$lChl~r' TableXIV.Itwasnecessarytomeasuretheairtemperatureinanoccupiedduct.sincetherewercnoemptyducts.Theloadingonthemachinevrasrecordedandthecurrentdivisionbetweenthesixcableswasdetcsmhscd.Themaximumdeparturefromequalloadingofthetwocablesoneachphasewasonly2%.After5daystheductairtemperaturewas43C.Theambientgroundtemperaturewas19.5Catthesamedepthasthecenterofthcductbank,Dividingthctemperatureriseby1/6ofthetotallosses,athermalre-sistanceof4.6ohmsisobtained.TableSos>>iIzss~l2us,gcnrrs.'1.'.Qi..'.QI~~5srZRsrrzrff,OVCZnrcovcagrg.ZUshowsthethermalresistancespertinenttothiscaseasdctesmincdbytheNeher-McGrathmethodandtheIPCEA-NELAznethod.Theexpcrisnentalvalue(occuyiedductairtoearthambientotTableXV)isingoodagrcemcncwiththeIPCEA-NELAvaluegivenin"ductwalltoearthambient"ofTableXV,whilethe¹her-Fig.6.Crosssectionofductbankbecausetheassociated~o-Lwstep-uptransfosmcrwasbeingrephccdwitha345.kvunit.Theexistingleadsconsistoftwo2,500-MCMcablesperphaseinstalledinaMuccbank.hccordingtotheNeher;McGrathmethod,thesecablesshouldbeapproximately3,500MCMeachifthcAEICallowabletemperatureof'F6Cisnottobeexceededatfullloadinsununertiine.Theunithasrunatfullloadforlongperiodsonmanyoccasionssincegoingintoservicein1949.Ifourapplica-tionoftheNeher-McGrathmethodiscorrect,one'mustconcludethattheexistingcableshavebeenseverelyoverloadedmanytimesduringtheirserviceperiodof8years.Noevidenceo!suchoverloadinghasbeenseen;thecableshavebeenentirelytrouble-Free.Therearetorootherunitsatthisplant,identicalinallrespectstotheonedescribedaboveexceptthatoneofthanhasbeeninserviceslightlylonger,theothernotquiteasIong.Notroublehasoccurredontheleadsoftheseunits.Itwasdecidedtomakeatemperaturesurveytoestablishthecorrectfacts.Theunitwasrunatfullloadfor5days.Testresultsshowedthattheductstructureatcaisscdequilibrisuntemperaturein24hours..Thebulbofarecordingthcsxnom-cterwasinserted20Eeetinthebottomxniddleduct.Thedetailsottheductbankandcableare,giveninPig.6andvaluei!thetwomethodsarctogivethesameresults,asisobviousbyinspectionofTableXV.TheNeher-McGrathvalueshouldbelowerthanourexperimentalvalue,sincethefosmcrrepresentsthethczmdresistancefromtheoutsidesurfaceoftheoccupiedductwalltoearthambient,whilethehtterrepresentsthissamere-sistanceplusthethcsmalresistancefromoccupiedductairtotheoutsidesurfaceottheoccupiedductwan.Oneisnotentitled,tosaythatthedis-crepancybetweentheNchcr-McGsathvalueandtheIPCEA-NELAvalueisrealunlessthevalueotthespecificthermalreshtivityoftheearthpsisthesameforboth.The¹her-MCGsathvalueinthetabulationisobtainedwhenavalueotearththermalresistivitypsm120Ccm/wattandthcsmalresistivityofconcreteps~85areusedmequation44(A}otthepaper.Therehasncvcrbccnaslygeneralagrec-meatonwhatvalueofearththcsmalresistivityisinherentintheIPCEA-NELAductconstants.SeveralyearsagoMr.G.B.Shank!inandhiscoworkersintheGeneralElectricCompanyinvestigatedthisextensivelyandconcludedthatthevalueisabout180Can/watt.Ifthisconclusioniscorrectthediscrepancybe-twomthcNchcr-MCGzathresultandtheIPCEA-NELAductheatingconstantisTableXIY.Cableandl.ossData2,500.MCMScgiaentolCopperCondsrctorrPepcrinzuf4tcd.teed-SheoshedSolid-Type,13.8Kvrealandserious.Ourtestresultcitedabovedoesnotgiveanyinformationonthispointbecausetheearththczsnalre-sistivitywasnotmeasured,duetolackoffacilities.Ifthediscrcyaucyisreal,onehledtoquestionthesoundnessoftheKennellyformulausedbythcauthors.Itisbasedonthepremisethatallheatgeneratedinthecableescapestotbesurfaceoftheearth.Someccnnpetentengineershavearguedchatpartoftheheatescapesbyanotherpath,namelytoasinkdeepintheearth.Mathe-maticddevelopmentofthispremisegivesaresultforthethermalresistancebetweenductbankandearththatisonlyabouttwo-thirdsaslargeastheresultbythCurreasDaringTeat,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............2.000Cottontapeshicxaess.laches...............0.01Tzasulssloathichaess,laches................0.210'lameseroverinsulation,laches............2.4S4sppcrtapeshichaess,laches..............0.003obeaibihichaess,inches...................0.12$Over.alldiaescser.laches..................2.T10h<resissaneeat5$C~$.41(Xo>>)ohms.faceKennellyformula.hccordingtothis,wemightexpecttheNehcr.McGrathmethodtoagreewiththeNELAvalueiEthecarchthcrzndresistivityistakenequalto2/3X180~120Ccrn/wattinequation44(A}.Itturnsoutthacagreementoccurswhen.McGsathvalueismuchhigher.The='-:Neher-McGrath*valueshouldbeap-proximatciyequaltotheIPCEA-NELATableXY.ThcrnNlResistancesPertainingtoTest'hermalEeshsaaee,lfehetIPCEhEzperi-CpcrWatsrryoosMcarashTfgchmensalZnsuiasioa...~........0.73..".O.TSShesihsodues....'....1,52,....1.82Ductwall.............0.13Ducewalliocarsh~mblen!............8.7$>>.~...4.0Occupiedduceairsoearthambient..........4.51>>Calculasedfromcriuasfoa44(hjusiagp>>~120Ccmlwasz.theearthresistbrityistakenas55Can/wattinequation44(h).Itdoesnotseanlikelythatthevalueof55isrepresentativeoftypicalsailaroundductbanks.Manymeasurementsinseverallaboratorieshave>-~-consistentlyshownthatthespecificthczma11r'esistivityofearthvariesfrosnabout100Ccm/wattEoramoisturecontent.of15%,toabout300or400Ccm/wattforseromoisturecontent.Avalueof180Ccm/wattseemsfairlyrepresentativeofaverageconditions.Iconcludethatthevalidityofthe¹her.McGrathmethodofcdcuhtingthethcrzndresistancefromductbanktoearth.ambientshouldbedesnon-stratedbytestswhczchsthe<<arththermalresistivityisdcfinitclyknown.Havetheauthozsverifiedtheirfindingsbysuchtests?RETERENCEt.CaaaaazRaznrosroaBaaczasocCosanncroaLAnacondaPssrrsstfenC4t,McCcaw-Hi0BooLCompaar,ZocRewYes¹Y.,erstedlcfoa,Ocs.1042.J.K,IfcherandM.ILMCGrathtWeareindebtedtoMr.BaznesandMr.Golden-bergfortheirdscuszionsinwhichtheysummarizethepresentcableratingprac-tkcsinGreatBritainandpointoutsomediifcrcnccswithhmczicxnpractice.Promthisitwould'ppeaz'hatinmostrespectsthepracticesinthetarocountriesareshnihr.Whilethemethodothandhnggroupcableratingsdevelopedby'x;GoldenbergmayappeartodifFerhoaxthemethodotthepaper,actuallybothmethodsarcderivedfromthesamebasicprhxciplcsandshouldgiveidenticalresultsforthesaznesetofconditions.Toanswertheirquestionswithregardtotcsnpcraturelnnitsandtherelationshipofthispapertothepublishedratingtables,wemaysaythatIPCEA,incollaborationwiththeAIEE,hasunderactivecon-siderationaxevisionoftheexistingcurrentratingtablesbasedonthemethodsofcal-cuhtionset!orthinthispaper.Thetem-yeraturelimitswfiibethosedready'doptedbyIPCEA,AEIC,ctc..inindustryspcclfications.Mr.Churchhasoutlinedaprocedurefordeterminingtheeffectoftheloadingcymeoncableratingswhichwillbe,wefear,ancnigsnatoznostcableengineersdespitethefactthaticrepresentsachdlengetothosemathmssaticallyinc8ned.Mr.Goldcnbcrgalsohasreferredtoadifferentbucneverthelessmachcsnaticallyinvolvedprocedurefordoingthis.Foruorsnalcablecalcuhtions,thecrcmmsdousasnountotcomputationsrequiredforeachindividual7TO1Vcher,McGrath-TerrsperatureandbroadCapabihtyofCableSysterrssOCTOBER1951 aa~~ee01' casi,'issimplynotwarranted<<veniEadigitalcomputermereavailabletothecableengineer.Iftheapplicationofaparticularloadcycletoagivencablesystemistobestudied,wesuggestthatthismaybedonemoresiniply,morcrapidly,andmoreeconomicallybyusingananalogcomputerdesignedforthepurpose.Wefeel,how-ever,thattheaccuracyofthcmethodgiveninthepaperascomparedtoaBexactcaI-culationswhichwehaveexamined,includ-ingthoseofMr.Church,issuificient,par-ticularlyinviewofthefactthatanypar-ticularloadcyclemayneverrepeatitself.Themethodgiveninthepaperisanapproximation,admittedly,butithasbeenderivedfromthesamefundamentalprin-cipleswhichunderlieMr.Church'smethodthroughaseriesofcareMIyconsideredsimplifications.Itshouldbeunderstoodthatthereisnothingsacredabout.thevalueof8.3inchesusedforthefictitiousdiameterDc.Thisvaluehappenstobethebestsinglevaluetousebasedonthestudiesdescribedinreference3.ForMr.Church'scasevaluesof7.1forthc75%loadfactorcycle,andof5.1forthe60%loadfactorcycleareindicated.Theerrorsinusing8.3,however,amounttoonly2and5%high,respectively,mtheconductorlosscomponentofconductortemperaturerise,whichwouldbeoffsetbya10%errorinthevalueofearththermalresistivityein-ployed.Dr.Wiseman'sconunentsinthiscon-nectionaremostinterestingsincehehasoftenexpressedtheopinionthat,prac-tically,itwassufiicienttoconsiderDctobeequaltoDs,orinotherwordstoapplythelossfactortoaBoftheearthportionoEthethezmalcircuit.Wecanagreewiththisinrespecttopipe-typecables,but,ashehasindicated,wedonotconsiderthisfurthersimplificationdesirableinthecaseofsmalldirectlyburiedcables.Neitherdoweconsidertheforznuiawhichhegivesforobtainingattainmentfactordirectlyframlossfactorsuitableinthiscase.ThisisreadByapparentframFig.2aftheGrstpaperofreference3inourpaper.SincetheuseofDchasconsiderabletheoreticaljustificationinouropinion,wefeelthatitshouldbemadeapartofthegeneralprocedureEorcalcuhtingtheeffect.oftheloadingcycle.Theintroductionofanadditionalthermalresistancetocareforsurfaceeffectsbe-tweencableandearthisanentirelydiffer-entnuttersincethiswillincreasethetemperaturerisebothforsteadyandforcyclicloads,whereastheuseofD>isintendedtogivethecorrectresultforcyclicloadsontheassumptionthatthetotalthermalresistanceinthecircuitwhichisunchangedbythevalueofDciscorrectforsteadyloading.Itisquitepossiblethatsuchasurfaceeffecttermispresentandthatitmayattainanappreciablemagnitudeinthecaseofsmalldirectlyburiedcables.WeconcurinthehopethatthismatterwBIbeinvestigatedfurther.Ivfr.ThomashasnotedthepioneerworkofW.B.KirkeinconnectionwithcableinductandindicatesthatthisworL:formedthcbasisofthepresentNELA-IPCEAmethod.Employingaductbankcon-GgurationsuchasshownbyWollastonandutilizingequations14and17oftheKirkearticle,weGndthatKiri:ewouldusearesultantthermalresistancefromloadedductmalltoearthambientof9.0fortheworstsoilinmetropolitanNewYorkand6.00forthebestsoiLThesevalues,whencomparedwithNELAconstantof4.9,scarcelyconfirmMr.Thomas'tatementtotheeffectthatthepresentIPCEA-NELAmethodisbasedonorisevencloselyrehtedtoKirke'swork,WhileKirkemadesomeattempttotakeintoaccounttheconfiguratioao!theductbankstructure,hedidnotutilizeresistivityassuch,andaspreviouslyindicatedwebelievethataknowledgeofthisandotherparametersignoredbyKirkeisessentialtoarealisticmethodo!handlingthisproblem,par-tlcuhrlywhenoneconsiderstheproblemofcomparisonbetweendifferenttypeso!+steals.hsMr.Thomashassuggested,theheatQominaductstructureiscomplex,butthiscomplexityresultsfromthesuperpositionofanumberofheatBowsanyoneofwhich,duetoaparticularcable,isreadilydeter-minedasindicatedinreference12.WearenotinterestedintheseheatQomsfrcrzc,butonlyintheresultingtemperaturedifferencebetNreenareferencecableandambientandthecorrespondingthermalresistancewhichisfullyexpressedbytherelativelysimpleequationgiven.True,thesituationiscomplicatedbytheconcreteenvelope,buthereextensivestudies,bothmathematicalandonaGeldplotter,in-dicatethattheequation44(A)issufii~cientlyaccurateinviewoftheinherenterrorsinGxingtheearthresistivityandlossfactorinaparticularsituation.Mr.Short,atthestartofhisdiscussion,statesineffectthatheconsidersthemethodfordeterminingtheloadcapability.ofdirectearth-buriedorpipe-typecabletobe"mellfounded"fora100%loadfactorbut,becauseofquestionsraisedbyvariousinvestigatorsinreference3ofourpaper.doesnotseemtobetoosure,thatthisisthecaseforotherloadandlossfactors.hllfourinvestigatorsmhoundertooLtoitudytheproblemfortheInsuhtedCon-ductorComniittee,however,areonrecordasrecommendingoragreeingtothemethodgiveninthepresentpaper.Inacceptingthegivenmethodforburiedandpipe-typecable,Mr.ShortdoesnotseemtorealizethatthismethodisbasedontheKennellyfozmulabecauseinthelatterportionofhisdiscussionhequestionsthcapplicabilityoEthispremisetocurrentratingdetermina-tionsforanytypeofundergroundinstalh-tion,andproceedstoattempttoresurrectanuinberoftheghostswhichplaguedtheInsuhtedConductorCommitteesome10yearsagowhenthelatterstartedworL:anacriticalreviewofthebasicparametersinvolvediuloadcapabilitycalculation.Theseghostsweresubsequentlyhidtorest,atleasttothesatisfactionofthevastnujorityofengineersinthiscountry.EvenatthattimetheKennellyforznuhhadbeeninexistenceforover50years.Despitethefactthatthisfozmuiaisbasedonscientificprinciplesfoundinmosttextbooksonphysicsandelectricalengineering,somecableengineershadmisgivingsastoitsapplicabilitymainlybecausecalculationsbyitdidnotappeartochecLwithmeasure-znentsintheGeld.Thissituationisdis.cussedinreference12ofourpaperwhereinitisshownthatthedisagreementwasnotduetothefozznulabuttothefactthatthe6eldmeauraaentshadnotbeencarrietoasteadystate,andthatlaboratorydeterminationsoftheearthresistivitywerenotrepresentativeofthcsoilinsitu.Also,theappareqtdiscrepancy(whichappearsbecausethcdirectionoEheatQowimpliedintheEozmu!aIstowardthesurfacewhereasinsummerthetotalheatQowintheearthisobviauslyinthereversedirec-tion)isexplainedbytheapplicationoftheprincipleofsuperpositiontotheseparateheatGeldsinvolved.Asaresult,cableengmeezs,withveryfemexceptions,haveacceptedtheformulaforcakulationsin-volvingpipe-typeanddirectlyburiedcablesystems.Themethodofhandlingcablesinduct,giveniathepaper,isalogicalextensionofthepriaciplesunder-lyingtheKennellyfozmuIainordertoincludeinthecalculationstmoveryim-portantvariableswhicharenotapartoftheNELA-IPCEA.method,namelytheduct.configurationandthethermalsistivityofthesurroundingsoB.Thismethodisalsonotnew.ItmasGzstdescribedbyN.P.BaBeyiaapaperin1929'ndsubsequentlyiareference13ofourpaper.Mr.Shortalsomentionsthetwo-thirdsfactor,anotherresurrectedghostofthepast.Long'gotheBritishestablishedthatthetwo.thirdsfactorrepresentsadiffezencebetweenlaboratoryandincitsmeasurementsofsoilresistivityandthatitdoesnotstemfromanylackofapplicabilityoftheKennellyformulatothepzablezn.NumerousBritishpublicationspointoutthatthetmo-thirdsfactorisnottobeusedwheretheresistivityismeasuredinsitsbyburiedsphereorbylongorshortcylinder.Inaddition,inrecentyearstheBritishhavedevelopedanewlaboratorysamplingprocedure'hichchecksnotonlywiththebuziedsphere,theburiedcylhider,thetransientneedle,butinadditionalsocheckswithresultsobtainedonloadedcableinstallations.AnotherghostmentionedbyMr.Shortisthedeepisothermalapproach(aproposalwhichmasGrstsuggestedbyLevyin1930)'itingthedeKus,Sandiford,andCamezanspapertogivenewlifetothisoldsuggestion.However,insodoingMr.ShortfaBstopointoutthatthedeepIsothermalinthiscaseconsistsofaconductingpaintelectrodeofananaloguemodelconnectedelectricaliytoanotherelectroderepresentingtheearth'ssurfaceandhencesimulatingalfrruiing(notstationary)groundwatersink,asomewhatunusualconditionthatisscaredypertinenttotheproblemathand.Incidentally,TableIofthispapergivesresultsofanexcellentanalogcheckofthegivenmethodasappliedtoaductbank.WewishtoassureMr.Shortthatwehavenotcorneredthenonferrousmetalmarket,norarewesaymgthatthreesingle~nductorcablesofagivensizeinsuBedinaburiedpipemusthavethesameratingasthreeconductorsofthesamesizeInstalledinseparateducts.Weshouldpointout,however,thatthishasbeenaruleafthumbforthepast10yearsormoreandtherearenowmanyznilesafhigh.voltagepipecableinsuccessfulservicewhichareratedandarebeingoperatedataloadcapabilitylevelwhichMr.Shortconsidersincomprehensible.Mr.Short'sdilemmaresultssolelyfromOCTOBER1957Nchcr,hfcGratli-T'crnpcraturcandLoadCapabih.'.;ofCableSystcrnz771

~-eat'd'ilt otheEactthatheisattemptingtocomparether,cultsofcalcrdationsmadeundera~~~~setofassumedconditionswiththeresultsofaprocedureforwhichthosesamecondi-tionsarenotstatedandinfactareunknown.ThisIsasituationwhichexistedimme-cHatelyEoHowingthewazandisoneoftheghostspreviouslynzentioned.ConductorsizedeterminationsforcableinductutHizfngtheNELAconstantsrequirenoknowledgenorconsiderationo!soilre-sistivityassuch.Ontheotherhand.suchdeterminationsforpipe-typecablesystemsbyanypracticalmethodrequireaspeciflcnumericaassumptiontobemadeastothevalueoEsoilresistivityinordertoaniveatananswer.BytakingthestandthattheconcealedresistivityinthcNELAconstantsis120oz'ore,iCisthuspossibletoobtain,anadvantageinfavorofduct-Iaycable.Furthermore,becauseoEtheuseofcablespacingfactorsandearthandconcretethermalresfstivltlesintheproposedmethod,itmillbeobviousthatcalcuhtionsbythegivenmethodwillcheckwiththoseoftheIPCEAmethodonlyforcertaincombina-tionsoEthevariableparametersinthemethosLSincetheseparameterswerenotGxedandinFactarenow'nknownasre-gardstheNELAductheatingconstants,itisobviouslyhnpossibletomakeafactualcomparisono!theresultsobtainedbythctwomethods.Hereagain,byassumingearthresistivitiesoE120or180asbothMr.ShortandMr.WoHastonhavedone,thcgivenmethodwHIresultinhrgerconductorsizesthantheIPCEAmethod.DespitetheFactthatbothMr.ShortandMr.ThomasrefertothepresumablylargeamounCofFactualdatawhichunderlietheNELAductconstants,wehavebeenunabletoascertainthespecfflc'conditionsonwhichtheseconstantswerebasednoristhereanyindicationChatearthresistivitymcaswementsweretakenasapartofthedata.AboutaHthatcanbedone,there-fore,IstoassumerepresentativecableandductconflguzationsandthentocaIcuhtetheearthresistiviCyrequiredinthegivenmethodtomatchthcvaluecalculatedbytheIPCEAmethod.Wecannotagreetothevaluesgivenas"theaveragecondi-tionsonwhichtheNELAductconstants~vereobtained"asstatedbyMr.Short.Rather,vrebelievethattheconditionsassumedinreference18aremuchmorerepresentative,on'thebasisofwhichanaverageearthresistivityof75wasobtainedat100%loadFactor.Wetaketheposition.therefore,thatthevalidityoftheproposedmethodisnottobejudgedbywhetherornotthecalcuh-tionsmadebyitusingparametersarbi-trarilypickedbyMr.Short(orbyMr.Wolhston)agreewithcalculationsmadebytheIPCEAmethod.RatherwefeelthattheapplicabilityoftheIPCEAmethodtoaparticularcasedependsuponhowwellitcheckswiththemethodwhichwehaveproposed,andwhichtakesintoaccountmoreproperlytheessentialparam-eterswhicharepertineuCtothecaseaChand.WithrespecttoMr.Short'sspeciflcquestion,wehopethatutilityengineersmill,adopttheproposedmethodbutwedonotthinkthattheywillGnditnecessarytoreduceloadsunlesstheyhaveveryhighvalueso!earthresistivity.Regardingtheneedforreductioninloadsonexistingdrcuits,iCshouldbekeptinmindthatitisonlyrehtivelyrecentlythatAEICspedflcatfonshavemadeprovisionEorIncreasedpermissibletemperatureHmitsEoremergencyperiods,andforthegreaterportionoftheperiodthattheseemergencylimitshavebeeninefectthenuznberofcompanieswhohaveutiHzedthemisrelativelysmaH.Asaresult,thegreaterportionoEthecablesnowinservicehave"beensdectedonthebasisthatnormal~permissiblecoppertemperaturewouldnot,beexceededunderemergencyconditions.Moreover,inrecentyearsanumberofasszsframeasurementshavebeenmadewiththetzansientneedle,thesphere,ortheburiecylinder.Theoreticalstudieshaveshownthatmeasurementofultimatesoilresistivitycanbeobtainedreadilyvrithsuchdevices.WhHeinmanycasesthesehavebeenmadeinconnectionwithpipe-typecableinstalhtions,theyapplyequaHyweHtoductbankinstalhtionsinsofarastheresistivityo!thesoilitselfiscon-caned.Thevaluesingeneralrangefronz50to100withsomehighervaluesastheexceptionatcertaintimesoftheyear.Moreover,overthepastdecadeanumberoEpipetypeInstaHatlonshavebeenin-staHedinthiscountrywithdesignre-sistivitiesinthe70to90range.Underthecircumstances,wedonotbelievethatitwillbefoundnecessaryinmostcasestoreducetheloadsonexistingcircuits.However.wedobelievethatengineersmillbewelladvisedtotakestepstoascer-tainthevalueio!thermalresistivitywhichareapplicablefortheirconditionsbecausewiththemoreliberaluseofemergencytemperaturelimitsandthetendencyforshiECinmanyareasintheloadpeaLfromwintertosummer,theexistingmarginmaybereducedtoalovrlevelhcthenottoodistantEuture.Thevaluesofsoilresistivityof80and120usedintheexamplesofAppendixIVwerechosenmerelyEorpurposesofiHustra-tionandthevalueof120ratherthan80wasusedinthcductIaycaseinordertoemphasizetheeffectofadifferencebetweentheresistivityo!earthat120andconcreteat85.UnlikeMr.Short,Mr.WolhstonisverycarefulinhisdiscussiontomakeitquitedearthathiscommentsrelatingtoacomparisonoftheresultsobtainedbythegivenmethodandtheNELA-IPCEAmethodispreznisedonhisownarbitraryassumptionofaconcealedsoilresistivityof120intheNELAconstantsandonbisimpression,presumablybasedhrgclyonanunpublished1947memorandumbyG.B.Shanklin,thataresistivityof180isrepresentativeofaverageconditions;conse-quently,thevalueof55whichwasobtainedbybackcalcuhtionfromthegivenmethodutIHzinghistestresultsindicatesadis-crepancyiathemethod.WebelievethatifMr.WolhstonwiHconsultsomcrsofthemanyreferenceswhichhaveappearedinthetechnicallitemtureoverthepastfewyearsondeterminationsofsoilre-sistivityhconnectionwithexperimentalductbank,buriedcableandpipe-typecableInstaHations,eitheraloneorinconjunctionwithburiedcylinders,spheresortransientneedles,thathewillGndthatthereisnolongeranyjustiflcatfonforanInferredresistivityoEtheorderof120intheNELAconstantsorforhisimpressionthatare-osistivityof180isrepresentativeofaverageconditions.InasmuchasnoactualmeasurementwasmadeofsoilresistivityatthesIteatwhichMr.WOHastonobtainedanindicatedvalueof55,thereare,ofcourse,severalpossibleexplanationsthatsuggestthemselves.As-sumingtheternperatur'emeasurementswercmadeaccurately.perhapsthesoilactuallyhadaresistivityofthisorderofmagnitude.Fromrecentstudiesonsoilsandtheeffectso!suchmattersascomposi-tion,density,compaction,particlesize,etc.,itIsevidentthatitisverydifGculttoestimatetheresistivityofasoilfroncappearancealone.Alternatively,itcouldbethatthemeasuredvalueofresistivityisnottheultimatevalueasaconstantloadappliedfor5dayswouldnotsuflicetobringtheductstructuretoitsulthnateteznpera-tureriseoverambient,unless,o!course,itbadbeencanyingsubstantiallyfuHloadforsomethnepriortothetestinquestion.Mr.Wolhstonmentionsthatthetempera-turewasmeasured20feetfromthenzan-holebutdoesnoCindicatethelengthoftheductzunorfwhichthetestwasconducted.Thisraisesaquestionastovrhetherinhisparticularcase,therecouldhavebeenanyaHeviatioaoftemperaturerisebylongi-tudinalheatflowor,alternatively.bylongi-tudinalconvectioneffectssuchaswereFoundinthetestsmadewithductsopenandplugged.'spsasscss1.HsATPaowrooseUscosaoaoUNDEtscralcPowsoCAsass,NeilPBaser,AEEETroarocrroer,voL48.Jao.1020.pp.15&45.2.hNEvAAUAcroscovTwoRarrobfavsroosovhsssssQcozsrsTosaMAlRssrsrsvtvvorSoralW.Marcosrsrd,E.blochrrarrcf./oreer,lascrcncroaolElcccri<<alEazlacers.London.Eacland.vol.103,pt.h,no.CZ,Ocz.103d,p.433.3.CAsanHoarrscoUcUscoeaoaoowoDUcrs.R.D.Levy.CcacrerErccrrlcEcvrcsc,SchcncccadrrBLY.,hpr.1030,p.230.4.Seereference2olMr.Shocc'sdrscnsslon.SToktoaAcnaoRrsoAooCUaaoscvRavncoorCAsassLArn'scDocTszEBoWedrnote>EEoHorchlass,Rcporr,Rr/rrcrrccP/Tlos,TheBclrlshElectricalaodhrricdindustriesResearchhssoelacloa,Loadoa,Eazla'ad,1035.""2Ndhdr,sVcGraffi-7drrrsrrr!UrncrtTer>Crrsntrr:rsrnr/nlnVvrlrmrArvnrsocr1rrX7 THXSPAGEXNTENTXONALLYLEFTBLANK 1~*CeiI0~

F.H.BULLER*-."=J-rH.NEHERMEM8ErtAlEEMEMEERAIEEONEstepinthecalculationofunder-groundcabletemperaturesinvolvesthedeterminationofthetemperatureriseofthe.cablesurfaceabovetheimmediatelysurroundinginclosuresuchasaductstruc-tureoragas-oroil-fliedpipe.SincetheinterveningmedimnisaQuid,themodeofheattransfersimultaneouslyinvolvesconvection,conduction,andradiation.Thesemiempiricalmethodsnowinuseforthisdeterminationinthecaseofcablesinductarenotentirelysatisfactory,andvriththeadventofgas-oroil-fliedpipe-typecablestherehasarisenadefiniteneedforamethodofevaluationforthesecabletypesasweU.Becauseofthecomplexnatureoftheproblemandthenumberofindependentvariablesvrhicharepresent,itisimprac-ticaltocovercompletelyallpossiblecom-'inationswhichmaybemetwithinprac-ticesolelybytests.Bydevelopingatheoreticalrelationshipbetweenthevari-ables,however,itispossibletodevelopproceduresbywhichthetestdataavail-ablemaybeanalyzedinsuchawaythatrelativelysimpleworkingexpressionsmaybederivedwhichmaybeappliedwithsuflicientaccuracyovertheentireworkingrange.Thetheoreticalrelationshipforthecaseofcablesinductwasrecentlypre-sentedinapaperbyoneoftheauthors.'nthepresentpaperthisrehitionshiphasbeenextendedtocoveroilandgaspipesystemsastvell,andfromthetestdatapresentedtherequisiteworkingexpres-sionsforthermalresistanceorsurfacere-sistivityfactorshavebeenobtained.TheoreticalConsiderationsThetheoreticalrckitionshipsgiveninAppendixIIofreference1forthecaseofcablesinducthavebeenexpressedmorecompletelytoaccountforthephysicalcharacteristicsofthemediainvolvedinAppendixIofthispaper.Theresultingequationsforthethetherinalconductiv-itybetvreencableandductorpipevrithairorgasastheinterveningmediumareQ0.092Ds"/'sT'/'P'/'sT1,39+Dr/Dd0.0213,+0.102Ds'c(1+0.0167Tm)IogtsD4/Ds'attsperdegreecentigradefoot(1)andwithoilasthemediumQ,0.053D"/'nT'/T'/s0.116-(oII)',+CsT1.39+Dr'/D4logisD4/Ds'attsperdegreecentigradefoot(2)ForasinglecableD,'aaDthediameterofthecable.ForthreecablesinthepipeorductitiscustomarytobaseD,'nthecircumscribingcircleofthecablesintri-angularconfiguration,D,'m.15D,.FortvrocablestherelationshiPDsraal.65D,issatisfactory.Itwillbenotedthattheprimaryvari-ableinequationIisDrAsaresultsllb-sequentanalysisanddevelopmenti>>illbefacilitatedifthisequationiswrittenintheequivalentformQ0.092CsT'/sP/'s'aTDs"/'(1.39+Dr'D4),+0.102c(1+0.0167Tm)0.0213D,'ogD4/Ds'attsperdegreeccntigrad>>footinch(1A)Fromthemethodofderivationwhichassulnesacoaxialarrangementofthecablewithintheductorpipe,thenumeri-calconstantsofthefirsttwotermsoiequationsI,1(A),and2mustbecon-sideredasbeingapproximateonly.Theywillserve,however,toevaluatetherela-Btdlcr,iVchcr-ThcrnrcfRcsislanccTheThermalResistanceBetweenCables<<s'4v~andaSurroundingPipeorDuctWalltivemagnitudesoftheterms,andthecorrespondingvaluesfinallyemployedwillbebasedontestdataAsapracticalmatter,ahighdegreeofaccuracyisnotrequiredsincethethesmalresistivitybetvreencableandductorpiperepresentsa'relativelysmallpartofthetotal.thermalcircuitandwearejustifiedinmateriallysimplifyingtheseequations.Fromthestandpointofanalysisofthetestdataandthesubsequentdevelop.mentofworkingexpressions,itisdesir-abletoutilizethesimplelinearrehtion-shipymax+bwhereyandxarevariablesandtiandbareconstants.Equations1and2areofthisformprovidedthatthesecond(con-duction)andthird(radiation)termsinaybeconsideredasconstantswithinthede-siredaccuracyoftheGnalresult.Con-sideringequation1Atheconductiontermconstitutesabout14percentofthetotalinthecaseofatypicalcableinductin-stallation,andabout8percentforatypicalgas-fliedpipe.typeinstallationat200poundspersquareinch.Thecorre.spondingvaluesfortheradiationtermare63and43percent.NormalvariationsinD,'/Ddmaypro-duceconsiderablevariationinthecon.ductionterm,buttheeffectontheover-allpictureissmall,becauseconductionissuchasmallpartofthetotalheatQotv.VariationsofTcanaffecttheradiationtermbyasmuchas20percentoverasullicientlywideoperatingrange;hot>>.ever,whencalcuhtingacablerating,withafixedcoppertemperatureoftheorderof70degreestoSOdegreescentigrade,th>>rangeofthisvariableisverysmall,andanaccuracyoftheorderof3percenttn>percentmaybeexpected.Inthecaseofequation2,theconduc.Paper50Sz,reeommcodedbytheAiEElatedCooductorsCommsttceaadapprovedtheAlasTcchnicalprotramCommitteeiorpres'otatioaattbchlEEWinterQcacrathfcctinc.He>>YoA,H.Y..January30.February3.I93".SfaauscriptsubcaittedOctobersl.t949:availableiorprioriesDecembery,19t9.F.H.Eot,tcais<<ithtbeGeneralElectricCom'aay.Scbcoeetady.H.YandJ.H.<<iththephiladelphiaElcetriecompany.Fhna'elphi~,Pa.AIEETEAishcTtoHs r

Tablel.TestDataonGas-RiledPip>>TypeCableSystemsTeatItumberSourceQal'/7'/D'rpQa7i'a'7D,"I'able1LTestDataonCableslnRberandTrantlteDuctsEncasedlnConcreteTestItomberSourceQa7'I7'IDlD,'DrQal','al'I5........Bareoseher........Fiber.......o.d9....3.S....1.0....d.4.....0.228........1.T41.7....11.8.....0.203........2.032.5..~.IS.L.....0.235........2.LT4.4...24.8.....0.25T.......2.44S.d....34.2.....0.281........2.SS8.1...39.T.....0.295........2.7812.3..~.Sd.1.....0.318........3.001.13....3.5....1.0....4.$..~..0.20l~.......1.411.7..~.7.1...7.0.207.....~..1.$94.S..~.Id.3.~...0.248........1.9S8.0....30.4.....0.233........2.2811.0..~.32.8.....0.300.~~.....2.3214.8....48.S.....0.288........2.8218.8....$2.4.....0.28$........2.dl18.4....S8.7.....0.278........2.893.13....3.5....0.9....I.d.....o.194........0.S4I.T....3.2.....0.173........1.002.4....3.8.....0.203........1.0$4.5....7.7.....0.188.....~~.1.758.1....12.1.....0.213..a.....1.40)4.8....21.9.....0.217........1.53S........Jobos-Matteille....Piber.......s38~~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........1.5019.8,19.4.....0,299......1.$523.3....22.0.....0.314........1.502d.4....24.$.....0.318......~.I.ditiontermconstitutesabout24percentofthetotalforatypicaloilpipeinstallation.Variationismoreimportantthanisthecasewiththegas.pipecable,butisstillwithintolerablelimits.Onepeculiarphenomenonhasbeenob-served.TheratioofDJDQ',whichap-pearsintheconductiontermaIso,ap-pearsinthefirst{convection)tennofequations1and2butinsuchawaythatachangeinthisratioproducesanoppo-site,thoughlesser,'ffectonthetotalvalueoftheseequations.Aminimumerrorshould,therefore,prevailwhentheconductiontermistreatedasaconstantifthedenominatoroftheconvectiontermalsoistreatedasaconstant.Thisprocedurewillsimplifytheconvectiontennbutitwillhavetheeffectofapproxi-matelyhalvingitsnumericalconstantascomparedwithequations1and'2sincethenumericalvalueofthedenominatoromittedisintheorderoftwo.ActuaUythetestdatCwasanalyzedbothwithandwithoutthissimplification,andnoap-parentchangeinconsistencyinthere-sultswasobserved.AnalysisofTestDataItfollowsfromtheprecedingdiscussionthatthetestdataforcablesinductandforgasfilledpipe.typeinstallationsmaybeanalyzedbyplottingtheobservedvaluesofQ.CaT'I'pV'~-'gainstx~(4)DD'II?"DID/DThedatagiveninTableIwerecompiledfromtestsongas.fillepipe.typecablesystemsbyTheDetroitEdisonCom-pany,'heGeneralElectricCompany,I.....DetroitBdlsotaCompaay....3.42...8.07...I.~.23.4...20...$2....0.34......1.$87.8...27.3...15.8...$1....0.51......4.0814.8...28.8...13.1...$1....0.84......5.3428.9...17.1...50....0.49......5.7128.9...14.4...$L....0.59......$.4827.5...14.0...51....0.$8......$.432..~~.CeoeraiBieetrieCompsoy...3.92...8.07...1,7...73...8.2.,39..0.30...I.d4Il.i".9.T...4$....0.30......1.83IS.2...12.4...50....0.31......1.737.8...8.8...4.7...39....0.37......2.9211.5...T.0...43....0.42......3.2214.9...8.9.~.4S....0.43...~..3.4211.2...5:8...40...;0.49..'.::;4;22""1$.9.~8.0...4$.~,0.$1~~.~.4.$S3.....CeoeralCableCorporatioo...4.90...d.07...14.8...2$.9...9.2...$d...'.0.'ST'.."..'.'.4'.47.4.....GeneralElectricCompaay...4.90...8.07...14.8...23.1...11.8...44....0.40......4.77andtheGeneralCableCorporation.ThesedataareplottedinFigure1andthevaluesofaandbinequation3areestablishedasa~0.0?0;baeOM.TableIIpresentssimilardataforcablesinsingledtyfiberandTransiteductsinconcretetakenfromtheBarcnscheraandJohnsManvilletestsdis-cussedinreference1.ThesedataalsoareplottedinFigure1whereitwillbeseenthattheTransiteductpointsfallonthegasinpipecalve,butthefiberductpointsresultinadifferentcurvehavingthesamevalueofa~0.07but5~0.10.Thisdifferencemaybeexplainedbythefactthattheductwalldepartsfromanisothermalasaresultoftherelativelyhighthermalresistanceofthematerialsused,thatofthedlyfiberbeingconsider-ablyhigherthanthatofthetransite.'hetestdataforoil-filledpipe-typecablesystemsfromtestsbyTheDetroitEdisonCompany,'heGeneralElectricCompany,andtheOkoniteCompanyarepresentedinTableIIIandplottedinFigure2.Inthiscase,theanalysishasbeenmadebyplottingtheobservedvaluesofy~-'itainstx~DQ"i'CaTi'Tea'5)CDTandresultsinthevaluesofam0.026b~0.60inequation3.Itwillbeseenfromtheanalysisofthetestdatathattheagreement.betweentheoreticalandobservednumericalcon-stantsofthesimplifiedconvectiontermisextremelygoodinthecaseofoilasthemedium,butinthecaseofgas,theob-servedvalueof0.07issomewhathigherthantheexpectedvalueofabout0.046.Thisisrathersurprisingsincetestsnum-ber2(withgas)andnumber9(withoil)whichareconsistentlydosetothees-tablishedcurvesinFigures1and2weremadewiththesamephysicalsetupwhichremainedunchangedthroughoutthetestsexceptforthechangeinthemediaemployed.Therefore,weshouldexpecttheratioofvaluesobtainedtobethesameastheratioofthenumericalcon-stantsoftheconvectiontermsinequa-tions1and2.Thisdiscrepancyseemstobeduetothefactthatinthecaseofseveralcableswithinthepipe,aconditionofthemajor-ityoftestdata,thereisanadditionalcir-culationofthegasbetweenthecablesthemselveswhichisnotproperlyac-countedforbytheuseofanequivalentdiameterforthcthreecables,butwhichisapparentlynoteffectivewhenamoreviscousmediumsuchasoilisemployed.Asindicatedbefore,however,ahighdegreeofaccuracyisnotrequired,anditis1960,VoLUME69Brtllcr,Nchcr-ThcrrrralRest'slancc343 R,~4 Tablelll.TestDataonOilFilledpipeTypeCabfcSyslerasS.e"o~.rietraiae~.e~........~e~....4.83...8.07"0.....o.CeaerelSlleetrioCogaPsay...3.02...8.0710.......0boaireCogapeay........4.50...5.1325.2..o8.0....40....2.04.~.~...e194S.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........10534.9...11.7....48....2.08...132feltthataworkingexpressionbasedontheforegoinganalysismillbesufficientlyaccurate.WorhingEzpressions=--'nformulatingthethermalresistancebetweencableandduct,itiscustomarytoexpressthisresistanceintermsofanequivalentsurfaceresistivityfactor,as-sumingthattheentireresistancewasconcentratedatthecablesurface,accord-ingtotheexpressionHgc0.00411-,thermalohmfeet(6)pDg'nwhichpisexpressedindegreescenti-gradesquarecentimetersperwatt.SinceHgc~chT//Qitfollowsfromequation6thatDg'chTp243-degreecentigradecentimeterQperwatt(7)andv~~L~aKa'(QDg"Tm')'+24feet(ll)Thevalueofpfromequations9and10isplottedinFigure"3asafunctionof(Q'P/Dg')'andthe,valueofZ,cfromequationllappearsinFigure4asafunctionon(QD,"T')'.Alsoindi-catedonthesefiguresarethevalues'ftheseparametersfortypicalconditions.Inthecaseofcableinfiberduct,thethermalresistanceoftheductwallisappreciableandshouldbeaccountedfor.Thisismostreadilyaccomplishedbymodifyingequation6toincludethisre-.sistance.Thusa7Tost0lrataborSourceD'a04TTol',/doT'/dT/iFpa'(Gber)0.00411-,+0.33thernialohmpD,'eet(12)inwhichthesecondtermrepresentsthedifferenceinthesmalresistancebetweena4-inchfiberductaadthecorrespondingsectionofconcretewhichitreplaces.DiscussionofValuesforCablesinDuctItwiHbeseenthatthemethodofde-terminingthethermalresistancebetween'ablean'dductpresentedhereindifferssomewhatfromthemethodgiveninreference1,althoughtheresultsaresub-stantiallythesameforterracottaandfibreducts.ForTransiteducts,thevaluesofthermalresistancI:derivedinamorefundamentalmannerinthepresentpaper,areslightlylowerthanthoseappearinginthereference,beingequaltothoseassumedforterracotta.itwillbereoaUedthatthereasoniagusedindevelopingeigebraioeapressionsforthese,vauesassumesanisothermalduetwall.ThetestdatapresentedinFigurc1~Analysisoflestdataforcablesinduct-andgas@liedpipes0pl/tQI/d4T'~0.253-/,(degreescentigrade)'/'8)Itisthuspossibletodevelopworkingex-pressionsintermsofpinthecaseofcablesinduct-orgas-filledpipebysub-stitutingequations7and8inequations3and4withtheappropriatevaluesofoandb.Inthecaseofoil-filledpipeasimplerexpressionisobtainedintermsofFI,a.Forcablesinsingledryfiberducts13,700pQ/i/gdegreescen1ip/e~+$7D,'radesquarecentimetersperwalt(9)Forcablesinothertypesofsingledryos~4OsoToR13,700p.,/,,/,degreesccuti-p/'11.3D,'radesquarecciitimclersperwalt(10)Forcablesinoil.filledpipe00ev'r"p,vBullcr,Ãchcr-ThermalRcsisksnccA,lEETR~wsocTlo~s

~Q"aadplottedinFigureI,how->"dicatea.goodcorrelationeven4~,thereissubstantialdeviationfrom,@/assumedisothermalasindicatedbyehi'sicdataonwhichthetableisbased.iliatherangecoveredbythedata,in-'agthedeparturefromtheisother-mchangestheresultingconstantssome-ha'tbutdoesaotinvalidatethemethodlrf."analysis.'.;.ItfollowsthereforethataconsiderabletioninPforcablesinsingle-fibre..maybeexpecteddependingupon.Qativethermalresistivitiesofthewailand-theisurroundiagmedium,'ther.datawhichhascometothe'.atteationconfirmsthis.Thus~e'ofFiucts~oulasideredasanulimit.y,theapplicationothevaluescafoisingleductstothecaseofcables.;multiductstructure,dependsuponQectwhichthetotalheatfieldhasin'erchangingthetemperaturegradi-'tj'i'aroundtheindividualductwaHs.e.datagivenbySmithiahisdiscussion7(ence1indicatesavalueofpfor'riuitiple-fiberductsinconcretecorre-"adiagdoselytothecurveforcable~mar:~~peindicatedinreferenceI,addi-aI:.testdatatakenonmultiple-ductbliesaredesirabletodefinitdylishthelimitsundertheseconditions.'reasonsalsoindicatedinreferenceIvaluesarenotdirectlycoinparable'ithevaluesadoptedbytheInsulatedower'CableEngineersAssociationsand"aotdirectlyadaptabletotheircalcula-oir'procedure,X":nclusioast":.~Thetheoreticalrelationshipsbetween'variousquaatitiesinvolvedintheeQee-,:thermalresistancebetweencablesand;surroundingsingleductorpipehavebeen'evelopediaamannerwhichproperly'tsfor'thesimultaneousmodesolheatcrbyconvection,conduction,andtlon.I.'Ilymeansoftheserelationshipscertain0:~.testdataoncablesinductandingas-andod.fiiledpipeshavebeenanalytedandwork.g,curvesare'.presentedfordeterminingthe'resistanceloranyparticularcase~..maYbeencounteredinpractice..~j'-'Undertypicalconditionsrepresentative.esoftheequivalentsurfaceresistivity4foruseinequationBare800degree,.tlgradesquarecentimetersperwattlorfcs.'npipe,singledryterracottaor,fslteductsatatmosphericpressure,450Scabiesingas-filledpipe.typeinstalla-at200poundspersquareinch,and350Iesinoilfillcdpipetypeinstallation.tativevaluesofISforcablesindryfiberductswillvaryfrom850to100.~..'Vot.vwitGOMfJ,~,'\p80Q.TAppendixl.Theoretical'evelopmentofThermalCon-ductivity6etweenConcentricIsothermalCyclinderswithGasorOilasthe!nterveningMediumThemechanismofheattransferbetweenacylindricalradiatorandanenvelopingiso-thernialenclosurethroughaninterveningQuidmediumissuchthataportionofthetotalheatQowQiscarriedbyconvectionQ<<,aportionbyconductionQrc,andthcre-mainderbyradiarionQi.lnfOrmuhtingthecomponentsofthcthermalcircuit.thcrcfore,itismorcconvenientto<<orkintermsofthermalconductanccsratherthanthermalresistancessincetheforinerquanti-tiesaredirectlyad<liiivc.Thus,if3TisthetemperaturedropindegreescentigradeacrossthecircuitQQcrQccQi-+-+-wattsperdegrcccenti-aTaTaTaT'gradefoot(13)Figuic2.Anclysisoflestcfctcforcc6lcsinoil4lfccfpipeThephenomenonofconvectioninvolvestheconceptionofthetemperaturedropbeingconccntratcdintwofilms,oneatthesurfaceofthecylindricalradiatorofdiame-tersubstantiallyequaltothediameteroftheradiatorD,ininches,andoneatthesurfaceoltheenclosingisothermalsurfacewhichwillbeconsideredalsobeingcylindricalofdiameterDc.ThefollowingformulabasedonMcAdams'equation42,page251,1steditiononly)isapplicabletoeitherfilm.Q<<~12"DI'GATI'I'Kwattspcrfoot(14)inwhichDIicininches,and/d'cghi'~(--)wattspcrcentimeter'~'c-(')greescentigrade'~'15)Thcsignificanccolthecomponentsolequation15andrcprcsentativcvalueslorgas(airornitrogen)andSunisonumberBoilaregiveninTablelv.Bullcr,IVchcr-ThcnnalRcsisfancc3400lo'0so40soCo70eo9000nolaol300','T~T gooogIaooTYPICAL,aIOOFCAP<<l81EuILINOUCT51100BLEI~eeoONFIBRFOUC4IIsed/Og+.33doe243NsdOs~aNOOUCTCABLEINPIPEsEAAACOTTAATAANSITE-1w2$OFcyoa.<<4.$FILLETv'SOPIPE0aooLEINPIPESFIL5.1,TYPICALOfCAPIPEAT200P.2SOs4.$LE204040oogoouolaogoogoogoorgo240Zootaiy,sTs>'AFigure3(left).Valuesolpfoccablesindcysingledgccfsandgao-filledpipeRgure4(above).YafueoofHgaforcablesinoif-flllecfpipe0x,a,o,alaaaL4aaLe24J.oxa3.43.4s~Ao42fo"P/0;l'*Inthecaseofairorinertgas,thesephysi-calpropestiesaresubstantiallyindependentoftemperatureovertheworkingrangebutthedensityisadirectfunctionofthepressure.Thus,ifPrepresentstheprcssureinacmospheres,fromequation15Kcaa0.000755P'/'attspercentimeter'/'egreescentigrade'/'l6)WhenoilIsemployedasthemediumthcphysicalconstantsaresubstantiallyinde-pendentofprcssureandtempesatureswiththeexceptionoftheviscositywhichforthetypeofoilcornrnonlyemployed(Sunisonumber6)maybetakenasvaryingin-verselyasth>>cubeofthetemperatureac-cordingtotherehtionship94,000gramsperccncimetcrsecond(17)ThevalueofKforoilthusbecomesK~0.000434Teg'/'accspercentimeter'/'egreescentigrade'/'18)~~ao*x24ao4.4Aa44SO4.2Thesolutionofequation14forthetwo6lmsiaseriesandmithequation16orISsubstitutedthereinisgivenwithsufficientaccuracybytheexpressionsQcrDcdT'/'P'-(gas)m0.092wattspesde-dT1.39+Dc/Dcgreccentigradefoot(19)degreecentigradefoot(20)Fromatheoreticalstandpointtheex.pressionfortheconductioncomponentshouldtakeintoaccountanyeccentricitybetweenthecyiindsicalradiatorandtheenvelopingisothermalenclosure.Inthepracticalcaseofcablesinduceorpipethecableswillnotrestuniformlyonthebottomoftheduct,andalsointhecaseofanon-metallicducttheductIeafiisnotstrictlymaintainedasanIsothermal.Sincetheseeffectscannotbeevaluated,thefamiliarexpressioafortheresistancebetweentwoconcentriccylindersintermsofthedimen-sionsofthecylindersandthethermalre-sistivityofchemediummillbeused.ThusQ00213(011CL4LC40gra-(gas)-'aasperdegreedTloggoDc/Dccentigradefooc(21)Qcgr.0.116-'goal)-wallspardegreedTloggoDa/Dccentigradefoot(22)TheradiationcomponentwithgasasthemediumisgivenwithsufficientaccuracybythefollowingexpressionbasedonMcAdamssequation5,page61,GssteditioI),I0cNIAc~~-(gas)aa0.102Dgc(1+0.0167Teg)wattsd1perdegreecentigradefoot(23)inwhicheistheemissivitycoefficientofthesurfaceofthecableandT<<istheaveragetenlperatureofthemedium.Theradiationtermisineffectivecohenoilisthemedium.Theover.allthermalconductivityisob-tainedbysubstitutingequations19,21,and23orequations20and22inequation13.TableIVAppendixILListofSymI3otsSymbolQuaaiityOaaalSOCOllalsOCp...........Tbcrcasiresiscivicy...........,........Ccm/<<atc.......3900..........~~.TISga.......e...Averageabsoluteviscogicy.............grains/cmscc.....,0.000l95........0.75a..~........Deasicy...grams/cmg......,..0.00l'loP.......0.904Cr.~~~.~~~~~Specificbessaccoascaacpressure......,<<accsee/C.......~.0.99S~~..~.~....2.IOgragaS...........AeeeleratiaaduetOgravity..........Cm/SCC1...........990.~~.~~~~~~.990r.s......,..TIgcrgnaleocil'ieicntoi~cpaasion........I/C.......~~,~~~~~0OOSIO.~~~~~~~.0.00008Q~totafheatfloggrfromequivalentsheathtoductwallorpipeinwattsperfootd7awtemperaturedropindegreescentigradePaaprcssureinatmospheresD,~diameterofthesheathininchesDc'<<equivalentdiacnetcrofagroupofcablesininchesDa~insidediameterofchcductwallorpipeininchesBuflcr,/I/cIIcr-Tr'crrnalRcsisfancc3,IEETILAwsAcTIo85 T~'~averag>>t>>mperatureofthemediumindegreescentigradecoefficientofemissivityofthecable.sur-facerandy~rectanguhrcoordinatesaandb~>>xperim>>ntallydeterminedcon-stantsH,a~thermalresistancebetweenequiva-lentsheathandductwallorpipeinther-malohmfe>>tHsa'~equivalentthermalresistancebe-tweenequivalentsheathandGbrcductwallincludingtheincreasedtb>>imalre.sistivityoftheductwalloverthatofthesurroundingmediulninthermalohmfeetJ)~equivalentsurfaceresistivityfactorindegre>>scentigradesquarecentimetersperwattsI~thermalresistivityin.degrc>>scentigradecciltlnic'terspcfwa'tt'verageabsoluteviscosityingramspercentimeterssecond8~densityingramspercubiccentisneterC~speciffcheatatconstantpressureinwattsecondsperdegreecentigradegramgaccelerationductogravityincentimeterspersecondsquaredc~th>>rmalcoefficientofexpansionincenti-meterspercentimeterdegreecentigrade.E~afactordependentuponthephysicalconstantsofthemediuminwattsperc>>ntim>>t>>r'iadegreescentigrade'<<.aReferences1,TNRTaxtRRATVRRRIRRotCARO'RsINADvcrBANC,JH.Licker.AlEETransassions,volume08,part1,1049,pages840-40.2.HRATTRAicsaisstoN(book)W,H.Mchdams,htcCsaas.HillBookCompany,)re>>York.Lc.Y.,dssteditloo,1033.3.TIIRRNAICRARAcraatsTIcsoFA120VvHICII'aessvaaGas.PIu.aoCARIRlnsTAttATICN,W.D.Sandcsson,J.Sticker,M.H.Mcasath.AlEE1raasassiaas,volumedT,Psst1,1948,pages487-08.4.ASrvorotTKRTaiitaaATvaeDts'salsaTio'IINEIRcsascCARtasINUaocacRovaoDvcrs,P.J.Baseacches.T'assis,DepastmeotolElectsicalEagioecsing,UaivessityolWisconsin(hfadlaon,Wis.),192S.S.CvaaRNTCARRTINoCAFAcITToFLNtaao.NATROPAFSR,RVS~RRANOVARNISKROCANRRIC1Nsw.ATRoCAaaas.PablisasionlruaIb<rP2P.Cgd,lasulatcdPoresCableEagineessAssociation(NcivYork,H.Y.),dsstcditioa,1043.DiscussionR.H.NorrisandMrs.B.O.Buckhtnd(Gen>>ralElectricCompany,Schenectady,N.Y.):Eiftci>>ntworkintheheat.transferfieldonavarietyofapplicationsrequiresawarenessofthedefinitionsandunits,inorderLoavoidconfusionandmisunder-standing.Inthispaperandotherpaperswrittenbycableengineers,confusionarisesastoth>>>>acctmeaningofth>>expression"thermalresistivity."R>>sistivityasnor-mallydeffncd(bytheAmericanStandardsAssociation(ASA)forcxasnple)isaprop-ertyofasubstanceandisnotaffectedbyitsgeometry;forexample,theresistivityofcopperhasaconstantvalueatanyspcciffedtemperature,whileitsresistancedep<<ndson,itssiteandshape.Thentheus>>ofthcword"resistivity"forsurfacephenomenaisamisuseofthcterra.Toshowho>>Lhcdistinctionbetweenresistanceandresistivitycatersintolhcpicture.thethermalcircuitforasingle-conductorcableinairisgiveninFigure1ofthediscussion.InthisGgure,iso,l,a,andraaretempera-turesofcopper,sheath,andambient.re-spectively,8isinsulationthickness,pisthermalresistivityofthcinsuhtingmaterial,sfz,isthelogmeanareaofthefnsuhtionforheatGow,s(saissheatharea,andficandigsarethecabl>>engineers'ermsfor"sur-faceresistivity"forfreeconvectionandradiation.EachfractioninthcFiguriisthcth>>rmalresistance;andwhenresist-ancesandtemperaturesarcknown,theheatdissipationofthecableisknown.Butinorderfortheresistancestobedimensionallyconsistent,th>>dimensionsofpmustbediffer-entfromthcdimensionsofl),andthereforepandffshouldnotbecalledbythcsamenanlcSincethed>>Gnitlonofpasthermalresis-tivityconformstoASAstandards,itmightbcbettertodenotellasth>>rmalresistanceofaunitsurface.Itsreciprocalh,isde6ncdassurfaceheattransfercoclffcient,oralter-nativelyassurfaceGhnconductance.Theconceptof~conductanceisparticuhrlyapplicablehere,asthetotalGlmconduct-anceisthesumofhrandhc.andthereforenumericallyeasiertohandle.Theunitsoflengthusedinthepaperseemtobeamixtureofmetricandengineeringunits.Acombinationofsquarecenti-meterswithfeethasnologicalbasis.Ifanycabledimensionswereexpr>>ss>>dincenti-meters,themixturelvouldbclogicalal-thoughnotstandard;butsincedimensionsarenotsoexpressed,itseemstimetoaban-donthispracticeandusetheengineerinsystemofunitsthroughout.ItisthereforeproposedthattheAIEECominitteeonInsuiat>>dConductorstakestepstop>>rsuadeitsadherentstobecomefamiliarwithASAstandardsandtousethem<<heretheyapply.ILW.Burrell(ConsolidatedEdisonCom-panyofNeirYork,Inc.,NewYorL,N.Y.):TheauthorshavepresentedadesirableelaborationofAppendixIlofapreviouspaperbyMr.N>>h>>r.'lthoughtheap-proachtotheproblemisuotchanged,thelnaterialpresentedintheAppendixreferredtoisofsufficientimportancetojustifyamoredetailedpresentation.ILisapparenttothoseengagedinthe6eldofcableheatingthattheInsulatedPoirerCableEngineersAssociationrecommendedvalueofl),whileperhapssufficientlyconser-vativeforgeneraldesign,lacksLhcflexibilityneededincomparingalternativeconstruc-tions.Precisedeterminationsofig'orvarioustypesofinslalhtionsmaynoLbepossiblebecauseofinherentvariationsinthephysicalconstantsinvolved;however,asadditionaltestdataarecompiled.then,AwFlgvsel.'hesinclcircuitfossingleconductorin~isprobablerangeofig,foraparticularcase,willbebetterunderstood,Lh>>rebymakingpossiblemorerealisticcomparisons.TheauthorschrifyourconceptionofthedfectofthevariousparametersinvolvedinthetemperaturedropbetweencablesurfaceandductorpipewalLForagivensystemofcablesinductorpipe,theth>>rmafresistancewilldecreasesensiblywithincreasingwattsloss.W.B.Kirk>>iintroducedthismodiffcationwhichistakenintoaccountindeterminingcableratingsfortheConsolidat>>dEdisonsystcfnAsonefollowstheassumptionsmadeinthispaper,thereappearvariouspointstowhichexception.mightbetaken.onthegroundthattheyarenotsubstantiated,forexampl>>ltheassumptionofthesameconstantintheexpressionfortheconvectionGhnat(hecablesurfaceandattheinnerductwall,thetreatmentofconductiononthcbasisofaconcentricsystem,andthearbitraryassumptionofancmlssivityco->>fffcientofthecablesurfaceof1.0.Yet,theimportantpointlsthatputtingallofthesevariousassumptionstogetherintheparticularformgiveninthepaper,theover-allendresultdoesproduceexpressionswhicharereasonablysatisfactory.Itisunfortunatethat,whilethebasicequationsandtheselectionofparametershardareasonablysoundtheoreticalbasis,theGnalworkingexpressionsgivenareessentiallyempiricalanddonotallowanaccuratedeterminationoftheseparateeffectofthethreemodesofheattransfer.Ontheaverage,thecalcuhtedvaluesofQfcaTfortheoil-6lledpipes,gas-611>>dpipes,andcableinductareabout5percent15percent.and55percenthigher,respectively,thanthemeasuredvahtesgiven'ablesI,II.andIIIofthepaper.Special-istsinthe6eldofcableheatingwouldbeinterestedinknowingwhichcomponentorcomponentsareresponsibleforthesedis-crepanciessothat>>xtrapoLttionintonewGeldscouldbeInadewithconffdence.Itisstatedinthepaperthattheagree-mentbetweentheoreticalandempiricalnumericalconstantsofthesimplifiedcon-vectiontermisdoseforthecaseofanoilmedium,butisoffappreciablyforthecaseofagasmedium.Italsocanbcsaidthattheconduction.radLttionconstantagreeslviththeoryforthecaseofagasmedium;however,forthecaseofanoilmedium.theconstanttheoreticallyapp>>arstorangefrom0.60,asgiveninthepaper,ton>>arlytwicethatvalue,dependinguponthevaluesofD,'andDainvolved.Fromtheover-allstandpoint,itneverthe-lessappearschattheexpressionsforJ)andH,a.asgiveninequations9,10,and11ofthepaperarequiteworkableandagreewithtestdataaswellascouldreasonablybeex-pected.Ahighdegreeofaccuracyinthecalculationofallowablecurrentratingsofcablesisnotycttobeexpectedbutimpor-tantworLhasbeendoneinthepastfcwyearsinchrifyingourunderstandingofheatflowthroughductstluctur>>sandtheearth,andthispaperisanimportantcontributiontosuchunderstanding.RBFBRBNcas1.Seeselcsence1olthepaper.2.TK~CaacvaastoaotCaataTallteaafva~sINSvaw*rDucts.W.B.Xlske.AlEEJoaraal.volume40,1030,paceSSS.1950,VOLUMEG9Bisllcr,iYchcr-Ther>>tnfRcsisfasscc347 f'a>>lieI~

R.J.Wlseman(TheOkoniteCompanycPassaic,N.J.):Ilikethcauthor'spaperverymuch.Itexplainsthethreemethodsofheatflowfromacabletoasurroundingmediutn,nameiy,conduction,convection,andradlaticn.Also,theygivethevariousparameterswhichinflueneceachfactornamely,cablediimeter,temperature,andtemperaturedifference,andviscosityofthemedium.Thevariousformulaslookquite"formidablewhenwenotetermsraisedtofractionalpowers.Itisnoteasytoobtainthcconstantsforeachformuhastheyaredependentoncondicionsnoteasilycalcuhblesoitisnecessarytogectestdataandworkbacktonurnericswhichwillgivethede-siredresults.Itsohappensthatasallthreemodesofheattransferarefunccioningatchesametime,achangeindimensioningtendstoworkinoppositedirections,reduc-ingthereby.chc,effectofdiame(er.AIsotherangeintemperatureisnotgreatandaswetaketheone.fourthpowerottemperaturedifferenceandthreefourthspoweroftemperature,thevariationwithtempera.tureisnotgreat.Abouttwoyearsagowedecidedtore-studythethermalconstantstreobtainedwhenweoriginallysetupthcOilostaticcablesystem.Atthattimeweusedthecylindricallogforlnulaofra(ioofinternalpipediatnetertocircumscribedcircleovertheassembledconductors,andalsoacon-stantwhichwasafunctionofthetempera-ture.Ourmorerecenttestsshowedchatthethermalresistancewasalmostindependent~oftemperature(avariationofabo'ut10percentbetween30and61degreescentigrade)foranoilpressurezoneandaveryfewpercentforagaspressurezoneat200poundspersquareinch.Wcalsonotedthatwithintheaccuracyoftestingwecouldsafelyassumethethermalresistancetovaryasinverselyasthediameteroftheshieldingtapeovertheinsulation.Asaresult,wehavesecuptwosimpleformulasforthedeterminationofthethermalresist-anceofchepressurezoneforthreecablesinapipe,namely,foroilpressuresystemH~1.60/Dthermalohmsperfootpercon-ductorwhere,Disthcdiameterininchesovertheshieldingtape;andH~2.58/Dthermalohmsperfootperconductorforagaspressurezoneoperatingat200poundspcrsquareinch.Youwillflndthesevaluesofthermalresistanceforthepressurezonesamplyaccurate.Astheauthorsrefertothesurfaceresis-tivityfactorP,thevaluesof4comparabletocheaboveconstantsinH~0.00411tt/DareIS390toranoil.pressuresystemascora-paredto350givenbytheauthorsandP~827foragaspressuresystemat200poundspersquareinchascomparedto450givenbytheauthors.Wearequtteconfldentinourvaluesandhavebeen'sin'g'theiiifoi'overayear.inthepaper,sincethisanalysisgivestheorderofmagnitudecontributedbyeachofthethreemechanismsofheattransfer.Theauthorshaveassumedforcableinductthatthecomponentofthethermalcon-ductivityductoradiationcanbetreatedasaconstantintherangeofnormaloperatingtemperatures.Onlythecomponentductoconvectionwasconsideredasvariablewithchangingcablediameterandheatflow.Thisassumptiondoesnotleadtoatruepic.tureofthevariationinthermalresis(ivitywithheatflow,ormorefundamen(ally,withcabletetnperature.Mr.Darncttand1havestatedinourpapertthatthedecreaseinthertnalresistivitywithincreasingsheathtemperatureiscausedprimarilybyvaria-tionintheradiationcomponentofheattransfer,andthattheeffectoftemperaturevariationsonconvectionarenegligibleoverthenormaloperatingrange..Thisstate-menCisverifiedbycalculationsbaseduponequation1AoftheHuller-Ychcrpaper,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)inwattsperdegreecentigradetootinch.Theemissivityfactor,c,isassumedtobeunityatattnosphericpressure.TableIofthediscussionliststworepre-sentativesheathtemperaturesfromourtestdataonflberductinconcrete,andthesetemperaturesmightverywellberepresent-ativeoftheoperatingrangeofacable.Theterm(Q/D,'hT)evaluatedinequation1Aisinverselyproportionaltothesurfaceresistivityfactor,tt.Thethreetermsintheequationgivethcthermalconductivitycomponentsduetoconvection,conduction,andradiationrespec-tively.Asweincreasethesheathtempera-tureovertherangeshowa,theincreaseintheradiationtennproducedbysubstitutingourexperimentaldataintheBuller-ocherequationisfivetimesgrezCerthanthatoftheconvectionterm.Thisshowsthattheexperimentallyobsetveddecreaseinttoverthisrangeisdueahnostentirelytothein-creaseintheradiationtetm.Thesecal-culationsarebased,ofcourse,ontheratherlargecablesizethatweemployedinourtests.Asmallercablesizewillincreasetheeffectottheconvectiontermonlyslightly,however,andnotnearlyenoughtomakeitsvariationwithtemperatureequaltoChatoftheradhtionterm.IdenticalcalculationswithourdataonTransitcinconcrete,Transiteinair,andfiberinair,showsimihrrelativevariationsintheradiationandcoti-vectionterms.Theauthorshaveneglectedthcvariationinradiationcomponentofconductivitywithtempenture,pointingouCthacthesevaria-tionsarequitesmalLThisisjustlfiablefromapracticalstandpoint.However,thevariationsintheconvectioncomponentwithtemperaturealsoshouldbeneglectedforpracticalconsiderations,since,asisshowninTable1ofthcdiscussionthisfactorisevensmallerthartthcchangeintheradia-tiontenn.Thiswouldconsiderablysirn-plifytheBailer-Heberequationsforthesur-faceresistivityfactor.lntheirequations9and10,(hesurfaceresistivityfactor.f4dependsuponthcfourthrootoftheheacflow.Thisdoesnochavemuchsignificanccsmceitisbaseduponthevariationinthcconvectiontenn,asecondorderelfccccom-paredwiththeradiationterm.Similarlythedependenceoftiuponthesquarerootofthesheathdiameterisdoubtful,sincechcchangefrom.afourthroottoasquareroocdependenceintheconvectiontermalsowasbasedontheverysmallchangeinconvectionconductivitywithtemperature.Theforegoingdiscussiontrasconfinedtocableinductwithairastheinterveningfluid.Itsapplicabilitytocableingas-filled'pipeathighpressures,whereconvectionbecomestheprincipalmechanismofheattranster,requiresfurtherstudy.Theauthorshavedoneanexcellentjobinhelpingcoestablishthetheoreticalground-worknecessarytobothencourageandguideexperimentalworkersintheductheatingproblem.RBFERENCEl.HearTU*ttsrcxSrvovottPoweaCast.aDvctsattoDvcrAssctcstses.Pau(Gteeblcr,GU7P.Batoctt.AlZZ7vaatoctioat,rolutoe09,panI,1950,paces$$7-07.Ii'~Irah0riL.~yitcTablel.Gtecblet-Becne((Da(~tsh.H.Kidder(PhiladelphiaElectricCom-pany,Phihdelphia.Pa.):ThispaperbyBullerandNeher,togetherwithtwopre.viouspapersbyMr.Neher,4tcompletespresentationofthesteady-stateconsidera-tionsinvolvedinaprojectwhichwasstartedaboutfouryearsagowhenPhiladelphiaElectricCompanyinterestedMr.archerinundertahnganinvestigationoffunda-mentalrelationships.'snecessarytodc(er-mineapproximatelywhatpipe.cypecablecircuitloadratingswouldbeaccuratelycomparablewiththcloadratingsofcon-ventionalcablecircuitsinducts.Thethermalresistancethroughthespacesbetweenthecablesheathsandthepipeorf'uctwallinclosuresisanimportantlinkinthethermalcircuit.Ithadbeenhopedthatageneralrehtionshipcouldbedevelopedini',suchaformthacallofchedifferencesbc-'>>~IPavlGreebler(JohnsManvilleCorpora-tion,Manville,N.J.):Inthispapertheauthorshavecontributedimrncnsclyto-wardanunderstandingofthemechanistnsofheattransferfrom(hecabletoicssur-roundingpipeorductavail.Thetheoreti-calanalysiswasnecessarilybaseduponthcsimplifyingassumptionofacoaxialcableinducearrangetnent.Thisdoesnot,however,detractfromthcvalueoftheanalysisgivenLeadSheathTemperatureCocldeDuctMesoV/allSot(aceTemperatureTemperatureulletNehetTemperatureEeuatloolADropCooccctlouRadlatlooarTctmTermGteebletBarnettDatattlo'C(cm)'/>>dd.2...77.2......40.$...........50.$......5$.0,....,.....0$.4...~~~ld.l.~...,00dx...o.Ipd....~~.990~..22.0.....,.0005...0.2ls~...,..020loctcaac000$...0.0l5,...,..00~decreaseTemperaturesacclodcrtcccceodetadc.Thclatldcduct>>attcut(acetemperaturelcauavctaeevalue.,'34SBttftcr,/V'cJtcr-ThcrnafRest'stattccAIEETRANSACTIONS

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

stweencablesinairinductsandcablesinhigh-pressuregasoroil-fliedpipescouldbeexplainedintermsofthephysicalconstantsichcharacterizetherespectivefiuidsandoertinentgeomctricatrelationships.:methodpresentedbyBullerandhasapproximatelyachievalthisre-sult,atleasttotheextentofpermittingthecorrelationofdataobtainedbyvariousin-vestigatorsatvarioustiinesinvariouscon-'structions.Itdoesnotdisturbinepar-ticularlytofindthatthereissomeapparentdifferencebetweentheelectsofTransiteandfiberductwalls,respectively,undertheconditionswhichprevailedatthetimethetestsweremade.Ithinkweshouldhesitatetoattachmuchsignificancctotheseappar-entdifferencesbecausetherewasnoattempttocontrolthemoisturecontentinthcfiberortheTransite,oreventomakethetestsunderconditionscomparabletothosetobcexpectedintheusualexposurestonaturalbutvariablemoistureconditionstobcen-counteredinundergroundstructures.ThesignificantpointisthatBullerandNeherhaveobtainedacorrelationivhichnowper-mitsestimatingthethermalresistancefroincabletopipeorductwallwithsufficicutaccuracy,sothatlittle,ifany,practicaliinprovementincableloadratingscanbegainedbyintroducingfurgherrefinementsintheiranalysisofthispartofthethermalcircuit.RspsRBNcssI.TaaTassraa*ruaaRiseorBvaiaoC*n,asAuoPiras,J.HNeher.AlEETroasersioar,olumeil8,pact1,1040,pages0-1T.Scerelcreace1olthepaper.F.H.BullerandJ.H.Neher:Mr.NorrisandMrs.Bucldandhavetakenussomewhattotaskforourapparent'inconsistencyinexpressingourphysicalunitsinonesystemandourgeometricunitsinanother.Forbetterorworseithaslongbeenthecustomincableratingproceduretoexpressthephysicalunitsinvolvedinthewatt-second-centimeter-gramsystem,andto~expresslength'sinfeetanddiametersininches.Indevelopingourequationsitwouldhavebeenmoreconsistenttohaveexpressedthelatterquantitiesalsoincentimeters,andtheatohaveconvertedthefinalexpressionsto'hesystemofmeasurementusedinpractice.Wcchosetousethemixedsystemthrough-out,however,inorderthagthereadermightbeabletouseanyequationinthcdrvelop-ment,directly,withoutencounteringtheuncertaintywhichinevitablyarisesastowhetheryoumultiplyordividebythetrans-formationconstants.Theuscofthetarn"surfaceresistivityfactor"isaslightlydifferentmatter.andasoursncntorshaveyoin]ed.out,ithasdimen-sionswhicharenotthoseoftrue,orvolu-metric,"resistivity."Hereagain,thisnomenclaturehasbeenhallowedbytiincandisthoroughlyunderstoodbycableengi~~~neers,forwhomthispaperwaswritten.Itshouldbestressed,however,thatthis"sur-rvceresistivity"isnotafundamentalrsicalquantity,inthesensethatvolu-..ctricresistivityis;butaspointedout,istheresistanceofaunitsurfaceofaflinwhich,purelyforpurposesofconvenience,isassumedarbitrarilytorepresenttheentirethermalresistanceofthecompositeheattransferelectsoperatinginther'egionbe-tweencablesheathandductwall.'ltisun-fortunatethatwedonothaveamoredis-tinctivenameforit.Mr.Burrellhaspresentedathoughtfuldis-cussionoftheassumptionswhichwehavemadeindevelopingthetheoryusedforcorrdatingthetestdata.Inthisrespect,abookbyProf.McAdamstgivesaconstantfortheconvectionfilmonthcoutsideofacylindricalsurfaceinafreemediumwhichisabout20pcrcentlowerthanthatforthein-sideofapipeandwhichwehaveusedforbothfilms.Wchavenotdistinguishalbe-tweentheLwoconstantsbecausenoinforma-tionisgivenastothcvaluesofthesecan-stantswhenthecylinderisplacedwithinthepipe.Whileaformulafortheconduc.lioncomponentinanonwoncentricsystemisgivenbyWhiteheadandHutchings'tisfartoocomplicatedtouseinthisanalysis,'anditreducessubstantiallytotheconcentricformulawhichwehaveemployedexceptforextremelysmallseparationsbetweenthecylindersatonepoint.Furtherthereisconsiderableexperimentalevidencetosup-porttheassumptionthattheemissivityconstantissubstantiallyunityforthetypesofcablesurfacesemployed.Discrepancieswereexpectal,becauseoftheassumptionswhichhadtobemade,a'ndbecausethephysicallocationofthecableswithinthepipecannotbecontrolled.Wehaveusedassumptionsandtheoryonlytoobtainasensibleunderstandingoftheproblemwithwhichwehavetodealandtodetermineivhatsimplificationscanjustifi-ablybemadeinordertoobtainpracticalworhngexpressions.Theseworkingex-pressionswerethendevelopeddirectlyfromactualtestsratherthanfromtheory.WedonotshareMr.Burrell'sdesireforworkingexpressionsofsufficientcomplexitytoidentifytheseparateelectsofthethreemodesofheattransfer.Dr.Wiseman'ssimplifiedformulasforcalculatingher(onapercablebasis)forthree'cablesinanoil-fliedpipeorinagas-filledpipeat200poundspersquareinchareveryintaestingandsimilarformulasmaybederivedfromFigures3and4ofthepaperassumingthatQ,P,andT~haveGxedtypicalvalues.UnfortunatelyDr.Wise-man'sderivationoftheequivalentPinhisformulasgivesvaluesivhicharenotcom-parabletoPasdefinedinthispaper.ThecorrespondingrehtionshipforPasdefinedinthepaperishgc0.00411032.15DNandthisyieldsP290fortheoil.pressuresystemandP~450forthegas-pressuresys-temWecannotaccepthisformulafortheoilsystemsinceitscorrespondingvalueonatotalheat'iowbasisis"Hrc"1.15/Dr'hichisequivalenttoQ/dT~3.9forDr'4.5.NoaeofthetestscitedinTable~IIIofthepapergivean('upportforsohighavalue.Dr.Wisemanalsoassumesthattheover-allthermalresistancevariesinverselywiththediameterwhereaswebelievethatamorerepresentativevariationmaybededucedfromtheslopeofthecurvesofFigures3and4inthevicinityofthetypicaloperatirgpoints.ThusforQ25wattsperfootandT~50degreescentigrade,wederivethesimplifiedexpressionsH,c(oil)~0.70/De"/sthermalohmteeL(I)Hrc(gasat200psi)~1.20/(Dr')'lthermalohinfeet(2)Theconespondingequationsonapercablebasisandwiththreecablesinthcpipeare1.442.07hrc~=andhrcm-respectivelyQp(D)~sFigures3and4areintendedtogiveprac-ticalworkingvaluesofhceorHrdoverawiderangeofoperatingconditions.Mr.Grecb-lerisrightinpointingoutthattheelectoftemperaturevariationsupontheradiationcomponentisconsiderablygreaterthantheeffectofvariationsintheconvectiontennwhichistheessentialvariantinFigure3.Theinclusionofthetemperatureofthcmediuminthcivorkingexpressionswouldvastfycoinplicatethem,however,andasapracticalmatterthisisunnecessary.InalloftheGreebler.Barnettdata'twillbeobservedthatPvariesinverselyasQ'/<withintheaccuracyofmeasurement.ThedependenceofPuponDrcannotbeevalu-atedfromthisdatasinceonlyasinglevalueofD,wasemployed,butsincetheconvectiontermtheoreticallyvariesdirectlyasQ'/</D'/swebelievethatthetemperatssrevariationintheradiationtermwhichGreeblerhasmentionedwillbeaccountedforwithsu%cientaccuracybyexpressingtheGreebler-BarnettdataforfiberandTransiteductsintheformJi(fiber)<<1120Ds'/'/Q'/'egreescenti-gradesquarecentimetersperwatt(3)lf(Transite)m990Dr'/'/Q'/'egreescenti-gradesquarecentimetersperivatt(4)Thiswillhavetheelectofchangingtheslopeofthecurves<<henplottedinac-cordancewithFigure3.'hecoirespondingvaluesofHrcassuming'worhngvalueofQm10wattsperfootHrc(Gber)m(2.59/Dr'/)+0.33thermalohmfeet(5)Hrc(Transite)2M/D,I'hermalohinfeet(8)Whilefurthertheoreticalandexperimen-talworkmaywellbeundertakeninordertoclearupsomeoftheapparentdiscrepanciesbetweentheoryandpracticeandtoyiddmorefactualdataonthcpafonnanccofcablesinduct;weagreewithMr.Kidderthatlittleofanypracticalimprovementincableloadratingswillresult.Wedonotwishtodiscouragefurtherelortsinthisdirection,butwefeelthatitissufficienttobasecableratingsonFigures3and4ofthepaperormoresimplyonequations(1,2,5,and,8)justgiven.Rspsasscss1Seeccfcreace2olthepaper.2,CvaaairrRarsuoorC*ai,asroaTaaNsaussiouauoDisraiavrsou,SeWhitehead,B.EHuichlags.sourceslastliutioaolElectricalBaciaecrs(toodoa,Eagieod),volume83,1038.cqueiioa10.3,page531.3.HearTaausraaSrvovoNPorvaaCaai.aDoersauoDoerAssausaas,PaulGreebler,Gusp.Beraeu.AIEETrcareaioas,volume80.pert'1,1030.paCes337-5Z.C.'DlscussioabrJ.H.Lleherolcclcreace3~bOvepegCs385~1950,VOL.URIB69Bsdlcr.>Vchcr-Thc.-nsalRess'starve ATTACHMENT3TOAEP:NRC:0692DFCABLETRAYALLOWABLEFILLDESIGNSTANDARD e~lp~sirmaoP

~J2.Inalltvpetrays,cablesshallbeplacedinthetravsinaneatworkmanshiplikemanner.Crossingofcablesshallbeavoided,cableoile-uosshallbekeottoaminimumandcablesshallnotextendabovethetopofthetray.(a)Wheninstallingcablesinapowertayplacetheoowercablesinasinglelayersoacedapproximately1/3theO.D.(outsidediameterofthecables)apart.SeeFigurel.(b)ThesurmtationoftheO.D.ofthepowercables~shallnotexceed75%ofthetraywidth.SeeTable1formaximumallowablefill.3.Wheninstallingcablesincontroland~strILRoentationtrytotalcrosssectionalareaofinstalledcablesshallnotexceed40%ofthetravcrosssectionalarea.SeeTable2formaximumallowablefill.4.Whenitisnecessarytoexceedthemaximumallowablefillapprovalfromtheresponsiblecableengineerisrequired.0FORSPACINGOISTAHCEKTWEEHCAMS5EEHOTE5IIZ.MLOWFIGUREfPOWERCABLESPACIAI6NOTES:f.FORCASLESOFEQIALQL,SPACIH6I&0EILZ.FORCAELESOFUHEOUALCLLSPAQH&ISI/AclL0FLARGER)casLE.~TRAYWIDTHALLOVYABLEFII.I.9TABLEIPOWERTRAYMA1IMUAIFILLTRAYVjIOTNALLOWASLEFIU.HI<&TRAY26.8AI.I.OWAOLiFILI.Ii.HIGHTRAY57.6w<TABLEZ~CONTROL(INSTRUMENTATIONTRAYMAXIMllMPILLHoTES:LASTRAYFILLAPPROACHESITSALLCWA8I~UAIITTHEFIELDSHALL'TAHENOTEItCAELESAREREACHIH6OVERTHE'SIDESCF'MTiIAY(Eli.OUETI5POOI4YTTAIHEOCASLES).IFHECESSARY,IMflED,ATITSOWAOISCRETIONSHALLINSTALLCoal.TRAYSIOEMAROPERI-Z-EOSC39(POS-.IIII).Z.INEATREAIECASESoRVIHERESIOEOOAROSc'AHHOTSGIIISTAuZO,&E,FIELO5HAu.INPORMTHE'ELECTRICAIPLANTACTIONTdCLONIC'THCThaY.IND(ANAclIVtCHlGANELECT.CO.D.C.COOKNUCLEARPLANTPos-II9I.Oc.LECTRICAIPLANTOESIGNSECTIONREVISION-CIPIANTOESIGNSTANOAROCABLETRAYA<<ONABL==AlAPPOOR.i'.CICH.LIST,IOATH'I-I'-54AM-RIC'NE'RICPC'A'KRS=RVICKCORP.I1EOSgy.QISHIOI.I ATTACHMENT4TOAEP:NRC:0692DFANALYSESANDMATHEMATICALMODELSThisattachmentincludesthepertinentsectionsofthereportonampacityprogramdevelopment.TheoriginalreportandthecomputerprogramweredevelopedbytheElectricalSectionteammembersAEPSC,NewYork.

l Vy~APPENDIXATHEORETICALDEVELOPMENTOFHEATTRANSFERPHENOMENAWITHRESPECTTOCABLEAMPACITYINLOWFILLCABLETRAYSA.lREVIEWOFBASICHEATTRANSFERMECHANISMSHeatenergywillflowthroughorfromabodybymeansofthreedifferentmechanisms:Conductionistheflowofheatfromapointofhighertemperaturetoapointoflowertemperature,throughabodyorfromonebodytoanotherbodyincontact,withoutsignizicantmolecularmovement.Theequationforonedimensionalsteadystatethermalconductionforasolidofconstantcrosssectionalareaisq=kA-b,TcdXWhere:qkAbT=XConductiveheattransfer.ThermalconductivityAreanormaltoheattransferflowTemperaturedifzerenceThicknessofsolidConvectionistheflowofheatawayfromthesurfaceofaheatedbodybythemotionofthesurroundingfluid(gasorliquid).Whenthemotionofthefluidisproducedmechanically,theactionisknownasforcedconvection.Whenthemotionofthefluidisproducedbydifferencesinthefluiddensityresultingfromtemperaturedifferences,theactionisknownasnaturalconvection.Theequationforheattransferbymeansofnaturalconvectionis:(2)Where:qhcvATssTaConvectiveheattransferConvectiveheattransfercoefficientSurfaceareaofthebodySurfacetemperatureofthebodyAmbienttemperatureofthesurround-ingfluid.Anybodyatatemperaturegreaterthanabsolutezerowillloseheatintheformofradian"energy.Likewiseanybodywillabsorbheatradiatecfromanyotherheatedbody.Thenetexchangeofheatisproportionaltothedifferenceoftheforthpowerofthe'rabsolutetemperatures.Thenettransferofenergybyraciationfromabodytoambientorfromabodytoasurroundingbodyseparatedbyanonabsorbingmediumisgivenby (3)Where:q=RadiantheattransferStefan-Boltzmanconstant(=Surfaceemissivity(afactorbetweenzeroandunity,unitybeingaperfectemitter-or"blackbody")A=SurfaceareaofradiatorsAbsolutertemperatureofsurfacesofradiator.Absolutetemperatureofambientaorofsurroundingbody.Inactuality,thetransferofheatwillbetheresultofthesummationofconductive,convectiveandradianttransmissionmechanismsor:@=a+q+q(4)Where:Q=thetotalheattransferA.2HEATFLOWINCABLETRAYSPresently,IPCEAStandardP-54-440istheindustrybenchmarkforcableampacitiesinopentgptray.MuchofthisstandardisbasedonworkdonebyStolpe.Theampacitiespresentedinthisstandarddependheavilyontheassumptionthatthecablesaretightlypackedandthatthereisnoairflowthroughthecablebundle.Thecablebundleistreatedasahomogeneousrectangularmasswithuniformheatgeneration.Basedontheabovecriteria,theallowablewattsperlinearfootofcabletrayisfoundtobeconstantforagiventotalcross-sectionalareaofcables(atagivenb,T).Referringtothefundamentalequationsforheattransferoutlinedintheprevioussection,itisclearthatconductiveheattransferisthegoverningheattransfermechanism.Thatistosay,allowableheatlossisinverselyproportionaltothethickness(i.e.,cross-sectionalarea)ofthebodythroughwhichtheheat,flows,foragivenb,T.Whenacabletrayisfilledwithcablestoadepthofonelayerorless,theassumptioncanbemadethateachcablewil'eexposedtoafreeflowofair.Inthiscasetheabovetreatmentofheattransferdoesnotapply.Forlowcabletrayfills,convectiveandradiantheattransferarethegovernincmechanism.Ifthisistrue,theallowableheatlossperlinea"footofcabletravwill.beconstantforagiventotalsurfaceareaofcablesasperequations(2)and(3)~Tnevalica"ronoftheabovetheorywhichisdevelopedinthenextsect'onisthemajoremphasisofthisdiscussion.

A.3HEATTRANSFERPHENOMENAFORCABLETRAYSWITHLOWFILLTheory:Whenacabletrayisfilledtoadepthlessthanorequaltoonelayerofcables,themaximumallowableheatlosswillbeconstantforagiventotalcablesurfaceareaatconstantaT.Aninitialassumptionwillbemadethattheabovetheoryistrue.Experimentaldatawillbeusedtovalidatethisassumption.Itwillthenbeshownthattheampacityforanycableinthetraymaybefoundbasedontheallowableheatloss.Theproblemwillbesimplifiedbyinitiallyassumingthatthetraycontainsonlyonesizecableandthateachcableiscarryingthesamecurrent.Inthisanalysis,perunitareareferstoperunitareaofcabletray.Thetotalcablesurfaceareapeiunitareais:A=nTt'dsWhere:Asnd(4)TotalcablesurfaceareaP.U.Numberof3PcablesperunitareaDiameterofeachcableP.U.Thepercentagefillofthetraycanbedefinedasthesummationoftheperunitcablediametersor:F=nd(5)Notetha"thisdiffersfromtheindustrystandardofdefiningpercentagefillbasedonthesummationofthecablescross-sectionalareas.Fromexaminationofequations(4)and(5)itisclearthatthesurfaceareaAwillbeconstantforagivenpercentagefillF.Thetotalheatgeneratedperunitareabyresistiveheatingofthecablesis:Q=3nIR2(6)Where:QIRacTotalheatgeneratedperunitarea.Conductorcurrenta.c.resistanceofconductorperunitlength.

Rearrangingequation(5)n=F/d(7)Substitutinginequation(6)Q=-IR3F2dac(8).Solvingforthecurrent(9)or(9a)AccordingtotheinitialassumptionQwillbeconstantforagivensurfaceareathatistosay,acertainoercentaaefill.Thereforeaplotoflva~dRacforagivenpercentfillahoulcyieldastraightlinethroughtheoriginwithslopeequaltoQ3F.PlotsofIvs.RacareshowninFigureA-1forseveralracewayconfigurationsataconstanttrayfillof67%,.ThisdatawasdeterminedexperimentallyatAEP'sCantonTestLab(seeAppendixC).Aspredicted,theplotsarelinearandpassthroughtheoiigin.Themaximumallowableheatforthistrayfillmaybedeterminedfromtheslopeoftheplotsasshownbelow:(10)A.4CALCULATIONOFAMPACITYIntheprevioussectionitwasshownthatthetotalallowableheat,Q,wasconstantforagivenpercentagetrayfill.Inordertoeliminatehotspotscausedbylocallvintenseheatsources,thisallowableheatgenera"ionshouldbedistributeduniformlyacrosstheoccupiedareaofthetray-ThisconceptofuniformheatdistributionisdiscussedindepthbyStolpeinReference2.However,whereasStolpe'sanalysisrequiredauniformheatdistributionperunitvolume(fortightlypackedcabletrays),thecalculationofampacityforlowfilltraysisdependentuponauniformheatdistributionperunitareaoffilledtray.

FIGUREA-I700ventilatedtraywithventilatedco600500solidtraywithsolidcoverI400ventilatedtraywith1hourfirebarriersystem3002001002040I100120 A.4CALCULATIONOFAMPACITY(contd).,FigureA-2illustratesthedifferingrequirementsofuniformheatdistribution.AsperStolpe'sanalysisoftightlypackedtrays,sevenOl2cablesoccupythesamevolumeasone4/0cableandthustheheatgeneratedbythetwoconfigurationsshouldbeequivalentunderuniformheatdistributionconditions.Forlowfilltrays,threeil2cablesoccupythesameareaoftraysurfaceasone4/0-..cableandthereforemustgeneratetheequivalenttotalheat.AdiscussionofthiseffectontheeffectivediameterofthecablegroupisgiveninAppendixB.Keepinginmindtheconceptofuniformheatdistributionandrearrangingequation,(8)itcanbeshownthat:d3IR=FQ(ll)ortheheatproducedbytheresistiveheatingphasecableisequaltothepercentageoftheheat,Q,asdeterminedbytheareathatcableinthecabletrays.ofonethreetotalallo~ableoccupies,d/F,Theallowableampacityofanycableintraycanbecalculatediftheallowableheatisknownforaspecifiedtrayfill,fromequation(9):(9)ThedeterminationofallowableheatforvarioustrayfillsandracewayconfigurationsisdiscussedinAppendixB,ComputerModel.

FlGUREA-2effectiveEquivalentheatsourcesfortightlypackedtraysasperStolpeinReference2.Equivalentheatsourcesforlot.illcabletravs

~~~.>>aeke~

B.2ProgramDevelopmentTheheattransmissionofcablescontainedinarectangulartrayenclosedwithmultiplelayersoffirebarriermaterialisquitecomplexandextremelydifficulttomodel.Therefore,anassumptionwasmade:treattherectangulartrayandfirebarriersascylindricalsectionswiththeequivalentsurfacearea.Initially,thevalidityofthisassumptionwasquestionable.However,becauseoftheexcellentcorrelationbetweencomputerdataandtestdata,.it.is,feltthatthisapproximationissound..Utilizingthepreviousassumption,theprogramwasdevelopedbasedontheexcellentworkdonebyNeherandMcGrathinreference3andBullerandNeherinreference4.Throughoutthissection,theconceptof"thermalresistance"and"thermalresistivity"willbeused,thesetermsbeingtheinverseofthermalconductanceandthermalconductivityrespectively.Itisofteneasiertovisualizethermalresistanceanalogoustoresistanceinanelectricalcircuit,withthethermalresistanceofeachmediumbe'nginseries,andwiththeconductive,convectiveancradiantresistanceactinginparallelthrougheachmedium.AtypicalthermalcircuitisshowninFig.Bl.Theequationforloadcapabilityasdevelopedinreference3isgivenbythefollowingequation:inequation(12)T-(T+~Td)caRd1+7)dccca(12)TcDTddcconductorcurrent(kiloamps)conductortemperature(C)0ambienttemperature(C)00dielectriclossesinconductor(C)D.C.resistance(microhms/ft.)incrementofac/dcratioRcaeffectivethermalresistanceconductortoambient(thermalohms-ft.)

1cd2cdRlcvR2cvTaR2TT=Q(R+R)c.a12where:Tc~conductortemperature(typically90C)'a=ambienttemperature(typically40C)Q=heatenergy(wattsp.u.)1111+-+RlRlcdR3Rl1111+-+22cd2cvR2r(Rinthermalohmp.u,)Intheabovethermalcircuittheconductive,convectiveandradiantthermalresistancecomponentsthrougheachmediumareaddedinparallel.TheequivalentthermalresistanceofeachmediumiRlandR2areaddedinseries.FIGURE8-1

'B.2.1DeterminationofElectricalResistanceTheD.C.resistanceofaconductormaybefoundfromthefollowingexpression:Rg~=-p<[(r+r)i(c+201]where:p,=electricalresistivityofconductor(circularMZLOHMS/FTat20C)CI=circularinchareaY=inferredtemaeratureofzeroresistance(C)Thefactor1+Ymaybedetermineiftheac/dcratioisknowncR/Rd=1+I+Y+YP(14)where:Y=incrementofac/dcratioatshieldsY=incrementofac/dcratioatpipeorconduitYwillbezeroprovidedshieldsare'pen-circuitedandYwillbenegligableinlightofthefactthatmostcablesinatPaywillbethreephasetwistedconductor.Thereforeequation(14)reducestoacdc1+YcB.2.2DeterminationofThermalResistance(14a)Ifshieldandpipelossesareneglectedaspreviouslydiscussed,thetotalthermalresistanceconductortoambient,Rcawillbethesummationoftheindividualthermalresistancesofeachmedium(i.e.,insulation,jacket,airspace,etc.).Thethermalresistanceoftheinsulationmaybecalculatedbythefollowing0~012(jlog(Dj/D)where:R.=thermalresistanceofinsulation(thermalohms-ft.)p>=thermalresistivity(C-CM/watt)D.=diameteroverinsulation(IN.)3.D=diameterofconductor(IN.)c(16)Thethermalresistancethroughrelativelythincylinders(i.e,cablejacke),tray,firebarrier)maybecalculatedfromthefollowingequationR=0.0104nn'D-t,>

3 where:R=thermalresistanceofthesection(thermalohms-ft.)thermalresistivityofthesection(C-CM/WATT).n'numberofconductorscontainedwithinthesection.thicknessofthesection(IN.)D'.outsidediameterofthesectionTheheattransferbetweensurfacesseparatedbya"dead-air"spaceinvolvesthemechanismsofconductionconvectionandradiation.Eachcorres'pondingt'hermalresistancemastbeaddedinparalleltoobtaintheeffectivethermalresistance.However,inthiscaseitissimpliertotaketheinverseoftheconductancesaddedinseries.Usingtheequationsdevelopedinreference4:Cd=lcd=0.0213aTlo~go/D'),D'ETDT(17)(18)Cr='2rATwhere:C0.102D'(1+0.016Tm)(19)thermalconductanceduetoconduction,convectionandradiationrespectively(watts/C-ft)respectiveheatloss(watts/ft)~T=temperaturedropthroughtheairspace(D'outsidediameteroinnersurface(IN.)D"=insidediameterofoutersurface(lb.)P=pressureofair(ATM.)surfaceemissivityofinnersurfaceT=meantemperatureofairspace(C)0mAtthispoint,someclarificationisnecessaryconcerningtheequivalentdiameterothecableorcablegroup,theequivalentdiameterofa3twistedconductorcableisobtainedbymultiplvingtheindividualcablediametersby2.15.Thisfactorwillacttoincreasethecalculatedthermalresistancewhichiswhatwouldbeexpectedduetotheclosespacingofa3TCcable.

4NI~~~

Theeffectivediameterofthecablebundleshouldbeobtainedbymultiplyingtheeffectivecablediameter(orjacketdiameter)bythenumberofthreephasecablesinthetray.ThiswillbeD'hencalculatingthethermalresistanceoftheairspaceinsidethetray.Theeffectistousethe,cablesurfaceareatocalculatetheheatloss,whichisinaccordancewiththetheorydiscussedinAppendixA.Thethermalresistanceperconductorwillbethetotalnumberofconductorsdividedbythetotalthermalconductance.If1atmospherepressureisassumedthethermalresistanceoftheairspacewillbegivenbytheexpression.n'--'".logD"D')'hethermalresistancefromthelastsurfacetoambient,instillaircanbefoundfromthefollowingequationderivedinreference3.1[(~T/D"'"+1.6p(1+0.0167Tm)]IIIwhere:D=outsidediameterofoutersurface(21)Aspreviouslystated,thetotalthermalresistanceconductortoambient,R'illbethesummationoftheindividualthermalresistancesthrSugheachmedium.B.2.3DeterminationofdielectriclossesFromreference3:Td=WdRda(22)where:WdW.=dielectriclossdthermalresistivitybasedondaindividualthermalresistivitiesatunitypowerfactor.0.00276E$cosg2logDEJ(23)where:E=phasetoneutralvoltage(KV)(=specificinductivecapacitanceofinsulatio.-.rcosP=powerfactorofinsulationD~i=diameterofinsulation(in.)

I~

Rd,=R,-R./2(24)B.3FireBarrierAmpacityDerating(FBAD2)TheprogramFBAD2wasdevelopedaccordingtothecriteriaoutlinedinsectionB.2.AprogramlistingisincludedinsectionB.4.Whenrunningtheprogramforcablesinventilatedtraywithcovers,enclosedinFireBarrierMaterialitwasdeterminedthatthethermaleffectsofthetraywasinsignificantandcouldbeneglected.Thisagreed,withtheresultsoftestsatCanton(seeAppendixC).WhenaventilatedtraywithoutacoverisenclosedinaFireBarriermaterial,thethermalresistanceintroducedbythetrayisnegligable.Thereforethetrayshouldnotbeinputasa"layer"intheprogram.Theassumptionsusedtodevelopthisprogramrequirethatthetraybefilledtolessthanorequaltoonelayerofcables.Thereforethenumberofcircuitsenteredmultipliedbythecablediametershouldbelessthanorequaltothetraywidth.'Whenentering"N"thenumberoflayers,thecableinsulationandjacketshouldnotbeenteredasalayer.Theprogramisdesignedtoaccountfortheireffect.B.3.1NDataInputThedatarequiredforrunningtheprogramisasfollows:Thenumberoflayersofmaterialenclosingthecable.SeeB.3D(I)TheequivalentdiameteroflayerIininches.T(I)S(I)E(I)P(I)ThethicknessoflayerIininches.ThedeadairspaceoutsideoflayerIininches.Enter~"1"iftheairspaceisambientair.Note:Enter'1"o~nlforambientair.TheemissivityofsurfaceI.Theemissivityisanumberlessthanorequalto1,usedtodeterminetheradiantlosses,1beingaperfectradiator(blackbody).Seereference1foradditionalinformation.ThethermalresistivityoflayerIinC-cm/watt.0Note:ThevariablesD(I),T(I),S(I),E(I)andP(I)shallbeenteredforeachlayerinput.

A~ie~w'J Tl=ConductortemperatureinoC.T2=AmbientTemperatureinC.P=Electricalresistivityoftheconductorincircularmilohmsperfoot.SeeReference3.TO=Inferredtemperatureofzeroresistancefortheconductormaterial.'eeReferenec3.V=LinetolinevoltageinKV.El=Specific.-inductivecapacitanceoftheinsulation.SeeReference3.Fl=Powerfactoroftheinsulation.T5=Thicknessofthecablejacketininches.P5=ThermalresistivityofthecablejacketinC-cm/watt.Nl=Thenumberofconductorspercable.C=Areaoftheconductorincircularinches.DO=Theconductordiameterininches.DI=Theinsulationdiameterininches.Pl=ThethermalresistivityoftheinsulationinC-cm/watt.A=TheAC/DCratioES=Theemissivityofthecablesurface.D5=Thediameterofthecableininches.B.4Computerprintout:FBAD2B.4.lTheprogramFBAD2isstoredintheWarnerComputerSystemundertheaccesscodeforElectricalPlantDesignSection.B.4.2ProgramListing:

  • If4 References1.HeatTransmission,W.H.McAdams.McGraw-HillBookCompany,NewYork,N.Y.,secondedition,1942.3."AmpacitiesforCablesinRandomlyFilledTrays,"J.Stolpe.IEEETransactions,Paper70TP557PWR."TheCalculationoftheTemperatureRiseandLoadCapabilityofCableSystems,"J.H.NeherandM.H.McGrath.AlEETransactions,Paper57-660.4"TheThermalResistanceBetweenCablesandaSurroundingPipeorDuctWall,"F.H.BullerandJ.H.Neher.AZEETransactions,Paper50-52.Appendixl.g5.6."EngineeringDataforCopperandAluminumConductorElectricalCables,"TheOkoniteCompany.OkoniteBulletinEHB-78.Pg.5.gcablesinTraysTraversingFirestopsorWrappedinFireproofing,"O.M.Esteves.ZEEETransactionsPaper82JPGC601-3.7."AmpacitiesCablesinOpen-topCableTrays,"ZPCEA-NEMAStandardsPublication.IPCEAPubNo..P-54-440~SecondEdition);NEMAPub.No.WC5-975.8.9.IndustrialHeatTransfer,AlfredSchack,Dr.-Ing.JohnWiley&Sons,Inc.1933.Pg.18TSZresponsetoAEPquestionairefromMarilynGrautoR.H.BozgodatedSeptember29,1982.

ATTACHMENT5TOAEP:NRC:0692DFREPRESENTATIVEAMPACITYDERATINGCALCULATIONRESULTS CableTray:1AZ-P8TotalHeatGenerationPerFootofRaceway:CalculatedAllowable:36.98Watts/Ft.Actual:9.70Watts/Ft.ConnectedLoadCalculated1470R1469R8067R8024R8187R8026R8027R2349R*1476R1488R1991R16666R-23TC412CU3TC412CU3TC412CU3TC412CU3TC412CU3TC412CU3TC412CU3TC412CU3TC412CU3TC412CU3TC42AL3TC412CU3.816.01.21.117.02.71.21.920.060.02.521.5821.5821.5821.5821.5821.5821.5821.5821.58'0.6721.58*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 CABLENCONDUITCONNECTEDLOADCALCULATEDALLOWABLEa2KCI5XESRZBLet+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.AMBIENTTEMPERATUREWASTAKENTOBE40C

~~

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

ATTACHMENT6TOAEP:NRC:0692DFRESULTSFROMTESTREPORTgCL-542 4

~,CegPageIof~TESTREPORTAmericanElectricPowerServiceCorp.CantonLaboratoryP.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)Cl0CLEClIZNTRODVCTZONForcompliancewith10CFR50,AppendixRattheD.C.CookNuclearPlant,testswereconductedonpowerandcontrolcablesenclosedinaTSZ,Znc.one-hourfirebarriersystem.Theresultsof-thetestwillbecomparedtocomputer-generateddatatodeterminethevalidityofthecomputermodelonheatrunflowandcableampacity.II.OBJECTIVEgo~~4JE0gThetestobjectivewastosimulateascloselyaspossibletheactualconditionsoftrayandconduitrunsproposedforCookPlantanddeterminethefinalconductortemperatureforthespecifiedamperageandtrayfill.ZII.TESTMETEODThegeneralizedtestmethodconsistedof:l.Installingcables.2.Attachingthermocouples.3.EnclosingtheTSZfirebarriersystem.4.Applyingthespecifiedamperages.5.Maintainingaconstantambienttemperatureof400C.6-Monitoringthetemperatureriseandfinalconductortemperature.CopiesTo:T.O.Argenta/B.R.Larson-CantonB.J.Ware-ColumbusC.B.Charlton-CantonT.E.King-ColumbusS.R.Kekane-Columbus TESTMETHOD(Cont'd.)Thedetailedtestprocedurewasasfollows:EquipmentCableTrayandCover1.1.1.Cabletraywasgalvanizedsteel,expandedmetalbottom;size12"x6"x8'-0"Long.1.1.2.Cabletraycoverwasgalvanizedsteel,ventilated12"wide.1.1.3.10'-0Originaltraylengthcutto8'-0"toaccommodateinstallationinenvironmentalchamber.1.1.4.Traycoverattachedtotraybyusing510x3/8"Parker-KalontypeB(Z)with"H"head.1.2.Conduit1.2.2.4"I.D.Galvanizedrigidsteel.1"I.D.ThinwallEMT1.2.3.Conduitscutto8'-0"toconformwithcabletraylengthandinstallationinchamber.1.3fireBarrierEnvelope1.3.1.Thermo-Lag330-1.sublimingcoatingmanufacturedbyTSI,Inc.foraonehourbarrier.Thicknessofbarrierwas.500"(+.125",-.000").1.3.2.1.3.3.1.3.4.1.4.Prefabricatedpanels6'-0"x4.6Prefabricatedconduitsections.':Steelbanding.CablesThefollowingcableswereusedfortesting:324339344348310131023103310431203TC012Cu600V3TCN6Al600V3TCN4Al600V3TC02Al600V3TC14Al5kVshielded3TCN2Al5kVshielded3TC'2/0Al5kVshielded3TCN4/0Al5kVshielded4/C512Cu600V.

~~"1 TestSetup2.1Raceway2.1.1.Cabletrayandconduitweresupoortedaoproximately2'-6"abovefloortoallowfornaturalventilation.2.1.2.Racewayendsweresealeddurincthetestwiththermalinsulatingmaterialtooreventheatlossthroughtheseareas.Note:Thisprocedurecouldcauseexcessiveheatingofthecablespassingthroughthethermalseal;therefore,alltemperaturereadingsweretakenaminimumof1'-0"fromthethermalseal.2.2TSlOneHourFireBarrierSystem2.2.1.Thetrayenvelopewasconstructedofthepre-fabricatedpanels,cutsoastofitasshownintheAppendix(seeFigurefl).2.2.2.2.3Theconduitswereencasedintheprefabricatedsections.Thermocouoles2.3.1.T-Typethermocoupleswereusedtomeasuretempera-turesofthefollowing:A.AmbientairB.TooandbottomofthefirebarrierenvelopeC.AirspaceintrayD.Conductors.2.3.2.Thermocoupleswereinstalledontheinwardsideoftheconductorinatriplexarrangement(seeFigure2).Aholewasboredintheinsulationandthethemocoupleswereplacedontheconductor.2.3.3.ThermocoupleswereimbeddedinOmegatherm201highthermalconductivitypaste.2.3.4.Thermocoupleswereinstalledinapositionlocatedonthecablesinthecente.ofthetraywhere:A.B~Heatgenerationisgreatest.:-:ardissipationistheleast(seeFigure3).

~ty,1'I~s~~

2.3.5.Theminimumnumberofthermocouplesusedtomeasuretheconductortemperaturewastwo(2)percablecircuitinstalledinthetrayandfive(5)forsinglecablesinstalledintheconduit.2.4.Cables2.4.1.Cableswerepositionedinthecabletrayinasinglelayerinsuchapositionthattherewasaminimumspacingof1/3thediameterofthelargeradjacentcable'.'Cableswerethensecuredwith"Ty-Raps".3.TestProcedure3.1Eachtestconsistedofinstallingthecablesinthetrayinoneofsix(6)configurationsasspecifiedinthetestrequest.3.2Oncethepropersetupwasattained,cablesweresubjectedtoaloadofthreephase,60HzsinusoidalcurrentasspecifiedinSection4~3.3Ambienttemperaturewassetto40oC.3.4.TemperatureriseofthecableswasrecordedonanEsterlineAngusHodelPD-2064dataacquisit-ionsystemat4-hourintervalsuntilthecabletemperaturesstabilized.3.5.Thevoltageandamperageofeachcircuitwasmonitoredperiodicallythroughoutthetest.4~TestConfigurations4.1TestSICircuitNo.ZtemNo.DescriptionRunsinTrayAmpacity3243TCr12Cu324'TCr12Cu3483TC02Al3243TC512Cu3.820.060.00 f4jpIHt 2.3.5.Theminimumnumberofthermocouplesusedtomeasuretheconductortemperaturewastwo(2)percablecircuitinstalledinthetrayandfive(5)forsinglecablesinstalledintheconduit.2.4.Cables2.4.1.Cableswerepositionedinthecable'trayinasinglelayerinsuchapositionthattherewasaminimumspacingof1/3thediameterofthelargeradjacentcable.Cableswerethensecuredwith"Ty-Raps".TestProcedure3.1Eachtestconsistedofinstallingthecablesinthetrayinoneofsix(6)configurationsasspecifiedinthetestrequest.3.2Oncethepropersetupwasattained,cablesweresubjectedtoaloadofthreephase,60HzsinusoidalcurrentasspecifiedinSection4.3.3Ambienttemperaturewassetto40oC.3.4.TemperatureriseofthecableswasrecordedonanEsterlineAngusModelPD-2064dataacquisit-ionsystemat4-hourintervalsuntilthecabletemperaturesstabilized.3.5.Thevoltageandamperageofeachcircuitwasmonitoredperiodicallythroughoutthetest.TestConfigurations4.1Testfl3243TC12Cu73243TC~412Cu33483TC~2Al13243TCe~l2Cu13.820.060.00 P

4.2Test02CircuitNo.ItemNo.DescriptionRunsinTrayAmpacity32432432434831203443TC512Cu3TCI12Cu3TC012Cu3TC$12Cu4/C412Cu3TC54Al.17.712.86.86.853.04.3Test43CircuitNo.ItemNo.DescriptionRunsinTrayAmpacity324324312032431203243393393443443483243TCf12Cu3TC$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-TESTRESULTSThecompletetemperaturerecordingsaretabulatedalongwithtestcommentsoncomputerprintoutsandlistedunderdatasheetsintheAppendix.Thefinalconductortemperaturesforeachtestarelistedbelow:TestNo.CableAmpacity(ampm)RunsinTrayHighestConductorTemperature(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*Thermocoupleinstalledoninsulation,notconductor 0

V.DISCUSSIONDuetoalimitedsupplyofvariablepowersources,severalcircuitswereconsoLidated.Inallcases,theloadsweremetorexceededthosethatwereoriginallyrequested.Aspertheoriginalrequest,conductorswereplacedinthecabletrayinasinglelayerinsuchapositionthattherewasaminimumspacingofll3thediameterofthelargeradjacentcable.'lthoughthisprobablyisnotthebestsimulationofactualconditions,itwasonecriterionofthetestrequest.DuringTestf3,theamountofcablesmadeitimpossibletofollowthiscriterion.ItwasfollowedascloselyaspossibleandtheresultscanbeviewedintheAppendixunder"Photographs".AllresultscontainedinthisreportwereforwardedtoW.F.Wilson,NewYork,immediatelyuponcompletionofthetest.Anyquestionspertainingtotheactualtestresultsascomparedtothecomputer-generateddatashouldbedirectedtohim.VI.APPENDIXA.DatasheetsB.TestsetuoC.Photographs.

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~~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<<ENTSTESTNo2THERM1AMB-.Ek'Tt'CH~9)THERMr".'OPTRAY'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.ESTERLINEANGUSDATATTtlECHUGCHCHir"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'TIONNQTTHLCONDUCTORCURP,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<<JIJCCJ~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'15CH=: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 Csgr~-CPL/!~,1si<osQglll>>CHNSPC'4C'(8S:4587:1587:4c~8'1c'S-4589-1589-4518:'518-411ei5'1-451":1.5'-151:":45'r4.4='9.74cc'8C'!>>>>~7Oa5S.75S.97rsJs~57.'J~~57.'::57c'7c7r>>4c=:9.S.n14S58a5e!ae>>~>>r54S75Se1cSc5S.75S.7C'I<GesCl5B,75SaE56e544':.'.549."5S.459.'re5>>~7S8.1S8,4S8SQ..:.SQ.~S+S8.='8.'.:4.4.r'.141.447.751.i-'~.9OsJe855.S55aFrO'5Ee1cS55a95F.156.1rr~~Iirsl4585'.9C'Ca!~<c'74595SCCs&4lrer58.u~LQ5>>LQSa4~~7147."54e1sJAaS84iS'.S7Ei.9gr'1Sr.1E".='toC4>>glcC'Crsada>>>>>>DMeSs~1F-'.4,S:-'.9S4.rS4.5S4.8E4.9E4..8S4.7,64.9S4i~7S4.S>>rg,~IaQPJeS4S.9C'CC'Jec9cSi.SSv.'"S~.SS5S5.~Sc'E5.9S5.6S5.7E5.7S5.SS5.74i1~>>51.Se!SeE='.4E4.9BS.567.5SE.7S7S7V7~~F7.1P7S7.1Su.9tS7>>~41.47.51.54.5S.5S.57e57.C'Pl4GaC'QWva57a57.57.57.57a9QlCbPl97%~~47.51Qi'C4e55a57a57.57a57.57.CiP57o57.57a99QlCHI:98C'4C'S:'585:4587:1587:458G:'58ge4c'9et589:45'8-1518-45':15'1-451r~451e~1C>>'~S.S4>>Ql48o448.548.748.748.748.748.748.S4848.94,1.148.941'0C'542 ~~~~ o~TESTNO.4E'ST=.LLNKANGUSDATPT::I"iECHNSCH-:.'H-.:"CH-..~CHI4CHN5CH-..SCHS7CHNSCHI9QW~PgSe'9:8889'p18:8818:>811-8811:.8~88~81i:88'i:~814:88'::"8<<'4oSl26.627,6Clo6r9.E:38Z8.~~8.4'v,8>8.7>8.7"6.6~6.~~9.1~9.5o,90v9.9~9.6484848,148.148.2~9.8c'oraJ~7~gw<Moo'Bo4Cmq~~v9.9v9.948."-'8.548.7484848Ql48~..9.4"B.4~o7-.948.148.548.641~541.948.54141.741.72Qu54\~7o.7~9:"9.448.~48.448.64848.848.S4148.848.57oMN7<<>9o548.;48.848.7414141.148.94f.1"S.1i7.179"9.748o448.548.548.741.242.948.941~148.9-6.8~5'VMoo,T4"9.148148.248.148.5484841.748.~48.67034.7i6.9~7.uv9.148o248.548.648.648.848.948.941~148o82".4~~So~>i5.6~6.4m5o7~~7.u~48.5~S.4v9.1"5.7COt"i."fENTSi.)='.)s.)4.)C'TES!VOLTQl[RACHANCURR4STARTAf'9.5B119.4Ci21.SSTARTA2.8B'.8C~.89NYALIDCL54'rTEST4,FINISHA=.8B2.8C2.8 m0 TESTNO.5ESTERLINEANGUSDATATIMECH08CHQiCH""CH03CHSACH~SCHC7CHC9CHc18CHn11CH51~8e~cgr8G8G:489ic8aeAc18:1518451>~111~4512~1~:451~:151':4514:1514:4515:151921.9'r3e4.6.ep.e.F=9.638,38.4'8738.95-.45Icif3II~6.7139.7ie.639.748,148AQ~9948v9.un939.739.9~9.939.648o'ro34.7'73e.439.348,2Ai4'.541.e41.741.441.741~635.637,1e"v~7"9.748.4.48.e41.54r.442.541.9'i.74:ArecArr7Ai.9.7.7C3-.54r.946.~Ae.A.58.451.e52e7CiD~~53o753.953.954454.354.5"8.147.458.7'3.5CCopereoi56e657.e58.6CaU>>~o59.559.759.96868.3'4~.e645.951.1c5rrr59.961.963.363.e64.564.364.464.S64.e6529ee.c41.e46e758.6C5~.~55e356.457.4cnerGeu58.6erGe959.159.359.538.2"574~.64e.1cr,Vo'44o057cnDGo~59.=68,68.568.968.968.961.261.~61.531.737.444.5585456.958.768.468.96'62n62.46~o6='.76=.86I~9o34.64'.546.e58ee5ere4cSn57.e5nc5ee959.459o59.659.659.759'.91~)".)...)Ao)5.)6.)7.)n9.)COMMENTSTEST5CL-54'8/28/e38738VOLTSTARTA.5S9B.844C.611CURRSTARTA72.8B72.8C7..8CHN1"ONOUTSIDEh!SULATION'-A.lBIENT2-TOPCONDUITBOTTO!"CONDUIT4-AIRSPACEYOLTFINISHA.631B-997C-S57CURRFIN1SHA7.8B7..1C71.9ENDTEST5CL54=18/r8/831545C-542 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