February 2011 

NASA/TM-2011-217063 

NESC-RP-09-00530 

 

Simulation Framework for Rapid Entry, 

Descent, and Landing (EDL) Analysis, 

Phase 2 Results 

Daniel G. Murri/NESC 

Langley Research Center, Hampton, Virginia 
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February 2011 

NASA/TM-2011-217063 

NESC-RP-09-00530 

 

Simulation Framework for Rapid Entry, 

Descent, and Landing (EDL) Analysis, 

Phase 2 Results 

Daniel G. Murri/NESC 

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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NESC Request No.: TI-09-00530 – Phase 2 

Simulation Framework for Rapid Entry, Descent, and Landing 

(EDL) Analysis, Phase 2 Results 

February 3, 2011
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NESC Request No.: TI-09-00530 – Phase 2 

Report Approval and Revision History 

NOTE: This document was approved at the February 3, 2011, NRB. This document was 

submitted to the NESC Director on February 10, 2011, for configuration control. 

Approved

Version:

Original Signature on File 2/10/11

1.0 NESC Director Date

Version Description of Revision Office of Primary 

Responsibility Effective Date

1.0 Initial Release Mr. Daniel G. Murri, 

NASA Technical Fellow

for Flight Mechanics

2/3/2011
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NESC Request No.: TI-09-00530 – Phase 2 

Table of Contents 

Volume I: Technical Assessment Report 

1.0 Notification and Authorization ................................................................................................ 5

2.0 Signature Page ........................................................................................................................... 6

3.0 Team List ................................................................................................................................... 7

4.0 Executive Summary .................................................................................................................. 8

5.0 Models and Script Descriptions ............................................................................................... 9

5.1 Multi-mode EKF ....................................................................................................................... 10

5.1.1 POST2 Sensor Models for mEKF ................................................................................ 11

5.1.1.1 IMU and Gyroscope Model .......................................................................................... 11

5.1.1.2 Star Tracker Model ...................................................................................................... 12

5.1.1.3 Altimeter and Velocimeter Models .............................................................................. 13

5.1.2 POST2 Inputs/Outputs for mEKF ................................................................................ 13

5.2 Aerodynamic Uncertainty Model.............................................................................................. 17

5.3 Terminal Point Control Guidance Algorithm ........................................................................... 22

5.4 Aerobraking Mission Design Module ....................................................................................... 27

5.5 Earth Environment Models ....................................................................................................... 30

5.5.1 2010 Earth Global Reference Atmosphere Model ....................................................... 30

5.5.2 Earth Gravity Model 96 ............................................................................................... 36

5.6 Attitude Control Models ........................................................................................................... 36

5.6.1 Pseudo-Controller for 3-axis Attitude Control............................................................. 37

5.6.2 Second Order Actuator Model ..................................................................................... 40

6.0 Observation and NESC Recommendation ........................................................................... 40

7.0 Other Deliverables .................................................................................................................. 41

8.0 Definition of Terms ................................................................................................................. 41

9.0 Acronyms List ......................................................................................................................... 42

10.0 References ................................................................................................................................ 43

List of Tables 

Table 5.0.1. Responsible Individuals for Models Implemented and Report Sections ..................... 10

Table 5.1-1. POST2 Inputs for the mEKF Algorithm ...................................................................... 13

Table 5.1-2. POST2 Outputs for the mEKF Algorithm ................................................................... 17

Table 5.2-1. POST2 Inputs for the Aerodynamic Dispersion Model ............................................... 19

Table 5.2-2. POST2 Outputs from the Aerodynamic Dispersion Model ......................................... 22

Table 5.3-1. POST2 Inputs for the TPC Guidance Algorithm ......................................................... 25

Table 5.3-2. POST2 Outputs for the TPC Guidance Algorithm ...................................................... 27

Table 5.4-1. POST2 Inputs for the Aerobraking Mission Design Module ...................................... 28

Table 5.4-2. POST2 Table Inputs for the Aerobraking Mission Design Module ............................ 29

Table 5.4-3. POST2 Outputs for the Aerobraking Mission Design Module .................................... 30

Table 5.5-1. POST2 Inputs for the Earth-GRAM 2010 Model ........................................................ 31

Table 5.5-2. POST2 Tables for the Earth-GRAM 2010 Model ....................................................... 34
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Table 5.5-3. POST2 Outputs for the Earth-GRAM 2010 Model ..................................................... 35

Table 5.6.1-1. POST2 Inputs for the 3-Axis Pseudo-Controller Model .............................................. 38

Table 5.6.1-2. POST2 Outputs for the 3-Axis Pseudo-Controller Model ........................................... 39

Volume II: Appendices 

Appendix A. Multi-Mode Extended Kalman Filter
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NESC Request No.: TI-09-00530 – Phase 2 

Volume I: Technical Assessment Report 

1.0 Notification and Authorization 

Mr. Daniel Murri, NASA Technical Fellow for Flight Mechanics, requested that the NASA 

Engineering and Safety Center (NESC) support an inquiry from Mr. Harold Bell, Director 

Advanced Planning and Analysis Division, NASA Office of Chief Engineer, to establish the 

Simulation Framework for Rapid Entry, Descent, and Landing (EDL) Analysis assessment. The 

principal focus of the proposed activity was to develop a simulation framework and a set of 

validated and documented subsystem models and scripts to allow rapid evaluation of EDL 

characteristics in systems analysis studies, preliminary design, mission development and 

execution, and time-critical assessments. 

The Initial Evaluation for this assessment was approved by the NESC Review Board (NRB) on

March 12, 2009. Mr. Daniel Murri was selected to lead this assessment. The Assessment Plan 

was presented and approved by the NRB on March 26, 2009. The Phase 1 Stakeholder Outbrief 

and final report were approved by the NRB on November 5 and December 17, 2009, 

respectively. 

The Phase 2 Assessment Plan was approved by the NRB on December 17, 2009. The Phase 2 

final report was presented to the NRB for approval on February 3, 2011. 

The key stakeholders for this activity are Mr. Harold Bell; Mr. Thomas Zang, EDL-Systems 

Analysis (EDL-SA) Team Lead; and the NESC. 
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NESC Request No.: TI-09-00530 – Phase 2 

2.0 Signature Page 

Submitted by: 

Team Signature Page on File – 2/14/11

Mr. Daniel G. Murri Date 

Significant Contributors: 

Dr. Scott A. Striepe Date Mr. Richard W. Powell Date 

Signatories declare the findings and observations compiled in the report are factually based from 

data extracted from Program/Project documents, contractor reports, and open literature, and/or 

generated from independently conducted tests, analysis, and inspections. 
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NESC Request No.: TI-09-00530 – Phase 2 

3.0 Team List 

Name Discipline Organization

Core Team

Dan Murri NESC Team Lead LaRC

Richard Powell Team Co-Lead LaRC/AMA

Scott Striepe Simulation Lead LaRC

Eric Queen Controls Lead LaRC

Mark Schoenenberger Aerodynamics Lead LaRC

Alicia Cianciolo Environments Lead LaRC

John Wagner Mass Lead LaRC/NIA

Loreyna Yeung Scripts Lead LaRC/ATK

John Aguirre Software LaRC/Vigyan

Carole Garrison Software LaRC/ATK

Michael Kelly Backup Principal Engineer LaRC

Dave Kinney Aerodynamics ARC

Jack Mulqueen Aerospace Engineer MSFC

Jill Prince Flight Mechanics LaRC

David Way Flight Mechanics LaRC

Carlos Westhelle Guidance JSC

Robert Bishop Navigation Marquette University

Consultants

Phil Calhoun Controls GSFC

Cornelius Dennehy NASA Technical Fellow for GN&C GSFC

Michael Hagopian Senior AETD Engineer GSFC

Kurt Kloesel Electrical Engineer DFRC

Gary Mosier Aerospace Engineer GSFC

Martin Steele Computer Engineer KSC

Administrative Support

Tricia Johnson MTSO Program Analyst LaRC

Melinda Meredith Project Coordinator LaRC/ATK

Linda Burgess Planning and Control Analyst LaRC/ATK

Erin Moran Technical Writer LaRC/ATK
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NESC Request No.: TI-09-00530 – Phase 2 

4.0 Executive Summary 

The NASA Engineering and Safety Center (NESC) was requested to establish the Simulation 

Framework for Rapid Entry, Descent, and Landing (EDL) Analysis assessment, which involved 

development of an enhanced simulation architecture using the Program to Optimize Simulated 

Trajectories II (POST2)1

simulation tool. The assessment was requested to enhance the 

capability of the Agency to provide rapid evaluation of EDL characteristics in systems analysis 

studies, preliminary design, mission development and execution, and time-critical assessments. 

Many of the new simulation framework capabilities were developed to support the Agency EDLSystems Analysis (SA) team that is conducting studies of the technologies and architectures that 

are required to enable human and higher mass robotic missions to Mars. 

The EDL-SA studies have been conducted using POST2, but with a variety of ad-hoc and 

undocumented sub-system models (e.g., mass, aerodynamics, atmosphere, guidance, control) and 

scripts. During Phase 1 of the assessment [ref.1], the NESC team developed a simulation 

framework and a set of validated and documented sub-system models (including mass models, a 

pseudo bank angle controller, aerodynamic trim, aerodynamic data models, atmospheric models, 

guidance algorithms) and scripts. Phase 2 augments the previous effort with several models that 

were not included in Phase 1, which add to the simulation support of the EDL-SA team, and 

Agency and NESC rapid assessments. These models include a navigation filter for EDL, 

aerodynamic uncertainty, second order actuator model, aerocapture guidance algorithm, 

aerobraking mission design, Earth-Global Reference Atmosphere Model (GRAM) 2010 [ref. 2], 

Earth Gravity Model (EGM) 96, and a three-axis pseudo-controller. A set of input cases was 

generated for the models and is maintained with the simulation. This test suite will be used to 

confirm that future software models added to the simulation do not adversely affect the operation 

of the existing models added from this assessment. In the POST2 simulation environment, the 

simulation framework developed during this assessment is referred to as Rapid EDL Analysis 

Simulation (REDLAS).

The observations and NESC recommendations are discussed in Section 6.0. Overall, the main

objective to increase the Agency’s ability to rapidly evaluate EDL characteristics in systems 

analysis studies, preliminary design, mission development and execution, and time-critical 

assessments was accomplished. It is recommended that the custodians of the POST2 simulation 

framework, the Atmospheric Flight and Entry Systems Branch at Langley Research Center 

(LaRC), should retain and maintain the REDLAS models, test cases, and scripts for use by 

current and future programs. 

 

1

POST2 is an ITAR restricted code and may only be distributed to approved persons. https://post2.larc.nasa.gov/
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NESC Request No.: TI-09-00530 – Phase 2 

5.0 Models and Script Descriptions 

The NESC was requested to establish the Simulation Framework for Rapid EDL Analysis 

assessment, which involved development of an enhanced simulation architecture using the 

POST2 simulation tool. The simulation developed in Phase 1 included mass models, a pseudo 

controller, aerodynamic models, atmospheric models, guidance algorithms, and various support 

scripts. Phase 2 augments the previous effort with several models that were not included in 

Phase 1, which add to the simulation support of the EDL-SA team and Agency and NESC rapid 

assessments. A set of input cases was generated for the models and is included with the 

simulation. This test suite can be used to confirm that future software models added to the 

simulation do not adversely affect the operation of the existing models from this assessment. 

The models described below were developed and/or implemented by the NESC team. This 

report is outlined and discussed as follows: 

Section 5.1: multimode Extended Kalman Filter (mEKF) 

Section 5.2: Aerodynamic Uncertainty Models 

Section 5.3: Terminal Point Control (TPC) Guidance Algorithm 

Section 5.4: Aerobraking Mission Design Module 

Section 5.5: Earth Environment Models (atmosphere and gravity) 

Section 5.6: Attitude Control Models (3-axis pseudo-controller (3APC), second order actuator 

model) 

Table 5.0.1 lists the individuals responsible for the various models and sections of this report. 
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Table 5.0.1. Responsible Individuals for Models Implemented and Report Sections 

Model Description Section(s) Responsible Individual

mEKF 5.1 and Appendix A Robert Bishop

POST2 sensor models 

and input/output 5.1.1 – 5.1.2 Scott Striepe

Aerodynamics 

Uncertainty Models 5.2 Mark Schoenenberger

POST2 Aerodynamic 

Uncertainty Inputs & 

Outputs

5.2.1 Scott Striepe

TPC Guidance

Algorithms 5.3 Eric Queen

Aerobraking Mission 

Design Module 5.4 Alicia Cianciolo

Earth-GRAM 2010 5.5.1 John Aguirre/Dick Powell

EGM96 POST2 inputs 5.5.2 Scott Striepe

Three-Axis PseudoController 5.6.1 Eric Queen/Scott Striepe

Second Order Actuator 

Model 

5.6.2 Eric Queen

5.1 Multi-mode EKF 

A significant area of investigation supporting the NESC’s Simulation Framework for Rapid EDL 

Analysis is the development of a mEKF for navigation. While using perfect navigation (i.e., 

perfect knowledge of the true state) with guidance systems is a reasonable first design step, 

errors from imperfect state knowledge help determine the robustness of the guidance and vehicle 

design. The mEKF navigation filter architecture for application to EDL is consistent with the 

methodology being used for flight systems that are currently under development. 

A key element of the mEKF is sensor error modeling. The objective is to construct a generalized 

information structure to represent sensors that encompass the requisite data required to compute 

and process mEKF measurements. The mEKF navigation filter architecture can be used in 

applications of EDL using a standard set of measurements including altimeters, velocimeters, 

star trackers, and inertial measurement units. The navigation architecture main computational 

unit is the mEKF algorithm employing a dual-inertial state implementation with integrated 
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position, velocity, and attitude. The filter described here is readily re-configurable to 

accommodate differing mission scenarios (e.g., lunar descent or Mars entry). 

Also, several sensor models were included in POST2 to provide mEKF measurements. These 

models create measurements from values calculated during the simulation and applying errors 

such as bias, scale factors, and random noise. The inertial measurement unit (IMU) model 

generates  -V and  - measurements sensed acceleration and angular velocity. The vehicle 

altitude and velocity relative to the surface are used for the altimeter and velocimeter, 

respectively. The star tracker model uses the inertial to body transformation to define attitude 

measurements. 

Details of the theory and equations used for the mEKF and its sensor error models are provided 

in Appendix A. Sensor models in POST2 to provide measurement data are given in Section 

5.1.1. Inputs and outputs associated with these models as implemented in POST2 are identified 

in Section 5.1.2.

5.1.1 POST2 Sensor Models for mEKF 

5.1.1.1 IMU and Gyroscope Model 

The POST2-developed IMU model is a statistically based accelerometer and gyroscope model. 

The accelerometer model takes the true body acceleration, with a random bias, noise, and scale 

factor errors to generate a measurement of accelerations that are then converted to -V before 

being passed to mEKF for processing. The acceleration measurement model is given by: 

 (5.1-1) 

and

 (5.1-2) 

where is the accelerometer measured acceleration vector in m/s2; is the true body sensed 

acceleration vector in m/s2; I3x3 is the identity matrix; 



SFacc

is the accelerometer scale factor 

diagonal matrix; is the accelerometer bias; and is the random noise. The accelerometer 

measurement updates begin at the start of the trajectory, and continue until touchdown at a user 

input rate. The integration of the sensed acceleration across a measurement interval defines the 

-V: 

a

acc

= I( ) 3 3+ SFacca

env

+ b

acc

+

acc

,
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 (5.1-3) 

and the accumulated -V is the sum of the -V generated between updates to the navigation 

filter.

Similarly, the gyroscope model takes the true body angular rates, with a random noise, bias and 

scale factor errors to generate a measurement of angular rates that are converted to - before 

being passed to navigation. Similar to the accelerometer, Equations (5.1-1), (5.1-2), and (5.1-3), 

the gyroscope angular rate measurement model is: 

 (5.1-4) 

where is the gyroscope measured angular rate vector in rad/s; is the true (environment) 

body angular rate vector in rad/s; 



SFgyro

is the gyroscope scale factor diagonal matrix; 



bg yro

is the 

gyroscope bias; and 



gyro

is the random noise. The integrated angular velocity, , is integrated 

across a measurement interval to provide the - measurement: 

 (5.1-5) 

which is then accumulated (summed) until the next call to the mEKF. The gyroscope 

measurement updates also begin at the start of the trajectory and continue until touchdown at a 

user-defined rate. 

5.1.1.2 Star Tracker Model 

The POST2-developed star tracker measurement model is a statistically based model. The star 

tracker model takes the true attitude quaternion, bias and noise to generate a star tracker 

measurement that is passed to the mEKF for processing as an external measurement. The noise 

 and bias are used to calculate an error quaternion (



q e(b, )

): 

 (5.1-6) 

where 

( ) gyro SF envgyro bgyro gyro  I  





 

33 += ++
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 (5.1-7) 

The star tracker measured attitude quaternion (



q st

) is determined as the product of the true 

quaternion (



q env

) and error quaternion (



q e(b, )

) yielding 



q st=q e(b,)q env

 (5.1-8) 

5.1.1.3 Altimeter and Velocimeter Models 

The measured altitude (hsensor) determined by the altimeter sensor is modeled in POST2 as: 

hsensor = htruth ( 1 + SFh) + ( pnoise htruth + hnoise) + hbias (5.1-9) 

where htruth is the true altitude, and pnoise, hnoise, hbias, and SFh are the noise percentage, noise 

addition, bias, and scale factor specifications, respectively. The sensor altitude measurement 

updates begin at a user defined truth altitude above the planet surface at a data rate also input by 

the user. The sensor velocity is separated into planet relative velocity vector components 

expressed in the body coordinate system. The sensor velocity for each component (vsensor)

independently determined by the velocimeter is modeled as: 

vsensor = vtruth ( 1 + SFv ) + vnoise + vbias (5.1-10) 

where vtruth is the true relative velocity component being modeled, and vnoise, vbias, and SFv are the 

noise, bias, and scale factor specifications, respectively. 

5.1.2 POST2 Inputs/Outputs for mEKF 

The inputs and outputs for use with the mEKF navigation filter have been integrated into the 

POST2 input/output dictionary. The inputs are identified in Table 5.1-1 and the outputs are 

identified in Table 5.1-2. 

Table 5.1-1. POST2 Inputs for the mEKF Algorithm 

Input

Symbol 

Units / 

Type

Stored

Value Definition

EKF_NX integer 0

Number of states in the filter

EKF_NP integer 0

Number of states in the covariance
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Input

Symbol 

Units / 

Type

Stored

Value Definition

EKF_NM integer 0

Number of measurements

EKF_NAV_RATE Hz 0.0 Update rate of the mEKF 

EKF_NAV_DT s 0.0 Inverse of the navigation rate 

EKF_Q_F_S_0,

EKF_Q_F_S_1,

EKF_Q_F_S_2,

EKF_Q_F_S_3

nd 1.0,

0.0,

0.0,

0.0

Quaternion of orientation of planetfixed reference frame with respect to the 

planet surface reference frame

EKF_R_REF_F_X,

EKF_R_REF_F_Y,

EKF_R_REF_F_Z

m 0.0,

0.0,

0.0

Location of the surface reference frame 

origin in the planet fixed-frame

EKF_OMEGA_FI_F_X,

EKF_OMEGA_FI_F_Y,

EKF_OMEGA_FI_F_Z

m 0.0,

0.0,

0.0

Spin axis of planet or moon at epoch

EKF_Q_IE_F_0,

EKF_Q_IE_F_1,

EKF_Q_IE_F_2,

EKF_Q_IE_F_3

nd 1.0,

0.0,

0.0,

0.0

Quaternion defining orientation of the 

inertial reference frame with respect to 

the planet-fixed reference frame at 

epoch

EKF_QIMU_i_j,

i=1,6

j=1,6

nd

0.0

IMU process noise matrix

EKF_QTUNE_i_i,

i=1,22

nd 0.0 Tuning process noise matrix

EKF_TE s 0.0 Epoch associated with Q_IE_F

EKF_MOON_AE m 1737400 Radius of the moon for gravity 

calculations

EKF_MOON_APO m 1735970 Polar radius of the moon

EKF_MOON_AEQ m 1738140 Equatorial radius of the moon

EKF_MOON_J2 nd 203.32E-06 Gravity J2 term of the moon

EKF_MOON_MU m

3

/s24902.8E09 Gravitational constant of the moon

EKF_MOON_OMEGA rad/s 2.6617E-06 Rotation rate of the moon

EKF_MARS_AE m 3397200 Radius of Mars for gravity calculations

EKF_MARS_APO m 3376200 Polar radius of Mars

EKF_MARS_AEQ m 3396190 Equatorial radius of Mars

EKF_MARS_J2 nd 0.0020 Gravity J2 term of Mars

EKF_MARS_MU m

3

/s24.2828376383e+13 Gravitational constant of Mars

EKF_MARS_OMEGA rad/s 7.088218e-05 Rotation rate of Mars

EKF_VEL_BIAS_X,

EKF_VEL_BIAS_Y,

EKF_VEL_BIAS_Z

m/s 0.0,

0.0,

0.0

Velocimeter measurement bias in the 

body X, Y, and Z axes
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Input

Symbol 

Units / 

Type

Stored

Value Definition

EKF_VEL_NOISE_COV_X_

X,

EKF_VEL_NOISE_COV_X_

Y,

EKF_VEL_NOISE_COV_X_

Z,

EKF_VEL_NOISE_COV_Y_

X,

EKF_VEL_NOISE_COV_Y_

Y,

EKF_VEL_NOISE_COV_Y_

Z,

EKF_VEL_NOISE_COV_Z_

X,

EKF_VEL_NOISE_COV_Z_

Y,

EKF_VEL_NOISE_COV_Z_

Z

nd 0.0,

0.0,

0.0,

0.0,

0.0,

0.0,

0.0,

0.0,

0.0

Velocimeter measurement noise 

covariance matrix

EKF_ATTC_BIAS_X,

EKF_ ATTC_BIAS_Y,

EKF_ ATTC _BIAS_Z

m/s 0.0, 

0.0, 

0.0

Attitude camera measurement bias in 

the body X, Y, and Z axes

EKF_ ATTC_

NOISE_COV_X_X,

EKF_ ATTC 

_NOISE_COV_X_Y,

EKF_ ATTC 

_NOISE_COV_X_Z,

EKF_ ATTC 

_NOISE_COV_Y_X,

EKF_ ATTC 

_NOISE_COV_Y_Y,

EKF_ ATTC 

_NOISE_COV_Y_Z,

EKF_ ATTC

_NOISE_COV_Z_X,

EKF_ ATTC 

_NOISE_COV_Z_Y,

EKF_ ATTC 

_NOISE_COV_Z_Z

nd 0.0,

0.0,

0.0,

0.0,

0.0,

0.0,

0.0,

0.0,

0.0

Attitude camera measurement noise 

covariance matrix

EKF_ALT_BIAS m 0.0 Spherical altimeter measurement bias
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Input

Symbol 

Units / 

Type

Stored

Value Definition

EKF_ALT_NOISE_COV nd 0.0 Spherical altimeter measurement noise

covariance

EKF_ACCEL_SPEC_BIAS m/s 0.0 IMU -V bias standard deviation (1-)

EKF_ACCEL_SPEC_NOISE nd 0.0 IMU -V noise covariance

EKF_GYRO_SPEC_BIAS rad 0.0 IMU  bias standard deviation (1-)

EKF_GYRO_SPEC_NOISE nd 0.0 IMU  noise covariance

EKF_XI_DELTA_ERR,

EKF_YI_DELTA_ERR,

EKF_ZI_DELTA_ERR

m 0.0,

0.0,

0.0

Initial navigation position error input as 

distance from true inertial state

EKF_VXI_DELTA_ERR,

EKF_VYI_DELTA_ERR,

EKF_VZI_DELTA_ERR

m/s 0.0,

0.0,

0.0

Initial navigation velocity error input 

relative to true inertial state

EKF_ERR_Q_0,

EKF_ERR_Q_1,

EKF_ERR_Q_2,

EKF_ERR_Q_0

nd 1.0,

0.0,

0.0,

0.0

Initial quaternion defining the inertial 

navigation attitude error
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Table 5.1-2. POST2 Outputs for the mEKF Algorithm 

Output

Symbol

Type/

Units Definition

ekf_x_km_x,

ekf_x_km_y,

ekf_x_km_z

m Propagated navigation inertial position estimate

ekf_x_km_vx,

ekf_x_km_vy,

ekf_x_km_vz

m/s Propagated navigation inertial velocity estimate

ekf_x_km_q0,

ekf_x_km_q1,

ekf_x_km_q2,

ekf_x_km_q3

nd Propagated navigation inertial to body quaternion estimate

ekf_P_km m

2

/s2

Propagated navigation covariance matrix

ekf_x_kp_x,

ekf_x_kp_y,

ekf_x_kp_z

m Navigation inertial position estimate after update

ekf_x_kp_vx,

ekf_x_kp_vy,

ekf_x_kp_vz

m/s Navigation inertial velocity estimate after update

ekf_x_kp_q0,

ekf_x_kp_q1,

ekf_x_kp_q2,

ekf_x_kp_q3

nd Navigation inertial to body quaternion estimate after update

ekf_P_kp m

2

/s2 Navigation covariance matrix after update

5.2 Aerodynamic Uncertainty Model 

Part of the Phase 1 effort was to include several aerodynamic models (i.e., the 70-, 60-, and 45-

degree sphere-cone aerodynamic database routines). However, the uncertainty values (used in 

Monte Carlo assessments) were required to be user input. This approach requires the user to 

have detailed knowledge of the uncertainty values and their application for the given database 

being used. To avoid user input errors associated with aerodynamic uncertainties, the method 

described below was developed wherein the uncertainty value and application are held within the 

aerodynamic database subroutine. The user inputs the desired standard deviation value (i.e., 

sigma value) of the uncertainty desired. The actual dispersion value and its application to the 

nominal aerodynamic coefficient values throughout the trajectory simulation are computed 

within the aerodynamic subroutine. This method is now used for the dispersion calculation 

associated with the Phase 1 aerodynamic models listed above.

The dispersions are input in specific flight regimes. The static coefficient dispersions are defined 

in three main regions of the flight regime: free molecular, hypersonic continuum, and supersonic 

continuum. The free molecular flight regime is defined by Knudsen number values > 1000 
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(indicated by _UNC1 in the variable name). For Knudsen number < 1000, the hypersonic 

continuum is defined by Mach numbers between 5 and 10 (_UNC2 in variable name) and the 

supersonic continuum region is defined by Mach < 5 (_UNC3 in variable name). The 

transitional aerodynamic uncertainties are determined using linear interpolation. Interpolation 

using log base 10 of the Knudsen number is applied between free molecular and supersonic 

continuum dispersion values. Whereas, interpolation using Mach number is utilized between 

hypersonic and supersonic continuum dispersion values. The only difference for dynamic 

derivative coefficient dispersions is that the hypersonic continuum is defined by Mach numbers 

below 6, and supersonic continuum is Mach number 3 and less. 

The dispersions are determined in the DISPERSION subroutine (in the file dispersion.f in the 

redl_Aero directory). This routine receives nominal aerodynamic coefficients (at respective 

database moment reference points) from the aerodynamic database routines and transforms 

moments to the center of gravity (cg). The aerodynamic coefficients are then dispersed about the 

cg using 3-sigma values [refs. 3, 4, 5] scaled by the user input (as described in Table 5.2-1). The 

dispersed aerodynamic coefficients are then transformed to the moment reference point for 

correct dispersion application by POST2 computations, which include the contribution of the 

aerodynamic forces to the aerodynamic moments. User input values of zero apply no dispersion 

and values may range from -1 to 1. Three-sigma values are multiplied by these input values (i.e., 

an input of 1 applies a +3 sigma dispersion as indicted in Table 5.2-1).

The general variables in Table 5.2-1 are associated with the aerodynamic inputs, whereas Table 

5.2-2 are the outputs in POST2. As shown parenthetically in Table 5.2-1, similar dispersed 

values are available for the other flight regimes with the variable name changed (specifically the 

_UNC1 portion) as described previously. The only exception to this information is the 

CMQ_CWR_UNC3_MULT. 
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Table 5.2-1. POST2 Inputs for the Aerodynamic Dispersion Model 

Input

Symbol Units 

Stored

Value Definition

CAT_UNC1_M

ULT

(UNC2 &UNC3)

nd 0.0

Axial force coefficient multiplicative uncertainty at cg

in free molecular flight regime. For IDISP_AERO=1, 

input dispersion value as fraction of 3-sigma value; 

that is +1 is + 3-sigma, -1 is -3-sigma and 0.5 is half of 

the 3-sigma value.

(Hypersonic and Supersonic flight regimes)

CAT_UNC1_

ADD

(UNC2 &UNC3)

nd 0.0

Axial force coefficient additive uncertainty at cg in 

free molecular flight regime. For IDISP_AERO=1, 

input dispersion value as fraction of 3-sigma value; 

that is +1 is + 3-sigma, -1 is -3-sigma and 0.5 is half of 

the 3-sigma value.

(Hypersonic and Supersonic flight regimes)

CMQ_CWR_

UNC1_ADD

(UNC2 &UNC3)

nd 0.0 Pitch damping and yaw moment damping due to yaw 

rate additive dispersion values at cg for free molecular 

flight regime. Input dispersion value as fraction of 3-

sigma value; that is +1 is + 3-sigma, -1 is -3-sigma and 

0.5 is half of the 3-sigma value. Same value is applied 

to both dynamic derivatives. 

(Hypersonic and Supersonic flight regimes)

CMQ_CWR_

UNC3_MULT

nd 0.0 Pitch damping and yaw moment damping due to yaw 

rate multiplicative dispersion values at cg in 

supersonic flight regime. Input dispersion value as 

fraction of 3-sigma value; that is +1 is + 3-sigma, -1 is 

-3-sigma and 0.5 is half of the 3-sigma value. Same 

value is applied to both dynamic derivatives. 
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Input

Symbol Units 

Stored

Value Definition

CMT_UNC1_M

ULT

(UNC2 &UNC3)

nd 0.0

Pitching moment coefficient multiplicative uncertainty

at cg in free molecular flight regime. For 

IDISP_AERO=1, input dispersion value as fraction of 

3-sigma value; that is +1 is + 3-sigma, -1 is -3-sigma 

and 0.5 is half of the 3-sigma value.

(Hypersonic and Supersonic flight regimes)

CMT_UNC1_

ADD

(UNC2 &UNC3)

nd 0.0

Pitching moment coefficient additive uncertainty at cg

in free molecular flight regime. For IDISP_AERO=1, 

input dispersion value as fraction of 3-sigma value; 

that is +1 is + 3-sigma, -1 is -3-sigma and 0.5 is half of 

the 3-sigma value.

(Hypersonic and Supersonic flight regimes)

CNT_UNC1_M

ULT

(UNC2 &UNC3)

nd 0.0

Normal force coefficient multiplicative uncertainty at 

cg in free molecular flight regime. For 

IDISP_AERO=1, input dispersion value as fraction of 

3-sigma value; that is +1 is + 3-sigma, -1 is -3-sigma 

and 0.5 is half of the 3-sigma value.

(Hypersonic and Supersonic flight regimes)

CNT_UNC1_

ADD

(UNC2 &UNC3)

nd 0.0

Normal force coefficient additive uncertainty at cg in 

free molecular flight regime. For IDISP_AERO=1, 

input dispersion value as fraction of 3-sigma value; 

that is +1 is + 3-sigma, -1 is -3-sigma and 0.5 is half of 

the 3-sigma value.

(Hypersonic and Supersonic flight regimes)

CW_UNC1_

MULT

(UNC2 &UNC3)

nd 0.0

Yawing moment coefficient multiplicative uncertainty 

at cg in free molecular flight regime. For 

IDISP_AERO=1, input dispersion value as fraction of 

3-sigma value; that is +1 is + 3-sigma, -1 is -3-sigma 

and 0.5 is half of the 3-sigma value.. 

(Hypersonic and Supersonic flight regimes)
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Input

Symbol Units 

Stored

Value Definition

CW_UNC1_

ADD

(UNC2 &UNC3)

nd 0.0

Yawing moment coefficient additive uncertainty at cg

in free molecular flight regime. For IDISP_AERO=1,

input dispersion value as fraction of 3-sigma value; 

that is +1 is + 3-sigma, -1 is -3-sigma and 0.5 is half of 

the 3-sigma value.

(Hypersonic and Supersonic flight regimes)

CY_UNC1_

MULT

(UNC2 &UNC3)

nd 0.0

Side force coefficient multiplicative uncertainty at cg

in free molecular flight regime. For IDISP_AERO=1,

input dispersion value as fraction of 3-sigma value; 

that is +1 is + 3-sigma, -1 is -3-sigma and 0.5 is half of 

the 3-sigma value.

(Hypersonic and Supersonic flight regimes)

CY_UNC1_

ADD

(UNC2 &UNC3)

nd 0.0

Side force coefficient additive uncertainty at cg in free 

molecular flight regime. For IDISP_AERO=1, input 

dispersion value as fraction of 3-sigma value; that is 

+1 is + 3-sigma, -1 is -3-sigma and 0.5 is half of the 3-

sigma value.

(Hypersonic and Supersonic flight regimes)

IDISP_AERO Integer 0 Flag to generate dispersed aerodynamics.

=0, use nominal (un-dispersed) aerodynamic 

coefficients

=1, disperse aerodynamics at cg using inputs as 

fractions of + 3-sigma dispersions.

REDL_AEROU

NCERT_j, 

j=1,50

nd 0.0 Array of aerodynamic uncertainties applied to nominal 

coefficients. Values input for standard or total 

aerodynamic uncertainties defined in this table also 

populate this array in the appropriate location.
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Table 5.2-2. POST2 Outputs from the Aerodynamic Dispersion Model 

Output

Symbol

Type/

Units Definition

CA_NOM nd Nominal Axial force coefficient

CAT_NOM nd Nominal total Axial force coefficient

CLL_NOM nd Nominal rolling moment coefficient

CLLP_NOM nd Nominal roll moment damping coefficient due to roll rate 

CLLR_NOM nd Nominal roll moment damping coefficient due to yaw rate 

CM_NOM nd Nominal pitching moment coefficient

CMQ_NOM nd Nominal pitch moment damping coefficient due to pitch rate 

CMT_NOM nd Nominal total pitching moment coefficient

CN_NOM nd Nominal Normal force coefficient

CNT_NOM nd Nominal total Normal force coefficient

CW_NOM nd Nominal yawing moment coefficient

CWP_NOM nd Nominal yaw moment damping coefficient due to roll rate 

CWR_NOM nd Nominal yaw moment damping coefficient due to yaw rate 

CY_NOM nd Nominal Side force coefficient

CA_DIS nd Dispersed Axial force coefficient

CAT_DIS nd Dispersed total Axial force coefficient

CLL_DIS nd Dispersed rolling moment coefficient

CLLP_DIS nd Dispersed roll moment damping coefficient due to roll rate 

CLLR_DIS nd Dispersed roll moment damping coefficient due to yaw rate 

CM_DIS nd Dispersed pitching moment coefficient

CMQ_DIS nd Dispersed pitch moment damping coefficient due to pitch rate 

CMT_DIS nd Dispersed total pitching moment coefficient

CN_DIS nd Dispersed Normal force coefficient

CNT_DIS nd Dispersed total Normal force coefficient

CW_DIS nd Dispersed yawing moment coefficient

CWP_DIS nd Dispersed yaw moment damping coefficient due to roll rate 

CWR_DIS nd Dispersed yaw moment damping coefficient due to yaw rate 

CY_DIS nd Dispersed Side force coefficient

KNUDSEN nd Knudsen Number

5.3 Terminal Point Control Guidance Algorithm 

A key element in developing rapid vehicle simulations is the vehicle guidance, navigation, and 

control (GN&C). The vehicle guidance (i.e., the "driver") takes input from the navigation 

system and user input targeting information to send signals to the flight control system that will 

guide the vehicle to its destination while remaining within the operating constraints. Several 

guidance algorithms were included in Phase 1. For this phase, the TPC guidance algorithm for 

aerocapture was added. 
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This guidance algorithm was implemented in order to examine vehicles that enter the atmosphere 

and aerocapture into orbit prior to EDL. The TPC guidance formulation was derived using the 

calculus of variations, which was the same methodology used to develop the Apollo Earth entry 

terminal phase guidance. A reference trajectory is used to determine the sensitivities of the final 

vehicle state to changes in the control at any point along the trajectory. For the TPC guidance, 

the control variable is the vehicle bank angle. The derivation differs from that of the Apollo 

terminal phase guidance in two significant ways. First, the boundary conditions for aerocapture 

are different from those for landing. Second, the aerocapture trajectory is not monotonic in 

altitude, so the simplification allowed by parameterization on altitude is not possible for 

aerocapture. The TPC guidance provides bank angle commands to reach a target orbit after a 

single atmospheric pass. 

As in the entry guidance, the bank angle magnitude controls the in-plane lift. For aerocapture, 

the in-plane lift targets to the desired apoapsis while maintaining periapsis as high as possible. 

The bank angle sign is used for out-of-plane control of either inclination or wedge angle. The 

TPC algorithm uses a lateral corridor that is indexed on energy. Whenever the wedge or 

inclination angle error is outside the corridor, the bank angle sign is negated to drive it back into 

the corridor. There is no general procedure to determine the shape of the corridor. It is tuned to 

meet the needs of each individual mission. The TPC guidance algorithm theoretical 

development with equations is provided in references 6 and 7. 

The process of tuning the TPC guidance starts with performing a reference 3-degree of freedom 

(DoF) trajectory. The reference trajectory is run using the input file PICKBANKNOM.INP. 

This input file can be set either to pick the required constant bank angle for a given entry flight 

path angle, or to pick the required entry flight path angle for a given bank angle profile. The 

latter allows a variable bank angle profile, typically a bank angle is used that is more lift up 

initially, more lift down at the end, and varies linearly with energy. The input file should be a 

nominal aerocapture trajectory except that the lift is in-plane and unguided (i.e., only an open 

loop bank angle profile is used). The input files PICKBANKSTP.INP and 

PICKBANKSHW.INP are the same except that one is steeper at entry, whereas the other is 

shallower. The amount of steepness or shallowness depends on the bank profile used. Targeting 

near, but not at the edge of the flyable corridor works best. Note that aerocapture trajectories can 

be sensitive. An initial bank angle estimate that results in the hyperbolic approach trajectory 

capturing into an elliptical orbit is required. A bank angle yielding in a flight path angle that is 

too steep at atmospheric interface results in the vehicle impacting into the planet’s surface, and 

thus an acceptable derivative can not be generated. If the flight path angle is too shallow, then 

the vehicle skips out (i.e., does not achieve elliptical orbit) and no acceptable derivative can be 

generated. Fortunately, first order calculations can be used to converge on initial parameters. 

After the reference trajectories are performed, form the .mat files with the extensions “_nom”, 

“_stp” and “_shw” for the nominal, steep and shallow trajectory cases, respectively. Then run 
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the script file “multimaster.m” in MATLABTM. For each of the three references, multimaster 

performs several functions: 

 Retrieves the relevant information from the .mat file and saves it to a .dat file 

(pbnom.dat, pbstp.dat and pbshw.dat). 

- The following variables are needed in the print block: TIME, ALTITO,

GAMIRV, VELR, RDOT, DRAGW, DENS, BNKANG, AEROCAP_DV,

ENERGY, GCRAD, GXI, GYI, GZI, DECLN, LONG, ENRGDT, MALTA,

WEIGHT, VELI, and CDW; 

 Identifies the terminal costate boundary conditions based on the exit states and the target 

orbit; 

 Integrates the costates backwards from the final condition and calculates the gains along 

the trajectory; 

 Reduces the number of data points to minimize storage requirements; 

 Plots the resulting data to check that the reduced data represents the original; and 

 Writes the gains in the form of POST2 tables, including comments. 

The gain tables are saved in the files TPC_gains_nom.dat, TPC_gains_shw.dat, and 

TPC_gains_stp.dat. The multimaster script calls: nomgenmulti.m, mgacdmulti.m, 

data_reduct.m, verify_plots.m, writepostinput_nom.m, writepostinput _stp.m, and writepostinput 

_shw.m. The script mgacdmulti.m is where the boundary conditions are calculated, the costates 

are integrated, and the gains are calculated. To run POST2 with the guidance in the loop, the 

input deck needs to include the three gain table files and the guidance setup file, tpc_setup.dat, 

and to have the guidance mode set to 15 (IGUID(14) = 15). Note that the parameters most 

adjusted to achieve a successful aerocapture are TPC_OVERKD, TPC_OVERKRD, and 

TPC_NSAMP. TPC_OVERKV is often set to zero. 

POST2 inputs and outputs for the TPC guidance algorithm are provided in Tables 5.3-1 and 

5.3-2, respectively. Note that all of the variables in the TPC guidance structure are prefixed with 

“tpc_”. Many of the input parameters are generated via MATLABTM scripts and the nominal 

trajectory. Additionally, all of the gain tables are generated using MATLABTM scripts. These 

gain table and input value files generated via the process must be included in the POST2 input 

file for the TPC guidance to function properly. 
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Table 5.3-1. POST2 Inputs for the TPC Guidance Algorithm 

Input

Symbol Units 

Stored

Value Definition

IGUID(14) integer 0 The TPC selection flag.

=15, Use TPC guidance

TPC_REQ m 0.0 Planet equatorial radius used in TPC

TPC_RPL m 0.0 Planet polar radius used in TPC

TPC_WIE rad/s 0.0 Planet rotation rate used in TPC

TPC_XMUE m

3

/s2

0.0 Planet gravitational constant used in TPC

TPC_DT s 0.0 TPC guidance call update time

TPC_GSTART,

TPC_GSTOP

m/s2

0.0,

0.0

Acceleration triggers to begin and end atmospheric 

phase of TPC guidance

TPC_TAU1, TPC_TAU2 s 0.0 TPC drag filter time constants

TPC_CDNOM nd 0.0 Nominal vehicle drag coefficient used by TPC

TPC_SNOM m

2

0.0 Nominal vehicle reference area used by TPC

TPC_DENSFACT nd 0.0 TPC over-density factor applied to the atmospheric 

density

TPC_

SCALEHEIGHT_NOM

km 0.0 Atmospheric scale height used to initialize the 

atmospheric density estimator in TPC

TPC_OVERKD nd 0.0 TPC overcontrol gain on drag acceleration

TPC_OVERKRD nd 0.0 TPC overcontrol gain on radius rate of change

TPC_OVERKV nd 0.0 TPC overcontrol gain on velocity

TPC_DELTA_APO m 0.0 Difference from the target apopasis radius 

(TPC_RA_TARG) at which aeroshell is jettisoned

(e.g., if =5000, aeroshell will jettison 5 km above 

target apoapsis)

TPC_RA_TARG m 0.0 The target apopasis radius at which aeroshell is 

jettisoned in TPC

TPC_RHO0 Atmospheric surface density used to initialize the 

atmospheric density estimator in TPC

TPC_NSAMPL integer 0 Number of acceleration measurements used by the 

atmospheric density estimator in TPC

TPC_IAXIALFLAG integer 0 Flag to determine which accelerations to use to 

estimate density in TPC 

= 2, use drag accelerations

TPC_MIN_RHO0, 

TPC_MAX_RHO0

0.0,

0.0

Lower and upper limits on the “sea-level” atmospheric 

density in the estimator in TPC
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Input

Symbol Units 

Stored

Value Definition

TPC_MIN_SCH, 

TPC_MAX_SCH

km 0.0,

0.0

Lower and upper limits on the atmospheric scale 

height in the estimator in TPC.

TPC_IFLG integer 0 TPC mode flag. If =2, then the vehicle is forced to 

follow input reference bank profile.

TPC_

BOTTOMETRIGGER

kg m

2

/s2

0.0 Energy trigger to change the roll reversal limits from 

TPC_BOTTOMHIE to TPC_BOTTOMLOE in TPC.

TPC_BOTTOMLOE, 

TPC_BOTTOMHIE

degree 0.0,

0.0

The low-energy and high-energy limits on bank 

reversal direction in TPC. If energy is more than 

TPC_BOTTOMETRIGGER and 

TPC_BOTTOMHIE=80, then reversals commanded 

when bank is less than 80 will go over the top, 

reversals commanded when bank is greater than 80 

will go underneath. Set to 90 will give shortest 

distance.

TPC_IDBG integer 0 TPC debug flag. Set =1 for additional output and 

generate an external file (fort.68) with more output.

TPC_LATFLAG integer 0 TPC flag to select the lateral logic variable.

= 0, inclination 

=1, wedge angle

TPC_BANKLIM degree 0.0 Limits closest command to lift up or lift down (e.g., if 

tpc_banklim=10 no commands will be issued between 

10 and -10, or above 170 or below -170).

TPC_NOMONLYFLAG integer 0 TPC flag to use only the nominal reference profile.

TPC_TOPINCX, 

TPC_TOPINCY, 

TPC_BOTINCX, 

TPC_BOTINCY

kg m2/s2

0.0,

0.0,

0.0,

0.0

TPC tables used to control roll reversals. The X tables 

are energy values and the Y tables are wedge angle (or 

inclination) values. Whenever the vehicle exceeds the 

interpolated Y values, a reversal is commanded. The 

tables currently have length 6.

TPC_XMASS 0.0 Mass of the vehicle used in TPC

TPC_NRDT1_NOM, 

TPC_NRDT1_STP, 

TPC_NRDT1_SHW

integer 0.0,

0.0,

0.0

Array lengths for the gains in each of the sets of tables 

in TPC
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Table 5.3-2. POST2 Outputs for the TPC Guidance Algorithm 

Output

Symbol

Type/

Units Definition

TPC_BANKC degree Commanded Bank Angle

TPC_JETTISO

N_ON

nd Flag indicating heatshield is to be jettisoned.

TPC_DIR nd Commanded bank maneuver direction

= -2, bank through 180 degree (underneath)

= -1, bank left

= 0, go shortest distance

= 1, bank right

= 2, bank through 0 degree (over)

5.4 Aerobraking Mission Design Module 

The program contains basic algorithms required to perform an aerobraking mission design 

simulation. It is a variation of the mission design software used for mission planning and 

aerobraking operations for Mars Odyssey and Reconnaissance Orbiter. The code allows for 

specific walk-in and operational maneuver strategies. Walk-in is the phase that transitions the 

spacecraft from its exo-atmospheric orbit to aerobraking without exceeding any of the spacecraft 

constraints (e.g., heat rate, temperature, dynamic pressure). This module is capable of 

monitoring eclipse times, lifetime constraints, and includes several options for aerobraking 

corridor control. 

The input requires the use of repeating roving events for critical events such as atmosphere entry, 

periapsis, atmosphere exit, and apoapsis. Aerobraking missions with more than 1000 orbits will 

require multiple sets of critical events in the input file. The aerobraking mission design option is 

operating when npc(9) = 3 and ab_flag=1. 

The general setup and procedure for using the aerobraking mission design module involves 

input files and scripts. Samples are provided in a redlasim_aerobraking directory. The contents 

of that directory include the following files: 

TEST.INP is a standard input used with an aerobraking case. The event structure can be 

changed, but AB_EVENT_FLAG input must adhere to the following values: 

AB_EVENT_FLAG = 30 in the atmosphere entry event; 

AB_EVENT_FLAG = 50 in the periapsis event; 

AB_EVENT_FLAG = 70 in the atmosphere exit event; and 

AB_EVENT_FLAG = 90 in the apoapsis event. 
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SPAWNP2.pl is called from PREDICT_DV.f. This script submits the POST2 spawned job 

that runs while the original aerobraking simulation is suspended. Once completed, data is 

placed into appropriate files by the script for the original run to continue. 

The RUNOUT4.PL script converts the variables saved in save_runout_variables.cpp to a 

MATLABTM format once an input case has completed. This script creates the 

TEST_APO.mat and TEST_PER.mat files containing apoapsis and periapsis data, 

respectively. 

The RUN_S_POST.PL script submits the jobs to the cluster for execution. Currently, only 

cluster execution is permitted (no local machine runs) due to the spawn case setup is for 

cluster use only at this time. 

PLOT_AB.m is a sample plotting routine is also included for use with MATLABTM. 

This script loads the TEST.mat, TEST_PER.mat, and TEST_APO.mat to plot the results of 

the aerobraking mission. 

Test cases were developed which employ this aerobraking mission design module. The POST2 

inputs, tables, and outputs for the aerobraking mission design module is provided in Tables 

5.4-1, 5.4-2, and 5.4-3, respectively. 

Table 5.4-1. POST2 Inputs for the Aerobraking Mission Design Module 

npc(9) integer 0 Propulsion type selection flag

= 0, no thrust

= 1, 2, Rocket or ramjet engine

= 3, Instantaneous delta V option also Calculate 

Aerobraking DV 

= 4, Instantaneous delta V addition using current 

weight of propellant and specific impulse

AB_END_VALUE decimal 0.0 Value of AB_END_CRITR_MODE to end simulation 

(i.e., if AB_END_CRITR_MODE = AB_MALTA, 

AB_END_VALUE = 450)

AB_END_FLAG integer 0 Flag to end aerobraking simulation 

= 1 ends sim

AB_EVENT_FLG integer 0 Aerobraking event flag

AB_FLAG integer 0 Aerobraking Mission Design module activation flag.

=1, module active

Input

Symbol 

Units Stored

Value Definition
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AB_DV_MODE integer 0 V magnitude selection flag

0 = NO_MANEUVER

1 = TABLE_LOOKUP

2 = PREDICT

SPAWN_END_VALUE decimal 0.0 Value of SPAWN_END_CRITR_MODE to end 

spawned case. 

AB_PREDICT_MODE integer 0 Type of AB corridor

1 = ALT_CORRIDOR

2 = DENS_CORRIDOR

3 = HTRT_CORRIDOR

4 = DYNP_CORRIDOR

SPAWN_END_CRITR_

MODE

integer 0 End of simulation criteria

1 = ALT

2 = ORB

3 = DAY

SPAWNP2_PATH character *132 Path to the SPAWNP2 to be used in the spawn cases.

Note that the path to executable must be changed 

inside SPAWNP2 file.

LAST_WALKIN_ORB integer 0 Value of the last walk in orbit.

LAST_WALKIN2_ORB integer 0 Value of last walk in orbit after solar conjunction.

Table 5.4-2. POST2 Table Inputs for the Aerobraking Mission Design Module

Input

Symbol 

Units Stored

Value Definition

LOWER_CORRT decimal 0.0 Aerobraking lower corridor limit.

UPPER_CORRT decimal Stored

Value 

Aerobraking upper corridor limit.

DAYS_B4_ABMT decimal 0.0 Days between aerobraking maneuvers.

CORR_TARGT decimal 0.0 Aerobraking corridor target (i.e., 0.5 targets the 

middle of the corridor).

AWALKIN_DVT decimal 0.0 Table of walk-in maneuvers as a function of orbit 

number.

WALKIN2_DVT decimal 0.0 Table of second walk-in maneuvers as a function of 

orbit number.
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Table 5.4-3. POST2 Outputs for the Aerobraking Mission Design Module 

Output

Symbol

Type/

Units Definition

ORBIT_NUM nd orbit revolution counter from first walkin. Orbit numbers start 

at periapsis

ORBIT2_NUM nd Orbit revolution counter from second walkin

AB_DAY_NUM days 24-hr period counter (days of aerobraking)

DOWN_MANEUVER_

DV

m/s down maneuver indicator, equal to DV magnitude (abs value)

UP_MANEUVER

_DV

m/s up maneuver indicator, equal to DV magnitude (abs value)

SUM_MANEUVER_D

V

m/s Cumulative maneuver DV

AB_MANEUVER

_COUNTER

nd Orbit maneuver counter

SIM_START_TIME s Simulation start time

LOWER_CORR Value of the lower aerobraking corridor. Type of corridor and 

units depend on AB_PREDICT_MODE

UPPER_CORR Value of the upper aerobraking corridor. Type of corridor and 

units depend on AB_PREDICT_MODE

CORR_TARG Target in the corridor. Type of corridor and units depend on 

AB_PREDICT_MODE

AB_MAX_DENS kg/m3 Maximum density on a particular aerobraking pass

AB_MAX_HTRT w/cm2 Maximum heat rate indicator (1/2 rho vel^3) on a particular 

aerobraking pass

AB_MAX_DYNP Pa Maximum dynamic pressure on a particular aerobraking pass

AB_ENTRY_LS degree Local Solar Longitude of a particular aerobraking pass entry

5.5 Earth Environment Models 

5.5.1 2010 Earth-Global Reference Atmosphere Model 

Earth-GRAM 2010 [ref. 2] uses an empirical database to provide atmospheric quantities (e.g., 

density, temperature, pressure, winds, and constituent concentrations) from the Earth’s surface to 

orbital altitudes based on geographic location and time of year. This version is an update to the 

previously released Earth-GRAM 2007. Specific changes for this latest release include an 

updated lower atmosphere database (Global Upper Air Climatic Atlas replaced by monthly 

global climatology by the National Centers for Environmental Prediction, or NCEP), revised 
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boundary layer model, updated thermosophere models, scaling parameters for standard 

deviations modified, auxiliary profiles option, moisture corrections, and additional output 

parameters. The Earth-GRAM 2010 models have been implemented into POST2 and are 

accessible via the standard input (npc(5)=19). The POST2 inputs, tables, and outputs for EarthGRAM 2010 are listed in Tables 5.5-1, 5.5-2, and 5.5-3, respectively. 

Table 5.5-1. POST2 Inputs for the Earth-GRAM 2010 Model 

Input

Symbol 

Type/

Units 

Stored

Value Definition

NPC(5) integer 2 The atmosphere model selection flag.

=x =19, Earth GRAM 2010 model

NPC(6) integer 0

Wind calculation flag 

= 4 Use GRAM determination of North-South, EastWest, and Vertical winds

AP decimal 0.0 Geomagnetic index

ATMPATH character “null” Path name for “atmosdat” atmospheric data file

F10 solar flux 

units

0.0 Daily 10.7-cm flux

F10b solar flux 

units

0.0 Mean 10.7-cm flux

IATMFL1 integer 1 The GRAM initialization flag. 

For first vehicle number that uses GRAM

=0, Do not initialize GRAM

=1, Initialize GRAM

Required for first call to GRAM

For other vehicles using GRAM

= 0, Do not update initial random number – will 

maintain same atmosphere density variability 

profile as another vehicle (correlated 

atmospheres)

= 1, Initialize atmosphere for new vehicle – no

correlation between vehicle atmospheres
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Input

Symbol 

Type/

Units 

Stored

Value Definition

IATMFL2 integer 0 Random number seed – used when variable 

atmosphere mode (IATMFL3=1) is used

IATMFL3 integer 0 Perturbed atmosphere property options

= 0, Mean density, temperature, pressure and 

 speed of sound.

= 1, Perturbed density, mean temperature and

 pressure, and perturbed speed of

 sound 

IATMFL4 integer 0 Winds to use if NPC(6)=4

= 0, nominal GRAM winds

= 1, nominal GRAM winds + perturbations

IAUXPROFILE integer 0 Flag to indicate POST2 tables are used to define 

auxiliary profile. The auxiliary profile is used to 

override the default density, temperature, pressure and 

wind profiles. The use of this option does not allow 

for DUSTAU perturbations.

= 0, Do not use POST2 tables for profile, use file 

define by PROFILE

= 1, Use POST2 tables AUXTEMPT, AUXPREST, 

AUXDENST, AUXEWWINDT, and AUXNSWINDT 

to define auxiliary profile

IOPR integer 0 random output option

1 = random output

2 = none

IDA integer 0 Day of the month

NCEPHR integer 5 Code for UT hour of day if NCEP climatology is used: 

1=00 UT,

2=06UT, 

3=12UT, 

4=18UT,

5=all times of day combined, 

0 to use NCEP time-of-day based on input UTC hour 

(ihro)

NCEPYR integer 9008 y1y2 to use NCEP climatology for period-of-record 

(POR) from year y1 through year y2
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Input

Symbol 

Type/

Units 

Stored

Value Definition

IHRO integer 0 Initial UTC (Greenwich) time hour 

INITPERT integer 0 Initial perturbations flag

= 0 GRAM-derived random initial perturbations 

values

= 1 User-selected initial perturbations

ITHERM integer 0 Thermosphere model selection flag.

= 1 MET (Jacchia)

= 2 MSIS

= 3 JB2006 

IUS

IUG

integer

integer

0

0

Unit number for atmosdat data

Unit number for NCEP files

IURRA integer 0 Unit number for Range Reference Atmosphere (RRA) 

data.

= 0 none

= xx actual unit number (recommend 42)

IYR integer 0 4 digit or 2 digit year. If 2 digits are used 

IYR>56=19xx, IYR<57 =20xx

MINO integer 0 Initial UTC (Greenwich) time minute

MN integer 0 Month (1-12)

PATCHY integer 0 Patchiness in perturbation model.

= 0 no patchiness

≠ 0 patchiness

PROFILE character “null” (Optional) auxiliary profile input file name. The 

auxiliary file is used to override the default density, 

temperature, pressure and wind profiles. 

RDINIT percent 0.0

Initial density perturbation model (percent of mean). 

Used if INITPERT = 1

RPINIT percent 0.0

Initial pressure perturbation model (percent of mean). 

Used if INITPERT = 1

RPSCALE decimal 1.0

Random density perturbation scale factor (0 = no 

perturbation) 0 ≤ RPSCALE ≤ 2. If the table 

RPSCALET is used, then the table value will override

this input.

RRAPATH character “null” Directory for RRA data.
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Input

Symbol 

Type/

Units 

Stored

Value Definition

RTINIT percent 0.0

Initial temperature perturbation model (percent of 

mean). Used if INITPERT = 1

RUINIT m/s 0.0

Initial eastward wind velocity perturbation model. 

Used if INITPERT = 1

RVINIT m/s 0.0

Initial northward wind velocity perturbation model. 

Used if INITPERT = 1

RWINIT m/s 0.0

Initial upward wind velocity perturbation model. Used 

if INITPERT = 1

SECO decimal 0.0 Initial UTC (Greenwich) time minute 

SITELIM degree 0.0 Lat-Lon radius from RRA or PROFILE outside of 

which the RRA or PROFILE data are not used.

SITENEAR degree 0.0 Lat-Lon radius from RRA or PROFILE inside of 

which the RRA or PROFILE data are used with 1.0 

weighting factor. Between SITENEAR and SITELIM 

the weighting factor transitions from 1.0 to 0.0 

smoothly.

S10 decimal 0.0 Extreme Ultraviolet (EUV) index (26-34 nm) scaled to 

F10 units, i.e., 0.0 corresponds to S10=F10

S10B decimal 0.0 EUV 81-day center-averaged index scaled to F10B 

units (i.e., 0.0 corresponds to S10B=F10B

XM10 decimal 0.0 MG2 index scaled to F10 units (i.e., 0.0 corresponds to 

XM10=F10

XM10B decimal 0.0 MG2 81-day center-average index scaled to F10 units 

(i.e., 0.0 corresponds to XM10B=F10)

Table 5.5-2. POST2 Tables for the Earth-GRAM 2010 Model 

Input

Symbol 

Type/

Units 

Stored

Value Definition

AUXDENST kg/m3 0.0 Auxiliary profile of natural log of atmospheric density. 

Used if IAUXPROFILE = 1.

AUXEWWINDT m/s 0.0 Auxiliary profile of East/West wind. Used if 

IAUXPROFILE = 1.

AUXNSWINDT m/s 0.0 Auxiliary profile of North/South wind. Used if 

IAUXPROFILE = 1.
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AUXPREST N/m2 0.0 Auxiliary profile of natural log of atmospheric 

pressure. Used if IAUXPROFILE = 1. 

AUXTEMPT degree K 0.0 Auxiliary profile atmospheric temperature. Used if 

IAUXPROFILE = 1. 

RPSCALET decimal 0.0 Random density perturbation scale factor (0 = no 

perturbation) 0 ≤ RPSCALET ≤ 2. If the table 

RPSCALET is used, then the table value will override 

the RPSCALE input.

Table 5.5-3. POST2 Outputs for the Earth-GRAM 2010 Model 

Output

Symbol

Type/

Units Definition

ARMOLE percent Percentage of AR by volume in atmosphere.

ATEM degree K Atmospheric temperature. 

AUXDENS kg/m3 Auxiliary profile density. Calculated if IAUXPROFILE = 1.

AUXEWWIND m/s Auxiliary profile East/West wind. Calculated if 

IAUXPROFILE = 1.

AUXNSWIND m/s Auxiliary profile North/South wind. Calculated if 

IAUXPROFILE = 1.

AUXPRES N/m2 Auxiliary profile pressure. Calculated if IAUXPROFILE = 1.

AUXTEMP degree K Auxiliary profile temperature. Used if IAUXPROFILE = 1.

CH4MOLE percent Percentage of CH4 by volume in atmosphere.

COMOLE percent Percentage of CO by volume in atmosphere.

CO2MOLE percent Percentage of CO2 by volume in atmosphere.

CS m/s Speed of sound. 

DENS kg/m3 Atmospheric density. 

DENS = DENS * GENTAB(DENKT)

DENSMEAN kg/m3 Mean atmospheric density.

DENSM3S kg/m3 3 sigma low atmospheric density.

DENSP3S kg/m3 3 sigma high atmospheric density.

DENSRAT decimal Ratio of density to mean density

DENS76STAND kg/m3 1976 standard atmospheric density. 

EWWINDMEAN m/s Mean East/West wind velocity. Positive to the East.

HEMOLE percent Percentage of HE by volume in atmosphere.

HMOLE percent Percentage of H by volume in atmosphere.

H2OMOLE percent Percentage of H2O by volume in atmosphere.

MOLWEIGHT decimal Molecular weight of atmosphere 

NMOLE percent Percentage of N by volume in atmosphere.

N2MOLE percent Percentage of N2 by volume in atmosphere.

N2OMOLE percent Percentage of N2O by volume in atmosphere.

NSWINDMEAN m/s Mean North/South wind velocity. Positive to the North.
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Output

Symbol

Type/

Units Definition

OMOLE percent Percentage of O by volume in atmosphere.

O2MOLE percent Percentage of O2 by volume in atmosphere.

O3MOLE percent Percentage of O3 by volume in atmosphere.

PRES N/m2 Atmospheric pressure. 

PRESMEAN N/m2 Mean atmospheric pressure.

PRES76STAND N/m2 1976 standard atmospheric pressure. 

TEMPMEAN degree K Mean atmospheric temperature. 

TEMP76STAND degree K 1976 standard atmospheric temperature. 

VERTWINDMEAN m/s Mean vertical wind velocity. Positive down. 

WINDEW m/s East/West wind velocity. Positive East. Used if NPC(6) =4

WINDNS m/s North/South wind velocity. Positive North. Used if NPC(6) =4

WINDV m/s Vertical wind velocity. Positive down. Used if NPC(6) =4

ZHPRES km Atmospheric pressure scale height.

ZHRHO km Atmospheric density scale height.

5.5.2 Earth Gravity Model 96

The EGM96 model was formatted for use with the POST2 gravity model. The EGM96 

(complete to degree and order 360) was generated by NASA and other Government agencies. 

This model is being used with various NASA simulations evaluating currently proposed Earth 

entry systems. Various data sets including satellite tracking and altimetry were used to generate 

this model. Standard POST2 inputs and outputs for gravity models are used; the spherical 

harmonic gravity model is invoked in POST2 using NPC(16)=7, and the file containing the 

sectoral and tesseral data is identified in the input (including system directory path) using the 

POST2 variable GRAVDATA. A test input file was generated using EGM96.

5.6 Attitude Control Models 

In an effort to balance faster executing and more easily developed 3 DoF simulations (versus the 

slower, higher fidelity 6 DoF simulations), control models that address vehicle attitude change 

are used. A pseudo controller model was included in Phase 1 which used a method of emulating 

a 6 DoF attitude control system for bank angle modulation. Additionally in Phase 1, the natural 

aerodynamic trim points in pitch and yaw to determine the angle of attack (AOA) and sideslip 

angle that the vehicle orients to at any time during the atmospheric entry were included to 

provide 3-axis vehicle control. For Phase 2, another method of 3-axis vehicle control based on 

the bank angle pseudo-controller was developed. Also, a utility function to provide a second 

order actuator model for use with models within POST2 (e.g., engine gimbal or sensor slewing 

motion) is included. Both of these models were incorporated in the simulation and their 

implementations are described in the following subsections.
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5.6.1 Pseudo-Controller for 3-axis Attitude Control 

The program contains a pseudo-controller module that emulates the performance of a feedback 

control system. The three-axis pseudo-controller (3APC is a generalization of the bank angle 

pseudo-controller (BPC) and allows a 3 DoF simulation to model some of the dynamic attitude 

behavior of a 6 DoF trajectory. The 3APC can be used for 3-axis attitude control of any 3 DoF 

vehicle trajectory. However, if the vehicle being modeled uses bank angle to modulate lift, then 

the BPC will be a more straightforward implementation. Note that this module does not solve 

the rotational equations of motion and does not require moments of inertia. Also, the 3APC 

module treats each axis independently and should not be used for systems with high angular rates 

or other significant cross-axis coupling. 

The 3APC expects three commanded angles from the guidance system: roll, pitch and yaw. The 

3APC attempts to achieve these commanded angles by applying angular accelerations under the 

constraint of second-order dynamics. Maximum allowed values for the angular acceleration and 

angular rate are given as inputs: 

2

0

2

1

 d td t



++=

The 3APC module maintains internal states of angle and angle rate for each axis, which are 

integrated within the model, not using the POST2 generalized integration procedure. Angular 

rate and acceleration can be adjusted based on current residual angle error (i.e., difference 

between commanded and actual angle) and when the actual angle overshoots the command. 

Several options are available to model behavior of the 3APC when the vehicle overshoots the 

command. Since the 3APC bases the angular acceleration, it uses on the current angle and the 

commanded angle, overshoots should only occur due to a change in the command. The 

“normal” option is to use all of the vehicles deceleration capability to reach the commanded 

angle. The “no overshoot” option allows the vehicle to exceed the maximum angular 

acceleration when the vehicle passes the commanded angle in order to prevent an overshoot. 

The “no wrong way” option ensures that the angle only moves toward the commanded angle. If 

the command changes in such a way that the current angular rate moves the vehicle away from 

the current command, the “no wrong way” option forces the angle to the new command. Finally, 

the “perfect” controller option instantly sets the angle to the command and the angular rate to 

zero. 

The angle command and the angle direction command are provided from the guidance or the 

input deck. There are several options for angle direction and for how the controller handles 

overshoots. The angle direction flag can be set to: under, left, shortest, right, or over. “Under” 

means the vehicle will rotate toward an angle of 180 degrees. “Left” means the vehicle will 

rotate to the left. “Shortest” means bank in the direction that minimizes the absolute angle error. 

“Right” means the vehicle will rotate to the right, and “over” means through an angle of 0 

degrees. 
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No limitations are placed on the size of the maximum acceleration or rate that are input. If large 

enough values are used, then the 3APC will operate as a near instantaneous angle controller. 

Once input, these limits are used to limit the maximum values in an absolute value sense (i.e., +

maximum value are the limit boundaries used). 

Inputs and outputs for the POST2 implementation of the 3APC are provided in Tables 5.6-1 and 

5.6-2, respectively. To use the 3APC, the relative euler angles steering option must be used 

(IGUID(1)=2), and the angle polynomial with constant term from input (IGUID(4) =1 or 

IGUID(9) =3*1, depending on value of IGUID(2). 

Table 5.6-1. POST2 Inputs for the 3APC Model

Input

Symbol 

Units Stored

Value Definition

CTRL_ROL_CMD,

CTRL_PIT_CMD,

CTRL_YAW_CMD

degree 0.0 Commanded angle about the X (ROL), Y (PIT),

and Z (YAW) body axes.

CTRL_ROL_DT,

CTRL_PIT_DT,

CTRL_YAW_DT

seconds 0.0 Pseudo-controller update cycle time for the X 

(ROL), Y (PIT), and Z (YAW) body axis 

controller.

CTRL_ROL_IDIR_FLAG,

CTRL_PIT_IDIR_FLAG,

CTRL_YAW_IDIR_FLAG

integer 0 Flag to control maneuver direction for the X 

(ROL), Y (PIT), and Z (YAW) body axis 

controller

= -2, bank through 180 degree (underneath)

= -1, bank left

= 0, go shortest distance

= 1, bank right

= 2, bank through 0 degree (over)

CTRL_ROL_

IPSEUDO_FLAG,

CTRL_PIT_

IPSEUDO_FLAG,

CTRL_YAW_

IPSEUDO_FLAG

integer 0 The Pseudo-controller selection flag for the X 

(ROL), Y (PIT), and Z (YAW) body axis 

controller.

=1, Use Pseudo-Controller

CTRL_ROL_MAXACCEL,

CTRL_PIT_MAXACCEL,

CTRL_YAW_MAXACCEL

deg/s2

5.0 Maximum angular acceleration used by the 

pseudo-controller flag for the X (ROL), Y (PIT), 

and Z (YAW) body axis

CTRL_ROL_MAXRATE,

CTRL_PIT_MAXRATE,

CTRL_YAW_MAXRATE

deg/s 20.0 Maximum angular rate used by the pseudocontroller flag for the X (ROL), Y (PIT), and Z 

(YAW) body axis
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Input

Symbol 

Units Stored

Value Definition

CTRL_ROL_OSMODE,

CTRL_PIT_OSMODE,

CTRL_YAW_OSMODE

integer 0 Overshoot mode selection flag for the X (ROL), Y 

(PIT), and Z (YAW) body axis

= 0, normal

= 1, no overshoot

= 2, no wrong way

= -1, perfect

IGUID(1) integer 0 Type of steering (guidance) desired.

=0, AOA, sideslip, and bank. Also

input values for IGUID(2) and IGUID(3) or

IGUID(6), IGUID(7), and IGUID(8).

IGUID(3) integer 0 A flag to specify the steering option when

commanding all channels simultaneously using 

aerodynamic AOA, sideslip, and bank angle. Must 

use option 1 with BPC.

= 1, Command AOA, sideslip, and bank as third 

order polynomials with the values of the constant 

terms of the polynomials are the input values.

IGUID(8) integer 0 Steering option flag when using separate channel 

for bank angle. Must use option 1 with BPC.

= 1, Command bank angle as third order 

polynomials except that the constant terms of the 

polynomials are the input values.

Table 5.6-2. POST2 Outputs for the 3APC Model

Output

Symbol

Type/

Units Definition

CTRL_ROL_CMD,

CTRL_PIT_CMD,

CTRL_YAW_CMD

degree Angle command for the X (ROL), Y (PIT), and Z (YAW) body 

axis

CTRL_ROL_DOT,

CTRL_PIT_DOT,

CTRL_YAW_DOT

deg/s Angular rate about the X (ROL), Y (PIT), and Z (YAW) body 

axis

CTRL_ROL_PC1,

CTRL_PIT_PC1,

CTRL_YAW_PC1

degree X (ROL), Y (PIT), and Z (YAW) body axis angle polynomial first 

coefficient – generated by pseudo-controller
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NESC Request No.: TI-09-00530 – Phase 2 

5.6.2 Second Order Actuator Model 

A general purpose second order actuator model has been developed for use internally with 

POST2 models (e.g., engine gimbal or sensor slewing). The routine, actu8, models second order 

dynamic system of the form: 



d

2

x

dt 2

+ 2

dx

dt

+

2

x = u

 (5.6-1) 

where x is the displacement of the system; is the damping; is the natural frequency; and u is 

the input to the system. The model expects to be called at every time step and integrates the 

internal state variables across a time interval that must be supplied. The user provides the 

actuator damping and natural frequency, the update cycle time, the position and rate limits, and 

the current position command. 

Inputs to the routine are: 

 System initial position 

 System initial rate 

 Time step 

 Actuator damping ratio 

 Actuator natural frequency 

 Commanded position 

 Plus and minus rate limits 

 Plus and minus displacement limits 

Outputs from the system are: 

 Final position after time step 

 Final rate after time step 

Note that the final position and rate from one call are used as the initial position and rate for the 

next call. This feature allows the same actuator model code to be used for multiple actuators, at 

the expense of external storage for the state variables. 

6.0 Observation and NESC Recommendation 

The following observation and NESC recommendation relate to technical aspects of this 

assessment: 

O-1. The validated and documented subsystem models, test cases, and scripts developed 

during Phases 1 and 2 of this assessment, and added to the POST2 simulation framework, 

have increased the Agency’s ability to rapidly evaluate EDL characteristics in systems 
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analysis studies, preliminary design, mission development and execution, and timecritical assessments. 

R-1. The custodians of the POST2 simulation framework, the Atmospheric Flight and Entry 

Systems Branch at LaRC, should retain and maintain the REDLAS models, test cases, 

and scripts for use by current and future programs. (O-1) 

7.0 Other Deliverables 

There are no other deliverables. 

8.0 Definition of Terms 

Corrective Actions Changes to design processes, work instructions, workmanship practices, 

training, inspections, tests, procedures, specifications, drawings, tools, 

equipment, facilities, resources, or material that result in preventing, 

minimizing, or limiting the potential for recurrence of a problem. 

Finding A conclusion based on facts established by the investigating authority. 

Lessons Learned Knowledge or understanding gained by experience. The experience may 

be positive, as in a successful test or mission, or negative, as in a mishap 

or failure. A lesson must be significant in that it has real or assumed 

impact on operations; valid in that it is factually and technically correct; 

and applicable in that it identifies a specific design, process, or decision 

that reduces or limits the potential for failures and mishaps, or reinforces a 

positive result. 

Observation A factor, event, or circumstance identified during the assessment that did 

not contribute to the problem, but if left uncorrected has the potential to 

cause a mishap, injury, or increase the severity should a mishap occur. 

Alternatively, an observation could be a positive acknowledgement of a 

Center/Program/Project/Organization’s operational structure, tools, and/or 

support provided. 

Problem The subject of the independent technical assessment. 

Proximate Cause The event(s) that occurred, including any condition(s) that existed 

immediately before the undesired outcome, directly resulted in its 

occurrence and, if eliminated or modified, would have prevented the 

undesired outcome. 
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Recommendation An action identified by the NESC to correct a root cause or deficiency 

identified during the investigation. The recommendations may be used by 

the responsible Center/Program/Project/Organization in the preparation of 

a corrective action plan. 

Root Cause One of multiple factors (events, conditions, or organizational factors) that 

contributed to or created the proximate cause and subsequent undesired 

outcome and, if eliminated or modified, would have prevented the 

undesired outcome. Typically, multiple root causes contribute to an 

undesired outcome. 

9.0 Acronyms List 

3APC Three Axis Pseudo-Controller 

AMA Analytical Mechanics Associates, Inc. 

AOA Angle-Of-Attack 

ARC Ames Research Center 

ATK Alliant Techsystems, Inc. 

BPC Bank Angle Pseudo-Controller 

CFD Computational Fluid Dynamics 

cg Center of Gravity 

DFRC Dryden Flight Research Center 

DoF Degree of Freedom 

EDL Entry, Descent, and Landing 

EDL-SA EDL Systems Analysis 

EGM Earth Gravity Model 

EKF Extended Kalman Filter 

EUV Extreme Ultraviolet 

GN&C Guidance, Navigation, and Control 

GRAM Global Reference Atmosphere Model 

GSFC Goddard Space Flight Center 

IMU Inertial Measurement Unit 

JSC Johnson Space Center 

KSC Kennedy Space Center 

LaRC Langley Research Center 

LOX Liquid Oxygen 

mEKF multimode EKF 

MER Mars Exploration Rover 

MSFC Marshall Space Flight Center 

MSL Mars Science Laboratory 
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NESC Request No.: TI-09-00530 – Phase 2 

N2 nitrogen 

NCEP National Centers for Environmental Prediction 

nd non-dimensional 

NESC NASA Engineering and Safety Center 

NIA National Institute for Aerospace 

NRB NESC Review Board 

O2 oxygen 

O3 the molecular formula for ozone 

POR period-of-record 

POST2 Program to Optimize Simulated Trajectories II 

REDLAS Rapid EDL Analysis Simulation 

RRA Range Reference Atmosphere 

TPC Terminal Point Control 

10.0 References 

1. Murri, D. G.; Striepe, S.A. Dr.; Powell, R.W. NESC Report Assessment #09-00530, Phase 1: 

Simulation Framework for Rapid Entry, Descent, and Landing (EDL) Analysis, NESC-RP09-00530. NASA-TM-2010-216867. December 17, 2009. 

2. Justus, C.G. and Leslie, F.W., “The NASA MSFC Earth Global Reference Atmospheric 

Model – 2007 Version,” NASA TM 2008-215581. 2010 Version in press. 

3. Braun, Robert D., Mitcheltree, Robert A., and Cheatwood, F. McNeil: “Mars Microprobe 

Entry-to-Impact Analysis,” Journal of Spacecraft and Rockets, Vol. 36, No. 3, May-June 

1999. 

4. Desai, Prasun N., Schoenenberger, Mark, and Cheatwood, F. McNeil: “Mars Exploration 

Rover Six-Degree-of-Freedom Entry Trajectory Analysis,” Journal of Spacecraft and

Rockets, Vol. 43, No. 5, September-October 2006. 

5. Desai, Prasun N. and Cheatwood, F. McNeil: “Entry Dispersion Analysis for the Genesis 

Sample Return Capsule,” Journal of Spacecraft and Rockets, Vol. 38, No. 3, May-June 2001. 

6. Ro, T.U.; Queen, E.M.; and Striepe, S.A.: “Martian Aerocapture Terminal Point Guidance: 

A Reference Path Optimization Study,” Presented at the 1999 Flight Mechanics Symposium 

at NASA Goddard Spaceflight Center, Greenbelt, MD, May 1999, NASA/CP-1999-209235, 

pp. 85-99.

7. Ro, T. U., Queen, E. M., "Mars Aerocapture Terminal Point Guidance," Paper No. 98-4571, 

AIAA Atmospheric Flight Mechanics Conference, Boston, MA, August, 1998. 

Volume II: Appendices

Appendix A. Multi-Mode Extended Kalman Filter 
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Appendix A. Multi-Mode Extended Kalman 

Work in this Appendix was performed under contract NNL07AA00B, 

Task Order NNL07AM00T

Filter 
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REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

2. REPORT TYPE 

Technical Memorandum

 4. TITLE AND SUBTITLE

Simulation Framework for Rapid Entry, Descent, and Landing (EDL) 

Analysis, Phase 2 Results

5a. CONTRACT NUMBER

 6. AUTHOR(S)

Murri, Daniel G.

 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center

Hampton, VA 23681-2199

 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

 8. PERFORMING ORGANIZATION

 REPORT NUMBER

L-19995 NESC-RP-09-00530

10. SPONSOR/MONITOR'S ACRONYM(S)

NASA

13. SUPPLEMENTARY NOTES

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Unclassified - Unlimited

Subject Category 16-Space Transportation and Safety

Availability: NASA CASI (443) 757-5802

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email: help@sti.nasa.gov)

14. ABSTRACT

The NASA Engineering and Safety Center (NESC) was requested to establish the Simulation Framework for Rapid Entry, 

Descent, and Landing (EDL) Analysis assessment, which involved development of an enhanced simulation architecture using 

the Program to Optimize Simulated Trajectories II simulation tool. The assessment was requested to enhance the capability of 

the Agency to provide rapid evaluation of EDL characteristics in systems analysis studies, preliminary design, mission 

development and execution, and time-critical assessments. Many of the new simulation framework capabilities were developed 

to support the Agency EDL-Systems Analysis (SA) team that is conducting studies of the technologies and architectures that 

are required to enable human and higher mass robotic missions to Mars. The findings, observations, and recommendations 

from the NESC are provided in this report.

15. SUBJECT TERMS

NASA Engineering and Safety Center; Entry, Descent, and Landing; Program to Optimize Simulated Trajectories II; Rapid 

EDL Analysis Simulation

18. NUMBER

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78

19b. TELEPHONE NUMBER (Include area code)

(443) 757-5802

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