PowerRequiredtoBreakBoardsFujiMaePolarBoardsvstheEquivalentWoodorFingerBoards
AthesispresentedtoiTKDbyRichardBurrinpreparationforgradingtoIVDan
SummaryExperimentaldatahasdeterminedthatsimpleadditionoftheenergyrequiredtobreakasingleboardisapoorpredictoroftheactualenergyrequiredformultipleboardbreaks.Amodelforpredictingtheenergyrequiredformultipleboardbreaksispresentedthatisaccuratetowithin10%.
Anincrementalrankingofboardsfromsingles,tomultiplesandmixedcolouredboardsispresented.Thisshouldbeofvalueforbothgradingsandcompetitiontoeitherincrementallyincrease(ordecrease)therequirements,orevaluatethepowergeneratedbytechniquesperformedonvariousboardcombinations.
IntroductionPowerbreakinginTaekwonDocompetitionandgradinghastraditionallyusedpineboardsasthematerialofchoicetodestroy.Theincreasingcost,availabilityandvariabilityofpineboardsofsuitablewidth(280-300mm)andqualityhasseenplasticre-breakableboardscommonlyusedasanalternative.
Whenevaluatingthepowerdevelopedforatechniquethewidevariabilityofpineboardsmakesvalidcomparisonbetweentechniquesandcompetitorsdifficult.ThecondensedencyclopediaofTaekwon-Dodescribesboardsfordestructionsas30cm(12inches)square,1.27cm(oneinch)thickpineboards.IntheNewZealandconstructionindustrypineboardsarecommonlyroughsawntonominally300mm(1113/16“)wideand25mm(63/64”)thick.Werarelyseegreen(undried)roughsawnboardsused.Morecommonlykilndried,‘clear’or‘dressinggrade’dressedtimberisused.Thistimberisforcedriedtoapproximately5-8%moisturecontentandmilledtoasmoothfinishof280mm(111/32”)wideand18mm(45/64”)thick.Thevariabilityofpowerrequiredtobreaktheseboardsismuchreducedcomparedtoungraded,green,roughsawntimber.Butevenstillthevariablesofgraindirection,density,defects,age,moisturecontentandspeciesmeansthatthereisstilllargevariationsfromboardtoboard.
Plasticre-breakableboardsthatsimulatetraditionalpineboardsaremanufacturedtotolerancesofdimensionsandmaterialsthatgreatlyreducethisvariabilitymakingthemwellsuitedformakingvalidcomparisonsbetweenbreaks.Mostcommonlyavailableboardsnowareofthe‘polar’(keyed)or‘finger’(interlockingfingers)type.Thepolarstyleofboardshavebeenfavouredforcompetitionandtrainingduetotheircloserresemblancetopineboardsinthemechanismofbreaking(explainedfurtherbelow).Ofthepolartype,FujiMaebrandisreadilyavailableinNewZealandandglobally.
Thereisalittleharddataonthedynamicforcerequiredtobreakinividualandcombinationsofthistypeofboards.Staticdata(forceconstantlyappliedtothesurfaceoftheboard)todeterminethepointof
© ITFNZ Inc 2016
destructionisoflimiteduseasitdoesnotrepresentthedynamicsofbreakingwithatool(hand,foot,elbow,knee,wrist)inafluidmotion.
Thisarticleaddressessomeofthecommonquestionsregardingtheapproximateenergyrequiredtobreakpolarboards(singlesandmultiples,ofdifferentcolours)andtheequivalentstopolarboardsintimberandfingerboards.Thedataobtainedfromtheseexperimantsformsthebasisforrecommendationsforpowercompetitionsandgrading.
TheDynamicsofBreakingAsimplemethodformeasuringtherelative‘strengths’ofboardsistoslowlyapplyanincreasingforce,orpressuretotheboarduntilitfails,orbreaks.Thismethodmaybeappropriateforthesamekind(polar,timber,finger)ofboard,butpoorlyrepresentstherealdynamicsofstrikingaboard.
Withallmaterials(whetheritiswood,concrete,glass,plastic)thereisadegreeofelasticityorflexthatthematerialwillwithstand,returningtoit’sstartingstateafterimpact(nobreak!).Ifsufficientenergyisappliedtoexceedthecriticaldeflectionthematerialwillbreak.
Inmorescientificterms–whenstrikingaboard,aforceisappliedtotheboardoveraveryshorttimeinterval.Theboardabsorbsthatenergy,storingitforashortperiod.Themaximumenergythattheboardcanstorebeforebeginningtofail,orbreakisdefinedas
Umax=V*σb/2E
WhereUmaxisthemaximumstoredenergy
Vistheboardvolume
σbisthebreakingstress
AndEisYoungsModulus–thespecificmeasureofamaterials’sstiffnessofaneleasticmateriali
IftheenergyimpartedtotheboardexceedsUmaxthentheboardwilldeflectpastit’scriticalpointandbreak.Iftheenergyislessthanthis,theboardwillstorethisenergymomentarily,returningitbacktothestrikingtool.Thisisthepainorshockofafailedbreak.
Thedynamicdescriptionofthebreakintermsofphysicsbecomesmorecomplexthen.Inrealtermsastrikingtoolisappliedtothesurfaceoftheboardwithaninstantaneousvelocityandmass.Theboardabsorbsthisenergyoveraperiodoftimeasthestrikingtoolattemptstodeflecttheboardpastit’scriticalpoint.Duringthistimetheattackingtoolisrapidlydeceleratedtoclosetozerovelocityifthebreakwas‘justachieved’.Theenergybeingappliedtotheboardoverthetimeittakestodeflectittothepointofdestructionismorecorrectlytermedimpulseorchangeinlinearmomentum.
J=Faverage(t2-t1)
WhereJistheimplseofforce
Faverageistheaverageforceapplied
Andt2-t1definesthetimeinterval.
Thetermimpulseisoftenusedtodescribeafastactingforceorimpact.Thistypeofimpulseisfrequentlyidealisedsothatthechangeinmomentumproducedbytheforcehappensinstantaneously.Thisisnotphysicallypossible,butservesasausefulmodelforcomputingtheeffectsofanidealcollision.
Theimpulsemayalsobethoughtofasachangeinmomentumofanobjecttowhichaforcehasbeenapplied.Ifthemassremainsconstant(inthecontextofthisexperimentitdoes),thenimpulsemayalsobeexpressedas
J=mv2-mv1
Wheremisthemassofthestrikingobject
v2isthefinalvelocityoftheobjectattheendofthetimeinterval
andv1istheinitialvelocityoftheobjectwhenthetimeintervalbegins.
GeneralisationsandassumptionsInthefollowingexperimentsanumberofassumptionshavebeenmade.Forthepurposesofcomparingtherelativeenergyrequiredtobreakdifferentboardsofdifferentmaterialsitisacknowledgedthatthefiguresobtainedwillbesomewhatinaccurateduetoerrorsofmeasurement,andsimplifyingtheanalysisofthedataobtained.
Withinthelimitsoftheequipmentandmaterialsreadilyavailable,aconcertedeffortwasmadetominimiseerrorswithattentiontoapplyingthesameconditionsandmeasurementstoeachexperiment,andrepeatingtoensurethedatawasconsistent.
Forthefollowingexperimentsitisassumedthat:
• Frictionallossesareneglible• Theenergyappliedtotheboardsisjustsufficienttobreakthem• Thevelocityoftheattackingtooliszeroatthemomentoftheboardsbreaking• Thetimeintervalbetweenimpactanddestructionisnegligible
Giventheassumptionsmade,thefiguresobtainedarenotintendedasbeingadefinitivequantity.Forthepurposesofthisreporttheyareonlyintendedtobeusedforcomparisonbetweenthedifferentboardsandcombinationsexamined.
Experimentaldesign
AttackingToolTosimulateascloselyaspossiblea‘real’break,ananatomicalfistmadeofleadwascastasanapproximationofarealfist.Theauthor’sclenchedfistwasfirstsetinclothreinforcedplasterofparis.Afterdryingthecastwascutoffintwopieces,thenre-assembledandgluedtogetherwithfurtherplasterofparis.Afterfurtherdryingaquantityofmoltenleadwaspouredintothecastfromtheopenwrist.Aftercoolingthecastwasonceagainremoved.Thesuspensionpointwasfoundwhichallowedthefisttocontactasurfacewiththefronttwoknucklesonly.Atthispointastronghookwasthreadedintothefist.Seefigure1.
Theleadfistandhookhadamassof5.1kg,similartothemassofahumanarmandhand.
Figure1-Leadfisttoolandcomparisontothemodelledfist
BoardHolderAsimpleboardholderwasconstructedofmelamineMDF,withguidestoallowconsistentplacementofboards.Theholderitselfwasdynaboltedtoaconcretefloortoensureconsistentplacement.Thedesignoftheholderallowedsupportatthetwoedgesof10mmeachside–similartomostmechanicalboardholdersinuse.
Theedgesupportswereprogressivelybuiltuptodeterminetheamountofdeflectionrequiredtoachieveacompletebreak,bothwithsingleboardsandmultiples.
Thefistwassuspendedfroma3mmstainlesswire,runningtoalowfrictionstainless/brassRonstanpulleyfixedtoapointapproximately2metersfromtheground,andterminatinginasmallclipusedasahandle.Ashortziptiewasfixedsecurelytothefistasapointtomeasurefrom.SeeFigure2,3,4.
Figure2BoardholderandguidesFigure3Ronstanlowfrictionpulley
Figure4Successfulboardbreak
ExperimentalDesign
MaterialsKilndried‘clear’graded,dressedPine(Pinusradiata)boards,280mmsquarex18mmthick
“TheUltimateMartialArtsBoard”and“NovelIndustries”brandsofgreenandblackfingerboards.Theseboardswereinawellusedstate.
FujiMaepolartypeboards–white,redandblack.Theseboardsvariedfromaveragelyusedtoverynew.Notewasmadeoftheconditionofeachboardbeforetheattemptedbreak.
DesignForeachattemptedbreakthetoolwasraisedtoameasuredpointabovetheboard.Itwasthenreleasedtofallundergravitytoimpactontheboard.Theheightfromwhichtheboardwasjustbrokenwasdeterminedbyaseriesofattempts,graduallyincreasingtheheightuntiltheimpactcompletelybroketheboard(s).Oftenwithmultipleboards,infindingthispointoneormoreboardswereincompletelybrokenwitheithersomeboardsnotbeingbrokenatall,orsomeboards‘bent’(aspertheITFcompetitionrulesdescription).Theseattemptswerenotrecordedasasuccessfulbreak.Theheightatwhichtheboard(s)justbrokewasrepeatedaminimumof3timestoensureconsistency.
Fromthecorrectedheights(allowingfortheheightofthemeasuringpointabovetheboardface),thetimetakentofall
t=√(2d/g)
wheret=timeinseconds
disthedistancefromtheboardface
gisthegravitationalconstant9.8m/s2
andthevelocity(v)ofthetoolatimpact
v=gtorv=√2gd
weredetermined.Evenatrelativelylowimpactvelocitiesthetimetakentodisplacetheboard(s)fromimpacttocriticalpointwasminimal.Thusasimplifiedmeasureofkineticenergyatimpact
Ek=1/2mv2
WhereEkisthekineticenergy
misthemassofthetool
andvisthevelocityofthetoolatimpact
wasusedforcomparisonstodeterminetherelativeamountofenergyrequiredtoachievedestruction.
Results
DeflectionrequiredtobreakTheheightoftheedgesupportsoftheboardholderwereincrementallyincreasedtodeterminetheamountofdelectionrequiredtoeffectacompletebreak.
Board Deflectionrequiredtobreak(mm)
18mmpine 10WhitePolar 13RedPolar 13BlackPolar 13GreenFinger 45BlackFinger 50MultiplePolar 45Table1Deflectionrequiredfordestruction
ConclusionsPineandpolarboards,singly,requireasimilaramountofdeflectiontoeffectabreak.Inpracticaltermsasinglepineorpolarboardmaybebrokenwithaminimalamountofpenetrationthroughthetarget.Withmultipleboardsitwasexpectedthattheamountofdeflectionappliedtothefirstboardwouldbetransferredtosubsequentboards–i.e.adeflectionof13mmofthefirstboard(andasuccessfulbreak)wouldalsodeflectthesecondandsubsequentboardsbythesameamount,breakingthemaswell.Theamountofdeflectiontoeffectacompletebreakonmultipleboardswasapproximately3timesgreaterthanexpected.Thereasonforthisisunclear.Itissuspectedthatthenatureoftransferringtheimpactfromoneboardtoanotherisnotasstraightforwardsasinitaillythought.
Fingerboards,singly,requiredvastlymorepenetrationtoeffectabreak.Itcanbeclearlyobservedthattheprocessofthefingersseparatingoccursgraduallyasdisplacementincreases,asopposedtowoodandpolarboards.
LocationofImpactIthasbeenlongknownthatfingertypeboardscanbeinducedto‘unzip’,separatingfromoneedgetotheotherprogressivelybyapplyinganalongthejointline,butclosetooneedge.Itissuspectedthatthepropogationofacriticalfractureinmostmaterialsmaytakelessenergytoinitiateifstartedclosertooneedgecomparedtostrikinginthediagonalcenteroftheboard.Iftheimpactisappliedtothediagonalcenter,atensionfracturelinewillbeinitiatedfromapointontheoppositefaceoftheboard,andspreadfromtheimpactpointineitherdirectiontotheedges.Thisisincontrasttostartingfromonedgeonlyandprogressingtotheoppositeedge.Thisphenomenoncanbeobservedwithslowmotionphotographyhttp://www.youtube.com/watch?v=ONotvKTqpEU
Theeffectofimpactlocationonasinglepolarboardwasinvestigatedbyvaryingthelocationoftheboardholderandmeasuringthedisplacementfromthediagonalcenteroftheboard.Displacementsweremadeinbothvertical(movingawayfromthejointline)andhorizontal(alongthejointline)directions.
Figure5Effectofvaryingimpactlocation
ConclusionVaryingtheimpactlocationverticallyfromthejointlinehadanegativeeffect.At80mmawayfromthejointlinetheenergyrequiredtobreakwasapproaching1.6timesthatrequiredwhenstrikingatthecenter.Conversely,strikingtheboardclosertotheedgehorizontally(alongthejointline),theenergyrequiredtobreakdiminishedbyapproximately20%atabout1/3oftheboardwidth.
Thisdemonstratestheimportanceofstrikingontheline.Abetterchanceofasuccessfulbreakwillbeachievedifstrikingtheboardatapproximately1/3ofthewidthoftheboard,ratherthaninthemiddle.
ComparisonofBoardTypesandCombinationsThreedifferentcoloursofpolarboards,18mm(senior)and15mm(junior)pineboardsandtwodifferentcolouredfingerboardswereinitiallyexaminedtodeterminerelativebreakingenergyrequired.Thenmultiplesandcombinationofpolarboardcolourswereexamined.
Resultsobtainedforgreen(3.25kJ)andblack(2.70kJ)fingerboardswereconsiderablylessthanasingle18mmpineboard(4.25kJ),contrastingwiththeiradvertisedrelativestrengths–green=1board,black=2.25boards.Thisisprobablyareflectionoftheirextremelywellusedstate,withsomefingersbroken.Asaresultofthistheresultsofthefingerboardswasnotconsideredtobeanaccuratereflectionofwhatcouldbeexpectedfromboardsingoodcondition.
Fivewhite,fourredandfiveblackpolarboardsweretested,rangingfromrelativelynew,tomoderatelyused.TheresultsfromtheseandwoodenboardsarepresentedinFigure6.
5
7
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15
17
19
21
23
0 20 40 60 80 100 120 140
Energyto
Break1W
hitePolar(J)
DisplacmentfromCenter(mm)
EffectofImpactLocationVertical
Horizontal
Figure6Energyrequiredtobreaktestedboards
Takingintoaccountthevariabilitywithineachboardcolour(reflectingit’sstateofuse),theresultscouldbegenerallystatedas:
• 1whitepolarboardrequiresapproximatelytwicetheenrergytobreakcomparedtoan18mmdressedpineboard.
• 1redpolarboardisrequiresaproximately4timestheenergyofawoodenboard• 1blackpolarboardrequiresapproximately6timestheenergyofawoodenboard
Whatisnotvalidistogeneralisethat1blackpolarboardisequivalenttobreaking6woodenboards.
Ithasbeenfeltbymanyexperiencedpowerbreakersthatmultipleboardsareconsiderablyhardertobreakthanwhathasbeenconsideredtheequivalentinadifferentcolour.Forexample,FujiMaedescribesthe3typesofboardsaswhite(easy)=1woodenboard,red(medium)=2woodenboardsandblack(hard)=3woodenboards.Fromthisyouwouldbeforgivenforassumingthatbreaking1blackboardwouldbelikebreaking3whiteones.
Multiplesofeachboardcolourweretestedtochallengethisnotion.
0510152025303540
Pine White Red Black
Energyto
Break(kJ)
BoardType
RelativeStrengthsofSingleBoards
Av.4.80
Av.12.09
Av.20.49
Av.31.99
Figure7Relativestrengthsofmultipleboards
Theobserveddatashowssomeinterestingcomparisons
• Asenior(18mm)pineboardtakesabouttwicetheenergytobreakthanajunior(15mm)board,eventhoughitisonly3mmor20%thicker
• Asingleredpolarboardrequiredabouttwicetheenergyasawhitepolarboard• Asingleblackpolarboardrequiredaboutthreetimestheenergyasasinglewhitepolarboard• Approximatelythesameenergyisrequiredtobreak2whitepolarboardsasasingleblackpolar
board• Approximatelythesameenergyisrequiredtobreak5xseniorwoodenboardsas2xredpolar
boards• Twoblackandthreeredpolarboardsweresimilarinenergyrequiredtobreak
Whatisevidentisthattheenergyrequiredtobreakmultipleboardsismorethanthesumoftheenergyrequiredtobreakasingleboard.
0
10
20
30
40
50
60
70
80
90En
ergyto
break
Typeandnumberofboards
RankedBoardsApproximate
EnergyrequiredtoBreak1xJrPine
1xSrP
ine
1xWpolar 1x
Rpo
lar
2xW
polar
1xBpolar 5x
SrP
ine
2xRpolar
3xW
polar
2xBpolar
3xRpolar
Analgorithmwasdevelopedtopredicttherequiredenergytobreakmultipleboards.
Themodelbestfittingtheobserveddatais:
Predictedkineticenergyrequiredtobreakmultipleboards=sumofindividualboardsxamultiplierfactorraisedtothepowerofthenumberofjunctionsbetweenboards
Ek=∑individualboards*Xj
WhereEkisthekineticenergyrequiredfordestruction
∑individualboardsisthesumoftheenergyofeachboardalone
Xisamultiplierfactor
Jisthenumberofinterfacesbetweenthenumberofboards–i.e.astackof3boardshas2interfaces,astackof5boardshas4interfaces.
Varyingthemultiplierfactor,thepredictedandobservedresultswerecompared.Themultiplierachievingtheminimalerrorbetweenpredictedandobservedresultsacrossallboardcombinationswasdeterminedtobe1.20
Multiplier %variationfromobserveddata
1.25 0.27–21.76%1.20 3.15-8.25%1.22 1.64-13.20%Table2Accuracyofmultipliers
ConclusionTheenergyrequiredtobreakanumberofpolarboards,andpossiblywoodenboardstoo,canbepredictedusingtheequationbelowwithanaccuracyofaproximately10%
Ek=∑individualboards*1.20(numberofboardinterfaces)
Assumingtheabovepredictivemodelholdsforcombinationsofdifferentcolouredpolarboards,theenergiestobreakthefollowingcombinationsofboardsweredeterminedbasedontheaboveaveragevaluesforindividualboards(Figure6above).Withcombinationsofjust2boardsofeachcolour,arangeofbreakingenergiescanbespecifiedfrom12kJto180kJ–a15foldrange.
CombinationSumindividual
Boardjunctions
Boardmultiplier Predicted
1W 12.09
12.091R 20.49
20.49
2W 24.18 1 1.2 29.0161B 31.99
31.99
1W+1R 32.58 1 1.2 39.0962R 40.98 1 1.2 49.1763W 36.27 2 1.2 52.22881W+1B 44.08 1 1.2 52.8961R+1B 52.48 1 1.2 62.9762W+1R 44.67 2 1.2 64.32481W+2R 53.07 2 1.2 76.42082B 63.98 1 1.2 76.7762W+1B 56.17 2 1.2 80.88484W 48.36 3 1.2 83.566083R 61.47 2 1.2 88.51681W+1R+1B 64.57 2 1.2 92.98082R+1B 72.97 2 1.2 105.07681W+2B 76.07 2 1.2 109.54082W+2R 65.16 3 1.2 112.59651R+2B 84.47 2 1.2 121.63683B 95.97 2 1.2 138.19682W+2B 88.16 3 1.2 152.34052R+2B 104.96 3 1.2 181.3709
Table3Predictedvaluesforboardcombinations
Figure8Predictedenergyforboardcombinations
0
20
40
60
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120
140
160
180
200
Pred
icteden
ergyre
quire
dtobreak(K
J)
BoardCombination
Predictedenergyrequiredtobreakboardcombinations
RecommendationsIncompetitionandingradingstherequirementsfordestructionsarefrequentlybasedonguessworkandassumptionthatsimpleadditiveenergytobreaksingleboardscanbeutilisedtopredictenergyrequiredtobreakmultipleboards.Afarmoreacuratemethodforpredictingtheenergyformultiplebreaksisoutlinedabove.
Incompetitionitisimportantthatcompetitorstrainappropriatelyfortherequirementsoftheevent.Thereislittlepointtrainingtobreak1blackpolarboardforaneventrequiring3whitepolarboards.Asseenabovetheenergyrequiredisapproximatelydoublethatofasingleblackpolarboard!
Forofficialsrunningtheevent–itisusefultohaveanaccuratemeasureofincrementallyincreasingtherequirementforbreakinginthecaseofatie,orbreakoffbeingrequired.Withvariouscolouredboardsavailabletherangemaybestepedupappropriately,ratherthanlargestepswhichmayprolongtheeventtryingtodetermineawinner,orunneccisarilyexposethecompetitorstoinjuryiftheyhavenotconditionedthemselvessufficientlyforatargetrequiringvastlymoreenergytobreak.
Alistofrankedboardcombinationswouldbeusefulinpreparingstandardsforbothgradingandcompetition.
References:JohnRennie,September2,2010.BustedExplanationsforKarateBreakinghttp://blogs.plos.org/retort/2010/09/02/busted-explanations-for-karate-breaking/
Feld,M.S.et.al.“ThePhysicsofKarate,”ScientificAmerican,pp.150-158,April1979
JasekWasilk“Powerbreakingintaekwon-do–physicalanaylsis”,ArchivesofBudo,2007;Vol3:68-71
Brainiac:BrickBreak,YouTube
www.youtube.com/watch?v=ONotvKTqpEU
MasterBillPottle,”PineBoardBreakingintheMartialArts”
www.kattaekwondo.com(personalcommunication)
iApproximateYoungsModulus(Gpa)pine–9,polypropylene1.5-2.0,highstrengthconcrete30,glass50-90
