an improved deflection energy method to normalise … · deflection energy versus deflection for...

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Abstract Normalisation is the process of modifying a set of postmortem human subject (PMHS) response data to better represent that of a standard sized human. This improved method is based on the fact that all plots of deflection energy versus deflection for the thorax are of constant slope. The deflection energy is the integral of the applied impact force over the deflection measured by a chestband up to the point of maximum deflection. Standard sized human thorax deflection energies and slopes are found from multivariate analyses relating energy and slope, separately, to the anthropometric data for all subjects. Force is the spatial derivative of the linear deflection energy curve and is a constant. The resulting rectangular force versus deflection curve leads to scale factors for force, deflection, elastic stiffness, the viscous constant, and time, assuming a two element solid viscoelastic model. Subject effective mass and postimpact velocity were calculated from conservation of energy and impulse equals momentum, solved simultaneously, providing scale factors for effective mass and subject velocity at maximum deflection. The time histories and force versus deflection have been plotted, the standard deviation targets overplotted, and coefficients of variation calculated. Results have been qualitatively and quantitatively compared to previous methods. Keywords biofidelity, data normalisation, postmortem human subject (PMHS), scaling I. INTRODUCTION The process of normalising postmortem human subject (PMHS) response data from impact testing to obtain a representation of the typical, or average, human response has been an important part of anthropometric crash dummy design and development for many years. Normalisation is the process of mathematically modifying the response data from a set of PMHS subjects to a standard human size. This normalised response is used as a standard against which the response of an anthropometric dummy is compared to assess the dummy biofidelity. A quantified measure of biofidelity is desirable to provide the basis for an objective decision as to the ability of a dummy to assess vehicle crash protection for a human of similar size. In 1984 a method for normalising PMHS data based on the ratio of the whole body mass of a subject to the standard total body mass (e.g. 50 th percentile male) was developed [1]. This methodology assumed that all subject responses will be related directly to the whole body mass. Clearly force, deflection and kinematic responses from widely varying sizes and shapes of humans are not likely to be related solely by whole body mass. An impulsemomentum and stiffnessbased normalisation method [2] was presented in 1984. Scale factors were developed from both anthropometry measures and ratios of the solution for the single degreeoffreedom (DOF) differential equation for a linear elastic system which represented a large impacting mass such as a sled type of impact. In 1989 an improvement to this methodology was presented [3] by expanding the derivation of scale factors to the two DOF linear elastic system which better represents pendulumtype impacts where the striking and struck masses are more nearly equal. Again the scale factors were developed from ratios of the solution to the system of differential equations. An improvement [4] was made to the two DOF method using the integral of the force versus deflection curve, the deflection energy, to develop an elastic effective stiffness directly from the force versus deflection response data rather than from characteristic subject dimensions. This latter study [4] also compared the effectiveness of the various normalisation methods in force versus deflection space using the standard deviation ellipse [5] and a modified coefficient of variation measure taking one half of the area of the ellipse divided by the product of force and deflection at each data point. This quantitative comparison indicated that effective stiffness collapsed the force versus deflection curves toward BR Donnelly is a PhD at Biomechanics Research Associates Ltd., USA, (+1 7406020531/[email protected]). HH Rhule is a BS and KM Moorhouse and JA Stammen are PhDs at the National Highway Traffic Safety Administration Vehicle Research and Test Center, USA. YS Kang is a PhD at the Ohio State University Injury Biomechanics Research Center, USA. An Improved Deflection Energy Method to Normalise PMHS Thoracic Response Data Bruce R. Donnelly, Heather H. Rhule, Kevin M. Moorhouse, YunSeok Kang, Jason A. Stammen IRC-17-72 IRCOBI Conference 2017 -577-

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  • AbstractNormalisationistheprocessofmodifyingasetofpostmortemhumansubject(PMHS)responsedatatobetterrepresentthatofastandardsizedhuman.Thisimprovedmethodisbasedonthefactthatallplotsofdeflectionenergyversusdeflectionforthethoraxareofconstantslope.Thedeflectionenergyistheintegraloftheappliedimpactforceoverthedeflectionmeasuredbyachestbanduptothepointofmaximumdeflection.Standardsizedhumanthoraxdeflectionenergiesandslopesarefoundfrommultivariateanalysesrelatingenergyandslope,separately,totheanthropometricdataforallsubjects.Forceisthespatialderivativeofthelineardeflectionenergycurveandisaconstant.Theresultingrectangularforceversusdeflectioncurveleadstoscalefactorsforforce,deflection,elasticstiffness,theviscousconstant,andtime,assumingatwoelementsolidviscoelasticmodel.Subjecteffectivemassandpostimpactvelocitywerecalculatedfromconservationofenergyandimpulseequalsmomentum,solvedsimultaneously,providingscalefactorsforeffectivemassandsubjectvelocityatmaximumdeflection.Thetimehistoriesandforceversusdeflectionhavebeenplotted,thestandarddeviationtargetsoverplotted,andcoefficientsofvariationcalculated.Resultshavebeenqualitativelyandquantitativelycomparedtopreviousmethods. Keywords biofidelity,datanormalisation,postmortemhumansubject(PMHS),scaling

    I. INTRODUCTIONTheprocessofnormalisingpostmortemhumansubject(PMHS)responsedatafromimpacttestingtoobtain

    a representationof the typical,or average,human responsehasbeen an importantpartof anthropometriccrash dummy design and development for many years. Normalisation is the process of mathematicallymodifyingtheresponsedatafromasetofPMHSsubjectstoastandardhumansize.Thisnormalisedresponse isusedasastandardagainstwhichtheresponseofananthropometricdummy is

    comparedtoassessthedummybiofidelity.Aquantifiedmeasureofbiofidelityisdesirabletoprovidethebasisforanobjectivedecisionastotheabilityofadummytoassessvehiclecrashprotectionforahumanofsimilarsize.In1984amethodfornormalisingPMHSdatabasedontheratioofthewholebodymassofasubjecttothe

    standard totalbodymass (e.g.50thpercentilemale)wasdeveloped [1]. Thismethodologyassumed thatallsubject responseswill be related directly to thewhole bodymass. Clearly force, deflection and kinematicresponses fromwidelyvarying sizesand shapesofhumansarenot likely tobe related solelybywholebodymass. An impulsemomentum and stiffnessbased normalisationmethod [2]was presented in 1984. Scalefactorsweredevelopedfrombothanthropometrymeasuresandratiosofthesolutionforthesingledegreeoffreedom(DOF)differentialequationforalinearelasticsystemwhichrepresentedalargeimpactingmasssuchasasled typeof impact. In1989an improvement to thismethodologywaspresented [3]byexpanding thederivationofscalefactorstothetwoDOFlinearelasticsystemwhichbetterrepresentspendulumtypeimpactswherethestrikingandstruckmassesaremorenearlyequal.Againthescalefactorsweredevelopedfromratiosofthesolutiontothesystemofdifferentialequations.Animprovement[4]wasmadetothetwoDOFmethodusing the integralof the forceversusdeflection curve, thedeflectionenergy, todevelopanelasticeffectivestiffness directly from the force versus deflection response data rather than from characteristic subjectdimensions.Thislatterstudy[4]alsocomparedtheeffectivenessofthevariousnormalisationmethodsinforceversusdeflectionspaceusingthestandarddeviationellipse[5]andamodifiedcoefficientofvariationmeasuretakingonehalfoftheareaoftheellipsedividedbytheproductofforceanddeflectionateachdatapoint.Thisquantitativecomparison indicated thateffectivestiffnesscollapsed the forceversusdeflectioncurves toward BRDonnellyisaPhDatBiomechanicsResearchAssociatesLtd.,USA,(+17406020531/[email protected]).HHRhuleisaBSandKMMoorhouseandJAStammenarePhDsattheNationalHighwayTrafficSafetyAdministrationVehicleResearchandTestCenter,USA.YSKangisaPhDattheOhioStateUniversityInjuryBiomechanicsResearchCenter,USA.

    AnImprovedDeflectionEnergyMethodtoNormalisePMHSThoracicResponseData

    BruceR.Donnelly,HeatherH.Rhule,KevinM.Moorhouse,YunSeokKang,JasonA.Stammen

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  • eachothermoreeffectivelythantheothermethods.MorerecentlytheauthorsofthiscurrentstudypresentedamethodfornormalisingPMHSthoracicimpactdatabasedonthedeflectionenergyandatwoDOFviscoelasticmodel [6]. Thisapproachwasmathematically cumbersomebutdid improve thequantitative results slightlyover the effective stiffness approach [4] asmeasured using a time based average coefficient of variationmeasureandtheellipsecoefficientofvariationmeasureforforceversusdeflection.Thisstudybuildsuponallof thispriorwork todevelopan improved,andsimpler,mechanisticmethod for

    normalisingthoracicPMHSdataagainusingatwoDOFviscoelasticmodel. PMHSdatafrom19subjectsfromthreestudies[5][7][8]ofthoracicpendulumtestswereanalysedtoillustratethemethodology.Thedeflectionenergyand theslopeof thedeflectionenergyversusdeflectioncurvewereused todevelopscale factors forenergy,slope,force,deflection,elasticstiffness,theviscousconstant,andtime.Scalefactorsforeffectivemassandsubjectvelocitywerederivedfromconservationofenergyandconservationofmomentum.Of thepreviousnormalisationstudies themassbasedmethodusedsubjectanthropometryand theknown

    anthropometryvaluesofstandardsizedhumanstodevelopscalefactorsfornormalisation. Theotherearliermethodsusedchestanthropometryratiosandaveragesoftheresponsesofthesubjectpoolbeinganalysedtoestimate thestandardsizedhumanresponsesused todevelopscale factors. Thecurrentstudymodifies thisapproachbyusing the responsemeasuresofdeflectionenergyand slope fromall19 subjectsasdependentvariablesandthesubjectanthropometrymeasuresasindependentvariablestodevelopstatisticalmultivariaterelationships for energy and slope. The resulting equations can then be used with any standard humananthropometry values to estimate standard human deflection energy and slope values and to calculate thecorrespondingscalefactorsforthestandardforce,deflection,elasticstiffness,viscousconstant,andtime.Results fromnormalisingall19subjectstothe50thpercentilemalearepresented,alongwithmeancurves

    andstandarddeviationbiofidelitytargets, inbothtimehistoryplotsand forceversusdeflectionplots. Theseplots have been compared with results from previous methods both qualitatively and quantitatively todemonstrate the improved grouping and smaller standard deviation targets of the deflection energynormalisationresults.

    II. METHODSResponsedataandanthropometrydatafrom19PMHStested in lateralandobliquependulumtype impact

    tests in three studieswereanalysedusingadeflectionenergymethodanda twoDOFviscoelasticmodel todevelopscalefactorsfornormalisationtothe50thpercentilesizemalehuman. Standardvaluesfordeflectionenergy and the slope of the deflection energy versus deflection curve were estimated using multivariaterelationshipsbetweenanthropometrymeasuresand impactvelocityas independentvariablesanddeflectionenergyandslopeofdeflectionenergyasdependentvariables.Mechanicalvaluesforenergy,force,deflection,stiffness, theviscousconstant,and timewerecalculated from thedatausing the twoDOFmodel. Effectivemassandsubjectvelocityvalueswere foundusing theequations forconservationofenergyandmomentumsolvedsimultaneously.Normalisationscalefactorstaketheform

    1 andareappliedtotherelevantparameterateachpointinthetimehistory.Adescriptionof the subjects and the data analysed, thederivationof the subjectmechanical values, the

    developmentofthemultivariaterelationshipforthestandardhumanmechanicalvalues,andthedevelopmentofscalefactorsispresentedbelow.

    SubjectDataNineteenPMHSfromthreethoracic impactstudieswereanalysed inthisstudy. Reference[6]testedseven

    PMHS innominal2.5m/s lateralandobliquethoracic impactsatthefourth intercostalspaceusinga23.86kgimpactorwitha15.24cmdiametercircularface.Reference[7]tested12PMHSin4.5m/sand5.5m/slateralandoblique thoracic impact testsat thexyphoidusinga23.99kg impactorwitha15.24cmhighx30.48cmwiderectangularface.Reference[8]alsotestedfiveadditionalPMHSin2.5and4.5m/sinlateralandobliquethoracic impact tests at either the fourth intercostal space or the xyphoid using either the circular face or

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  • rectangularfaceimpactors.Ofthese24PMHS,19wereselectedforanalysisinthisstudy.Thefivethatwerenotusedwereeliminated forvarious reasons suchas the impulseandmomentumcalculatedat the timeofmaximum thoracic deflection beingmore than 30% different [5][9]. Many of these subjects were testedmultipletimesbutonlythefirsttestwasusedinthisstudy.The19subjectsincludedwerejudgedtohaveverygoodqualitydataforanalysisandwouldlendconfidencetoademonstrationoftheprocedure.Theappliedforceversustimeandthechestbanddeflectionversustimewerecrossplottedandintegratedup

    tothepointofmaximumdeflectiontoobtainthedeflectionenergy.Forreasonsofconsistencytimezerowassetatthepointoffirstcontinuouspositivechestbanddeflectionforeverysubject. Generallytherewassomeappliedforcebeforethechestbandregistereddeflectionduetocontactwiththethoraxskinandsubcutaneousfat. Asaresult, attimezerothereusuallywasan initialpositiveforce. Thealternativewouldbetosettimezeroattheinitialpositiveforcebutinthatcasetherewouldbenomeasureddeflectionatthattime.Thedataused in thisanalysis included lateralandoblique testsaswellas circularand rectangular impact

    faces.Reference[8]testedameasureofelasticstiffnessandindicatednosignificantdifferenceinlateralversusoblique responseamong thevarious testsexcept for testswith thecircular impact face. Thestandard ttestprobabilityof=0.05wasused inthatanalysistoprotectagainsttype Ierrorandappropriatelyrejectedthenullhypothesisthatthedifferenceinthemeansofthestiffnesswaszero.Inthisstudyitwasdesirabletohavealargesetofsubjectstodemonstratethemethod.Thestandardforassumingthesubjectsarefromthesamepopulationwaslessstringentthaninastudydevelopingbiomechanicalresponsetargets.Thedatawastestedcomparingthedeflectionenergycurveslopesofthelateralteststotheobliquetestsandcircularimpactorfaceteststotherectangular impactorfacetests inallcombinations(seeAppendixA). Thenullhypothesis ineachcasewas that the difference in the slope valueswas zero. The pvalues for slope varied from 0.4 to 0.9indicatingitwasnotpossibletorejectthenullhypothesisoftheslopesbeingthesame.Itwasfeltthatforthepurposeofdemonstrating themethod itwasacceptable to considerallof the testsasbeing from the samepopulation. This isnotacontradictionofthepreviousresultbutratherpresentsadifferentviewofthedata,examiningadifferentvariable,forthepurposeofdemonstratingthenormalizationmethod. Ifthebiofidelityresponseofadummyinaparticulartestconfigurationwasbeingassessedonemightchoosetouseasubsetofthedata.

    TwoDegreeofFreedomViscoelasticModelThemaximumdeflectionenergyistheintegralofappliedforcewithrespecttothoracicdeflection.

    2

    where E=deflectionenergy F=appliedforce t=time S=thoracicdeflectionfromchestband.Thedeflectionenergyversusdeflectioncurvesforallofthethoracicimpactsexaminedinthisstudyarevirtuallystraight linesofconstantslopeupto,and including,themaximumdeflection. Fig.1showsthreeexamplesofthisphenomenonwhicharetypicalofall19subjects.

    (a) (b) (c)

    Fig.1.Plotsofintegrateddeflectionenergyversusdeflectiondemonstratingthestraightlineslope.

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  • In this study the term deflection energy is used indicate the energy absorbed and dissipated during the

    thoracicimpacteventuptothepointofmaximumdeflection.Deflectionenergyisaonedimensionalanalogtostrainenergy[10]wherethespatialderivativeofdeflectionenergyisforceratherthanstress.Ifthedeflectionenergyversusdefelctioncurvehasaconstantslopeandappliedforce isthespatialderivativeofenergy,thenappliedforceisconstant.Theslopeofthecurveis

    .

    andtherefore

    . 3

    Wehavearelationshipamongenergy,constantforce,anddeflectionthatcanbeusedtodevelopscalefactorsfornormalisation.This relationship also leads directly to a twoDOF viscoelasticmodel that can be used to find the elastic

    stiffness,viscousconstant,damped frequencyand theperiod. The forceversusdeflectioncurvewouldhaveconstantforceuptothemaximumdeflectionasseeninFig.2.

    Fig.2.Schematicofaconstantforcevs.deflectioncurve

    withelasticandviscousenergyareaslabeled.Thetotaldeflectionenergyistheareaunderthecurve,E=Fconstant*Smax.Theelasticenergyportion(stored)of

    theenergyisthelowerrighttriangle,*E=*Fconstant*Smax.Theviscousenergyportion(dissipated)istheupperlefttriangleandhasthesamearea.TheequationfortheforceinatwoDOFviscoelasticmodelis

    (4) where =elasticstiffness =viscousconstant =timederivativeofdeflection(velocity).Theelasticenergyis (5)and

    K= (6)

    Theviscousenergyis (7) where =velocityatzerodeflectionor and (8)

    ThedampednaturalfrequencyfromthedifferentialequationforatwoDOFviscoelasticsolidis

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  • (9)

    where =dampednaturalfrequency =(mI+ms)/(mI*ms) (10) mI=impactormass ms=subjecteffectivemassand theperiodis 2 / . (11)Itshouldalsobenotedthatbecausetheviscousenergy is linearlydependentontherateofdeflection,the

    ratemustbeastraight line in equaltothe impactvelocity, ,whendeflection iszeroandequaltozeroatmaximumdeflection, (12) where =rateofdeflection =impactvelocity =maximumdeflection =deflection.Fora constant force thedifferentialequationabove isequivalent to thedifferentialequation for the two

    element viscoelastic solid (Equation 4). Solving the differential equation for deflection, S(t), results in anincreasing exponential function in time [11]. The rate, , is a complementary decreasing exponentialfunction. Whenmultipliedby their respective coefficientsand combined the result isa constant forceas isrequiredbytheconstantslopeofthedeflectionenergyversusdeflectioncurve.Theeffectivemassofthesubjectandthesubjectvelocityatthetimeofmaximumdeflectioncanbefoundby

    solving the equations for conservation of energy, including the deflection energy, and conservation ofmomentumsimultaneouslyfromtimezerotothepointofmaximumdeflection.Theresultingequationsare

    2 11

    and

    2 12

    where effectivemassofthesubject

    impactormass =impactvelocity,V0= deflectionenergy velocityofsubjectatmaximumdeflection.Finally, it shouldbenoted that thisapproach isapplicable toa twodegreeof freedom system (pendulum

    impact)ortoonedegreeoffreedomsystemssuchassledordroptestsbymodifyingthesizeoftheimpactingmass,i.e.,aninfinitemassforadroptestandaverylargemassforasledtest.

    MultivariateRegressiontoEstimate50thPercentileDeflectionEnergyandSlope Wenowhaveamodelthatprovidesvaluesforenergy,slope,force,deflection,stiffness,theviscousconstant,time, effectivemass, and subject velocity for each subject that can be used to develop scaling ratios tonormalise the response to thatofa standardhuman. The standardhuman responsewasestimated fromamultivariaterelationshipdevelopedusingthedeflectionenergyandtheslopeoftheenergycurve,respectively,asdependentvariablesandtheanthropometrymeasuresforallsubjectsasindependentmeasures.TheMatlabfunction stepwiselm [12]wasused todevelop this relationship. The analysisusing the stepwiselm function

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  • considered all of the independent anthropometry variables available from the three studies and eliminatedthosevariablesthatwerenotsignificantleavinganequationforthedependentvariablebasedonlyonthemostimportantvariablesandtheinteractions.Thisprocedureisgenerallyreferredtoasstepwiseforwardestimation[13]. The considered variableswere gender, age,height,mass,bodymass indexBMI, chestbreadth, chestdepth,andimpactvelocity.Thetwomultivariateequationsfoundforenergyandslopewerebasedonsubjectage,mass,height,BMI,andimpactvelocity.Theanthropometricdataforthestandardhuman(50thpercentilemale),alongwith thedesired impactvelocity,were then input to themultivariateequation toobtainenergyand slopevalues for the standardhuman. The standardhumanenergyand slopevaluesand theequationsderived above provide the standard human values for force, deflection, stiffness, the viscous constant, andtime. The standardhumanenergy isused in the equations for conservationofenergy and conservationofmomentumtosolveforthestandardeffectivemassandsubjectvelocityatmaximumdeflection.NormalisationFactorsRatios,showninTableI,madeupofthestandardparametervaluesrelativetothesubjectparametervalues

    providenormalisationscalingfactorsforeachsubjectthatwereusedtonormalisetheresponsetimehistoriesandforceversusdeflectioncurvestothatofthestandardhuman.ImpactvelocityisalinearcoefficientinthedifferentialequationsforthetwoDOFviscoelasticmodeland,therefore,velocitywasscaledbeforecalculatingthe normalisation factors in Table I, i.e., the applied force, chestband deflection, and the equations forconservationofenergyandmomentumwereallscaledforimpactvelocityofacommonvalue.The19subjectsanalysedherewere testedatnominal impact velocitiesof2.5,4.5and5.5m/s (as shown inTable II in theResultssection).Todemonstratethemethodthenormalisationimpactvelocitywasselectedtobe3.5m/sforall19subjectsinthisanalysis.Themultivariateequationwasdevelopedusingtheactualimpactvelocitiesbutwhenestimatingenergyandslopevaluesforthe50thpercentilemalethenormalisationvalueof3.5m/swasinput.

    TableI.Normalisationscalefactors.

    Impactvelocity Energy Slope Force Deflection Stiffness

    Viscousconstant Time

    Effectivemass

    Subjectvelocity

    ForceVersusDeflectionStandardDeviationEllipsesThestandarddeviationellipsescanbeconstructedfromthestandarddeviationsforforceandfordeflection

    calculatedateachpoint in time. Inpreviousstudies [4][14] the timebasedstandarddeviationellipseswereplotted in force versus deflection spacewhich ismisleading since the force versus deflection pairs of eachsubject based on the time point are not colocated in force versus deflection space. The result of thisphenomenon isthatthetimebasedstandarddeviationellipsesdonotaccuratelyrepresentthevariance,andthegrouping,of the forceversusdeflection curves in forceversusdeflection space. Interpolating forceanddeflectiontoacommondeflectionenergybaseresolvesthisproblemandtheellipsescanthenbecalculatedand located accurately in force versus deflection space. However, comparing the effectiveness of thisdeformation energy based normalisation methodology to previous methods using the average ellipsecoefficientofvariationcanonlybedoneaccuratelyifthecoefficientsofvariationarecalculatedthesameway.In order tomake a reasonable comparison among the several normalisationmethods, the coefficients ofvariationwerecalculatedbasedonstandarddeviationscalculatedfromtheforceanddeflectiontimehistorieseven though this is, strictly speaking,not correct. Since thedeformationenergywasnot calculated for thepreviousmethods,therewaslittlechoice.Thecoefficientofvariationforthemoreaccuratemethodwasalsocalculated for the deflection energy normalisationmethod presented in this study and is both plotted andtabulated.

    III. RESULTSThetestinformationandtheanthropometricdataforthe19subjectsanalysedinthisstudyarepresentedin

    TableIIalongwiththeanthropometricvaluesandimpactvelocityusedforthe50thpercentilemalehuman.

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  • TableII.Testandsubjectcharacteristics.

    Subject#

    Ref.Vo

    (m/s)SideAngle

    Plate(cm)

    Impactormass(kg)

    GenderAge(yrs)

    Height(cm)

    Mass(kg)

    BMI(kg/m2)

    0503 [6] 2.62 left60o circle 23.86 male 79 180.3 65.8 20.20504 [6] 2.43 left90o circle 23.86 male 80 165.1 80.7 29.60505 [6] 2.46 right90o circle 23.86 male 77 177.8 66.2 21.00506 [6] 2.54 right60o circle 23.86 male 87 175.3 65.8 21.40507 [6] 2.45 left60o circle 23.86 male 53 165.1 65.3 24.00601 [6] 2.57 left90o circle 23.86 male 63 185.4 93.0 27.00802 [7] 4.77 left90o rectangle 23.99 male 67 169 81.6 28.60803 [7] 4.58 left60o rectangle 23.99 male 77 178 64 200804 [7] 4.47 left60o rectangle 23.99 male 81 159 52 20.70902 [7] 4.63 left90o rectangle 23.99 male 60 183 89 26.50903 [7] 4.68 left90o rectangle 23.99 female 29 175 79 25.60904 [7] 5.64 left90o rectangle 23.99 female 81 177 79 25.50905 [7] 5.50 left60o rectangle 23.99 male 81 175 93 30.11001 [7] 4.76 left90o rectangle 23.99 male 82 175 72 23.51002 [7] 4.44 left90o rectangle 23.99 male 87 186 71 20.61003 [7] 4.56 left60o rectangle 23.99 male 48 175 78 25.51201 [8] 2.63 right60o rectangle 23.99 male 56 176.0 88.0 28.41202 [8] 2.57 right60o circle 23.99 male 76 183.5 97.5 29.01203 [8] 2.56 right60o rectangle 23.99 male 71 172.0 75.8 25.650th [15] 3.5 45 175 77 25.5

    Asmentionedpreviouslytheenergyandslopevaluesestimatedbythemultivariateequationsarefoundfor

    thenominal impactvelocityof3.5m/s. Themultivariateregressioncoefficients forenergyand forslopearepresentedinTableIIIandwereentirelydeterminedbytheanthropometricpropertiesofthesubjectandimpactvelocity. The coefficients in Table III, columns two and three, are multiplied by the individual subjectanthropometricvariables listed in columnone (theactual subjectdata ispresented inTable II) toobtainanestimateofthesubjectdeflectionenergyandslope.Table IVpresentsboththe integratedandtheestimatedvalues for energy and for slope for each subject, at the actual impact velocities, aswell as the differencebetweenthetwovalues.

    TableIII.Multivariateregressioncoefficientsforenergyandslope.

    Variables EnergyCoefficients SlopeCoefficientsconstant 5.0140 352.5938Age 0.1688 2.4432

    Height 0.0288 1.8116Mass 0.0095 2.0358BMI 0.1845 8.4510

    impactvelocity 2.3992 43.4126age*height 0.0010 0.0132age*mass 0.0009 0.0200age*BMI 0.0029 0.0662

    age*impactvelocity 0.0005 0.0031height*mass 0 0height*BMI 0.0012 0

    height*impactvelocity 0.0136 0.2389mass*BMI 0 0.0102

    mass*impactvelocity 0.0143 0.2464BMI*impactvelocity 0.0451 0.8103

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  • TableIV.Integratedandestimateddeflectionenergyandslope.

    Integratedenergy&slope

    Multivariateestimate

    Difference

    SubjectV0

    (m/s)E

    (Nm)b

    (Nm/mm)Eest(Nm)

    best(Nm/mm)

    energy(Nm)

    %error

    slope(Nm/mm)

    %error

    0503 2.62 32.69 1.16 32.70 1.21 0.01 -0.03 0.05 4.530504 2.58 44.41 1.27 44.84 1.29 0.43 -0.96 0.02 1.500505 2.46 30.00 1.04 25.66 1.04 4.34 14.46 0.00 0.150506 2.54 35.44 1.24 42.55 1.19 7.10 -20.04 0.04 3.470507 2.45 43.27 1.00 41.56 1.01 1.70 3.93 0.02 1.620601 2.57 43.77 1.38 43.89 1.39 0.13 -0.29 0.01 0.800802 4.77 144.71 2.64 137.57 2.58 7.14 4.94 0.05 2.010803 4.58 130.91 2.19 136.47 2.07 5.56 -4.25 0.13 5.730804 4.47 115.44 1.94 113.47 1.93 1.97 1.71 0.01 0.470902 4.63 118.21 1.97 109.48 2.01 8.73 7.38 0.04 2.110903 4.68 85.31 1.74 90.15 1.66 4.84 -5.67 0.08 4.610904 5.64 147.37 2.53 151.52 2.59 4.14 -2.81 0.06 2.530905 5.50 143.94 2.58 149.06 2.55 5.12 -3.55 0.03 1.091001 4.76 126.08 2.76 123.77 2.79 2.31 1.83 0.03 1.161002 4.44 108.33 2.48 104.98 2.52 3.35 3.09 0.04 1.511003 4.56 109.75 2.18 109.17 2.24 0.58 0.52 0.06 2.581201 2.63 41.60 1.75 46.85 1.83 5.25 -12.62 0.08 4.491202 2.57 49.58 1.61 48.73 1.65 0.85 1.72 0.04 2.401203 2.56 46.77 1.65 45.16 1.62 1.60 3.43 0.04 2.1350th 2.5 55.47 1.59 Avg.error 0.38 Avg.error 0.2950th 3.5 81.54 1.88 50th 4.5 107.61 2.18 Deflection energies for each subject were calculated from the test data by integrating the force versus

    deflectionfromthepoint intimeofthe initialpositive increase indeflectiontothemaximumdeflection. Theslopesofeachdeflection energy curveweredeterminedbydividing themaximumenergyby themaximumdeflectionwhich occur simultaneously. The remaining valueswere calculated as described in theMethodssection. The calculated values for the scale factors at the impact velocity of 3.5m/s are presented in theAppendix.Plotsoftheoriginalunscaledandnonnormalisedsubjectforceanddeflectionversustimeandforceversus

    deflectionarepresentedinFig.3(ac).PlotsofthesameresponsedatascaledforimpactvelocityarepresentedinFig.4(ac). Plotsoftheresponsedatanormalisedusingtheeffectivestiffnessmethod[4]arepresented inFig.5(ac). Plotsofthedeflectionenergynormalisedresponsecurves intimearepresented inFig.6(ac). Aplotof thedeflectionenergynormalisedresponsecurveswith thestandarddeviationellipsesshown in forceversusdeflectionspaceispresentedinFig.7(b)withFig.6(c)repeatedasFig.7(a)forpurposesofcomparison.

    For the time history curves the standard deviation and the CVwere calculated at each time point andaveragedovertheentiretimeoftheevent.Thisapproacheliminatesneckingintheplottedstandarddeviationtimeplotswhich isbeneficialwhenqualitativelycomparingPMHStargetstodummyresponses forbiofidelityassessment.TheellipseCVresultswerefoundbydividingonehalfoftheareaofthestandarddeviationellipsebytheproductoftheforceanddeflectionatthatpoint.TheresultswerethenaveragedovertheentireeventtogettheellipseCV. AllCVswerecalculatedfromastartingpointof10%ofthemaximumdeflectiontotheendingpointofmaximumdeflectionanddirectcomparisonsofCVsaremeaningful.ThecoefficientofvariationresultsarepresentedinTablesVandVI.

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  • (a)

    (b)

    (c)

    Fig.3.O

    riginalre

    spon

    sedataun

    scaledandno

    nno

    rmalise

    d.

    (a)

    (b)

    (c)

    Fig.4.R

    espo

    nsedatasc

    aled

    forimpactvelocity

    .

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  • (a)

    (b)

    (c)

    Fig.5.R

    espo

    nsedatanormalise

    dusingtheeffectivestiffne

    ssm

    etho

    d[4].

    (a)

    (b)

    (c)

    Fig.6.Re

    spon

    sedatano

    rmalise

    dusingde

    flectionen

    ergywith

    forceversusdeflectionplottedusingtim

    ebasedstandarddeviatio

    ns.

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  • (a) (b)

    Fig.7.Normalisedresponsedatawith(a)timebasedstandarddeviationellipsesand(b)deflectionbasedstandarddeviationellipses(note:Fig.7(a)isFig.6(c)repeated).

    TableV.Comparisonofaveragecoefficientsofvariationcalculatedfromtimehistories.Method ForcevsTime DeflectionvsTime ForcevsDeflection

    Original 0.312 0.352 0.176ScaledforImpactVelocity 0.203 0.167 0.056EppingerMethod 0.167 0.203 0.083MertzVianoMethod 0.170 0.170 0.039MoorhouseMethod 0.117 0.143 0.042DeflectionEnergyMethod 0.096 0.119 0.019

    TableVI.Averageellipsecoefficientofvariationcalculatedinforceversusdeflectionspace.

    Method ForcevsDeflectionNormalisedinForceversusDeflectionSpace 0.011

    IV. DISCUSSIONTheobjectiveofnormalisation is todevelopscale factors,basedonsoundmechanicalprinciples, thatare

    used toadjust thePMHS response to representa standard sizedhuman: in thisexample the50thpercentileadultmale. It has been generally accepted that reducing the variation in a set of response data curves issuccessful normalisation. Previous normalisation methods assumed that PMHS subjects, and the impactresponses,arenormallydistributedandthatasetofsubjectresponsedatacouldbeusedtocalculateameanresponse to represent a standardhuman (50thpercentilemale). Reference [2]was the first to suggest thisresponse data approachwith the effectivemass approximation and Reference [4] also used it for effectivestiffness. Thisstudydoesnotuse themeanof the responsedata tonormalise the responsedatabut ratheruses the statistical approach of multivariate regression based on the independent variables of subjectanthropometrytoestimatetheresponseofthe50thpercentilemale.Inasensetheapproachusedinthisstudyharkens back to the mass based approach [1] where the response data was normalised based only onanthropometrymeasures.ThisstudythendevelopedsubjectresponsevaluesbasedonatwoDOFviscoelasticmodel and basicmechanical principles, conservation of energy andmomentum, to develop normalisationfactors that reduce the effectofhuman variationon response. Theuseof an elasticmechanicalmodel tonormalise response data has been used by all researchers since themass basedmethod and the use of aviscoelasticmodelisalogicalstepformodellingastructurewithaviscousresponse,i.e.,thehumanbody.Theassumptionofnormalityisstillusedandthenormalisedresponsesareaveragedandthestandarddeviationsintime, or standard deviation ellipses in force vs deflection space, provide a target againstwhich a dummyresponsecanbebothqualitativelyandquantitativelycomparedwhentested inthesameway. Normalisation

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  • provides the appropriate biofidelity response specification for the design and assessment of standard sizeddummiessuchthatthedummyaccuratelymodelsthehumanresponse.

    Thisstudyimprovesseveralaspectsofthedeflectionenergymethodpresentedin[6].Itwasrecognisedthattheslopeoftheenergyversusdeflectioncurve isastraight lineand isequaltoaconstantforce inatwoDOFviscoelastic model. This observation makes the calculation of all necessary values for normalisationstraightforwardandmakes theuseofaviscoelasticmodeleasilyapplied tonormalisationofPMHS responsedata. The use of themultivariate analysis approach for estimating the deflection energy and the slope of thedeflectionenergyversusdeflectioncurveforstandardsizedhumansprovidedanindependentlydeterminedsetofstandardhumanpropertiestobeusedinthescalefactors.Unfortunatelythedatasetof19subjectswasnotlargeenoughor sufficientlywelldistributedenough in termsofanthropometric characteristics toeffectivelymodel the human population. In particular there were only a few smaller subjects and only two femalesubjects.Alsoaproblemwasthepreponderanceofolderagedsubjects.Theresultwasaregressionequationthatdidnotmodelthe5thpercentilefemalesizeverywell. TableVII liststheestimateddeflectionenergyforthe5thpercentile femaleandthe50thand95thpercentilemalesatthreeagesof45,65,and85yearsofage.Clearly the 5th percentile female values are not useful. Fig. 8 shows the same data graphically. However,regressionestimatesforallofthevarioussizedsubjects inthisstudyarereasonableasseen inTable IV. Theaveragedifferencesbetweenthe integrateddataandtheestimatedvaluesforenergyandslopewere 0.38%and 0.29% respectively. Themaximumdifference for slopewas4.61%but forenergy itwas 20.04%. Thislattercasewasasmallersubject,subject0506. Theregressionequationmatchesthemodeledsubjectvaluesfairlywell. There is no indication of outlier subjects in the results. Nonetheless the estimate for the 5thpercentile female is poor. Only the 50th percentile male estimated values were utilized in this study todemonstratethemethod.

    TableVII.EstimatedDeflectionEnergyforSeveralSizes

    andAgesofPMHSat3.5m/sec.Size/Age 45years 65years 85years

    5thpercentilefemale 99.9Nm 58.1Nm 216.1Nm50thpercentilemale 81.4Nm 53.2Nm 25.1Nm95thpercentilemale 62.0Nm 46.5Nm 31.0Nm

    Fig.8.EstimatedDeflectionEnergyforSeveralSizesandAgesofPMHSimpactedat3.5m/sec.

    Toimprovethemodelalargersampleofthoracicimpactsubjectswithwelldistributedanthropometriccharacteristicswouldberequired,particularlyincludingsmallersubjects.Thoseanthropometriccharacteristicswouldbethevariablesidentifiedbytheregressionmodel:age,height,mass,andBMI.Inadditiontoalinearregressionmodelitwouldbeinterestingtoexaminenonlinearpolynomialmodelstobetterfitthedataalthoughfittingmultiplevariablenonlinearpolynomialmodelscanbeanexercisefraughtwithunexpectedresults.Thisstudywasintendedtoexaminetheuseoftheconstantslopedeflectionenergyversusdeflectioncurveandthedevelopmentofenergyandslopeestimatesofstandardsizedhumansusinganapproachthatisindependentoftheresponsedatathatistobescaled,i.e.,moreindependentthanaveragesoftheanthropometrymeasures.Ofcourse,withalargeanddiversesampleonewouldexpectresultsfromtheregressionmodelandaveragingtoconverge.

    Acomparisonamongthepreviousmethodswaspresented in[5]andplotsofallresultsarenotpresentedhere; however, the coefficients of variation were calculated and presented in tabular form. The twodimensionalstandarddeviationellipsemethodologyforquantifyingandplottingvariancewasfirstpresentedin[6]. Thesetofstandarddeviationellipsesplottedateachpointoftheforceversusdeflectioncurvecreatesatargetagainstwhichadummy response curve canbebothqualitativelyandquantitativelyassessed in force

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  • versusdeflectionspaceinthesamewaythattimehistorieswereevaluatedusingtheBiofidelityRankingSystem[14]. Theuseof the timeaveragedcoefficientofvariation (CV)and theellipseaveragedCV forquantitativecomparisonswerefirstpresentedby[4]andthenusedby[6]tocompareallofthevariousmethods.ThetimeaveragedCVswere againused in this study. It is clear from theplots and from theCVmeasures that thismodifieddeflection energybasednormalisationmethod eliminates a substantial amountof variation in theresponsedatafromthissetofPMHSandtheCVsfordeflectionenergynormalisationaresmallerthanthoseofpreviousmethods.

    The effective stiffnessmethod [4] used a singleDOF elasticmodel to develop normalisation factors andfound a stiffness factorby integratingdeflection energy andmodelling that energy as elastic energywith aconstantslope.Althoughthatstudydidnotrecognisetheconstantenergyversusdeflectionslopephenomenoninthoracicimpact,ineffectitwasutilisedinthatstudyandresultedinimprovednormalisation.Therecognitionof the constant energy versus deflection slope and the addition of a viscous response further improvenormalisationasevidencedinbothplotsandtabulatedCVvalues.It can be seen in Fig. 7 and Table VI that calculating the standard deviation accurately in force versus

    deflectionspaceratherthanintimespacereducestheellipsesizesandreducestheCVforthedatasetstudiedhere. Thisconceptcanbedifficult tograsp. Consider that forceanddeflectionareparametrically linkedbytime.CrossplottingtheforceanddeflectionfromeachPMHStestprovidesanaccurateforceversusdeflectionplotforeachPMHS.However,thetimepairedsetofforceanddeflectionpointsforasubjectarenotplottedatequaldeflection increments in force versusdeflection spacebecause each subject timepaired setofpointsoccursatdifferentandunequalincrementsofdeflection.Byinterpolatingthetimepairedforceanddeflectionpointsontoacommondeflectionenergybaseanaccuratemeancurveandassociatedstandarddeviationscanbecalculateddirectlyinforceversusdeflectionspace.The essential weakness in the approach of using a relatively small sample size to characterise a large

    population isobviousbutuntila large,welldefinedsamplebecomesavailablethedependenceonsmalldatasets is unavoidable. The best knownmodel of a human is currently the PMHS and PMHS response dataprovides thebestbiofidelity target for crashdummy response. The sample sizeof19 subjects tested fairlyrecently, all at the same laboratory (the InjuryBiomechanicsResearchCenterofOhio StateUniversity) is alargersamplethanisoftenavailablebutisstilltoosmallandinsufficientlydiverseinanthropometrytodevelopa robust regressionmodel that proves reasonable accuracy for all sizes of humans. The development of amultivariate regression model based on the independent variables of subject anthropometry and impactvelocity does provide an independent and reasonably accurate estimate of the 50th percentilemale humanresponse. TheapproachhasmeritandshouldbepursuedwithabettersampleofPMHSexposedtothoracicimpact.Thismethodology clearly reduces the variance among the subject response curves asmeasured by the

    averaged coefficients of variation for this thoracic side impact test data. Future work will examine themethodologyforotherbodyregionssuchasfrontalthoracicimpact,abdominalimpact,kneethighhipimpact,andshoulderimpact.Allofthesebodyregionshavelargedeflectionsandthemethodmaybeapplicable.Bodyregionswithminimaldeflection,suchasthehead,maynotbeappropriatefordeflectionenergynormalization.It shouldalsobenoted thatanenergyversusdeflection curve thathasa secondorderpolynomial shape,

    rather thana constant slope, is stillamenable to thismethodofdevelopingnormalisation factors. The firstderivativeofa secondorderdeflectionenergyversusdeflection curvewillbea straight line,althoughnotaconstant,and the twoelementviscoelastic solidmodel isapplicable. However, theenergyversusdeflectioncurvewillrequiretwocoefficientstodefineitandthemultivariateregressionprocessandthedevelopmentofscalefactorswillbecomemorecomplicated.Itmaybebettertoregressdeflectiondirectlyinthatcaseratherthantheshapeoftheenergycurve.Finally, the kinematics of the impacted subject (acceleration, velocity, and displacement) can also be

    normalisedbyusing the scale factors for forceandeffectivemass to finda scale factor foraccelerationandintegratingtofindvelocityanddisplacement.Alternativelythescalefactorforpostimpactsubjectvelocitycanbeusedbydifferentiatingandintegratingthescaledvelocitytofindaccelerationanddisplacement.Notethatwhenintegratingordifferentiatingscaledresponsedatathescalefactorfortimemustalsobeincluded.

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  • V. CONCLUSIONSThe use of deflection energy provides an improvedmethodology for normalising PMHS thoracic impact

    responsedata. Theconstantslopeofthedeflectionenergyvsdeflectioncurve leadstotheuseofatwoDOFviscoelastic model for development of normalisation factors. The energy and slope values for the 50th

    percentilemalehumanwereestimatedusingmultivariateregression.Inthedataanalysedherethisimproveddeflectionenergymethodprovides lessvariation (tightergroupingof response curves) thando thepreviousmethodswhencomparedusingtheaveragecoefficientofvariation.

    VI. REFERENCES[1] EppingerRH,MarcusJH,MorganRM.Developmentofdummyand injury indexforNHTSA'sthoracicside

    impactprotectionresearchprogram.SAETechnicalPaper.1984.No.840885.[2] MertzHJ.Aprocedurefornormalizingimpactresponsedata.SAETechnicalPaper.1984.No.840884.[3] Viano,DC. Biomechanicalresponsesand injuries inblunt lateral impact. SAETechnicalPaper1989.No.

    892432.[4] MoorhouseKM. An improvednormalizationmethodologyfordevelopingmeanhumanresponsecurves.

    InternationalTechnicalConferenceontheEnhancedSafetyofVehicles,2013,Seoul,Korea.[5] ShawJM,HerriottRG,McFaddenJD,DonnellyBR,BolteJHIV.Obliqueandlateralimpactresponseofthe

    PMHSthorax.StappCarCrashJournal.2006. Vol. 50.[6] DonnellyBR,MoorhouseKM,RhuleHH, Stammen JA. ADeformationEnergyApproach toNormalizing

    PMHS Response Data and Developing Biofidelity Targets for Dummy Design. Proceedings of IRCOBIConference.2014.Berlin,Germany.

    [7] RhuleHH,SuntayB,HerriottR,AmensonT,StricklinJ,BolteJIV.ResponseofPMHStohighandlowspeedobliqueandlateralpneumaticramimpacts.StappCarCrashJourna.2011.Vol.55.

    [8] RhuleHH,SuntayB,HerriottR,StricklinJ,KangYS,BolteJH IV. ResponseofthePMHSThorax inLateralandObliquePneumaticRam Impacts Investigationof ImpactSpeed, ImpactLocationand ImpactFace.ProceedingsofIRCOBIConference.2014.Berlin,Germany.

    [9] NusholtzGS,HsuTP,ByersLC.AproposedsideimpactATDbiofidelityevaluationschemeusing a crosscorrelation approach. Proceedings of the 20th International Technical Conference on theEnhancedSafetyofVehicles.2007.Lyon,France.

    [10] Tschoegl, NW. The Phenomenological Theory of Linear Viscoelastic Behavior. SpringerVerlag, Berlin,Heidelberg,1989.P.14.ISBN0387191739.

    [11] Shames,IH,Cozzarelli,FA.ElasticandInelasticStressAnalysis.PrenticeHall,EnglewoodCliffs,NewJersey.1992.pp.119122.ISBN0132454653.

    [12] MATLAB6.1.TheMathWorksInc.,Natick,MA,2000.[13] Hair, JF Jr.,Anderson,RE,Tatham,RL. MultivariateDataAnalysis. MacmillanPublishingCompany,New

    York,NewYork,USA.1987.P41.ISBN0023489804.[14] RhuleHH,Donnelly BR,Moorhouse KM, Kang YS. Amethodology for generating objective targets for

    quantitatively assessing the biofidelity of crash test dummies. Proceedings of the 25th InternationalTechnicalConferenceontheEnhancedSafetyofVehicles.2013.Seoul,Korea.

    [15] Robbins,DH. AnthropometricSpecificationsforMidSizedMaleDummy,Vol.2. Finalreport. December1983.UMTRI83532,UniversityofMichiganTransportationResearchInstitute.

    VII. APPENDIXAnalysis of Mean Responses from Oblique versus Lateral Impacts and Circular versus Rectangular FaceImpacts Results from testing thehypothesis that themeansof several comparisonsof the slopesof thedeflectionenergyversusdeflection curvesare from the samepopulationare shown inTableAI. Thecomparisonpairswerea rectangular face impacting laterallyandobliquelyat4.5m/sec;acircular face impacting laterallyandobliquely at 2.5m/sec; lateral impactswith circular and rectangular faces scaled to 3.5m/sec; and obliqueimpactswithcircularand rectangular facesscaled to3.5m/sec. Thenullhypothesis ineachcase is that thedifference in the slope values is zero. The pvalues in each case are quite large,well above the generallyaccepted value of 0.05, indicating it is not possible to reject the null hypothesis. Itwas assumed, for thepurposesofdemonstrating thisnormalizationmethod that the subject responsedata comes from the samepopulation.

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  • TableAIComparisonoftheslopesfromobliqueversuslateralimpactsandcircularversusrectangularfaceimpacts.

    testtype reclat4.5 recobl4.5 cirlat2.5 cirobl2.5 reclat3.5 cirlat3.5 recobl3.5 cirobl3.52.64 2.19 1.27 1.16 1.94 1.72 1.67 1.551.97 1.94 1.04 1.24 1.49 1.48 1.52 1.711.74 2.18 1.38 1.00 1.30 1.88 1.64 1.432.76 1.57 1.67 2.192.48 2.03 2.33

    1.95 2.26mean 2.32 2.10 1.23 1.13 1.71 1.69 1.85 1.72

    stddev 0.44 0.14 0.17 0.12 0.30 0.20 0.35 0.34degreesfreedom v=3.8 v=3.6 v=6 v=6.7

    tvalue t=.94 t=0.83 t=0.12 t=.59pvalue p>.4 p >.45 p >.90 p >.55

    SubjectResponseValuesandNormalisationFactorsforallSubjectsThevaluesforthe50thpercentilemaleasdeterminedusingthemultivariatepredictionsareshowninthefirst

    rowofTableAII.Thefollowingrowscontaintherelevantvaluesforeachsubjectandtheassociatedscalefactorwhich isaratioofthe50thvalueoverthesubjectvalue,exceptforthetimescalefactorwhich isthe invertedfrequencyvalues.

    TableAII.Scalevaluesandnormalisationfactorsforallsubjectsat3.5m/simpactvelocity.

    SubjectEnergy(Nm)

    Slope(Nm/mm)

    Force(N)

    Deflection(mm)

    Stiffness(N/m)

    Viscousconstant(Nsec/m)

    Time(sec)

    EffectiveMass(kg)

    Subjectvelocity(m/s)

    50th E=81.54 b=1.88 F=1880 S=43.37 K=43346 C=537 =8.50 m=30.88 Vs=1.51

    0503 E=58.33E=1.40b=1.56b=1.20

    F=2620F=1.20

    S=37.33s=1.16

    K=41890k=1.03

    C=596c=0.90

    =10.05t=1.10

    m=16.06m=1.92

    Vs=2.08vs=0.73

    0504 E=81.74E=1.00b=1.72b=1.09

    F=6020F=1.09

    S=47.52s=0.91

    K=36206k=1.20

    C=666c=0.81

    =10.85t=0.86

    m=31.06m=0.99

    Vs=1.50vs=1.00

    0505 E=60.72E=1.34b=1.48b=1.27

    F=6390F=1.27

    S=41.09s=1.06

    K=35969k=1.21

    C=600c=0.89

    =10.79t=0.98

    m=17.20m=1.80

    Vs=2.02vs=0.75

    0506 E=67.30E=1.21b=1.67b=1.13

    F=0290F=1.13

    S=40.41s=1.07

    K=41220k=1.05

    C=655c=0.82

    =11.32t=1.00

    m=20.71m=1.49

    Vs=1.86vs=0.81

    0507 E=88.30E=0.92b=1.41b=1.34

    F=9680F=1.34

    S=62.77s=0.69

    K=22416k=1.93

    C=574c=0.94

    =11.06t=0.64

    m=37.55m=0.82

    Vs=1.34vs=1.12

    0601 E=81.17E=1.00b=1.91b=0.98

    F=6730F=0.98

    S=42.44s=1.02

    K=45066k=0.96

    C=744c=0.72

    =9.81t=0.96

    m=30.56m=1.01

    Vs=1.52vs=0.99

    0802 E=77.91E=1.05b=1.91b=0.98

    F=15630F=0.98

    S=40.70s=1.07

    K=47030k=0.92

    C=401c=1.34

    =9.30t=1.10

    m=27.87m=1.11

    Vs=1.60vs=0.94

    0803 E=76.45E=1.07b=1.65b=1.14

    F=7200F=1.14

    S=46.40s=0.93

    K=35516k=1.22

    C=359c=1.49

    =7.27t=0.96

    m=26.75m=1.15

    Vs=1.63vs=0.92

    0804 E=70.77E=1.15b=1.49b=1.26

    F=4780F=1.26

    S =47.51s=0.91

    K=31350k=1.38

    C=333c=1.61

    =8.29t=0.94

    m=22.83m=1.35

    Vs=1.77vs=0.85

    0902 E=67.55E=1.21b=1.50b=1.26

    F=6660F=1.26

    S=45.15s=0.96

    K=33145k=1.31

    C=323c=1.66

    =8.51t=0.99

    m=20.86m=1.48

    Vs=1.85vs=0.82

    0903 E=47.72E=1.71b=1.26b=1.49

    F=4070F=1.49

    S=37.81s=1.15

    K=33379k=1.30

    C=269c=1.99

    =5.42t=1.18

    m=11.68m=2.64

    Vs=2.33vs=0.65

    0904 E=56.75E=1.44b=1.60b=1.17

    F=9120F=1.17

    S=35.43s=1.22

    K=45215k=0.96

    C=284c=1.89

    =8.13t=1.28

    m=15.34m=2.01

    Vs=2.11vs=0.71

    0905 E=58.29E=1.40b=1.64b=1.15

    F=9140F=1.15

    S=35.56s=1.22

    K=46114k=0.94

    C=298c=1.80

    =9.35t=1.27

    m=16.04m=1.93

    Vs=2.08vs=0.73

    1001 E=68.17E=1.20b=2.03b=0.93

    F=6480F=0.93

    S=33.59s=1.29

    K=60413k=0.72

    C=426c=1.26

    =8.17t=1.33

    m=21.22m=1.46

    Vs=1.84vs=0.82

    1002 E=67.32E=1.21b=1.97b=0.96

    F=4900F=0.96

    S=34.21s=1.27

    K=57528k=0.75

    C=443c=1.21

    =7.97t=1.30

    m=20.72m=1.49

    Vs=1.86vs=0.81

    1003 E=64.65E=1.26b=1.67b=1.12

    F=4960F=1.12

    S=38.65s=1.12

    K=43311k=1.00

    C=366c=1.46

    =8.41t=1.16

    m=19.23m=1.61

    Vs=1.92vs=0.79

    1201 E=73.64E=1.11b=2.44b=0.77

    F=4420F=0.77

    S=30.16s=1.44

    K=80980k=0.54

    C=928c=0.58

    =11.53t=1.36

    m=24.73m=1.25

    Vs=1.70vs=0.89

    1202 E=91.96E=0.89b=2.22b=0.85

    F=2150F=0.85

    S=41.52s=1.04

    K=53352k=0.81

    C=861c=0.62

    =8.32t=0.98

    m=41.89m=0.74

    Vs=1.25vs=1.20

    1203 E=87.42E=0.93b=2.34b=0.80

    F=3410F=0.80

    S=37.34s=1.16

    K=62709k=0.69

    C=914c=0.59

    =9.24t=1.09

    m=36.59m=0.84

    Vs=1.37vs=1.11

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