Whipple ࣂࣥࣃ࣮㜵ᚚᶵᵓ㛵ࡍࡿ⪃ᐹ
ۑ∦ᒣ 㞞ⱥ㸦CTC㸧
䝇䝨䞊䝇䝕䝤䝸ศ㔝䛷ᶆ‽ⓗ䛺㜵ᚚ᪉ἲ䛸䛧䛶ㄆ▱䛥䜜䛶䛔䜛 Whipple 䝅䞊䝹䝗䛿䚸Harvard Ꮫኳᩥྎ䛾 F.
L. Whipple 䛜䚸1947 ᖺ䛻 The Astronomical Journal ㄅ䛻Ⓨ⾲䛧䛯䚸ഹ䛛༙㡫䛻䜒‶䛯䛺䛔 䇾Meteorites and space travel䇿䛸䛔䛖グ䜢㉳※䛸䛩䜛䚹Whipple 䛜䛣䛾ㄽᩥ䛷㏙䜉䛯䛂䛣䛾Ᏹᐂ⯪䛻䝭䝸䜾䝷䝮䜸䞊䝎䛾㉸㧗㏿䛾㣕
⩧య䛜⾪✺䛩䜛䛸䚸㣕⩧య䞉ᶆⓗඹ䛻Ẽ䜒䛧䛟䛿䜲䜸䞁䛜⏕䛨䜛䚹䛃䛸䛔䛖グ㏙䛿䚸ᖹᆒ㏿ᗘ䛜 20 km/s 䛻䜒ཬ䜆 meteoroid 䛾ሙྜ䛻䛿┿䛷䛒䜛䛜䚸 2 ẁᘧ㍍䜺䝇㖠➼䛻䜘䜚䚸ᆅୖ䛷ຍ㏿䛷䛝䜛㏿ᗘ䛿㧗䚻 8km/s 䛻㐣䛞䛪䚸䜲䜸䞁
䛿䛚䜝䛛ᗈᇦ䛷Ẽ䛜⏕䛨䜛䛣䛸䜒䛺䛔䚹䛧䛛䛧䚸1960 ᖺ௦䛾⭾䛺⾪✺ᐇ㦂䛾⤖ᯝ㔜せ䛺ᐇ䛜ุ᫂䛧䛯䚹䛭 䛾௦⾲ⓗ䛺ᡂᯝ䛾୍䛴䛜 Fig.1 䛻♧䛩㈏㏻㝈⏺᭤⥺䛷䛒䜛䚹䛣䛾୍ぢወጁ䛺᭤⥺䛜ᣢ䛴ព䛸䚸䛭䛾㜵ᚚᶵᵓ䛻 䛴䛔䛶᫂䜙䛛䛻䛧䚸ᚋ䛾㜵ᚚ䝅䝇䝔䝮䛾᳨ウ䛻㈨䛩䜛䛣䛸䛜䛷䛝䜜䜀ᖾ䛔䛷䛒䜛䚹
Impact Dynamics Engineering Team
╙3࿁䉴䊕䊷䉴䉧䊷䊄⎇ⓥળ 䋧 䋧
╙4࿁䉴䊕䊷䉴䊂䊑䊥䊪䊷䉪䉲䊢䉾䊒 at ARD / JAXA
16– 17 December, 2010 Masahide KATAYAMA 䓖⼀ 楔 楔喀
⑼ቇ䉲䉴䊁䊛ᬺㇱ ⴣ ⴣ᠄ᛛⴚ⺖
The 4th Space Debris WS
General Concept of Ballistic Limit
DEFINITIONS OF PERFORATION AND PARTIAL PENETRATION FOR DEFINING THE BALLISTIC LIMIT
ARMY BALLIST IC LIMIT
PROT ECT ION BALLIST IC LIMIT
NAVY BALLIST IC LIMIT
PARTIAL
PENETRATION PARTIAL PARTIAL
COMPLETE
PENETRATION COMPLETE
COMPLETE
WITNESS PLATE 6 in
Fig.1 Various definitions for complete and partial penetration.
(Ed. by J.A. Zukas et al., Impact Dynamics , Krieger, 1982.)
V
IV
Rv
L, 0Ballis
tic Lim it
V
IV V V
RV V
v
L, 0Ballis
tic Lim it
Fig.2 Typical ballistic limit curve.
©2010 CTC 2
The 4th Space Debris WS
1947
Origin of Whipple Bumper Shield
©2010 CTC 3
The 4th Space Debris WS
Sorry! To use Japanese only here.
F. L. Whipple䈲 䈲ᄤᢥቇ⠪䈫䈚䈩䇮ᒰᤨ⍮䉌䉏䈩䈇䈢᷹ⷰታ䈮ၮ䈨䈇䈩䇮
ੱ
ੱ㘃䈏ᄥ㓁♽ౝ䉕ቝቮᣏⴕ䈜䉎㓙䈮䈲䇮
ෘ ෘ䈘 PP 䈱 䈱㍑ജኈེ䈎䉌䈭䉎䇮⋥ᓘ P 䈱 䈱ᒻቝቮ⦁䉕ᗐቯ䇯 ᐕ
ᐕ䈮৻ᐲ䈱⏕₸䈪 PJ 䉥 䉥䊷䉻䊷䈱meteorite䈏 䈏ജኈེ䉕⽾ㅢ䈜䉎䇯 ᣢ ᣢ⍮䈱ᵹᤊ⟲䉕࿁ㆱ䈜䉎એᄖ䈮䉅ኻ╷䈏ᔅⷐ䇯
ㆇ ㆇേ㊂䈫䉣䊈䊦䉩䊷䈱ሽೣ䈎䉌䇮ജኈེ䈱ෘ䈘䈫ห⒟ᐲ䈱⋥ᓘ䈱
meteorite䈏 䈏ⴣ⓭䈚䈢႐ว䇮⊒↢䈜䉎㜞᷷䈱䈢䉄䈮䇮᳇ൻ䉅䈚䈒䈲䉟䉥䊮
ൻ
ൻ䈏⊒↢䇯
“meteor bumper” 䈲 䈲ജኈེ㕙䈎䉌 PP ᄖ ᄖ䈮㈩⟎䈘䈞䈢䇮
ෘ
ෘ䈘 PP 䈱 䈱㊄ዻ᧼䈎䉌䈭䉎䈪䈅䉐䈉䇯 Summarizing the paper in Japanese:
©2010 CTC 4
The 4th Space Debris WS
Subsequent Progress of Whipple Bumper Shield
T. D. Riney and E. J. Halda, AIAA Journal, Vol. 6 No.2, pp.338-344 (1968). [Reprinted in "R. Kinslow (Ed.),
HIGH-VELOCITY IMPACT PHENOMENA,
Academic Press (1970)"]
Schematics depicting (a) the impact onto a thin bumper plate, (b) its penetration, (c) the subsequent formation of spallation cone, and (d) the loading transmitted by the cone to the main structure downstream.
3.2 mm STEEL SPHERE 7 KM/SEC
1.016 mm NICKEL SHIELD
Fig.4 X ray of thin sheet impact. by C.
J. Maiden et al., GMDRL, 1965 (NASA CR-65222)
3.2 mm STEEL SPHERE 3.2 mm
EC 7 KM/SE
mm NICKEL SHIELD 1.016 m
Fig.4 X ray of thin sheet impact. by C.
J. Maiden et al., GMDRL, 1965 (NASA CR-65222)
©2010 CTC 5
The 4th Space Debris WS
Whipple Bumper Shield for Apollo Program
Optimum ts/d(projectile completely molten) versus impact velocity.
Optimum ts/d (projectile and shield completely molten) versus impact velocity.
Optimum ts/d (shield completely molten) versus impact velocity.
Optimumtts/d(projectile completely molten) versus impact velocity.
Optimum ts/d (projectile and shield completely molten) versus impact velocity.
Optimum ts/d (shield completely molten) versus impact velocity.
Theoretical shield optimum t
s/d ranges for melt of projectile and bumper.
(B. G. Cour-Palais, Int. J. of Impact Engng., Vol.23, pp.137-168, 1999.)
Shield Thickness Particle Length
0 5 10 15 20
0.0 0.1 0.2 0.3
0.4 Molten Aluminum Shield-
Glass Projectile
Molten Aluminum Projectile
FOR SHIELD MELT LIMIT
( t
s/d ) Hf= 0.04 H
aNo Molten Aluminum Shield- Glass Projectile
Impact Velocity (km/sec)
(ts/d)FOR ALUMINUM PROJECT ILE MELT ING
(
ts/d )
B. G. Cour-Palais, “Meteoroid Protection by Multiwall Structures,” AIAA Paper No. 69-372, AIAA Hypervelocity Impact Conf., Cincinnati Ohio, Apr. 30 — May 2, 1969.
Modified (Optimum) Cour-Palais Equation
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“Buckup Sheet” of Whipple Bumper Shield
Fig.6 GMDRL double-wall shielding spectrum for Al 7075-T6 at 7.4 km/s. (B. G. Cour-Palais, Int. J. of Impact Engng., Vol.23, pp.137-168, 1999)
Originally published as:
B. G. Cour-Palais, “Meteoroid Protection by Multiwall Structures,”
AIAA Paper No. 69-372, AIAA Hypervelocity Impact Conf., Cincinnati Ohio, Apr. 30 — May 2, 1969.
Modified (Optimum) Cour-Palais Equation
t
s/ d
0 1 2 3 4 5 6
1 2 3 4 5 6
0
Theoretical Semi-Inf inite = 2.3p / d GMDRL Data
MSC Data 5.3
5.3 ( t
s+T
B) / d
Rear sheet thickness versus ts/d of type 2024- T3 aluminum alloy.
(B. G. Cour-Palais, “Space Vehicle Meteoroid Shielding Design, Proc. Comet Halley Micro- meteoroid Hazard Workshop, ESA SP-153, 85- 92, 1979.)
©2010 CTC 7
The 4th Space Debris WS
Ballistic Limit Equation (Curve)
single wall
double wall
ballistic shatter hypervelocity region
v [km/s]㪊 㪎
ts
,
S and constant ts tBtB
S v
d
Fig. 3 Behaviour of the bumper protection concept.
(H.-G. Reimerdes et al., Proc. 1
stEuropean Conf. on Space Debris, ESA SD-01, Darmstadt pp.433-439, 1993.)
Fig.8 Ballistic limits for equal mass monolithic target and Whipple shield. (E. L. Christiansen, “Meteoroid/Debris Shielding,” TP-2003-210788, NASA, 2003.)
㵰failure” occurs above curves
Whipple dCrit @ 0 deg monolithic dCrit @ 0 deg
Ballistic Limit Improvement due to Shield Standoff
㰱 dCrit
Complete Melt Regime Fragmentation &
Partial Melt Regime Velocity [km/s]
Ballistic Regime Few Solid Fragments
Many (increasing with velocity) solid fragments
& liquid droplets
Fine droplets, few solid fragments, some vapor
Bumper density, EOS Standoff Rear Wall Strength Bumper strength
density, EOS, thermal characteristics
Standoff Rear Wall Strength Strength
Velocity [km/s]
Critical Al Diameter [cm]
Velocity Region State of Debris Cloud (for Al on Al impacts)
Important Shield &
Material Propperties Region
After Apollo Program:
Modified Cour-Palais Equation New Cour-Palais Equation (Christiansen Equation)
d, t
s, S = constant
t
s, t
B, S = constant
©2010 CTC 8
The 4th Space Debris WS
Debris Cloud Formation: 500 to 20,000 m/s
3URMHFWLOH7 6KLHOG7
%DFN:DOO7 G PP W
VPP
W
%PP 6 PP
500 m/s 1000 m/s 1500 m/s 2000 m/s 3000 m/s
4000 m/s 5000 m/s 6000 m/s 7000 m/s 8000 m/s
10000 m/s 15000 m/s 20000 m/s
Perfectly Vaporized Partially
Vaporized
Perfectly Vaporized Partially
Vaporized
Partially Vaporized
3URMHFWLOH7 6KLHOG7
%DFN:DOO7 G PP W
VPP
W
%PP 6 PP
©2010 CTC 9
The 4th Space Debris WS
Debris Cloud Formation and Penetration Process
in the Whipple Bumper Shield (I); no shock-induced vaporization
Debris: 10 mmI Sphere, Bumper Thickness: 2 mm, Standoff: 50 mm 1 to 6 km/s by every 1 km/s
©2010 CTC 10
The 4th Space Debris WS
Debris: 10 mmII Sphere, Bumper Thickness: 2 mm, Standoff: 50 mm 7 km/s, 8 km/s
Debris Cloud Formation and Penetration Process
in the Whipple Bumper Shield (II); no shock-induced vaporization
©2010 CTC 11
Debris: 10 mmI Sphere, Bumper Thickness: 2 mm, Standoff: 50 mm 10 km/s, 15 km/s and 20 km/s
Debris Cloud Formation and Penetration Process
in the Whipple Bumper Shield (III); shock-induced vaporization
㪇
Change of Phase
Es-Isoenergy Pressure
V/V0 Vs 1 I
II
IV
㩷㩷㩷㩷
Materail Phase Compression mode in solid phase Expansion mode in solid phase Solid/gas multiple-phase Gas phase Region No.
I II III IV
Forp< 1 TPa, Mie-Grüneisen type shock Hugoniot EOS Forp> 1 TPa,
Thomas-Fermi theoretical III EOS
Hugoniot
The 4th Space Debris WS
©2010 CTC 13
The 4th Space Debris WS
1. Reviewed a series of the ballistic limit equations (BLE’s) for the Whipple bumper shield which were developed experimentally during the Apollo program and improved mainly in the latter half of 1980’s at NASA/MSC /JSC.
2. Although the shatter region of the BLE’s looks eccentric at first glance, the fundamental mechanism of the BLE’s was clarified and depicted by the present numerical simulations
3. The BLE’s are empirical equations derived from the vast amounts of experimental test results at Ames, GMDRL, MSC, JSC, etc., however, their various coefficients are not always evident, although not shown here individually.
4. It is of great importance to comprehend the essential concept of the BLE’s to be developed, in order to develop new equations for other purposes, as well as to apply existing BLE’s to current problems.
CONCLUDING REMARKS
©2010 CTC 14
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