November 2009

NASA/TM-2009-215950

A Multidisciplinary Tool for Systems Analysis 

of Planetary Entry, Descent, and Landing 

(SAPE)

Jamshid A. Samareh

Langley Research Center, Hampton, Virginia
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November 2009

NASA/TM-2009-215950

A Multidisciplinary Tool for Systems Analysis 

of Planetary Entry, Descent, and Landing 

(SAPE)

Jamshid A. Samareh

Langley Research Center, Hampton, Virginia
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 

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National Aeronautics and Space Administration. 
Abstract

SAPE is a Python-based multidisciplinary analysis tool for systems analysis of planetary entry, 

descent, and landing (EDL) for Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, and Titan. The 

purpose of SAPE is to provide a variable-fidelity capability for conceptual and preliminary analysis 

within the same framework. SAPE includes the following analysis modules: geometry, trajectory, 

aerodynamics, aerothermal, thermal protection system, and structural sizing. SAPE uses the Python 

language—a platform-independent open-source software—for integration and for the user interface. The 

development has relied heavily on the object-oriented programming capabilities that are available in 

Python. Modules are provided to interface with commercial and government off-the-shelf software 

components (e.g., thermal protection systems and finite-element analysis). SAPE runs on Microsoft

Windows and Apple Mac

 OS X and has been partially tested on Linux.

Nomenclature

c = gas mass fraction

CD = drag coefficient

CH = heat transfer coefficient

Cp = pressure coefficient

D = drag, N

g = gravity, m/s2

h = height above planet, m

H = ellipsled height, m

K = heating constant

L = lift, N

m = mass, kg

M = molecular mass

q = stagnation-point heating rate, W/m2

r = radius, m

R = body radius, m

s = distance downrange, m

t = time, s

u = velocity, m/s

V = velocity, m/s

W = ellipsled width, m

β = backshell half-cone angle, deg

θ = forward shell half-cone angle, deg

γ = flight path angle, deg

ρ = density, kg/m3

Subscripts

b = base

c = convective heating

e = boundary layer edge

n = nose

p = planet

r = radiative heating

s = probe shoulder
I. Introduction

Systems analysis of a planetary entry, descent, and landing (EDL) is a multidisciplinary activity in nature. 

The purpose of the analysis is to gain a better understanding of various entry system concepts and their 

limitations. Systems analysis teams typically include one or more systems engineers and disciplinespecific experts in flight mechanics, aerodynamics, aerothermodynamics, structural analysis, and thermal 

protection systems (TPS). Other discipline experts, for example, propulsion experts, are consulted as 

needed. The systems analysis process may take from several weeks to several years (references 1 and 2

provide a good summary of typical systems analysis activities). Integrated tools, like SAPE, improve the 

performance of the systems-analysis team by automating and streamlining the process, and this 

improvement can reduce the errors that stem from manual data transfer among discipline experts. The role 

of discipline experts in the systems-analysis process is indispensable and cannot be replaced by any tool.

Several efforts have been made to develop integrated tools with a focus on different aspects of planetary 

EDL. For example, the integrated design systems3 (IDS) initiative developed an integrated tool by using a 

common gateway interface (CGI) to integrate codes for various disciplines from a distributed network. 

The IDS program used the Perl script for integration. Allen et al.4 provide more details on the IDS design 

and implementation. The Hyperprobe program5 is another IDS-like Web-based implementation, with the 

addition of a relational database management system. Unlike IDS and Hyperprobe, the Planetary Entry 

Systems Synthesis Tool6 (PESST) is based on Matlab*

. 

The key goals for SAPE development are:

1) Perform EDL systems analysis for any planetary body with an atmosphere. 

2) Operate cross-platform (i.e., Windows, Mac, and Linux operating systems).

3) Use existing software components.

4) Use open-source software to avoid software licensing issues.

5) Perform low-fidelity systems analysis in one hour on a computer that is comparable to an average 

laptop. 

6) Keep discipline experts in the analysis loop.

The next section discusses the use of the Python language for tool integration. Section III presents the 

design structure matrix for planetary EDL analysis. Section IV reviews the eight planetary bodies with 

atmospheres. Sections V through X introduce the six major modules that are included in SAPE. The last 

section presents recommendations for future enhancements.

The next section discusses the use of the Python language for tool integration. Section III presents the 

design structure matrix for planetary EDL analysis. Section IV reviews the eight planetary bodies with 

atmospheres. Sections V through X introduce the six major modules that are included in SAPE. The last 

section presents recommendations for future enhancements.

II. Use of Python for Integration Environment

SAPE uses the Python†

*

language to develop and integrate various modules. Python is a free, object-oriented, highlevel programming language that is often used as a scripting language. Python is open source and is supported by a 

large community and managed by the Python Software Foundation. Python is available for most computer platforms 

and has a large number of standard libraries, which range from scientific to Web applications. Python users include 

http://www.mathworks.com

† http://www.python.org

2
Google, Yahoo, YouTube, Disney, the New York Stock Exchange, the European Organization for Nuclear 

Research (CERN), and many other large commercial entities. The United Space Alliance has used Python to 

streamline space shuttle-mission design.*

 

III. EDL Design Structure Matrix (DSM)

The multidisciplinary EDL problem can be decomposed into a set of key disciplines. These discipline 

areas, modules, can be represented in matrix form using the DSM approach. The matrix is a graphical 

approach for representing the interdependencies among these various modules. The DSM is a square 

matrix with the analysis modules positioned along a main diagonal. Table 1 shows a typical DSM 

representation for the integrated EDL analysis. For each analysis module shown on the DSM diagonal, 

relevant outputs are listed in the corresponding row; the inputs are listed in the corresponding column. For 

example, the required inputs for structural analysis are the outer mold line (OML), mass distribution, and 

loads. Structural analysis outputs include an estimate for the structural mass as well as displacements. 

DSM analysis tools, such as DeMAID,7 can be used to analyze the DSM and identify the critical 

dependencies. 

The EDL integrated analysis process is a complex system, and SAPE currently includes only the six most 

important disciplines: geometry, trajectory, aerodynamics, aerothermodynamics, TPS, and structural 

sizing.

IV. Planetary Bodies with Atmosphere

Eight planetary bodies in our solar system have an appreciable atmosphere; these are Venus, Earth, Mars, 

Jupiter, Saturn, Uranus, Neptune, and Titan. The data that are included in SAPE for all eight planetary 

bodies are based on the NASA Goddard Planetary Fact Sheet† (see table 2). These bodies can be divided 

further into small bodies (Venus, Earth, Mars, and Titan) and large gas giants (Jupiter, Saturn, Uranus,

and Neptune). Planetary entry characteristics8 for each body are listed in table 3. 

SAPE users can either use the nominal atmospheric profiles9 that are built into SAPE or provide the 

atmospheric profile in a tabular form. Details on the nominal atmospheric profiles are available for Earth, 

Mars, Neptune, Titan, and Venus in Justus et al.10 and for Jupiter, Neptune, Saturn, and Uranus in Justus 

et al.11 (see figure 1.) 

* http://www.python.org/about/success/usa (last visited on February 09, 2009)

† http://nssdc.gsfc.nasa.gov/planetary/factsheet/index.html (last visited on February 05, 2009)

3
Table 1. Design Structure Matrix for EDL Analysis

Optimization 

module

Database 

module

Geometry 

module

Pack'g & 

mass pro

Trajectory 

analysis

Propulsion 

analysis

Aero

analysis

Aerothermal 

analysis TPS sizing Structural analysis

Stability 

and control

Cost

analysis 

Reliability 

analysis

Optimization 

module

Optimization

module

Design 

variables 

Database 

module Obj & const. Database 

module

Geometry 

variables

Design 

variables

Design 

variables

Design 

variables

Design 

variables

Design 

variables

Design 

variables

Design 

variables

Design 

variables

Design 

variables

Design 

variables

Geometry 

module TBD Geometry 

module OML Parameters Flow path OML OML OML OML Dimensions 

Pack'g & 

mass pro Weight 

breakdown Pack'g & 

mass pro Dry mass Mass 

distribution

Mass, C.G., 

& inertias 

Trajectory 

analysis Trajectory profile Fuel weight 

Trajectory 

analysis

Flight 

conditions

Flight 

conditions

Flight 

conditions G-load Inertia loads 

Propulsion 

analysis TBD Propulsion 

weight TSFC Propulsion 

analysis

Propulsion 

environment

Propulsion 

heating Propulsion loads

Propulsion 

loads 

Aerodynamics 

analysis TBD Integrated aero

Aero 

environment

Aero 

analysis

Pressure 

distribution Aero load Distributed loads

Integrated 

aero 

Aerothermal 

analysis TBD Heating corrections Aerothermal 

analysis

Thermal 

environment

Temperature 

distribution 

TPS Sizing TBD TPS 

weight TPS Sizing TPS Size 

Structural 

analysis TBD Structural weight Structural displacements Sizing data Structural 

analysis 

Stability and 

Control Control margins 

Stability 

and 

control

 

Cost analysis Cost Cost 

analysis 

Reliability 

analysis Reliability index Reliability 

analysis

Columns are inputs, and Rows are outputs

4
Earth Mars Titan Venus NeptuneJupiter Saturn Uranus

6378 3397 2575 6052 24764 71492 60268 25559

9.8 3.7 1.35 8.9 11 23.1 9 8.7

1.22 0.02 1.55 65 0.45* 0.16* 0.19* 0.42*

8.5 11.1 10 15.9 20 27 59.5 27.7

120** 120** 800** 130** 630** 395 750 555

28.870 43.501 28.269 43.450 2.373 2.219 2.081 2.271

Table 2. Planetary Body Characteristics

Planets

Radius, km

Gravity, m/s2

Surface atmo. ρ kg/

Atmo. height, km

Atmo. interface, km

Atmo. mole. wt.

* at one bar

** based on refs. 9-11 at 10-9 < ρ < 10-8

Composition Entry speeds Heat rates and loads

Small planets: Venus, Earth, 

Mars, Titan Co2, N2, O2 5–12 km/sec 10's to 100's W/cm2

103–104

 J/cm2

Gas giant planets: Jupiter, 

Saturn, Uranus, Neptune

H2, He 25–60 km/sec 1000's W/cm2

105

–106

 J/cm2

Table 3. Planetary Entry Characteristics

Figure 1. Nominal atmospheric profiles.10-11

5
V. Geometry Module

The geometry module is written entirely as an object in Python, and three types of geometries can be 

created: sphere-cone probes, tori, and asymmetric ellipsleds. 

SAPE can model most existing sphere-cone probes (See appendix A.) The creation of sphere-cone probe 

geometry uses five flags and a set of geometry parameters. The flags are used to define various probe 

sections: spherical nose (0, 1), conical forward section (0, 1), shoulder fillet (0, 1), aft-body conical 

section (0, n), and back-end section (1). The numbers in parentheses indicate the possible number of 

individual sections. The possible back-end shapes are flat, spherical cap, ellipsoid cap, and fillet. Figure 

2(a) shows a sample sphere-cone model, which consists of a spherical nose, a conical forward section, a 

shoulder fillet, three aft-conical sections, and a flat backend (flags: 1, 1, 1, 3, and flat). Additional 

information and figures on sphere-cone geometry models are given in appendix A.

The ellipsled is an elliptically blunted cylinder that was originally proposed by Muth et al.12 for an Earthreturn aerocapture application. Edquist et al.13 present a modified version of the ellipsled in which the 

nose is defined by two ellipsoids with different minor axes. The modified ellipsled is defined by five 

parameters (figure 2(b)): total length, nose length, width, height, and offset ratio. The geometry module 

can also generate tori, which are donut-like shapes that are defined by major and minor radii (figure 2(c)).

Figure 2. Available geometry shapes and parameters.

Rup

Rbottom

W

H

Total length

Nose length

H

H

up RR bottom Offset − =

(b) Ellipsled. (c) Torus.

Rmajor Rminor

(a) Sphere cone.

∑

=

i

i

i L

L ratio

2Rb

L

Rn

Rs

β2

θ β1

β3

L3 L2 L1

6
VI. Aerodynamics

SAPE currently includes two aerodynamic models: an analytical expression for aerodynamic drag at a 

zero angle of attack and DACFREE code. The analytical expression for the drag of a sphere cone14

21( cossin 4sin )] 2 [sin2 22 4

max = θ −+ − θθθ

b

n

pD R

R CC

 

(1)

The DACFREE15 code has been used in many planetary entry studies and uses standard free-molecular 

and modified Newtonian methods. The geometry that is input is a set of triangles with appropriate 

boundary conditions. Python was used to wrap the DACFREE code and integrate it into SAPE. Figures 3 

shows comparisons of integrated DACFREE results with those of Moss et al.16 (top), Moss et al.17

13 (center), and Edquist et al. (bottom). 

VII. Aerothermodynamics

SAPE currently includes a simple analytical expression for stagnation-point heating. However, the plan is 

to include the Langley Approximate Three-Dimensional Convective Heating (LATCH) code18, which is 

an approximate three-dimensional heating code that is based on the axisymmetric analog for general 

three-dimensional boundary layers.

SAPE currently uses the analytical expression for stagnation heating rate that was developed by Sutton 

and Graves19: 

Rn

VKq 3 ρ =

 (2)

where V is the velocity, ρ is the atmospheric density, and Rn is the nose radius. What makes Sutton and 

Graves’s analytical expression unique is that the constant K is derived for a general gas mixture. The 

coefficient K is a function of the atmospheric mass fractions, the molecular weights, and their individual 

transport properties. Sutton and Graves provide two expressions for K: 

∑ ∑

=

2

1

= ,

1106.0

i K

c

K

M

c

K

i

ii

i

γ (3) 

where ci are the mass fractions. The parameters γi that are used in Eq. (3) are the transport parameters of 

the base gas of a mixture and should not be confused with the flight-path angle that is used in the 

trajectory section (other constants are presented in table 4). 

7
Figure 3. Comparisons of DACFREE results with those in references 13, 16, 17.

(a) Microprobe (reference 16).

(b) Pathfinder (reference 17).

(c) Ellipsled (reference 13).

8
Tauber and Sutton20 present a simple procedure to approximate the radiative heating for Earth and Mars. 

Both the Sutton/Graves and the Tauber/Sutton procedures provide only approximations and should be 

corrected with available higher fidelity numerical solutions and experimental results.

The plan is to include TSCAAPE21, which is a script that is tailored to perform aeroheating analysis for 

sphere cones using LAURA22 computer code. The script currently supports Earth, Mars, Titan, Venus, 

Saturn, and Neptune.

VIII. Trajectory

SAPE includes a simple trajectory code. Work is underway to include POST-2,23 which is a more 

sophisticated trajectory code. The simple trajectory code is based on equations for planar flight,24

cos , sin , d

d

sin , )( cos ,

2

γ γ

γ γ γ

V

dt

dh

dt

dr V

r

R

t

s

r

V

g

m

L

dt

Vd

g

m

D

dt

dV

p = ==

−−= −−=

as 

shown in figure 4.

(4)

where 

2

















+ = rR

R

gg

p

p

s . 

Readers should consult Griffin 

and French24 for additional 

information. The above equation 

set is a system of first-order 

differential equations with its 

initial values—V, h, and γ—

defined at atmospheric entry.

Figure 4. Planer flight.

Rp r

γ

h

V

D L

Entry interface

Rp r

γ

h

V

D L

Entry interface

Mi Ki Earth Mars Titan Venus Neptune Jupiter Saturn Uranus

N2 28.013 0.11 0.785 0.027 0.984 0.035

O2 31.999 0.12 0.215 0.001

H2 2.016 0.04 0.8 0.898 0.967 0.825

He 4.003 0.08 0.19 0.102 0.033 0.152

Ne 20.180 0.15

Ar 39.948 0.15 0.016

CO2 44.010 0.12 0.956 0.016 0.965

NH3 17.031 0.1 0.01 0.023

CH4 16.042 0.08

K*10 1.7623 1.8980 1.7407 1.8960 0.6719 0.6556 0.6356 0.6645 -4 (eq. 1)

Coeff. for equation Mass fractions

Table 4. Constant K

9
SAPE uses the Cash and Karp Runge-Kutta method with the adaptive step size25. This particular method 

is fifth-order accurate and more efficient by a factor of two than standard step-doubling methods. The 

method accuracy is controlled by defining a maximum error, and the method adjusts the time step to the 

user-defined level of accuracy. Users also can force a minimum time step to create a larger number of 

data points along the trajectory. A simple, one-dimensional minimization algorithm based on Ridder’s25

approach is included for the aerocapture applications. The Ridder algorithm is a variation of the falseposition root finding approach with superlinear convergence property.

The trajectory code implementation is in C++ for efficiency, and the code was verified against several test 

cases. Figure 5 shows a comparison of the results from the simple trajectory code with those of POST-2,23

and the results are in excellent agreement.

The second set of test cases was based on the aerocapture study of Hall and Lee,26 in which shallow and 

steep entries into four planetary bodies (Mars, Neptune, Titan, and Venus) were analyzed. Table 5 

compares the results from SAPE trajectory with those from Hall and Lee, and the results are in good 

agreement. 

Figure 5. Comparison with POST (symbols). 

(a) L/D = 0

(b) L/D = 0.25)

10
IX. Thermal Protection System (TPS)

SAPE currently provides an interface to the TPS sizing code FIAT27. The actual FIAT code is not part of 

SAPE and should be obtained directly from NASA Ames Research Center. Necessary inputs to FIAT 

includes the recovery enthalpy Hr, the heat flux term ρeueCH, pressure p, and radiative heat flux qr. 

Trajectory and aerothermal modules generate the free stream density ρ∞, velocity V∞, convective heat flux 

qc, and radiative heat flux qr variables. Figure 6 shows a sample TPS result, which is for a Stardust-class 

vehicle with a ballistic coefficient of 60 kg/m2

, an L/D of 0.2, an entry velocity of 12 km/s, and a flightpath angle of –10o

. The heat rate includes a margin of 30%. Figure 6(a) shows the resulting heat rates and 

the total heat load, and figure 6(b) shows the back wall temperature and the recession rate for Phenolic 

Impregnated Carbon Ablator (PICA) concept. FIAT calculated the optimal thickness to be 2.8 cm.

Figure 6. Heating and TPS sample results for a Stardust-class probe.

(a) Heat rate and heat load. (b) Wall temperature and recession rate.

Hall et al. Current % Error

Titan (shallow) 1030.0 1033 0.28

Titan (steep) 1073.0 1077 0.36

Neptune (shallow) 1257.0 1293 2.83

Neptune (steep) 1369.0 1369 0.00

Venus (shallow) 908.0 901 0.77

Venus (steep) 974.0 967 0.73

Mars (shallow) 805.0 804 0.15

Mars (steep) 868.0 866 0.22

Peak ballute temperature (K)

Table 5. Comparison SAPE Results with Results of Hall and Lee

11
X. Finite-Element Analysis and Sizing

SAPE is capable of analyzing and sizing certain classes of planetary probes. Automating the generation 

and the analysis of the finite-element model (FEM) are quite challenging. These tasks can be simplified 

by restricting the analysis to sphere-cone shapes. The current FEM topology that is used in SAPE is based 

on the existing structural topology, which consists of the shell, the external support structure, and the 

internal payload support. Figure 7 shows various structural topologies for a generic probe.

After generating the FEM, finite-element analysis (FEA) codes are used to automatically size the vehicle. 

The FEA code provides estimates for the structural mass for given launch and entry loads. Figure 8 shows 

the von Mises stresses on a typical aeroshell structural model.

Figure 7. Sample structural topologies for Pathfinder class probe.

(c) Warren truss

on forward shell.

(a) Bar truss

on backshell.

(b) Warren truss

on backshell.

Figure 8. Sample FEA result.

12
XI. Summary

SAPE is a Python-based multidisciplinary analysis tool that has been developed for systems analysis for 

planetary entry, descent, and landing (EDL) for Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, 

and Titan. SAPE includes the following analysis modules: geometry, trajectory, aerodynamics, 

aerothermal, thermal protection system, and structural sizing. The geometry module can model most 

existing sphere-cone probes, ellipsleds, and tori. The aerodynamic module includes an analytical 

expression for drag and DACFREE code. The aerothermal module is based on Sutton-Graves 

approximation, and the plan is to include the Langley Approximate Three-Dimensional Convective 

Heating (LATCH) code. SAPE includes a simple trajectory code, which is based on equations for planer 

flight. The work is underway to include POST-2. SAPE currently provides an interface to the TPS sizing 

code FIAT. SAPE is capable of analyzing and sizing certain classes of planetary probes. The current FEM 

topology that is used in SAPE is based on the existing sphere-cone structural topology, which consists of 

the shell, the external support structure, and the internal payload support. SAPE modules have been 

validated against existing tools; however, the integrated system has not been fully validated yet. One 

major short-term goal is to verify the current integrated system. The medium-term goals are to

1. Integrate an updated version of the FEA script discussed in section X.

2. Integrate POST-2. 

3. Include sensitivity analysis capability.

4. Include system-based Monte Carlo simulation capability.

5. Include LATCH and TSCAAPE codes. 

XII. Acknowledgement

The author would like to acknowledge Jim Hoffman for his work on FEM generation, Alireza Mazaheri 

for developing TSCAAPE, Aaron Olds for developing scripts for POST-2, and Erik Tyler for his help 

with FEM sizing (all from Analytical Mechanics Associates, Inc.). 

13
Appendix A: Possible Sphere-Cone Shapes

Figure A1 shows the existing sphere-cone probes that are presented by Davies and Arcadi.28 The numbers 

that are shown below the name of each probe are the SAPE geometry flags, as used in figure 2(a). Table 

A1 shows geometry parameters for shape shown in figure A1.

Figure A1. Existing sphere-cone probes. 

(s) spherical nose, (c) conical section, and (f) fillet

MIRKA

(s1,c0,f0,c1,flat)

Reentry-F

(s0,c1,f0,c0,flat)

Fire-II

(s1,c0,f0,c4,flat)

BEAGLE

(s1,c1,f1,c1,flat) HAYABUSA

(s1,c1,f0,c3,flat)

Genesis

(s1,c1,f0,c2,flat)

Stardust

(s1,c1,f1,c1,flat)

Microprobe

(s1,c,f1,s)

Pioneer-Venus

(Sounder)

Galileo Probe

(s1,c1,f0,c2,sphere)

OREX

(s1,c1,f0,c2,flat)

Viking

(s1,c1,f1,c2,flat)

PAET

(s1,c1,f0,s)

Apollo

(s1,c0,f1,c1,fillet)

Pioneer-Venus

(s1,c1,f0,c5,sphere)

Huygens

(s1,c1,f0,c3,flat)

MER

(s1,c1,f1,c1,flat)

ARD

(s1,c0,f1,c3,flat)

MIRKA

(s1,c0,f0,c1,flat)

Reentry-F

(s0,c1,f0,c0,flat)

Fire-II

(s1,c0,f0,c4,flat)

BEAGLE

(s1,c1,f1,c1,flat) HAYABUSA

(s1,c1,f0,c3,flat)

Genesis

(s1,c1,f0,c2,flat)

Stardust

(s1,c1,f1,c1,flat)

Microprobe

(s1,c,f1,s)

Pioneer-Venus

(Sounder)

Galileo Probe

(s1,c1,f0,c2,sphere)

OREX

(s1,c1,f0,c2,flat)

Viking

(s1,c1,f1,c2,flat)

PAET

(s1,c1,f0,s)

Apollo

(s1,c0,f1,c1,fillet)

Pioneer-Venus

(s1,c1,f0,c5,sphere)

Huygens

(s1,c1,f0,c3,flat)

MER

(s1,c1,f1,c1,flat)

ARD

(s1,c0,f1,c3,flat)

14
r b L/r b r n /r b rs /r b α β Backshell Conic Length Ratios

Backend 

Shapes

ARD 1.4 1.457 2.4 0.1 0 33, 90,0 0.75, -0.31, 0.25 Flat

Apollo 1.955 1.85166 2.4 0.1 0 33 1 Fillet

Beagle 0.45 1.11 0.93 0.0644 70 47, 47 0.5, 0.5 Flat

Fire-II 0.336 1.564 2.78 0 0 90, 0, 90, 33 0.04,.11, -0.04, 0.89 Flat

Galileo_Probe 0.63 1.47 0.35 0 44.86 0, 60, 0 0.07, 0.07, 0.07 Ellipsoid

Genesis 0.75 1.267 0.57 0.044 60 20, 60 0.5, 0.5 Flat

HAYABUSA 0.202 1 1 0 45 45, 90, 45 0.79, -0.06, 0.21 Flat

Huygens 1.35 0.73 0.926 0 60 90 -0.6 Ellipsoid

MER 1.325 1.138 0.5 0.05 70 46.63 1 Flat

Microprobe 0.175 1.561 0.5 0.05 45 Sphere

MIRKA 0.5 2 -1 0 135 0 1 Flat

MSL 2.25 1.116 0.5 0.05 70 36.9, 59 0.5, 0.5 Flat

OREX 1.7 0.888 0.794 0 50 0, 75, 60 0.1, 0.7,0.2 Flat

PAET 0.457 1.4 1 0 55 Ellipsoid

Pathfinder 1.325 1.066 0.5 0.05 70 49, 49 0.5, 0.5 Flat

Reentry-F 0.3965 10 0 0 5.7 Flat

Stardust 0.4135 1.347 0.5625 0.05 60 30, 30 0.5, 0.5 Flat

Venus_Pioneer_Probe 0.38 1.342 0.5 0 45 0, 90 0.3,-0.15 Ellipsoid

Venus_Pioneer_Sounder 0.71 1.465 0.5 0 45 90,0,90,0,60 -0.12,0.37,-0.044,0.08,0.55 Flat

Viking 1.75 0.9381 0.5 0.015 70 39, 62.2 0.5076, 0.4924 Flat

Table A1. Geometry Parameters for Existing Planetary Probes

References

1 Lockwood, M.: “Neptune Aerocapture Systems Analysis,” AIAA-2004-4951, August 2004. 2 Lockwood, M.: “Titan Aerocapture Systems Analysis,” AIAA-2003-4799, July 2003. 3 Johns, B.; Fan, K.; Tveten, T.; Yeung, L.; Cheatwood, N.; and Qualls, G.: “Framework for Analysis and 

Collaborative Engineering (FACE),” AIAA 2002-0755, January 2002. 4 Allen, G. A.; Gage, P. J.; Venkatapathy, E.; Olynick, D. R.;, and Wercinkski, P. F.: “A Web-based Analysis for 

Planetary Entry Vehicle Design,” AIAA-98-4826, September 1998. 5 Papadopoulos, P. and Subrahmanyam, P.: “Web-Based Computational Investigation of Aerothermodynamics of 

Atmospheric Entry Vehicles,” Journal of Spacecraft and Rockets, Vol. 43, No. 6, November-December 2006, pp. 

1184–1190. 

6 Alemany, K.; Wells, G.; Theisinger, J.; Clark, I.; and Braun, R.: “Mars Entry, Descent, and Landing Parametric

Sizing and Design Space Visualization Trades,” AIAA-2006-6022, August 2006. 7 Rogers, J. L.: “DeMAID – A Design Manager’s Aid,” NASA TM-101575, March 1989. 8 Hall, J.: “Mission Design and Systems Analysis for Ablative TPS Applications,” Presented at JPL during Tutorial 

on Ablative TPS, August 2, 2005. 9

 Justus, C. G. and Braun, R. D.: “Atmospheric Environments for Entry, Descent and Landing (EDL),” Fifth 

International Planetary Probe Workshop, Bordeaux, France, June 2007. 

http://nssdc.gsfc.nasa.gov/planetary/factsheet/index.html, Accessed February 05, 2009. 10 Justus, C. G.; Duvall, A.; and Keller, V. W.: “Atmospheric model for aerocapture Studies,” AIAA-2004-4952, 

August 2004. 

11 Justus, C. G.; Duvall, A.; Keller, and V. W.; Spilker, T. R.; and Lockwood, M. K.: “Connecting Atmospheric 

Science and atmospheric Models for Aerocapture at Titan and the Other Planets,” Planetary and Space Science, 

Vol. 53, 2005, pp. 601–605. 

15
12 Muth, W. D.; Hoffmann, C.; and Lyne, J. E.: “Earth Return Aerocapture for the TransHab / Ellipsled Vehicle,”

NAG1-2163, October 2000 13 Edquist, K. T.; Prabhu, R.; Hoffman, D.; and Rea, J.: “Configuration Aerodynamics, and Stability Analysis for a 

Neptune Aerocapture Orbiter,” AIAA-2004-4953, August 2004. 14 Regan, F. J. and Anandakrishnan, S. M.: Dynamics of Atmospheric Re-Entry. AIAA, Washington D. C., 1993. 15 Wilmoth, R. G.: “DACFREE—A Free-Molecular/Newtonian Code for Hypersonic Flow, A Users Guide,” 1999. 16 Moss, J. N.; Wilmoth, R. G.; and Price, J. M.: “Direct Simulation Monte Carlo Calculations of 

Aerothermodynamics for Mars Microprobe Capsules,” Journal of Spacecraft and Rockets, Vol. 36, No. 3, May-June 

1999, pp. 399–404. 17 Moss, J. N.; Wilmoth, R. G.; and Price, J. M.: “Direct Simulation Monte Carlo Calculations of 

Aerothermodynamics for Mars Pathfinder and Mars Microprobe Capsules,” AIAA-1997-2508, June 1997. 18 Hamilton, H. H.; Greene, F. A.; and DeJarnette, F. R.: “An Approximate Method for Calculating Heating Rates on 

Three-Dimensional Vehicles,” AIAA-93-2881, July 1993. 

19 Sutton, K. and Graves, R. A.: “A General Stagnation-Point Convective-Heating Equation for Arbitrary Gas 

Mixtures,” NASA-TR-R-376, November 1971. 20 Tauber, M. E. and Sutton, K.: “Stagnation-Point Radiative Heating Relations for Earth and Mars Entries,” Journal 

of Spacecraft, Vol. 28, No. 1, Jan-Feb 1991, pp. 40–42. 21 Mazaheri, A.: “Tool for Sphere-Cone Aerothermodynamic Analysis for Planetary Entry (TSCAAPE),” NASACR-2008-215346, August 2008. 22 Gnoffo, P.A.: “Users’s Manual for the Langley Aerothermodynamic Upwind Relaxation

Algorithm(LAURA),” NASA TM-4674, April 1996. 23 Brauer, G. L.; Cornick, D. E.; and Stevenson, R.: “Capabilities and Applications of the Program to Optimize 

Simulated Trajectories (POST),” NASA CR-2770, Feb. 1977. 24 Griffin, M. D. and French, J. R.: Space Vehicle Design. Second Edition, AIAA, 2004. 25 Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; and Flannery, B. P.: Numerical Recipes in C. Second Edition, 

Cambridge University Press, 1992.

26 Hall, J. L. and Lee, A. K.: “Aerocapture Trajectories for Spacecraft with Large Tow Ballutes,” AAS/AIAA, AAS01-235, Feb 2001. 27 Chen, Y.-K. and Milos, F. S., “Ablation and Thermal Response Program for Spacecraft Heatshield Analysis,” 

Journal of Spacecraft and Rockets, Vol. 36, No. 3, 1999, pp. 475–483. 28 Davies, C. and Arcadi, M.: “Planetary Mission Entry Vehicles Quick Reference Guide: Version 3.0,” NASA/SP2006-3401, last updated December 12, 2007.

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