ML17256A708

App C to Structural Reanalysis Program, Utility Pole Tornado Missile Trajectory Analysis.

ML17256A708
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Issue date:	03/08/1983
From:	DUNN W L, TWISDALE L A APPLIED RESEARCH ASSOCIATES, INC.
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APPENDIXCtotheSTRUCTURALREANALYSISPROGRAMForTheR.EGINNANUCLEARPOWERPLANT8305310157830519PDRADOCK05000244PPDR March8,1983ARAReportC556RTIReport44T-2488-1UTILITYPOLETORNADOMISSILETRAJECTORYANALYSISL.A.TwisdaleW.L.DunnAppliedResearchAssociates,Inc.SoutheastDivision4917ProfessionalCourtRaleigh,NorthCarolina27609PreparedforResearchTriangleInstituteP.O.Box12194ResearchTrianglePark,NorthCarolina27709andGilbertAssociates,Inc.P.O.Box1498Reading,Pennsylvania19603UnderPurchaseOrder201494 TABLEOFCONTENTSl.INTRODUCTION.2.APPROACH.a.TornadoWindfield...................b.TrajectoryModelc.MissileAerodynamicsd.InjectionModelPage53.TRAJECTORYSIMULATIONRESULTS...............84.COMPARISONSTOOTHERWORKANDFIELDOBSERVATIONS......13a.6-DTrajectoryModelPredictions...........14b.3-DBallisticModel..................14c.UtilityPoleTransport:Xenia,OhioTornado.....15d.StoredUtilityPoles:Brandenburg,Kentucky.....165~CONCLUSIONS~~~~~~'~~~~~~~~~~'~~~~~~18REFERENCES19

-UTILITYPOLETORNADOMISSILETRAJECTORYANALYSIS1.INTRODUCTIONTheobjectiveofthisstudywastoperformtrajectorycalculationsofutilitypolemissilesintornadowindfields.TheNuclearRegulatoryCoomission(NRC)-definedutilitypole[1]wasspecifiedasthepostulatedmissilefortheseanalyses.Tornadowindfieldswithpeakvelocitiesof132,150,and188mphwerespecified.Theutilitypoleswereinjectedat20ftabovegrade,whichcorrespondsapproximatelytothecenterofmassofastanding35ftpole.Trajectorycalculationsweremadeusingtherandom-orientationsix-degree-of-freedom(R06-D)trajectorymodel[2,3,4g,whichaccountsfordrag,lift,andsideaerodynamicforcesinatimehistoryintegrationoftheequationsofmotion.Themaximumheight,range,andspeedattainedbythemissileswereextractedfromthetime-historyflightdata.Inadditiontothesenumericalcalculations,severalcomparisonsoffieldobservationsandtrajectorypredictionsofutilitypolemissileshavebeenmade.Thisreportdocumentsthemethodsandresultsofthisstudy.2.APPROACHTheapproachusedforthetrajectoryanalysesisbasedprimarilyonthemodelsanddatareportedinRefs.2-10.Abriefsummaryofthetornadowindfieldmodel,traj'ectorymodel,missileaerodynamics,andinjectionmodelarepresentedinthefollowingparagraphs.a.TornadoWindfield,ThetornadowindfieldmodelusedhereinisdocumentedindetailinRef.4.Thissynthesizedwindfieldmodelwasdevelopedexplicitlyformissiletransportanalysisandincludes5basicparametersthatdefinethe3-dimensionalflowcharacteristicsgiventhepeakspeedUmaxandpathwidth

-I-Mt.Theseparametersare:translationalspeed(UT);theratioofradialtotangentialflowcomponents(y);theradiustomaximumwindspeed(pm);coreslope(S);andreferenceboundarylargerthickness(6o).Asensitivityanalysiswas,performedI4,6]usingaone-at-a-timeexperimentaldesignandthreelevelinputpattern.ThebasicconclusionsofthisanalysisfortornadoeswithUax=300mphandtwotypesofmissileswere:(1)Forgiventornadointensity,thenumberofmissilesgeneratedandtheirtransportcharacteristicsaremostsensitivetothetranslationalspeed(UT)ofthestorm.LowvaluesofUTresultinmoremissileinjectionsandhighermissilevelocitiesforspecifiedUmax.(2)Forgiventornadointensity,anincreaseintheradialinflowcomponentrelativetothetangentialcomponentincreasesthenumberofmissilesinjectedandleadstohigheraveragevaluesofmaximumvelocities,ranges,andaltitudes.(3)Missilesinjectedandtransportedbylarge-coretornadoesgenerallyattainhighermaximumvelocitiesbutlowerpeakaltitudesthanthosepredictedwithsmallerpm.Theabsolutenumbersofmissilesproducedareproportionaltotheradiusofthecore.(4)Theslopeofthecoredoesnothaveanappreciableeffectonmissiletransport,evenformissilesinjectedathighelevations.(5)Relativelysmallvariationsinairdensitycanproduceproportionalchangesinmissilerange,buttheeffectofairdensity(duetoentraineddust,etc.)onmaximumvelocitiesisheavilydependentonthemissileinjectionheight.Hence,fromthisanalysiswehaveabetterunderstandingofhowtocharacterizethetornadowindfield(giventhepeakwindspeed)tomaximizemissiletransportparameters.Asecondsensitivityanalysiswasmadetoassesstheimportanceofcertainuniqueflowcharacteristicsthatexistinseveralprominenttornado models.Toevaluateexplicitlytheeffectsofbasicdifferencesamong'indfielddefinitions,apairwisecomparisonstudywasperformedL4,6]withthesynthesizedmodelinaseriesofmatchedcomparisonswithothermodels.Fromtheresultsofthefirstphaseofthesensitivityanalysis,themoreimportantvariablesinthesynthesizedwindfieldwereidentifiedasUT,y,andpm.Inthisphase,thepairwisemodelcomparisonsweremadewiththeUT,y,andpmvaluesinthesynthesizedmodelmatchedtotherespectivevaluesusedinthewindfieldmodelselectedforcomparison.Threemodelswereselectedonthebasisoftheirdistinguishingfeaturesrelativetothesynthesizedmodelandrecentnessofdevelopment:theFujitaDBT-77tornadomodel[11],theFujitasuctionvortexDBT-78flip,andtheTRWPhaseIIImodelL12].Theresultsofthecomparativemissiletransportanalysisindicateinsignificantdifferencesformostofthevelocityandrangestatistics.FortheFujitaDBT-77comparisons,thesynthesizedmodelinjectsmoremissileswithhighermeanvaluesofmaximumvelocities,whereastheFujitamodelpredictsslightlyhighervariancesandextremevalues.ThecomparisondataexhibitdifferencesthataremuchlessthanthoseobtainedfromvariationsinUTandyforthesynthesizedmodelalone.Forthesuctionvortexmodel,anumberofsimulationsweremadewithsingleandmultiplesuctionvorticeswithboththepipeandautomissiles.Theresultsindicatethatthemissilegenerationandimpactpositionsareinfluencedbyembeddedvortices.However,forthesamereferencewindspeedintensity,atornadowithnosuctionvorticesyieldshighermissiletransportcharacteristicswhencomparedtoasysteminwhichthesamemaximumwindsoccurinthefast-movingembeddedvortices.Thus,forconservative l

-predictionsofmissiletransport,thereisnoneedtomodelsuctionvorticesformissi1etrajectoryanalysis.FortheTRWmodel,moreinjectionsresultforthepipemissile,butthesynthesizedmodelpredictshighervelocityandrangestatistics.Ingeneral,thedatasuggestthatthetransportdifferencesinthemodels,withthesameUma,p,andy,arelimitedprimarilytolowinjectionheights.TheTRWmodelgenerallydominatesatz=10ft,andthesynthesizedmodelat33ftwithsimilartransportstatisticsoverthecombinedelevations.OnthebasisofthesesensitivitystudiesandtheresultingupdatingoftheUT,y,andpparametersinRef.4,thesynthesizedwindmodelprovidesatestedwindfieldmodelfor'utilitypoletransportcalculations.b.TrajectoryModelrTrajectorymodelsthathavebeenusedintornadomissiletrajectoryanalysesinclude:(1)theballistic3-Dmodel,whichassumesaconstantdragforceandneglectsliftandsideforces;(2)therandomorientation,6-D(R06-D)model,inwhichaerodynamicdrag,lift,andsideforcesaredependentonmissileorientation,whichisperiodicallyupdated;and(3)theconventional6-0model,whichtracksmissiletranslationandrotationusingasystemof6coupleddifferentialequations.DetaileddiscussionandcomparisonsofthesemodelsarepresentedinRef.4.TrajectorycomparisonsofthesemodelshavebeenmadeusingutilitypolemissilesL2],.12-inpipeandautomobilemissiles[43.Onthebasisofthesecomparisons,theballistic3-Dmodelhasbeenshowntounderpredictvelocity,lift,andrangecharacteristics.TheR06-Dmodelprovidespredictionsthattendtoboundthoseofthe6-Dmodelanditisconsiderablymorecomputationallyefficient.

c.MissileAerodynamicsAmodeloftheaerodynamiccoefficientsforageneralclassofmissileswasdevelopedinRef.2andlaterupdated[4)toreflectnewaerodynamicdatabasedonfullandsubscaletests(12,133.Amodifiedcrossflowtechniquehasbeendevelopedtopredictdrag,lift,andsideforcecoefficientsasafunctionofangleofattackandrollangle,giventhedragforcecoefficientsfortheobjectinflownormaltothemajorbodyaxes.Table1summarizesthemodelforcylindralmissilessuchastheutilitypole.Aplotofthemodelpredictedvs.utilitypolewindtunneldata[13]for3differentRenumbersisshowninFigure1.Theseresultsindicatecloseagreementbetweentheaerodynamicmodelandmeasuredcoefficients.d.InjectionModelAsthetornadowindfieldpassesoveranobject,thedynamicpressureinducesaerodynamicforcesthataredependentonthemissileshape,orientation,surfaceroughness,andproximitytootherobjectsandsurfaces.Iftheseaerodynamicforcesaregreaterthantherestrainingforces,suchasgravity,slidingfriction,andfoundationembedment,theobjectwillbedisplacedbythewindfield.Ingeneral,theseaerodynamicforceswillnotactthroughthecenterofmassofthebodyandthemissiletumblesandinteractswiththegroundandotherobjectsduringthisinjectionphase.Hence,detailedmodelingofinjectionrequiresinformationonrestrainingforcetime'historiesandinteractionmodelstosimulatemissilecollisions.Inviewofthecomplexitiesofmissileinjection,tornadomissiletrajectoryanalysesgenerallytreatinjectionparametricallythroughthespecificationoftheinitialconditionsofthemissileattheinstantitisreleasedtothetornado.Oncereleased,themissileisassumedtobeactedon ll

'TABLEl.AERODYNAMICCOEFFICIENTSFORCYLINDRICALMISSILESGeometricalshapeMissiletypeMissilesetnumbers[2]Axialdragcoefficient,CDaSkinfrictioncorrection,fCross-flowcoefficient,CDcRightcircularcylinderRods,pipes,poles1,2,3,41.16Solid(rods,poles)0.812Hollow(pipes)1,L/dc10.724+0.276e2(L/d-1)1<L/d<4'0.681+0.0108L/d,L/del.25,(subcritica1)1.80.85[1.9--a],(supercritical)Aspect-ratiocorrection,k1-8(d/L),d/LC.02058q042e-(0.51+5.6(d/L-0.02))d/L>0.02Dragcoefficient,CDmd4La--.CDf)cosa(+CDcksinaLiftcoefficient,CLSidecoefficient,CSRef.area,A1fd---CDafcosa[cose)sinu+4LCDckcosasjn2aLd 0lI Table1oooo44oo<<IW~4I.<<4I.NoRef.(13)p~<<r<<<<<<<<<<<<<<w(a)DragCoefficientTable144oo4oo4ooo<<~l04E.S04lgloLwooRef.(13)oo~<<<<<<<<<<<<<<<<~y<<4(b)LiftCoefficientFigure1.AerodynamicCoefficientsforUtilityPoleHissile

!onlybygravityandaerodynamicforces.AmissileinjectionmethodologywasdevelopedinRef.[2]andsubsequentlyrefined[4]toconservativelyaccount"forthecomplexitiesanduncertaintiesinaparametricinjectionmodel.Theapproachinvolvesatwo-stepprocedure:(1)theverticalandhorizontalaerodynamicforcetimehistoriesonthemissilearecalculatedasfunctionoftornadoposition,and(2)thepositionofthetornadocorrespondingtopeakaerodynamicforcesarethendetermined.Thispositiondefinesthetimeofreleaseofthemissilewithrespecttothemovingwindfield.Injectionstudieshaveshownthatthismethodprovidesforoptimummissiletransportandtendstoresultinmissiletrajectoriesthatboundthosedocumentedinfieldobservations.Thisoptimumreleasecriterionisusedhereinintheutilitypoletrajectoryanalysis.!-:3.TRAJECTORYSIMULATIONRESULTSUsingthemodelspreviouslydescribed,trajectorycalculationshavebeenmadefortheutilitypolemissle[1].Thepostulatedmissileis35ftlongwithadiameterof13.5inchesandweightof1,122lbs.Thecenterofmassofthemissileispositionedat20ftabovegrade.PeakUmaxwindspeedsof132,150,and188mphareconsidered.Giventhesepeakwindspeeds,theremainingtornadoparametershavebeendefinedfromtheinformationinRef.4.Amediancasewindfield,correspondingtothemeansofthedistributionsonUT,y,pm,S,and6fortherespectiveintensitylevelhasbeenspecified,asnotedinTable2.Forexample,fora150mphtornado,thedistributionontranlationalspeedisassumedinRef.4tobetruncatednormal,rangingfrom5to55mphwithameanof35mphandastandarddeviationof11mph.Hence,forthemediancase,UTisassignedavalueof35mph.Inaddition,amoreseveresetofparametershasbeendefinedusingtheresultsofthepreviouslyreported

TASLE2.TORNADOWINDFIELDPARAMETERS(-.ParameterCaseParameterValuesForEachWindfieldUm=132mphUm=150mphUm=188mphTranslationalMedianSpeed,UT(mph)2o30535134520RadialInflow,yMedian260.71.1,0.71.10.71.1Rax(<<)Median20375200375200500300Median200.1500.1500.150I-s(ft)Median20450500450500450500 IIsensitivityanalysis[4,6].Thissetisdenotedasthe2acaseinTable2sinceeachparameterhasbeensetatitsp+2a(ory-2adependingonthesignthatmaximizesmissiletransport).Thus,sincelowUT,highY,arelowpmaximizemissiletransport(givenU),theseparametersaresetmax'espectivelyatp-2a,p+2o,andp-2o,respectively.This2vcasewasincludedtostudytheinfluenceofvariationsinthethreedimensionalwindfieldonthetrajectoryoftheutilitypolemissile.Theycorrespondtoaboutthe95percentileofeachrespectivedistribution.Thetornadoispositioned(seeFig.2)relativetothemissileatthat'offsetpositionthatcorrespondstothepeakwindswithinthetornado.AsnotedinRefs.L3,4],thisoffsetpositionisgivenbypcos(tany).Themissileisreleasedtothemovingtornadoatpeakaerodynamicforce.and.theequationsofmotionarenumericallyintegratedtotrackthemotiontimehistoryofthemissile.Drag'ndliftforces(theradiallysymmetricutilitypolehasnosideforce)arecalculatedusingthecross-flowequationsinTable1.Themissileistrackeduntilthecenterofmassofthepolereachesgroundelevation(z=0).Thehorizontaldistancetraveleduntilthecenterofmassofthepolefallsfromz=20fttoz=0isdefinedastherangeofthetrajectory.Table3summarizestheresultsofthesetransportsimulationsforboththe.medianand2awindfields.Forthe132mphtornado,theutilitypoledoesnotliftforanyoftheorientationsconsidered.Thepeakaerodynamicforceatinjectionisabout1,800,lbsandisdirectedhorizontallyfortheverticalandhorizontalpoleorientations.Whenthepoleispitchedintowind(orientations3and4),thepeakverticalinjectionforceisabout700lbs.Hence,thepoledropsassoonasitisreleased.Forthe132mphtornado,weestimateapeakrangeofabout34ftandapeakvelocityof37mph.10 0

PlantTargetArea~mo(X;,Y;,Z;)MissiIeInitiaIPositionfi,gure2.TrackLengthandOffsetCoordinateSystemforMissileInjectionModel11 MI'.'lTABLE3.TRANSPORTCHARACTERISTICSOFUTILITYPOLEMISSILESimulationParametersTransportCharacteristicsByPeakNndspeed(mph)CaseDescriptionHissileOrientationAAA(x,y,z)IHaximumHeight(ft)2HaximumRange(ft)3HaximumVelocity(mph)Um~132Um~150Um~188Um~132Um~150U'm~188Q~132UmI150Um~188Hedianllindfield:(UT~YPm,60~5atmidvalue)Vertical(0,0,1)Horizontal(0,1,0)45X(-0.71,0,0.71)45XY(-0.5,-0.5,0.71)2020202020202020202020.1202726232735342941495411188243330304040323650536457Hedian+2oWndfield:(UT,Y,P,ao,satu+2o)Vertical(0,0,1)Horizontal(0,1,0)45'(-0.71,0,0.71)45'Y(-0.5,-0.5,0.71)202020202020202020202221273127343641345854571549435-4335383735364555577658Heightabovegrade;missileinjectedat20ft.lRangeinX-Yplaneuntilgroundimpact.3Usuallyoccursatgroundimpact.

!--Theresultsforthe150mphtornadoaresimilartothoseforthe132mphtornadointhattheaerodynamicforcesarenotsufficienttoliftthepole.Thepeakaerodynamicforceatinjectionisabout2,200lbs,ofwhichabout900lbsactverticallyforthefavorableorientations.Sincethepoleweighs1,122lbs,itacceleratesdownwarduponrelease.Maximumpredictedrangeandspeedare41"ftand45mph,respectively.Forthe188mphtornado,thewindspeedsproduceverticalaerodynamicforcesthatexceedtheweightofthemissile(fororientations3and4),whichproducesliftatinjection.Themaximumliftisabout2ft(from20to22ftabovegrade),amodestamountthatisconsistentwiththepeakverticalaerodynamicforceofabout1,400lbs.Thisliftresultsinamuchlongerrange(upto154ft),andimpactvelocity(76mph)sincetheobjectissustainedinthewindsabouttwiceaslongasbefore(2secvs1sec).AfewadditionalsimulationsweremadewiththepolepositionedatzerooffsetforthecasesgiveninTable3.TheresultsshowreducedtransportcharacteristicswhencomparedtothevaluesinTable3.ItisnotedthatotheroffsetsmightresultintransportthatcouldapproachorslightlyexceedthoseinTable3.However,previousstudieswithratherdenseinjectiongridshaveshownthattheoffsetpmcos(tan-1.y)generallyprovidesaccurateestimatesofpeaktransportparameters.4.COMPARISONS,TOOTHERWORKANDFIELDOBSERVATIONSThepreviousresultsindicateverylittleliftandtransportlessthan200ftforutilitypoletypemissilesinjectedintornadoeswithpeakwindspeedsupto188mph.Thesepredictionscanbecomparedtoothercalculationsandfieldobservations.Theavailablecomparisonsgenerally13 correspondtohigherwindspeeds,butwillneverthelessprovidesomebasisforjudgingtheseresults.a.6-DTrajectoryModelPredictionsRedmannetal.513)simulatedthetrajectoriesofutilitypolemissilesin255mphtornadoes.Withtheutilitypoleat20ftelevationpitchedintothewindata45degreeangle,themissileliftedtoamaximumheightof40ftduringa339ftflightandimpactedthegroundat113mph.Foraninitialangularvelocityof10rpm,whichisamorerealisticinjectioncondition,thepoleliftedonly4fttoanelevationof24ftandlandedat91mphwitha140ftrange.TheseresultstendtosupportthetrendestablishedinTable3.At188mph,wenotedthattheverticalaerodynamicforceswerebeginningtoexceedmissileweightandsomeliftwasnoted.At255mph,onewouldexpectthemissiletoliftsubstantiallyhighersincetheaerodynamicforceswouldbeabout(255/188)2='1.8timesgreater.AsafurthertestoftheR06-DmodelusedinthedevelopmentofTable3,10simulationsweremadeusinga255mphtornadowithinitialorientation3,similartothatreportedinRef.13.TheR06-Dmodelpredictsanaveragemaximumheightof43feetwithrangesuptoabout500ftandimpactspeedsupto133mph.Theseresultstendtoboundthe6-Dmodelpredictions,andaresimilartopreviouscomparisonsofthe6-DandR06-DmodelsI2,4].b.3-DBallisticModelSimiuandCordesf14]usedthesimplifiedballistic3-Dmodelforcalculationofmaximumhorizontalmissilespeeds.Forthe35ftutilitypole,theypredictpeakhorizontalspeedof60mphina240mphtornadowhentheutilitypoleisinjectedat131ftelevation.Theseresultsareclearly

unconservativewhencomparedtothe6-DandR06-Dmodelpredictions(forzo=20ft)presentedpreviouslyandraisequestionsregardingtheadequacyofthe3-Dballisticmodelforslenderbodyshapes.~~I.:c.UtilityPoleTransport:Xenia,OhioTornadoVMcDonald$15]andMehtaetal.I16]reportthetransportofautilitypoleintheXenia,Ohio,tornadoofApril3,1974.Thepolefailed2ftabovethegroundandwastransportedatotaldistanceof160ftbyF5tornadowindsestimatedatabout'250mph.Thepolewas10in.indiameterand25.5ftinlength.Mehtaetal.[16]notethattheotherutilitypolesthathadfailedatthislocationinthetornadopathwerefoundwithin10to15ftoftheiroriginalpositions.TheR06-Dtrajectorymodelandpeakaerodynamicforceinjectionmodelhasbeentestedagainstthesefieldobservations[4g.TosimilatetheF5tornadowindspeeds,a250mphtornadowithpm=500ft,y=0.7,andUT=40mphwasusedastheinputtothetransportmodel.The250-mphintensityat33ftisbaseduponTwisdale's[2,8]estimatedmidrangeofF'5storms.Theutilitypolewaspositionedatzo=15fttocorrespondtotheinitialheightofthecenterofmassabovethegroundplane.Simulationswithaninitialverticalorientationofthepoleresultinmaximumpredictedtransportrangeslessthan53ft.Usingfavorableorientationstoaccountforinitialrepositioningafterthepolefails,maximumtransportrangesof283,651,and161ftarepredictedformissileoffsetsontherightsideofthetornadocenter.Amaximumimpactvelocityofabout140mphispredicted.Fora200-mphtornadowithpmo=300ft,thepredictedrangesare62,121,and91ftforoffsetsof100,150,and200ft,andthemaximumimpactvelocityis63mph.Theresultssuggestthat,withafavorableinitialmissileorientation,windspeedsinthe15

I

200to250mphintervalcouldhaveproducedtheobserved160-fttransportrange.Thefactthatmanyofthefailedpoleswerenotsignificantlydisplacedconfirms,thepredictionsoftheR06-DtrajectoryanalysiswithunfavorableinitialorientationsandtendstosupporttheuseoftheR06-Dtransportmodel.d.StoredUtilityPoles:Brandenbur,KentuckTheBrandenburgtornadoofApril3,1974,witharatedintensityofF5passeddirectlythroughthestorageyardoftheRuralElectricCooperative.HcDonald[15]andMehtaetal.[16)presentphotographsthatdocumenttheeffectsofthestormonvariousobjectsinitspath.Ofparticularinterestisanumberof8-in.-diameterby20-ft-longutilitypolesthatwerestoredhorizontallyonarackabout5ftabovethegroundelevation.Thepolesweredisplacedfromtherack,butnoneweretransportedsignificantly.TheeffectsofanF'5tornadoontheseobjectshasbeensimulated[4gwiththeuseofboththeinitialhorizontalstorageconditionsofthemissilesandafavorableinitialorientation.A250-mphtornadowasassumedinbothcases.Forthehorizontalinjectionmode,themodelpredictsthatthepolesmayexperiencetotalforcesthatapproach1,400lb,butonlyasmallfractionofthisisdirectedvertically.Hence,thepredictedtrajectoriesareparabolic,andthepolesdroptothegroundwithin30ftoftherack,asindicatedinFigure3.Thistransportcomparescloselytothepost-tornadoobservationsofthemajorityofthepoles.Favorableinitialmissileorientationswerealsosimulatedthatcouldhaveresultedforseveralmissilesinthestackastheyinteractedduringtheirinitialresponsetothetornadicwinds.Transportrangesbetween50and273ftresultedforthesesimulations,dependingupontheexactorientation16

Uma=250mph5ft//Xw/PredictedRange~30ft(a)HorizontalInitialOrientationUmax250mph32ftPredictedRange<273ft(b)FavorableRandomInitialOrientationFigure3.PredictedRangesforBrandenburgUtilityPoles17 CJandtheoffsetfromthetornadocenter.Themaximumheightandrangepredictedare32feetand273ft,respectively,asnotedinFigure2.Thepeakvelocityattainedbythepolewas95mph.ItisnotedthatsimulationswithUmax=200mphpredictrangesof13ftand100ft,respectively,forthehorizontalandrandominitialorientations.TheBrandenburgpolesaresignificantinthesensethattheobjectsrespondedtothewihdfield,butfew,ifany,alignedfavorablytobeliftedbythewindsandhencetobetransportedthedistancethatwaspredictedforfavorableinitialorientation.5.CONCLUSIONSOnthebasisofthisbriefstudy,thefollowingconclusionsaremade:'2.Tornadoeswithpeakwindspeedsof132and150mphgenerateaerodynamicliftforcesthatarelessthantheweightofthepostulatedutilitypolemissile.Estimatesofthepeakrange,foraninjectionheight(heightabovegradeofpolecenterofmass)of20ftare27ftand41ft,respectively,forthe132and150mphwindfields.Rangeisdefinedasthehorizontaldistancetraveledasthepolecenterofmassfallsfromz=20fttoz=0.Maximumvelocitiesareestimatesatabout37and45mph,respectively,forthe132and150mphtornadoes.Tornadoeswithpeakwindspeedsof188mphcanproduceabouta2ftlift(from20ftinitialelevation),arangeupto154ft,andapeakvelocityofabout76mphfortheutilitypolemissile.These.conditionsoccurwhenthepoleispitchedintothewindatabouta45degreeangleandreleasedatpeakaerodynamicforce.Theseareidealizedandveryconservativereleaseconditionsthatwouldbedifficulttoduplicateinanactualtornadostrike.3.Maximumheightattainedduringatumblingwind-bornetransportforUmax<188mphbyanypartofa35ftutilitypolewouldprobablynotexceed35to40ft.Otherinjectionmodes,suchasaramp-typeinjectioncouldproduceupwardricochetofahorizontally-translatingpole.However,thisinjectionmodewouldrequire"ideal"missileoriginposition,terrain,andtargetconfigurationinordertoposearealisticthreattoelevatedtargets.Theseresultsareconservativeinthemissileinjectionreleasecriterion,definitionofrangeandpeakvelocity,positioningofthemissilerelativetothewindfield,andthewindfieldflowcharacteristics.Forexample,thetipofthepolewillstrikethegroundasthepolebeginstodropandthis18 interactionwillreducethehorizontalmomentum.Hence,theestimatesofpeakrangeandhorizontalvelocityareveryconservative.Inaddition,theweightofthepoleislessthanthe1,490lbsusedinsometornadomissilecalculations=[e.g.,17].Usingthe1,490lbweight,themaximum154ftrangeinthep+2cr188mphtornado(seeTable3)reducestolessthan100ft.Ingeneral,fieldobservationsdonotconfirmsignificantutilitypoletransportforthewindspeedsconsideredherein.OurbestestimateoftypicalutilitypoleresponseforUmax<188mphwouldbeatrajectoryrangefrom0to50ftwithhorizontalmissilespeedsapproaching50-60mph.REFERENCESl.U.S.NuclearRegulatoryCommission,StandardReviewPlan,"MissilesGeneratedbyNaturalPhenomena,"Section...,Washington,D.C.,November1975.2.Twisdale,L.A.,etal.,"TornadoMissileRiskAnalysis,"ElectricPower,ResearchInstitute,PaloAlto,California,NP-768andNP-769,May1978.!3.Twisdale,L.A.,Dunn.W.L.,andDavis,T.L.,"TornadoMissileTransportAnalysis,"NuclearEnineerinandDesin,52,1979,pp.296-308.4.Twisdale,L.A.,andDunn,W.L.,"TornadoMissileSimulationonDesignMethodology,"EPRINP-2005,ElectricPowerResearchInstitute,PaloAlto,California,August1981.5.Dunn,W.L.,andTwisdale,L.A.,"ASynthesizedWindfieldModelforTornadoMissileTransport,"NuclearEnineerinandDesin,52,1979,pp134-144.6.Twisdale,L.A.,"AnAssessmentofTornadoWindfieldCharacteristicsforMissileLoadingPrediction,"Proceedins,FourthU.S.NationalConferenceonWindEngineeringesearch,UniversityofWashington,Seattle,Washington,July1981.7,.Twisdale,L.A.,"ARisk-BasedDesignAgainstTornadoMissiles,"ProceedinsoftheThirdASCESpecialtyConferenceonStructuralDesignoucearPlantFacilities,Boston,Massachusetts;April1979.8.Twisdale,L.A.,"TornadoDataCharacterizationandWindspeedRisk,"JournaloftheStructuralDivision,ProceedingsASCE,Vol.104,No.ctober8.9.Twisdale,L.A.,"RegionalTornadoDataHaseandErrorAnalysis,"Prerints,AMS12thConferenceonSevereLocalStorms,SanAntonio,exas,anuary1982.19 10.Twisdale,L.A.,andDunn,W.L.,ProbabilisticAnalysisofTornadoWindRisks,"JournalofStructuralEnineerin,Vol.109,No.2,February1983.12.13.14.Fujita,T.T.,"WorkbookofTornadoesandHighWinds,"SMRP165,UniversityofChicago,Chicago,Illinois,September1978.Redmann,G.H.,etal.,"WindFieldandTrajectoryModelsforTornado-PropelledObjects,"ElectricPowerResearchInstitute,PaloAlto,California,Draft,1980.Redmann,G.H.,etal.,"WindFieldandTrajectoryModelsforTornado-PropelledObjects,"EPRINP-748,ElectricPowerResearchInstitute,PaloAlto,California,May1978.Simiu,E.,andCordes,M.,"TornadoBorneMissileSpeeds,"NBSIR-76-10-50,NationalBureauofStandards,Washington,D.C.,April1976.15.McDonald,J.R.,"Tornado-GeneratedMissilesandTheirEffects,"ProceedingsoftheSymposiumonTornadoes,Texas,TechUniversity,Lubbock,Texas,June1976.16.Mehta,K.C.,etal.,"EngineeringAspectsoftheTornadoesofApril3-4,1974,"CommitteeonNationalDisasters,NationalAcademyofsciences,1976."SafetyRelatedSiteParametersforNuclearPowerPlants,"WASH-1361,U.S.AtomicEnergyComission,DirectorateofLicensing,OfficeofSafety,Washington,D.C.,January1975.20 4tI