JOURNAL OF GEOPHYSICAL
RESEARCH, VOL. 104, NO. El2, PAGES 30,825-30,845, DECEMBER
25, 1999
Spectroscopiccharacterization of hypervelocity jetting:
Comparison with a standard theory
SeijiSugita
•'2andPeterH. Schultz
Departmentof GeologicalSciences,Brown University,Providence,RhodeIsland
Abstract. Symmetriccollisionbetweentwo identicalplateshasyieldedsuccessful
theoretical
modelsfor thejetting process.Consequently,assessment
of impactjetting at planetaryscaleshas
beenlargelybasedon the theoriesdevelopedfor suchspecifictypesof collisions.Little
experimentalwork hasbeendone,however,to measurebothtemperatureandtarget-to-projectile
massratio of jetting createdby sphericalprojectilesimpactingplanartargets,whichtypify
planetaryimpacts.The goal of this studyis to examinethe validity of applyingplanar-impact
theoriesto jetting due to impactsof sphericalprojectilesinto planartargets.Using a newly
developed
spectroscopic
approach,
we observe
jettingcreatedby Copper
spheres
impacting
planar
dolomitetargetsat hypervelocities.
In contrastwith previousexperimentsusingquartzprojectiles,
the observedmeantemperatures
of jets dueto copperprojectilesdoesnot correlatewell with the
verticalcomponentof impactvelocity.Instead,the observedtemperatures
of jets showmuch
bettercorrelationwith impactvelocitythanthe verticalcomponentof impactvelocityandimpact
angle.The experimentsalsorevealthatthe target-to-projectile
massratio within a jet increases
with impactangle (measuredfrom the horizontal).In orderto understandthe significanceof these
experimentalresults,they were thencomparedwith a jetting modelfor asymmetriccollisions
basedon standardtheories.Sucha comparisonindicatesqualitativeconsistencies,
suchas
completevaporizationof the carbonatetarget(as opposedto meredegassingof carbondioxide
dueto incompletevaporizationof carbonate)andhighertarget-to-projectile
massratio in a jet at
higherimpactangles.Quantitativecomparison,however,alsorevealssignificantinconsistencies
betweentheoryandexperiments,suchas an impact-angleeffect onjet temperatureand a
correlationin jet temperatures
betweenprojectileandtargetcomponents.In orderto resolvethese
inconsistencies,
new factorssuchas viscousshearheatingandthe nonsteadystatenatureof the
jettingprocesses
may needto be considered.
1. Introduction
Al'tshuler et al., 1962] and experiments with cone-shaped
High-speed ejection of a small mass of highly shocked
materialhasbeen observedin variousconfigurations
of obliquely
collidingsurfaces,suchas a collapsinglined cavity [e.g., Birkhoff
et al., 1948; Walsh et al., 1953; Al'tshuler et al., 1962], a sphere
impacting a flat target [e.g., Gault et al., 1968], and a coneshapedprojectile impactinga flat target [e.g., Allen et al., 1959;
Jeanand Rollins, 1970]. This phenomenonis calledjetting. Such
jets exhibit extremely high ejection velocity, which is several
times the velocities of the colliding surfaces.It is worth noting
that so-calledbazookacannonstake advantageof the penetration
power of shaped-charge
jets resultingfrom this extremelyhigh
ejection velocity. It is also observedthat jetting has a critical
anglebelow which the phenomenado not occur [e.g., Walshet
al., 1953]. The characteristic
high ejectionvelocity of jetting and
the existenceof a critical angle of colliding surfacesfor jetting
have been successfullyexplained by analytical models and
verified by both flat-plate experiments [Walsh et al., 1953;
projectiles
[Allenet al., 1959;JeanandRollins,1970].
Anotherimportantaspectof jetting is its high degreeof shock
heating.Kieffer[1977]usedthe symmetric
jettingtheoryto show
thatthejettingprocesscaninduceshockmeltingat relativelylow
impactvelocities,i.e., velocitiesinsufficientto producemelting
for head-on collisions.Such jet-inducedmelting/vaporizationat
relativelylow impactvelocitieshasmanyimportantimplications
in planetaryscience.For example,jettinghasbeenconsidered
as
a mechanism
for the originsof chondrules[Kieffer, 1975],Pluto
[McKinnon, 1989ab], the Moon [Melosh and Sonett, 1986],
tektites,andimpactglasses[Vickery,1993].
Calculationsfor most planetary applications,however, are
basedon jetting modelsdevelopedfor a symmetriccollision
betweentwo thin plates [Walshet al., 1953; Al'tshuleret al.,
1962] and a methodto estimateshockheatingfrom the pressure
at a stagnation
pointby Kieffer [1977]. Thesemodels,however,
have several potential problems: (1) Shock waves due to
asymmetric
blunt-bodycollisionmay not be approximated
by a
steadystatesolution,which is assumedin the symmetricflatplatemodels.(2) The methodto approximate
a shockpressure
by
a stagnation
pressureoverestimates
the shockheating.Although
ion leaveat NASA Ames ResearchCenter,Moffett Field, California.
2permanently
at Department
of EarthandPlanetary
Physics,
Faculty the discrepancyis reasonablysmall in symmetricthin-plate
of Science,Universityof Tokyo, Tokyo,Japan.
collisions[Kieffer, 1977], it may be much more significantin
asymmetric
blunt-bodycollisions.(3) By definition,a symmetric
Copyright1999 by the American GeophysicalUnion.
jettingmodelcannottakeinto accounteitherimpedance
contrasts
or differencein effective impact velocity with respectto the
Paper number 1999JE001061.
0148-0227/99/1999JE001061 $09.00
collisionpoint betweenimpactorand target.Collisionbetween
30,825
30,826
SUGITA AND SCHULTZ: SPECTROSCOPICOBSERVATION OF IMPACT JETTING
unequalmaterialsis expectedto characterizethe surfacesof both
planetsand small bodiesin the solar system,which consistof a
variety of materials such as silicates, ices, and metals. As
discussedin detail in section4, blunt-bodyimpactsconstantly
change the "wedge" angle between the surfacesof target and
projectile with respect to the collision point during the
penetrationstage. Consequently,the effective impact velocities
of target and projectile are unequalin general.Thus effects of
asymmetryin material propertiesand impact velocity deserve
significantconsiderations.(4) Effect of viscousshear heating is
jettingcreatedby sphericalimpactsinto planartargets.We use
projectiles
with materialproperties
very differentfrom quartzin
order to determineif the resultsby Sugitaet al. [1998] can be
generalized.
An appropriate
selectionof projectilesalsoallows
temperature
measurement
of jettingderivedfrom a projectileas
well asa target.Suchsimultaneous
temperature
measurements
of
bothcomponents
permitthetarget-to-projectile
massratioin a jet
to be estimated.Here, both temperatureand mass ratio are
determinedfrom the measuredspectraas a function of time,
impactvelocity,and angle.The experimental
resultsare then
nottaken
intoaccount
in previous
theories.
All heating
hasbeen comparedto predictionsof theoreticalmodelsin the literature
ascribedto pure shock heating by Rankine-Hugoniotequations.
This assumptionis justified for a symmetriccollision between
two identicalplatesbecausethereis no velocity shearexpectedin
sucha collision.As shownin section4, however,an asymmetric
collision between two surfacesleads to a large velocity shear
along the contact surface.Consequently,the effect of viscosity
may be significantin jetting duringplanetaryimpacts.
One reasonwhy suchissuesremain understudiedmay be the
absenceof observationaldata. Althoughjetting velocity has been
measuredfor many different conditions,few observationshave
focusedon the degreeof heatingof jets, particularlyfor bluntbody collisions. Kieffer et al. [1976] showed that microscopic
textures
of
shocked
Coconino
sandstone
are consistent
with
heatingin excessof 3000 K, which is most likely due to shock
heatingby the local jetting process.Yanget al. [1992] observed
radiation from jetting and obtained a blackbody temperature
higherthan3000 K, even at relativelylow impactvelocities(< 2
km/s). In spite of the value of thesepioneeringworks, however,
their resultsmay not be readilyusedfor testingtheoriesof jetting
created by planetary impacts. For example, the shocked
sandstoneobservationby Kieffer et al. [1976] does not provide
preciseconstraintsfor the intensityof the shockthat causedthe
jet-induced melting. The jetting experimentsby Yang et al.
[1992] used flat plates instead of (three-dimensional)blunt
bodies,and the impact velocitiesare low (< 2 km/s). Such lowvelocity impactsmay not reach the hydromechanical
regime of
the impact material used in the experiments[see, e.g., Kieffer,
1977]. At much higher impact velocities,however, it may be
difficult to use Planck'sradiationlaw. The extremelyhigh shock
heatingfor the jet may vaporize the jetted material. A radiation
spectrum from a high-temperaturevapor is not generally
approximatedby the Planck function.In fact, the radiation of
higher'velocity impacts at early times often contains strong
atomic line emissionand molecularband emission[e.g., Gehring
and a new semi-analytical
modelbasedon the standardjetting
theoriesdevelopedby Walshetal. [1953] and Kieffer [1977].
Finally,we discuss
plausiblecauses
for thediscrepancy
revealed
by the comparison.
2. Experiments
A seriesof hypervelocity
impactexperiments
wereconducted
at NASA-Ames Vertical Gun Range (AVGR). The two-stage
lightgasgunat AVGR allowedbothhighimpactvelocities
(3.95.8 km/s) and variableimpactangles(15ø-90ø, measuredfrom
thehorizontal).The experimental
setupis essentially
the sameas
givenby Sugitaet al. [ 1998]andillustrated
in Figure1.
Copperprojectiles
wereselected
in thisstudyfor a numberof
reasons.First, copperhas muchhighershockimpedancethan
quartz,therebyleadingto a higherpeak pressureat a given
impactvelocity.Second,
because
copper
is a ductilematerial,
the
projectilefailurepatternis expected
to be differentfrombrittle
quartz,particularly
in obliqueimpacts[e.g.,Schultz
andGault,
1990]. Third, emissionlines of copperare widely separatedin
wavelength
[e.g.,Readeretal., 1980].Thisseparation
minimizes
interferencewith emissionlines from target materials.Transition
elementssuchas iron and chromiumhave sucha large numberof
emissionlines that very high spectralresolutionis required to
IC
ro
ImpactChamber
and Warnica, 1963; Jean and Rollins, 1970; Schultz, 1996;
Schultzet al., 1996; Adams et al., 1997; Sugita et al., 1998],
indicating that it is dominatedby optically thin gas phases.
Consequently,the pyrometer approach based on blackbody
radiationis not applicableto jettingcreatedby highervelocity
impacts. Recent spectroscopicobservationsof hypervelocity
impacts, however, have shown that the temperatureof such
vaporizedjets canbe determinedby measuringrelativeintensities
of atomic emission lines [Sugitaet al., 1998] and molecular
emissionbands [Sugitaand Schultz,1998]. The observationsby
Sugitaet al. [1998] revealed that the jet temperaturedue to
impactsby quartzspheresinto soliddolomitetargetsrangesfrom
4000 to 6000 K and moderately correlates with the vertical
componentof impact velocity.It is uncertain,however,if these
results are unique to quartz impactors, and temperature
informationonjets derivedfrom the projectilewasnot obtained.
The goal of this study is to assessthe validity of standard
jetting theories based on symmetric thin-plate experimentsto
•"':-"
Tar
Figure 1. Schematic diagram of the setup for impact
experiments.The spectrometersequipped with intensified
charge-coupled
devices(ICCD) view the target plane througha
windowon the top of the impactvacuumchamber.
SUGITA AND SCHULTZ: SPECTROSCOPIC OBSERVATION OF IMPACT JETTING
resolveeach emissionline [e.g., Readeret al., 1980]. Although
aluminumdoesnot have a large numberof atomicemissionlines,
previous experiments have shown that intense molecular
emissionfrom aluminumoxide (A10) moleculescan causestrong
interference with other emission [Schultz, 1996; Schultz et al.,
1996, Adamset al., 1997]. Fourth, the upper statesof electronic
transitionsof dominant emission lines of copper are widely
distributedin energy level [e.g., Fu et al., 1995]. The wide
energyseparationis very beneficialfor determiningtemperatures
accurately[Sugitaet al. 1998].
The same solid polycrystallinedolomite target blocks were
used here as in the previousexperimentsby Sugitaet al. [1998],
thereby allowing target temperature measurementsfrom the
calcium emission line. Because the spectral distributions of
emissionlines of copper and calcium are similarly sparse,the
samespectroscopic
systemwith the identical setup(i.e., spectral
rangeand resolution)as in the previousexperimentscan be used.
The use of the identical observation system greatly reduces
possiblesystematicmeasurementerrorsbetweenthe presentand
the previousexperiments.
Only a brief summary of the method to determine
temperatures is described here because the theoretical
backgroundand detailedproceduresare describedby Sugita et al.
[1998]. First, both the source element and the electronic
transitionof eachemissionline are identifiedfrom its wavelength
and relative intensity. Here, the relative intensity of observed
spectraare calibratedwith a National Institute of Standardsand
Technology (NIST) traceable standardtungstenfilament lamp.
Second,the intensityof the line is measuredand then normalized
by its Einstein A coefficient, statisticalweight, and frequency.
When the normalized intensitiesare plotted againstthe energy
levels of the upper states of the correspondingelectronic
transitions(i.e., Boltzmannplot), they follow a straightline if the
emissionsourceis in thermalequilibriumand its opacityis small.
The inverseof the slopeof this straightline gives the temperature
of the radiation source.Here, it is noted that the temperature
determinedin an impactexperimentis an averagetemperatureof
the radiation source,which may be heterogeneous.
This average
temperature,however, is shifted toward the highesttemperature
with respect to the mass-averagedtemperature.An observed
emission line from an impact vapor cloud is the sum of
luminescenceof each part of the impact vapor cloud with
different radiation temperatures.Because radiation intensity is
generally a very strong function of temperature, the highest
temperature component in a radiation source dominates the
observedemissionspectrum.
EinsteinA coefficientsof calcium and copperatomsused for
the analysisin this study are given by Sugitaet al. [1997] and
Table 1, respectively.Relatively old data by Kockand Richter
[1968] are used for the analysisin this study.Althougha recent
comprehensive
compilationby Fu et al. [1995] lists more recent
data, thesenewer data do not provideaccuraciesin temperature
determinationas goodas thoseby KockandRichter [ 1968]. The
newer data are either drawn from even older experimental
measurements
or representnew experimentalmeasurements
for
much fewer Einstein A coefficients.Data by Kock and Richter
[1968] are still the newestvalues derived directly from a single
set of experimentsthat coverall the emissionlinesnecessaryfor
our study.In fact, a relativelynew compilationby Readeret al.,
[1980] adoptsthe data by KockandRichter [1968] for emission
linesof Cu I in the experimentalwavelengthregionfor our study,
i.e., 430-650 nm. However, it is importantto note that both Kock
and Richter [ 1968] and Reader et al. [1980] do not cover some of
30,827
Table 1. Einstein A Coefficients of Cu I Emission Lines
Observedin This Study
• (nm)
g•,
Eu/k(K)
Atu
(108s
-1)
Error %
448.035
2
76042.4
0.030 a
450.735
6
96609.6
0.25 b
-50 ½
450.937
2
92767.3
0.275 a
18
452.511
4
97802.8
0.46 b
-50 ½
12.2
453.079
453.970
458.700
464.258
465.112
2
4
6
4
8
76042.4
91489.9
90574.4
93900.8
89790.3
0.084a
0.212•
0.320•
0.12 •
0.380•
15
15
12
-50 ½
12
1.11d
5.60d
12.5a
3.10
19.6a
467.472
469.749
6
4
90574.4
91489.9
0.12 •
0.10 •
-50 ½
-50 ½
4.62
2.65
470.459
510.554
515.324
521.820
522.007
529.252
570.024
578.213
8
4
4
6
4
8
4
2
89790.3
44293.7
71850.3
71860.1
71850.2
89790.3
44293.7
43936.3
0.055a
0.020a
0.604a
0.750a
0.150a
0.109a
0.0024a
0.0165a
20
15
12
12
12
12
15
14
12
g•Atuvt•
(1022s'2)
0.401
9.98
3.66
2.80a
0.470
14.1d
25.9a
3.45a
4.94a
0.0505
0.171
Here •, g•, Eat'k,
At,,,andvt,,are wavelength
in nanometer,
the
statisticalweightof the upperenergystateof electrontransition,
the energyof the upperstatedividedby Boltzmannconstantin
Kelvin,EinsteinA coefficient
in 108s-1, andfrequency
in s'l,
respectively.
The valuesfor bothwavelengths
andenergylevels
are taken from Fu etal. [1995]. The sourcesof the Einstein A
coefficientsare indicatedby footnotesc and d.
aKockand Richter [ 1968].
•Corliss[ 1970].
CCorliss[1970] estimatesthat
errors for the Einstein A
coefficients are at least 30-66 %.
aValuesusedin actualspectralanalysis.
the moderately strong emission lines in our experimental
wavelengthrange.Theselines are coveredby Corliss[1970], and
the samedataare listedby Fu et al. [ 1995].Theseparticularlines
are often located very close to other Cu I emissionlines and
cannot be resolved with the current configuration of our
spectrometers,
which are intendedto capturea wide range of
wavelengthwith moderatespectralresolution.As a result, the
intensityof the omitted lines would be measuredas a part of
other lines listed by Kockand Richter [1968] and Readeret al.
[1980], leadingto a significantoverestimate
of the intensitiesof
some emission lines. To avoid this problem, we removed
emissionlines that are contaminatedby these"hidden"lines. The
emission lines used in the actual temperature analysis are
indicated in Table 1.
Here it is important to discussthe effect of an ambient
atmosphere on the measured jet temperatures.All the
experimentsin this study were conductedin -0.5 torr of air
pressure.Sinceimpactjets collidewith an ambientatmosphere
at
extremely high velocities,reheatingof jets by this interaction
could be a significantconcernin interpretingthe experimental
results.Experimentaldata by Gehringand Warnica [1963] and
Schultz [1996], however, indicate that the emissionintensity of
early-time impact-inducedlight emission is not influenced
significantly by ambient air pressure less than - 1 torr.
Hydrodynamiccalculationsusing Rankine-Hugoniotequations
also indicate that the collision between an expanding high-
30,828
SUGITA AND SCHULTZ: SPECTROSCOPIC OBSERVATION OF IMPACT JETTING
pressurejet anda low-pressureambientatmosphere
will not form
a shock front within the jet until a significant mass of the
atmospherehasbeen traversed.An extremelyintenseshockfront
then forms only in the surroundingatmosphere,
therebyleading
to intenseheatingof ambientair. Consequently,
the temperature
insidethe impactjet shouldnot be influenceddirectlyby sucha
collisionwith the thin ambientatmospherefor the experimental
conditionsin this study.If the massand densityof an impactjet
is extremely small, the interactionbetweenjetting vapor and
ambient air may be describedas free-molecularflow, in which
collisionsbetweenindividualatomsandmoleculesare important.
Then atoms/molecules
in both an impactjet and ambientair
shouldbe heatedsimultaneously.
If eitherheatingmechanisms
is
significant,emissionsfrom heated air molecules(e.g., N2 and
N2+) shouldbe observed,as well as emissionsfrom molecules
and atoms(e.g., Ca, Mg, Cu, and CaO) in the jet. However, we
have not observedany light emissionfrom ambientair species.
Consequently,
the possibleeffect of an ambientatmosphereon
radiation from impact jetting is not important for the
experimentalconditionsin our study. When the atmospheric
pressureis as high as 10-100torr (a factorof 20-200 greaterthan
this study), the effect of an ambient atmosphereon impactinducedlight emissionbecomesvery prominent[e.g., Schultz,
1996; Sugitaand Schultz, 1998]. However, detailed discussionof
the natureof this phenomenon
is beyondthe scopeof this study
and is discussedelsewhere[Sugita, 1999].
When temperature is determined, normalized emission
intensitiescan be extrapolatedto the zero energy level. This
extrapolated intensity (i.e., intercept on the vertical axis)
corresponds
to the numberof ground-state
atomsin the emission
source [e.g., Sugitaet al., 1998]. When an emissionspectrum
3. Experimental Results
First we describe qualitative characteristicsof emission
spectra and their temporal variation. Then the results of
temperature measurementsand the mass ratio of target to
projectilecomponentsare presented.Comparisonwith theoretical
expectationsis deferredto section4.
3.1. Impact Flash as a Function of Time
Emission spectra were captured with several different
exposuretimesin orderto observethe temporalvariationof the
radiation.The earliestand shortestexposuretime is 0-2 ps after
the first contactof impact,whichwasdetectedwith a photodiode
placednearthe impactsite.This exposuretime is the sameas in
many previousexperimentsof quartz impacts [Sugitaet al.,
1998]. This allowsa directcomparisonof the resultsbetweenthe
currentand previousexperiments.
However,it shouldbe noted
that the diameterof copperprojectilesused in this study(3.18
mm) is half that of quartzprojectilesused previously[Sugitaet
al., 1998].
All the emissionspectrawith this early exposuretime exhibit
strongline emissionsfrom both copperand calcium atomsas
well as strongbandemissionof CaO but do not showthe strong
MgO band observedfor quartz impacts[Sugitaet al., 1998].
Typical spectrograms
are shownin Figure 2. Little interference
betweencalciumand copperlines occursfor the selectedspectral
resolution and coverage. This ensures accurate temperature
measurements of both elements. The level of continuum thermal
backgroundis muchlower for copperimpactorsthan for quartz
impactorsat all the impact angles.In fact, copperprojectiles
impactingat 15ø exhibit emissionlines large enoughto allow
contains lines from two different elements, the ratio of the
quantitativeintensity measurements,
whereasthose by quartz
ground-stateatomsof the two elementsin the emissionsource impactsshow few significantemissionlines but a very strong
can be estimatedfrom the differencein the vertical interceptsof
thermal background[Sugitaet al., 1998]. The weak blackbody
radiationand strongline emissionfrom copperimpactorsindicate
two Boltzmannplots. In the presentstudy, the numberratio of
copperand calciumatomscan be usedto estimatethe target-to- that the radiation sourceis dominatedby a gas phasewith very
projectilemassratio in a jet. However,it is notedthatthe number little liquid/solidphasesduring this early stageof the collision
ratio doesnot exactly match the massratio. Mass refersto atoms process.
The small thermal blackbody background also allowed
not only in the groundstatebut alsoin all theexcitedandionized
states.The degreeof excitationand ionizationof atomscan be observationof atomiclinesat later stagesof the impactwith high
estimatedfrom the intensity of an ion line [e.g., Griem, 1964; precision.Figures 2a-2c show the emissionspectrataken in
after
Sugitaet al., 1998]. However, becauseno emissionline of copper exposuretimesof 0-2 •s, 2-5 •s, and 5-15 •s, respectively,
ions was observedin the experiments,sucha direct estimatewas the first contactof impactswith the identicalviewing geometry
The field of view of the spectrometers,
not possible.The number ratio of ground-stateatoms,however, of the spectrometers.
generally approximates the mass ratio well because the which are lookingdownon the target,is -2 cm in radiusand its
contributionof excited states and ionized states are relatively centeris located2.5 cm downrangefrom the point of impact.The
uprangeedge of the field of view is adjacentto the point of
minor at moderatetemperatures.
Another sourceof uncertaintyis the fact that the calcium is impactbut doesnot includeit. All the emissionspectrawere
taken with this viewing configuration, unless mentioned
only one componentof the target material of dolomite. As we
discuss below, emission of calcium oxide is observed, and a
otherwise.Great care was taken to maintain this setup of the
during the three impact experimentspresentedin
significantamount of carbon dioxide is inferred to be released spectrometers
during an impact. Consequently,the spectroscopically
observed Figures 2a-2c. Thus direct comparisonof emissionintensity
massof calcium is most likely a small fraction of the total mass among the three experimentsis valid despite the arbitrary
of jetting vapor. This possiblesmall fraction of vapor mass, intensityunit. It is notedthat the arbitraryunit usedin this study
however, has rather well-defined significance. Since the is calibratedin terms of relative intensity within a spectrogram
generationof atomic calcium (also magnesium)vapor requires but is not calibrated for an absolute scale of irradiance. The
methodof intensitycalibrationand its uncertaintyare described
much higher energy than that for molecularvapor (suchas CaO
and COO, atomic vapor representsthe highest temperature by Sugitaet al. [1998].
As shownin Figures2b and2c, the emissionintensityat later
componentwithin impact-inducedvapor. Thus the massratio of
Ca to Cu atomsmay be usableas a measurefor the target-to- times is much weaker than that in the earliest time (Figure 2a).
projectilemassratio within the highesttemperatureportionof an Note that intensityscalesof Figures2b and2c are 1/2 and 1/4 of
that of Figure 2a, respectively.Unlike in quartz impacts,the
impactjet.
SUGITAANDSCHULTZ:
SPECTROSCOPIC
OBSERVATION
OFIMPACTJETTING
30,829
24000
a Ca CuCaCu
•
ß
ß
'
20000
Ca
CaCu Cu Ca Ca
::
Ca Ca Cu Cu CaNa
Mg :: ::
::
Ca Ca
CaJ
::I
16000
o
._
e
•
12000
8000
o
-!ps
,,i :: ,
4000
0
450
500
550
Wavelength
600
650
600
650
600
650
(nm)
12000
60 ø
4.94
10000
km/s
2-5ps
8000
6000
4000
2000
450
500
550
Wavelength
5000
(nm)
60ø
•.0•
- 5km/s
NS
4000
-
3000
2000
1000
450
500
550
Wavelength (nm)
Figure
2. Emission
spectra
ofjetting
duetocopper
impacts
intodolomite
blocks.
Theimpact
angle,
velocity,
and
exposure
timeafterthefirstcontact
ofimpact
areindicated
ineach
part.
Thefieldofviewofthespectrometers,
which
arelooking
down
onthetarget,
is-2 cminradius,
anditscenter
islocated
2.5cmdownrange
fromthepoint
ofimpact.
Theconstant
setup
ofthespectrometers
maintained
during
theexperiments
(Figures
2a-2c)
allows
direct
comparison
among
their
radiation
intensities.
Although
theviewing
geometry
was
changed
between
Figures
2dand
2e,thechange
isverysmall,
andtheintensity
scale
wasnotaltered
significantly.
However,
theintensity
scales
may
besignificantly
different
between
thecases
at60øofimpact
angle
(i.e.,Figures
2a-2c)
and
those
at30ø(i.e.,Figures
2dand2e)because
ofalarge
change
inviewing
geometry.
Thesource
atoms
andmolecules
ofemission
lines
and
bands are indicated.
30,830
SUGITAAND SCHULTZ:SPECTROSCOPIC
OBSERVATIONOF IMPACTJETTING
70000
'
60000
I
'
30 ø
5.12
km/s
O-2ps
50000
o
40000
30000
o
20000
10000
i
450
500
i
i
i
550
I
i
i
ß
ß
600
650
Wavelength (nm)
100000
'
I
'
e
80000
30 ø
5.47
km/s
2-5ps
o
60000
40000
o
20000
I
I
450
500
550
I
I
I
[
,
I
i
600
.
650
Wavelength (nm)
Figure 2. (continued)
blackbody radiation does not dominate at later times. This
precludesthe possibilitythat the late-time reductionin the
distancecorrespondto a velocity -20 km/s. Both the high
velocityand rapid generationof the self-luminous
gasconfirms
intensity
of atomic
emission
linesmaybedueto absorption
by that the gas is predominantlyjetting material.Also note that the
opaque
fine-grained
debris/droplets,
whichwouldexhibitstrong relative intensity ratios among different emission lines are
blackbody
radiation.
Thusthe amount
of self-luminous
vapor significantlydifferentbetweenFigures2d and 2e. However,this
withinthefieldof viewdoesreducesignificantly
at latertimes. differenceresultsfroma changein temperature
of a jet notfroma
Two alternative
interpretations
are possible:
(1) The high- compositionalchangeas shownin section3.3.
temperature self-luminousvapor observed in the earliest
exposure
timecooledveryrapidlyto a temperature
toolow to be
self-luminous
and(2) the self-luminous
vaporhasphysically3.2. Temperature
movedbeyondthe field of view. Two consecutive
impact Strong emissionlines and the low thermal background
experiments
at 30øof impactanglewereconducted
to resolvethis
alloweddetermination
of the temperatures
of bothcopperand
calciumfor almostall impacts
duringthefirst2 Us.Herecopper
in thefirst2 Usandin a fieldof view2.5cmfarther
downrangeand calcium representprojectile-and target-derived
jets,
issue.Observations
were madein both the nominalfield of view
thanthe nominalcases2-5 Us afterimpacts.
Althoughthe respectively.
A typicalexampleof a Boltzmannplot to obtain
intensity
unitsin thetwoexperiments
arenotstrictlythesame, temperatures
is shownin Figure3. Measuredtemperatures
are
thechange
in theabsolute
intensity
scaleis expected
to be small shownas functionsof impactvelocity,angle,and the vertical
because
thechange
in viewing
geometry
of thespectrometers
is component
of impactvelocityin Figures4 and5. Unlikejetting
verysmall.Theexperimental
results
revealthattheintensity
of dueto quartzprojectiles
[Sugita
etal., 1998],thetemperature
of
atomic/molecular
radiationfartherdownrange
at later times jetting due to copperprojectilesdoes not show significant
(Figure2e)is comparable
to thatin thefirst2 Usin thenominal correlationwith the verticalcomponent
of impact velocity.
view area(Figure2d). Thisclearlydemonstrates
thatthe second Although
jet temperatures
dueto copperimpactsexhibitslight
interpretation
is correct;mostof the emission-source
gasis increases
asfunctions
of impactangle,thistrendis weak.Instead,
formedrapidly but travelsbeyondthe nominalfield of view calciumandcoppertemperatures
generallyshowa flat trendwith
withinthefirst2 gs afterimpact.The timedifference
andtravel impactangle.However,the temperatures
havegoodcorrelation
SUGITAAND SCHULTZ:SPECTROSCOPIC
OBSERVATION
OFIMPACTJETTING
30,831
clearlyshowsthat the target-to-projectile
massratio (Ca/Cu)
increasessteadilywith impact angle 0 (measuredfrom the
horizontal).Sincethe scaleof the verticalaxis of Figure6 is
logarithmic,
the massratioactuallychanges
dramatically.The
2O
18
10000
=14
Ca Temperature
9000 • a
ß,•-.•- CuEmission;
T = 6060K
8000
•12
•
• 7000•
o10
,- 6000
'-
8
,,
Ca
Emission;
T=5740
K'•',
•
',
a. 5000
•
E
,
4000!
0
20,000
40,000 60,000 80,000 100,000
E/k: EnergyLevel (K)
0=45 ø
_
3000•
Figure3. A Boltzmann
plot of atomicline emission.
The
emission
is induced
by a copperimpactintoa dolomite
blockat
45øof impact
angleand5.48km/sof velocity.
Theexposure
time
is 0-2 gs afterthefirstcontact
of impact.
Thedistributions
of
intensitiesof emissionlines of copperand calciumindicate
6060+_150
K and5740_+410
K of temperatures,
respectively.
4
3
6
5
7
Velocity (kin/s)
9000• b
Ca Temperature
8000i
7000L
with impact velocity.As impact velocityincreases,
the
temperatures
of bothprojectileandtarget-derived
jetsincrease
significantly
overtheexperimental
range
(Figures
4 and5).
Anotherresult of the temperaturemeasurements
is the
correlation
between
temperatures
for thetwoelements.
Figure6
revealsthatthe two temperatures
alsocorrelate
well with each
otherbut that the temperature
for copperis roughly1000K
higher
thanthatfor calcium.
In somecases,
thetemperature
of
projectile-derived
(Cu)jet is 2000K higher
thanthatof targetderived
(Ca)jet. Estimated
temperatures,
however,
areexpected
to have considerableerrorsdue to uncertaintiesin both Einstein
A coefficientsand measurements
of emissionintensities.Such
errorscan be assessed
from the scatterin Boltzmannplots.The
uncertainty
in temperature
based
onthemethod
by Press
etal.,
[1992]is presented
aserrorbarsin Figures
4, 5, and6. Further
6000
,
5000•
4000•
I
3000f
The method to estimate the mass ratio involves an
60
80
100
,
,
,
Ca Temperature
8000
6000
3.3. Mass Ratio
I,,,
40
C
9000
significantly
greaterthanthe errors,we conclude
that the
temperature
gapis probably
a realsignal.
Consequently,
copper
targetmaterials.
V=5.43:e0.33km/s
I,,,
20
10000
7000
ratesof adiabaticcoolingare differentbetweenprojectileand
.......
Impact Angle (degrees)
discussion
abouterroranalysis
is givenby Sugitaetal. [1998].
Because
theoffsetin temperature
between
calciumandcopperis
andcalciumatomsmaynotbe in the samethermalequilibrium;
instead,
theymaybelong
to twophysically
separated
vaporjets
with differenttemperatures.
Perhapsa jet derivedfrom the
projectile
overrides
a jet derivedfrom the target.Different
temperatures
evenfor the samepeakshockpressure
maybe
possible
because
theirshockHugoniot
equations
of states
and
[
0
[sooo
4000
3000
'
I
2
3
4
5
678
VsinO (kin/s)
Figure4. Temperatures
of jets dueto copperimpactsinto
dolomite blocks. The temperatureof the target component
(calcium
vapor)is shown
asa function
of (a)impact
velocity,
(b)
extrapolation
procedure
of emission
intensity
withanequilibrium impact
angle,and(c) thevertical
component
of impact
velocity.
temperature;
consequently,
it is verysusceptible
to uncertainty
in Theexposure
timeis0-2}asafterthefirstcontact
of impact.
Note
angleis fixedat45øin Figure
4a andimpact
velocity
our temperature
measurements.
Estimation
of the massratio thatimpact
requires
a reliabletemperature
measurement.
Figure7, however, is limitedto be 5.43_+0.33km/sin Figure4b.
30,832
SUGITAAND SCHULTZ:SPECTROSCOPIC
OBSERVATIONOF IMPACT JETTING
0000
9000
9000
8000
8000
'
7ooo
6000
7000
ß
5000
6000
4000
5000
I Cu Temperature
0=45 ø
3000[
4
5
Velocity
10000
exposure time
40 0 0
,,
9000!
Impact
angle
and
6
(km/s)
'
O
[
•
•
b
3000
8000•
3000
[]45ø-60
ø0-2us
A
ß
f/
v' ....
ß
I ....
4000
I ....
I ....
5000
7000•
6000
15ø-30ø 0-2us
75ø-90ø 0-2us
30ø 2-5us
60 ø 2-5us
• ....
• ....
7000
8000
9000
Ca Temperature (K)
Figure6. Correlation
of jet temperatures
between
theprojectile
and targetcomponents.
The coppertemperatures
represent
the
projectilecomponent;the calcium components
representthe
•6000•
••5000•
,
targetcomponents.
The impactanglesand exposuretimes after
thefirstcontactof impactaregiven.
4000 i
3000'.,,
0
CuTemperature
• ,
, •,,,
20
40
15030 ø 45 ø
V=5.43+0.33km/s
I,,,
• , , ,
60
80
100
60 ø
75 ø
90 ø
ß Iog(Ca/Cu
Iog(Ca/Cu
I 2-5us
0-2us
•t
Impact Angle (degrees)
10000
9000
8ooo•
,ooo
6000
5ooo
4000
3000L
I Cu Temperature
I
2
3
4
5
6
7 8
-2
Vsin0 (kin/s)
Figure5. Temperatures
of jets due to copperimpactsinto
dolomite
blocks.The temperature
of the projectile
component
(copper
vapor)is shownasa function
of (a) impactvelocity,(b)
impactangle,and(c) thevertical
component
of impactvelocity.
Theexposure
timeis0-2psafterthefirstcontact
of impact.
Note
thatimpactangleis fixedat45øin Figure5a andimpactvelocity
is limitedto be5.43+0.33krn/sin Figure5b.
V=5.35+0.41km/s
I
0.8
0.6
0.4
0.2
0
cos 0
Figure 7. The mass ratio of the target componentto the
projectilecomponentin jets due to hypervelocityimpactsof
copperprojectilesinto dolomiteblocksas a functionof impact
angle.Calciumand copperrepresentthe targetand projectile
massratioof calciumto copperat theverticalimpactangle(90ø)
components,respectively.The values of the massratio shown in
is -10 timesthatat 15ø of impactangle.The datafollowa linear
the diagramincludeonly atomsin the groundstatenot thosein
trend when cos0 is used for the horizontal scales.When other
the excitedor ionizedstates.The exposuretimesafter the first
variables,
suchas 0, sin& andtan& are used,the logarithmic contactof impact are shown in the diagram.Resultsfrom a
mass ratio does not follow a linear trend.
limitedrangeof impactvelocity(5.35+0.41krn/s)areshown.
SUGITA AND SCHULTZ: SPECTROSCOPIC OBSERVATION OF IMPACT JETTING
The increasesin the target-to-projectilemassratio with impact
angle is not uniqueto the combinationof a copperprojectileand
a dolomitetarget.Time-exposedobservationsof emissionspectra
createdby aluminum projectilesimpacting pumice powder also
shows that the projectile signature (A10 band emission) is
dramatically reduced at the vertical impact angle [Schultzet al.,
Vx- sin•p
Vø,
30,833
(1)
where Vo and q0 are impact velocity and deflection angle,
respectively
[Walshet al., 1953]. When this systemis observed
in the collision-centered coordinate, in which the shock front is
1996].
stationary(Figure8b), the platesare collidinginto the shockfront
The experimentalresults also constraintemporalvariation in
the mass ratio in impact jets. With the limited data available at
later times,the massratio doesnot changewith time even though
there is a large change in temperature. This observation
demonstratesthe reliability of this measurementmethod and also
suggeststhat recombinationprocesses
of free atoms(e.g., Ca + O
--> CaO) may not be very rapid in thesehigh-temperature
jets.
with the velocity of V•:
Consequently, theoretical calculations based on asymmetric
jetting providea usefulframeworkfor interpretation.Meloshand
Sonett [1986] and Vickery [1993] developedtheoreticalmodels
for jetting due to impactsby sphericalprojectiles.Their models,
however, approximate an asymmetric collision that occurs
betweensurfacesof a sphericalprojectileand either a sphericalor
a planar target with symmetriccollision between two identical
surfaces. This simplification prohibits us from assessingthe
effects of differences in both shock impedance and impact
velocity with respectto the collisionpoint betweenthe projectile
and the target. These effects are important because our
experiments with quartz and copper projectiles yielded
significantly different results. Then we construct a new
theoreticalmodel for jetting due to an asymmetriccollision by
taking into account the effects of differences in both shock
impedanceand collision velocitieswith respectto the collision
point. Our model is based on an asymmetricjetting theory by
Walshet al. [1953] and a method to assessmaximum shock
heatingof jettingby Kieffer[ 1977].
First, we briefly describethe classicalsymmetricjetting theory
impactvelocityV•. Thusthe jettingvelocityV• in a laboratory
V7= Vo cotq0.
(2)
Note that the effective impact velocity V• in the collisioncenteredcoordinatesystemis much larger than impact velocity
Voin the laboratorycoordinatesystemwhenthe deflectionangle
q0is small.When the deflectionangleq0exceedsa certainvalue,
the regular-regime
flow becomesunstableandtransforms
into the
"irregular
regime"
with
jetting
[Walsh
et
al.,
1953;
Al'tshuler
et
4. Theoretical
Calculations
al., 1962]. Both laboratoryexperiments[e.g., Walshet al., 1953]
Impact velocity, angle, and projectile propertiesall contribute and numerical calculations [e.g., Harlow and Pracht, 1966]
indicatethat the velocity of the jetting in the collision-centered
to the temperatureof a jet simultaneously.Isolatingthe effectsof
these factors is difficult based just on the experimental data. coordinate(Figure8c) is approximatelythe sameas the effective
coordinateis approximated
by
=Vs =+cøSv
o,
sinq0
(3)
which is severaltimes the impact velocity Vo at low deflection
angles q0.This is experimentallyconfirmedby Birkhoffet al.
[1948] and Walsh et al. [1953]. Here it is emphasized that
majorityof the massof collidingplate is not incorporated
into a
jet but staysin the lessshockedzonedownrange,whichis often
called "slug" (Figure 8c).
In the regular regime, the pressurebehind the oblique shock
front and the deflectionangle q0of the plates are connectedby
geometryandthe Rankine-Hugoniotrelation:
cos2
q>
= (1Ps)
1_•+2ps
'
/,t+l
(4)
whereStand b• arecompression
andnormalized
shockpressure
by Walshetal. [1953] andKieffer[1977]. Modelsby Melosh definedby the following:
and Sonett[1986] and Vickery[1993] usedthis combinationof
/,t--P.•_s_
1
(5)
theories.Second,an extensionof the jetting theoryto asymmetric
Po
collision done by Walsh et al. [1953] and its validity are
discussed.
Third, the applicationof the asymmetric
jettingtheory
to a blunt-bodyimpactis presented.
The model described in section 4 assumesboth pure shock
heatingandsteadystateconditionin shock.Suchassumptions
are
used not becausethey preciselyrepresentthe experimental
The symbolsP•, Po, and Ps are dimensionalshockpressureand
conditionsin this studybut ratherbecausethey have been the
densitiesbefore and after shock compression,respectively.The
standardassumptions
usually used in both analytical and
detail of the derivationof expressions
similarto (4) are givenby
numericalmethodsin the literature.Comparisonbetweensucha
Walsh et al. [1953], Kieffer [1977], and Vickery [1993]. The
model basedon the standardassumptions
and the experimental
Ps
: Ps
resultswill helpus understand
bothvalidityandlimitationof the
assumptions.
relationbetween
compression
Standshockpressure
b,.aregiven
by shockHugoniotequationof state[e.g.,Meyers,1994];
bs=
+
4.1. Symmetric Jetting Theory
When two identicalplatescollide at an angle,obliqueshock
fronts develop at the contactpoint O of the two plates (Figure
8a). This type of simpleflow with oblique shocksis called the
"regularregime" [Al'tshuleret al., 1962]. The shockfrontstravel
at a velocityV• givenby
(6)
(7)
whereM• is Mach numberof the effectivevelocity V• and given
by
M•= VJco.
(8)
30,834
SUGITA AND SCHULTZ: SPECTROSCOPIC OBSERVATION OF IMPACT JETTING
Shock
Front
•,.,•:•.
•
,• •.•..`.•?.`•`•;•.•(`.*•...``.•...•••:•.•::•.•..•`:•<•
•:•
......
•i•re
8m A schematicdiagramof the flow field arounda symmetricoblique impact of two identical plates.
Velocitiesare measuredin a laborato• coordinate.The flow is in the regularregime•that is, •etting doesnot occur.
The symbolsV•, V•.,and • are impactvelocity,shockvelocity, and deflectionangle of the plates,respectively.The
thick solidline dividingthe regionswith differentgray colorsindicatesthe shockfront.
The constants is defined in a linear relation betweenparticle
velocity
V•,speed
ofsound
Co,
andshock
wavevelocity
V*:
V*= Co+ sV•
(9)
This relation is observedfor a variety of material over a wide
range of impact velocities[e.g., Marsh, 1980]. Substituting(7)
into (4) yieldsthe deflectionangleq0as a functionof compression
# andMach numberM•,
•= • (•, MO.
(10)
A graphicalapproachshowsthat (10) has a maximum value,
above which a regular-regimeflow does not exist [Walshet al.,
1953; Kieffer, 1977; Vickery, 1993]. This critical condition is
accordingly
given
by 0.__•_½
=0
Equation(13) is solvediterativelyusingthe shockequationof
state(7), yieldingboth the critical deflectionangle (•0cr
and the
criticalshockpressure
bcr.
In the irregularregimeabovethiscriticalangle,the flow field
is very complex,and no generalanalyticalsolutionhas been
found. The pressureof the stagnationpoint, however,can be
estimated.Assumingthat the pressureP•t at the stagnationpoint
is approximatelythe same as the pressureP• just behind the
shockfront and that the enthalpyof colliding materialbefore
shock compressionis much smaller than thereafter, Kieffer
[1977] derived an expressionrelating the effective impact
velocityV• andthestagnation
pressure
P•tfromBernoulli's law:
(11)
1V•
2=2Po
Ps•t
•s•t.
2
•st + 1
(14)
and equivalentlyby
(12)
Substituting
(4) into(12) gives
From (5), (6), (7), (8), and (14), the pressure
P•, andcompression
#•.,at the stagnation
pointare iterativelyobtainedas functionsof
the effectiveimpactvelocity V•. The internalenergyE•, at the
stagnationpoint is given by the Rankine-Hugoniot
relationfor
energy
{•-(•+1)fix
(g+1)2-sg2
=(g+l)
}' (13)
M/2
{•(1-s)+
1}
3
•st
+l'
Es
t=2Po
Pst
gst
Vo
.... •,.....:•
.............
::..............
:......................
• -;:........
Figure 8b. A schematic
diagramof the flow field arounda symmetricobliqueimpactof two identicalplates.
Velocitiesare measured
in the collision-centered
coordinate,
in whichthe conversion
pointof the two platesO is
stationary.
The symbolV• is theeffectiveimpactvelocityof theplatewithrespect
to theshockfront.
(15)
SUGITA AND SCHULTZ: SPECTROSCOPIC OBSERVATION OF IMPACT JETTING
30,835
ShocksFront
Fibre 8c. A schematicdiagramof the •ow field arounda symmetricobliqueimpactof two identicalplates.The
•ow is in the i•eg•lar regime; that is, jetting occurs. The velocities are measuredin the collision-centered
coordinate.
Thesymbol• isjettingvelocity.
The energy given by (15) can be used as a referencefor shock
heatingwithin the jet. In reality, however,the shockfront does
not elevatethe pressuredirectly to the stagnationpressure.The
matedhal compressed at the shock front is adiabatically
compresseduntil it reachesthe stagnationpressure.Thus (15)
overestimatesthe internal energyof a jet. Kieffer [ 1977], in fact,
pointsout that the internalenergyat the stagnationpoint obtained
by numericalcalculationsby Harlow and Pracht [1966] is -80%
of that predicted by this method. Moreover, the maximum
internalenergyof jetted matedhal
whosestreamlinedoesnot pass
the stagnationpoint is less than the internal energy at the
stagnationpoint. Consequently,the energygiven by (15) should
approximatean upperlimit for shockheatingof jetting.
For a given impact velocity Vo, the effective impact velocity
V• decreaseswith deflectionangle 9 (see (2)). Becauseshock
heatingduringjetting increaseswith the effectiveimpactvelocity
V•, a lower deflectionangle9 resultsin a higherenergy(see(2)).
However,becausethere is no jetting below the critical deflection
angle 9cr,the maximumheatingof jetting occursat the critical
angle.
4.2. Asymmetric Jetting
Unlesstwo collidingplateshave symmetricimpact velocities
as well as identical thickness and material properties, the
collision becomes asymmetric. The flow field in such an
asymmetric collision is schematically shown in Figure 8d.
Becauseof the asymmetry,the effectiveimpact velocitiesV• and
V2 and the deflectionanglesq0•and q02
of the two surfacesare not
equal. The ratio of the two deflection angles q0• and q02is
determinedby the boundaryconditionon the matedhalboundary
behind the shock fronts. Walshet al. [1953] assumesa free-slip
boundarycondition at the material boundary.This assumption
requires that both the velocity componentperpendicularto the
boundaryand the pressuregap acrossthe boundaryis zero but
allowsa jump in the velocitycomponentparallelto the boundary.
Such an assumption,however, is not correct in a strict sense
becauseno real fluids are inviscid; hence, no velocity jump is
allowed anywhere.Thus it can alsobe assumedthat two velocity
componentsare equal acrossthe boundary[Ang, 1990]. For the
latter assumption,however, a pressurejump exists acrossthe
boundary.The pressuregradientis in the directionto changethe
deflectionanglesto thosepredictedin the free-slipassumption.In
reality, the boundary may not strictly follow either boundary
conditionbut may undergooscillationas observedin explosive
welding experiments [e.g., El-Sobky, 1983], analytical
calculations [e.g., Godunov et al., 1970], and numerical
simulations[Miller, 1998]. Nevertheless,impact experimentsof
asymmetric collisions using cone-shapedprojectiles and flat
Figure8d. Schematic
diagramof the flow field aroundan asymmetric
obliqueimpact.The deflectionanglesq0•and
q02,
effectiveimpactvelocitiesV• and V2, and shockfront velocitiesV• and V•2in the two platesare different,
respectively.
The wedgeangleo•of thetwoplatesis equalto thesumof thetwodeflection
anglesq0•andq02.
30,836
SUGITAAND SCHULTZ:SPECTROSCOPIC
OBSERVATIONOFIMPACTJETTING
targetsby Allen et al. [1959] show that the critical conditionis
predictedwell by the asymmetriccollisionmodel with the freeslip boundary condition assumed by Walsh et al. [1953].
Consequently,we adoptthe free-slip boundaryconditionin this
studyas a reasonableworking assumptionand neglecteffectsof
shear around the material boundary. The significance of this
simplificationis discussed
in section5.
The solution for this boundary condition problem needs an
iterative procedure.First, initial values of deflectionangles •0•
and % (= a- q9•)are assumed.For the assumeddeflectionangles
and given effective impact velocities V• and V2, the shock
pressuresP,. behindthe shockfronts are calculatedfor both sides
of the materialboundaryusing (4) and (7). Second,the deflection
angles are adjusted.For example, if the shock pressurein the
upperzone is higherthan the lower zone, the deflectionangle •0•
of upper zone is decreasedand hence that % of lower zone is
increased. Third, the shock pressuresare recalculated. This
procedureis repeateduntil both shockpressures
coincide.
As the wedge angle a of the plates increases,the shock
pressureP,. and the deflectionanglesq9•and % increase.When
the wedge anglea reachesa certain value, one of the deflection
angles reaches its critical value. Above this angle, a regularregime flow cannotexist, and jetting occurs[Walshet al., 1953].
This critical angle a•.rof asymmetricjetting is calculatedin the
following way.
For the given effectiveimpactvelocitiesV• and V2,the critical
pressures
Pcrand the critical deflectionanglesq)lcrand q)2cr
can be
calculatedfor both plates of the collisionusing the method for
symmetricjetting (i.e., (7) and (13)). If the critical shockpressure
of the upper plate is lower than that of lower plate, the shock
pressureof the lower plate for the deflectionangle of oc- q)lcris
calculated,where q)lcris the critical deflectionangle of the upper
plate. If the newly calculatedshock pressureis lower than the
critical pressureof the upper plate, the deflection anglesof the
upper and lower platesmust decreaseand increase,respectively,
in orderto achievebalancein pressureacrossthe boundary.Then
the deflection angle of the upper plate becomessmaller than the
critical angle. The deflection angle of the lower plate is also a
subcritical value because the shock pressurefor the critical
conditionfor the lower plate is higherthan that of the upperplate
here. Thus a regular-regimeflow exists in this condition.If the
newly calculated shock pressure is higher than the critical
pressureof the upper plate, however,jetting occurs.If the two
pressuresare equal,it is a critical condition.
As in the symmetricjetting case,shockheatingin asymmetric
jetting maximizes at a critical condition for a given impact
velocity. The energy of a jet is calculatedwith the method by
Kieffer [1977], i.e., (7), (14), and (15). Becausethe effective
impact velocitiesV• and V2 of the two platesof an asymmetric
collision are generally unequal, different degrees of shock
heatingare obtainedfor jetting from the upperand lower plates.
This method for symmetricjetting assumesthat the ejection
velocity of jet is aligned to the material boundarybehind the
shockfronts.Althoughsuchalignmentis not strictly guaranteed,
analytical calculationsby Pack and Curtis [1990] indicate that
departurefrom suchalignmentis small.
a
Projectile
b
Figure 9. Geometric configurationof an oblique impact by a
sphericalprojectile into a half-spacetarget. (a) The geometric
configuration is shown in a three-dimensionalperspective.
Impact angle, the vector of impact velocity, and horizontal
azimuthalangle from the impactdirectionare denotedby 0 and
¾im,and •, respectively.The impactvelocity is measuredin the
laboratorycoordinateand decomposed
to V//and Vt. The central
plane is also shown.This plane is definedhere as a vertical plane
4.3. Application to Spherical Impactors
that constrainsthe projectilecenterand is parallel to the impactWhen a sphericalprojectile impacts a half-spacetarget, the velocity vector. (b) The crosssectionalong the central plane is
wedge angle oc between the surfacesof projectile and target shown.Note that the deflectionanglesof projectileq9•and target
continuouslyand rapidly increasesas the projectile penetrates q92and wedge angle a• changewith time as projectilepenetrates
into the target (Figure 9). Thus the effectiveimpactvelocitiesfor into the target.
SUGITAAND SCHULTZ:SPECTROSCOPIC
OBSERVATION
OFIMPACTJETTING
30,837
material
fromtheleading
sideisexpected
tobeobserved.
a projectile
V• anda targetV2withrespect
to theshock
fronts(see jetting
with the leading-edge
velocities
givenby (16)
Figure8dfor definition)
change
withtimeandareexpressed
as Thuscalculations
and
(17)
are
appropriate
for
comparison
with
the
experimental
functions
of impactvelocityV,....impactangle0, andwedgeangle
data.
Thenusingtheasymmetric
jettingtheorydescribed
above,
the
V/-sin•0
V/m
(16) criticalwedgeangle%r for an impactof a spherecan be
sin o•
calculated
fora givenimpact
velocityVim
andanimpact
angle0.
The maximumshockheatingof jettingfrombothprojectile
and
V2
=0•)
sin(a
+ V/m.
withtheasymmetric
theory.
(17)targetmaterialisalsocalculated
sina
Theserelationsare graphically
shownin Figure10. Note that
(16) and(17) arevalidonlyat theleadingedgeof a projectile.
The effectiveimpactvelocities
dependgenerallyon azimuthal
directionfrom the centerof a projectile[seeMeloshandSonett,
1986;Vickery,1993].Our spectroscopic
observations,
however,
are focusedon the downrangeside of the impactpoint, where
It is noteworthy
thatthe abovetwo-dimensional
formulation
forshock
compression
onthevertical
planeincluding
theleading
edgeof a spherical
projectile
is identical
to thatfor shock
compression
of impact
of a cylinder
intoa planar
target.
Thereis
noparticle/shock
velocity
component
perpendicular
to thetwodimensional
planein eithercase.Thereis, however,
a subtle
but
distinctivedifferencebetweenthe two cases.In the following,the
•. , \",,•
', / \',,,•
•. ,\",•
Impact
angle,
0
•90
o
.........75ø
, ",•,\?,,•,,
-.-_
_-'•_-_
•30
ø
60ø
45 ø
-
a
_
illllllllllllllllllllllllllllllllllllllll
IIIIIIIIIIIIItlilllllllllllllllllllllllllllllll
30
60
90
Wedge Angle,o•(degree)
',,",,i•,.
4.-
:
i
Impact
angle,
O::
/ '. •,
', • ,•;,
'•
•
ø
.•
---60
ø
:
......... 75ø
• \•,
, \x;:.
____45
: 15ø', •, '•',
.....
s 3 }- • 3øøx,45x,o•,'•,,
2•
---90
ø
30
-- .... 15ø
.,.• x.••
1:
"•'•' •' •
30
:
:
•
•
.......
0 ,,........
,.........
,.........
,.........
,.........
,.........
,.....
0
:
60
90
Wedge Angle,a (degree)
Fibre 10. Theeffective
impact
velocities
fortheprojectile
V]andthetarget
V2in animpact
of a spherical
projectile
intoahalf-space
target
asfunctions
ofbothimpact
angle
0 andwedge
angle
•. (a)Theeffective
impact
velocity
fortheprojectile
normalized
byimpact
velocity
Velcro.
(b)Theeffective
impact
velocity
forthetarget
no•alJzed
byimpact
velocity
Vff½•.(c)Theratioofeffective
impact
velocities
fortheprojectile
tothatforthe
target
'V•2. (d)Thedifference
between
theeffective
impact
velocities
oftheprojectile
andthetarget
no•alized
by
impactvelocity(V2-V•)•i•.
30,838
SUGITA AND SCHULTZ: SPECTROSCOPIC OBSERVATION OF IMPACT JETTING
Impact angle, 0
90
75
60
45
.........
2
ø
ø
ø
ø
30 ø
15 ø
ß
/
..........
c
0
30
60
90
Wedge Angle, c• (degree)
d
0
......... 75......
--
--
- 60 ø
-
30ø
•
- 15 ø
30
60
90
Wedge Angle, c• (degree)
Figure 10. (continued)
directionperpendicular
to the aboveverticalplaneis referredto
as • direction,and the verticalplaneis referredto as the central
plane(seeFigure9a). A spherical
impacthasdivergence
dueto •
directionvelocityevenon the centralplanebecause• direction
velocityin the neighborof the centralplaneis not zero,whereas
thereis no divergence
dueto • directionvelocityanywherein a
cylindricalcase.
This finite differencein velocity divergence,however,is not
importantfor the shockcalculationin the presentstudy.Sincethe
widthof a shockfrontis practicallyinfinitesimalin general,the
divergenceof particlevelocitiesperpendicular
to a shockfrontis
virtually minus infinity [e.g., Landauand Lifshitz, 1987]. The
size of this negativeinfinity of velocitydivergencedetermines
the degreeof shockheating.Thus finite differencein velocity
convergence
does not influencethe degreeof shockheating.
Consequently, the above two-dimensional formulation is
applicableto the shockwithin the centralplaneof a spherical
approach.It requiresfurtherconsideration.
The vectorof impact
velocityVimcan be decomposed
to the vertical(Vñ --V/msin0)
and horizontal
(V//= V/mcos0) components
for impactangle0
measuredfrom the horizontal,where gi,--IV•ml.When the vector
of impactvelocityVimis projectedto a verticalcrosssectionthat
containsthe centerof the sphericalprojectileand azimuthalangle
• measured
fromthe impactdirection(Figure9a), it has Vñ of
vertical componentand V//cos• of horizontalcomponent.
The
componentperpendicular
to the crosssectionis V//siny/.It does
not contributeto shockcompression
on the collisionbetweenthe
target and the projectile, however, because this velocity
componentis perpendicularto the local collisional contact
surface. Consequently,the shock compressionat the contact
surfaceat • of azimuthalangleawayfromthe leadingedgeof the
projectilecanbe estimated
by the samemethoddescribed
above
with an azimuthalcorrectionfactor of cos• for the horizontal
velocitycomponent.
The azimuthalcorrectionfactoris equalto 1
impactor.
for • = 0ø, 0.99 for • = +8ø, and 0.9 for • = +_26
ø. Thus the
However,it is obviousthat shockcompression
off the central effect of azimuthalangleis relativelyminor over a considerable
plane is different from the result of the above two-dimensional rangeof angle.
SUGITA AND SCHULTZ: SPECTROSCOPIC OBSERVATION OF IMPACT JETTING
4.4.
Calculation
Results
30,839
conditionswherethe projectilecanreacha criticalconditionprior
to the target is much narrowerin a coppercasethan in a quartz
case. At low impact angles,however, a projectile will reach a
critical condition first, even if the impedance of projectile
dolomite are not available, calcite data are used here. All the
material is much higher than that of the target material. The
Hugoniotdata are takenfrom Marsh [ 1980] and Meyers [ 1994]. reasonis the following. The effective impact velocity V• of a
Figure 11 alsoshowsdeflectionangles(p•and (p:of the projectile projectileis much smallerthan that of a target V2 at all wedge
and targetat critical conditionsand revealsthe materialreaching anglesa when the impactangle t9is small (Figures10c and 10d).
its critical condition first.
Both theoryand experimentsindicatethatjetting occurswhen an
The deflectionangle (p•of the projectileis larger than that of effective impact velocity is lower than a critical velocity for a
the target q•: in the quartz impacts. However, the relation is given deflectionangle [e.g., Walshet al., 1953; Kieffer, 1977].
reversedin copperimpacts.This resultsfrom the differencein the Consequently,a projectileis more susceptible
to jetting at lower
impedancebetweenthe two projectilematerials.Becausecopper impactangles.At higherimpactangles19,however,the effective
has a much higherdensitythan both quartzand carbonates,it is impactvelocityV2 of the targetis similarto or smallerthanthat
more resistantto deflectionowing to shockcompression.
As a V• of the projectile (Figures 10c and 10d). Thus the target
result of the small deflection angle, the range of impact becomesmoreproneto jetting at higherimpactangles.
The critical angle %r for jetting was calculated for
experimentalconditionsof impactvelocity Vimand impact angle
0 and materialproperties(Figure 11). Since Hugoniot data for
35
•:•- ....................................................................
-•
Target
Projectile
a
(• 30
•
•
25
< 20
•
15
•- 10
o
(•
5
QuartzProjectile
i
I,,
0
o
30
, I,,I,,,,,,,
I,,,,,,,,,I,,,,•,
60
90
ImpactAngle, 0 (degree)
35
Target
e
30
e
25
v
< 20
•
15
c
10
o
5
0
30
60
90
ImpactAngle, 0 (degree)
Figure 11. Critical conditionsfor impactsby (a) quartzand (b) copperprojectilesinto calcitetargets.The critical
wedgeangleO•cr
anddeflectionanglesof boththe projectile(Dlcr
andthe target(D2cr
are shownas functionsof impact
angle 19.The jet-initiating material is shown at the top of the diagrams.Impact velocity of 6 km/s is used for
calculation.
30,840
SUGITA AND SCHULTZ' SPECTROSCOPICOBSERVATION OF IMPACT JETTING
The criticalwedgeangle O•cr
at differentimpactvelocitiesVim
is comparedin Figure 12. The criticalwedgeangleactis greater
at higher impact velocities Vi,n becausethe effective impact
velocitiesof both projectileand target V• and V2 increasewith
impactvelocity.It is alsonotedthat a criticalwedgeangle%r as
a functionof impactangle0 hasa maximum(Figures11 and 12).
At lower impact angles,the effective impact velocity V• of a
projectileincreaseswith impact angle 0 and reachesa critical
condition first (Figure 10a). Since a higher impact velocity
requiresa higher wedge angle cr for jetting [e.g., Walshet al.,
1953; Kieffer, 1977], the critical wedge angle Crc•
increaseswith
impactangle 0. At higherimpactangles0, however,the critical
wedge angle is controlledby the target becauseit reachesa
critical conditionfirst. For wedge angle cr higher than -25 ø, the
effective impact velocity V2 of a target has its maximum at an
impact angle 0 of-60 ø (Figure 10b). Thus, for impact angles0
higherthan -60 ø, the critical wedge angle %• decreases
with
impact angle 0. Consequently,
the critical angle%• has a
maximum
value.
Maximumshockheatingof jets derivedfrom botha projectile
and a targetis calculatedwith (7), (14), and (15) and shownin
Figure13. The heatof vaporization
and shockheatingof calcite
by plane-normalshockare also shownfor comparison.
The
plane-normalshock cases are calculated with impedance
matchingmethod[e.g., GaultandHeitowit, 1963]. The heat of
vaporization(11.3 MJ/kg) of calcite is calculatedfrom
thermodynamic
data [Chaseet al., 1985; Woodsand Garrels,
1987] assumingthat the vaporphaseof calciteconsistsof CO2
and CaO gasesand that the vaportemperature
is 3000 K. It is
worth noting that the heat of incomplete vaporization or
degassing
of calciteis much smaller;2.5 MJ/kg [Chaseet al.,
1985; Woodsand Garrels, 1987]. Here the end products of
...............................................
35 __•
6,i
km/s
•
Target
..........................................
Projectile -><
-•
•
3o
6 km/s
•
25
4 km/s
•
20
ß
15
•
10
m
o
QuartzProjectile
0
30
60
90
Impact Angle, 0 (degree)
Projectile
35 •' ................................
.
-o
"'"
Target
b
6
km/s
•,
4 km/s
•
6 km/s
25
4 km/s
•!/ 20
o
15
g
lO
5
Copper
Projectile:
_
0
30
60
90
Impact Angle, e (degree)
Figure 12. Critical wedge angle %• of (a) quartzimpactsand (b) copperimpactsas a functionof both impact
velocity Vimand impactangle 0. Solid calcitetargetsare assumedfor thesecalculations.The jet-initiatingmaterialis
shownat the top of the diagrams.Impactvelocityis indicated.
SUGITA AND SCHULTZ: SPECTROSCOPIC OBSERVATION
35
i
a.
i
i
,
,
I
i
l
i
i
I
i
i
,
[
3O
30,841
35
i
b. Copper projectile
Quartz projectile
..........
OF IMPACT JETTING
Projectile jet
Target jet
.....
Projectile
jet
3O
6km/s
Target
jet
•
,
ß' 6 km/s
ß
25
25
'
,
,
ß
,,'
ß
6 km/.s,.
ß
o
,
ß
ß
ß
ß
,,
2O
ß
ß
,,
ß
4 km/s
Heat
of
vaporization
'• ..,,'
15
of calcite
Heatofvaporization,,"
ofcalcite
.c'
.
4 km/,s
...-'
ß
ß
10
10
ß
-'
4 km/s
.
.
.
ß
ß
.
ß-'
.,,
__
ß-'
,
Plane-normalshock-
...
at6 km/s
ß
o
ß
ß
ß
Plane-normal shock at 6 km/•
Plane-normal
ß
ß
60
90
..-
•
. .
i
I
.
Plane-normalshock,
:::.-'
0
30
o
ß
shock at 4 kmh
0
0
.
ß
ß
-
at4 km/s
i
0
Impact Angle (degree)
I
i
I
I
I
I
30
I
I
I
I
I
I
I
60
90
Impact Angle (degree)
Figure 13. Comparisonof shockheatingof asymmetricjets, heat of vaporizationof carbonate,and shockheating
of plane-normalimpacts.Calculationsused(a) quartzand (b) copperprojectiles.The maximumshockheatingof
both projectileand targetcomponents
in asymmetricjets is shown.The jetting model assumesthat a spherical
projectileimpactsa half-spacecalcitetarget.The plane-normal
impactmodelshowsshockheatingof calcitetargets
only. Impactvelocitiesare indicatedin the diagram.The heatof vaporizationof carbonateusedhereis the enthalpy
to vaporizecalciteat roomtemperatureto carbondioxideandcalciumoxidegasesat 3000 K.
incompletevaporizationare assumedto be CO2 gas and CaO
solid at 1000 K. Consequently,
much weaker shockheatingthan
jetting may induce significant vaporization of carbonate.
Nevertheless,resulting impact vapor due to such weak shock
shouldnot containsignificantamountsof CaO or Ca gasses.
There is a significantdifferencebetween the projectile and
targetcomponentsof jetting. The maximum shockheatingof the
projectile componentat .low impact angles is very small; even
smallerthan plane-normalshockheating. However, it increases
monotonicallywith impact angle and becomescomparableto or
even greaterthan shockheatingof the target componentat high
impactangles.These are readily explainedby the behaviorof the
effectiveimpactvelocity V• of a projectile,which is very smallat
low impact angles 0 and increasesmonotonicallywith impact
angle 0 (Figure 10a). However, shock heating of the target
componentis alwaysmuchhigherthanthat due to a plane-normal
shockand has a maximum value at an intermediateimpactangle
0 (Figure 13). This is also consistentwith the behavior of the
effectiveimpact velocity V2 of a target,which is significantly
larger than impact velocity Vimfor relevant wedge angles a
however, the critical wedge angle O•crreachesa plateau (O•cr•
200-25ø) at relativelylow impactangles:0- 45ø (Figures1lb
and 12b). For a constantwedge angle tx, the effective impact
velocity V2 of a target increaseswith impact angle 0 until it
reachesits maximumat relativelyhigh impactangles,0 = 60-75ø
(Figure10b).Thus shockheatingof the target-component
jet due
to a copperimpactorhasits maximumat higherimpactangles0
thanthat for a quartzimpactor.
5. Comparison Between Theory and Experiments
In this section, we comparethe results of the theoretical
calculationswith the spectroscopicobservationdata, showing
both consistencies and inconsistencies.
Then the causes for the
disagreements
betweentheoryandtheexperimentsare discussed.
5.1. Jet Temperature
One of the most important consistenciesbetween jetting
theory and the experimentalresultsmay be the extremely high
(<45ø) and has a maximumat an intermediateimpactangle 0 degreeof heating.The observedhigh-temperaturegas with little
(Figure 10b).
liquid/solid phasescannot be attainedby plane-normalshock
Copperand quartzimpactshavedifferentdependencies
for the (Figure 13). Shock due to jetting, however, can easily heat
degreeof shockheatingin thejet as a functionof impactangle0 carbonate target to its complete vaporization. Another
(Figure 13). This difference results from the behavior of the consistency
betweentheoryand experimentsis the velocity effect
criticalwedgeangle %r (Figures11 and 12). The critical angle on jet temperatures. Theoretical calculations indicate the
O•crfor quartz impactorsincreasesup to an impact angle 0 of temperaturesof both projectile- and target-derivedjets increase
-70 ø, where the transitionof jet-initiating material occurs.The with impact velocity. This result applies to both quartz and
increasein wedgeangletx lowersthe effectiveimpactvelocities copperprojectilesimpactingcarbonatetargets(Figure 13). This
and hence decreasesshock heating. For copper impactors, theoreticalpredictionis very consistentwith experimentalresults.
30,842
SUGITAAND SCHULTZ:SPECTROSCOPIC
OBSERVATION
OFIMPACTJETTING
Spectroscopicobservationin this study indicates that the
temperatures
of both target-and projectile-derived
jets increase
with impact velocity for the combinationof copperprojectiles
and dolomitetargets(Figures4a and 5a). Resultsof previous
experimentsby Sugitaet al. [1998] also indicate that the
temperature
of target-derived
jets createdby quartzimpactsinto
dolomite targets increases with impact velocity. Here the
experimental
resultswell; specifically,
the target-to-projectile
massratioincreases
steadilywithimpactangle.Hereit shouldbe
notedthatthe definitionof impactangleby Vickery[1993],who
measures
it from the vertical,is oppositefrom the usagein this
study.Thepredicted
change
in target-to-projectile
massratioin a
jet as a functionof impactangle[Vickery,1993],however,is
smallerthantheexperimental
resultsby abouta factorof 5.
temperature
Of projectile
component
wasnotmeasured
because
of the lack of strongemissionlines/bandsfrom quartzprojectiles
in the observedwavelengths.
Comparison
of the effectsof bothimpactangleandimpedance
contrast on jet temperatures,however, reveals significant
inconsistenciesbetween theory and the experimental results.
First,the high temperature
in the projectilecomponentfor copper
impactorsat low impact anglesobservedin the experiments
(Figure5) is not readilyexplainedby thejettingmodel.Predicted
degreesof shockheatingat low impactanglesshownin Figure
13b are comparableto or less than the enthalpy(6.2 MJ/kg;
Chaseet al. [1985]) to generatecoppervapor at 3000 K. Here it
is emphasized
that the shockheatingcalculatedin the modelis
the internalenergyat a peak shockpressure,after which the
internal energyof jetting vapor decreasesrapidly by adiabatic
decompression.
Our spectroscopic
observationscapture the
temperature
of jetting vapor,whichhas experienced
substantial
adiabaticdecompression.
Consequently,
the calculatedinternal
energy shownin Figure 13 providesan upper limit for the
observedjet temperatures.
Second,the theoreticalmodelcannot
accountfor the quantitative
dependence
of temperature
on impact
angleandimpedance
contrast.
The theoretical
modelpredicts
that
thetargetcomponent
of jettingdueto quartzimpactsshouldhave
a lower temperature
at the impactangle 0 of 90ø than at 45ø
(Figure13a).The experimental
datafor quartz,however,reveala
trend of increasingtemperatureas a functionof impact angle
between30ø and 60ø [Sugitaet al., 1998]. Third, the minimal
effect of impact angle on the jet temperaturefor impactsof
copperprojectiles
intodolomitetargets(Figures4b and5b) is not
consistent
with a largeincreasein temperature
obtainedfrom the
model calculations(Figure 13b). Fourth, the theoreticalmodel
predictsthatshockheatingof thetarget-component
jettingshould
be significantly
higherwith a copperprojectilethanwith a quartz
projectileat all impactanglesfor a givenvelocitybecause
of the
highershockimpedance
of copper(Figure13).Experimental
data
of both the presentstudy (Figures4 and 5) and Sugitaet al.
[1998], however,indicatethat the range of distributionin the
calciumtemperature
for copperimpactsis comparable
to thatfor
quartzimpacts.
Anotherimportantdiscrepancy
in jet temperature
betweenthe
theoryand the experiments
is the correlationbetweenthe target
and projectile components.As mentioned above, the
experimental results indicate that the copper temperature
(projectilecomponent)
correlateswell with calciumtemperature
(target component)and that the projectile componentis
constantlyabout1000 K higherthanthe targetcomponent
for a
wide range of impact angles(Figure 6). The jetting model,
however,doesnot predictsucha correlationbetweentargetand
projectilecomponents
(Figure13).
5.2. Mass Ratio
The observedtarget-to-projectile
massratio in a jet can be
comparedto theoreticalpredictionin the literature. Vickery
[1993] estimatedtarget-to-projectile
massratio within the whole
jetting phaseejectedfrom all the azimuthalanglesarounda
projectile.Her theoreticalmodel qualitativelyreproduces
the
5.3. Model
Reassessment
The aboveagreements
anddiscrepancies
betweentheories
and
experimental
resultsindicatethat the jettingmodelbasedon
standard
theoriesaccounts
for somequalitativecharacteristics
of
thejetting phenomenadue to obliqueimpactsby bluntbodiesbut
cannotpredict specificfeaturesquantitatively.We will discuss
threepossiblecausesfor the discrepancies
on jet temperature
and
a possibleexplanationfor disagreement
on massratio in a jet.
5.3.1. Stagnation-pointapproximation. First, the methodto
estimate shock heating of jetting material is potentially
problematic.The maximum shock heating of a target and a
projectileis estimatedat a stagnationpoint independentlyusing
(7), (14), and (15). This approachby Kieffer [1977] implicitly
assumesthat the stagnationpressuresof the two components
are
different.If the flow duringjetting is steadystate,however,the
stagnation
pointsof the two components
mustcoincideandhence
havethe samepressure.
A proofis the following.
The flow in the central plane is considered(see Figure 9).
Them is no velocitycomponentacrossthe centralplane.If the
flow is in a steadystate,the materialboundaryis stationaryand
has no velocity component'
perpendicularto it. When jetting
occurs,the velocity componentparallel to the boundaryline in
thejet hasthe oppositedirectionof that in the slugpart,viewed
from the collision-centered
coordinatein which the apex of the
two colliding surfacesappearsstationary(compareFigure 8c).
Consequently,there is a point on the boundaryline where the
velocitycomponentparallel to the materialboundaryis zero.
Becausethe verticalvelocitycomponentis alwayszero alongthe
boundary,this point has no velocity, i.e., a stagnationpoint. If
boththe targetandprojectilecomponents
havejetting flows,then
both have a stagnationpoint on the boundaryline. The whole
boundaryline belongsto a streamline.As a result,pressurealong
the material boundaryon each side has its maximum at the
stagnationpoint according to Bernoulli's law. Because the
pressureson the both sidesof the boundaryare the same,the
locationandthe pressure
of the maximum-pressure
pointsof both
projectileand target componentsmust coincide.Consequently,
the stagnationpointsof the both sidesof the materialboundary
coincideand have the samepressure.In reality, however,a large
differentialvelocityexistsnearthe boundariesandviscouseffects
becomeimportant. Thus Bernoulli'slaw may not apply strictly
at the boundary.Nevertheless,if viscosityis relatively small, a
thin viscousboundarylayer forms along the interfacearoundthe
boundary,in which pressureis approximatelyconstantin the
directionperpendicularto the interfaceboundary[e.g., Landau
and Lifshitz, 1987]. Becausemost of the velocity gradient is
concentratedin the viscousboundarylayer, the flow field and
pressuredistributionoutsidethe viscousboundarylayer may be
approximatedwell by the inviscid model [e.g., Landauand
Lifshitz, 1987]. Thus the aboveargumenton stagnationpressure
in an inviscid fluid is approximatelyapplicableto flow with a
thin boundarylayer.
The coincidencein stagnationpressure,however, does not
necessarilyaccount for the observedcorrelationbetween the
projectileandtargetjet components.
Becausethe effectiveimpact
SUGITA AND SCHULTZ: SPECTROSCOPICOBSERVATION OF IMPACT JETTING
velocitiesV• and V2 of a projectileand a target are different,the
ratio of pressureincreaseby adiabaticcompression
to that by
shockcompression
must be differentbetweenthe target and the
projectilein order to attain the samestagnationpressure.More
specifically,this ratio is higher for the componentwith a lower
effective impact velocity becauseadiabaticcompression
raises
pressurehigher than shock compressionfor a given collision
velocity.Thusthe ratio of adiabaticcompression
is largerfor the
projectilecomponentthan the target componentin low-angle
impacts,in whichthe effectiveimpactvelocityof a projectileis
smaller than that of a target (Figures 10c and 10d). Because
adiabaticcompressiondoes not contributeto an increasein
thermalenergy,the contrastin degreeof heatingin Figure 13
30,843
the cone-shapedprojectile may not be controlledby shock
compression
but by Huygens' law. Their experimentalresults,
however,showedthat the critical conditionis predictedwell by
an asymmetric jetting theory based on the steady state
assumptionby Walsh et al. [1953]. Thus the effect of timedependentflow may not be very importantfor a critical condition
for impactjetting.
5.3.3. Inviscid approximation. The effectsof viscousshear
heating may also contribute to the difference between the
theoreticaland experimentalresults. The differencein velocity
acrossthe materialboundarybetweena projectileand a targetis
unavoidablein an asymmetriccollision. Here, it is emphasized
that the differentialmotion on the material boundarydoes not
would be increased further when the effect of coincidence of
occur in a symmetric impact of two identical plates. The
stagnationpressure is taken into account. Consequently, differential motion may cause significant shear heating as
uncertaintyin the methodby Kieffer [1977] to estimateshock inferred for later stagesof impact vaporization[Schultz,1996].
heatingdoesnot accountfor the discrepancy
betweenthe theory This processmay greatly change the jet temperature.Because
lower angleimpactshavelargerdifferentialvelocity(Figure 10d)
andthe experiments.
5.3.2. Steady state approximation. A secondpossiblecause at probablecritical wedge angles(30ø < 0 < 40% greatershear
heating will occur along the material boundary. This may
for the discrepancy between observed and expected jet
contributeto greaterheatingof the projectilecomponentat low
temperaturemay involvethe assumptionof a steadystateflow. A
colliding matehal may not stop at the mean material boundary impact anglesand may fill the gap in temperaturebetweenthe
but may overshootand penetratethroughit; that is, the material theory and experiments. The good correlation between the
boundary departs from its average line. Then the overshoot projectileand target componentsin a jet is also consistentwith
through the mean boundarymay lead to backlash;that is, the viscousheating,sincethe differentialvelocity (i.e., shear)across
materialboundarymovesback beyondthe meanboundary.Such the materialboundaryand resultingviscousheatingare sharedby
oscillatory motion of the material boundary (i.e., Kelvin- bothsidesof the boundary.
Among the three factorsdiscussedabove,the effect of viscous
Helmholtz instability) is observed in explosive welding
experiments with jetting [e.g., EI-Sobky, 1983], analytical shearheatingcan accountfor the discrepancyin jet temperature
calculations [e.g., Godunov et al., 1970], and numerical between theoreticalpredictionsand experimentalresults most
successfully.Nevertheless,the effects of nonsteadystate flow
simulations[Miller, 1998]. Becausesuch oscillatorymotion of
and other unknown factors still need to be considered viable and
the materialboundarygivesrise to motionof shockfrontsaround
will be the focus of future studies.
the collisionpoint,the effectiveimpactvelocityof incomingflow
5.3.4. Alternation in material to jet. One possiblecausefor
with respect to the shock front will also fluctuate. Thus the
is thatthe massratio in a jet asmodeledby
resultingshockheatingin the jet shouldhave fluctuation.Since the large discrepancy
our observation
usingemissionspectroscopy
is more sensitiveto Vickery [1993] is solely based on the difference in ejection
jets. This model
a highertemperaturecomponent,the fluctuationin shockheating velocitiesbetweentarget-and projectile-derived
may bias the measuredjet temperatureupward.This may reduce assumedthat the thicknessof target-derivedjet and that of
the temperature gap between 'theoretical predictions and projectile-derivedjet are the same. The thicknessof the two
components
of a jet, however,does not necessarilyhave to be
experimentalresults.
Anotherpossibleconsequence
of break down of steadystate identical.In fact,Ang [1990] arguesthat a jetting phasemay be
approximationis an inaccuratepredictionof the critical condition dominatedby material from either projectileor target depending
for jetting. When the flow aroundan asymmetriccollisionis not on which componentreachesthe critical condition for jetting
in a steady state, the angle of shock front with respectto a first. Both the effective impact velocity and wedge angle
colliding surfacemay not be controlledsimply by the ratio of between projectile and target change during penetration. In
shockcompression
as shownin Figure 8d but may be controlled general,neitherprojectilenor targetmeetsa criticalconditionfor
directly by Huygens' law wherein a shock wave front is an jetting at the first contactof impact.During penetration,eitherthe
envelope of wave circles from preceding collision points. projectileor targeteventuallywill reach a critical conditionfor
Huygens' law, however, needsto be modified to accommodate jetting. If the projectile reachesa jetting conditionfirst, Ang
the effect of nonlinearsuperposition
of shockwaves.Unlike an [1990] argues that the resultingjet will be dominatedby
impact of long thin flat plates, the shockconditionof a blunt- projectilematerial.Using an analytical approach,he found that
has impact
body impact changesconstantlywith time. Consequently,the some combinationof projectile and target matedhals
flow field aroundthe collisionmay not be approximated
properly velocitiesat which the matedhal(i.e., either projectileor target)
by a steadystatemodel. Then the critical conditionfor jetting, reachinga jetting condition alternates.Ang [1990] suggests
whichis stronglycontrolledby the angleof the shockfronts,may further that this transitionmay causethe anomalousluminosity
not match predictions from a steady state model, thereby changeas a functionof impactvelocityobservedin micro-impact
contributingto the observeddiscrepancy.
experiments[Eichhorn,1976].
A seriesof impactexperimentswith cone-shaped
projectiles
Although Ang [1990] discussesonly velocity effects for
describedby Allen et al. [1959] may be useful in understanding vertical impacts, the same argument may hold for oblique
the effect of angleof the shockfrontswith respectto colliding impacts. It is noted here that the model by Vickery [1993] was
surfaces. Because the thickness of the cone is not small, the
developedfor a collisionbetweenthe samematerialof projectile
steadystate assumptionis not strictly applicablein this case. and target. Hence,any effectsof impedancecontrastbetweenthe
Then the angleof the shockfront with respectto the surfaceof two cannotbe assessed.
If a jetting phaseis dominatedby the
30,844
SUGITA AND SCHULTZ: SPECTROSCOPIC OBSERVATION OF IMPACT JETTING
material that reachesa jetting conditionfirst, then this may
accountfor the large variationin massratio within a jet as a
functionof impactangle.In fact,theprojectilereaches
thejetting
conditionfirst at lowerimpactangles,whereasthe targetreaches
this conditionat higher angles(Figures 11 and 12). This is
consistent
with the observation
that the target-to-projectile
mass
ratioincreases
with impactangle.
Ang [1990] alsopredictsan abrupttransitionin the observed
massratio as a functionof impact angle;however,we do not
observesucha jump or an abrupttransitionhere (Figure7).
Therearetwo factorsaccounting
for thisdiscrepancy.
First,when
eitherthe targetor the projectilemeetsa jetting condition,the
othermay be mixedinto a jet by a Kelvin-Helmholtz
instability
[Miller, 1998] and/or a viscousdrag force acting along the
materialboundary
betweentheprojectileandtarget.Suchmixing
will makethe transitionin the massratio of thejettingmaterial
gradual,ratherthan suddenas expectedby Ang [1990]. Second,
when the impactangleis the transitionanglefor alternationin
materialthatreachesa jettingconditionfirst, bothprojectileand
target reach the jetting conditionat the same stage of the
penetrationprocess.Since local impact conditions,such as
effectiveimpactvelocitiesV• and V2 for a givenwedgeanglea
(compare(16) and (17)), do not changeabruptlyas a functionof
impactangle,bothprojectileandtargetreachjettingconditions
at
similarstagesduringpenetration
whenthe impactangleis close
to the critical angle. When one side (i.e., either projectileor
target) reaches a jetting condition, the other side is almost
"ready" to form a jet. Then, the secondside will be easily
draggedout as a jet once the first side forms a jet. As the
projectilepenetratesfarther into the target, the secondside
reachesa jetting conditionsoon as well. Consequently,this
alternationin jettingmaterialmay resultin a gradualtransitionin
mass ratio with a jet. The above argument,nevertheless,is
qualitativeanddeservesfurtherstudy.
6. Conclusions
A new spectroscopic
methodallowsdetermination
of boththe
temperature and the target-to-projectile mass ratio in
hypervelocity
jets. Suchdataare not accessible
with conventional
observationaltechniques.Jettingdue to blunt-bodyimpactswas
the focus for this study becauseof its relevance in planetary
science.The experimentshave yielded new insightsfor the
jetting phenomena:(1) The observedhigh temperatureand
almostpuregasphasesin jets indicatethatthe degreeof heating
of the jetting phaseis severaltimeshigherthanheatingexpected
from plane-normalshock.(2) The temperatureof a jet is strongly
controlledby projectileproperties.The jet temperaturefor copper
impactorsdoesnot showsignificantcorrelationwith the vertical
componentof impactvelocity,in contrastwith resultsfor quartz
impactors.(3) The temperatureof the projectilecomponentof
jettingcorrelates
well with thatof the targetcomponent.(4) The
massratio of the targetcomponentto the projectilecomponentin
a jet increasessteadily with impact angle from 15ø to 90ø
(verticalangle).
These data are qualitativelyconsistentwith the predictionsof
the asymmetric-collisionmodel in this study and the model by
Vickery [1993] as follows: (1) Shock heating in jets createdby
impactsof sphericalcopperprojectilesinto half-spacecarbonate
targetsrangesfrom valuescomparableto the vaporizationenergy
of carbonatesto twice this value. (2) The impedancecontrast
between a projectile and a target stronglycontrolsthe effect of
impactangleon jet temperature.(3) The target-to-projectile
mass
ratio within a jet increaseswith impactangle[Vickery,1993].
However, quantitative comparisonsalso reveal significant
differencesbetweenobservationsand theoreticalpredictions:(1)
The theoreticalpredictionfor the effect of impact angle on jet
temperaturedepartsfrom our observations,particularly for the
projectilecomponentat low impactangles.(2) The jetting theory
doesnot accountfor the correlationin jet temperaturesbetween
projectile and target components.(3) The observedchange in
massratio within a jet as a functionof impactangleis largerthan
the predictionof the model due to Vickery [1993] by about a
factor of 5.
The differencein the jet temperaturebetweenthe experiments
and theoretical calculations may reflect new factors that
conventionaljetting theories have not yet addressed,such as
viscousshear heating along the projectile/targetboundaryand
perhaps the nonsteady state nature of the flow around the
collision points. The larger-than-expected
increasein target-toprojectilemassratio within a jet with impact angle may indicate
alternatingmaterials(i.e., either projectileor target) reachingthe
jetting condition.Furtherinvestigationof suchfactorsusingboth
experimentaland theoreticalapproaches
will contributegreatlyto
understanding
of jetting phenomenacreatedby planetaryimpacts.
Acknowledgments. The authorswould like to thank Wayne Logsdon
and John Vongrey at the NASA Ames Vertical Gun Range for their
indispensableand excellent technicalsupport.J. T. Heineck provided
critical help and creativeinsights.This studyhas benefitedgreatly from
discussions with O. S. Barnouin-Jha, E. M. Parmentier, and M. B.
Boslough.This researchwas supportedby NASA Grants NAGW-705
and NAGS-3877 and Jet PropulsionLaboratoryDirector's Discretionary
Fund (JPL-960879) led by M. A. Adams.The supportby M. A. Adams
andJPL for part of thiseffort is gratefullyacknowledged.
References
Adams, M. A, P. H. Schultz, S. Sugita, and J. D. Goguen,Impact flash
spectroscopyas a meansto characterizeasteroidsurfacecompositions
(abstract),Lunar Planet. Sci. Con.
l'i XXVIII, 3-4, 1997.
Allen, W. A., H. L. Morrision, D. B. Ray, and J. W. Rogers,Fluid
mechanicsof copper,Phys.Fluids,2,329-333, 1959.
Al'tshuler, L. V., S. B. Kormer, A. A. Bakanova, A. P. Petunin, A. I.
Funtikov, and A. A. Gubtin, Irregular conditionsof oblique collision
of shock waves in solid bodies, Sov.Phys.JETP, Engl. Transl., 14,
986-994, 1962.
Ang, J. A., Impact flashjet initiationphenomenology,
lnt. J. ImpactEng.,
10, 23-33, 1990
Birkhoff, G., D. P. MacDougall, E. M. Puch, and G. Taylor, Explosives
with linedcavities,J. Appl. Phys.,19, 563-582, 1948.
Chase, M. W., C. A. Davies, J. R. Downey, D. R. Frurip, R. A.
McDonald, and A. N. Syverud, JANAF thermochemicaltables 3rd
ed.,J. Phys.Chem.Ref Data, 14, suppl.1, 1-1856, 1985.
Corliss,C. H., A review of oscillatorstrengthsfor lines of Cu I, J. Res.
Nalt. Bur Stand., Sect/A, 74A, 781-790, 1970.
Eichhorn,G., Analysisof the hypervelocityimpact processfrom impact
flashmeasurements,
Planet. SpaceSci., 24, 771-781, 1976.
EI-Sobky, H., Mechanicsof explosive welding, in ExplosiveWelding,
Formingand Compaction,edited by T. Z. Blazynski, pp. 189-217,
Appl. Sci.,London,1983.
Fu, K., M. Jogwich, M. Knebel, and K. Wiesemann, Atomic transition
probabilitiesand lifetimes for the Cu I system, At. Data Nucl. Data
Tables, 61, 1-30, 1995.
Gault, D. E., and E. D. Heitowit, The partition of energy for
hypervelocity impact craters formed in rock, Proc. Sixth
Hypervelocity
ImpactSymp.,2,419-456, 1963.
Gehring,J. W., andR. L. Wamica, An investigation
of the phenomena
of
impact flash and its potential use as a hit detection and target
discriminationtechnique,Proc. 6th HypervelocityImpact Symp.,2,
627-682, 1963.
Godunov, S. K., A. A. Deribas, A. V. Zabrodin, and N. S. Kozin,
Hydrodynamiceffects in colliding solids,J. Comput.Phys., 5, 517539, 1970.
Griem,H. R., PlasmaSpectroscopy,
580 pp., McGraw-Hill,New York,
1964.
SUGITA AND SCHULTZ: SPECTROSCOPIC OBSERVATION OF IMPACT JETTING
Harlow, R. H., and W. E. Pracht, Formation and penetrationof highspeedcollapsejets, Phys.Fluids,9, 1951-1959, 1966.
Jean, B., and T. L. Rollins, Radiation from hypervelocity impact
generatedplasma,AIAA J., 8, 1742-1748, 1970.
Kieffer S. W., Dropletchondrule,Science,189, 333-340, 1975.
Kieffer, S. W., Impactconditionsrequiredfor formationof melt by jetting
in silicates,in Impactand ExplosionCratering,editedby R. J. Roddy,
R. O. Pepin, and R. B. Merrill, pp. 751-769, Pergamon,Tarrytown,
30,845
Schultz,P. H., and D. E. Gault, Prolongedglobal catastrophes
from
oblique impact, in Global catastrophes
in Earth history,An
Interdisciplinary
Conj'brence
on Impacts, Volcanism,and Mass
Mortality,editedby V. L. Sharpton
andP. D. Ward,Spec.Pap.Geolo.
Soc. Am., 247, 239-261, 1990.
Schultz,P. H., M. A. Adams,J. W. Perry,J. D, Goguen,and S. Sugita,
Impactflashspectroscopy
(abstract),
LunarPlanet.Sci.ConfXXVII,
1149-1150, 1996.
Sugita,S., Generation
and evolutionof impact-induced
vaporclouds:
Kieffer, S. W., P. P. Phakey, and J. M. Christie, Shock processesin
Spectroscopic
observations
and hydrodynamic
calculations,
Ph.D.
porousquartzite;Transmissionelectronmicroscopeobservations
and
thesis,268 pp.,BrownUniv., Providence,
May 1999.
theory,Contrib.Mineral. Petrol. 59, 41-93 1976.
Sugita,S., andP. H. Schultz,
Spectroscopic
observation
of atmospheric
Kock,M., andJ. Richter,Experimentelle
[2bergangswahrsheinlichkeiten
interaction
of impactvaporclouds(abstract),
LunarPlanet.Sci.Con/i,
N.Y., 1977.
und die solare H•iufigkeit des Kupfers, Z. Astrophys.,69, 180-192,
1968.
Landau, L. D., and E. M., Lifshitz, Fluid Mechanics,2nd ed., 536 pp.,
Pergamon,Tarrytown, N.Y., 1987.
Marsh, S. P., LASL ShockHugoniotData, 658 pp., Univ. of Calif. Press,
Berkeley, 1980.
McKinnon, W. B., On the origin of the Pluto-Charonbinary,Astrophys.
J., 344, L41-L44, 1989a.
McKinnon, W. B., Impact jetting of water ice, with applicationto the
accretionof icy planetesimalsand pluto, Geophys.Res. Lett., 16,
1237-1240, 1989b.
Melosh, H. J., and C. R. Sonett, When worlds collide: Jetted vapor
plumesandthe Moon'sorigin,in Originof theMoon, editedby W, K,
Hartmann,R. J. Phillips, and G. J. Taylor, pp. 621-642, Lunar and
PlanetaryInst., Houston,Tex. 1986.
Meyers, M. A., DynamicBehaviorof Materials, 668 pp., John Wiley,
XXIX, CD-ROM #1751, 1998.
Sugita,S., P. H. Schultz,
andM. A. Adams,Spectroscopic
measurements
of vaporclouds
duetooblique
impacts,
J. Geophys.
Res.,103,19,42719,441, 1998.
Vickery,A.M., Thetheory
ofjetting:Application
totheoriginof tektites,
Icarus, 105, 441-453, 1993.
Walsh,J. M., R. G. Shreffier,andF. J. Willig, Limitingconditions
forjet
formationin high velocitycollisions,
J. Appl.Phys.,24, 349-359,
1953.
Woods, T. L., and R. M. Garrels, Thermodynamic
Valuesat Low
Temperature
j'br Natural InorganicMaterials:An Uncritical
Summary,
270pp.,OxfordUniv.Press,New York, 1987.
Yang,W., T. J. Ahrens,G. H. Miller,andM. B. Petach,
Jetejectamass
uponobliqueimpact,in ShockCompression
of Condensed
Matter,
editedby S.C. Schmidtet al., pp. 1011-1014,NorthHolland,New
York, 1992.
New York, 1994.
Miller, G. H., Jettingin oblique,asymmetricimpacts,Icarus, 134, 163175, 1998.
Pack, D.C., and J.P. Curtis, On the effect of asymmetrieson thejet from
a linearshapedcharge,J. App1.Phys.,67, 6701-6704, 1990.
Press,W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery,
NumericalRecipesin FORTRAN.' The Art of ScientificComputing,
2nd ed., pp. 963, CambridgeUniv. Press,New York, 1992.
Reader, J., C. H. Corliss, Wiese, W. L., and G. A. Martin, Wavelengths
and TransitionProbabilitiesfor AtomsandAtomicIons, 415 pp., U.S.
Dept. of Commerce.,1980.
Schultz,P. H., Effect of impactangleon vaporization,J. Geophys.Res.,
101, 21,117-21,136, 1996.
P. H. Schultz,Department
of GeologicalSciences,
BrownUniversity,
Box 1846, Providence,RI 02912. ([email protected])
S. Sugita,Department
of Earthand PlanetaryPhysics,Facultyof
Science,Universityof Tokyo, 7-3-1 Hongo,Bunkyo-ku,Tokyo 1330033, Japan.([email protected])
(ReceivedApril 5, 1999;revisedSeptember
28, 1999;
acceptedOctober5, 1999.)