Mars Microprob e Entry Analysis

 y

Rob ert D. Braun Rob ert A. Mitcheltree F. McNeil Cheatwo o d

NASA Langley Research Center NASA Langley Research Center Vigyan Inc.

Hampton, VA 23681-0001 Hampton, VA 23681-0001 Hampton, VA 23666-1325

(757) 864-4507 (757) 864-4382 (757) 864-2984

r.d.braun@larc.nasa.gov [email protected] f.m.cheatwo o [email protected]

Abstract{The Mars Microprob e mission will 1 Introduction

provide the rst opp ortunity for subsurface

The ob jective of NASA's New Millennium pro-

measurements, including water detection, near

gram is to demonstrate and ight qualify tech-

the south p ole of Mars. In this pap er, p er-

nology elements required for the science mis-

formance of the Microprob e aeroshell design is

sions of the next century [1 ]. The program's

evaluated through development of a six-degree-

second ight pro ject, Deep Space Two (DS{

of-freedom (6-DOF) aero dynamic database and

2) is fo cused on the design of two small Mars

ight dynamics simulation. Numerous mission

entry prob es. As a result, DS{2 is often re-

uncertainties are quanti ed and a Monte-Carlo

ferred to as the Mars Microprob e mission. This

analysis is p erformed to statistically assess mis-

pro of-of-concept system is intended to demon-

sion p erformance. Results from this 6-DOF

strate key elements of future network science

Monte-Carlo simulation demonstrate that, in a

missions [2 , 3]. Attached to the cruise stage

ma jority of the cases (approximately 2{ ), the

of the Mars 98 Surveyor Lander, these two

p enetrator impact conditions are within current

Microprob e vehicles will b e launched to Mars

design tolerances. Several tra jectories are iden-

by a Delta II ro cket in January 1999, arriving

ti ed in which the current set of impact re-

in Decemb er 1999. Each of these Microprob e

quirements are not satis ed. From these cases,

capsules houses instrumented p enetration de-

critical design parameters are highlighted and

vices designed to analyze the subsurface layers

additional system requirements are suggested.

by p erforming soil sampling and water detec-

In particular, a relatively large angle-of-attack

tion. On impact, the p enetrators are designed

range near p eak heating is identi ed.

to pierce their protective aeroshells, driving this

subsurface instrumentation 0.3-2.0 m b elow the

Table Of Contents

surface. Subsurface data will b e relayed back to

Earth through a link with the Mars Global Sur-

1. Introduction

veyor orbiter (Septemb er 1997 Mars arrival).

2. Nomenclature

3. Impact Requirements

The entry, descent, and impact (EDI) phase of

4.1 Aeroshell Selection

the DS{2 mission b egins as the two capsules are

4.2 Aerodynamics

mechanically separated from the cruise stage [4].

4.3 Atmos. Flight Dynamics

This event is preceded by separation of the Mars

5.1 Impact Sizing

98 Lander from the cruise stage (approximately

5.2 Monte-Carlo Simulation

1.5 s earlier). As a result of (1) the brief p erio d

6. Conclusions

b etween these two separation events, (2) the



lack of control of the cruise-stage after the 98

Space Systems and Concepts Division, Mail Stop 365

y

Aero and Gas Dynamics Division, Mail Stop 408A Lander separation, and (3) geometric mounting

2

Q dynamic pressure, N/m

constraints which do not allow the Microprob e

V velo city, m/s

vehicles to b e aligned with the ight path, the

angle-of-attack, deg

capsules will separate in an unknown angular

 

m

2

orientation with non-zero angular rates. Sta-

kg/m ballistic co ecient

C A

D

ble ight of the Microprob e vehicles must b e

ight-path or incidence angle, deg

achieved passively, and maintained until surface

impact.

Subscripts

a relative to the atmosphere

Design of the DS{2 entry prob es is compli-

A axial force

cated by several unique aero dynamic challenges.

D drag force

The vehicles must p ossess enough aero dynamic

l static rolling moment

stability to achieve passive re-orientation from

m static pitching moment

an arbitrary initial motion prior to p eak heat-

mq dynamic pitching moment

ing. Since stable ight at impact is required,

n static yawing moment

the sup ersonic and transonic dynamic stability

N normal force

problems which have plagued other entry mis-

nr dynamic yawing moment

sions [5, 6 , 7 ] must also b e mitigated. Addi-

p p enetrator

tionally, the p enetrators must b e protected from

r relative to the horizon

the intense aerothermo dynamic environment of

t total

a 7.0 km/s Mars entry and satisfy a stringent

Y side force

set of surface impact constraints.

3 Surface Impact Requirements

In this pap er, the criteria used to select the

aeroshell geometry are presented. After re-

The p enetrators have b een designed to op er-

view of the aeroshell shap e and mass prop-

ate prop erly under a range of impact condi-

erties, compilation of the Microprob e aero dy-

tions. Mission success demands that the EDI

namic database is discussed. This database is

system meet several surface impact constraints.

compiled from past studies, computational uid

Three{ requirements on surface impact velo c-

dynamic calculations, and ground-based test

ity (140  V  200 m/s), p enetration angle-

r

data. Development of a six-degree-of-freedom

of-attack (0   10 degrees), and p en-

p

(6-DOF) Monte-Carlo tra jectory simulation for

etration incidence angle (j j  20 degrees)

p

Microprob e EDI is also presented. Results from

have b een sp eci ed [4 ]. These requirements

this 6-DOF Monte-Carlo simulation are used to

are currently b eing validated through a rigor-

statistically assess the e ect of combinatorial

ous ground-testing program.

variations in the signi cant EDI parameters.

The dynamics of the surface impact event are

illustrated in Fig. 1. The Microprob e aeroshell,

2 Nomenclature

lo cal horizon, and lo cal surface slop e are shown,

2

A reference aero dynamic surface area, m

along with the velo cities with resp ect to the

b yaw/roll reference length, m

ground (V ) and atmosphere (V ). By conven-

r a

c pitch reference length, m

tion, the ight-path angles shown are negative.

C aero dynamic force or moment co ecient

Atmospheric winds cause the di erence b etween

g Mars surface slop e, deg

V and V . Total angle-of-attack ( in Fig. 1)

r a t

Kn Knudsen numb er

is de ned as the angle b etween the vehicle's axis

m mass, kg

of symmetry and V .

a

M Mach numb er

2

I b o dy{axis moments of inertia, kg{m

During ight, the forces on the aeroshell are a

2

q_ stagnation{p oint heat rate, W/cm

function of the relationship b etween the vehicle

tolerances until impact. Finally, it must Vehicle small

symmetry

the payload from intense aero dynamic

axis protect

heating. To meet these ob jectives a 45-degree

cone with rounded nose and shoul- Horizon half-angle

γ

. The afterb o dy r g ders is selected for the foreb o dy α γ

t a

is hemispherical with its center at the vehicle's

Vr

ter-of-gravity lo cation. Va cen

Surface

Blunted 45-degree sphere-cones were used for

the successful Pioneer-Venus and Galileo mis-

sions [8 ]. Both of these missions entered at-

Figure 1. De nition of Mars Microprob e sur-

mospheres much denser than Mars. For the

face impact angles.

Mars entries of Viking and Mars Path nder,

70-degree sphere-cones with a zero angle-of-

and the atmospheric velo city vector ( and V ).

t a

attack drag co ecient near 1.7 (versus the 45-

However, at impact, the orientation of the Mi-

degree cone value of 1.05) were selected [9].

croprob e payload relative to the surface is of sig-

Choice of cone angle calls for a compromise of

ni cance. The p enetration angle-of-attack and

drag, stability and packaging. Blunter cones ex-

incidence angle are de ned as:

hibit more drag p er surface area; sharp er cones

= + ( ) (1)

p t a r

p ossess more stability. Viking and Path nder



= + 90 g (2)

make use of high drag aeroshells since b oth

p r

of these entries required deceleration of much

As discussed b elow, the surface impact velo city

heavier spacecraft at suciently high altitudes

and incidence angle constraints may b e achieved

for parachute deployment. In contrast, the

through the selection of the appropriate ballis-

Mars Microprob e vehicles are more than two

tic co ecient (see Section 5); whereas, satis-

orders of magnitude lighter and must impact

faction of the impact angle-of-attack constraint

the surface at a high velo city (140-200 m/s).

is a function of the vehicle's aero dynamic sta-

Additionally, each Microprob e capsule requires

bility (geometry and center-of-gravity lo cation).

the highest p ossible aero dynamic stability to re-

Aero dynamic design of the Microprob e capsules

cover quickly from any initial tumbling motion.

is presented in Section 4. The variance in each

of the signi cant impact parameters as well as

The degree of nose bluntness has little e ect

statistical data regarding the aeroshell heating

on the drag co ecient for a 45-degree half-

environment is presented in Section 5.

angle cone, although increased bluntness do es

slightly decrease static stability. On the other

4 Analysis hand, increased bluntness decreases the stagna-

tion p oint heat rate during the hyp ersonic p or-

Aeroshel l Selection

tion of the tra jectory. Selecting the appropri-

ate degree of nose bluntness is a compromise

Selection of the aeroshell for Mars Microprob e

of these factors. For Microprob e, a nose radius

requires consideration of the unique ob jectives

equal to half of the vehicle's overall base radius

of the mission. A passive enclosure is required

is an acceptable value. This is the same ra-

to safely deliver the p enetrator payload through

tio used in the Pioneer-Venus and Galileo entry

entry to impact with the surface. The aeroshell

prob es [7, 10 , 11 ]. Similarly, rounding the ve-

must decelerate the vehicle during its descent

hicle's shoulders is p erformed to decrease lo cal

to a prescrib ed impact velo city. It must p ossess

heating. Rounding the shoulders decreases b oth

sucient stability to correct any initial tum-

drag and stability. Again, the Pioneer-Venus

bling motion to forward-facing ight early in the

value of shoulder radius equal to one tenth the

tra jectory and maintain that orientation within

radius is sp eci ed for Microprob e. Al-

nose 350

it is p ossible to optimize the amount

though R 183

of nose and shoulder rounding for the sp eci c

Microprob e mission, the selection of previously

used ratios app ears adequate and also allows

use of an extensive b o dy of existing aero-

the R 8.75

dynamic test and ight data.

m ...... 2.73 kg

of the hemispherical afterb o dy is Selection 90.2 2

x Ixx ...... 0.0105 kg-m

on the Planetary Atmosphere Exp eri- based I , I . . . .0.0106 kg-m2 R 87.5 yy zz

z

ts Test (PAET) prob e [12 ]. The hemispher- men b,c ...... 0.350 m

All dimensions in mm β ...... 27 kg/m2

ical afterb o dy sp eci ed for Microprob e serves

two purp oses. First, since the vehicle may

b e tumbling initially, it may encounter the at-

Figure 2. Mars Microprob e aeroshell geometry

mosphere while traveling backwards. A hemi-

and mass prop erties.

spherical afterb o dy with center at the vehicle's

center-of-gravity is not stable in this orienta-

and will foster rotation to a forward fac-

tion Transonic Supersonic Hypersonic Transitional

attitude. Second, this afterb o dy has b een

ing Free Molecular

wn to decrease the dynamic instability ob- sho Eglin ARF Bridging/DSMC

CFD: LAURA

ed in blunt vehicles traversing the transonic

serv CFD: TLNS3D

ight regime [13 ]. Regarding backwards stabil-

ity, it is of interest to note that Pioneer-Venus,

Windtunnel:Nichols 0.001 0.1 10

Viking and Mars Path nder were all

Galileo, Windtunnel:Brooks Knudsen Number

hyp ersonically stable in a backwards orienta-

0 1 2 3 4 5 6 10 20 30 40

To prevent this o ccurrence, each entry ve-

tion. Mach Number

hicle was oriented nose- rst and spin-stabilized

to assure a forward-facing attitude at the at-

Figure 3. Sources used to assemble Mars Mi-

mospheric interface. Spin stabilization is not

croprob e aero dynamic database.

an option for Microprob e; however, the hemi-

spherical afterb o dy assures the vehicle will not

trim in a backwards-facing attitude.

ground-based test data. A detailed description

of the vehicle's aero dynamic characteristics is

The geometry of the Mars Microprob e aeroshell

provided in Ref. [14 ]. Sources of the static aero-

is depicted in Fig. 2. As shown, a 45-degree

dynamic predictions are illustrated in Fig. 3.

sphere cone with nose radius of 0.0875 m, shoul-

Free molecular and Direct Simulation Monte

der radius of 0.00875 m, and maximum radius

Carlo (DSMC) computations were p erformed to

of 0.175 m has b een selected. The afterb o dy

characterize the rare ed and transitional ow

shap e is a hemispherical section with radius of

regimes. These results were supplemented by

0.183 m centered ab out the vehicle's center-of-

thermo chemical nonequilibrium computational

gravity. The center-of-gravity is lo cated 0.0902

uid dynamic calculations obtained with the

m aft of the nose on the vehicle's symmetry axis.

Langley Aerothermo dynamic Upwind Relax-

ation Algorithm (LAURA in Fig. 3) in the con-

tinuum hyp ersonic ow regime. This analysis

Aerodynamics

to ol was extensively used in the prediction of the

Mars Path nder aero dynamics [15 ]. Pioneer- The Mars Microprob e aero dynamic database

Venus wind tunnel data was used in the sup er- was derived from a combination of computa-

sonic, transonic, and subsonic regimes [16 , 17]. tional uid dynamic (CFD) calculations and

alidation and extrap olation of these exist-

V 2.5

results was made p ossible through addi-

ing 1.5

tional computational solutions obtained in the

CD 1.0

and subsonic ight regimes with the transonic 2.0 .5

0 5 15 25

Thin-Layer Navier-Stokes 3-Dimensional pro- M Free

molecular gram [18 ] (TLNS3D in Fig. 3).

CD 1.5

Dynamic damping co ecients were extracted

Pioneer-Venus and Viking wind tunnel from α °

t = 0

data [5, 6, 7 ]. In addition, transonic bal-

test 1.0

listic range data was pro duced on a Micro-

Continuum Transitional

prob e mo del with the correct center-of-gravity

[19 , 20 ]. Dynamic stability estimates lo cation .5

10-6 10-4 10-2 100 102 104

not b e obtained computationally within

could Log Kn

the time constraints of the present analysis. Be-

Figure 4. Mars Microprob e 0-degree angle-of-

cause of the transonic dynamic instability prob-

attack drag co ecient.

lems which have plagued other entry vehicle de-

signs, additional data is b eing gathered in a

and 1.3. Finally, to account for small di erences

pressurized facility in which the ight Reynolds

in the aeroshell geometry, the axial force wind

numb er can b e duplicated [19 ].

tunnel values were scaled to match the compu-

tational results.

To pro duce a cohesive database from these di-

verse sources, mo di cation of the original data

Early versions of the aero dynamics routine used

set was required [21 ]. A bridging function

simple linear interp olation, providing value-

(shap ed by the DSMC results) was used in the

continuity b etween segments. Although a

transitional region b etween the free molecular

twice-di erentiable database was sought, pro-

and continuum results. Explicit calculation of

viding this level of continuity at the data

the transitional aero dynamics by DSMC meth-

p oints resulted in unacceptable b ehavior b e-

o ds, although p ossible, is computationally pro-

tween the data. As a compromise, an overlap-

hibitive. Instead, selected DSMC results were

ping parab ola technique, which provides slop e-

used to anchor and shap e the bridging function.

continuity, was used. As the FORTRAN rou-

This function provides a smo oth variation of the

tine was develop ed, care was taken to minimize

vehicle's aero dynamic characteristics based on

memory overhead. Furthermore, since the rou-

the free molecular and continuum hyp ersonic

tine is called many times by 6-DOF POST, an

computations.

e ort was made to create a computationally ef-

cient algorithm. For a given ight condition

Within the database [21 ], the continuum hy-

and vehicle angular orientation, the database

p ersonic aero dynamics were assumed to vary

provides estimates of C ,C ,C ,C ,C ,C ,

A N Y m n

l

with angle of attack in a similar manner to

C , and C for use in the 6-DOF tra jectory

mq nr

that predicted by Newtonian ow. This New-

simulation [21 ].

tonian variation was then scaled to repro duce

sp eci c LAURA computations obtained at 0

The 0-degree angle-of-attack Microprob e drag

and 10-degrees angle of attack. The sup ersonic

co ecient is shown in Fig. 4 as a function

and transonic wind tunnel data overlapp ed, so

of Knudsen (Kn) and Mach (M) numb ers.

the two sets were blended in the Mach numb er

Knudsen numb er is de ned as the ratio of the

region b etween 1.65 and 2.16. Similarly, the

gas' mean free path to the vehicle's diameter.

Pioneer-Venus and Viking dynamics data were

This similarity parameter is used as the in-

blended in the Mach numb er region b etween 1.2

dep endent variable in the rare ed and transi-

tional aero dynamic regimes. Initially, Kn will and landing (EDL) strategy [23 , 24]. Six-DOF

b e large. For values larger than 10, the aero- POST is also b eing used by the Path nder EDL

dynamic forces are computed solely from the op erations team [25 , 26 ]. In the present study,

free molecular ow solutions. Free molecular POST is used to numerically integrate the 6-

ow assumes there are no collisions b etween gas DOF equations of motion from a given entry

molecules in the ow eld. Unlike hyp ersonic state to surface impact. An eighth-order Runge-

continuum aero dynamics (where forces exerted Kutta integration technique is employed [27 ].

on the b o dy are essentially the integrated ef- The Microprob e aero dynamic database as well

fect of surface pressures alone), free molecular as Mars atmospheric, gravitational, and surface

ow aero dynamics contain a signi cant shear mo dels are inputs to the simulation. Atmo-

stress contribution. As the entry pro ceeds into spheric mo deling for this mission is hamp ered

the upp er atmosphere, b oth the mean free path by the lack of surface measurements for the

and Knudsen numb er decrease and collisions southern hemisphere of Mars (the target im-

b etween particles must b e taken into account. pact site is 73{77 degrees South latitude). Using

In this regime, where 0:001 < K n < 10, the pro jected data obtained from the Viking lan-

aero dynamics are computed from the DSMC- ders and a global circulation mo del, Zurek and

anchored bridging function. Richardson have constructed nominal and p er-

turb ed atmospheric pro les [28 ]. These mo dels

As lower altitudes are reached (b elow 55 km al-

are used in the current simulation.

titude for Microprob e), the Knudsen numb er

drops b elow 0.001 and the continuum meth- In the present analysis, uncertainties are applied

o ds are used to compute vehicle aero dynamics. in all simulation mo del inputs. These uncertain-

Here, Mach numb er is the appropriate aero dy- ties arise from numerous sources including (1)

namic similarity parameter. Fig. 4 shows that technology limitations (e.g., current interplane-

drag co ecient (at a given angle of attack) is tary navigation or mass-balance accuracies), (2)

approximately constant ab ove Mach 5. The in- a lack of knowledge concerning the Mars atmo-

crease in drag co ecient sup ersonically, is a re- sphere, (3) computational or measurement un-

sult of the sonic line shifting from the nose re- certainty asso ciated with the aero dynamic anal-

gion to the shoulder region of the aeroshell b e- yses, and (4) unknown separation orientation

tween Mach 5 and 2. This shift has a signi - and angular rate. Therefore, in this analysis,

cant impact on the pressure distribution caus- an attempt was made to quantify and mo del

ing axial force (equivalent to drag at 0-degree the degree of uncertainty in each of 29 ma jor

angle-of-attack) to increase while normal force parameters.

and moment co ecient decrease. Transonically,

The uncertainty range attributed to each of

drag co ecient decreases. Here the data of

these parameters is listed in Table 1. For a

Refs. [17 , 20] and the TLNS3D computational

parameter with more than one variance (e.g.,

solutions are used. The axial force data of

aero dynamics or winds), the uncertainty is es-

Ref. [17 ] is decreased to account for the Micro-

timated using linear interp olation b etween the

prob e con guration's large hemispherical after-

regions given in Table 1. Gaussian distributions

b o dy.

are sampled for most parameters. However, the

initial orientation, center-of-gravity o set quad-

Atmospheric Flight Dynamics

rant, and wind direction quadrant are deter-

mined from uniform distributions. The top og-

Six-degree-of-freedom (6-DOF) tra jectory anal-

raphy variation is mo deled by a non-symmetric

ysis is p erformed using the Program to Opti-

Gaussian distribution centered at 5 km. This

mize Simulated Tra jectories (POST) [22 ]. This

distribution is illustrated in Fig. 5.

program has b een used previously in the devel-

opment of the Mars Path nder entry, descent,

Table 1. 6-DOF Monte-Carlo variables. 100

90

arameter Nominal 3{

EDI P 80

alue Variance

V 70

Initial state, , deg -13.25  0.4

60

Initial , deg 90.0  90.0

t Altitude,

h rate, deg/s 6.0  5.0

Initial pitc km 50

aw rate, deg/s 6.0  5.0

Initial y 40

6.0  5.0

Initial roll rate, deg/s 30

X-axis cg p osition, mm 90.2  5.0

20

0.0  1.0 X-axis cg o set, mm Atmospheric model

courtesy Ref. 27

2.73  0.273

Mass, kg 10

2

I , kg-m 0.0106  0.0003

xx 0

2 -.5 0 .5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

I ,I , kg-m 0.0105  0.0003 z z y y Dens/dens

2 nom

I ,I ,I , kg-m 0.0  0.0003

xy xz y z

C , Kn  0.1 See Fig. 4  10%

A

Figure 6. 3{ density variation used in the

C , Kn  0.1 See Ref. [14 ]  0.10

N

6-DOF Monte-Carlo simulation.

C , Kn  0.1 See Ref. [14 ]  0.006

m

C , Kn < 0.1, M  10 See Fig. 4  2%

A

C , Kn < 0.1, M  10 See Ref. [14 ]  0.05 N

100

C , Kn < 0.1, M  10 See Ref. [14 ]  0.003

m

, Kn < 0.1, M  5 See Fig. 4  10%

C 90

A

C , Kn < 0.1, M  5 See Ref. [14 ]  0.10

N 80

C , Kn < 0.1, M  5 See Ref. [14 ]  0.006

m 70

C and C ,M  6 See Ref. [14 ]  20%

mq nr

60

C and C ,M  3 See Ref. [14 ] -50, +110% nr

mq Altitude,

y See Ref. [28 ] See Fig. 6

Densit km 50

emp erature See Ref. [28 ]  150%

T 40

ve 50 km See Ref. [28 ] See Fig. 7

Wind ab o 30

w 10 km See Ref. [28 ] See Fig. 7

Wind b elo

20

0.0  30.0 Wind gust, m/s Atmospheric model

courtesy Ref. 27

5.0 -4, +1 Surface altitude, km 10

Surface slop e, deg 0.0  5.0 0 20 40 60 80 100 120 140 160 180 200

Wind speed, m/s

Figure 7. 3{ wind pro les used in the 6-DOF

Monte-Carlo simulation.

3{ variances in atmospheric density and

500 The

wn in Figs. 6 and 7. As illustrated 450 winds are sho

400 in these gures, three atmospheric pro les with

arying levels of visible column depth, or opac-

350 v

y (0.05, 0.2, 0.5), are used in the present sim- 300 it

Number

Within the Monte-Carlo simulation, of 250 ulation. cases

200 these three nominal and p erturb ed atmospheric

enly. 150 pro les are sampled ev

100

Results And Discussion 50 5

0 1 2 34 5 6 7

act Sizing and Nominal Trajectory

Surface altitude, km Imp

For zero angle-of-attack ight of the Microprob e

Figure 5. Impact altitude distribution.

capsules, the impact conditions are completely

determined by ballistic co ecient ( ) and sur-

40 220 Design V 18 170 210 space r Vr design

35 requirement 200 17 165

30 190 γ p 16 160

180 25 γ , V , 15 155 p r 170 Vr

deg m/s γ 20 p, Vr, γ 160 14 150 p

deg m/s

15 150 13 145

140 12 140 10 130

11 135 5 120

15 20 25 30 35 40 45 50 55 10 130 β, kg/m2 1 2 3 4 5 6

Surface altitude, km

Figure 8. Mars Microprob e ballistic co ecient Figure 9. E ect of surface altitude on Micro-

2

requirements, surface altitude = 5 km. prob e impact conditions, = 27 kg/m .

face altitude. Assuming a surface slop e of 5 de-

The impact of surface altitude on the Fig. 8 grees, an altitude of 5 km, the mean density

trade-space is shown in Fig. 9. For the impact pro le [28 ], and negligible wind sp eed, the fol-

site of interest, a surface altitude of 1 to 6 km lowing values are determined from Fig. 8. For

ab ove the Mars reference ellipsoid may b e en- an impact sp eed of 160 m/s, a ballistic co e-

2

countered [4 ]; however, a ma jority of this terrain cient of 27 kg/m is required. Furthermore, the

is thought to b e 5 km ab ove the Mars reference ballistic co ecient must b e within the range of

2

ellipsoid (see Fig. 5). As shown in Fig. 9, im- 20:6   47 kg/m to satisfy the impact ve-

pact velo city changes approximately 5 m/s for lo city criterion (140  V  200 m/s), and b e-

r

2

each km of surface altitude and the p enetration low 33.1 kg/m to satisfy the p enetration in-

incidence angle decreases with surface altitude cidence angle constraint (j j  20 degrees).

p

(at a rate of ab out 1.4 deg/km). For = 27 Hence, the Microprob e design space is restricted

2 2

kg/m , the impact velo city criterion is satis ed such that 20:6   33:1 kg/m .

ab ove 1.6 km altitudes; whereas the p enetra-

The design approach selected by the Mars Mi-

tion incidence angle constraint is satis ed over

croprob e pro ject oce is to baseline the largest

the complete range of exp ected surface altitude.

diameter aeroshell that do es not adversely im-

The nominal Microprob e EDI tra jectory is pact the Mars 98 Lander. This approach, which

shown in Fig. 10. As shown, the atmospheric allows for mo dest mass growth, yields the 350

entry velo city is 6.9 km/s. The atmospheric mm maximum diameter depicted in Fig. 2. As

interface is de ned at a radius of 3522.2 km discussed earlier, a 45-degree sphere-cone has a

(surface altitude of 141.8 km). The p eak de- continuum hyp ersonic C of 1.05. Thus, for the

D

2

celeration of 12.6 Earth g's is achieved at an nominal value of = 27 kg/m , a Microprob e

altitude of 44.1 km. Surface impact o ccurs mass of 2.73 kg is required. Without ballast, the

roughly 290 sec after atmospheric interface, at current system mass estimate is 2.63 kg. This

160 m/s (Mach 0.66). Fig. 11 shows that the yields a mass margin of 3.8% at the nominal

2

p eak stagnation-p oint heat rate of 160 W/cm impact sp eed. As mentioned ab ove, the impact

is achieved at approximately 80 sec (altitude of constraints can b e met with a ballistic co e-

2

49.2 km) and is followed by p eak dynamic pres- cient as high as = 33:1 kg/m ; hence, the Mi-

2

sure (3380 N/m ) at approximately 94 sec into croprob e heatshield is b eing sized for this value.

the EDI sequence. At impact, the integrated At this upp er limit of , the current design mass

2

stagnation-p oint heat load is 7165 J/cm . margin is 27.1%.

100 15 7.5 150 Vr 80 β = 27 kg/m2

10 5.0 100 60 α t, Decel., Vr, Altitude, Deceleration deg Earth g's km/s km 40

5 2.5 50 20

Altitude

0 0 0 50 100 150 200 250 300 0 50 100 150 200 250 300

Time, s Time, s

Figure 10. Mars Microprob e nominal tra jec- Figure 12. Mars Microprob e total angle-of-

tory. attack pro le, initial 90-degree angle-of-attack.

4000 200

This hyp ersonic re-orientation issue is discussed Q

qá further in the nal section of this pap er.

3000 150

In addition to demonstrating the hyp ersonic 2

Q, qá, β = 27 kg/m

tation capability of the Microprob e 2000 100 re-orien

N/m2 W/cm2

aeroshell, Fig. 12 also demonstrates that stat-

ically stable ight can b e maintained passively

1000 50

throughout EDI. In fact, for this case, the angle-

of-attack at impact ( ) is 1.5 degrees. Note t

0

the presence of the transonic dynamic in- 0 50 100 150 200 250 300 that

Time, s

stability is evident in Figure 12. This phenom-

ena is the cause for the small increase in total

Figure 11. Stagnation-p oint heat-rate and dy-

angle-of-attack from 225 to 275 sec.

namic pressure pro les.

Because of Microprob e's small moments of in-

The nominal entry shown in Figs. 10 and 11 as- ertia (see Fig. 2), large angular rates are likely

sumes a zero angle-of-attack entry interface ori- during the entry. This high frequency motion is

entation, mean atmosphere without wind, and evident in Fig. 12, particularly when dynamic

no error in the center-of-gravity p osition, mass pressure is large. Pitch and yaw rates as high

prop erties, or aero dynamic mo deling. Figure 12 as 200 deg/sec and an angle-of-attack oscilla-

presents the total angle-of-attack history for a tion frequency of approximately 5 Hz are likely

similar entry initiated with a 90-degree angle- near p eak Q. In comparison, Mars Path nder's

of-attack. As shown, total angle-of-attack is angular motion is characterized by pitch and

damp ed b elow 10 degrees within the rst 50 yaw rates two orders of magnitude lower in

sec of atmospheric ight (by 76 km altitude) the p eak dynamic pressure region and a much

and continues to decrease as the dynamic pres- lower angle-of-attack frequency [23 ]. Although

sure (Q) builds (see Fig. 11). Thus, although Microprob e's angular frequency diminishes as

high angles-of-attack may o ccur early in the dynamic pressure decreases, an increased fre-

mission, the Microprob e aeroshells p ossess suf- quency o ccurs during transonic ight as a result

cient aero dynamic stability to provide passive of the vehicle's dynamic instability. At impact,

re-orientation while in the upp er atmosphere. the vehicle's pitch and yaw rates are more than

350 700

300 600 Design 250 Design requirement 500 requirement

200 Number Number 400 of of cases

150 cases

300 100

200

50 100

0 130 140 150 160 170 180 190 0 5 10 15 20 25 V , m/s α

r p, deg

Figure 13. Impact velo city distribution.

Figure 14. Penetration angle-of-attack distri- bution.

300

an order of magnitude lower than at p eak dy-

pressure and the angle-of-attack oscilla-

namic 250 ximately 2.5 Hz. tion frequency is appro Design requirement 200

Number Monte-Carlo Simulation of 150

cases

During ight of the Mars Microprob e space-

100

craft, a combination of o -nominal e ects is

ely to b e encountered. Hence, it is imp or-

lik 50

tant to statistically assess the e ect of combi-

0

variations in all of the EDI parame- natorial -5 0 5 10 15 20 25 30

γ , deg

able 1. To accomplish this, two-

ters listed in T p

thousand o -nominal cases were randomly esti-

mated and simulated in a Monte-Carlo fashion.

Figure 15. Penetration incidence angle distri-

A 99.7% probability exists that each random pa-

bution.

rameter will remain within the 3{ uncertainty

b ounds of Table 1. In addition to a detailed set

Table 2. 6-DOF Mars Microprob e Monte-

of impact conditions, the total angle-of-attack

Carlo analysis results.

was monitored at discrete p oints along the heat

pulse. Peak deceleration, stagnation-p oint heat-

EDI Parameter Mean 3{

rate, and integrated heat load were also moni-

Value Variance

tored.

Impact velo city, V , m/s 156.1  22.0

r

Pen. angle-of-attack, , deg 4.6 + 14.7

p

Pen. incidence angle, , deg 8.7  14.4

p

Impact Conditions{Histograms of the probable

Impact Mach numb er, km 0.65  0.09

ranges in impact velo city, p enetration angle-of-

Impact time, sec 298.0  29.8

Impact latitude, deg -74.7  1.7

attack and surface incidence angles are shown

Impact longitude, deg 148.0  1.1

in Figs. 13 { 15. Monte-Carlo statistics for

these impact parameters are tabulated in Ta-

2

Peak q_ , W/cm 154.1  11.9

ble 2. These data indicate that the current set

Peak deceleration, Earth g's 12.4  1.6

2

Integrated heat load, J/cm 6875.  416.7 of Microprob e impact requirements are not sat-

is ed in a 3{ sense. In particular, the 3{ low

Peak q_ angle-of-attack, , deg 13.1 + 27.0

t

impact velo city criteria (140 m/s) and the 3{

Peak Q angle-of-attack, , deg 7.8 + 4.2

t

 high p enetration incidence angle (20 degrees)

30 7

25 6

20 5

15 4 γ Altitude, p km 10 3

5 2

0 1

-5 0 0 5 10 15 20 25 260 270 280 290 300 310 320330 340 α

p Time, sec

Figure 16. Penetration angles disp ersion. Figure 18. Impact altitude and time disp er- sion. .74 .72 -73.0

.70 -73.5 × .68 180 20 km ellipse -74.0 .66 -74.5 M .64 Latitude, .62 deg -75.0

.60 -75.5 .58 -76.0 .56 .54 -76.5 130 140 150160 170 180 190 -77.0 Vr, m/s 147.0 147.5 148.0 148.5 149.0 149.5

E. Longitude, deg

Figure 17. Impact Mach numb er and velo city

Figure 19. Impact fo otprint.

disp ersion.

blance to the Mars 98 Lander fo otprint, since

are mildly violated. Note that these two crite-

b oth spacecraft approach Mars on the same in-

ria are currently satis ed to a 2{ probability

terplanetary tra jectory. As a result of Micro-

level. While a small increase in ballistic co e-

prob e's lower ballistic co ecient, the range of

cient could b e used to adjust the impact velo city

impact sites shown in Fig. 19 do es not extend as

range, such an increase is not recommended as

far southeast as the Mars 98 Lander fo otprint.

this would only exacerbate the p enetration in-

However, Microprob e's 180 x 20 km ellipse is

cidence angle problem (see Fig. 8).

similar in downrange and larger in crossrange

Distributions of the signi cant impact parame- (Mars 98 Lander is actively controlled) than the

ters are shown in Figs. 16 { 19. The two p en- predicted Mars 98 Lander ellipse [29 ].

etration angles show a signi cant degree of clus-

Peak stagnation-p oint heating, integrated heat

tering for  4:0 degrees and 2:0   13:0.

p p

load, and p eak atmospheric deceleration statis-

Note that the variation exhibited in Fig. 17 b e-

tics are also presented in Table 2. Histograms of

tween impact velo city and Mach numb er is a

these EDI parameters are presented in Figs. 20{

result of atmospheric temp erature variability.

22. The variation in intensity of this aerother-

The Microprob e impact fo otprint is presented in mo dynamic environment do es not currently

Fig. 19. This fo otprint should b ear some resem- constrain the mission design space b ecause the

α p design requirement 1.0 350 γ p design .9 requirement 300 .8 α p 250 .7 γ .6 p Number 200 Probability .5 of function cases 150 .4 .3 100 .2 50 .1

0 0 140 145 150 155 160 165 170 175 -5 0 5 10 15 20 25 30

Peak qá , W/cm2 Penetration angles, deg

Figure 23. Penetration angles of attack and

incidence probability distribution.

Figure 20. Peak stagnation-p oint heat rate

distribution.

heatshield is designed to withstand a p eak heat

2

of approximately 200 W/cm and an in-

350 rate

2

heat load of more than 8550 J/cm ,

300 tegrated

2

based on entry with a of 33.1 kg/m . Sim-

250

ilarly, the deceleration levels shown in Fig. 22

during atmospheric ight pale in comparison to

Number 200 Earth g's exp ected at impact. of 30000

cases 150

presented in Table 2, the mean angle-of- 100 As

attack at p eak heating and impact do not ap-

50

p ear to o severe. Since total angle-of-attack is ariables do not ex- 0 a one-sided function, these v

6400 6600 6800 7000 7200 7400 7600

Gaussian distribution. Hence, symmet-

Integrated heat load, J/cm2 hibit a

ric 3{ variances are not listed for angle-of-

Figure 21. Integrated heat load distribution.

attack parameters. Instead, probability curves

have b een generated and are presented in

Fig. 23 for the two signi cant impact angles (

300 p

and ). These curves give the probability that

p

k will b e b elow a given value.

250 the angle-of-attac

Hence, from Figs. 23, a 93% probability (less

200

than 2{ ) currently exists that the p enetration

Number

k will b e b elow 10 degrees. Simi- of 150 angle-of-attac

cases

larly, there is a 96% probability (slightly more

2{ ) that the p enetration incidence angle

100 than

will b e b elow 20 degrees. Note that as a result

50

of surface slop e variability, the p enetration inci-

angle may b e slightly negative (as much 0 dence

10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 as obtained).

Peak deceleration, Earth g's as -2.78 degrees w

Figure 22. Peak atmospheric deceleration dis-

The variances in all of the impact conditions

tribution.

may b e reduced through improved mo deling of

1.0 140 3-σ .9 120 .8 100 99% .7 qá = 10 á .6 q = 40 qá = 70 80 Probability á α function .5 q = 100 t, deg 60 .4 90%

.3 40 Mean .2 20 .1

0 20 4060 80 100 120 140 160 180 0 25 50 75 100 125 150 α á 2

t, deg q, W/cm

Figure 24. Angle-of-attack probability dis- Figure 25. Statistical variation in angle of at-

tribution at several p oints along the increasing tack as a function of stagnation-p oint heat rate.

side of heat pulse.

ure also provides a measure of the aeroshell's

the surface winds, altitude, and slop e. For ex-

hyp ersonic re-orientation capability. As a re-

ample, most of the impact velo city variance

sult of the aeroshell's aero dynamic stability, this

observed in Fig. 13 is a result of surface al-

re-orientation o ccurs relatively early in the at-

titude uncertainty. Similarly, a large p ercent-

mospheric ight. For example, by the time a

age of the p enetration angle variances presented

2

q_ of 10 W/cm is achieved, the angle-of-attack

in Figs. 14 and 15 are the result of the  5-

range has converged such that there is a 50%

degree surface slop e currently assumed. The ex-

chance that the angle-of-attack will b e b elow 30

p ected range in these p enetration angles could

degrees. On the nominal tra jectory, this heat

also b e reduced by moving the center-of-gravity

rate o ccurs just 28.2 sec past the atmospheric

forward.

interface at an altitude of 99.1 km.

2

Hypersonic Re-orientation{Through this analy- By the time 40 W/cm (45.1 sec, 78.8 km alti-

sis, a relatively large angle-of-attack range near tude) is achieved, there is a 70% chance that the

p eak heating has also b een identi ed. As yet, angle-of-attack will b e b elow 20 degrees and a

heating calculations at this ight condition have 96% chance that the angle-of-attack will b e b e-

2

only b een p erformed at angles of attack b elow low 30 degrees. As 100 W/cm is approached

10 degrees. However, in this analysis, angles- (60.6 sec, 62.8 km altitude), the probability is

of-attack as high as 45 degrees were obtained 95% that the angle-of-attack will b e b elow 20

in the p eak heating region. In fact, the mean degrees. This information is shown as a func-

angle-of-attack at p eak heating (see Table 2) is tion of stagnation-p oint heat rate in Fig. 25.

13.07 degrees. These results have necessitated In this gure, the p eak heating region is at 150

2

the p erformance of additional afterb o dy heating W/cm . At p eak heating, there is a 99% proba-

analyses. bility that the angle-of-attack will b e b elow 30.0

degrees and a 90% probability that the angle-

To b ound this aerothermo dynamic assessment,

of-attack will b e b elow 18.0 degrees.

angle-of-attack probability functions at discrete

p oints along the increasing side of heat pulse The vehicle's hyp ersonic re-orientation capabil-

were generated from the present set of Monte- ity is largely a function the vehicle's aero dy-

Carlo results. This data is shown in Fig. 24. namic shap e and center-of-gravity p osition. For

Since EDI is initiated from a random angular a given vehicle con guration, the damping pro-

orientation (0  < 180 degrees), this g- vided by the atmospheric forces dep ends on dy- t

namic pressure, Q. Unfortunately, as shown tration incidence angle is 18 degrees. The Mi-

in Fig. 11, p eak Q o ccurs approximately 15 croprob e impact fo otprint extends 180x20 km

sec past p eak q_ . Hence, the forces providing with its center at -74.73 degrees South latitude,

this passive angle-of-attack convergence are not 147.98 degrees East longitude. Suggestions for

at their greatest level until b eyond p eak heat- improvement are made to enhance Microprob e

ing. In fact, in 97% of the cases simulated, EDI p erformance.

the angle-of-attack stays b elow 10-degrees from

In addition, a relatively large angle-of-attack

p eak dynamic pressure to Mach 2 (see Fig. 12).

range near p eak heating is identi ed which

Improvements in the hyp ersonic re-orientation

has necessitated the p erformance of additional

level prior to p eak q_ can b e achieved by moving

afterb o dy heating analyses. These afterb o dy

the center-of-gravity p osition forward, reducing

heating analyses are strongly coupled to the

the pro ducts of inertia, or reducing the angular

hyp ersonic re-orientation p erformance derived

rates asso ciated with the initial separation ma-

from the present results. In particular, a 50%

neuver. This is currently the numb er one issue

probability exists that the angle-of-attack will

confronting the EDI team. In an e ort to de-

2

b e b elow 30 degrees b efore a q_ of 10 W/cm

termine the mission impact of this phenomenon,

is achieved; whereas, a 96% probability exists

additional afterb o dy heating analyses are b eing

that the angle-of-attack will b e b elow 30 de-

p erformed.

2 2

grees b efore q_ = 40 W/cm . As 100 W/cm

is approached, there is a 95% chance that the

6 Conclusions

angle-of-attack will b e b elow 20 degrees. At

p eak heating, a mean angle-of-attack of 13.07

Scheduled for ight in 1999, the New Millen-

degrees was obtained and a 90% probability ex-

nium Mars Microprob e mission will provide the

ists that this parameter will b e b elow 18 de-

rst opp ortunity for subsurface measurements,

grees.

including water detection, near the south p ole

of Mars. Design of the Microprob e aeroshells

p oses several unique aero dynamic challenges in-

Acknowledgments

cluding passive hyp ersonic re-orientation of an

initially tumbling b o dy and stringent stability

The authors are indebted to Eric M. Slimko

constraints during a subsonic impact. The cri-

of the Jet Propulsion Lab oratory for providing

teria used in the selection a 45-degree sphere-

technical insight and program co ordination of

cone foreb o dy with hemispherical afterb o dy are

the Microprob e EDI design strategy, Scott A.

presented in this pap er.

Striep e of NASA Langley Research Center for

implementing the eighth-order Runge-Kutta in-

The p erformance of the Microprob e aeroshell

tegration technique within POST, and William

design is then evaluated through the develop-

L. Kleb of NASA Langley Research Center for

ment of a six-degree-of-freedom (6-DOF) aero-

A

assistance with the L T X do cument prepara-

E

dynamic database and ight dynamics simula-

tion system.

tion. Numerous mission uncertainties are quan-

ti ed and a Monte-Carlo analysis is p erformed

to statistically assess mission p erformance. Re-

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