4. 4-1. !"#$%&'(
!)*+,-&./$%01%2345
6789:;<=>?@ABC"DE0FG9!
0FHI$JKLMNOAPQR$%STUVWCCXYC
"Z[\]^WFW_`a!b"C!FW]!FcdZ[efUVWg#
XY!"#Z[a!hi!jWkl"m,nop&-4pqr
st7$%*u3H4589Holsapple’s v-?@ABY_`HI$J
wsqF-xyzC"{E9mZ[hi|}~,
4-1-1. $%
npd=
4 km/sec p0F9m
rs]$%& 30 % (x& 3-1-1x& 3-1-2
!"# Table V +Onose and Fujiwara, 2006c) ,yzw"m0spall
&$%9m"$%& pit +Fp ¡¢9m,-Xppit £¤¥Y89C"¦R9m pit rs§$%9mrs
t7*u+¨7Y 50 %©ª,X$%9mrspit rst7*u+
«. 4-1 ¬,pit rs§$%®¯°±&²³"|´µW¶
´XYqF¡¢p´!Cd,
« 4-1. pit rs§$%
Fig. 4-1. Fraction of compacted mass to estimated ejecta mass by pit volume
·¸0F9m¹$%9mrs©ªº&
yz»E9m¼<=>+qYrs+½¦x-m¾m%®+¿À
- 90 -
XY0dq¦RXYWp´,yz&Áy
y
ÂÃYÁy
9mC|$%9mÁ
9m-ÄÃWÅ5ÆÇÈ+!x
W»E9m(«. 3-5),ÉXm"ÊËY3H45ÌÍ+ 3-1-2 0ÀÎ
,pit YXm+F¼Ï+ÐÑÒ
YXmYÓzY+ÔÆ
Õ¹ÂÃYÄürs+¨7(«. 4-2),ÂÃ%®&ÖFRx
×nYÅØÙ01 = 1300 kg/m3 Y,ÄÃ%®&ÂÃ%®Y$%+Ú¹
!Û%®Ù0t = 920 kg/m3 Y4V(Ù01 +Ù0t)/2 pY¿Àx,Xm"¼
rsY%®C"¨7$%YpÂÜxÝ"mº& 7 g ©ªx
Xm&$%9mºÞE(ßà 4 g)0FÝݶ´áXm&Áy
9mÄÃ
%®â¡À±ã¹"mäå±W,
« 4-2. $%9mrs+¨7æç«
Fig. 4-2. Schematic figure of estimation of compacted volume
Holsapple (1980)&-mÉp!"#3Þè²-+é73ê+6
789 Deq Yëìã¹+d,XY´íî9m34589Óï]
ðqñòxóôµõq&Brikhoff et al. (1948)Wö÷®øRù jet ÷®+½¦
úûp¨7ü34589 DeqýYÅØqpþr¸¥ DprojþrY
%®¼Ù0pÙ0t +ôçpÓ9m,
Deq = D proj
ρ0 p
(4-1-1)
ρ 0t
Xçnp Dproj=7.1 mmÙ0p=1146 kg/m3 Ù0t =920 kg/m3 +Y3H45
89& 8 mm pY½¦9m,X&Þyzw"mÅ5ÆÇÈ+
x¨73H45ÌÍ 13.41.4 mm Y`~G9áWþr
F Y0F8ÌÍp
$xXY+¬x,
- 91 -
« 4-3. 1 $%²Aæç«: ÃÃÏ+¬,
Fig. 4-3. Schematic figure of one-dimensional compaction: columns in right and left side represent target before
and after the impact, respectively.
ÔqY%®Ù0t ÓzWþrF 89 Dpp ÉpxÁ
y
ÂÃ89 Dpc ÉpW%®Ù01 Ép$%9mXXC"ÄÃ89 Dps É
pW%®(Ù01 +Ù0t)/2 Ép$%9mY 1 ²A¹º°+(«. 4-3),
Xñò29m²ApþrF 89& 9 mm pd,þr89L¸¥ 0.6 9ö$W9mY,Xm&Nakazawa et al. (2002)
ßÞè0F9mö$9&þr9
0.6 pdXY+Äqp, F 89W 9 mm
$9W 3.6 mm
pY¿ÀYö$ÐÑÉp!"& 12.6 mm Y!FXm&ÞEY#$ap
,
4-1-2. <=>%&'
n0F("mëìY<=>Y)YHousen and Holsapple (2003)
0*º+,(-.=)+ô/0%ÞèÔY+Holsapple v?@A
B+ô_`x,Holsapple and Schmidt (1979)p&rs VcÒ¥ Rcr89 Dp
'J g +ëì+Ó12pþrÒ¥ rp÷® v iþr!"#
%®Ù0pÙ0t3® Y t +ô42x12vVvRv2 +5L0
ÀÎxXm")+Àç2x,
πV =
ρ 0t Vc
mp
(672rs)
- 92 -
(4-1-2)
ρ
π R = Rcr 0t
mp
π Dp
ρ
= D p 0t
mp
π 2 = 3.22
1
3
(672Ò¥)
(4-1-3)
(67289)
(4-1-4)
(672'J)
(4-1-5)
1
3
gRcr
vi2
Housen and Holsapple (2003)ô& 44 % 70 %96 %-3®& 10 C
" 30 MPa pFnÞèp9ôx(60 %)$:3®(13 MPa)+;
p,«. 4-4 Housen "<C"=ôx<=>?@0>-.?v2 YvV
!"#v2 Y$%)+Ó>.@nÔ+;q+¬,+A|Br
pC§ÞèÔ& Schmidt (1980)qp,$% Ecompaction &r
s Vcþrº mp%®Ù0tDºhE Me
+ô5LFÓ9mºp,
Ecompaction =
ρ 0tVc − M e
mp
($%)
(a)
(4-1-6)
(b)
?@AB: Housen and Holsapple (2003)*º+,+ô/0
« 4-4. $%Yv-?
ÞèY_` (a) 672rsY672'J,C
ÞèÔ& Schmidt (1980)Schmidt and Housen (1987)Holsapple and Housen (2003)0,Xmn
p¨7"m+;,(b) 672'JY$%
Fig. 4-4. v-scaling and target’s compactions: comparison with the experimental data from Housen and Holsapple
(2003) (a) Cratering efficiency and gravity scaled size. The data for sand from Schmidt (1980), Schmidt and Housen
(1987), and Holsapple and Housen (2003) are shown. (b) Compaction efficiency and gravity scaled size.
p=dGF3®+A|ùvV &ÞèHmv2 W 10-8 C" 10-5 µp
IJ
xáxWdhE,Xm&Åû®+A|C%
- 93 -
&v V &v2 WhE|m~´Kp:;Y§ap,nÞ
è0F("mW 60 % v V q 100 û®pFXm& Housen and
Holsapple (2003)¹ 70 %§x("mY#$ap,L7
§x½¦9mvV &®5ÄëìW
x·¸0qY`~G
9á!,Mp672'JY$%p&%¯°W¢7"m®
q³"|´µÂp,nÞè$%q Housen and Holsapple (2003)Ô³"|´
µÂNÉd,
4-1-3. HI$J{À
nO&ÉP%!ùÅQHI$J¨7+ Mizutani et al.
(1983)RSTUx-
!ù§HI$J+wsq,
P%!ù§HI$J&5L0! Rankine-Hugoniot ûç+ô
¨7"m,
ρ j (U j − u pj )= ρ 0 jU j
(º°)
(4-1-7)
Pj − Poj = ρ 0 jU j u pj
(Vº°)
(4-1-8)
(NOAP°)
(4-1-9)
E j − E0 j =
(P
j
+ P0 j )(V0 j − V j )
2
bxÙ0j Ùj &Z[Wú%®Uj &Z[÷®upj &Z[WúBX
÷®P0jPj &Z[Wú$JE0jEj &Z[WúÂNOAPV0j
Vj &Z[Wú_rsp,YZ j &p(þr)& t()+Ó,
XXpþrù!"#ùÊË[&ãfpp$J Pp Y Pt
ÂNOAPEp Et &
x,Z[Wú$JÂNOAPY_~Y
$JÂNOAP&4\p´IjG9pP0jE0j + 0 Y,
BX÷®+ 0 YYþrBX÷®& vi pFZ[Wú&
]BX÷®W
xá!XYC" upp Y upt & vi +ô0Ó9m,
u pt = vi − u pp
(4-1-10)
Z[÷®YZ[WúBX÷®V&0!ÞèçW°^,
U j = C j + s j u pj
(2-1-2)
bx
Cj &_A`÷
sj & Grüneisen )2Yã¹"m412p,
(4-1-7) - (4-1-10)
!"#(2-1-2)+ôY0FHI$J Pcore &5L0ÓXYWp´,
1
v v
1
Pcore = ξρ 0t C t2 1 + s t ξ i i
2
Ct Ct
2
(4-1-11)
bxa&þr]%®+ô5L0Ó9m,
- 94 -
2
ξ=
1+
δj =
ρ 0t δ p
ρ j − ρ0 j
ρj
(4-1-12)
ρ 0 pδ t
Zel’dovich and Raizer (1964)!"# Shen et al. (2003)RS
·¸0FHI$Jbc+,nFd
&%®Ù0tÙ01 _WÙ01/Ù0t = 1.4 pF_`a¶´,X0!
$%Weu&$%DdHIMÝM$J&'W¶´
pZ[÷® Ut YBX÷® upt [)ç
U t = Ct + st u pt
(2-1-2)
(Ct &_A`÷st & Grüneisen )2Yã¹"m412)+-ÉÉôXYW
p´!,xWdn&Shen et al. (2003)YÅF Mie-Grüneisen )2+_r
s2Yx¨7Xm+9ôf(W,
ÉW
P-V «^pjF$%9mC+¿À, P-V g[
&«. 4-5 _rsW 1/Ù0t ÌÍC"hÉij[ PHt +Y,&$J 0_r
s 1/Ù0t kC"-$:3® 12 MPa Ép& ±a$:9m,-Wðla!
+ÉpV&$JW 12 MPa ÉÉpW|9mXY0$%Wfá,ðla
!W("m&Resinyansky and Bourne (2004)pô"m¿ÀYÅF
üÅû®
$%+mèx 0 ùý Hugoniot g[ß!g[+náqY¿À,
ùZ$C"oøpq¹12&4\p´Y"m(Fomin and
Kiselev, 1997)p$%r$Ïp("m$%%® 1300 kg/m3 C"½¦9
m 44 %+ðla!Y,Zel’dovich and Raizer (1964)pdd&
$%0FstW!á!deuppn& Resinyansky and
Bourne (2004)YÅF« 4-5 g[ PHt(V)+%ðla!%®Ù01 Y 2 uv%®Ù0s
W'! PH2(V)Épw9xXY+,PH2(V)& PH2(V02)=0 hÉg[pV02 &q
YqY_rs V0t +ô
1
1
V02 = V0t −
−
ρ 01 ρ 0 s
(4-1-13)
YÓ9m,Hugoniot g[ PHt &yz$J 0 Y´_rs V02 +F$JW3®
x 12MPa Ép&
±a$:9m,X$J
WhÉF
W 0 !Ép$%W{,W 0 !Y_rshEcd|#$JW^}
,PHt(V)Y PH2(V)&ßpp
1
1
V ' = V −
−
ρ
ρ
0s
01
(4-1-14)
YÍáY´PHt(V) = PH2(V’)p,
~$J V’% Hugoniot g[ PH2(V’, V02)+ Zel’dovich and
r$p_rs V02 C"hÉd
- 95 -
Raizer (1964)¬9m+ô¨7,MaP%!ù%0d("m
Hugoniot g[^$J PH YñÌrsFÂNOAPH &
Ma! PTT XYWp´,
±a! PCC Y
±a! PCC &ùXVáJ
qpF®&4)p,MpMa! PTT &ù®ã
p,npx®&2®+!Y"mp(Kadono and Fujiwara
(1996)nYëì»E9m®& 5000 K)X
Ï
+f(&!,
PH = PC + PT
(4-1-15)
ε H = εC + εT
(4-1-16)
« 4-5. Z$% P-V «: PHt &Þ9ôx%® 920 kg/m3 P-V g[Y
x¿Àxq,PH2 & PHt YßpV02 C"hÉF 0 Ép$%9mY¿ÀxU P-V «
Fig. 4-5. P-V diagram for shock compression of the porous gypsum: PHt represents a Hugoniot curve of gypsum
target, whose original density was 920 kg/m3. PH2 was set parallel to PHt, originated from V02 and compacted into
solid.
Ma$J PT YMaNOAPT +Ô#|¹ Mie-Grüneisen )2(V‘)&_rs2p
Γ(V ') =
PT V '
εT
(4-1-17)
YÀÎ9mqp,Shen et al. (2003)&X Mie-Grüneisen )2_rs¯°±+F
²A2x,
- 96 -
q V ' q '
Γ(V ') = Γ0 exp 0 − 1
q ' V0
(4-1-18)
XXp
V'
d ln(Γ )
= q0 = q
d ln(V ')
V0
q'
-x q ' =
d ln (q )
d ln(V ')
,
(4-1-19)
XXpq0q’& Shen et al. (2003)kl"m 1.070.9 +ô,Érs12W
4\p´YxU Mie-Grüneisen )20 &P%!ùZ[÷® Ut YBX÷
® upt +Ô#|¹ st +óôx5LFÓXYWp´,
Γ0 =
162s t2 − 360 st + 215
18s t
(4-1-20)
np0FHI$J&r$Y`~¶´Y"mpyzÏ
$J P0 !"#ÂNOAP0 &4\XYWäåp,xWdZ[¹
NOAP°ç(4-1-9)&(4-1-21)FáXYWp´,
εH =
PH (V02 − V ')
2
(4-1-21)
ç(4-1-14)(4-1-15)(4-1-16)-x(4-1-21)+ôZ;$0F("mÂNOAP
H +çFÓY5Lç!,
εH =
PH (V02 − V ')
V (PH − Pc )
= εC + εT = εC +
2
Γ
(4-1-22)
Xç+ PH x¹³5L0! Hugoniot g[+Óûç!,
PH 2 (V ' , V02 ) =
(K − 1)PC (V ')− 2 ε C (V ')
V'
V
K − 02
V'
ε C = ∫ PC (V ')dV '
V02
(4-1-23)
(4-1-24)
V'
XXp K = 2/+1 p,
$JMaYrsY)+ÓçPC(V’)&Þèa¨7"mqp,Stretton
et al. (1997)0dÏ+a$:xÞèÔ+ÓxW«. 4-6 p,
Xm"k+ç(4-1-25)p¬9m Birch-Murnghan ûçpXY0FM$J PC
Y_rs V’)+¨7,X Birch-Murnghan ûç&rÏûç$J%®§
[¯°±+;xqp
$:9mù§rsY%®)+Óq
p,
- 97 -
Vos n
PC (V ') = Ap
− 1
V '
(4-1-25)
XXp Ap Y n &À2pV0s Y V’&r$Y$:9mÏpP%!_rs+Ó,n
qg[0F¨7"m~´pWn W 3.5 C" 4.5 µp12Y´g
[12&_rs½EY`~G9pStretton et al. (1997)RS´ n=4 Y
Xm+g[Y Ap & 9.1 GPa Y!d,
« 4-6. a$%¹$JY_rs): & Stretton et al. (1997)Þè0F("m
q,Birch-Murnghan ûç n +1@x,
Fig. 4-6. Pressure and specific volume of the powdered gypsum under the static compression: data were
obtained by Stretton et al. (1997). Three fitting lines are corresponding to three values of the coefficient n.
yz%® 1322 kg/m3 W0F 0 Ép$%+Ú¹Y¿ÀxU
Hugoniot ûç PH2(V’)&ç(4-1-18)(4-1-24)-x(4-1-25)+ç(4-1-23)XY0
F("m,Þyz%® 920 kg/m3 Hugoniot ûç PHt(V)¸&X
mç(4-1-14)+ ô9xm³0,
¹Z[÷® Ut YBX÷
® upt Y)&Z[zpº°ç(4-1-7)YVº°ç(4-1-8)0F5LF
Ó9m,
u pt = PHt (V0t − V )
(4-1-26)
Mp=
þr&P%!ùC"!7Z[÷® Up YBX÷® upp Y
[)ç+ôXYWp´,
U p = C p + s p u pp
(4-1-27)
- 98 -
XXp Cp sp &þrùZ[+ÓÀ2p,XmYZ[zpVº°
ç(4-1-8)+uHxXYpþrZ[Âp$J+"Hç PHp WçF("m
,
PHp = ρ 0 p (C p + s p u pp )⋅ u pp
(4-1-28)
ÓzYþrÓz&$JYBX÷®+¡Sp÷® vi +ô
5L)WF\|,
PHp = PHt
(4-1-29)
u pt = vi − u pp
(4-1-30)
5^Fx¨7"m!"#þr Hugoniot g[+ô«. 4-7 0
0FHIx$J+wsqXYWp´,ëì+1
!"#P%!IØ$J+ Table XII ¬,¹yz%®âà
M9 92044 kg/m3 +¢Y0FHI$J& 141 GPa Y!,X&P
%!x¨7HI$J 25GPa Y`~ 0.56 xC!"!,
« 4-7. Y=þr P-up «: þr Hugoniot g[&÷®p 4.2
km/sec C"n,Xm"g[£kWZ[p$JBX÷®+Ó,
Fig. 4-7. P-up diagram for porous gypsum and nylon projectile; the projectile’s Hugoniot is plotted backwards
and starting at a particle velocity equal to the impact velocity vi. A curves’ intersection gives a pressure and a particle
velocity, behind the shock waves in both the target and projectile.
- 99 -
Table XII. Shock induced pressure and parameters
Parameter
<Target>
Initial density
Compacted density
Non porous density
Shock wave's constant
Birch-Murnghan parameter
Mie-Grüneisen parameter
<Projectile>
Impact velocity
Initial density
Shock wave's constant
Impact induced pressure
Symbol
Unit
Case
1
2
3
4
5
solid
gypsum
920
1300
2280
1.79
3.5
10.7
2.78
920
1300
2280
1.79
4.0
9.1
2.78
920
1300
2280
1.79
4.5
7.9
2.78
964
1300
2280
1.79
4.0
9.1
2.78
876
1300
2280
1.79
4.0
9.1
2.78
2280
2280
2280
1.79
3.5
10.7
2.78
0t
01
0s
st
n
Ap
o
kg/m3
kg/m3
kg/m3
vi
0p
Cp
sp
m/sec
kg/m3
m/sec
4200
1160
3945
1.17
4200
1160
3945
1.17
4200
1160
3945
1.17
4200
1160
3945
1.17
4200
1160
3945
1.17
4200
1160
3945
1.17
Pcore
GPa
14.40
14.35
14.30
14.18
14.54
20.98
GPa
4-1-4. Z[hi!"#¤¥%&'
ùÂ+¦§Z[&P%!ùÂ+¦§q0Fq3hi!"#¤
¥+Ú¹YHm,Xop&yzp»E9mÁy
9m<
=>Yop¨7HI$J+ôÂpZ[hi+¨x,
·¸0F9myz&3-1-24-1-1 ¬xF
pit ©zYÁy
9mWÅ5ÆÏ°^,
$45WXÅ
5Æ45ÌÍY¿ÀxXXp$JWop¨7HI$J
xY¿À
,Áy
ÄÃÊË&$:[ð¶$JW 1 ª$:
3®Y
x
á!dkéupY"m,xWdHI$J
$Ò¥
Áy
<=>-x3®C"ÂpÒ
Ϧ§
Z[hi+¨7XYWp´,
=þr§ 4.2 km/sec p0FHI$J&o
0F 141 GPa p,
$Ò¥&nÞè&½E9m"ɧ
0F9m
$Ò¥½E«&!,-XpNakazawa et al. (2002)¹
§ßzÞè¹
$9Wþr9 0.6 pdXYC"
0F9m
$ +þrÓzC"-Ò¥ 0.6 C" 1.2 pY¿
À,Áy
Ò¥& 22 mm pF 1 ª$:
3®& 12 MPa
p,Ma¬ ÷®W:;xW$:3®&:;pXm+ 12 MPa
- 100 -
C" 50 MPa Ép129x-&'+bcx,45C"!" r ¹Z[$J Pt(r)
&
$pHI$J Pcore
$Ò¥ r0 Z[!"0hi+ô
0!!"2pÓ9m,
r
Pt (r ) = Pcore 0
r
β
(r>r0)
nÞèEÀ9mÁy
(4-1-31)
9mÒ¥Mª$:3®
$Ò¥
$J+^®0¿ÀYhi& 3.5 û®Y½¦9m(Table XIII),¬ ÷®
W¶´XY0$:3®:;&'&$:3®W 5 !Y´½¦9mhi
& 3.2 C" 2.6 hE,É
$ W 2 !Y´hi& 3.2 C"
4.8 :;,X&Nakazawa et al. (2002)px¨7"mhi 1.8 0F
qArakawa et al. (1995)¯§x¨7"m 2.2 0Fq¶´áZ[hi+
F+¢f(±+¬x,ɹ
Z[hiW¶´XY&Fujiwara et al. (1977)%
!°zC" spall Þèp»E9m0
Wp&»E9m!!jï±&'+
äå±W,
Table XIII Decay Indices of Gypsum Target
Shock pressure
Pcore
GPa
14
10
18
14
14
14
14
Transmitting distance
rs
mm
19
19
19
15
25
19
19
Compressive strength
Ysh
MPa
12
12
12
12
12
20
50
- 101 -
Decay coefficient
r0=2.16
3.2
3.1
3.4
3.6
2.9
3.0
2.6
r0=4.32
4.8
4.5
4.9
5.7
4.0
4.4
3.8
4-2. !"#$%&'"()*+
,-./+"0%123%1 2 1
4526789:(Onose
and Fujiwara, 2004a);<"==1!">?
2CD4+
pit GH#
I
;E5
2 1"spall 2@AB
+1!"#$%&'/+F spall GH2
CD4+
526JK
STR"5
;LM9!"NO/+PQR
+12>?9U+
spall "@AB
2CD4V"==1WR1XYZ[S
2\"5
+-.]^ spall _`a"*+, Z-_`a2bcR"de;
4-2-1. 0%123%1ST: Lfghi
/+ 2.5 msec jk
! 23l11m/sec"m! 60l15 bcno9pqr6Ks+
(3-4-2-2);tuvwfg=!"5
+xyz2{|6 spall GH/+
"5
526JK
;<
+xy}~*F!vw spall GHs529~F
^R"0%12 spall 2
R;5
+ spall GH/+
2o0%12R"jSTR;/+ 5 msec jk
xy"$%&'6 pit /+ 13 mm spall GH:F9"/
6 12 m/sec /YZ6 0.01 g jF9:;bcn}~9
spall !"3%12"mF"(
)6 5 msec j
F6:6"N6 spall 2F!0%1
2R"9XR;
()R~ 5 msec R!"/+ 2.5 /+ 5 msec 9: ¡GH=
0%1¢£2*s9:;tuvwfg=!"5
¡GH9!"pqr
R¦§
K
0%1xyF2"vw¤¥
3%1xy0F6(
;L©ª9PQ
¨6"J
0%1¢!"2«fg¬ 0_01 =!
224/1090 (Table XIV)9:"3%1¢2c®¯*9"5 ¡GH
/+3%1W78°o±~"²0%1W2R;<"
5³ 12 m/sec !"tuvwfg9´s+
¥2¦§µ¶·6¸<2~PQ
pit GH/+vw¤
"3%1W¹o9
:;
ºµ9"/+ 5 msec j»¼R3!" pit GH/+ 1 mm j6"
m 80l8 vw¤¥2z½¦§*µ¶
|6 10 m/sec j9:;5
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+!#z2{
+3%12R"jSTR;/+ 2.5
- 102 -
/+ 5 msec jk
R!"/+ 13 mm jk pit GH/+
="/"YZ6 0.01 g j9"/"6 12 m/sec jF;/+ 5 msec
j¾
R!"#/+¿+/ spall 9:2ÀS9~Fj;
9:;3%1WÁÂÃ!#z2{|6 2 mm j9:"NO9
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s"$%&'1ØÙ!V*;R6"Ðs=
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I
4 msec"3 msec"2 msec 9:;5
()2m*+,$%&'ÝÞß(à. 3-
27, 28)/+áâSs9:;ãQS
xy"ä1WF
å¢"*+,"m"vw¤¥9$%&'"*+,æ
ç1è2éê Table XIV ;
Table XIV Number and average of fragments in early and late fragments
run
Impact
conditions
Threshold
Slit
in
ejection No.
Group
No. Angle Projectile
time
diameter or not
degree mm
0_01 0
7.1
slit early t(z=0) <5 224
late 5< t(z=0) 866
0_02 0
7.1
slit early t(z=0)<5 54
late 5< t(z=0) 694
0_04 0
7.1 no-slit early t(z=0)<5 34
0_06 0
7.1 no-slit early t(z=0) <5 35
late 5< t(z=0) 500
7.1
early
t(z=0)<4 81
45_01 45
slit
late 4< t(z=0) 146
3 no-slit early t(z=0)<1.5 151
45_21 45
late 1.5< t(z=0) 288
60
7.1
early
t(z=0)<3 92
60_01
no-slit
late 3< t(z=0) 196
7.1 no-slit early t(z=0)<2 67
70_01 70
late 2< t(z=0) 61
Averaged value of fragments in each group
- 103 -
Ve
m/sec
28.18 l14.47
2.50 l1.97
18.86 l6.94
3.53 l2.38
12.38 l7.28
15.67 l19.27
2.96 l2.05
23.05 l9.05
7.21 l4.08
19.77 l12.64
4.45 l2.70
14.42 l9.00
2.41 l1.82
18.98 l16.59
3.59 l2.53
ìe
x(z=0)
degree
mm
59.0 l15.9 14.4 l5.6
78.7 l10.0 3.9 l4.3
68.6 l12.2 18.7 l6.7
80.2 l8.0
6.4 l6.5
74.3 l11.4 12.9 l8.3
91.5 l20.9 9.2 l7.1
87.8 l14.5 7.5 l5.9
92.0 l22.0 3.1 l18.8
85.9 l9.7
7.8 l13.7
79.5 l19.7 4.3 l4.2
64.3 l22.6 1.7 l5.3
91.6 l30.2 -2.6 l11.7
75.3 l19.5 4.1 l7.6
86.2 l26.5 3.7 l10.2
85.5 l20.3 2.6 l8.0
Fragment
radius
mm
0.6 l0.6
0.5 l0.1
1.5 l0.9
0.7 l0.2
3.8 l1.3
2.9 l1.8
0.7 l0.2
1.4 l0.6
1.0 l0.2
0.6 l0.3
0.5 l0.2
1.0 l0.6
0.7 l0.3
1.6 l0.7
1.2 l0.7
4-2-2. 1XYZ[S2íîYZ
ï
4-2-2-1. 0%1YZ[S
>?
spall xy§ç6 4 mm jFR!"5
+6Æv
w2ðñòkRÅóY9:52"ôb! 1: 0.68: 0.22 éê2
9:526JK
(3-3-1);#59"0%1YZ[S:"õ
!ÆvwõöR2R"6ð9!*52÷ø2"
>ù÷øØÙ;
äR"PQVÍúû=4ü¥í"ýô"þô()/+
>ù´sF Table XV *+,à. 4-8 ;5
! Appendix C ®
Vfg¬ 0_06 =RÚ>ù¢RF9
:;>ù¢ 100 1/sec jF"6ðF"ÁÂÃF>
ù!PQ9~*/;PQ9~=4>ù
%!=F 0.1 /+ 0.02 sec 9:"
5!"N¥9 20 cm 2 m/sec"16 m/sec 6*("0.1 sec"
0.013 sec 2z½öR;+"*iö9"fRÜ45
2678*(!+þ"Å=#>ù
%æ
jR/Q9~
*°6
22F;
à 4-8. >ù2YZ: Nakamura (1993)2
Fig. 4-8. Rotation and mass of fragments: with Nakamura (1993)
- 104 -
Table XV
Rotational frequency of fragments
Observed longer than half
rotational period
Rotational
Mass
frequency
g
1/sec
0.0500
50
0.5600
29
0.4500
33
0.2700
21
0.0500
38
0.0700
16
0.6900
26
0.3800
22
0.1790
19
Early fragments
Mass
g
0.0044
0.0072
0.0163
0.0098
0.0034
0.0019
0.0171
0.0015
0.0017
Late Fragments
Rotational
frequency
1/sec
16
49
29
33
28
51
19
16
12
Mass
g
0.0238
0.0016
0.0199
0.0011
0.0002
0.0009
0.0011
0.0011
0.0081
0.0027
0.0003
0.0026
0.0006
0.0004
0.0007
0.0007
0.0003
0.0014
0.0010
0.0010
0.0007
0.0023
0.0008
0.0015
0.0006
0.0022
0.0010
0.0003
0.0007
0.0005
0.0003
0.0009
0.0006
0.0019
0.0004
0.0010
0.0027
0.0008
0.0009
0.0008
0.0009
0.0019
0.0019
0.0003
0.0004
0.0028
0.0056
0.0045
0.0017
0.0038
0.0005
- 105 -
Rotational
frequency
1/sec
33
17
36
17
13
50
6
100
12
16
8
15
13
26
23
12
99
28
11
41
8
15
17
18
17
25
50
40
47
18
16
34
23
8
14
22
9
21
29
9
61
20
24
33
67
7
7
4
4
34
25
Lfg9QSRxy"NO92>?C6DFR"3-41-3 9ü¥íéê/+´s+
YZ2">?R!//4
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YZ
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YZ¹}2¹! 10 !«+~;R6"¢¯*>
ù"xN9(6"#/R/>ùR*F
R!"<<Q
GH9¶~R6¹} 3 !$6%&;
à 3-14
x"YZ!K'9~*9"ü¥í
éê/+[S
YZ Mestimated 2>?RYZ Mmeasured b(6
)2SR*+,Vx2"YZ6 10 mg /+ 1 g -.k9"/06+
M measured = 0.38M estimated
j"NO2>?
Q
;
(4-2-1)
C6D4+
*/R!"
ü¥íéê/+ð2RYZ´s(3-4-1-3)"5
0.38 152YZ2;YZ[S2!36´<426"L
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7¶852!9
789:;
à 4-9. N O/ + ´s Y Z 2> ? YZ : ÊË!N¥9´s+
ü¥í/+Pî
¹}¹
YZ
Fig. 4-9. Fragment mass estimated from the averaged area of fragment’s silhouette and one measured with
balance: error-bar represents two ends of fragment mass estimated from max and minimum area of each fragment’s
silhouette.
- 106 -
4-2-2-2. 3%1YZ[S
3%1=!"F:sÎi6}~"<>?R2§;
C4+
FF*9"#YZ[S!<=Ö×9:;2«"fg¬ 0_01
/+ 70 msec 3úû=>?wtV 424 åxy"4 pixel j
9@
6 80 %:s;3-4-1-3 =®"5ÁÂÃGH=
!>?dA"#/*K'Ë6YZ}~*üBC52*
(Table IX);! 3-3-2 ® 1: 0.6: 0.8 9:"spall 2c®2bcnð
"üB>ùüB!>?dDxÊËF2E+
;
R6"3%1R!"FG*;
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5
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pit GHkM2ºNR"5 pit O.PGHvwõ! 1300
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oU`VWXÞORNü¥íYRÁÂô
s"1ãFGÕ[SYZ"YZ mf 2#YZ}~*
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+à=4]¹}^2!"/+
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s"JfüBgI4¢6 10 h
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(®~¢!">?R2( Table VIII R;
N (m f )∝ m b
(3-3-1)
- 107 -
à 4-10. N/+ ´s í îYZ ï : YZzxl:é+*GH!ÁÂÃ
GH9df¤(3-4-1-4);¹}!/+
9¹}
9:;(a) 0_02: ¦§"tuvw: (b) 0_06: ¦§"tuvw*R (c) 45_01: m 45 "
tuvwD~ (d) 60_01: m 60 "tuvw*R (e) 70_01: m 70 "tuvw*R
Fig. 4-10. Cumulative number-mass distributions of fragments measured through movies: flat regions in
small fragment mass end represent detection limits for small fragments (3-4-1-4). The largest fragment means
largest one which ejected from the crater. (a) 0_02: vertical impact with the slit, (b) 0_06: vertical impact without
slit, (c) 45_01: impact at an angle of 45 degrees with the slit, (d) 60_01: impact at an angle of 60 degrees without
slit, (e) 70_01: impact at an angle of 70 degrees without the slit.
tuvwfg(0_02, 45_01)=!"}~*6mn
the
the
the
the
;fg
oS!"QS9~YZ-.6 1 3
4R/*(45_01"0_01 3%1)"
®~¢´sp*FF:;<"m6}~*fg(60_01"70_01)
=!"0%123%1
6ÄÌÍ9:s"ä1YZ
ïq
6U+
;
- 108 -
*6
à 4-11. ¦ § [@ í îY Z
ï: Í!r1|y+FW*
Ä8*
6É<
;
Fig. 4-11. Cumulative number-mass distributions of fragments ejected at a reconstructed vertical impact: the
all fragments include those, which belong to neither early fragments nor late fragments.
5
+ÉsÍfg="0%1YZ
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1®~¢F*O="#!-0.23 /+-0.55 9:;5!"3-31 R>?
spall ÚíîYZ
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16 spall /+)2xSstn9:;<"5®~¢!
d³uv<9"YZ*GH=F¿J*6Ks+
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YZ}~*GH=!0%1YZ
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F"YZR5 1 3*;spall 2!p®~¢y6}~
9"YZ6GH=!"ÍkYZ
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j2"N/+´sYZ
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3%1®~¢O;<"fg¬ 0_06 *+,¦§[@=!"
¢6¯*GH9{*)y63"bcn}~*6|/*7~2"
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- 109 -
*66U+
;
YZ}~*GH=!"spall 6z2{|:s"YZGH=!
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oBfg=>?
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BfgV">?
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ïq
;<"Takagi et al. (1984)!""
YZ
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4+
®;à. 4-12(a) Takagi et al. (1984)=´s+
ª9>?/+´s+
+
52
YZ
ï"(b)L©
fg¬ 0_04 YZ
ï;L©ª9>?
YZ
ï=F"N[Q
al. (1984)®+
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YZ
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3 GH6^;Takagi
+Bfgø!Å¢:6"#9
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¢6Å"/q
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*6!~UF
R!xV"*/
9"0_04 YZ
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6U¼z*;
5
+YZ
ï!"¢¯*YZ}~*GH(GH I)=!"{
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!"
GH6e³9:52÷ø9:2E+
(Melosh et al., 1992);<">fg=!5x*}~*
6
//R!"å<=Jfn9:"L©ª=
F"0.1 g jbcn}~*6 20 å
fg(0_05"0_06)2"¯*
fg(0_07 *|)6^;fg=5GH I 6¤
n5
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+}~*6Åfg=9:;
GH II !bcn*+/*7~;à 4-12(a)R Takagi +fg=4
®~¢!-0.23 9:R"L©ª9>?/++
/++
F!-0.62"NO
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®~¢!"äfg= spall /+*0%1R´s+
;
GH III =!"YZ
ï7~![,{*"Takagi +fg9!-0.53"L©
ª>?/+!-0.86"NO/+!-0.96 /+-1.55 O;L©ª+
H III 9®~¢!"Takagi et al. (1984)
G
-0.5 /+-0.6 "Kato et al. (1995)
+
-0.7 /+-0.9 2c®2/*}~*7~2*;5
#
*¤R"5bg*g2YZ
ï®~¢
s® Kun and Herrmann (2005)®+
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YZ
ï=4"GH III SGH®~¢!"äfg=@AB/
- 110 -
+*3%1R´s+
<!5
y**
;
(a)
(b)
à 4-12. >?YZíîå¢
ï: (a) Takagi et al. (1984)/+bR"
B
YZ
ï (b) fg¬ 0_04 =>?
}!"/+
xy¹}F
YZ
ï;¹
;
Fig. 4-12. Fragment mass-cumulative number distributions for collected fragments: (a) quoted from Takagi et al.
(1984), impact disruption experiment at low impact velocity range. (b) mass-No. distribution of collected fragments
in experimental run No. 0_04The largest fragment means the one ejected from the crater.
íîYZ
ï=4GH II 2GH III ®~¢c®2"#GH III ®~
¢yµ6}~*;5
!"spall 2@AB]B/ ^$
¡¢F9:78°6:;Kadono et al. (1997)!"£Þt¤o
*+,BfgV">?RYZ
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xy"F2¤¤¥2¥¥\ÉP]2
/ ^®~¢6"-0.1 /+-0.3 9:R"¦fg2RV"
tðBfg=
¤+
£Þ
3 / YZ
ï®~¢!-0.5 9:"
FF}~*R;Åstrom et al. (2005)!"
- 111 -
+
FF}~*R;Åstrom et al. (2005)!"
Þv§¨¨w52"YZ
ï®~¢"2 / n
*BF"3 / n*BF#
9
R"-0.5"-0.7 2R;
spall !vw¤¥h
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vw¤¥ÉP9:"5
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I
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spall YZ
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1.55 yzx6}~2xLfgø!"kn*!Ò*F Kadono et al.
(1997) Åstrom et al. (2005)®2stn9:;
4-2-3. ]^fg"_`a2bc
L©ª9+
"=
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4-2-3-1. Ò*vw·=42
1ST
L©ª9´s+
"m2"°V©ª
F2bcà.
4-13 ;Gault et al. (1963)fgFL©ª
³´fgø22Fà. 4-13 (a)"Cintala et al. (1999)µo=4
à. 4-13 (b)"Onose et al. (1998)B
à. 4-13(c);Lfg=4 2 >fgø/+i
¦§[@`
\vwF"bcsà. 4-13 (d);
Gault et al. (1963)ofg=
L©ª³´fg=PQ
"
`¶Fà. 4-13(a);Gault et
al. (1963)=!"·a¸¹º»¼k 6.1 km/sec 99:R"L©ª
³´fg=!"½Â¾»¼k 4.2 km/sec 99:"¿À!Ñ
Ò*6"Áµ2Fo9:52"tÂaÃ6J)R*5
2/+"Áµ2FÄÅV"#&`<<R;Gault et al. (1963)!"
- 112 -
(a)
(b)
(c)
à 4-13.
"5
(d)
2m : m!vw¤¥Æxµ¶ 0
2§Çµ¶ 90 2;(a) =
: Gault et al. (1963)oGH"L©ª³´fgGH(½Â¾ð"4.2 km/sec)
(b) Cintala et al. (1999)µ
(c) 4.2 km/sec 9B (Onose et al. 1998) (d) ¦§[@(à. 3-26)[È
Fig. 4-13. Ejection velocity and angle of fragments: 0 degree and 90 degree in the ejection angle mean directions
parallel and perpendicular to the target’s surface. (a) Impact cratering on basalt targets: empirical data from Gault et
al. (1963) are quoted with ones obtained in my preliminary experiment (Nylon-Basalt impact at 4.2 km/sec). (b)
Impact cratering on a sand target quoted from Cintala (1999). (c) Impact disruption of a gypsum target at 4.2 km/sec,
(d) reconstructed data-set of fragments ejected at one vertical impact cratering on gypsum at 4.2 km/sec
- 113 -
=
!"É$%o"m9
jet 6:"#
3"{m6}~*3m 45 4pqr6:"¹3
[,m6}~*¨6U+
9"QS
2R;Ê+fg!ËáRF
xy¹FF9F5 100 m/sec 9:;#59L©ª9
QSVGH9¶s®s"³´fgV
#`¶;³´fgs"ARvwºµl6Ì4R<
"¦¿¿À6ÄÍ
Rs"T78*`¢!¯*6"L³´fg=
+
`xyoF2"Gault et al. (1963)GH`2!s
tn*R;
5
+
+fg=Q
#
1. 9!U+
2bc2"j526
2"L©ª9
;
o"m jet S6"L©ª¦§
=!"N/+F"Qη 2 /PQ
/+FJK
*/;5
!"Love et al. (1993)=4£ÞtUÃÏko
fg="jet 6JK
=4vwÐÑf·^°6
*/522stn9:"jet %&
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=!"¦§hiFvw2»¼k;Q/+vw
¤¥Ó
2E+
jet 6JK
="vwõ÷øR!Sn9:
;
2. jet b~GH=U+
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m9pqr!""·Áµ=JK
r6Q
b~
;R"pq
!"hi6 200 /+ 800 m/sec 9:R"
hi! 20 /+ 80 m/sec 9:"hi=!6 1 3;=
!"mF526Ks+
;=Q
0%19:"spall 2
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"5GH!
9"5GHR!
spall ÔÉÚ 4-2-3-2 ®;
3. pqrµ¶3"Gault et al. (1963)9!m6ÔÕ7¶6U+
57¶!L©ª+
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:R"=Õ
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3%1
¢!F2c®<<=¯*;R6"!~2R52®
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5x"2vwfg=!"
- 114 -
Dm6Ks+
2x,Q6Ks+
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;#59"*|
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3%12;
Cintala et al. (1999)9µ 1.9 km/sec ¦§(run No. 4207, Al sphere, 4.76 mm in
diameter)=4ßÞvÛÜÝü+
2m
à. 4-13 (b)R;Cintala et al. (1999)=!()PQ!V"
6}~*
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6"m! 45 D
jet F"6vw¤¥2
*;Gault et al. (1968)=!"µ· 6
km/sec 9fg6V"
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º
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;R/R"#µ¶!"«+!6 45 2RF9:"
9z½()=JK
"vw¤¥¦§*µ¶·
2!Ò*R;£ÞtU÷¨"
vwµ/+ÝüR"áWâ¨ãäaå+52"¨
PQRfg Anderson et al. (2004)6Ô+
6"Êæ+º
fg=F
vw¤¥R¦§*µ¶·!Ks+
*;j/+"µ·
=!""·=U+
"G
Hm!*;
à 4-13 (c)! Onose et al. (1998)vw 4.2 km/sec B
-m
ï;0%1SGH"
/+ 2.5 msec jk
6Q
;vw¤¥/+
spall F"N=JK5269~;R6"B=F0
%1!^2Rç;
bcn}~*6âèé¡R3!"vwkhl%6"
vwI4¥/+]^
52*"z½ê£¨6Q
;Bfg=F"6 12 m/sec j"m6 75 j3%
12GH·6Ks+
!
;R/R*6+"=
Í:s3%1Îi6 60 %R"5Bfg=
5GH
Îi! 7 %¼z*;5fg!"F2F2!
=4 20 m/sec jPQ52án2RF9:9"Q¿
À!L©ª
z/fg2ÛLn!º9:;6 1 /+ 3
m/sec m!"=!vw¤¥¦§*µ¶6®9:
6"B=!i¶~"vw¤¥2}~*m**
- 115 -
µ¶
¢zx6Å*;R6"B=3%
1!Ks+
*2E+
;
Gault et al. (1963)!"=
+
-.!"µ#
2!Í6Ò*526®+
U
;L©ª=
F"Ù<9:229!()!Ò*F"
Dxm6Ks+
*|,Q6Ks+
;ºµ9"µök
=!"Gault et al. (1963)j¾V"
©ªFÉs"^©ªU
³=!"Dxm!Ks+
*/;55
2!"vw¤¥¦§*µ¶·9:3%1eë!"vw6Ù
<9:/k9:/^R52R;<"B=!3
%16Q9~*52/+"3%1!vw6B
/69:526
/
;
4-2-3-2. 0%1-.2 spall _`a2bc
Melosh (1984)"Melosh (1989)®+
=
spall
-.!"$%&'26:52"2YZ
6:526Ô+
(1-2-3-2);5M9!"L©ª=PQ
0%1-.6 spall #
"
2ìíR*52;
spall !"vw¤¥/+î Deq ïQ
æç r0 Hi Pcore
öHð/+vwkhñòfó9ñòR*6+ôõö÷6"vw¤¥9
ãä
52"öHð/+ r 9:Q="ö÷¥§39¨
upt(r)5 2 ! vspall 9"vw¤¥ÉP6
1989);öHð/+ r 9:QHi Pt(r)!0(4-1-31)9¤
r
Pt (r ) = Pcore 0
r
F9:(Melosh,
;
β
(r>r0)
(4-1-31)
(4-1-31)øù"Hi:+" Rankine-Hugoniot µ40(4-1-8)2¨ upt(r)2ö÷
Ut +S¢ Ct"st ¤(2-1-2)úû2" r 9ö÷k9¨
upt(r)!"0(4-2-2)9¤
;
U t = C t + s t u pt (r )
ρ 0t u pt
(r )(C
t
+ s t u pt
(2-1-2)
(r ))= P
r0
core
r
β
(r>r0)
(4-2-2)
52~ü0t !HÓI4Ævwõ9:;ö÷vw¤¥2¦§*
6vw¤¥=ãä
A spall 6
9"ýC
!¨xyvw¤¥¦§*
Ú9:;R6"spall vspall !¨ 2 !þwavw¤¥¦§*
öR2E+
- 116 -
;
v spall = 2u pt (r )
1
s
1+
D
eq
(4-2-3)
2
r = s 2 + Deq2
L©ª=V"
(4-2-4)
4.2 km/sec ¦§vwk%&RHi!"4-
1-3 14 GPa 9:;öHðÚ»¼kæç 0.6 /+ 1.2 !9:2S2 2.2 /
+ 4.3 mm 2*"52~ñòf!"@ABGHu=4Hi 12 MPa 2
'2~"4-1-4 #
I
3.2"4.8 2*;ö÷S¢ Ct"st Simakov et al. (1974)
2490"1.70 2=~"%î Deq 6vwA¥/+, 12.5 mm 9:2S
R("$%&'2à. 4-14 ;
à 4-14. 0%12 spall $%&'2: 3 / !tuvwD~
vwQSRF2"2 WXÞQSRF6É<
Melosh (1989)_`aR6"L©ª9+
;2f+!
"î 12.5 mm"%&Hi 14 GPa"
öHðæç 2.2"4.3 mm"ñòf 3.2"4.8 úûRF;
Fig. 4-14. Initial positions and ejection velocities of early fragments: 3-D velocities were measured both with the
target box having the slit and with two cameras. Black and blue lines represent velocity of spalled fragments from
each given initial position, which was calculated using Melosh (1989). The equivalent center of burst was set 12.5
mm in depth, and the pressure of the isobaric core was set 14 GPa, as measured and estimated in this study. Radii of
the isobaric core were assumed to be 2.2 and 4.3 mm, and they result in attenuation ratio as 3.2 and 4.8, respectively.
- 117 -
0%1W¢!"3%1#
F¯*"<"$%&'
6 20 mm j9:¢!2fgD~o10 å9:9"L©ª9V"
3.5 km/sec /+ 4.6 km/sec 9¦§fgÍ=+
0%1
`
È:;tuvw"< 2 WXÞ 3 / +
FQ9(0_01, 0_02, 0_04)"1 WXÞ 2 / PQRF
Q9R(0_04(C/*/F),
ÉP), 0_06);L©ª+
®2"Lfg+
0_05(oWXÞ Shimazu HPV-1 9Ýü
ä Melosh (1989)0úûR´s+
!"«+~6}~F"5
*+2c
2stn9:;
<"Melosh (1989)"/+ r =
spall ls !"
vspall"»¼k§ç Dproj"vwbg Tt"vwõ2÷
ü0t"cLt jx¤
l s ρ 0t v spall = Tt
øù!
D proj
;
(r>r0)
c Lt
(4-2-5)
spall Z"ù!5
C+
ií¤R;spall
Polansky and Ahrens (1990)Âo9%&R spall ôb2
1: 1: 0.2 §µk2S2"spall YZ mspall ! 0.2ü0tls3 9:"5
"È2"spall 2YZjx*6)2E+
2(4-2-5)i
;
1
vspall
D proj 0.2 3 − 13
mspall
= Tt
cLt ρ 02t
(4-2-6)
L©ª=4" 4 km/sec D9¦§fg=
QS
Í0%1W2YZà 4-15 ¤;3 / PQRm9"2 / ÚO
q9¤;<"N¥
2>?C6D~"YZfAQS5269~!"R
Q9¤R:;ÝÞßÍkRYZ6ÔÕ
6JK
6R¨
;YZ20(4-2-7)*+,;
k
v spall ∝ m spall
(4-2-7)
Í k !-0.26 9:"YZ6fQ
;5
+!\ Melosh (1984)8n´s+
FÚR!-0.29 2*
-1/3 6"`Q«
+~6}~"/7~y6s"¢ R !#
I
0.180.23 9:
;
#59"YZ[SÊË6}~ 1 mg j"2 !è2YZU
ûéê´s6à. 4-16 9:;46 mg 2U=4"
ñ¯!"ü¥í/+YZ´sAV`a(ý
b~c«RFG
78°6:;5
+éêR0(4-2-7)9*+,V
x2"#!-0.26l0.04 2*"#¢ R ! 0.94 2*;YZS2
- 118 -
ç 60 mg jR"Uãéê*+,2#7~!-0.43
9"¢ R ! 0.99 2*;
à 4-15. 0%1 -Y
YZ : 3 / +
9¤;N¥2>?C64+
Fm9"2 / +
F
FR9"ü¥í/+[S
F
+9¤;
Fig. 4-15. Mass-velocity relation of early fragments: triangles and circles represent fragments those 3-D and 2-D
velocities were measured, respectively. Open and closed symbols represent ones those masses were measured and
estimated, respectively.
YZ[S6Ö×9:52"<`ê«+~6}~52/+"`
µ"7~ k !-0.26 /+-0.43 -.96"5
(1984)9´s+
+!"Melosh
-1/3 2R
ïR="
ìí2!*;
<"
Nakamura and
Fujiwara (1991)oBfg´s+
-0.34 2Fstn9:;
jL©ª=40%1`!"Melosh (1984)
spall -."$%&'26:52"2YZ6:
52Áµ2stn9:"5fF<0%16 spall 9:52};
- 119 -
à 4-16. YZUãéêRYZ-
ï
Fig. 4-16. Mass-velocity relation of averaged fragments for each fragment mass bin.
4-2-3-3. 3%12 Z-_`a2bc
µ*|k=
#
9
2"*|Ù<
F29!LYnÒ*52 4-2-3-1 9®;R/R"5 Z-_
`a!"]^8="kí}h
¿D4
º_`a2R&'R9"
s"Lfg+
3%12bcd
!V;
µ*|k=4"+h¤s"Z_`a6ç+
;5
!"1-2-3-3 ®"Maxwell(1977)#+
¦
§=4"+_`a9:"$. vwkh9Y
"!<HÓ"2. vw¤¥/+
Y!Ñ%&R*"3. ï9¨
ÛQ2絶
UR !/+ R"ä"'"
(¢((t)=,®~¢ Z 0(4-2-8)9C+
g¤
;2xSF2
)(à. 4-17 (a));
UR =
α (t )
RZ
(4-2-8)
®~¢ Z !":+";Z 6}~*2"+*fæç6
*"vw¤¥9
()m!}~*;Maxwell (1977)9!vw2
¦§µ¶Z*^R"iüBëâ2xS9"
- 120 -
=¹Fp* Z ! 2.7 9:2R;<"Maxwell (1977)!ä"'6<HÓ°9
:"((t)*+, Z 6S¢9:"6vw¤¥:2S2"
vw¤¥9+§µ¶
uV",鵶
uH"*+,vw¤¥/+
mìe !jx*9¤
2R;
α (t )
sZ
(4-2-9)
u H = (Z − 2 )uV
(4-2-10)
tan θ e = Z − 2
(4-2-11)
uV =
(a)
(b)
_`a -0à.(a) Maxwell (1977)ÛÜ6vw¤¥:Vu/½
à 4-17. Z-_
a Z-_`a
(b) Croft (1980)Ú
"shi Z-_`a(R"Croft L0
àsî}~R:)
Fig. 4-17 Schematic figures of Z-model: (a) Original type of Z-model whose explosive center was set on the
surface. (b) Z-model modified by Croft (1980) whose explosive center was buried. Its buried depth was a little larger
than the one in Croft (1980).
- 121 -
tuvwD~vw 3 / PQR"fg¬ 0_02 =4
3%1R"åvw¤¥/+mF2"0(4-2-11)
Z PîR6à. 4-18 (a)9:;3%1m!vw¤¥2¦
§*µ¶"R6"´s+
Z !"µp* 2.7 2c®"1/
}~*R;
62s+
hiR Z-_`aÚR(à. 4-17(b))"5
î6}~z|")m6}~*52R6 Croft (1980)9:;R/R
*6+"5 Croft(1980)VÚ6pC9~!"î6æç
0.03 jhiRÚ9:;Anderson et al. (2004)
x"Z=3 ¿À
9F"î}~2"Z-_`a9!"¶/x"
³QRR<
x52*;
(a)
(b)
à 4-18. ä $%&'2 m/+´s Z : fg¬ 0_02 `;(a) 6vw¤¥:2SRhi (b) 6vw¤¥/+ 12 mm î:2
SRhi
Fig. 4-18. Initial position and Z of each fragment estimated from its ejection angle: fragments’ data are obtained
by empirical run No. 0_02. (a) an explosive center is set on the target’s surface, (b) an explosive center is buried 12
mm from the target’s surface.
- 122 -
&'69
2hi"mìe ! Z 2/+&'Um3
(4-2-12)x44;<"5
p2m2î/+ Z ´s526Ï(4-2-13);
tan ∆
− tan 2 ∆ + (Z − 2)
tan θ e = cos ∆
1
− tan ∆( Z − 1)
cos ∆
Z=
(4-2-12)
tan θ e (1 + cos ∆ tan ∆ )− tan ∆ + cos ∆ tan 2 ∆ + 2 cos ∆
cos ∆(tan θ e tan ∆ + 1)
(4-2-13)
%6î 12 mm :2SR("åm/+³Q
Z "
0(4-2-13)´sFà. 4-18 (b);Z ê! Maxwell (1977)6µ
2RR 2.7 Oºµ"748 å 137 åR"Z STH/+
2 j6î
;
î2 Z È("+">?"*+,
þwaà. 4-19 ;6 12 mm 2~"Z=2.2 22fAþw
a2"³Q
"+¶~6stn*6"Z-_`a6³Q"h/+
6
ùh/+#
F39*5!"fA9!U+
*/;+""+67îF"fA>?æ
¼z*;Z
}~R"î}~R
al. (2004)
¶/x"
6"Anderson et
x"5x*Él*¿À=!"Z-_`a/+
6³Q
52*"Z-_`apC-.9:52R;
5"L©ª9´s+
:;5
«î676+
3%1 Z-_`a¿D4!ë6
!"Z-_`a6"#F#F<HÓ°"k,6)hi_`a9:
R"Lfg9vw!Hõ÷øgI4Ùk9:52¡¢28
"
;<"µ=!"§ç»¼k§
çÎi! 3 %9:"Q«
6"L©ª9
oHGHQ92S526789:
pit §ç»¼k§çÎi! 26 %9:"
oHGH"F!Q92RS9~*52F
28"
- 123 -
;
(a)
(b)
(c)
à 4-19. Z-_
_`a/+´s+
"+"2"fg/++
>?"þ
w a b c : >?"*+,þwa!fg¬ 0_02 F;ôvw
¤¥/+î"ô/+O; (a) Deq = 12"Z = 2.2, (b) Deq = 12"Z = 8, (c)
Deq = 20"Z = 2.5.
Fig. 4-19. Streamlines and ejection velocities estimated from Z-model and the outline of the crater and
fragments’ velocity vectors obtained by the experiment run No. 0_02: vertical and horizontal axes represent
depth from the target’s surface and distance from the center of the pit, respectively. (a) Deq = 12"Z = 2.2, (b) Deq = 12"
Z = 8, (c) Deq = 20"Z = 2.5.
- 124 -
4-3. !(4-3-1)"#$%&'(!
)*+$,-./0123456789:;<!(4-3-2)=
$>?:@ABC"#DE 5 msec DE 50 msec $F.GH$I:@J
K-.(4-3-3)L
4-3-1. MN$O:@PQ0/0RS$T.U: pit VWDEXY
Z[\C"#DE 5 msec ]^$/0123_`abcde$12 m/sec ]f
gh.iT&j_klCbm 2 mm ]fT.(3-4-2-24-2-1)Lno
pqab"#$O:@.rs!0/0t23$O\.uvw
ghxyzii${. 4-20 $|-L$}-.
{ 4-20. uvwgh: spall ~DE spall iL2
ghC:LEarly gh HPV-1 iL
Fig. 4-20. Initial positions and ejection velocities of fragments: spall fragments means those were recognized as
spalled ones from the shape of its silhouettes. This group includes fragments measured in two dimensionally. Early
fragments contain those measured with hyper-velocity camera, HPV-1.
- 125 -
PQ0/0RS$T. pit(m 13 mm)DE6gh@:.CE
.Lvwgh$EI:ix5C|.z
$,!@uvw"#RS-. 1C 5.8 mm VW$ R!
@O&jghi 1 DE 5 m/sec ¡:VW$ R!@:.L2
gh¢!
£@¤: spall R$¥D\=¦§¨©ª.iC«¬-.LGray
@:.iz$i$i®@nEcD¯
T&°"#!±²5CT.i={³c:Cgh 2
´¯i$O:@µ¶DET.:µ¶$eD¯@iCn@:.L
{ 4-21. rs pqab"#$%& .·¸¹ghº»: =rsic¯
$O\.¼½¾2pixel %&¿¿T.LÀÁÂÃgh HPV-1 $O:@
¼ÄC'(-.VWÅÆÂÃgh E-2 $O\.¼ÄC'(-.VWT
.LzÇÈDEÉ!·¸$ 0.35 ʧÇÈDE
É!ËÈ$Ìh 1.3 g/cm3 ʧiT.Í$}-.¼½¾$ÎC(§.L
Fig. 4-21. Mass-velocity relation of fragments listed in reconstructed data set simulating all fragment ejected
in one vertical impact: fragments smaller than 2 pixel shows a decrease in mass-cumulative number distribution
which represents detestability of fragments fall here. Blue, green, and red hatching means detect ional limit of the
hyper-velocity video camera(HPV-1), the high-speed video camera(E-2) for early and late fragments respectively.
The mass of early and late fragments obtained by multiplying 0.35 and 1300/920, respectively.
- 126 -
Ï:@·¸ghxy$I:@JÐ.({. 4-21)L==iz
·¸gh$xC¥E.C¤£@ÑD:VW$ R!
@O&$O:@¼ÒÓcVW$O:@gh·¸$xy¥Ec:L
Ç 4 pixel %&iÔ:iC_klT&=%ÕcÖ×ØVW
·¸ÙÚhC£c.(3-4-1-3Table IX)L¼ÛÜCf!Ý.C
ÇÈÞßàC 2 pixel %&Ô:Ö×ØVWT.-.{. 4-21 $O\.
Âú¼ÛÜCáân·¸ÙCãä$åæ$c¯@:.VW|!
@:.Lç!=EÑD:ij_klCèé]êë@O&g
hì.$íºcîïCðE@:.L
(a)
(b)
(c)
{ 4-22. ghñò: ghó$ºô!L(a) ab"#pqºrs0/0t23
(b) ö÷ 0_02 (c) ö÷ 0_21
Fig. 4-22. Histogram of ejection time bin: (a) reconstructed data set made by one vertical impact. (b) 0_02, (c)
0_21
- 127 -
njÇÈøSC/0123ùÇDEú.ABC¤:=$%¯@
i
û\E.L{ 4-22 $ABüýó$òcEþ$gh
s|!Lab"#rs$!:ghcEþ$gh9:@
ghCn.¼zòC°@$
£c¯@:.L@ab"#$O:@ghC 10 m/sec ]fj:o
iC 5 msec DE 40 msec 6¤:AB$@O&
=à/0123 18 cm
2 g 2200 m/sec !à 0.16 msec 30 DE 300 $®-.Ln
6z:AB$.jghi6g:$,!6¤:AB$
.jghi6¤£c¯@:.Lab"#rsö÷ 0_02 AB
:$û:@ö÷ 0_02 $O:@Slit û/0123R$O\./0
123vwCo@:=C|@:.(Appendix D)L
ghüýó$òì.
{. 4-23 $ghC 2 m/sec DE 4 m/sec
vw$0PIL=gh$O:@¨ëÃ$O\.
vwEI%&ìghÎÞß-.gh 4 %T.L2
39:$O:@¤:C23$%&Ý.j
uvwPQ0/0-.0.9 m/sec %&i¤: !T.ghC 2 m/sec
DE 1 m/sec VW$O\.ò"³#$$%&-.ic:JÐE.Ln
gh:VW$O\.¼'"³CÝn.gh=R(i#$):i
20 m/sec T&gh!:à 12 m/sec T.=E*
[\@:.ÒÓ5i:JÐE.LÔc+,Ë9: 0_21 $O\.ghº
»ËCbm 7 mm -×.ý/9:$,!@¿¿ghg:VW$«¬-.0e
CT.CË!@EIi:nö÷ 0_21 q1/0123C2
I$ô@:PQ0/0sZ3¾$T.4T.=DE¯&!56
ð.$0/7C8n.L
{ 4-23. ghò: 0_010_020_06 bm 7 mm -×.ý/+,Ë$%.
"#0_21 Ôc+,Ë$%."#T.L
Fig. 4-23. Ejection velocity and number of late fragments: in empirical run No. 0_01, 0_02, and 0_06, nylon
spheres, 7 mm in diameter, were employed as projectiles. In the empirical run No. 0_21, a polycarbonate sabot shot
the target.
- 128 -
4-3-2. /012345678
XYZVWDE/0123ùÇabde9ghZ-
:;«$%&<=-.=åæT.(4-2-3-3)Ln4-2-3-1 i
$>C?.@¿clA¯B&ChI/012
3$,-."#PQ0/0s$O:@¢T.LA¯B&Chc:DË/0123
(EFü0Øcl)$,-."#PQ0/0s¿PQ0/0$®-.ºCGò
$ºú!@!nÕZ$O:@>-.=HcD
¯L!C¯@$I!@PQ0/0J$«¬-."#
icOA¯B&ChK-./0123L·«¬CøMcNôO!@:.=CC£|
.Lj=Onose and Fujiwara (2006a)|!$/0123A¯B&C
hK-.ºC"#$%&'(!)*+$,!456$78-.=$%&C
P!Q!=¼R-.L"#PQ0/0sA$=C45
6ST!ÒÓ5$I:@Dence (2004)$%.-Ubm 52 km Charelevoix PQ0
/0?$O:@i|@:.LnKadono et al. (2005)$O:@igh"#Z
$O:@456C¥E.=CïV@:.L
4-3-2-1. WM
"#PQ0/0s/0123YÇ$PQ0/0J/0123)Ì
VW¿XYZVWC¦SXY$ª&k:.ZC?K.LjXY
ZVW[\$>C.]dVW(3-1-2)$ò radial-crack C.¢T&
I$ crack ^¯@:._`6cVW][$O:@A¯B&7'$,!@i456$78
-.=CÒÓT.L$,-."#PQ0/0s$O:@C
.abcd6$e:fg{/0123YÇ{({. 3-5 rh){. 4-24 $|-L
=$O:@/0123XYZVWj[\ª&A¯B&
7'$,!@456$ijÕ=ÒÓc]dVW$ºô-.L=XYZVW
]dVW3¾k SF-Ç(the outer boundary of the shear-fractured region)lmLnË6$
=Ç{. 4-24 (a) ({. 3-5 rh)/0123YÇ$|.o:XYÇ-./p
pT.Lfg{(b)DE(d)$O:@qÁrÃeDXC SF-Ç|-L"#
$%&s"s+/0123R"t!cCEuv!SF-Ç$w¯A/
0123px)*ZChn"t!JÐE.Lno=)*+C SF-Ç$y-.
/0123]dVWmde[e$*¢zo¢{ÐE.i$=b|
-.Jde$}þzo¢C{ÐE.({. 4-24 (b))L)*+~Ïi$=Ezo¢
SF-Ç$[-.]dVW$È.L¿C@+C SF-Ç$w&=$F¯@:
)*7'Cª&E.SF-Ç$[-.]dVW$Èzo¢C456$q
-.
({. 4-24 (c))Lzo¢q
$!C¯@SF-ÇË$mdeeghC'(!=
~CXYZRuF&j\ùÇ$!$==DEXY
- 129 -
(a)
(b)
(c)
(d)
{ 4-24. Øfg{: (a) /0123YÇ$¥E.
ò({. 3-5 r
h) (b) SF-Ç9)*+y (c) )*+DE SF-Çû$ÐEzo¢q
(d) SF-Ç
~ùÇ9
Fig. 4-24. Schematic figure of an ejection mechanism of late fragments: (a) cross section of the crater and
definitions of variables. (b) input of the compressive wave on SF-surface (shear-fractured surface), (c) release from
the compaction wave and elastic rebound of the SF-surface, (d) ejection of late fragments
- 130 -
ZC!@ùÇ$:iDE$.({. 4-24 (d))P.LI/0123$O\. SF-ÇY/0123ùÇ$abcx$x!@,T
.SF-Ç$O:@'(!eghÕâ/0123ùÇabcsº][:$
â!!Õ=$c.L!C¯@!@?./01
23ùÇ$,!@_`abci$½E.=$c.L
$O:@no 4-3-1-2 SF-Ç$y-.)*+¥Èi&=+P.LÏ:@ 4-3-1-3 $O:@SF-Ç[$T./0123A¯B&Ch!º
/I½45Ë!= Green xò9:@
P!)*+4-3-1-3
-.L($4-3-1-2
! Green xò$y-.=$%&SF-ÇT&
ghcEþ$j~ÏAÉ!=MN$%¯@ðE5O-.(4-31-4)L
4-3-2-2. )*+
·L·9"#$%&'(-.I)*+Z)Ì$K½cAC
DD.$jâC& £c.@:.Ln+$¡Õ)'"³i¢
¿DT.JÐE@:.LÐ Bonnan et al. (1998)·£¤¥$,-. 201
m/sec DE 350 m/sec "#´: 5 mm ¦§¶Ç¨Ç)'cEþ$"
#¦§¨Çgh!L=$%&ÜC 9 %17 ©T.¦§¨
Ç"s+âC&$DD.Ajª 500«40 nsec380«20 nsec T.=
|!LnXu and Thadhani (2004)ÜC 50% Ni-Ti ¬!$,-.500 m/sec
DE 1000 m/sec "#´:¦§¶Ç¨Ç)'!L"#ghC 1000
m/sec 3 mm ¦§®a!"s+âC&A 40.5 nsec T&=
"#ÇâC&A¯ 6 $c¯@:.L
=%Õ$·°}¿±²$,-."#$x!@"s+âC&$³Mc
A$O\.´cïVCT.L!D!cCE;«MN$O:@"s+âC
&ACL·Ü"#ghcEþ$¦§:#$MN
³M.gh 4.2 km/sec "#$O:@s"s+CÜ 60©
µú 22 mm u-.
!£¶c¯@O&MNì@:.)*+·-.
$b=E9:.=åæT.L!D!cCEMN¸9!$O:@
i"s+C·L·uv-.=$%&6¹:âC&AIJÐ.
=;«MNº»!c:L
=%Õ$SF-Ç$y-.)*+Y 0.5 DEòµsec ]âC&A¡Õ=
C·¼.C$O:@=+!L=MN³M.)*+Y½$·-.=Cåæc+][YP-.=$%&
C¾¿$c.À\.T.L
)*+)' P1 /0123px)*ZCh$:!:P!L4-1-4 i|!
- 131 -
$L·ZCh$zo¢ghÁ«5CT.=CÂE@:.C==à 12
MPa 9:LnghcEþ$j~ÏA${Ð.)*+)'*Ã
Ä-.=C 1 Å:T.:Ô: !É´¯L
~ÏA t1 $x!@=nË6$ÃÄ-.=ãä$åæT.C³c£i+
,,bm"s+CÆ
-.$³McA@:àTÇÕJÐE.L
$O:@9:+,ËÌh 1146 kg/m3"s+ù-ò CÈsÈàOO 3945É1.171
T.(LASA Shock Hugoniot Data %&)L"#$O:@+,Ë$'(!)'g(4-1-28)
ù-=C.L
PHp = ρ 0 p (C p + s p u pp )⋅ u pp
(4-1-28)
== 4-1-3 %&-×.ý$,-. 4.2 km/sec "#$%&'(!)' 14.4GPa b
hT.+,ËDZgh uppcEþ$"s+gh Up OO 2200 m/sec
6500 m/sec ¥ÈiE.L!C¯@"#$%&'(!"s+C+,Ëbm 7.1 mm
Æ
-.$³McA 1.1Êsec bhT.Lj=SF-Ç$)*+CË9-.A t1 1Êsec cEþ$=C·uv-.=$%&A}àf-.
3Êsec10Êsec 9:@É´¯L=EàÉ$9:_Dòi$ Table
XVI $|-L
Table XVI Elastic response of the target to compressive wave
Material
Gypsum
Basic
Young's x0.
Modulus 1
x10
SF-radius /2
x1.5
Pressure x0.1
x10
Duration /3
x3
Basalt
Basic
radius
/2
Material properties
Size Compressive wave
SFSound Young's Poisson's
Pressure Duration
Lame's parameter
Density
radius
velocity modulus ratio
a
P1
cLt
E
t1
0t
t
kg/m3 m/sec
Pa
Pa
Pa
m
Pa
sec
Out put
Velocity Duration
vre_max t_0.1vremax
m/sec
sec
920
2200 4.0E+09
0.2
1.2E+09 1.9E+09 0.02 1.2E+07 3.0E-06
1.5
2.0E-05
920
696
4.0E+08
0.2
1.2E+08 1.9E+08 0.02 1.2E+07 3.0E-06
1.7
6.5E-05
920
920
920
920
920
920
920
6957
2200
2200
2200
2200
2200
2200
4.0E+10
4.0E+09
4.0E+09
4.0E+09
4.0E+09
4.0E+09
4.0E+09
0.2
0.2
0.2
0.2
0.2
0.2
0.2
1.2E+10 1.9E+10
1.2E+09 1.9E+09
1.2E+09 1.9E+09
1.2E+09 1.9E+09
1.2E+09 1.9E+09
1.2E+09 1.9E+09
1.2E+09 1.9E+09
3.0E-06
3.0E-06
3.0E-06
3.0E-06
3.0E-06
1.0E-06
1.0E-05
1.1
2.5
0.26
0.15
15
0.55
3.2
6.2E-06
1.0E-05
3.0E-05
2.0E-05
2.0E-05
1.8E-05
1.7E-05
2650
2650
5418 7.0E+10
5418 7.0E+10
0.2
0.2
2.2E+10 3.2E+10 0.02 1.6E+08 3.0E-06
2.2E+10 3.2E+10 0.01 1.6E+08 3.0E-06
5.5
7.7
8.0E-06
3.4E-06
0.02
0.01
0.03
0.02
0.02
0.02
0.02
1.2E+07
1.2E+07
3.0E+06
1.2E+06
1.2E+08
1.2E+07
1.2E+07
4-3-2-3. Green xò9:
ÌÍ(1962)ÎÏ(1957)i$Green xò9:45Ë/0123
ρ$F¯'$%&A%=
´ÕLGreen xò G(r, t; ρ, τ)T.ABτ$O:@pρ
.AB t r $O\.òÐ6$g!iT.L
- 132 -
[' f(r, t)Ë9-.Ñi~dbgvw rAB t v w(r, t)9:@g(4-3-1)
$ù.L
∂ 2 w(r , t )
2
= Ct ∇ 2 w(r , t )+ f (r , t )
2
∂t
(4-3-1)
==Ct gT&/0123ÒýÓÜ Et ÌhÔ0t 9:@g(4-3-2)ù.L
Ct =
Et
ρ 0t
(4-3-2)
:n3¾Ç S #$Cg(4-3-3)ùt = 0 g(4-3-4)Cs&â½]$O:
@ w 'Õ+ù|ª.i-.L==Φ(r, t)h1h2 (h1,h2>0)3¾#$ù-
òT.Lnh1 C 0 T.ÖHT.=h2 C 0 T.×T.
=ØÙ-.LÚ3¾Ç S $abT&[\e£ÛvdeÜP3T.L
h1w(r , t )+ h2
∂w(r , t )
= Φ (r , t )
∂ν
w(r , t ) = f (r ) ,
(4-3-3)
∂w(r , t )
= F (r )
∂t
(4-3-4)
pÝ$3¾ÇT. ! Green xò G(r, t; ρ, τ)ÖH$O\. Green xòT.Þ
Mß G0 3¾#$|-à3¾#$ G1 áù.LÖH-cFâ3¾Çc
:½$>:VW$O\. Green xò G0 âxò9:g(4-3-6)ÞMßT.L
∂ 2G0 (r , t; ρ ,τ )
− Ct2∇ 2G0 (r , t ; ρ ,τ ) = δ (r − ρ )δ (τ − t )
2
∂t
(4-3-6)
nà3¾#$ G1 g(4-3-7)!DI G = G0+ G1 C t = τ$O\.#$g(4-3-8)
O%þ3¾ S #$g(4-3-9)-%ÕcßT.L
∂ 2G1 (r , t; ρ ,τ )
− Ct2∇ 2G1 (r , t; ρ ,τ ) = 0
2
∂t
(4-3-7)
G (r , t ; ρ , τ ) = 0 ,
∂G (r , t ; ρ ,τ )
=0
∂t
(4-3-8)
h1G (r , t ; ρ ,τ )+ h2
∂G (r , t; ρ ,τ )
=0
∂ν
(4-3-9)
ãØAB t (t>τ)
vw r $O\.(r W) v w(r, t)
]#$- Green
xò G(r, t; ρ, τ)cEþ$[' f(r, t)9:@g(4-3-10)ù-=C.L
w(r , t ) = ∫∫ G (r , t ; ρ , τ )f (ρ , τ )dρdτ
(4-3-10)
$MN$O\.45Ë/0123Yj3¾#$
-.L$
O:@SF-Ç[\ª&¢45Ë!@ä.n:-.=CÒÓT./012
3]dVWRS$/I½Ë-.L=/RS/0123YÇ
DEìEåRS$jm SF-Çm 20 mm $jªpæ-.i-.L
- 133 -
I/0123½ËT&ÚÌcç6´Õ$/0123"#
´¯ÇCÖHT.=Jè-.³M5CT.L!D!cCEPQ0/0
!SF-Çm¯ 20 mm $,[email protected] mm 6U:vw$åRSC«¬-.=D
EnÛé==/0123ùÇ*ê-.Lëpì5p
j@:=CïV@:.(íî et al., 2003)SF-ÇëÇ!@
-.=$%&/0123ì5aÃÄ!@:.ÒÓ5CT.LnI/0
123$O:@SF-Ç\$XYZC«¬-.C$O:@/
\ÖHT.P!LcïcEXYZ[\ðËc¯=EX
YZ[\VWñ~
-.=ãä$åæçDET.L
/0123Y$x!@SF-Çm¢ò!SF-ÇT&ghj~Ï
A=$,-.Á«5ÃÄ!LTable XVI $-O&I$ 4.2 km/sec ab"#
$%&PQ0/0s/0123YÇ$¥E.XYZVW[JX
!Am 20 mm >!=C 1/2 T¯ !É!LnSF-Ç
[\$«¬-. radial-crack *JÐ%&[\Ç456S7JÐ.$m
C 30 mm T. !$x!@iÉ´¯L30 mm mde7'σr C 4-1-4 %Õ$"t-.Jde7'σθàCòó6A¯B&ZCh(¯ 1MPa)Ð
c£c.vw$:LSF-ÇmC 30 mm !AÉy-.)*+)'σr !
@ 3 MPa {ÐL
½Ë$\CÖHT./CT.
!=/RSô-.õö$O:
@/m a %&i:ãØm r (r > a)$O\.AB t v w(r, t)ÌÍ(1952)
%&g%Õ$ù-=C.L
Ct
r −a
r −a
t −
Ct
C a − a t − C
w(r , t ) = t e t
r
∫
0
Φ (τ )e
Ct
τ
a
dτ
(4-3-11)
Φ(τ)/\$F.[
==aCt jª SF-Çm
gT.LΦ
'TEF-3¾#$T&g(4-3-12)ù.L=nË6$ SF-Ç9)*+
yù!@:.L$O:@Ûé=)*+g(4-3-13)ù.+
!@P!L=ù9:.)*+7'C÷-.
÷-.
!¿)*+~ÏAC
!$+DEoC¥E.É´Õ"s+~ÏA 3 µsec n
!L
Φ (τ ) = −
∂w(r , t )
∂r
P1
Φ (τ ) = λ − 2µ
0
(4-3-12)
(0 < τ < t1 )
(4-3-13)
(τ ≤ 0, t1 ≤ τ )
==P1 t1 jª)*+)'~ÏAλµ Lame’s yòù-.Lg(4-3-13)Ⱥ-.ãØm r (r > a)$O\.AB t v w(r, t)gù
- 134 -
.L
0
C
r
Ct r
2
− t t + −1
t − +1
a P1
a a a a
w(r , t ) =
e
e
− 1
r (λ + 2 µ )
C
C
r
2
t
t
a P1 e − a t + a −1 e a t1 − 1
r (λ + 2 µ )
r−a
t ≤
Ct
r−a
r−a
<t <
+ t1 (4-3-14)
Ct
Ct
r−a
+ t1 ≤ t
Ct
g(4-3-14)AB t øùº-.=$%&w(r, t)ghCìE.L
0
C
r
− t t + −1
∂w(r , t ) aCt P1
e a a
=
∂t
r (λ + 2 µ )
C
C
r
aC P
− t t + −1 − t t1
t 1
a a
a
e
e
1
−
r (λ + 2 µ )
r−a
t ≤
C
t
r−a
r−a
<t <
+ t1
Ct
Ct
r−a
+ t1 ≤ t
Ct
(4-3-15)
$O:@³Mc SF-Çú~ghjvq
$³McAcr = a -.==vcEþ$ú~ghg(4-3-16)g(4-3-17)ù.L
0
C
− tt
aP1
a
−
w(a, t ) =
e
1
(λ + 2µ )
Ct
Ct
aP1 e a (t1 −t ) − e − a t
(λ + 2µ )
(t ≤ 0)
(0 < t < t1 )
(4-3-16)
(t1 ≤ t )
0
C
− tt
∂w(a, t ) Ct P1
e a
=
∂t
(λ + 2 µ )
C
C
CP
− t t − t t1
t 1
e a e a − 1
(λ + 2 µ )
(t ≤ 0 )
(0 < t < +t1 )
(t1 ≤ t )
g(4-3-14)RSDEµú r øùº-.g(4-3-18)c.L
- 135 -
(4-3-17)
0
a − Cat t + ar −1 a
∂w(r , t ) aP1
=
−
− 1e
∂r
+
r
2
r
r
λ
µ
(
)
a − Cat t + ar −1 Cat t1
aP1
1− e
e
− 1
r (λ + 2µ ) r
r−a
t ≤
C
t
r−a
r−a
<t <
+ t1
Ct
Ct
r−a
+ t1 ≤ t
Ct
(4-3-18)
=9:.mdecEþ$Jde7'σr (r, t)σθ(r, t)g(4-3-19)g(4-3-20)
ù.L
0
C
− t t
σ r (r , t ) =
2λ
a
−
−
−
P
1
1
e
1
+ 2µ
λ
(t < 0, t1 < t )
(0 ≤ t1 ≤ t )
0
C
− tt
σ θ (r , t )= P1
a
λ + 2 µ (λ + 2 µ )− 2(λ + µ ) e
(4-3-19)
(t < 0, t1 < t )
(0 ≤ t1 ≤ t )
(4-3-20)
/0123ÌhcEþ$û+
g$x!@¸9!i¦A$¦§µ
üËs!ý&ç!!i9:.L/0123Ìh 920«44 kg/m3
T&û+
g 2170«150 m/sec T¯LPoisson’s σpt 0.2 -.Òý
ÓÜg(4-3-21)9:@ì.=CÒÓT.L
Et =
(1 + ρ
0t
)(
)
Ct2 1 − 2 ρ 0t Ct2 σ pt
1 − ρ 0t C
2
t
(4-3-21)
nLame’s yòλµg(4-3-22)(4-3-23)ù.L
λ=
ρ 0t Ct2σ pt
(1 + σ ) (1 − 2σ )
(4-3-22)
ρ 0t Ct2
2(1 + σ pt )
(4-3-23)
pt
µ=
pt
$O:@SF-Ç~/0123L5Á«5JÐ.$I/0
123DEÌh
g9:@É!ÒýÓÜ Et = 4 x 109 >!= 0.1
10 $,!@É´¯Ln$pÝ6cþ@$O\.ÒýÓÜÌ
hpx)*Ch9:Éi´¯Lò@ Table XVI $-L
4-3-2-4. SF-ÇSTghj~ÏA
SF-Ç9)*+yDE=$,-./012345678$¡Õ SF-ÇghC?
- 136 -
gh@íº$Ô£c.nSF-ÇmÙú=Çú~g
h[\$eDÕde½!@{. 4-25 $|-L+ù)*+$%& SF-Ç$
[e7'CF.cd$O:@AB÷$¡:vC÷!==$zo¢CÈ
@:.=|-LnSF-Çgh[ej==$y-.)*+
Ch$Á«-.L+ù-$g(4-3-13)9:@:.)*+7'C÷-.
¿)*+~ÏAC÷-.
!
!$+DEoC¥E.LSF-ÇC)*+DE
.SF-ÇJ$ÐEzo¢q
CÝn&SF-ÇghdeIn
&RS$eDÕdec.LSF-ÇT&gh(à=C)*+DEß
àT&==DEÈzo¢q
i$Û"³! 0 $-.L
{ 4-25. SF-Ç
ÇvghA6Ùú
Fig. 4-25. Displacement and velocity of the SF-surface
MN$O:@SF-ÇT&gh(à vmax =C(à 1/10 n"t-.
$M-.Aτ0.1vmax £¥323ò!@9:LT&~ÏA SF-Çgh
Cj(à 0.1 $"t-.n!GHgh¯ 1 Å$
1n¯@:.DET.({. 4-23)LTable XVI $ñ#$$O\. vmax τ0.1vmax à{. 4-26
$|-Lno>c.u#$T.ÒýÓÜ 4 x 109Pa /0123$sbm
20 mm SF-Ç$Ch 12 MPa~ÏA 3 µsec )*+Cy!
!T&gh 1.5
m/sec T&ìEghá6T.LpdT&~ÏA
0.02 msec T&I$?.A¤cEþ$jEI$
.$Ô:àT.L
- 137 -
{ 4-26. SF-Ç
ÇT&gh(à=C(à 0.1 $c.nT&~ÏA: G $,-. 4.2 km/sec "#f!>c.u#$$,-.É5OLþ@$,-. 4.2 km/sec
"#f!u#$$O\.É5O B |-L
Fig. 4-26. Velocity and duration of the rebound of the SF-surface: G and B represent each result calculated to
simulate impact cratering on gypsum and basalt target at an velocity of 4.2 km/sec, respectively.
/0123ÒýÓÜC 1 ÅÔ£c¯ !~ÏAC¯ 3 c.LAi and Ahrens
(2004)"#$%&PQ0/0Cs/0123p 1cm dË$ýY!
´
g! `$%¯@
gC"#¶ 1/4 $c.=|!LAi and Ahrens (2004)
$O:@_`6c
gT&$O:@³M./0123
ËÒýÓÜT.c[±²T.CMN$O:@i"#Z$¡:/01
23ÒýÓÜCf!~ÏAC¿¿þÒÓ5c:L
SF-ÇmCº$c¯
!T&gh 1.7 $c&j~ÏA 0.5 $c
.L-cFâj°#$C¦§cE%&ÔcPQ0/0%&g:C:A
.=C|.L=Ôc+,Ë9:ö÷ 0_21 $O:@
gh
òº»$O\.(àC¿¿ghg:de$¯
@:.=({. 4-23)á6T.C=D.$c.0/ÈC³M
- 138 -
T.L
à$,!@ÒýÓÜC 18 )*ZChC 13 T.þ@$,-.bm 7 mm
-×.ý/ 4.2 km/sec "#f!u#${Ð.jT&gh 3.8 ~ÏA¯º$c¯LE$Gault et al. (1963)9:E 3 mm /$%.þ@
$,-."#$%&sPQ0/0¼!òy-.jgh 5.5 ~ÏA 1/10 $c¯L===þ@9"#PQ0/0s$O\
.ghC$O\.i%&i£nABi:=$á
6T.C=D.$c.0/ÈC³MT.L
)*+)'cEþ$~ÏAOi$gh$*{Ð.LÐ)*+Ch
C 10 $cT&ghi 10 $c&)*+ChC 1/10 $cgh
i 1/10 c.L!C¯@ÔC%& 1 Å)*Ch:·L·s
@:.P-.=$%&É.T&gh 0.15 m/sec c&
!@CÔË$r È-.=CÒÓ5T.LnSF-ÇmC
£c.T&ghCÔ£c.=DE"#PQ0/0sfC£c.$
ÔË$r È-.=.ô!C÷!%&ÛO6$Qs-.L
4-3-3. AB$x-.JK
4-3-3-1. ¨ëDE[!uUcEþ$uU
/0123ùÇDEC"#DE 5 msec DE 40 msec n~Ï.GH!@U:vwDE$¡Õi(4-3-3-1)·L·uv-."s+Õ
$¡Õi(4-3-2-2)SF-ÇT&$K½AC³MT.=(4-3-2-4)j!@ SF-Ç
(§T&~CRuF.$³McA(4-3-3-2)CJÐE.L
noÝ$U:vwDEgh.=$¡Õú~A¼-.L"#
DE¨ë$w.n$ø'¢C£iP!@
´¨ë
"#n[!=EuUìLghDE"#ABì
.=$¡Õgh¥Èi&o´0.3 msec T&=$¡Õuvw
Î 5 m/sec 1.5 mm1 m/sec 0.3 mm T&PQ0/0U 24 mm
.íº$Ô:L[$%&ðEà{. 4-27 $|-$$%.bh:
T.CPQ0/0U%&iU:VW$im=C|L=
ABCU:vwDEgh=$%.ú~A¢<=û\
Ec:=|!@:.L
- 139 -
{ 4-27. ¨ë%&[!@ì t=0 U
Fig. 4-27. Initial depth of fragments at t = 0, extrapolated from their trajectories
+,˶Ç$«¬!/0123L·C"#$I! 1
6$)Ì[\ù
vw-.iDE$
$
!$I:@JK-.L=/0123 1
6)Ì
4-1-1 {. 4-3 |!i¦)Ì{$O\.+,Ë!yUDEPQ0/0
[email protected]:i
ghig£n¦A$.®¯ghIiC:=DE({.
4-22)=Euvwjghüýó$
"c!@:.JÐ.=CÒÓ
T.L/0123YÇ´¯@:c:$O\.XYZVWcEþ$)Ì
[\VWU=ECPQ0/0U$4-.iP!@ìLn
ghüýóuvwgh´Õ=Õâ#ghüý$
}-.i·¸$4-.i!L=%Õ$!@ì#ghüýó$=
- 140 -
$}-.$,!@ìuUüýghüýñuU-.L
gh´Õ=C#¨ëghüýñuUn[!A
B#$,-.AB!#ghüýó$=ÞßìC Table XVII
T.LóEIT.C=)ÌJè!uUDEJÐ@i#
ghüý$}-.ghüýñuUDEú~Ý-.AB"#DE 1.5
msec DE 7 msec T.É/0123)ÌU:vwDE/0123ùÇnú
~A¢AB¤<=-.=c:L
/0123)Ì$DD.A$x!@$$!#$$O\.;«0/C
c£=Ñ$ÃÄ-.=%ÒÓT.L4-3-2-2 $|!±²¿°})Ì$O:
@"s+âC&A(i 0.5 µsec T&=àn
ÞßA@ 4 Å]iÔcàT.L
Table XVII Modified ejection time of fragments from the buried depth for each velocity bin
Initial depth bin
mm
Modified ejection time
msec
0_01
ve<0.6
0.6<ve<1.25
1.25<ve<2.5
2.5<ve<5
5<ve<10
10<ve<20
23.7
20.2
14.3
11.3
9.6
9.5
-
24.1
23.7
20.2
14.3
11.3
9.6
-17.4
5.2
6.5
4.0
2.6
1.6
30.5
13.9
6.8
1.9
1.6
1.2
ve<0.6
0.6<ve<1.25
1.25<ve<2.5
2.5<ve<5
5<ve<10
23.8
21.8
14.7
9.8
9.4
-
24.1
23.8
21.8
14.7
9.8
0.9
5.0
6.9
4.2
1.5
2.8
6.8
7.0
4.5
1.8
0_02
4-3-3-2. Ë
gAB¤
MN;<!$O:@SF-ÇÝn¯RS$eDÕ+
CXYZVW$«¬-.Rnu.³MCT.L=
$³McA56$ÃÄ!L
Teramoto et al. (2004)bm 40 µm DE 220 µm Fü0Ø
g&R!=
EC 92 m/sec DE 171 m/sec 'ÌcpÝ6cF
g 5 km/sec (!£:à|
-=nËR
g Cpowder fDm df $Á«-.=|!L)0/({. 428)g(4-3-2-4)Ã-.yòàαpowderβpowder jª0.3 O%þ 33 c.L
α
C powder = β powder d f powder
(4-3-24)
- 141 -
MN$O:@JK´¯@:.Teramoto et al. (2004)C
g!Ë
!@DmÜs!@:.L· 3 $O:@¶c&jnn[´Õ
=HåæT.CT£n*!@noDm$x!@JK´ÕLðE
Dm 1µm DE 10µm T&= Teramoto et al. (2004)C
g!F
ü0ØDm$ 1 Å]Ô:VW$T.Lg(4-3-24)$+:=Dm 3µm n[
-.j
g 46 m/sec T.L$s-.iL·
gC Teramoto et al.
(2004)9:EF(5 km/sec)$,!9: 2 km/sec T&Ô£c¯
@:.LË
g${Ð.iL·
g{$x!@nç,£FD¯@:c:C
=C4xy$T.P-.uv-.
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g 91 m/sec cEþ
$ 18 m/sec u-.P-.j`MAOO 0.3 msec cEþ$ 1.4 msec c.L
{ 4-28. Teramoto et al. (2004)$
$|Fü0ØDm-P
g
Fig. 4-28. Diameter of glass beads and bulk sound velocity employing data from Teramoto et al. (2004)
C/0123ùÇDE.n$DD.AÕâ 8 ô£C=
ECph)Ì[\/0123DET.=$%&<=û\E.L
Table XVII $|!.κABÕâ 0.3 DE 1.4 msec SF-Ç$O\.)*+$,
-.45678$¡ÕeghCXYZuv-.$³McA
xû\E.=C·.L$SF-Ç78$K½AC³MT.L4-3-2
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ÏA 0.02 msec T&~ÏA. 3 Å]Ô:Ccrack
$%./0123ÒýÓÜf¿SF-Ç45678Cuv-.I$$A
}.ÒÓ5Jè-.I~ÏA$?£ÒÓ5CT.Ln
SF-Çëp!=$%.Y$¡Õ/0123ì5aÃÄÒÓ5Jè
-.=âEiÉ~ÏA-de$£L
- 142 -
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300 m/sec)
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29 ij,o!ÏÐ-bwÑ&kØ8"#
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- 143 -
I-Ù
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!
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4-30 -ká%o8
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,A9
!NO䪽DÙåDA#V-J-æ
çèJ(%¸éêD!#V&ëT!V-ìíÇA9T!jî
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n
ǽ~-\»+½ÏÐâ)òA#VX!ó5-X
(p
9A!(I. 4-10)"
(a)
- 144 -
(b)
- 145 -
(c)
I 4-29. ij X(
Ï ÐVb wÑ: Rdeª½DÙôij,
A9°Þß
9A!j-ÀÁ¤¥X(Ó
÷øD
gÏÐù»úµ<T!/0
¶&JVj9õH8"iö$-
(a) 45 (¤¥üý 45_01-45_03-45_04)
(b) 60 (¤¥üý 60_01) (c) 70 (¤¥üý 70_01-70_02-70_03)
Fig. 4-29. Mass-velocity relations of fragments ejected in oblique impact cratering: some datasets from different
experiments shearing the same impact angle are combined, in order to increase number of data points in large mass
region. Hatched area represents those where detestability of fragment shows obvious decrease. (a) impacts at an
angle of 45 degrees (45_01, 45_03, 45_04), (b) an impact at an angle of 60 degrees (60_01), (c) impacts at an angle
of 70 degrees (70_01, 70_02, 70_03)
- 146 -
I 4-30. VÏÐ-b
bwÑ
Fig. 4-30. Impact angle dependence of mass-velocity relation of fragments
4-4-2. æ
pit $%4L-æ
V89þ=
4LVVA}+$8~
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- 147 -
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9,(-*VVp pit $%+$qDZ9A!#VVpwo
!
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I 4-31. æ
T!4LEFG
Fig. 4-31. Impact angle dependence of evacuated volume, which thought to be responsible to late fragments
ijX(
!æ
-,D!Ç<;5
66t!(I. 4-32)"#½-xy56U
-.õ>U
60 V½,A9p-
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- 148 -
ǽ+!j-#
I 4-32. æ
-.EFG: 0 45 60 3 56+-.
B¤¥+-.V 17&8
89õØ89A!"
Fig. 4-32. Impact angle dependence of the averaged ejection angle of late fragments: averaged data from impact
experiments at angles of 0, 45, and 60 degrees are shown. Data sets for the 0 degree’s impacts and 45 degrees’
impacts are shifted a little.
I 4-33. æ
b%ÒV: 9xy-: 60 Fig. 4-33. Impact angle dependence and ejection velocity of late fragments: red and blue lines represents number
of fragments ejected in each ejection velocity bin at a vertical impact and a 60-degrees’-impact, respectively.
xyD
g 60 +ijX!¦X(
æ
-
bzPkÙ&I. 4-33 H8";<Vp-y$ 7 mm =O>P?
X! 4.2 km/sec ++t(-1 m/sec U
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- 149 -
T!G&HÈ89A!"8U8D
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¤¥-ij+ 60_01 VqA234&aA 45_21 8UD-#&CDT!j
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4-4-3. NOä7T!ijVÂÃ
±¤¥X(Gj
¤¥X(Gj
-NO¦NOäEFG&-P
-CDZÂÃ,o!-NOäEFGVR
d8(Table XVIII)"Gault et al. (1973)-Moore et alQ(1965)R Comerford(1967)DÅfb
¦-pm-STU~VWU7T!ij,o!
ÏÐ Meject Dp -y$ Dc-.89y$RwT!XYZ&-234V[0p[0t -234
Ekp -\i MNOP.B]½QLVA}+õ8
"pV^,A9-õ>V-D56& 0 -xyD56& 90 VT!
NOPaA
9,(-õ_p cgs `+t!-±²³VaGj-##+
xy& 0 VT!-mks `+Øb8"
M eject = 10 −13.061
D p = 10
Dc = 10
− 5.450
− 4.823
ρ 0t
1.133
(cosϑi )
E kp
2
(4-4-1)
1
6
0p
1 0.357
0.66
E kp (cos ϑi )
ρ 0t
(4-4-2)
1
6
0p
1 0.370
0.86
E kp (cosϑi )
ρ 0t
(4-4-3)
ρ
ρ
ρ0p
Dc
0.2
= 10 0.617 E kp0.013 (cos ϑi )
Dp
(4-4-4)
2347T!R~-.ÂÃ{xyX(¦!
&234y$+cdÉ8p7T!-NOäEFG
&õTMNOP]½Q/É&-I. 4-34 H8"2347T!R
ª½D!Ç-t!A234y$7T!Rª½D!Ç4LEFG&õT]½ÑÙqD!6
!"##V
-7T!234ª½D!Å-NOäEF
- 150 -
GqD!#V&HÈ8 Burchell and Mackay (1998)¢£7T!¤¥¶Vv
·e+t!"#
¤¥,A9-2347T!eðGfA,A
9-4LEFGqA#V&HÈT!Vm!#Vp+t!"
8U8D
-fGg7T!ij¦¤¥ÙJàåD-#
¤¥-234VhD
8-b/0~ijø-
,o! spall kl6p.BCD!ÂÃ,o!¤¥¶&-mT!#
VÊË&T]½+t!"
Table XVIII Impact angle dependence and density ratio
Projectile
Target
Impact velocity
material density (g/cc) material density (g/cc)
km/sec
This study
Nylon
1.2
Gypsum
1
4.2
Gault (1973)
Al
2.8
Basalt
3
6.25
Grey (2002)
Al
2.8
ice
1
5.2
Onose (1995)
ice
0.92
ice
1
0.5
Vc
Dp/Dproj.
Ek1.0cos1.37i
Ek1.13cos2.0i
Ek1.2cos1.42i
Ek2.3cos2.6i
3.4
3.1
9
2
I 4-34. ÂÃX!-NOäEFG&HT]½ÑÙ/É
Fig. 4-34. Crater depth’s dependence on the impact angle and impact conditions
- 151 -
4-5. bkÏÐ%Ò
4-5-1. bVLWÏÐ
±¤¥b 4.2 km/sec &{|V8-¤qnop+bVËD!b
/0+¤¥+t!-234~V89qa8=O>P~NO.pqno
p+_r,A9steDÏ+DA"J-±¤¥X(¦
NOäy$ 10 cm +t(-¤qno:,o!Äâ)u!NOä
¦-D
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A"±^+HÈ9A!æ
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ÎÜxyX(
!¦-¤¥üý 0_01 V 0_05 &aAp(3-4-2-4)
V-¤¥üý 0_02-0_04 ,Xg 0_06 &aAp(ìí Appendix E &H)&1"
;¦,A9c\æ
LWÏÐ-0.58 g-2.8 g Vª½CD!-#
æ
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j->:U
ÏÐù»éê+t!#V+t!Vm
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£T!-%6Dpmp&KV8"
±²³,o!xy¤¥,A9bc\¦B8cÏÐ-4LU
ù»!ÏÐ 38 %U
50 %T!"¤¥üý 0_01-0_05 &aA¦
,A9-5 m/sec r<-1.25 m/sec r<b+
ÏÐ-bc\&}#
V+½ÏÐ.B 32 %-12 %T!"1õTV-
ÏÐ 21 %-10 %-æÏÐ 88 %-29 %-.B 5 m/sec r<1.25 m/sec r<b+
9A!#VD!(Table XIX)"
- 152 -
Table XIX Total mass of fragments ejected lower than the given ejection velocity in the
reconstructed vertical impact
all
ve<10 m/sec
ve <5 m/sec
ve <2.5 m/sec
ve <1.25 m/sec
late
g
0.59
0.58
0.52
0.4
0.17
early
g
4.62
3.15
0.99
0.47
0.44
gray
g
0.24
0.23
0.22
0.02
0.02
ij¦,A9[\cÏÐ4LU
cW
!ÏÐj!-xyX!pVd]qDZ9A!"#-I. 4-35
SH8 45 ¤¥Xwǽ &qa8phU
¦(C
Z9A!j-Rdeª½D spall [\ÙåDA#V-J- 60 ,A9 spall Ð4åDA#Vwo
- 153 -
!"
(a)
(b)
(c)
(d)
(e)
I 4-35. ¡ r <b +
LW ÏÐ: ©ª4LU
cW
ÏÐ+t!"T!ÏÐpX(¢UÇT!VA}£+
#I¤Ø8 (a) ¤¥üý 0_01 V 0_05 U
ý 0_02-0_04-.89 0_06 U
¦xyÎÜ%. (b) ¤¥ü
¦xyÎÜ%. (c) 45_01: 45 -
Xw½ qa. (d) 60_01: 60 -<6½. (e) 70_01: 70
.
Fig. 4-35. Cumulative mass of fragments ejected at a velocity lower than the given one. Vertical axes represent
the evacuated masses estimated from crater volumes. Parts of the evacuated mass corresponding to compaction are
also indicated. (a) reconstructed data set for one vertical impact employing data from 0_01 and 0_05. (b)
reconstructed dataset for one vertical impact employing data from 0_02, 0_04, and 0_06. (c) 45_01: impact
experiment at an angle of 45 degrees employing the target box with the slit. (d) 60_1: impact experiment at an angle
of 60 degrees. (e) 70_01: impact at an angle of 70 degrees.
- 154 -
4-5-2. b1LW¥Ù%Ò
m
br<+
!NOä¦&T!j-ÎÜxyX
(
}Am
r<b+
ÏÐ%Ò(I. 4-36-I. 4-
37)-NOäzPk
Ù(I. 4-38)D
(a)
(c)
g?zPcÏÐ(I. 4-39)&H8"
(b)
(d)
(e)
-0_05 X(¦-xyÎÜ%¦
bkÏ
I 4-36. ¤¥üý 0_01Ð%Ò: (a) 1.25 m/sec r<b+
h (b) 2.5 m/sec r<b+
h (c)
5 m/sec r<+
h (d) 10 m/sec r<+
h §e¨K9
Fig. 4-36. Fragment mass-cumulative number distributions of fragments produced by a vertical impact
reconstructed from empirical runs No. 0_01, 0_05: (a) ve < 1.25 m/sec, (b) ve < 2.5 m/sec, (c) ve < 5 m/sec, (d) ve
< 10 m/sec, (e) all fragments
- 155 -
(a)
(b)
(c)
(d)
(e)
-0_06 X(¦-xyÎÜ%¦
bk
-0_04I 4-37. ¤¥üý 0_02ÏÐ%Ò: (a) 1.25 m/sec r<b+
h (b) 2.5 m/sec r<b+
h (c) 5 m/sec r<+
h (d) 10 m/sec r<+
h §e¨K9
Fig. 4-37. Fragment mass-cumulative number distributions of fragments produced by a vertical impact
reconstructed from empirical runs No. 0_02, 0_04, 0_06: (a) ve < 1.25 m/sec, (b) ve < 2.5 m/sec, (c) ve < 5 m/sec,
(d) ve < 10 m/sec, (e) all fragments
- 156 -
(a)
(b)
(d)
(c)
(e)
I 4-38. ? N O ä z P £ T ! Ù : (a) 1.25 m/sec r<b+
h (b) 2.5
m/sec r<b+
h (c) 5 m/sec r<+
h (d) 10 m/sec r<+
h §e¨K9
Fig. 4-38. Number of Fragments belongs to each fragment mass bin: (a) ve < 1.25 m/sec, (b) ve < 2.5 m/sec, (c) ve
< 5 m/sec, (d) ve < 10 m/sec, (e) all fragments
##H8ÏÐ-.V*Å
:+ª½&pVLp
p+t(-qDpw89.ÏÐù»
㪽Aj©ÌÍ+t!Vmn 2.5 m/sec r<µb+
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V 16 mg
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2NOäqD/0{89A!78-
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!"
b:ß&:!A-X(íUD spall p#J!
X}D(-{ÔNOä
!X}D!"
- 157 -
(a)
(b)
(d)
(c)
(e)
I 4-39. ?NOäzP£T!cÏÐ: (a) 1.25 m/sec r<b+
h (b)
2.5 m/sec r<b+
h (c) 5 m/sec r<+
h (d) 10 m/sec r<+
h §e¨K9
Fig. 4-39. Mass of Fragments belongs to each fragment mass bin: (a) ve < 1.25 m/sec, (b) ve < 2.5 m/sec, (c) ve <
5 m/sec, (d) ve < 10 m/sec, (e) all fragments
- 158 -
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