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Mars Microprobe Entry Analysis
Robert D. Braun�
NASA Langley Research Center
Hampton, VA 23681-0001
(757) 864-4507
Robert A. Mitcheltreey
NASA Langley Research Center
Hampton, VA 23681-0001
(757) 864-4382
F. McNeil Cheatwood
Vigyan Inc.
Hampton, VA 23666-1325
(757) 864-2984
Abstract{The Mars Microprobe mission willprovide the �rst opportunity for subsurfacemeasurements, including water detection, nearthe south pole of Mars. In this paper, per-formance of the Microprobe aeroshell design isevaluated through development of a six-degree-of-freedom (6-DOF) aerodynamic database and ight dynamics simulation. Numerous missionuncertainties are quanti�ed and a Monte-Carloanalysis is performed to statistically assess mis-sion performance. Results from this 6-DOFMonte-Carlo simulation demonstrate that, in amajority of the cases (approximately 2{�), thepenetrator impact conditions are within currentdesign tolerances. Several trajectories are iden-ti�ed in which the current set of impact re-quirements are not satis�ed. From these cases,critical design parameters are highlighted andadditional system requirements are suggested.In particular, a relatively large angle-of-attackrange near peak heating is identi�ed.
Table Of Contents
1. Introduction
2. Nomenclature
3. Impact Requirements
4.1 Aeroshell Selection
4.2 Aerodynamics
4.3 Atmos. Flight Dynamics
5.1 Impact Sizing
5.2 Monte-Carlo Simulation
6. Conclusions
�Space Systems and Concepts Division, Mail Stop 365yAero and Gas Dynamics Division, Mail Stop 408A
1 Introduction
The objective of NASA's New Millennium pro-gram is to demonstrate and ight qualify tech-nology elements required for the science mis-sions of the next century [1]. The program'ssecond ight project, Deep Space Two (DS{2) is focused on the design of two small Marsentry probes. As a result, DS{2 is often re-ferred to as the Mars Microprobe mission. Thisproof-of-concept system is intended to demon-strate key elements of future network sciencemissions [2, 3]. Attached to the cruise stageof the Mars 98 Surveyor Lander, these twoMicroprobe vehicles will be launched to Marsby a Delta II rocket in January 1999, arrivingin December 1999. Each of these Microprobecapsules houses instrumented penetration de-vices designed to analyze the subsurface layersby performing soil sampling and water detec-tion. On impact, the penetrators are designedto pierce their protective aeroshells, driving thissubsurface instrumentation 0.3-2.0 m below thesurface. Subsurface data will be relayed back toEarth through a link with the Mars Global Sur-veyor orbiter (September 1997 Mars arrival).
The entry, descent, and impact (EDI) phase ofthe DS{2 mission begins as the two capsules aremechanically separated from the cruise stage [4].This event is preceded by separation of the Mars98 Lander from the cruise stage (approximately1.5 s earlier). As a result of (1) the brief periodbetween these two separation events, (2) thelack of control of the cruise-stage after the 98Lander separation, and (3) geometric mounting
constraints which do not allow the Microprobevehicles to be aligned with the ight path, thecapsules will separate in an unknown angularorientation with non-zero angular rates. Sta-ble ight of the Microprobe vehicles must beachieved passively, and maintained until surfaceimpact.
Design of the DS{2 entry probes is compli-cated by several unique aerodynamic challenges.The vehicles must possess enough aerodynamicstability to achieve passive re-orientation froman arbitrary initial motion prior to peak heat-ing. Since stable ight at impact is required,the supersonic and transonic dynamic stabilityproblems which have plagued other entry mis-sions [5, 6, 7] must also be mitigated. Addi-tionally, the penetrators must be protected fromthe intense aerothermodynamic environment ofa 7.0 km/s Mars entry and satisfy a stringentset of surface impact constraints.
In this paper, the criteria used to select theaeroshell geometry are presented. After re-view of the aeroshell shape and mass prop-erties, compilation of the Microprobe aerody-namic database is discussed. This database iscompiled from past studies, computational uiddynamic calculations, and ground-based testdata. Development of a six-degree-of-freedom(6-DOF) Monte-Carlo trajectory simulation forMicroprobe EDI is also presented. Results fromthis 6-DOF Monte-Carlo simulation are used tostatistically assess the e�ect of combinatorialvariations in the signi�cant EDI parameters.
2 Nomenclature
A reference aerodynamic surface area, m2
b yaw/roll reference length, mc pitch reference length, mC aerodynamic force or moment coe�cientg Mars surface slope, degKn Knudsen numberm mass, kgM Mach numberI body{axis moments of inertia, kg{m2
_q stagnation{point heat rate, W/cm2
Q dynamic pressure, N/m2
V velocity, m/s� angle-of-attack, deg
� ballistic coe�cient�
mCDA
�kg/m2
ight-path or incidence angle, deg
Subscriptsa relative to the atmosphereA axial forceD drag forcel static rolling momentm static pitching momentmq dynamic pitching momentn static yawing momentN normal forcenr dynamic yawing momentp penetratorr relative to the horizont totalY side force
3 Surface Impact Requirements
The penetrators have been designed to oper-ate properly under a range of impact condi-tions. Mission success demands that the EDIsystem meet several surface impact constraints.Three{� requirements on surface impact veloc-ity (140 � Vr � 200 m/s), penetration angle-of-attack (0 � �p � 10 degrees), and pen-etration incidence angle (j pj � 20 degrees)have been speci�ed [4]. These requirementsare currently being validated through a rigor-ous ground-testing program.
The dynamics of the surface impact event areillustrated in Fig. 1. The Microprobe aeroshell,local horizon, and local surface slope are shown,along with the velocities with respect to theground (Vr) and atmosphere (Va). By conven-tion, the ight-path angles shown are negative.Atmospheric winds cause the di�erence betweenVr and Va. Total angle-of-attack (�t in Fig. 1)is de�ned as the angle between the vehicle's axisof symmetry and Va.
During ight, the forces on the aeroshell are afunction of the relationship between the vehicle
g
Horizon
Surface
αtγa
γr
Vr Va
Vehicle symmetry
axis
Figure 1. De�nition of Mars Microprobe sur-face impact angles.
and the atmospheric velocity vector (�t and Va).However, at impact, the orientation of the Mi-croprobe payload relative to the surface is of sig-ni�cance. The penetration angle-of-attack andincidence angle are de�ned as:
�p = �t + ( a � r) (1)
p = r + 90� � g (2)
As discussed below, the surface impact velocityand incidence angle constraints may be achievedthrough the selection of the appropriate ballis-tic coe�cient (see Section 5); whereas, satis-faction of the impact angle-of-attack constraintis a function of the vehicle's aerodynamic sta-bility (geometry and center-of-gravity location).Aerodynamic design of the Microprobe capsulesis presented in Section 4. The variance in eachof the signi�cant impact parameters as well asstatistical data regarding the aeroshell heatingenvironment is presented in Section 5.
4 Analysis
Aeroshell Selection
Selection of the aeroshell for Mars Microproberequires consideration of the unique objectivesof the mission. A passive enclosure is requiredto safely deliver the penetrator payload throughentry to impact with the surface. The aeroshellmust decelerate the vehicle during its descentto a prescribed impact velocity. It must possesssu�cient stability to correct any initial tum-bling motion to forward-facing ight early in thetrajectory and maintain that orientation within
small tolerances until impact. Finally, it mustprotect the payload from intense aerodynamicheating. To meet these objectives a 45-degreehalf-angle cone with rounded nose and shoul-ders is selected for the forebody. The afterbodyis hemispherical with its center at the vehicle'scenter-of-gravity location.
Blunted 45-degree sphere-cones were used forthe successful Pioneer-Venus and Galileo mis-sions [8]. Both of these missions entered at-mospheres much denser than Mars. For theMars entries of Viking and Mars Path�nder,70-degree sphere-cones with a zero angle-of-attack drag coe�cient near 1.7 (versus the 45-degree cone value of 1.05) were selected [9].Choice of cone angle calls for a compromise ofdrag, stability and packaging. Blunter cones ex-hibit more drag per surface area; sharper conespossess more stability. Viking and Path�ndermake use of high drag aeroshells since bothof these entries required deceleration of muchheavier spacecraft at su�ciently high altitudesfor parachute deployment. In contrast, theMars Microprobe vehicles are more than twoorders of magnitude lighter and must impactthe surface at a high velocity (140-200 m/s).Additionally, each Microprobe capsule requiresthe highest possible aerodynamic stability to re-cover quickly from any initial tumbling motion.
The degree of nose bluntness has little e�ecton the drag coe�cient for a 45-degree half-angle cone, although increased bluntness doesslightly decrease static stability. On the otherhand, increased bluntness decreases the stagna-tion point heat rate during the hypersonic por-tion of the trajectory. Selecting the appropri-ate degree of nose bluntness is a compromiseof these factors. For Microprobe, a nose radiusequal to half of the vehicle's overall base radiusis an acceptable value. This is the same ra-tio used in the Pioneer-Venus and Galileo entryprobes [7, 10, 11]. Similarly, rounding the ve-hicle's shoulders is performed to decrease localheating. Rounding the shoulders decreases bothdrag and stability. Again, the Pioneer-Venusvalue of shoulder radius equal to one tenth the
nose radius is speci�ed for Microprobe. Al-though it is possible to optimize the amountof nose and shoulder rounding for the speci�cMicroprobe mission, the selection of previouslyused ratios appears adequate and also allowsthe use of an extensive body of existing aero-dynamic test and ight data.
Selection of the hemispherical afterbody isbased on the Planetary Atmosphere Experi-ments Test (PAET) probe [12]. The hemispher-ical afterbody speci�ed for Microprobe servestwo purposes. First, since the vehicle maybe tumbling initially, it may encounter the at-mosphere while traveling backwards. A hemi-spherical afterbody with center at the vehicle'scenter-of-gravity is not stable in this orienta-tion and will foster rotation to a forward fac-ing attitude. Second, this afterbody has beenshown to decrease the dynamic instability ob-served in blunt vehicles traversing the transonic ight regime [13]. Regarding backwards stabil-ity, it is of interest to note that Pioneer-Venus,Galileo, Viking and Mars Path�nder were allhypersonically stable in a backwards orienta-tion. To prevent this occurrence, each entry ve-hicle was oriented nose-�rst and spin-stabilizedto assure a forward-facing attitude at the at-mospheric interface. Spin stabilization is notan option for Microprobe; however, the hemi-spherical afterbody assures the vehicle will nottrim in a backwards-facing attitude.
The geometry of the Mars Microprobe aeroshellis depicted in Fig. 2. As shown, a 45-degreesphere cone with nose radius of 0.0875 m, shoul-der radius of 0.00875 m, and maximum radiusof 0.175 m has been selected. The afterbodyshape is a hemispherical section with radius of0.183 m centered about the vehicle's center-of-gravity. The center-of-gravity is located 0.0902m aft of the nose on the vehicle's symmetry axis.
Aerodynamics
The Mars Microprobe aerodynamic databasewas derived from a combination of computa-tional uid dynamic (CFD) calculations and
z
x90.2
350
R 183
R 87.5
R 8.75
All dimensions in mm
m . . . . . . . .2.73 kg
Ixx . . . . . . .0.0105 kg-m2
Iyy, Izz . . . .0.0106 kg-m2
b,c . . . . . . .0.350 m
β . . . . . . . .27 kg/m2
Figure 2. Mars Microprobe aeroshell geometryand mass properties.
0 1 2 3 4 5 6 10 20 30 40
Mach Number
0.001 0.1 10Knudsen NumberWindtunnel:Brooks
Free Molecular
CFD: LAURA
Windtunnel:Nichols
CFD: TLNS3D
Eglin ARF
Transonic Supersonic Hypersonic Transitional
Bridging/DSMC
Figure 3. Sources used to assemble Mars Mi-croprobe aerodynamic database.
ground-based test data. A detailed descriptionof the vehicle's aerodynamic characteristics isprovided in Ref. [14]. Sources of the static aero-dynamic predictions are illustrated in Fig. 3.Free molecular and Direct Simulation MonteCarlo (DSMC) computations were performed tocharacterize the rare�ed and transitional owregimes. These results were supplemented bythermochemical nonequilibrium computational uid dynamic calculations obtained with theLangley Aerothermodynamic Upwind Relax-ation Algorithm (LAURA in Fig. 3) in the con-tinuum hypersonic ow regime. This analysistool was extensively used in the prediction of theMars Path�nder aerodynamics [15]. Pioneer-Venus wind tunnel data was used in the super-sonic, transonic, and subsonic regimes [16, 17].
Validation and extrapolation of these exist-ing results was made possible through addi-tional computational solutions obtained in thetransonic and subsonic ight regimes with theThin-Layer Navier-Stokes 3-Dimensional pro-gram [18] (TLNS3D in Fig. 3).
Dynamic damping coe�cients were extractedfrom Pioneer-Venus and Viking wind tunneltest data [5, 6, 7]. In addition, transonic bal-listic range data was produced on a Micro-probe model with the correct center-of-gravitylocation [19, 20]. Dynamic stability estimatescould not be obtained computationally withinthe time constraints of the present analysis. Be-cause of the transonic dynamic instability prob-lems which have plagued other entry vehicle de-signs, additional data is being gathered in apressurized facility in which the ight Reynoldsnumber can be duplicated [19].
To produce a cohesive database from these di-verse sources, modi�cation of the original dataset was required [21]. A bridging function(shaped by the DSMC results) was used in thetransitional region between the free molecularand continuum results. Explicit calculation ofthe transitional aerodynamics by DSMC meth-ods, although possible, is computationally pro-hibitive. Instead, selected DSMC results wereused to anchor and shape the bridging function.This function provides a smooth variation of thevehicle's aerodynamic characteristics based onthe free molecular and continuum hypersoniccomputations.
Within the database [21], the continuum hy-personic aerodynamics were assumed to varywith angle of attack in a similar manner tothat predicted by Newtonian ow. This New-tonian variation was then scaled to reproducespeci�c LAURA computations obtained at 0and 10-degrees angle of attack. The supersonicand transonic wind tunnel data overlapped, sothe two sets were blended in the Mach numberregion between 1.65 and 2.16. Similarly, thePioneer-Venus and Viking dynamics data wereblended in the Mach number region between 1.2
Log Kn
CD
CD
.5
1.0
1.5
2.5
2.0
Continuum Transitional
Free molecular
10-4 10-2 100 102 10410-6
αt = 0°
0 5 15.5
1.0
1.5
M25
Figure 4. Mars Microprobe 0-degree angle-of-attack drag coe�cient.
and 1.3. Finally, to account for small di�erencesin the aeroshell geometry, the axial force windtunnel values were scaled to match the compu-tational results.
Early versions of the aerodynamics routine usedsimple linear interpolation, providing value-continuity between segments. Although atwice-di�erentiable database was sought, pro-viding this level of continuity at the datapoints resulted in unacceptable behavior be-tween the data. As a compromise, an overlap-ping parabola technique, which provides slope-continuity, was used. As the FORTRAN rou-tine was developed, care was taken to minimizememory overhead. Furthermore, since the rou-tine is called many times by 6-DOF POST, ane�ort was made to create a computationally ef-�cient algorithm. For a given ight conditionand vehicle angular orientation, the databaseprovides estimates of CA, CN , CY , Cm, Cn, Cl,Cmq, and Cnr for use in the 6-DOF trajectorysimulation [21].
The 0-degree angle-of-attack Microprobe dragcoe�cient is shown in Fig. 4 as a functionof Knudsen (Kn) and Mach (M) numbers.Knudsen number is de�ned as the ratio of thegas' mean free path to the vehicle's diameter.This similarity parameter is used as the in-dependent variable in the rare�ed and transi-
tional aerodynamic regimes. Initially, Kn willbe large. For values larger than 10, the aero-dynamic forces are computed solely from thefree molecular ow solutions. Free molecular ow assumes there are no collisions between gasmolecules in the ow �eld. Unlike hypersoniccontinuum aerodynamics (where forces exertedon the body are essentially the integrated ef-fect of surface pressures alone), free molecular ow aerodynamics contain a signi�cant shearstress contribution. As the entry proceeds intothe upper atmosphere, both the mean free pathand Knudsen number decrease and collisionsbetween particles must be taken into account.In this regime, where 0:001 < Kn < 10, theaerodynamics are computed from the DSMC-anchored bridging function.
As lower altitudes are reached (below 55 km al-titude for Microprobe), the Knudsen numberdrops below 0.001 and the continuum meth-ods are used to compute vehicle aerodynamics.Here, Mach number is the appropriate aerody-namic similarity parameter. Fig. 4 shows thatdrag coe�cient (at a given angle of attack) isapproximately constant above Mach 5. The in-crease in drag coe�cient supersonically, is a re-sult of the sonic line shifting from the nose re-gion to the shoulder region of the aeroshell be-tween Mach 5 and 2. This shift has a signi�-cant impact on the pressure distribution caus-ing axial force (equivalent to drag at 0-degreeangle-of-attack) to increase while normal forceand moment coe�cient decrease. Transonically,drag coe�cient decreases. Here the data ofRefs. [17, 20] and the TLNS3D computationalsolutions are used. The axial force data ofRef. [17] is decreased to account for the Micro-probe con�guration's large hemispherical after-body.
Atmospheric Flight Dynamics
Six-degree-of-freedom (6-DOF) trajectory anal-ysis is performed using the Program to Opti-mize Simulated Trajectories (POST) [22]. Thisprogram has been used previously in the devel-opment of the Mars Path�nder entry, descent,
and landing (EDL) strategy [23, 24]. Six-DOFPOST is also being used by the Path�nder EDLoperations team [25, 26]. In the present study,POST is used to numerically integrate the 6-DOF equations of motion from a given entrystate to surface impact. An eighth-order Runge-Kutta integration technique is employed [27].The Microprobe aerodynamic database as wellas Mars atmospheric, gravitational, and surfacemodels are inputs to the simulation. Atmo-spheric modeling for this mission is hamperedby the lack of surface measurements for thesouthern hemisphere of Mars (the target im-pact site is 73{77 degrees South latitude). Usingprojected data obtained from the Viking lan-ders and a global circulation model, Zurek andRichardson have constructed nominal and per-turbed atmospheric pro�les [28]. These modelsare used in the current simulation.
In the present analysis, uncertainties are appliedin all simulation model inputs. These uncertain-ties arise from numerous sources including (1)technology limitations (e.g., current interplane-tary navigation or mass-balance accuracies), (2)a lack of knowledge concerning the Mars atmo-sphere, (3) computational or measurement un-certainty associated with the aerodynamic anal-yses, and (4) unknown separation orientationand angular rate. Therefore, in this analysis,an attempt was made to quantify and modelthe degree of uncertainty in each of 29 majorparameters.
The uncertainty range attributed to each ofthese parameters is listed in Table 1. For aparameter with more than one variance (e.g.,aerodynamics or winds), the uncertainty is es-timated using linear interpolation between theregions given in Table 1. Gaussian distributionsare sampled for most parameters. However, theinitial orientation, center-of-gravity o�set quad-rant, and wind direction quadrant are deter-mined from uniform distributions. The topog-raphy variation is modeled by a non-symmetricGaussian distribution centered at 5 km. Thisdistribution is illustrated in Fig. 5.
Table 1. 6-DOF Monte-Carlo variables.
EDI Parameter Nominal 3{�Value Variance
Initial state, , deg -13.25 � 0.4Initial �t, deg 90.0 � 90.0Initial pitch rate, deg/s 6.0 � 5.0Initial yaw rate, deg/s 6.0 � 5.0Initial roll rate, deg/s 6.0 � 5.0X-axis cg position, mm 90.2 � 5.0X-axis cg o�set, mm 0.0 � 1.0Mass, kg 2.73 � 0.273Ixx, kg-m
2 0.0106 � 0.0003Iyy, Izz, kg-m
2 0.0105 � 0.0003Ixy, Ixz, Iyz, kg-m
2 0.0 � 0.0003CA, Kn � 0.1 See Fig. 4 � 10%CN , Kn � 0.1 See Ref. [14] � 0.10Cm, Kn � 0.1 See Ref. [14] � 0.006CA, Kn < 0.1, M � 10 See Fig. 4 � 2%CN , Kn < 0.1, M � 10 See Ref. [14] � 0.05Cm, Kn < 0.1, M � 10 See Ref. [14] � 0.003CA, Kn < 0.1, M � 5 See Fig. 4 � 10%CN , Kn < 0.1, M � 5 See Ref. [14] � 0.10Cm, Kn < 0.1, M � 5 See Ref. [14] � 0.006Cmq and Cnr , M � 6 See Ref. [14] � 20%Cmq and Cnr , M � 3 See Ref. [14] -50, +110%Density See Ref. [28] See Fig. 6Temperature See Ref. [28] � 150%Wind above 50 km See Ref. [28] See Fig. 7Wind below 10 km See Ref. [28] See Fig. 7Wind gust, m/s 0.0 � 30.0Surface altitude, km 5.0 -4, +1Surface slope, deg 0.0 � 5.0
Surface altitude, km
Number of
cases
1 2 3 54 6 70
100
200
300
400
450
500
50
150
250
350
Figure 5. Impact altitude distribution.
Dens/densnom
0
10
20
30
40
50
60
70
80
90
100
-.5 0 .5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Altitude, km
Atmospheric model courtesy Ref. 27
Figure 6. 3{� density variation used in the6-DOF Monte-Carlo simulation.
Wind speed, m/s
Altitude, km
0
10
20
30
40
50
60
70
80
90
100
Atmospheric model courtesy Ref. 27
20 40 60 80 100 120 140 160 180 200
Figure 7. 3{� wind pro�les used in the 6-DOFMonte-Carlo simulation.
The 3{� variances in atmospheric density andwinds are shown in Figs. 6 and 7. As illustratedin these �gures, three atmospheric pro�les withvarying levels of visible column depth, or opac-ity (0.05, 0.2, 0.5), are used in the present sim-ulation. Within the Monte-Carlo simulation,these three nominal and perturbed atmosphericpro�les are sampled evenly.
5 Results And Discussion
Impact Sizing and Nominal Trajectory
For zero angle-of-attack ight of the Microprobecapsules, the impact conditions are completelydetermined by ballistic coe�cient (�) and sur-
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15 20 25 30 35 40 45 50 55120
130
140
150
160
170
180
190
200
210
220
β, kg/m2
5
10
15
20
25
30
35
40
Vr, m/s
γp, deg
Design space Vr
γp
Figure 8. Mars Microprobe ballistic coe�cientrequirements, surface altitude = 5 km.
face altitude. Assuming a surface slope of 5 de-grees, an altitude of 5 km, the mean densitypro�le [28], and negligible wind speed, the fol-lowing values are determined from Fig. 8. Foran impact speed of 160 m/s, a ballistic coe�-cient of 27 kg/m2 is required. Furthermore, theballistic coe�cient must be within the range of20:6 � � � 47 kg/m2 to satisfy the impact ve-locity criterion (140 � Vr � 200 m/s), and be-low 33.1 kg/m2 to satisfy the penetration in-cidence angle constraint (j pj � 20 degrees).Hence, the Microprobe design space is restrictedsuch that 20:6 � � � 33:1 kg/m2.
The design approach selected by the Mars Mi-croprobe project o�ce is to baseline the largestdiameter aeroshell that does not adversely im-pact the Mars 98 Lander. This approach, whichallows for modest mass growth, yields the 350mm maximum diameter depicted in Fig. 2. Asdiscussed earlier, a 45-degree sphere-cone has acontinuum hypersonic CD of 1.05. Thus, for thenominal value of � = 27 kg/m2, a Microprobemass of 2.73 kg is required. Without ballast, thecurrent system mass estimate is 2.63 kg. Thisyields a mass margin of 3.8% at the nominalimpact speed. As mentioned above, the impactconstraints can be met with a ballistic coe�-cient as high as � = 33:1 kg/m2; hence, the Mi-croprobe heatshield is being sized for this value.At this upper limit of �, the current design massmargin is 27.1%.
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Surface altitude, km
10
11
12
13
15
14
16
17
18
Vr, m/s
γp, deg
130
135
140
145
150
155
160
165
170
1 2 3 4 5 6
Vr
γp
Vr design requirement
Figure 9. E�ect of surface altitude on Micro-probe impact conditions, � = 27 kg/m2.
The impact of surface altitude on the Fig. 8trade-space is shown in Fig. 9. For the impactsite of interest, a surface altitude of 1 to 6 kmabove the Mars reference ellipsoid may be en-countered [4]; however, a majority of this terrainis thought to be 5 km above the Mars referenceellipsoid (see Fig. 5). As shown in Fig. 9, im-pact velocity changes approximately 5 m/s foreach km of surface altitude and the penetrationincidence angle decreases with surface altitude(at a rate of about 1.4 deg/km). For � = 27kg/m2, the impact velocity criterion is satis�edabove 1.6 km altitudes; whereas the penetra-tion incidence angle constraint is satis�ed overthe complete range of expected surface altitude.
The nominal Microprobe EDI trajectory isshown in Fig. 10. As shown, the atmosphericentry velocity is 6.9 km/s. The atmosphericinterface is de�ned at a radius of 3522.2 km(surface altitude of 141.8 km). The peak de-celeration of 12.6 Earth g's is achieved at analtitude of 44.1 km. Surface impact occursroughly 290 sec after atmospheric interface, at160 m/s (Mach 0.66). Fig. 11 shows that thepeak stagnation-point heat rate of 160 W/cm2
is achieved at approximately 80 sec (altitude of49.2 km) and is followed by peak dynamic pres-sure (3380 N/m2) at approximately 94 sec intothe EDI sequence. At impact, the integratedstagnation-point heat load is 7165 J/cm2.
Time, s
Altitude, km
Altitude
50
100
150
50 100 150 200 250 3000
Vr, km/s
Vr
0
2.5
5.0
7.5
Decel., Earth g's
Deceleration
0
5
10
15
β = 27 kg/m2
Figure 10. Mars Microprobe nominal trajec-tory.
Time, s
q· , W/cm2
q·
50
150
200
50 100 150 200 250 3000
Q, N/m2
Q
β = 27 kg/m2
0
1000
3000
1002000
4000
Figure 11. Stagnation-point heat-rate and dy-namic pressure pro�les.
The nominal entry shown in Figs. 10 and 11 as-sumes a zero angle-of-attack entry interface ori-entation, mean atmosphere without wind, andno error in the center-of-gravity position, massproperties, or aerodynamic modeling. Figure 12presents the total angle-of-attack history for asimilar entry initiated with a 90-degree angle-of-attack. As shown, total angle-of-attack isdamped below 10 degrees within the �rst 50sec of atmospheric ight (by 76 km altitude)and continues to decrease as the dynamic pres-sure (Q) builds (see Fig. 11). Thus, althoughhigh angles-of-attack may occur early in themission, the Microprobe aeroshells possess suf-�cient aerodynamic stability to provide passivere-orientation while in the upper atmosphere.
Time, s50 100 150 200 250 3000
20
40
60
80
100
αt, deg
Figure 12. Mars Microprobe total angle-of-attack pro�le, initial 90-degree angle-of-attack.
This hypersonic re-orientation issue is discussedfurther in the �nal section of this paper.
In addition to demonstrating the hypersonicre-orientation capability of the Microprobeaeroshell, Fig. 12 also demonstrates that stat-ically stable ight can be maintained passivelythroughout EDI. In fact, for this case, the angle-of-attack at impact (�t) is 1.5 degrees. Notethat the presence of the transonic dynamic in-stability is evident in Figure 12. This phenom-ena is the cause for the small increase in totalangle-of-attack from 225 to 275 sec.
Because of Microprobe's small moments of in-ertia (see Fig. 2), large angular rates are likelyduring the entry. This high frequency motion isevident in Fig. 12, particularly when dynamicpressure is large. Pitch and yaw rates as highas 200 deg/sec and an angle-of-attack oscilla-tion frequency of approximately 5 Hz are likelynear peak Q. In comparison, Mars Path�nder'sangular motion is characterized by pitch andyaw rates two orders of magnitude lower inthe peak dynamic pressure region and a muchlower angle-of-attack frequency [23]. AlthoughMicroprobe's angular frequency diminishes asdynamic pressure decreases, an increased fre-quency occurs during transonic ight as a resultof the vehicle's dynamic instability. At impact,the vehicle's pitch and yaw rates are more than
Vr, m/s
Number of
cases
130 140 150 160 170 180 1900
100
200
300
350
50
150
250
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Design requirement
Figure 13. Impact velocity distribution.
an order of magnitude lower than at peak dy-namic pressure and the angle-of-attack oscilla-tion frequency is approximately 2.5 Hz.
Monte-Carlo Simulation
During ight of the Mars Microprobe space-craft, a combination of o�-nominal e�ects islikely to be encountered. Hence, it is impor-tant to statistically assess the e�ect of combi-natorial variations in all of the EDI parame-ters listed in Table 1. To accomplish this, two-thousand o�-nominal cases were randomly esti-mated and simulated in a Monte-Carlo fashion.A 99.7% probability exists that each random pa-rameter will remain within the 3{� uncertaintybounds of Table 1. In addition to a detailed setof impact conditions, the total angle-of-attackwas monitored at discrete points along the heatpulse. Peak deceleration, stagnation-point heat-rate, and integrated heat load were also moni-tored.
Impact Conditions{Histograms of the probableranges in impact velocity, penetration angle-of-attack and surface incidence angles are shownin Figs. 13 { 15. Monte-Carlo statistics forthese impact parameters are tabulated in Ta-ble 2. These data indicate that the current setof Microprobe impact requirements are not sat-is�ed in a 3{� sense. In particular, the 3{� lowimpact velocity criteria (140 m/s) and the 3{� high penetration incidence angle (20 degrees)
αp, deg
Number of
cases
5 10 15 20 250
100
200
300
400
500
600
700
�������
�������
�������
�������
�������
�������
�������
Design requirement
Figure 14. Penetration angle-of-attack distri-bution.
γp, deg
Number of
cases
0
50
100
150
200
250
300
-5 0 5 10 15 20 25 30
������
������
������
������
������
������
������
Design requirement
Figure 15. Penetration incidence angle distri-bution.
Table 2. 6-DOF Mars Microprobe Monte-Carlo analysis results.
EDI Parameter Mean 3{�Value Variance
Impact velocity, Vr, m/s 156.1 � 22.0Pen. angle-of-attack, �p, deg 4.6 + 14.7Pen. incidence angle, p, deg 8.7 � 14.4Impact Mach number, km 0.65 � 0.09Impact time, sec 298.0 � 29.8Impact latitude, deg -74.7 � 1.7Impact longitude, deg 148.0 � 1.1
Peak _q, W/cm2 154.1 � 11.9Peak deceleration, Earth g's 12.4 � 1.6Integrated heat load, J/cm2 6875. � 416.7
Peak _q angle-of-attack, �t, deg 13.1 + 27.0Peak Q angle-of-attack, �t, deg 7.8 + 4.2
αp
0 5 10 15 20 25
γp
-5
0
5
10
15
20
25
�30
Figure 16. Penetration angles dispersion.
Vr, m/s
M
130 140 150 170160 180 190.54
.58
.62
.66
.70
.72
.74
.56
.60
.64
.68
Figure 17. Impact Mach number and velocitydispersion.
are mildly violated. Note that these two crite-ria are currently satis�ed to a 2{� probabilitylevel. While a small increase in ballistic coe�-cient could be used to adjust the impact velocityrange, such an increase is not recommended asthis would only exacerbate the penetration in-cidence angle problem (see Fig. 8).
Distributions of the signi�cant impact parame-ters are shown in Figs. 16 { 19. The two pen-etration angles show a signi�cant degree of clus-tering for �p � 4:0 degrees and 2:0 � p � 13:0.Note that the variation exhibited in Fig. 17 be-tween impact velocity and Mach number is aresult of atmospheric temperature variability.
The Microprobe impact footprint is presented inFig. 19. This footprint should bear some resem-
Time, sec
Altitude, km
260 270 280 290 300 310 320 3403300
1
2
3
4
5
6
7
Figure 18. Impact altitude and time disper-sion.
E. Longitude, deg147.0 147.5 148.0 148.5 149.0 149.5
Latitude, deg
�-77.0
�-76.5
�-76.0
�-75.5
�-75.0
�-74.5
�-74.0
�-73.5
�-73.0
180 × 20 km ellipse
Figure 19. Impact footprint.
blance to the Mars 98 Lander footprint, sinceboth spacecraft approach Mars on the same in-terplanetary trajectory. As a result of Micro-probe's lower ballistic coe�cient, the range ofimpact sites shown in Fig. 19 does not extend asfar southeast as the Mars 98 Lander footprint.However, Microprobe's 180 x 20 km ellipse issimilar in downrange and larger in crossrange(Mars 98 Lander is actively controlled) than thepredicted Mars 98 Lander ellipse [29].
Peak stagnation-point heating, integrated heatload, and peak atmospheric deceleration statis-tics are also presented in Table 2. Histograms ofthese EDI parameters are presented in Figs. 20{22. The variation in intensity of this aerother-modynamic environment does not currentlyconstrain the mission design space because the
Peak q· , W/cm2
Number of
cases
0
50
100
150
200
250
350
300
140 145 150 155 160 165 170 175
Figure 20. Peak stagnation-point heat ratedistribution.
Integrated heat load, J/cm2
Number of
cases
0
50
100
150
200
250
350
300
6400 6600 6800 7000 7200 7400 7600
Figure 21. Integrated heat load distribution.
Peak deceleration, Earth g's
Number of
cases
0
50
100
150
200
250
300
10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0
Figure 22. Peak atmospheric deceleration dis-tribution.
Penetration angles, deg
Probability function
0
.2
.5
.7
.8
1.0
.1
.3
.4
.6
.9
-5 0 5 10 15 20 25 30
αp
αp design requirement
γp design requirement
γp
Figure 23. Penetration angles of attack andincidence probability distribution.
heatshield is designed to withstand a peak heatrate of approximately 200 W/cm2 and an in-tegrated heat load of more than 8550 J/cm2,based on entry with a � of 33.1 kg/m2. Sim-ilarly, the deceleration levels shown in Fig. 22during atmospheric ight pale in comparison to30000 Earth g's expected at impact.
As presented in Table 2, the mean angle-of-attack at peak heating and impact do not ap-pear too severe. Since total angle-of-attack isa one-sided function, these variables do not ex-hibit a Gaussian distribution. Hence, symmet-ric 3{� variances are not listed for angle-of-attack parameters. Instead, probability curveshave been generated and are presented inFig. 23 for the two signi�cant impact angles (�pand p). These curves give the probability thatthe angle-of-attack will be below a given value.Hence, from Figs. 23, a 93% probability (lessthan 2{�) currently exists that the penetrationangle-of-attack will be below 10 degrees. Simi-larly, there is a 96% probability (slightly morethan 2{�) that the penetration incidence anglewill be below 20 degrees. Note that as a resultof surface slope variability, the penetration inci-dence angle may be slightly negative (as muchas -2.78 degrees was obtained).
The variances in all of the impact conditionsmay be reduced through improved modeling of
αt, deg
Probability function
0
.2
.5
.7
.8
1.0
.1
.3
.4
.6
.9
20 40 80 100 12060 140 160 180
q· = 10 q· = 40 q· = 70 q· = 100
Figure 24. Angle-of-attack probability dis-tribution at several points along the increasingside of heat pulse.
the surface winds, altitude, and slope. For ex-ample, most of the impact velocity varianceobserved in Fig. 13 is a result of surface al-titude uncertainty. Similarly, a large percent-age of the penetration angle variances presentedin Figs. 14 and 15 are the result of the � 5-degree surface slope currently assumed. The ex-pected range in these penetration angles couldalso be reduced by moving the center-of-gravityforward.
Hypersonic Re-orientation{Through this analy-sis, a relatively large angle-of-attack range nearpeak heating has also been identi�ed. As yet,heating calculations at this ight condition haveonly been performed at angles of attack below10 degrees. However, in this analysis, angles-of-attack as high as 45 degrees were obtainedin the peak heating region. In fact, the meanangle-of-attack at peak heating (see Table 2) is13.07 degrees. These results have necessitatedthe performance of additional afterbody heatinganalyses.
To bound this aerothermodynamic assessment,angle-of-attack probability functions at discretepoints along the increasing side of heat pulsewere generated from the present set of Monte-Carlo results. This data is shown in Fig. 24.Since EDI is initiated from a random angularorientation (0 � �t < 180 degrees), this �g-
q· , W/cm2
αt, deg
0
20
40
60
80
100
140
120
25 50 75 100 125 150
Mean
90%
99%
3-σ
Figure 25. Statistical variation in angle of at-tack as a function of stagnation-point heat rate.
ure also provides a measure of the aeroshell'shypersonic re-orientation capability. As a re-sult of the aeroshell's aerodynamic stability, thisre-orientation occurs relatively early in the at-mospheric ight. For example, by the time a_q of 10 W/cm2 is achieved, the angle-of-attackrange has converged such that there is a 50%chance that the angle-of-attack will be below 30degrees. On the nominal trajectory, this heatrate occurs just 28.2 sec past the atmosphericinterface at an altitude of 99.1 km.
By the time 40 W/cm2 (45.1 sec, 78.8 km alti-tude) is achieved, there is a 70% chance that theangle-of-attack will be below 20 degrees and a96% chance that the angle-of-attack will be be-low 30 degrees. As 100 W/cm2 is approached(60.6 sec, 62.8 km altitude), the probability is95% that the angle-of-attack will be below 20degrees. This information is shown as a func-tion of stagnation-point heat rate in Fig. 25.In this �gure, the peak heating region is at 150W/cm2. At peak heating, there is a 99% proba-bility that the angle-of-attack will be below 30.0degrees and a 90% probability that the angle-of-attack will be below 18.0 degrees.
The vehicle's hypersonic re-orientation capabil-ity is largely a function the vehicle's aerody-namic shape and center-of-gravity position. Fora given vehicle con�guration, the damping pro-vided by the atmospheric forces depends on dy-
namic pressure, Q. Unfortunately, as shownin Fig. 11, peak Q occurs approximately 15sec past peak _q. Hence, the forces providingthis passive angle-of-attack convergence are notat their greatest level until beyond peak heat-ing. In fact, in 97% of the cases simulated,the angle-of-attack stays below 10-degrees frompeak dynamic pressure to Mach 2 (see Fig. 12).Improvements in the hypersonic re-orientationlevel prior to peak _q can be achieved by movingthe center-of-gravity position forward, reducingthe products of inertia, or reducing the angularrates associated with the initial separation ma-neuver. This is currently the number one issueconfronting the EDI team. In an e�ort to de-termine the mission impact of this phenomenon,additional afterbody heating analyses are beingperformed.
6 Conclusions
Scheduled for ight in 1999, the New Millen-nium Mars Microprobe mission will provide the�rst opportunity for subsurface measurements,including water detection, near the south poleof Mars. Design of the Microprobe aeroshellsposes several unique aerodynamic challenges in-cluding passive hypersonic re-orientation of aninitially tumbling body and stringent stabilityconstraints during a subsonic impact. The cri-teria used in the selection a 45-degree sphere-cone forebody with hemispherical afterbody arepresented in this paper.
The performance of the Microprobe aeroshelldesign is then evaluated through the develop-ment of a six-degree-of-freedom (6-DOF) aero-dynamic database and ight dynamics simula-tion. Numerous mission uncertainties are quan-ti�ed and a Monte-Carlo analysis is performedto statistically assess mission performance. Re-sults from this 6-DOF Monte-Carlo simulationdemonstrate that, in a majority of the cases(generally 2{�), the penetrator impact condi-tions are within current design tolerances. Inparticular, the 3{� range of impact velocity is134{178 m/s. The 2{� high penetration angle-of-attack is 12 degrees and the 2{� high pene-
tration incidence angle is 18 degrees. The Mi-croprobe impact footprint extends 180x20 kmwith its center at -74.73 degrees South latitude,147.98 degrees East longitude. Suggestions forimprovement are made to enhance MicroprobeEDI performance.
In addition, a relatively large angle-of-attackrange near peak heating is identi�ed whichhas necessitated the performance of additionalafterbody heating analyses. These afterbodyheating analyses are strongly coupled to thehypersonic re-orientation performance derivedfrom the present results. In particular, a 50%probability exists that the angle-of-attack willbe below 30 degrees before a _q of 10 W/cm2
is achieved; whereas, a 96% probability existsthat the angle-of-attack will be below 30 de-grees before _q = 40 W/cm2. As 100 W/cm2
is approached, there is a 95% chance that theangle-of-attack will be below 20 degrees. Atpeak heating, a mean angle-of-attack of 13.07degrees was obtained and a 90% probability ex-ists that this parameter will be below 18 de-grees.
Acknowledgments
The authors are indebted to Eric M. Slimkoof the Jet Propulsion Laboratory for providingtechnical insight and program coordination ofthe Microprobe EDI design strategy, Scott A.Striepe of NASA Langley Research Center forimplementing the eighth-order Runge-Kutta in-tegration technique within POST, and WilliamL. Kleb of NASA Langley Research Center forassistance with the LATEX document prepara-tion system.
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