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2 *,1DivisionofMediaSoftware,Sungkyu lUniverstiy,SouthKorea,XicomLab.
2DivisionofMediaSoftware,Sungkyu lUniverstiy,SouthKorea,XicomLab.http://xicomlab.re.kr
*Correspondingauthor
: s d r o w y e
K Balilsitccoefifcient,Bresenham’salgortihm,Cavtiy,Forensicbalilsitcs
.t c a r t s b
A In recen tyears ,game and virtua lreality contents using next-generation weapons have y l t n a t s n o
c beenemerging .In thecontex tofstory development ,themarksofthetarge'tsbulle tare n a o s l a s i e r e h T . s t e l l u b d n a e l f i r e h t f o s c i t s i r e t c a r a h c e u q i n u e h t o t g n i d r o c c a d e v r e s b o y l t n e r e f f i d r t l a n i m i r c h c i h w n i e l p m a x
e aces are investigated by using forensic ballistics during crimina l
h t n I . n o i t a g i t s e v n
i isprocess ,i tis quitecritical to recognizethe relationship between the ballistic n I . e c r o f c i t s i l l a b e h t o t e u d y t i v a c e h t d n a t n e i c i f f e o
c thispaper ,weproposeaphysica -llybasedcavtiy
m s i l a e r e c n a h n e n a c t a h t n o i t a l u m i s . n o it c u d o r t n I y r t n a f n i f o e c n a t r o p m i e h t t u b , e g r e m e o t s e u n i t n o c s n o p a e w f o n o i t a r e n e g t x e n e h t , s r a e y t n e c e r n I e h T . s e u n i t n o c s n u g n o p a e w y v a e h d n a s e l f i r f o n o i t u l o v e e h t , s u h T . d e z i s a h p m e l l i t s s i g n i t h g i f v e e h t o t d e k n i l y l t c e r i d s i s n u g f o n o i t u l o v
e olution ofbullets ,atypica lexamplebeing the Sovie t
K A d l o s ' n o i n
U -47riflein the80sand90s .TheAK-74 ,animprovedversionoftheAK-47 ,would
9 3 * 2 6 . 7 e h t g n i y o l p m e e l i h w d e r a e p p a e v a
h mmusedi n5.45*39mm.I nr ecen tyears,t herehasbeen
e v o m
a toreplacet heG36 ,whichwashiredbyGermany'sflagshiprifle ,withHK433 .Iti sbasically 5 4 * 6 5 . 5 d e s
u mmNatobulle tbuti tcanbemixedwith300BLK ,7.62*39mm ,7.62*51mm[1] .In
R A T M ( 5 9 X e h t g n i y a p n i g e b l l i w y m r a i l e a r s I e h t , n o i t i d d
a -21) ,ashortenedversionoft heTAR- 21
. 8 1 0 2 y b e s u n i y l t n e r r u c s e l f i r 4 M d n a 6 1 M e h t g n i c a l p e r , 3 1 0 2 m o r f , 9 0 0 2 n
i Basedon5.56*45mm
9 3 * 5 4 . 5 , o t a
N mm ,300 BLK ,9mm can be mixed [2] .These rifles mus tundergo continuous
y r t n e o t r o i r p y l e t a i d e m m i s n o i t a l u m i
s and delivery ,usually to check accuracy ,penetration ,and
s i t i d n a , t n e m e c a l p e r r e t f a d e c a l p e r e b y l n o l l i w s e l f i r d e l f i r y l l a i t r a p , n o i t i d d a n I . e r i f o t e c n a t s i s e r a m o n a y n a r o f k c e h c o t e s u e r o f e b y l e t a i d e m m i e g a t s n o i t a l u m i s e h t h g u o r h t o g o t e l b a s i v d
a lies .
t o n s i s t e l l u b f o n o i t p m u s n o c e h t ,t c e p s a l a c i m o n o c e e h t g n i r e d i s n o c , s e l f i r f o s n o i t a l u m i s e h t g n o m A k a e r b o t n o i t a l u m i s l a u t r i v r o f d e e n e h t , y l s u o i v b O . y s a
e isnecessary. Forensicballisticsbased on
s c i t s i l l a b d n u o
w a nd collision mechanisms tha tinduce permanen tjoints and temporary collision
s a w , w o l e i t S e i l r a h C , r e k r o w m r a f a , 5 1 9 1 n I . ] 3 [ s e s o p r u p c i s n e r o f r o f d e i l p p a e r a s m s i n a h c e m a d n a r e m r a f a g n i r e d r u m h t i w d e g r a h
c housekeeper .This incident led by an unscientific firearm
n o i t a g i t s e v n
i motivated et h appearanceoft heUSBureauofForensicBallistics,t hefirsti ndependen t . s e t a t S d e t i n U e h t n i e t u t i t s n i h c r a e s e r e m i r
c Analysis of microscopic evidence such as firearms ,
c i f i t n e i c s r o f k r o w e m a r f a d e d i v o r p s a h d o o l b d n a , s t n i r p r e g n i
f investigations [4]. However ,the
f o n o i t c e r i d e h t , d e d d a s i e g a m a d e h t f i d n a , r a e l c s y a w l a t o n s i e n e c s t n e d i c c a n u g e h t f o n o i t a v r e s e r p e s o l c o t d a e l n a c s n o i t a l u m i s c i s n e r o F . d e t a c i l p m o c e r o m d n a r e d a o r b s e m o c e b n o i t a g i t s e v n i e h t s a e l p i t l u m n o d e s a b s n o i s u l c n o
c sumptions ,buti ti si nefficienti nt ermsoft ime ,consideringt hatt here
f o e c n e t s i x e e h t , e r o f e r e h T . t o h s a f o h c n u a l e h t d n a h c n u a l e h t m o r f g n i g n a r , s e l b a i r a v y n a m e r a s i t n e v e e h t g n i v l o s e r r o f n o i t a l u m i s l a u t r i
v inevitable.
In this paper ,we propose a method to simulate the shape of the cavity associated with the e h t f o t n e i c i f f e o c c i t s i l l a b e h t n o d e s a b t e l l u b e h t f o e c r o f e v i t c u r t s e
d bullet using a modified
m h t i r o g l a e n i l s ' m a h n e s e r
s d o h t e M
t n e i c if f e o C c it si ll a B
s e d i l l o c t o h s a n e h w , l a r e n e g n
I withat arge ta thighspeed,t hepenetrationdependsont het arge tand
e l i h W . t e l l u b e h t y b t i h s i t e g r a t e h t h c i h w t a e l g n a e h t h t i w s e i r a v y l t a e r g d n a , s e i t r e p o r p c i s n i r t n i s t i
e l t t i r b , y t i l i t c u d , h t g n e r t s , s s e n d r a h s a h c u s s e i t r e p o r p l a c i s y h p e r a e r e h
t ness and mechanica l
h t s l a i r e t a m e h t f o s t n i o p n o i t a c i l p p a d n a s e i t i s n e d d n a s e i t r e p o r
p a tmakeupt het arge,tt hebullet ah s
d e e p s e h
t , itsshapeandmateria lproperties .Asaresult ,thepenetrationphenomenon ofthesho tis t
a r u c c a d n a k c a r t o t t l u c i f f i
d elyi nterpre t[5] .Therefore,i nt hispaper ,wehavestudiedt hesimulation
e h t n o g n i s u c o f d o h t e
m ballisticcoefficien twhichrepresentsthebehavior fo thebulle.t
e r u g i
F 1 .G1andG7 bulle tmodel.
e v i t a l e r e h t f o e r u s a e m a s i t n e i c i f f e o c c i t s i l l a b e h
T resistanceofaparticularbullett oi tsdrag .The
t i w o h t u o d n i f o t t n e i c i f f e o c c i t s i l l a b e h t e r u s a e m n a c u o y d n a , y r o t c e j a r t f o e p y t t n e r e f f i d a s a h l e d o m
u y l n o m m o c e r a h c i h w f o o w t , s t e l l u b f o s l e d o m n i a m e n i n e r a e r e h T . t e l l u b e h t o t n i s t i
f sedi nt heG1
n i s l e d o m 7 G d n
a Figure1 .Theballisticcoefficien treflectingthephysica lpropertiesofthesho tis s
a d e n i f e
d BC=M/ ( D2)I[6] .Mist hemassoft hebulle tusinggrainunits ,Dist hediameteroft he
d n a , t e l l u
b Iist heformfactor ,whichist heintrinsicshapeoft hebulle.t
d e s s e s s o p e b l l i w t a h t y g r e n e c i t e n i k f o e t a r s s o l e h t n o t c e f f e t a e r g a s a h t n e i c i f f e o c c i t s i l l a b a h c u S
d e e p s e h t d n a y g r e n e c i t e n i k h g u o n e e v a h u o y f i , o s l A . t o h s e h t f o d n e e h t o t t o h s e h t f o e m i t e h t m o r f
e h t , h g u o n e s
i nt hebulle tpenetratest hesubjec tasi ti s .Thekineticenergyt hati sno tenoughcomes h
t i
w slowspeed . I thasapenetratingpowert ha trelativelyretreatst ot heelectron .Thismovemen tof c
e b h c i h w , y t i n u m m o c y r a r o p m e t e g r a l y l e v i t a l e r a s e t a e r c s n u
g omesapermanen tcommunityover
. e m i
t Figure 2 shows the visualization of the temporary cavity and the permanen tcavity in an d
e r i f s a w n u g e h t h c i h w n i t n e m i r e p x
e att hegelatin[7] .
e r u g i
F 2 .Permanen tcavityandtemporarycavityexperimen twithgelati . n
d e if i d o
M Bresenham’ sL i Ane lgortihm r
e t s a
R ization isan algorithm tha tdetermineswhich pixe lvalueshould be selected when mapping t n e i c i f f e y r e v a s i m h t i r o g l a e n i l s ' m a h n e s e r B . ] 8 [ e c a p s t c e j b o n a o t s e c a f r u s d n a , s e n i l , s t n i o p
f o s m r e t n i m h t i r o g l
a standardcomputerarchitecture ,usingonlyi ntegeraddition ,subtraction ,andbi t .
e W . t e g r a t e h t e d i s n i y t i v a c e h t t n e s e r p e r o t t e g r a t a s a l e x o v 0 3 * 0 3 * 0 3 e m u s s a e w , y d u t s s i h t n I
s l e x o v t h g i e h m u m i x a m e h t n o d e s a b e p o l s e h t e t a l u c l a
c andt hevoxelst ha tstartt hecavity ,andstore
m u m i x a m e h
t sizevoxelsofeachf ramei nt hearrayt hrought heBresenham’s algorithm .Basedont he m u m i x a m e h t d n a t e l l u b e h t h g u o r h t g n i s s a p e m a r f e h t f o l e x o v h t d i w m u m i x a m e h t n e e w t e b e p o l s
, l e x o v t h g i e
h thej oin tvoxelsoft hecorrespondingf ramearepaintedusingt heBresen mha ’s algortihm onceagainasshowni nFigure3 .T eh pseudocodeisshowni nFigure4.
e r u g i
F 3 .VoxelsofeachframeinSimulationwitht hestrar ,middle ,maxsizeframesandt hesimulatedvoxels.
e r u g i
F 4 .Virtua lcavitysimulationalgorithm.
s t n e m i r e p x E
O d e s u e w , y d u t s s i h t n
I penGLi nMFC(Microsof tFoundationClass)tocreateasimulationprogram
f e o c c i t s i l l a b n o d e s a
b ficients .Afteryouselec tthebulle tmodel ,enterthemassand diameter ,and
d n a d e t a l u c l a c s i t n e i c i f f e o c t e l l u b e h t , '! T O O H S ' e h t s s e r
p the simulation resul tis shown ,by
g n i y a l p s i
d thet emporarycavitywheret het rajectoryoft hebulle tandt hebulle tpass .Att hist ime,t he e
j a r t e h t g n i t a l u c l a c f o d o h t e
m ctory of the bulle tusing the Bresenham’s algorithm is to confirm
e h t g n i t u t i t s n o c s t n i o p t h g i e e h t n e e w t e b d e t a c o l s i t e l l u b e h t g n i t u t i t s n o c t n i o p h c a e t o n r o r e h t e h w
. n o i t a r t e n e p e h t m r i f n o c d n a , l e x o
v Also,t hesizeoft hecavityi sadjustedaccordingtot hecalculated
.t n e i c i f f e o c c i t s i l l a
b
l a c it y l a n
A Vailda iton
d n a s s a m e h t d n a , d e t a l u m r o f e r e w , d e s u y l n o m m o c e r a h c i h w , 7 G d n a 1 G s t e l l u b e h t f o s e p a h s e h T
f I . s e l b a i r a v r e s u s a d e n i m r e t e d e r e w t e l l u b e h t f o r e t e m a i
d M is proportiona lto the trajectory
e h t , t n e i c i f f e o
c D squared value is inversely proportional .As a result ,the higher the trajectory
t n e i c i f f e o
c we have ,the higher the preservation of the kinetic energy of the bullet is observed .
y l r a l i m i
S , thel owert heenergyl ossrateweobtain,t hehighert hepenetrationpowerisshown ,which t
t a h t t c a f e h t n i s t l u s e
r hesmallerthesizeofthevoid in thevoxel .Conversely ,ifthecoefficien tof
d n a d e c u d e r t a h w e m o s s i e c r o f n o i t a r t e n e p e h t d n a , r o o p s i n o i t a v r e s n o c y g r e n e e h t , w o l s i y r o t c e j a r t
e h
t stoppingpoweri si ncreased ,sot ha tal argecavitycanbef ormedi nt heobjec.tInt hiscase,t hesize e h t f o r e t e m a i d t s e g r a l e h t d e i f i t n e d i e v a h e w f i , y l l a n i F . e g r a l s e m o c e b l e x o v e h t n i y t i v a c e h t f o
e l l u b e h t f o t i x e e h t s s e r p x e e w , y t i v a
c tfromthevoxe lusing theBresenham’s algorithmforvisua l
. n o i t a t n e s e r p e
r Figure 5 shows the resul tof executing the simulation program .In the above two
a t a h t n e e
s largeandsmal lcavityoccurs .Thefollowingt woimagesshowt hatt hebulle tmodeli sse t a
, 1 G o
t ndtherightsideisse tto8gand 6mm respectively ,and thel eftsideisse tto 16gand 4mm i
t c a r t f o t n e i c i f f e o c e h t t a h t d e m r i f n o c e b n a c t I . y l e v i t c e p s e
r onbecomeslargeandt hecavtiybecomes
.l l a m s
e r u g i
F 5 .Theresults o ifsmulation (Toprow :comparisonofbulle tmodel ,bottomrow :comparisonofM &D).
e r u g i
F 6 .Maxsizeofwoundaccordingt oballisticcoefficients.
e r u g i
F 6 hs owst her esul tofplottingt hemaxsizeoft hewoundaccordingt ot heballisticcoefficien t x
a M . n o i t a l u m i s e h t n
i sizeofwoundi sdefinedast hemaximumnumberofvoxelsamongt heframes
e h t f o e z i s e h t e c n i S . y t i v a c e h t g n i s s e r p x e n e h
w cavity caused by the bulle tcanno tbe precisely
y b 8 o t 1 o t t e s s i l e v e l t n e i c i f f e o c c i t s i l l a b e h t , n o i t a l u m i s s i h t n i ,t n e i c i f f e o c c i t s i l l a b e h t y b d e n i f e d
2 . 0 y b t n e i c i f f e o c c i t s i l l a b e h t g n i d i v i
d unitssot hatt hesizeoft hecavitycanbeconfirmed .Thecavtiy
d e n i m r e t e d e r p a m o r f d e m r o f s
i valueandbecomesl argerasi tpassest hrought hef rame ,andbecomes
a s e h c a e r t i n e h w n i a g a r e l l a m
Conclu ison d u t s s i h t n
I y ,wedesignedasimulationbasedont heballisticcoefficien tandt hephysica lparameters o
c e v a h e W . y t i v a c e h t f
o nfirmedt hedirec trelationshipbetweent hebulle tandt heobjec tbyactively
l i t
u izingt heballisticcoefficient. Andwealsoconfirmedt hef easibilityoft hesimulationoft heactua l c
e n s i t i , e r o m r e h t r u F . s t n e t n o c s c i h p a r g e h t g n i s u n o n e m o n e h p d e v r e s b
o essary to consider the
y l i a d e h t n i r u c c o t a h t s r o t c a f l a c i s y h p e h t d n a s m r a e r i f f o s c i t s i r e t c a r a h c e h t s a h c u s s e c r o f l a n r e t x e
e s e h t f I . y t i v a c e h t d n a y r o t c e j a r t e h t n e e w t e b p i h s n o i t a l e r t c e r i d e h t m o r f g n i d n e t x e y b t n e m n o r i v n e
d e h s i l b a t s e e r a s r e t e m a r a
p ,adeepergraphicsalgorithmneedst obedesignedforfutureresearch.
s t n e m e g d e l w o n k c A
. o N ( F R N , n o i t a d n u o F h c r a e s e R l a n o i t a N y b d e d n u f y l l a i t r a p s a w h c r a e s e r s i h T
. ) 5 2 7 7 5 0 1 0 A 1 A 1 D 1 R 5 1 0 2
s e c n e r e f e R
] 1
[ Heckler&KochGroup,http://www.heckler-koch.com ca cessedi nDecember .2017. I
] 2
[ srae lWeaponIndustries,http://iw.inet ,accessedi nDecember .2017.
s s e r P a n a m u H , s w e i v e R y g o l o h t a P c i s n e r o F , ) . s d E ( l e a h c i M . T : n i , s c i t s i l l a b c i s n e r o F , r e g r a K . B ] 3 [
9 3 1 . p p , 8 0 0 2 , k r o Y w e N , . c n
I -172.
d o o l B , t e g d i r B . H ] 4
[ ,Bullets ,andBones :TheStoryofForensicSciencefromSherlockHolmesto
. 6 1 0 2 , k r o Y w e N , s n i l l o C r e p r a H , a n d
l l a b f o n o i t a m r o f e d e p a h s e h t n o y d u t S A , m i K . T . Y d n a g n o H . H . S , e e L . S . D , n h o S . W . S ] 5 [
e r o K , t c a p m i y t i c o l e v w o l e h t r e d n u ) m m 6 5 . 5 ( e l i t c e j o r
p anSocietyforPrecisionEngineering (2002)
5 6
8 -868.
[6] .CL .Farrar ,D.W .Leeming ,Brassey's Land Warfare Series: Military Ballistics ,Brassey’ ,s 5
9 9 1 , m a h n e v i r h
S .
7
[ ]https://youtu.be/fX4ODh1g4eM ,accessedi nDecember .2017.
[8] WS. . Shin ,K . .S Kim , MS. . Lee and C.G. Song ,Image Enhancemen twith Rotating Kerne l m
h t i r o g l A s ' m a h n e s e r B y b d e t a r e n e G r e t l i F n o i t a m r o f s n a r
T ,Thet ransactionsofTheKoreanI nsttiute
s r e e n i g n E l a c i r t c e l E f
