© ITFNZ Inc 2016
PowerRequiredtoBreakBoards
FujiMaePolarBoardsvstheEquivalentWoodorFingerBoards
AthesispresentedtoiTKDbyRichardBurrinpreparationforgradingtoIVDan
Summary
Experimentaldatahasdeterminedthatsimpleadditionoftheenergyrequiredtobreakasingleboardis
apoorpredictoroftheactualenergyrequiredformultipleboardbreaks.Amodelforpredictingthe
energyrequiredformultipleboardbreaksispresentedthatisaccuratetowithin10%.
Anincrementalrankingofboardsfromsingles,tomultiplesandmixedcolouredboardsispresented.
Thisshouldbeofvalueforbothgradingsandcompetitiontoeitherincrementallyincrease(ordecrease)
therequirements,orevaluatethepowergeneratedbytechniquesperformedonvariousboard
combinations.
Introduction
PowerbreakinginTaekwonDocompetitionandgradinghastraditionallyusedpineboardsasthe
materialofchoicetodestroy.Theincreasingcost,availabilityandvariabilityofpineboardsofsuitable
width(280-300mm)andqualityhasseenplasticre-breakableboardscommonlyusedasanalternative.
Whenevaluatingthepowerdevelopedforatechniquethewidevariabilityofpineboardsmakesvalid
comparisonbetweentechniquesandcompetitorsdifficult.ThecondensedencyclopediaofTaekwon-Do
describesboardsfordestructionsas30cm(12inches)square,1.27cm(oneinch)thickpineboards.In
theNewZealandconstructionindustrypineboardsarecommonlyroughsawntonominally300mm(11
13/16“)wideand25mm(63/64”)thick.Werarelyseegreen(undried)roughsawnboardsused.More
commonlykilndried,‘clear’or‘dressinggrade’dressedtimberisused.Thistimberisforcedriedto
approximately5-8%moisturecontentandmilledtoasmoothfinishof280mm(111/32”)wideand
18mm(45/64”)thick.Thevariabilityofpowerrequiredtobreaktheseboardsismuchreduced
comparedtoungraded,green,roughsawntimber.Butevenstillthevariablesofgraindirection,density,
defects,age,moisturecontentandspeciesmeansthatthereisstilllargevariationsfromboardtoboard.
Plasticre-breakableboardsthatsimulatetraditionalpineboardsaremanufacturedtotolerancesof
dimensionsandmaterialsthatgreatlyreducethisvariabilitymakingthemwellsuitedformakingvalid
comparisonsbetweenbreaks.Mostcommonlyavailableboardsnowareofthe‘polar’(keyed)or
‘finger’(interlockingfingers)type.Thepolarstyleofboardshavebeenfavouredforcompetitionand
trainingduetotheircloserresemblancetopineboardsinthemechanismofbreaking(explainedfurther
below).Ofthepolartype,FujiMaebrandisreadilyavailableinNewZealandandglobally.
Thereisalittleharddataonthedynamicforcerequiredtobreakinividualandcombinationsofthistype
ofboards.Staticdata(forceconstantlyappliedtothesurfaceoftheboard)todeterminethepointof
destructionisoflimiteduseasitdoesnotrepresentthedynamicsofbreakingwithatool(hand,foot,
elbow,knee,wrist)inafluidmotion.
Thisarticleaddressessomeofthecommonquestionsregardingtheapproximateenergyrequiredto
breakpolarboards(singlesandmultiples,ofdifferentcolours)andtheequivalentstopolarboardsin
timberandfingerboards.Thedataobtainedfromtheseexperimantsformsthebasisfor
recommendationsforpowercompetitionsandgrading.
TheDynamicsofBreaking
Asimplemethodformeasuringtherelative‘strengths’ofboardsistoslowlyapplyanincreasingforce,
orpressuretotheboarduntilitfails,orbreaks.Thismethodmaybeappropriateforthesamekind
(polar,timber,finger)ofboard,butpoorlyrepresentstherealdynamicsofstrikingaboard.
Withallmaterials(whetheritiswood,concrete,glass,plastic)thereisadegreeofelasticityorflexthat
thematerialwillwithstand,returningtoit’sstartingstateafterimpact(nobreak!).Ifsufficientenergyis
appliedtoexceedthecriticaldeflectionthematerialwillbreak.
Inmorescientificterms–whenstrikingaboard,aforceisappliedtotheboardoveraveryshorttime
interval.Theboardabsorbsthatenergy,storingitforashortperiod.Themaximumenergythatthe
boardcanstorebeforebeginningtofail,orbreakisdefinedas
Umax=V*σb/2E
WhereUmaxisthemaximumstoredenergy
Vistheboardvolume
σbisthebreakingstress
AndEisYoungsModulus–thespecificmeasureofamaterials’sstiffnessofaneleasticmateriali
IftheenergyimpartedtotheboardexceedsUmaxthentheboardwilldeflectpastit’scriticalpointand
break.Iftheenergyislessthanthis,theboardwillstorethisenergymomentarily,returningitbackto
thestrikingtool.Thisisthepainorshockofafailedbreak.
Thedynamicdescriptionofthebreakintermsofphysicsbecomesmorecomplexthen.Inrealtermsa
strikingtoolisappliedtothesurfaceoftheboardwithaninstantaneousvelocityandmass.Theboard
absorbsthisenergyoveraperiodoftimeasthestrikingtoolattemptstodeflecttheboardpastit’s
criticalpoint.Duringthistimetheattackingtoolisrapidlydeceleratedtoclosetozerovelocityifthe
breakwas‘justachieved’.Theenergybeingappliedtotheboardoverthetimeittakestodeflectitto
thepointofdestructionismorecorrectlytermedimpulseorchangeinlinearmomentum.
J=Faverage(t2-t1)
WhereJistheimplseofforce
Faverageistheaverageforceapplied
Andt2-t1definesthetimeinterval.
Thetermimpulseisoftenusedtodescribeafastactingforceorimpact.Thistypeofimpulseis
frequentlyidealisedsothatthechangeinmomentumproducedbytheforcehappensinstantaneously.
Thisisnotphysicallypossible,butservesasausefulmodelforcomputingtheeffectsofanideal
collision.
Theimpulsemayalsobethoughtofasachangeinmomentumofanobjecttowhichaforcehasbeen
applied.Ifthemassremainsconstant(inthecontextofthisexperimentitdoes),thenimpulsemayalso
beexpressedas
J=mv2-mv1
Wheremisthemassofthestrikingobject
v2isthefinalvelocityoftheobjectattheendofthetimeinterval
andv1istheinitialvelocityoftheobjectwhenthetimeintervalbegins.
Generalisationsandassumptions
Inthefollowingexperimentsanumberofassumptionshavebeenmade.Forthepurposesofcomparing
therelativeenergyrequiredtobreakdifferentboardsofdifferentmaterialsitisacknowledgedthatthe
figuresobtainedwillbesomewhatinaccurateduetoerrorsofmeasurement,andsimplifyingthe
analysisofthedataobtained.
Withinthelimitsoftheequipmentandmaterialsreadilyavailable,aconcertedeffortwasmadeto
minimiseerrorswithattentiontoapplyingthesameconditionsandmeasurementstoeachexperiment,
andrepeatingtoensurethedatawasconsistent.
Forthefollowingexperimentsitisassumedthat:
•
•
•
•
Frictionallossesareneglible
Theenergyappliedtotheboardsisjustsufficienttobreakthem
Thevelocityoftheattackingtooliszeroatthemomentoftheboardsbreaking
Thetimeintervalbetweenimpactanddestructionisnegligible
Giventheassumptionsmade,thefiguresobtainedarenotintendedasbeingadefinitivequantity.For
thepurposesofthisreporttheyareonlyintendedtobeusedforcomparisonbetweenthedifferent
boardsandcombinationsexamined.
Experimentaldesign
AttackingTool
Tosimulateascloselyaspossiblea‘real’break,ananatomicalfistmadeofleadwascastasan
approximationofarealfist.Theauthor’sclenchedfistwasfirstsetinclothreinforcedplasterofparis.
Afterdryingthecastwascutoffintwopieces,thenre-assembledandgluedtogetherwithfurther
plasterofparis.Afterfurtherdryingaquantityofmoltenleadwaspouredintothecastfromtheopen
wrist.Aftercoolingthecastwasonceagainremoved.Thesuspensionpointwasfoundwhichallowed
thefisttocontactasurfacewiththefronttwoknucklesonly.Atthispointastronghookwasthreaded
intothefist.Seefigure1.
Theleadfistandhookhadamassof5.1kg,similartothemassofahumanarmandhand.
Figure1-Leadfisttoolandcomparisontothemodelledfist
BoardHolder
AsimpleboardholderwasconstructedofmelamineMDF,withguidestoallowconsistentplacementof
boards.Theholderitselfwasdynaboltedtoaconcretefloortoensureconsistentplacement.The
designoftheholderallowedsupportatthetwoedgesof10mmeachside–similartomostmechanical
boardholdersinuse.
Theedgesupportswereprogressivelybuiltuptodeterminetheamountofdeflectionrequiredto
achieveacompletebreak,bothwithsingleboardsandmultiples.
Thefistwassuspendedfroma3mmstainlesswire,runningtoalowfrictionstainless/brassRonstan
pulleyfixedtoapointapproximately2metersfromtheground,andterminatinginasmallclipusedasa
handle.Ashortziptiewasfixedsecurelytothefistasapointtomeasurefrom.SeeFigure2,3,4.
Figure2BoardholderandguidesFigure3Ronstanlowfrictionpulley
Figure4Successfulboardbreak
ExperimentalDesign
Materials
Kilndried‘clear’graded,dressedPine(Pinusradiata)boards,280mmsquarex18mmthick
“TheUltimateMartialArtsBoard”and“NovelIndustries”brandsofgreenandblackfingerboards.
Theseboardswereinawellusedstate.
FujiMaepolartypeboards–white,redandblack.Theseboardsvariedfromaveragelyusedtovery
new.Notewasmadeoftheconditionofeachboardbeforetheattemptedbreak.
Design
Foreachattemptedbreakthetoolwasraisedtoameasuredpointabovetheboard.Itwasthen
releasedtofallundergravitytoimpactontheboard.Theheightfromwhichtheboardwasjustbroken
wasdeterminedbyaseriesofattempts,graduallyincreasingtheheightuntiltheimpactcompletely
broketheboard(s).Oftenwithmultipleboards,infindingthispointoneormoreboardswere
incompletelybrokenwitheithersomeboardsnotbeingbrokenatall,orsomeboards‘bent’(asperthe
ITFcompetitionrulesdescription).Theseattemptswerenotrecordedasasuccessfulbreak.Theheight
atwhichtheboard(s)justbrokewasrepeatedaminimumof3timestoensureconsistency.
Fromthecorrectedheights(allowingfortheheightofthemeasuringpointabovetheboardface),the
timetakentofall
t=√(2d/g)
wheret=timeinseconds
disthedistancefromtheboardface
gisthegravitationalconstant9.8m/s2
andthevelocity(v)ofthetoolatimpact
v=gtorv=√2gd
weredetermined.Evenatrelativelylowimpactvelocitiesthetimetakentodisplacetheboard(s)from
impacttocriticalpointwasminimal.Thusasimplifiedmeasureofkineticenergyatimpact
Ek=1/2mv2
WhereEkisthekineticenergy
misthemassofthetool
andvisthevelocityofthetoolatimpact
wasusedforcomparisonstodeterminetherelativeamountofenergyrequiredtoachievedestruction.
Results
Deflectionrequiredtobreak
Theheightoftheedgesupportsoftheboardholderwereincrementallyincreasedtodeterminethe
amountofdelectionrequiredtoeffectacompletebreak.
Board
18mmpine
WhitePolar
RedPolar
BlackPolar
GreenFinger
BlackFinger
MultiplePolar
Deflectionrequiredto
break(mm)
10
13
13
13
45
50
45
Table1Deflectionrequiredfordestruction
Conclusions
Pineandpolarboards,singly,requireasimilaramountofdeflectiontoeffectabreak.Inpracticalterms
asinglepineorpolarboardmaybebrokenwithaminimalamountofpenetrationthroughthetarget.
Withmultipleboardsitwasexpectedthattheamountofdeflectionappliedtothefirstboardwouldbe
transferredtosubsequentboards–i.e.adeflectionof13mmofthefirstboard(andasuccessfulbreak)
wouldalsodeflectthesecondandsubsequentboardsbythesameamount,breakingthemaswell.The
amountofdeflectiontoeffectacompletebreakonmultipleboardswasapproximately3timesgreater
thanexpected.Thereasonforthisisunclear.Itissuspectedthatthenatureoftransferringtheimpact
fromoneboardtoanotherisnotasstraightforwardsasinitaillythought.
Fingerboards,singly,requiredvastlymorepenetrationtoeffectabreak.Itcanbeclearlyobservedthat
theprocessofthefingersseparatingoccursgraduallyasdisplacementincreases,asopposedtowood
andpolarboards.
LocationofImpact
Ithasbeenlongknownthatfingertypeboardscanbeinducedto‘unzip’,separatingfromoneedgeto
theotherprogressivelybyapplyinganalongthejointline,butclosetooneedge.Itissuspectedthatthe
propogationofacriticalfractureinmostmaterialsmaytakelessenergytoinitiateifstartedcloserto
oneedgecomparedtostrikinginthediagonalcenteroftheboard.Iftheimpactisappliedtothe
diagonalcenter,atensionfracturelinewillbeinitiatedfromapointontheoppositefaceoftheboard,
andspreadfromtheimpactpointineitherdirectiontotheedges.Thisisincontrasttostartingfromon
edgeonlyandprogressingtotheoppositeedge.Thisphenomenoncanbeobservedwithslowmotion
photographyhttp://www.youtube.com/watch?v=ONotvKTqpEU
Theeffectofimpactlocationonasinglepolarboardwasinvestigatedbyvaryingthelocationofthe
boardholderandmeasuringthedisplacementfromthediagonalcenteroftheboard.Displacements
weremadeinbothvertical(movingawayfromthejointline)andhorizontal(alongthejointline)
directions.
EnergytoBreak1WhitePolar(J)
23
EffectofImpactLocation
21
19
Vertical
17
Horizontal
15
13
11
9
7
5
0
20
40
60
80
100
120
140
DisplacmentfromCenter(mm)
Figure5Effectofvaryingimpactlocation
Conclusion
Varyingtheimpactlocationverticallyfromthejointlinehadanegativeeffect.At80mmawayfromthe
jointlinetheenergyrequiredtobreakwasapproaching1.6timesthatrequiredwhenstrikingatthe
center.Conversely,strikingtheboardclosertotheedgehorizontally(alongthejointline),theenergy
requiredtobreakdiminishedbyapproximately20%atabout1/3oftheboardwidth.
Thisdemonstratestheimportanceofstrikingontheline.Abetterchanceofasuccessfulbreakwillbe
achievedifstrikingtheboardatapproximately1/3ofthewidthoftheboard,ratherthaninthemiddle.
ComparisonofBoardTypesandCombinations
Threedifferentcoloursofpolarboards,18mm(senior)and15mm(junior)pineboardsandtwodifferent
colouredfingerboardswereinitiallyexaminedtodeterminerelativebreakingenergyrequired.Then
multiplesandcombinationofpolarboardcolourswereexamined.
Resultsobtainedforgreen(3.25kJ)andblack(2.70kJ)fingerboardswereconsiderablylessthanasingle
18mmpineboard(4.25kJ),contrastingwiththeiradvertisedrelativestrengths–green=1board,black=
2.25boards.Thisisprobablyareflectionoftheirextremelywellusedstate,withsomefingersbroken.
Asaresultofthistheresultsofthefingerboardswasnotconsideredtobeanaccuratereflectionof
whatcouldbeexpectedfromboardsingoodcondition.
Fivewhite,fourredandfiveblackpolarboardsweretested,rangingfromrelativelynew,tomoderately
used.TheresultsfromtheseandwoodenboardsarepresentedinFigure6.
RelativeStrengthsofSingleBoards
Av.
31.99
EnergytoBreak(kJ)
40
35
Av.20.49
30
25
20
15
Av.12.09
Av.
4.80
10
5
0
Pine
White
Red
Black
BoardType
Figure6Energyrequiredtobreaktestedboards
Takingintoaccountthevariabilitywithineachboardcolour(reflectingit’sstateofuse),theresultscould
begenerallystatedas:
•
•
•
1whitepolarboardrequiresapproximatelytwicetheenrergytobreakcomparedtoan18mm
dressedpineboard.
1redpolarboardisrequiresaproximately4timestheenergyofawoodenboard
1blackpolarboardrequiresapproximately6timestheenergyofawoodenboard
Whatisnotvalidistogeneralisethat1blackpolarboardisequivalenttobreaking6woodenboards.
Ithasbeenfeltbymanyexperiencedpowerbreakersthatmultipleboardsareconsiderablyharderto
breakthanwhathasbeenconsideredtheequivalentinadifferentcolour.Forexample,FujiMae
describesthe3typesofboardsaswhite(easy)=1woodenboard,red(medium)=2woodenboardsand
black(hard)=3woodenboards.Fromthisyouwouldbeforgivenforassumingthatbreaking1black
boardwouldbelikebreaking3whiteones.
Multiplesofeachboardcolourweretestedtochallengethisnotion.
70
Energytobreak
60
1xWpolar
10
1xJrPine
20
1xSrPine
30
1xBpolar
1x Rpolar
40
2xWpolar
50
3xRpolar
2xBpolar
Approximate
EnergyrequiredtoBreak
3xWpolar
80
2xRpolar
RankedBoards
5xSr Pine
90
0
Typeandnumberofboards
Figure7Relativestrengthsofmultipleboards
Theobserveddatashowssomeinterestingcomparisons
•
•
•
•
•
•
Asenior(18mm)pineboardtakesabouttwicetheenergytobreakthanajunior(15mm)board,
eventhoughitisonly3mmor20%thicker
Asingleredpolarboardrequiredabouttwicetheenergyasawhitepolarboard
Asingleblackpolarboardrequiredaboutthreetimestheenergyasasinglewhitepolarboard
Approximatelythesameenergyisrequiredtobreak2whitepolarboardsasasingleblackpolar
board
Approximatelythesameenergyisrequiredtobreak5xseniorwoodenboardsas2xredpolar
boards
Twoblackandthreeredpolarboardsweresimilarinenergyrequiredtobreak
Whatisevidentisthattheenergyrequiredtobreakmultipleboardsismorethanthesumofthe
energyrequiredtobreakasingleboard.
Analgorithmwasdevelopedtopredicttherequiredenergytobreakmultipleboards.
Themodelbestfittingtheobserveddatais:
Predictedkineticenergyrequiredtobreakmultipleboards=sumofindividualboardsxamultiplier
factorraisedtothepowerofthenumberofjunctionsbetweenboards
Ek=∑individualboards*Xj
WhereEkisthekineticenergyrequiredfordestruction
∑individualboardsisthesumoftheenergyofeachboardalone
Xisamultiplierfactor
Jisthenumberofinterfacesbetweenthenumberofboards–i.e.astackof3boardshas2
interfaces,astackof5boardshas4interfaces.
Varyingthemultiplierfactor,thepredictedandobservedresultswerecompared.Themultiplier
achievingtheminimalerrorbetweenpredictedandobservedresultsacrossallboardcombinationswas
determinedtobe1.20
Multiplier
1.25
1.20
1.22
%variationfrom
observeddata
0.27–21.76%
3.15-8.25%
1.64-13.20%
Table2Accuracyofmultipliers
Conclusion
Theenergyrequiredtobreakanumberofpolarboards,andpossiblywoodenboardstoo,canbe
predictedusingtheequationbelowwithanaccuracyofaproximately10%
Ek=∑individualboards*1.20(numberofboardinterfaces)
Assumingtheabovepredictivemodelholdsforcombinationsofdifferentcolouredpolarboards,the
energiestobreakthefollowingcombinationsofboardsweredeterminedbasedontheaboveaverage
valuesforindividualboards(Figure6above).Withcombinationsofjust2boardsofeachcolour,arange
ofbreakingenergiescanbespecifiedfrom12kJto180kJ–a15foldrange.
Sum
Combination individual
1W
12.09
1R
20.49
2W
24.18
1B
31.99
1W+1R
32.58
2R
40.98
3W
36.27
1W+1B
44.08
1R+1B
52.48
2W+1R
44.67
1W+2R
53.07
2B
63.98
2W+1B
56.17
4W
48.36
3R
61.47
1W+1R+1B
64.57
2R+1B
72.97
1W+2B
76.07
2W+2R
65.16
1R+2B
84.47
3B
95.97
2W+2B
88.16
2R+2B
104.96
Board
Board
junctions multiplier Predicted
12.09
20.49
1 1.2
29.016
31.99
1 1.2
39.096
1
1.2
49.176
2
1.2 52.2288
1
1.2
52.896
1
1.2
62.976
2
1.2 64.3248
2
1.2 76.4208
1
1.2
76.776
2
1.2 80.8848
3
1.2 83.56608
2
1.2 88.5168
2
1.2 92.9808
2
1.2 105.0768
2
1.2 109.5408
3
1.2 112.5965
2
1.2 121.6368
2
1.2 138.1968
3
1.2 152.3405
3
1.2 181.3709
Table3Predictedvaluesforboardcombinations
Predictedenergyrequiredtobreak(KJ)
200
180
Predictedenergyrequiredtobreakboardcombinations
160
140
120
100
80
60
40
20
0
BoardCombination
Figure8Predictedenergyforboardcombinations
Recommendations
Incompetitionandingradingstherequirementsfordestructionsarefrequentlybasedonguesswork
andassumptionthatsimpleadditiveenergytobreaksingleboardscanbeutilisedtopredictenergy
requiredtobreakmultipleboards.Afarmoreacuratemethodforpredictingtheenergyformultiple
breaksisoutlinedabove.
Incompetitionitisimportantthatcompetitorstrainappropriatelyfortherequirementsoftheevent.
Thereislittlepointtrainingtobreak1blackpolarboardforaneventrequiring3whitepolarboards.As
seenabovetheenergyrequiredisapproximatelydoublethatofasingleblackpolarboard!
Forofficialsrunningtheevent–itisusefultohaveanaccuratemeasureofincrementallyincreasingthe
requirementforbreakinginthecaseofatie,orbreakoffbeingrequired.Withvariouscolouredboards
availabletherangemaybestepedupappropriately,ratherthanlargestepswhichmayprolongthe
eventtryingtodetermineawinner,orunneccisarilyexposethecompetitorstoinjuryiftheyhavenot
conditionedthemselvessufficientlyforatargetrequiringvastlymoreenergytobreak.
Alistofrankedboardcombinationswouldbeusefulinpreparingstandardsforbothgradingand
competition.
References:
JohnRennie,September2,2010.BustedExplanationsforKarateBreaking
http://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)
i
ApproximateYoungsModulus(Gpa)pine–9,polypropylene1.5-2.0,highstrengthconcrete30,glass50-90